WorldWideScience

Sample records for regular singular point

  1. 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

  2. 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

  3. 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...

  4. 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.

  5. On the use of blowup to study regularizations of singularities of piecewise smooth dynamical systems in R^3

    DEFF Research Database (Denmark)

    Kristiansen, Kristian Uldall; Hogan, S. J.

    2015-01-01

    In this paper we use the blowup method of Dumortier and Roussarie, in the formulation due to Krupa and Szmolyan, to study the regularization of singularities of piecewise smooth dynamical systems in R3. Using the regularization method of Sotomayor and Teixeira, we first demonstrate the power of our...... approach by considering the case of a fold line. We quickly extend a main result of Reves and Seara in a simple manner. Then, for the two-fold singularity, we show that the regularized system only fully retains the features of the singular canards in the piecewise smooth system in the cases when...... the sliding region does not include a full sector of singular canards. In particular, we show that every locally unique primary singular canard persists the regularizing perturbation. For the case of a sector of primary singular canards, we show that the regularized system contains a canard, provided...

  6. 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...

  7. 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)

  8. Symplectic finite element scheme: application to a driven problem with a regular singularity

    Energy Technology Data Exchange (ETDEWEB)

    Pletzer, A. [Ecole Polytechnique Federale, Lausanne (Switzerland). Centre de Recherche en Physique des Plasma (CRPP)

    1996-02-01

    A new finite element (FE) scheme, based on the decomposition of a second order differential equation into a set of first order symplectic (Hamiltonian) equations, is presented and tested on one-dimensional, driven Sturm-Liouville problem. Error analysis shows improved cubic convergence in the energy norm for piecewise linear `tent` elements, as compared to quadratic convergence for the standard and hybrid FE methods. The convergence deteriorates in the presence of a regular singular point, but can be recovered by appropriate mesh node packing. Optimal mesh packing exponents are derived to ensure cubic (respectively quadratic) convergence with minimal numerical error. A further suppression of the numerical error by a factor proportional to the square of the leading exponent of the singular solution, is achieved for a model problem based on determining the nonideal magnetohydrodynamic stability of a fusion plasma. (author) 7 figs., 14 refs.

  9. Symplectic finite element scheme: application to a driven problem with a regular singularity

    International Nuclear Information System (INIS)

    Pletzer, A.

    1996-02-01

    A new finite element (FE) scheme, based on the decomposition of a second order differential equation into a set of first order symplectic (Hamiltonian) equations, is presented and tested on one-dimensional, driven Sturm-Liouville problem. Error analysis shows improved cubic convergence in the energy norm for piecewise linear 'tent' elements, as compared to quadratic convergence for the standard and hybrid FE methods. The convergence deteriorates in the presence of a regular singular point, but can be recovered by appropriate mesh node packing. Optimal mesh packing exponents are derived to ensure cubic (respectively quadratic) convergence with minimal numerical error. A further suppression of the numerical error by a factor proportional to the square of the leading exponent of the singular solution, is achieved for a model problem based on determining the nonideal magnetohydrodynamic stability of a fusion plasma. (author) 7 figs., 14 refs

  10. Robust regularized singular value decomposition with application to mortality data

    KAUST Repository

    Zhang, Lingsong; Shen, Haipeng; Huang, Jianhua Z.

    2013-01-01

    We develop a robust regularized singular value decomposition (RobRSVD) method for analyzing two-way functional data. The research is motivated by the application of modeling human mortality as a smooth two-way function of age group and year. The Rob

  11. Unusual poles of the {zeta}-functions for some regular singular differential operators

    Energy Technology Data Exchange (ETDEWEB)

    Falomir, H [IFLP, Departamento de Fisica-Facultad de Ciencias Exactas, UNLP, CC 67 (1900) La Plata (Argentina); Muschietti, M A [Departamento de Matematica-Facultad de Ciencias Exactas, UNLP, CC 172 (1900) La Plata (Argentina); Pisani, P A G [IFLP, Departamento de Fisica-Facultad de Ciencias Exactas, UNLP, CC 67 (1900) La Plata (Argentina); Seeley, R [University of Massachusetts at Boston, Boston, MA 02125 (United States)

    2003-10-03

    We consider the resolvent of a system of first-order differential operators with a regular singularity, admitting a family of self-adjoint extensions. We find that the asymptotic expansion for the resolvent in the general case presents powers of {lambda} which depend on the singularity, and can take even irrational values. The consequences for the pole structure of the corresponding {zeta}- and {eta}-functions are also discussed.

  12. 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

  13. 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

  14. Singular pontentials and analytic regularization in classical Yang-Mills equations

    International Nuclear Information System (INIS)

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

    1978-11-01

    The class of instanton solutions with 'extension' parameter lambda 2 positive is extended to lambda 2 negative. The nature of the singular sphere of radius 'lambda' is analized in the light of the analytical regularization method. This leads to well defined solutions of the Yang-Mills equations. Some of them are sourceless ('+-io' and 'Vp'), others correspond to currents concentrated on the sphere of singularity ('+' and '-'). Although the equations are non-linear, the 'Vp' solution turns out to be real part of the '+-io' solutions. The anzats of t'Hooft for the superposition of instantons is used to sum the contributions corresponding to lambda 2 with positive and negative signs. A subsequent limiting process allows then the construction of solutions of the 'multipole' type. The general situation of potentials having a denominator D, with a corresponding surface of singularity at D=0, is also considered in the same light [pt

  15. Comparative analysis of gradient-field-based orientation estimation methods and regularized singular-value decomposition for fringe pattern processing.

    Science.gov (United States)

    Sun, Qi; Fu, Shujun

    2017-09-20

    Fringe orientation is an important feature of fringe patterns and has a wide range of applications such as guiding fringe pattern filtering, phase unwrapping, and abstraction. Estimating fringe orientation is a basic task for subsequent processing of fringe patterns. However, various noise, singular and obscure points, and orientation data degeneration lead to inaccurate calculations of fringe orientation. Thus, to deepen the understanding of orientation estimation and to better guide orientation estimation in fringe pattern processing, some advanced gradient-field-based orientation estimation methods are compared and analyzed. At the same time, following the ideas of smoothing regularization and computing of bigger gradient fields, a regularized singular-value decomposition (RSVD) technique is proposed for fringe orientation estimation. To compare the performance of these gradient-field-based methods, quantitative results and visual effect maps of orientation estimation are given on simulated and real fringe patterns that demonstrate that the RSVD produces the best estimation results at a cost of relatively less time.

  16. The Analysis of Two-Way Functional Data Using Two-Way Regularized Singular Value Decompositions

    KAUST Repository

    Huang, Jianhua Z.

    2009-12-01

    Two-way functional data consist of a data matrix whose row and column domains are both structured, for example, temporally or spatially, as when the data are time series collected at different locations in space. We extend one-way functional principal component analysis (PCA) to two-way functional data by introducing regularization of both left and right singular vectors in the singular value decomposition (SVD) of the data matrix. We focus on a penalization approach and solve the nontrivial problem of constructing proper two-way penalties from oneway regression penalties. We introduce conditional cross-validated smoothing parameter selection whereby left-singular vectors are cross- validated conditional on right-singular vectors, and vice versa. The concept can be realized as part of an alternating optimization algorithm. In addition to the penalization approach, we briefly consider two-way regularization with basis expansion. The proposed methods are illustrated with one simulated and two real data examples. Supplemental materials available online show that several "natural" approaches to penalized SVDs are flawed and explain why so. © 2009 American Statistical Association.

  17. Singular potentials and analytic regularization in classical Yang-Mills equations

    International Nuclear Information System (INIS)

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

    1978-10-01

    The class of instanton solutions with 'extension' parameter Λ 2 positive is extended to Λ 2 negative. The nature of the singular sphere of radius |Λ| is analized in the light of the analytical regularization method. This leads to well defined solutions of the Yang - Mills equations. Some of them are sourceless ('+- i o' and 'Vp'), others correspond to currents concentrated on the sphere of singularity ('+' and '-'). Although the equations are non-linear, the 'Vp' solutions turns out to be the real part of the '+- i o' solutions. The anzats of t'Hooft for the superposition of instantons is used to sum the contributions corresponding to Λ 2 with positive and negative signs. A subsequent limiting process allows then the construction of solutions of the 'multipole' type. The general situation of potentials having a denominator D, with a corresponding surface of singularity at D=0, is also considered in the same light. (Author) [pt

  18. 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

  19. 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

  20. Coexistence of Two Singularities in Dewetting Flows: Regularizing the Corner Tip

    NARCIS (Netherlands)

    Peters, I.R.; Snoeijer, Jacobus Hendrikus; Daerr, Adrian; Limat, Laurent

    2009-01-01

    Entrainment in wetting and dewetting flows often occurs through the formation of a corner with a very sharp tip. This corner singularity comes on top of the divergence of viscous stress near the contact line, which is only regularized at molecular scales. We investigate the fine structure of corners

  1. 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.

  2. 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

  3. 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.

  4. 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.

  5. 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.

  6. C-point and V-point singularity lattice formation and index sign conversion methods

    Science.gov (United States)

    Kumar Pal, Sushanta; Ruchi; Senthilkumaran, P.

    2017-06-01

    The generic singularities in an ellipse field are C-points namely stars, lemons and monstars in a polarization distribution with C-point indices (-1/2), (+1/2) and (+1/2) respectively. Similar to C-point singularities, there are V-point singularities that occur in a vector field and are characterized by Poincare-Hopf index of integer values. In this paper we show that the superposition of three homogenously polarized beams in different linear states leads to the formation of polarization singularity lattice. Three point sources at the focal plane of the lens are used to create three interfering plane waves. A radial/azimuthal polarization converter (S-wave plate) placed near the focal plane modulates the polarization states of the three beams. The interference pattern is found to host C-points and V-points in a hexagonal lattice. The C-points occur at intensity maxima and V-points occur at intensity minima. Modulating the state of polarization (SOP) of three plane waves from radial to azimuthal does not essentially change the nature of polarization singularity lattice as the Poincare-Hopf index for both radial and azimuthal polarization distributions is (+1). Hence a transformation from a star to a lemon is not trivial, as such a transformation requires not a single SOP change, but a change in whole spatial SOP distribution. Further there is no change in the lattice structure and the C- and V-points appear at locations where they were present earlier. Hence to convert an interlacing star and V-point lattice into an interlacing lemon and V-point lattice, the interferometer requires modification. We show for the first time a method to change the polarity of C-point and V-point indices. This means that lemons can be converted into stars and stars can be converted into lemons. Similarly the positive V-point can be converted to negative V-point and vice versa. The intensity distribution in all these lattices is invariant as the SOPs of the three beams are changed in an

  7. 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.

  8. Finite Element Quadrature of Regularized Discontinuous and Singular Level Set Functions in 3D Problems

    Directory of Open Access Journals (Sweden)

    Nicola Ponara

    2012-11-01

    Full Text Available Regularized Heaviside and Dirac delta function are used in several fields of computational physics and mechanics. Hence the issue of the quadrature of integrals of discontinuous and singular functions arises. In order to avoid ad-hoc quadrature procedures, regularization of the discontinuous and the singular fields is often carried out. In particular, weight functions of the signed distance with respect to the discontinuity interface are exploited. Tornberg and Engquist (Journal of Scientific Computing, 2003, 19: 527–552 proved that the use of compact support weight function is not suitable because it leads to errors that do not vanish for decreasing mesh size. They proposed the adoption of non-compact support weight functions. In the present contribution, the relationship between the Fourier transform of the weight functions and the accuracy of the regularization procedure is exploited. The proposed regularized approach was implemented in the eXtended Finite Element Method. As a three-dimensional example, we study a slender solid characterized by an inclined interface across which the displacement is discontinuous. The accuracy is evaluated for varying position of the discontinuity interfaces with respect to the underlying mesh. A procedure for the choice of the regularization parameters is proposed.

  9. Hilbert schemes of points on some classes surface singularities

    OpenAIRE

    Gyenge, Ádám

    2016-01-01

    We study the geometry and topology of Hilbert schemes of points on the orbifold surface [C^2/G], respectively the singular quotient surface C^2/G, where G is a finite subgroup of SL(2,C) of type A or D. We give a decomposition of the (equivariant) Hilbert scheme of the orbifold into affine space strata indexed by a certain combinatorial set, the set of Young walls. The generating series of Euler characteristics of Hilbert schemes of points of the singular surface of type A or D is computed in...

  10. Constraints on Stress Components at the Internal Singular Point of an Elastic Compound Structure

    Science.gov (United States)

    Pestrenin, V. M.; Pestrenina, I. V.

    2017-03-01

    The classical analytical and numerical methods for investigating the stress-strain state (SSS) in the vicinity of a singular point consider the point as a mathematical one (having no linear dimensions). The reliability of the solution obtained by such methods is valid only outside a small vicinity of the singular point, because the macroscopic equations become incorrect and microscopic ones have to be used to describe the SSS in this vicinity. Also, it is impossible to set constraint or to formulate solutions in stress-strain terms for a mathematical point. These problems do not arise if the singular point is identified with the representative volume of material of the structure studied. In authors' opinion, this approach is consistent with the postulates of continuum mechanics. In this case, the formulation of constraints at a singular point and their investigation becomes an independent problem of mechanics for bodies with singularities. This method was used to explore constraints at an internal singular point (representative volume) of a compound wedge and a compound rib. It is shown that, in addition to the constraints given in the classical approach, there are also constraints depending on the macroscopic parameters of constituent materials. These constraints turn the problems of deformable bodies with an internal singular point into nonclassical ones. Combinations of material parameters determine the number of additional constraints and the critical stress state at the singular point. Results of this research can be used in the mechanics of composite materials and fracture mechanics and in studying stress concentrations in composite structural elements.

  11. 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

  12. 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

  13. 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

  14. Total variation regularization of the 3-D gravity inverse problem using a randomized generalized singular value decomposition

    Science.gov (United States)

    Vatankhah, Saeed; Renaut, Rosemary A.; Ardestani, Vahid E.

    2018-04-01

    We present a fast algorithm for the total variation regularization of the 3-D gravity inverse problem. Through imposition of the total variation regularization, subsurface structures presenting with sharp discontinuities are preserved better than when using a conventional minimum-structure inversion. The associated problem formulation for the regularization is nonlinear but can be solved using an iteratively reweighted least-squares algorithm. For small-scale problems the regularized least-squares problem at each iteration can be solved using the generalized singular value decomposition. This is not feasible for large-scale, or even moderate-scale, problems. Instead we introduce the use of a randomized generalized singular value decomposition in order to reduce the dimensions of the problem and provide an effective and efficient solution technique. For further efficiency an alternating direction algorithm is used to implement the total variation weighting operator within the iteratively reweighted least-squares algorithm. Presented results for synthetic examples demonstrate that the novel randomized decomposition provides good accuracy for reduced computational and memory demands as compared to use of classical approaches.

  15. 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.

  16. Singular Buildings on Regular Grids. Churches in L’Eixample and La Baixa

    Directory of Open Access Journals (Sweden)

    Alba Arboix-Alió

    2016-10-01

    Full Text Available A building is considered unique when it outstands within the common fabric of the city due to its form, its nature, and its production and serialization process. If this architectural singularity is accompanied by an urban distinction, the result is much more effective because the compound becomes an urban enclave capable of arranging and hierarchically organising the city. The most illustrative example for historic cities with a Catholic tradition may probably be the church with the public space that materializes around it. For centuries, the sacred building and the atrium that precedes it have represented the city’s reference point and articulating centre of social, economic and cultural life. Nevertheless, if this is more or less evident in old towns consolidated over time; how is this solved in modern cities formed by a regular urban layout whose grid is put before the freedom of the buildings? With Barcelona and Lisbon as case studies, the paper focuses on the implementation and typology of the most paradigmatic churches in the neighbourhoods of L’Eixample Cerdà and La Baixa Pombalina.

  17. On the theory of drainage area for regular and non-regular points

    Science.gov (United States)

    Bonetti, S.; Bragg, A. D.; Porporato, A.

    2018-03-01

    The drainage area is an important, non-local property of a landscape, which controls surface and subsurface hydrological fluxes. Its role in numerous ecohydrological and geomorphological applications has given rise to several numerical methods for its computation. However, its theoretical analysis has lagged behind. Only recently, an analytical definition for the specific catchment area was proposed (Gallant & Hutchinson. 2011 Water Resour. Res. 47, W05535. (doi:10.1029/2009WR008540)), with the derivation of a differential equation whose validity is limited to regular points of the watershed. Here, we show that such a differential equation can be derived from a continuity equation (Chen et al. 2014 Geomorphology 219, 68-86. (doi:10.1016/j.geomorph.2014.04.037)) and extend the theory to critical and singular points both by applying Gauss's theorem and by means of a dynamical systems approach to define basins of attraction of local surface minima. Simple analytical examples as well as applications to more complex topographic surfaces are examined. The theoretical description of topographic features and properties, such as the drainage area, channel lines and watershed divides, can be broadly adopted to develop and test the numerical algorithms currently used in digital terrain analysis for the computation of the drainage area, as well as for the theoretical analysis of landscape evolution and stability.

  18. Robust regularized singular value decomposition with application to mortality data

    KAUST Repository

    Zhang, Lingsong

    2013-09-01

    We develop a robust regularized singular value decomposition (RobRSVD) method for analyzing two-way functional data. The research is motivated by the application of modeling human mortality as a smooth two-way function of age group and year. The RobRSVD is formulated as a penalized loss minimization problem where a robust loss function is used to measure the reconstruction error of a low-rank matrix approximation of the data, and an appropriately defined two-way roughness penalty function is used to ensure smoothness along each of the two functional domains. By viewing the minimization problem as two conditional regularized robust regressions, we develop a fast iterative reweighted least squares algorithm to implement the method. Our implementation naturally incorporates missing values. Furthermore, our formulation allows rigorous derivation of leaveone- row/column-out cross-validation and generalized cross-validation criteria, which enable computationally efficient data-driven penalty parameter selection. The advantages of the new robust method over nonrobust ones are shown via extensive simulation studies and the mortality rate application. © Institute of Mathematical Statistics, 2013.

  19. Regularized semiclassical limits: Linear flows with infinite Lyapunov exponents

    KAUST Repository

    Athanassoulis, Agissilaos; Katsaounis, Theodoros; Kyza, Irene

    2016-01-01

    Semiclassical asymptotics for Schrödinger equations with non-smooth potentials give rise to ill-posed formal semiclassical limits. These problems have attracted a lot of attention in the last few years, as a proxy for the treatment of eigenvalue crossings, i.e. general systems. It has recently been shown that the semiclassical limit for conical singularities is in fact well-posed, as long as the Wigner measure (WM) stays away from singular saddle points. In this work we develop a family of refined semiclassical estimates, and use them to derive regularized transport equations for saddle points with infinite Lyapunov exponents, extending the aforementioned recent results. In the process we answer a related question posed by P.L. Lions and T. Paul in 1993. If we consider more singular potentials, our rigorous estimates break down. To investigate whether conical saddle points, such as -|x|, admit a regularized transport asymptotic approximation, we employ a numerical solver based on posteriori error control. Thus rigorous upper bounds for the asymptotic error in concrete problems are generated. In particular, specific phenomena which render invalid any regularized transport for -|x| are identified and quantified. In that sense our rigorous results are sharp. Finally, we use our findings to formulate a precise conjecture for the condition under which conical saddle points admit a regularized transport solution for the WM. © 2016 International Press.

  20. Regularized semiclassical limits: Linear flows with infinite Lyapunov exponents

    KAUST Repository

    Athanassoulis, Agissilaos

    2016-08-30

    Semiclassical asymptotics for Schrödinger equations with non-smooth potentials give rise to ill-posed formal semiclassical limits. These problems have attracted a lot of attention in the last few years, as a proxy for the treatment of eigenvalue crossings, i.e. general systems. It has recently been shown that the semiclassical limit for conical singularities is in fact well-posed, as long as the Wigner measure (WM) stays away from singular saddle points. In this work we develop a family of refined semiclassical estimates, and use them to derive regularized transport equations for saddle points with infinite Lyapunov exponents, extending the aforementioned recent results. In the process we answer a related question posed by P.L. Lions and T. Paul in 1993. If we consider more singular potentials, our rigorous estimates break down. To investigate whether conical saddle points, such as -|x|, admit a regularized transport asymptotic approximation, we employ a numerical solver based on posteriori error control. Thus rigorous upper bounds for the asymptotic error in concrete problems are generated. In particular, specific phenomena which render invalid any regularized transport for -|x| are identified and quantified. In that sense our rigorous results are sharp. Finally, we use our findings to formulate a precise conjecture for the condition under which conical saddle points admit a regularized transport solution for the WM. © 2016 International Press.

  1. 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...

  2. 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)

  3. Modified truncated randomized singular value decomposition (MTRSVD) algorithms for large scale discrete ill-posed problems with general-form regularization

    Science.gov (United States)

    Jia, Zhongxiao; Yang, Yanfei

    2018-05-01

    In this paper, we propose new randomization based algorithms for large scale linear discrete ill-posed problems with general-form regularization: subject to , where L is a regularization matrix. Our algorithms are inspired by the modified truncated singular value decomposition (MTSVD) method, which suits only for small to medium scale problems, and randomized SVD (RSVD) algorithms that generate good low rank approximations to A. We use rank-k truncated randomized SVD (TRSVD) approximations to A by truncating the rank- RSVD approximations to A, where q is an oversampling parameter. The resulting algorithms are called modified TRSVD (MTRSVD) methods. At every step, we use the LSQR algorithm to solve the resulting inner least squares problem, which is proved to become better conditioned as k increases so that LSQR converges faster. We present sharp bounds for the approximation accuracy of the RSVDs and TRSVDs for severely, moderately and mildly ill-posed problems, and substantially improve a known basic bound for TRSVD approximations. We prove how to choose the stopping tolerance for LSQR in order to guarantee that the computed and exact best regularized solutions have the same accuracy. Numerical experiments illustrate that the best regularized solutions by MTRSVD are as accurate as the ones by the truncated generalized singular value decomposition (TGSVD) algorithm, and at least as accurate as those by some existing truncated randomized generalized singular value decomposition (TRGSVD) algorithms. This work was supported in part by the National Science Foundation of China (Nos. 11771249 and 11371219).

  4. 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

  5. Degree of a isolated real point or a singular complex point on a plane curve defined over Q

    DEFF Research Database (Denmark)

    Hansen, Johan Peder

    2010-01-01

    Let $X$ be a curve in the affine plane defined by a reduced polynomial of degree $d$ with rational coefficients. Assume that $P$ is an isolated real point or a singular complex point on the curve $X$. The coordinates of $P$ are algebraic numbers over the rationals of degree at most $d^2$. The res......Let $X$ be a curve in the affine plane defined by a reduced polynomial of degree $d$ with rational coefficients. Assume that $P$ is an isolated real point or a singular complex point on the curve $X$. The coordinates of $P$ are algebraic numbers over the rationals of degree at most $d^2...

  6. Regularization of the big bang singularity with random perturbations

    Science.gov (United States)

    Belbruno, Edward; Xue, BingKan

    2018-03-01

    We show how to regularize the big bang singularity in the presence of random perturbations modeled by Brownian motion using stochastic methods. We prove that the physical variables in a contracting universe dominated by a scalar field can be continuously and uniquely extended through the big bang as a function of time to an expanding universe only for a discrete set of values of the equation of state satisfying special co-prime number conditions. This result significantly generalizes a previous result (Xue and Belbruno 2014 Class. Quantum Grav. 31 165002) that did not model random perturbations. This result implies that the extension from a contracting to an expanding universe for the discrete set of co-prime equation of state is robust, which is a surprising result. Implications for a purely expanding universe are discussed, such as a non-smooth, randomly varying scale factor near the big bang.

  7. 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.

    2012-04-01

    The study of fully developed turbulence has given rise to the development of new methods to describe real data of scalars submitted to the action of a turbulent flow. The application of this brand of methodologies (known as Microcanonical Multifractal Formalism, MMF) on remote sensing ocean maps open new ways to exploit those data for oceanographic purposes. The main technique in MMF is that of Singularity Analysis (SA). By means of SA a singularity exponents is assigned to each point of a given image. The singularity exponent of a given point is a dimensionless measure of the regularity or irregularity of the scalar at that point. Singularity exponents arrange in singularity lines, which accurately track the flow streamlines from any scalar, as we have verified with remote sensing and simulated data. Applications of SA include quality assessment of different products, the estimation of surface velocities, the development of fusion techniques for different types of scalars, comparison with measures of ocean mixing, and improvement in assimilation schemes.

  8. Solving Singular Two-Point Boundary Value Problems Using Continuous Genetic Algorithm

    Directory of Open Access Journals (Sweden)

    Omar Abu Arqub

    2012-01-01

    Full Text Available In this paper, the continuous genetic algorithm is applied for the solution of singular two-point boundary value problems, where smooth solution curves are used throughout the evolution of the algorithm to obtain the required nodal values. The proposed technique might be considered as a variation of the finite difference method in the sense that each of the derivatives is replaced by an appropriate difference quotient approximation. This novel approach possesses main advantages; it can be applied without any limitation on the nature of the problem, the type of singularity, and the number of mesh points. Numerical examples are included to demonstrate the accuracy, applicability, and generality of the presented technique. The results reveal that the algorithm is very effective, straightforward, and simple.

  9. 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.

  10. Singular points in moduli spaces of Yang-Mills fields

    International Nuclear Information System (INIS)

    Ticciati, R.

    1984-01-01

    This thesis investigates the metric dependence of the moduli spaces of Yang-Mills fields of an SU(2) principal bundle P with chern number -1 over a four-dimensional, simply-connected, oriented, compact smooth manifold M with positive definite intersection form. The purpose of this investigation is to suggest that the surgery class of the moduli space of irreducible connections is, for a generic metric, a Z 2 topological invariant of the smooth structure on M. There are three main parts. The first two parts are local analysis of singular points in the moduli spaces. The last part is global. The first part shows that the set of metrics for which the moduli space of irreducible connections has only non-degenerate singularities has codimension at least one in the space of all metrics. The second part shows that, for a one-parameter family of moduli spaces in a direction transverse to the set of metrics for which the moduli spaces have singularities, passing through a non-degenerate singularity of the simplest type changes the moduli space by a cobordism. The third part shows that generic one-parameter families of metrics give rise to six-dimensional manifolds, the corresponding family of moduli spaces of irreducible connections. It is shown that when M is homeomorphic to S 4 the six-dimensional manifold is a proper cobordism, thus establishing the independence of the surgery class of the moduli space on the metric on M

  11. Singularities, swallowtails and Dirac points. An analysis for families of Hamiltonians and applications to wire networks, especially the Gyroid

    International Nuclear Information System (INIS)

    Kaufmann, Ralph M.; Khlebnikov, Sergei; Wehefritz-Kaufmann, Birgit

    2012-08-01

    Motivated by the Double Gyroid nanowire network we develop methods to detect Dirac points and classify level crossings, aka. singularities in the spectrum of a family of Hamiltonians. The approach we use is singularity theory. Using this language, we obtain a characterization of Dirac points and also show that the branching behavior of the level crossings is given by an unfolding of A n type singularities. Which type of singularity occurs can be read off a characteristic region inside the miniversal unfolding of an A k singularity. We then apply these methods in the setting of families of graph Hamiltonians, such as those for wire networks. In the particular case of the Double Gyroid we analytically classify its singularities and show that it has Dirac points. This indicates that nanowire systems of this type should have very special physical properties.

  12. Singularities, swallowtails and Dirac points. An analysis for families of Hamiltonians and applications to wire networks, especially the Gyroid

    Energy Technology Data Exchange (ETDEWEB)

    Kaufmann, Ralph M.; Khlebnikov, Sergei; Wehefritz-Kaufmann, Birgit

    2012-08-15

    Motivated by the Double Gyroid nanowire network we develop methods to detect Dirac points and classify level crossings, aka. singularities in the spectrum of a family of Hamiltonians. The approach we use is singularity theory. Using this language, we obtain a characterization of Dirac points and also show that the branching behavior of the level crossings is given by an unfolding of A{sub n} type singularities. Which type of singularity occurs can be read off a characteristic region inside the miniversal unfolding of an A{sub k} singularity. We then apply these methods in the setting of families of graph Hamiltonians, such as those for wire networks. In the particular case of the Double Gyroid we analytically classify its singularities and show that it has Dirac points. This indicates that nanowire systems of this type should have very special physical properties.

  13. A New Continuous-Time Equality-Constrained Optimization to Avoid Singularity.

    Science.gov (United States)

    Quan, Quan; Cai, Kai-Yuan

    2016-02-01

    In equality-constrained optimization, a standard regularity assumption is often associated with feasible point methods, namely, that the gradients of constraints are linearly independent. In practice, the regularity assumption may be violated. In order to avoid such a singularity, a new projection matrix is proposed based on which a feasible point method to continuous-time, equality-constrained optimization is developed. First, the equality constraint is transformed into a continuous-time dynamical system with solutions that always satisfy the equality constraint. Second, a new projection matrix without singularity is proposed to realize the transformation. An update (or say a controller) is subsequently designed to decrease the objective function along the solutions of the transformed continuous-time dynamical system. The invariance principle is then applied to analyze the behavior of the solution. Furthermore, the proposed method is modified to address cases in which solutions do not satisfy the equality constraint. Finally, the proposed optimization approach is applied to three examples to demonstrate its effectiveness.

  14. Exponential spreading and singular behavior of quantum dynamics near hyperbolic points.

    Science.gov (United States)

    Iomin, A

    2013-05-01

    Quantum dynamics of a particle in the vicinity of a hyperbolic point is considered. Expectation values of dynamical variables are calculated, and the singular behavior is analyzed. Exponentially fast extension of quantum dynamics is obtained, and conditions for this realization are analyzed.

  15. 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.

  16. 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

  17. Describing chaotic attractors: Regular and perpetual points

    Science.gov (United States)

    Dudkowski, Dawid; Prasad, Awadhesh; Kapitaniak, Tomasz

    2018-03-01

    We study the concepts of regular and perpetual points for describing the behavior of chaotic attractors in dynamical systems. The idea of these points, which have been recently introduced to theoretical investigations, is thoroughly discussed and extended into new types of models. We analyze the correlation between regular and perpetual points, as well as their relation with phase space, showing the potential usefulness of both types of points in the qualitative description of co-existing states. The ability of perpetual points in finding attractors is indicated, along with its potential cause. The location of chaotic trajectories and sets of considered points is investigated and the study on the stability of systems is shown. The statistical analysis of the observing desired states is performed. We focus on various types of dynamical systems, i.e., chaotic flows with self-excited and hidden attractors, forced mechanical models, and semiconductor superlattices, exhibiting the universality of appearance of the observed patterns and relations.

  18. Architecture of chaotic attractors for flows in the absence of any singular point

    Energy Technology Data Exchange (ETDEWEB)

    Letellier, Christophe [CORIA-UMR 6614 Normandie Université, CNRS-Université et INSA de Rouen, Campus Universitaire du Madrillet, F-76800 Saint-Etienne du Rouvray (France); Malasoma, Jean-Marc [Université de Lyon, ENTPE, Laboratoire Génie Civil et Bâtiment, 3 Rue Maurice Audin, F-69518 Vaulx-en-Velin Cedex (France)

    2016-06-15

    Some chaotic attractors produced by three-dimensional dynamical systems without any singular point have now been identified, but explaining how they are structured in the state space remains an open question. We here want to explain—in the particular case of the Wei system—such a structure, using one-dimensional sets obtained by vanishing two of the three derivatives of the flow. The neighborhoods of these sets are made of points which are characterized by the eigenvalues of a 2 × 2 matrix describing the stability of flow in a subspace transverse to it. We will show that the attractor is spiralling and twisted in the neighborhood of one-dimensional sets where points are characterized by a pair of complex conjugated eigenvalues. We then show that such one-dimensional sets are also useful in explaining the structure of attractors produced by systems with singular points, by considering the case of the Lorenz system.

  19. The 'crisis of noosphere' as a limiting factor to achieve the point of technological singularity

    Directory of Open Access Journals (Sweden)

    Rafael Lahoz-Beltra

    2018-03-01

    Full Text Available One of the most significant developments in the history of human being is the invention of a way of keeping records of human knowledge, thoughts and ideas. In 1926, the work of several thinkers such as Edouard Le Roy, Vladimir Vernadsky and Teilhard de Chardin led to the concept of noosphere, the idea that human cognition and knowledge transforms the biosphere into something like a thinking layer of the planet. At present, it is commonly accepted by some thinkers that the Internet is the medium that will give life to noosphere. According to Vinge and Kurzweil's technological singularity hypothesis, noosphere would in a future be the natural environment in which a 'human machine superintelligence' would emerge to reach the point of technological singularity. In this article we show by means of numerical models that it is impossible for our civilization to reach the point of technological singularity in a near future. We propose that this point could be reached only if Internet data centers were based on "computer machines" that are more effective in terms of hardware and power consumption than the current ones. Finally, we speculate about 'Nooscomputers' or N computers, as hypothetical machines oriented not only to the management of information, but also knowledge, and much more efficient in terms of electricity consumption than current computers. Possibly a civilization based on N-computers would allow us to successfully reach the point of technological singularity.

  20. 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.

  1. 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

  2. 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.

  3. Pressure fluctuations induced by fluid flow in singular points of industrial circuits

    International Nuclear Information System (INIS)

    Gibert, R.J.; Villard, B.

    1977-01-01

    Flow singularities (enlargements, bards, valves, tees,...) generate in the circuits of industrial plants wall pressure fluctuations which are the main cause of vibration. Two types of pressure fluctuations can be considered. - 'Local ' fluctuations: They are associated to the unsteadiness downstream from the singularity. These fluctuations may be characterized by frequency spectra, correlation length and phase lags. These parameters are used to calculate forces on the walls of the circuit. - 'Acoustic' fluctuations: The singularity acts as an acoustical source; its frequency spectrum and the acoustical transfer function of the circuit are needed to evaluate the acoustical level at any point. A methodical study of the most current singularities has been performed at C.E.A./D.E.M.T.: - On one hand a theory of noise generation by unsteady flow in internal acoustics has been developed. This theory uses the basic idea initiated by LIGHTILL. As a result it is shown that the plane wave propagation is a valid assumption and that a singularity can be acoustically modelled by a pressure and a mass-flow-rate discontinuities. Both are random functions of time, the spectra of which are determined from the local fluctuations characteristics. - On the other hand, characteristics of several singularities have been measured: (i) Intercorrelation spectra of local pressure fluctuations. (ii) Autocorrelation spectra of associated acoustical sources (the measure of the acoustical pressures in the experimental circuit are interpreted by using the D.E.M.T. computer code VIBRAPHONE which gives the acoustical response of a complex circuit). (Auth.)

  4. 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.

  5. 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.

  6. Using many pilot points and singular value decomposition in groundwater model calibration

    DEFF Research Database (Denmark)

    Christensen, Steen; Doherty, John

    2008-01-01

    over the model area. Singular value decomposition (SVD) of the normal matrix is used to reduce the large number of pilot point parameters to a smaller number of so-called super parameters that can be estimated by nonlinear regression from the available observations. A number of eigenvectors...

  7. Regular non-twisting S-branes

    International Nuclear Information System (INIS)

    Obregon, Octavio; Quevedo, Hernando; Ryan, Michael P.

    2004-01-01

    We construct a family of time and angular dependent, regular S-brane solutions which corresponds to a simple analytical continuation of the Zipoy-Voorhees 4-dimensional vacuum spacetime. The solutions are asymptotically flat and turn out to be free of singularities without requiring a twist in space. They can be considered as the simplest non-singular generalization of the singular S0-brane solution. We analyze the properties of a representative of this family of solutions and show that it resembles to some extent the asymptotic properties of the regular Kerr S-brane. The R-symmetry corresponds, however, to the general lorentzian symmetry. Several generalizations of this regular solution are derived which include a charged S-brane and an additional dilatonic field. (author)

  8. Fractional charge and inter-Landau-level states at points of singular curvature.

    Science.gov (United States)

    Biswas, Rudro R; Son, Dam Thanh

    2016-08-02

    The quest for universal properties of topological phases is fundamentally important because these signatures are robust to variations in system-specific details. Aspects of the response of quantum Hall states to smooth spatial curvature are well-studied, but challenging to observe experimentally. Here we go beyond this prevailing paradigm and obtain general results for the response of quantum Hall states to points of singular curvature in real space; such points may be readily experimentally actualized. We find, using continuum analytical methods, that the point of curvature binds an excess fractional charge and sequences of quantum states split away, energetically, from the degenerate bulk Landau levels. Importantly, these inter-Landau-level states are bound to the topological singularity and have energies that are universal functions of bulk parameters and the curvature. Our exact diagonalization of lattice tight-binding models on closed manifolds demonstrates that these results continue to hold even when lattice effects are significant. An important technological implication of these results is that these inter-Landau-level states, being both energetically and spatially isolated quantum states, are promising candidates for constructing qubits for quantum computation.

  9. Point-splitting regularization of composite operators and anomalies

    International Nuclear Information System (INIS)

    Novotny, J.; Schnabl, M.

    2000-01-01

    The point-splitting regularization technique for composite operators is discussed in connection with anomaly calculation. We present a pedagogical and self-contained review of the topic with an emphasis on the technical details. We also develop simple algebraic tools to handle the path ordered exponential insertions used within the covariant and non-covariant version of the point-splitting method. The method is then applied to the calculation of the chiral, vector, trace, translation and Lorentz anomalies within diverse versions of the point-splitting regularization and a connection between the results is described. As an alternative to the standard approach we use the idea of deformed point-split transformation and corresponding Ward-Takahashi identities rather than an application of the equation of motion, which seems to reduce the complexity of the calculations. (orig.)

  10. 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 ...

  11. 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.)

  12. Singular point detection algorithm based on the transition line of the fingerprint orientation image

    CSIR Research Space (South Africa)

    Mathekga, ME

    2009-11-01

    Full Text Available there is another core immediately afterwards, as in fig- ures 1 and 2. Thus, the transition columns where this condition is satisfied is set as the location of the core singular point. a and c or b and f in figure 4 must be comparable as ridges are expected... of Singularities and Pseudo Ridges”, Patt. Recog., Vol. 37, 2004, p 2233– 2243. [9] Msiza, I.S., Leke-Betechuoh, B., Nelwamondo, F.V., and Msimang, N., “A Fingerprint Pattern Classification Ap- proach Based on the Coordinate Geometry of Singulari- ties”, In...

  13. Hilbert scheme of points on cyclic quotient singularities of type (p,1)

    OpenAIRE

    Gyenge, Ádám

    2016-01-01

    In this note we investigate the generating series of the Euler characteristics of Hilbert scheme of points on cyclic quotient singularities of type (p,1). We link the appearing combinatorics to p-fountains, a generalization of the notion of fountain of coins. We obtain a representation of the generating series as coefficient of a two variable generating series.

  14. The method of normal forms for singularly perturbed systems of Fredholm integro-differential equations with rapidly varying kernels

    Energy Technology Data Exchange (ETDEWEB)

    Bobodzhanov, A A; Safonov, V F [National Research University " Moscow Power Engineering Institute" , Moscow (Russian Federation)

    2013-07-31

    The paper deals with extending the Lomov regularization method to classes of singularly perturbed Fredholm-type integro-differential systems, which have not so far been studied. In these the limiting operator is discretely noninvertible. Such systems are commonly known as problems with unstable spectrum. Separating out the essential singularities in the solutions to these problems presents great difficulties. The principal one is to give an adequate description of the singularities induced by 'instability points' of the spectrum. A methodology for separating singularities by using normal forms is developed. It is applied to the above type of systems and is substantiated in these systems. Bibliography: 10 titles.

  15. Evaluating the change of directional patterns for fingerprints with missing singular points under rotation

    CSIR Research Space (South Africa)

    Dorasamy, Kribashnee

    2016-12-01

    Full Text Available Overcoming small inter-class variation when fingerprints have missing singular points (SPs) is one of the current challenges faced in fingerprint classification, since class information is scarce. Grouping the orientation fields to form Directional...

  16. Preconditioners for regularized saddle point matrices

    Czech Academy of Sciences Publication Activity Database

    Axelsson, Owe

    2011-01-01

    Roč. 19, č. 2 (2011), s. 91-112 ISSN 1570-2820 Institutional research plan: CEZ:AV0Z30860518 Keywords : saddle point matrices * preconditioning * regularization * eigenvalue clustering Subject RIV: BA - General Mathematics Impact factor: 0.533, year: 2011 http://www.degruyter.com/view/j/jnma.2011.19.issue-2/jnum.2011.005/jnum.2011.005. xml

  17. 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.)

  18. To d, or not to d. Recent developments and comparisons of regularization schemes

    Energy Technology Data Exchange (ETDEWEB)

    Gnendiger, C.; Pruna, G.M. [Paul Scherrer Institut, Villigen (Switzerland); Signer, A.; Ulrich, Y.; Visconti, A. [Paul Scherrer Institut, Villigen (Switzerland); Universitaet Zuerich, Physik-Institut, Zuerich (Switzerland); Stoeckinger, D. [Institut fuer Kern- und Teilchenphysik, Dresden (Germany); Broggio, A. [Technische Universitaet Muenchen, Physik Department T31, Garching (Germany); Cherchiglia, A.L. [Centro de Ciencias Naturais e Humanas, UFABC, Santo Andre (Brazil); Driencourt-Mangin, F.; Rodrigo, G. [Universitat de Valencia, Insituto de Fisica Corpuscular, UVEG-CSIC, Paterna (Spain); Fazio, A.R. [Universidad Nacional de Colombia, Departamento de Fisica, Bogota D.C. (Colombia); Hiller, B. [University of Coimbra, CFisUC, Department of Physics, Coimbra (Portugal); Mastrolia, P. [Universita di Padova, Dipartimento di Fisica ed Astronomia, Padua (Italy); INFN, Sezione di Padova, Padua (Italy); Peraro, T. [The University of Edinburgh, Higgs Centre for Theoretical Physics, Edinburgh (United Kingdom); Pittau, R. [Universidad de Granada, Dept. de Fisica Teorica y del Cosmos yd CAFPE, Granada (Spain); Sampaio, M. [ICEX, UFMG, Departamento de Fisica, Belo Horizonte (Brazil); Sborlini, G. [Universitat de Valencia, Insituto de Fisica Corpuscular, UVEG-CSIC, Paterna (Spain); Universita di Milano, Dipartimento di Fisica, Milan (Italy); INFN, Sezione di Milano, Milan (Italy); Bobadilla, W.J.T. [Universitat de Valencia, Insituto de Fisica Corpuscular, UVEG-CSIC, Paterna (Spain); Universita di Padova, Dipartimento di Fisica ed Astronomia, Padua (Italy); INFN, Sezione di Padova, Padua (Italy); Tramontano, F. [Universita di Napoli, Dipartimento di Fisica, Naples (Italy); INFN, Sezione di Napoli, Naples (Italy)

    2017-07-15

    We give an introduction to several regularization schemes that deal with ultraviolet and infrared singularities appearing in higher-order computations in quantum field theories. Comparing the computation of simple quantities in the various schemes, we point out similarities and differences between them. (orig.)

  19. 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.

  20. 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.

  1. 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

  2. Extreme values, regular variation and point processes

    CERN Document Server

    Resnick, Sidney I

    1987-01-01

    Extremes Values, Regular Variation and Point Processes is a readable and efficient account of the fundamental mathematical and stochastic process techniques needed to study the behavior of extreme values of phenomena based on independent and identically distributed random variables and vectors It presents a coherent treatment of the distributional and sample path fundamental properties of extremes and records It emphasizes the core primacy of three topics necessary for understanding extremes the analytical theory of regularly varying functions; the probabilistic theory of point processes and random measures; and the link to asymptotic distribution approximations provided by the theory of weak convergence of probability measures in metric spaces The book is self-contained and requires an introductory measure-theoretic course in probability as a prerequisite Almost all sections have an extensive list of exercises which extend developments in the text, offer alternate approaches, test mastery and provide for enj...

  3. 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.

  4. 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.

  5. 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.

  6. Positive solutions of three-point boundary-value problems for p-Laplacian singular differential equations

    Directory of Open Access Journals (Sweden)

    George N. Galanis

    2005-10-01

    Full Text Available In this paper we prove the existence of positive solutions for the three-point singular boundary-value problem$$ -[phi _{p}(u']'=q(tf(t,u(t,quad 0points and $g$ is a monotone continuous function defined on the real line $mathbb{R}$ with $g(0=0$ and $ug(ugeq 0$. Our approach is a combination of Nonlinear Alternative of Leray-Schauder with the properties of the associated vector field at the $(u,u'$ plane. More precisely, we show that the solutions of the above boundary-value problem remains away from the origin for the case where the nonlinearity is sublinear and so we avoid its singularity at $u=0$.

  7. Regularity of p(ṡ)-superharmonic functions, the Kellogg property and semiregular boundary points

    Science.gov (United States)

    Adamowicz, Tomasz; Björn, Anders; Björn, Jana

    2014-11-01

    We study various boundary and inner regularity questions for $p(\\cdot)$-(super)harmonic functions in Euclidean domains. In particular, we prove the Kellogg property and introduce a classification of boundary points for $p(\\cdot)$-harmonic functions into three disjoint classes: regular, semiregular and strongly irregular points. Regular and especially semiregular points are characterized in many ways. The discussion is illustrated by examples. Along the way, we present a removability result for bounded $p(\\cdot)$-harmonic functions and give some new characterizations of $W^{1, p(\\cdot)}_0$ spaces. We also show that $p(\\cdot)$-superharmonic functions are lower semicontinuously regularized, and characterize them in terms of lower semicontinuously regularized supersolutions.

  8. HIERARCHICAL REGULARIZATION OF POLYGONS FOR PHOTOGRAMMETRIC POINT CLOUDS OF OBLIQUE IMAGES

    Directory of Open Access Journals (Sweden)

    L. Xie

    2017-05-01

    Full Text Available Despite the success of multi-view stereo (MVS reconstruction from massive oblique images in city scale, only point clouds and triangulated meshes are available from existing MVS pipelines, which are topologically defect laden, free of semantical information and hard to edit and manipulate interactively in further applications. On the other hand, 2D polygons and polygonal models are still the industrial standard. However, extraction of the 2D polygons from MVS point clouds is still a non-trivial task, given the fact that the boundaries of the detected planes are zigzagged and regularities, such as parallel and orthogonal, cannot preserve. Aiming to solve these issues, this paper proposes a hierarchical polygon regularization method for the photogrammetric point clouds from existing MVS pipelines, which comprises of local and global levels. After boundary points extraction, e.g. using alpha shapes, the local level is used to consolidate the original points, by refining the orientation and position of the points using linear priors. The points are then grouped into local segments by forward searching. In the global level, regularities are enforced through a labeling process, which encourage the segments share the same label and the same label represents segments are parallel or orthogonal. This is formulated as Markov Random Field and solved efficiently. Preliminary results are made with point clouds from aerial oblique images and compared with two classical regularization methods, which have revealed that the proposed method are more powerful in abstracting a single building and is promising for further 3D polygonal model reconstruction and GIS applications.

  9. Topological effects in QCD and the problem of short-distance singularities

    International Nuclear Information System (INIS)

    Luescher, Martin

    2004-01-01

    The topological susceptibility and the higher moments of the topological charge distribution in QCD are expressed through certain n-point functions of the scalar and pseudo-scalar quark densities at vanishing momenta, which are free of short-distance singularities. Since the normalization of the correlation functions is determined by the non-singlet chiral Ward identities, these formulae provide an unambiguous regularization-independent definition of the moments and thus of the charge distribution

  10. Thin accretion disk around regular black hole

    Directory of Open Access Journals (Sweden)

    QIU Tianqi

    2014-08-01

    Full Text Available The Penrose′s cosmic censorship conjecture says that naked singularities do not exist in nature.So,it seems reasonable to further conjecture that not even a singularity exists in nature.In this paper,a regular black hole without singularity is studied in detail,especially on its thin accretion disk,energy flux,radiation temperature and accretion efficiency.It is found that the interaction of regular black hole is stronger than that of the Schwarzschild black hole. Furthermore,the thin accretion will be more efficiency to lost energy while the mass of black hole decreased. These particular properties may be used to distinguish between black holes.

  11. Examples of integrable and non-integrable systems on singular symplectic manifolds

    Science.gov (United States)

    Delshams, Amadeu; Kiesenhofer, Anna; Miranda, Eva

    2017-05-01

    We present a collection of examples borrowed from celestial mechanics and projective dynamics. In these examples symplectic structures with singularities arise naturally from regularization transformations, Appell's transformation or classical changes like McGehee coordinates, which end up blowing up the symplectic structure or lowering its rank at certain points. The resulting geometrical structures that model these examples are no longer symplectic but symplectic with singularities which are mainly of two types: bm-symplectic and m-folded symplectic structures. These examples comprise the three body problem as non-integrable exponent and some integrable reincarnations such as the two fixed-center problem. Given that the geometrical and dynamical properties of bm-symplectic manifolds and folded symplectic manifolds are well-understood [10-12,9,15,13,14,24,20,22,25,28], we envisage that this new point of view in this collection of examples can shed some light on classical long-standing problems concerning the study of dynamical properties of these systems seen from the Poisson viewpoint.

  12. Singular point analysis during rail deployment into vacuum vessel for ITER blanket maintenance

    International Nuclear Information System (INIS)

    Kakudate, Satoshi; Shibanuma, Kiyoshi

    2007-05-01

    Remote maintenance of the ITER blanket composed of about 400 modules in the vessel is required by a maintenance robot due to high gamma radiation of ∼500Gy/h in the vessel. A concept of rail-mounted vehicle manipulator system has been developed to apply to the maintenance of the ITER blanket. The most critical issue of the vehicle manipulator system is the feasibility of the deployment of the articulated rail composed of eight rail links into the donut-shaped vessel without any driving mechanism in the rail. To solve this issue, a new driving mechanism and procedure for the rail deployment has been proposed, taking account of a repeated operation of the multi-rail links deployed in the same kinematical manner. The new driving mechanism, which is deferent from those of a usual 'articulated arm' equipped with actuator in the every joint for movement, is composed of three mechanisms. To assess the feasibility of the kinematics of the articulated rail for rail deployment, a kinematical model composed of three rail links related to a cycle of the repeated operation for rail deployment was considered. The determinant det J' of the Jacobian matrix J' was solved so as to estimate the existence of a singular point of the transformation during rail deployment. As a result, it is found that there is a singular point due to det J'=0. To avoid the singular point of the rail links, a new location of the second driving mechanism and the related rail deployment procedure are proposed. As a result of the rail deployment test based on the new proposal using a full-scale vehicle manipulator system, the respective rail links have been successfully deployed within 6 h less than the target of 8 h in the same manner of the repeated operation under a synchronized cooperation among the three driving mechanisms. It is therefore concluded that the feasibility of the rail deployment of the articulated rail composed of simple structures without any driving mechanism has been demonstrated

  13. Regularity results for the minimum time function with Hörmander vector fields

    Science.gov (United States)

    Albano, Paolo; Cannarsa, Piermarco; Scarinci, Teresa

    2018-03-01

    In a bounded domain of Rn with boundary given by a smooth (n - 1)-dimensional manifold, we consider the homogeneous Dirichlet problem for the eikonal equation associated with a family of smooth vector fields {X1 , … ,XN } subject to Hörmander's bracket generating condition. We investigate the regularity of the viscosity solution T of such problem. Due to the presence of characteristic boundary points, singular trajectories may occur. First, we characterize these trajectories as the closed set of all points at which the solution loses point-wise Lipschitz continuity. Then, we prove that the local Lipschitz continuity of T, the local semiconcavity of T, and the absence of singular trajectories are equivalent properties. Finally, we show that the last condition is satisfied whenever the characteristic set of {X1 , … ,XN } is a symplectic manifold. We apply our results to several examples.

  14. 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.

  15. Singularities in the general theory of relativity

    International Nuclear Information System (INIS)

    Treder, H.J.

    1980-01-01

    'Regular solutions of Einstein's equations' mean very different things. In the case of the empty-space equations, Rsub(ik) = o, such solutions must be metrics gsub(ik)(xsup(l)) without additionaly singular 'field sources' (Einstein's 'Particle problem'). However the 'phenomenological matter' is defined by the Einstein equations Rsub(ik) - 1/2gsub(ik)R = -kappaTsub(ik) itselves. Therefore if 10 regular functions gsub(ik)(xsup(l)) are given (which the inequalities of Lorentz-signature fulfil) then these gsub(ik) define 10 functions Tsub(ik)(xsup(l)) without singularities. But, the matter-tensor Tsub(ik) must fulfil the two inequalities T >= o, T 0 0 >= 1/2 T only and therefore the Einstein-equations with 'phenomenological matter' mean the two inequalities R >= o, R 0 0 <= o which are incompatible with a permanently regular metric with Lorentz-signature, generally. (author)

  16. 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.)

  17. Singularity of the London penetration depth at quantum critical points in superconductors.

    Science.gov (United States)

    Chowdhury, Debanjan; Swingle, Brian; Berg, Erez; Sachdev, Subir

    2013-10-11

    We present a general theory of the singularity in the London penetration depth at symmetry-breaking and topological quantum critical points within a superconducting phase. While the critical exponents and ratios of amplitudes on the two sides of the transition are universal, an overall sign depends upon the interplay between the critical theory and the underlying Fermi surface. We determine these features for critical points to spin density wave and nematic ordering, and for a topological transition between a superconductor with Z2 fractionalization and a conventional superconductor. We note implications for recent measurements of the London penetration depth in BaFe2(As(1-x)P(x))2 [K. Hashimoto et al., Science 336, 1554 (2012)].

  18. Regularization of the Boundary-Saddle-Node Bifurcation

    Directory of Open Access Journals (Sweden)

    Xia Liu

    2018-01-01

    Full Text Available In this paper we treat a particular class of planar Filippov systems which consist of two smooth systems that are separated by a discontinuity boundary. In such systems one vector field undergoes a saddle-node bifurcation while the other vector field is transversal to the boundary. The boundary-saddle-node (BSN bifurcation occurs at a critical value when the saddle-node point is located on the discontinuity boundary. We derive a local topological normal form for the BSN bifurcation and study its local dynamics by applying the classical Filippov’s convex method and a novel regularization approach. In fact, by the regularization approach a given Filippov system is approximated by a piecewise-smooth continuous system. Moreover, the regularization process produces a singular perturbation problem where the original discontinuous set becomes a center manifold. Thus, the regularization enables us to make use of the established theories for continuous systems and slow-fast systems to study the local behavior around the BSN bifurcation.

  19. The Large-g Observability of the Low-Lying Energies in the Strongly Singular Potentials V(x) = x(2) + g(2)/x(6) after their PT-symmetric Regularization

    Czech Academy of Sciences Publication Activity Database

    Znojil, Miloslav

    2014-01-01

    Roč. 53, č. 8 (2014), s. 2549-2557 ISSN 0020-7748 Institutional support: RVO:61389005 Keywords : quantum evolution * Triple-Hilbert-space picture * Strongly singular forces * Regularization by complexification * strong-coupling dynamical regtime * unitarity Subject RIV: BE - Theoretical Physics Impact factor: 1.184, year: 2014

  20. 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.

  1. Regularization of fields for self-force problems in curved spacetime: Foundations and a time-domain application

    International Nuclear Information System (INIS)

    Vega, Ian; Detweiler, Steven

    2008-01-01

    We propose an approach for the calculation of self-forces, energy fluxes and waveforms arising from moving point charges in curved spacetimes. As opposed to mode-sum schemes that regularize the self-force derived from the singular retarded field, this approach regularizes the retarded field itself. The singular part of the retarded field is first analytically identified and removed, yielding a finite, differentiable remainder from which the self-force is easily calculated. This regular remainder solves a wave equation which enjoys the benefit of having a nonsingular source. Solving this wave equation for the remainder completely avoids the calculation of the singular retarded field along with the attendant difficulties associated with numerically modeling a delta-function source. From this differentiable remainder one may compute the self-force, the energy flux, and also a waveform which reflects the effects of the self-force. As a test of principle, we implement this method using a 4th-order (1+1) code, and calculate the self-force for the simple case of a scalar charge moving in a circular orbit around a Schwarzschild black hole. We achieve agreement with frequency-domain results to ∼0.1% or better.

  2. On the regularization of extremal three-point functions involving giant gravitons

    Directory of Open Access Journals (Sweden)

    Charlotte Kristjansen

    2015-11-01

    Full Text Available In the AdS5/CFT4 set-up, extremal three-point functions involving two giant 1/2 BPS gravitons and one point-like 1/2 BPS graviton, when calculated using semi-classical string theory methods, match the corresponding three-point functions obtained in the tree-level gauge theory. The string theory computation relies on a certain regularization procedure whose justification is based on the match between gauge and string theory. We revisit the regularization procedure and reformulate it in a way which allows a generalization to the ABJM set-up where three-point functions of 1/2 BPS operators are not protected and where a match between tree-level gauge theory and semi-classical string theory is hence not expected.

  3. 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.

  4. Determine point-to-point networking interactions using regular expressions

    Directory of Open Access Journals (Sweden)

    Konstantin S. Deev

    2015-06-01

    Full Text Available As Internet growth and becoming more popular, the number of concurrent data flows start to increasing, which makes sense in bandwidth requested. Providers and corporate customers need ability to identify point-to-point interactions. The best is to use special software and hardware implementations that distribute the load in the internals of the complex, using the principles and approaches, in particular, described in this paper. This paper represent the principles of building system, which searches for a regular expression match using computing on graphics adapter in server station. A significant computing power and capability to parallel execution on modern graphic processor allows inspection of large amounts of data through sets of rules. Using the specified characteristics can lead to increased computing power in 30…40 times compared to the same setups on the central processing unit. The potential increase in bandwidth capacity could be used in systems that provide packet analysis, firewalls and network anomaly detectors.

  5. Unique solvability of some two-point boundary value problems for linear functional differential equations with singularities

    Czech Academy of Sciences Publication Activity Database

    Rontó, András; Samoilenko, A. M.

    2007-01-01

    Roč. 41, - (2007), s. 115-136 ISSN 1512-0015 R&D Projects: GA ČR(CZ) GA201/06/0254 Institutional research plan: CEZ:AV0Z10190503 Keywords : two-point problem * functional differential equation * singular boundary problem Subject RIV: BA - General Mathematics

  6. 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)

  7. 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.

  8. 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...

  9. Regularization of Hamilton-Lagrangian guiding center theories

    International Nuclear Information System (INIS)

    Correa-Restrepo, D.; Wimmel, H.K.

    1985-04-01

    The Hamilton-Lagrangian guiding-center (G.C.) theories of Littlejohn, Wimmel, and Pfirsch show a singularity for B-fields with non-vanishing parallel curl at a critical value of vsub(parallel), which complicates applications. The singularity is related to a sudden breakdown, at a critical vsub(parallel), of gyration in the exact particle mechanics. While the latter is a real effect, the G.C. singularity can be removed. To this end a regularization method is defined that preserves the Hamilton-Lagrangian structure and the conservation theorems. For demonstration this method is applied to the standard G.C. theory (without polarization drift). Liouville's theorem and G.C. kinetic equations are also derived in regularized form. The method could equally well be applied to the case with polarization drift and to relativistic G.C. theory. (orig.)

  10. A direct solver with reutilization of LU factorizations for h-adaptive finite element grids with point singularities

    KAUST Repository

    Paszyński, Maciej R.

    2013-04-01

    This paper describes a direct solver algorithm for a sequence of finite element meshes that are h-refined towards one or several point singularities. For such a sequence of grids, the solver delivers linear computational cost O(N) in terms of CPU time and memory with respect to the number of unknowns N. The linear computational cost is achieved by utilizing the recursive structure provided by the sequence of h-adaptive grids with a special construction of the elimination tree that allows for reutilization of previously computed partial LU (or Cholesky) factorizations over the entire unrefined part of the computational mesh. The reutilization technique reduces the computational cost of the entire sequence of h-refined grids from O(N2) down to O(N). Theoretical estimates are illustrated with numerical results on two- and three-dimensional model problems exhibiting one or several point singularities. © 2013 Elsevier Ltd. All rights reserved.

  11. A direct solver with reutilization of LU factorizations for h-adaptive finite element grids with point singularities

    KAUST Repository

    Paszyński, Maciej R.; Calo, Victor M.; Pardo, David

    2013-01-01

    This paper describes a direct solver algorithm for a sequence of finite element meshes that are h-refined towards one or several point singularities. For such a sequence of grids, the solver delivers linear computational cost O(N) in terms of CPU time and memory with respect to the number of unknowns N. The linear computational cost is achieved by utilizing the recursive structure provided by the sequence of h-adaptive grids with a special construction of the elimination tree that allows for reutilization of previously computed partial LU (or Cholesky) factorizations over the entire unrefined part of the computational mesh. The reutilization technique reduces the computational cost of the entire sequence of h-refined grids from O(N2) down to O(N). Theoretical estimates are illustrated with numerical results on two- and three-dimensional model problems exhibiting one or several point singularities. © 2013 Elsevier Ltd. All rights reserved.

  12. 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)

  13. 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.

  14. Remarks about singular solutions to the Dirac equation

    International Nuclear Information System (INIS)

    Uhlir, M.

    1975-01-01

    In the paper singular solutions of the Dirac equation are investigated. They are derived in the Lorentz-covariant way of functions proportional to static multipole fields of scalar and (or) electromagnetic fields and of regular solutions of the Dirac equations. The regularization procedure excluding divergences of total energy, momentum and angular momentum of the spinor field considered is proposed

  15. Predictive error dependencies when using pilot points and singular value decomposition in groundwater model calibration

    DEFF Research Database (Denmark)

    Christensen, Steen; Doherty, John

    2008-01-01

    A significant practical problem with the pilot point method is to choose the location of the pilot points. We present a method that is intended to relieve the modeler from much of this responsibility. The basic idea is that a very large number of pilot points are distributed more or less uniformly...... over the model area. Singular value decomposition (SVD) of the (possibly weighted) sensitivity matrix of the pilot point based model produces eigenvectors of which we pick a small number corresponding to significant eigenvalues. Super parameters are defined as factors through which parameter...... combinations corresponding to the chosen eigenvectors are multiplied to obtain the pilot point values. The model can thus be transformed from having many-pilot-point parameters to having a few super parameters that can be estimated by nonlinear regression on the basis of the available observations. (This...

  16. 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

  17. 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)

  18. 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)

  19. Spacetime completeness of non-singular black holes in conformal gravity

    Energy Technology Data Exchange (ETDEWEB)

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

    2017-05-01

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

  20. 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.)

  1. 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.

  2. Identifying Initial Condition in Degenerate Parabolic Equation with Singular Potential

    Directory of Open Access Journals (Sweden)

    K. Atifi

    2017-01-01

    Full Text Available A hybrid algorithm and regularization method are proposed, for the first time, to solve the one-dimensional degenerate inverse heat conduction problem to estimate the initial temperature distribution from point measurements. The evolution of the heat is given by a degenerate parabolic equation with singular potential. This problem can be formulated in a least-squares framework, an iterative procedure which minimizes the difference between the given measurements and the value at sensor locations of a reconstructed field. The mathematical model leads to a nonconvex minimization problem. To solve it, we prove the existence of at least one solution of problem and we propose two approaches: the first is based on a Tikhonov regularization, while the second approach is based on a hybrid genetic algorithm (married genetic with descent method type gradient. Some numerical experiments are given.

  3. 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.

  4. Multiple Positive Solutions of a Nonlinear Four-Point Singular Boundary Value Problem with a p-Laplacian Operator on Time Scales

    Directory of Open Access Journals (Sweden)

    Shihuang Hong

    2009-01-01

    Full Text Available We present sufficient conditions for the existence of at least twin or triple positive solutions of a nonlinear four-point singular boundary value problem with a p-Laplacian dynamic equation on a time scale. Our results are obtained via some new multiple fixed point theorems.

  5. 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

  6. 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. Gauge invariance properties and singularity cancellations in a modified PQCD

    CERN Document Server

    Cabo-Montes de Oca, Alejandro; Cabo, Alejandro; Rigol, Marcos

    2006-01-01

    The gauge-invariance properties and singularity elimination of the modified perturbation theory for QCD introduced in previous works, are investigated. The construction of the modified free propagators is generalized to include the dependence on the gauge parameter $\\alpha $. Further, a functional proof of the independence of the theory under the changes of the quantum and classical gauges is given. The singularities appearing in the perturbative expansion are eliminated by properly combining dimensional regularization with the Nakanishi infrared regularization for the invariant functions in the operator quantization of the $\\alpha$-dependent gauge theory. First-order evaluations of various quantities are presented, illustrating the gauge invariance-properties.

  8. 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

  9. Spatial Attention Is Attracted in a Sustained Fashion toward Singular Points in the Optic Flow

    Science.gov (United States)

    Wang, Shuo; Fukuchi, Masaki; Koch, Christof; Tsuchiya, Naotsugu

    2012-01-01

    While a single approaching object is known to attract spatial attention, it is unknown how attention is directed when the background looms towards the observer as s/he moves forward in a quasi-stationary environment. In Experiment 1, we used a cued speeded discrimination task to quantify where and how spatial attention is directed towards the target superimposed onto a cloud of moving dots. We found that when the motion was expansive, attention was attracted towards the singular point of the optic flow (the focus of expansion, FOE) in a sustained fashion. The effects were less pronounced when the motion was contractive. The more ecologically valid the motion features became (e.g., temporal expansion of each dot, spatial depth structure implied by distribution of the size of the dots), the stronger the attentional effects. Further, the attentional effects were sustained over 1000 ms. Experiment 2 quantified these attentional effects using a change detection paradigm by zooming into or out of photographs of natural scenes. Spatial attention was attracted in a sustained manner such that change detection was facilitated or delayed depending on the location of the FOE only when the motion was expansive. Our results suggest that focal attention is strongly attracted towards singular points that signal the direction of forward ego-motion. PMID:22905096

  10. A new method for the regularization of a class of divergent Feynman integrals in covariant and axial gauges

    International Nuclear Information System (INIS)

    Lee, H.C.; Milgram, M.S.

    1984-07-01

    A hybrid of dimensional and analytic regularization is used to regulate and uncover a Meijer's G-function representation for a class of massless, divergent Feynman integrals in an axial gauge. Integrals in the covariant gauge belong to a subclass and those in the light-cone gauge are reached by analytic continuation. The method decouples the physical ultraviolet and infrared singularities from the spurious axial gauge singularity but regulates all three simultaneously. For the axial gauge singularity, the new analytic method is more powerful and elegant than the old principal value prescription, but the two methods yield identical infinite as well as regular parts. It is shown that dimensional and analytic regularization can be made equivalent, implying that the former method is free from spurious γ5-anomalies and the latter preserves gauge invariance. The hybrid method permits the evaluation of integrals containing arbritrary integer powers of logarithms in the integrand by differentiation with respect to exponents. Such 'exponent derivatives' generate the same set of 'polylogs' as that generated in multi-loop integrals in perturbation theories and may be useful for solving equations in nonperturbation theories. The close relation between the method of exponent derivatives and the prescription of 't Hooft and Veltman for treating overlapping divergencies is pointed out. It is demonstrated that both methods generate functions that are free from unrecognizable logarithmic infinite parts. Nonperturbation theories expressed in terms of exponent derivatives are thus renormalizable. Some intriguing connections between nonperturbation theories and nonintegral exponents are pointed out

  11. SENR /NRPy + : Numerical relativity in singular curvilinear coordinate systems

    Science.gov (United States)

    Ruchlin, Ian; Etienne, Zachariah B.; Baumgarte, Thomas W.

    2018-03-01

    We report on a new open-source, user-friendly numerical relativity code package called SENR /NRPy + . Our code extends previous implementations of the BSSN reference-metric formulation to a much broader class of curvilinear coordinate systems, making it ideally suited to modeling physical configurations with approximate or exact symmetries. In the context of modeling black hole dynamics, it is orders of magnitude more efficient than other widely used open-source numerical relativity codes. NRPy + provides a Python-based interface in which equations are written in natural tensorial form and output at arbitrary finite difference order as highly efficient C code, putting complex tensorial equations at the scientist's fingertips without the need for an expensive software license. SENR provides the algorithmic framework that combines the C codes generated by NRPy + into a functioning numerical relativity code. We validate against two other established, state-of-the-art codes, and achieve excellent agreement. For the first time—in the context of moving puncture black hole evolutions—we demonstrate nearly exponential convergence of constraint violation and gravitational waveform errors to zero as the order of spatial finite difference derivatives is increased, while fixing the numerical grids at moderate resolution in a singular coordinate system. Such behavior outside the horizons is remarkable, as numerical errors do not converge to zero near punctures, and all points along the polar axis are coordinate singularities. The formulation addresses such coordinate singularities via cell-centered grids and a simple change of basis that analytically regularizes tensor components with respect to the coordinates. Future plans include extending this formulation to allow dynamical coordinate grids and bispherical-like distribution of points to efficiently capture orbiting compact binary dynamics.

  12. Regularization of the light-cone gauge gluon propagator singularities using sub-gauge conditions

    Energy Technology Data Exchange (ETDEWEB)

    Chirilli, Giovanni A.; Kovchegov, Yuri V.; Wertepny, Douglas E. [Department of Physics, The Ohio State University,191 W Woodruff Ave, Columbus, OH 43210 (United States)

    2015-12-21

    Perturbative QCD calculations in the light-cone gauge have long suffered from the ambiguity associated with the regularization of the poles in the gluon propagator. In this work we study sub-gauge conditions within the light-cone gauge corresponding to several known ways of regulating the gluon propagator. Using the functional integral calculation of the gluon propagator, we rederive the known sub-gauge conditions for the θ-function gauges and identify the sub-gauge condition for the principal value (PV) regularization of the gluon propagator’s light-cone poles. The obtained sub-gauge condition for the PV case is further verified by a sample calculation of the classical Yang-Mills field of two collinear ultrarelativistic point color charges. Our method does not allow one to construct a sub-gauge condition corresponding to the well-known Mandelstam-Leibbrandt prescription for regulating the gluon propagator poles.

  13. 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.

  14. 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.

  15. Pressure fluctuations induced by fluid flow in singular points of industrial circuits

    International Nuclear Information System (INIS)

    Gibert, R.J.; Villard, B.

    1977-01-01

    Flow singularities (enlargements, bards, valves, tees, ...) generate in the circuits of industrial plants wall pressure fluctuations which are the main cause of vibration. A methodical study of the most current singularities has been performed at C.E.A./D.E.M.T. On one hand a theory of noise generation by unsteady flow in internal acoustics has been developed. This theory uses the basic ideas initiated by LIGHTILL. As a result it is shown that the plane wave propagation is a valid assumption and that a singularity can be acoustically modelled by a pressure and a mass-flow-rate discontinuities. Both are random functions of time, the spectra of which are determined from the local fluctuations characteristics. On other hand, characteristics of several singularities have been measured: intercorrelation spectra of local pressure fluctuations. Autocorrelation spectra of associated acoustical sources (the measure of the acoustical pressures in the experimental circuit are interpreted by using the D.E.M.T. computer code VIBRAPHONE which gives the acoustical response of a complex circuit. Experimental atmospheric air and water loops have been used. The Reynolds number has been changed between about 10 5 and 10 6 ; the Mach number between about 0,01 and 0,5. Simple laws with dimensionless parameters are formulated and can be used for the estimation of the acoustical and mechanical vibration level of a circuit with given singularities

  16. Thermodynamics of a class of regular black holes with a generalized uncertainty principle

    Science.gov (United States)

    Maluf, R. V.; Neves, Juliano C. S.

    2018-05-01

    In this article, we present a study on thermodynamics of a class of regular black holes. Such a class includes Bardeen and Hayward regular black holes. We obtained thermodynamic quantities like the Hawking temperature, entropy, and heat capacity for the entire class. As part of an effort to indicate some physical observable to distinguish regular black holes from singular black holes, we suggest that regular black holes are colder than singular black holes. Besides, contrary to the Schwarzschild black hole, that class of regular black holes may be thermodynamically stable. From a generalized uncertainty principle, we also obtained the quantum-corrected thermodynamics for the studied class. Such quantum corrections provide a logarithmic term for the quantum-corrected entropy.

  17. 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

  18. Modelling aggregation on the large scale and regularity on the small scale in spatial point pattern datasets

    DEFF Research Database (Denmark)

    Lavancier, Frédéric; Møller, Jesper

    We consider a dependent thinning of a regular point process with the aim of obtaining aggregation on the large scale and regularity on the small scale in the resulting target point process of retained points. Various parametric models for the underlying processes are suggested and the properties...

  19. Yang-Mills theories in axial and light-cone gauges, analytic regularization and Ward identities

    International Nuclear Information System (INIS)

    Lee, H.C.

    1984-12-01

    The application of the principles of generalization and analytic continuation to the regularization of divergent Feynman integrals is discussed. The technique, or analytic regularization, which is a generalization of dimensional regularization, is used to derive analytic representations for two classes of massless two-point integrals. The first class is based on the principal-value prescription and includes integrals encountered in quantum field theories in the ghost-free axial gauge (n.A=0), reducing in a special case to integrals in the light-cone gauge (n.A=0,n 2 =0). The second class is based on the Mandelstam prescription devised espcially for the light-cone gauge. For some light-cone gauge integrals the two representations are not equivalent. Both classes include as a subclass integrals in the Lorentz covariant 'zeta-gauges'. The representations are used to compute one-loop corrections to the self-energy and the three-vertex in Yang-Mills theories in the axial and light-cone gauges, showing that the two- and three-point Ward identities are satisfied; to illustrate that ultraviolet and infrared singularities, indistinguishable in dimensional regularization, can be separated analytically; and to show that certain tadpole integrals vanish because of an exact cancellation between ultraviolet and infrared singularities. In the axial gauge, the wavefunction and vertex renormalization constants, Z 3 and Z 1 , are identical, so that the β-function can be directly derived from Z 3 the result being the same as that computed in the covariant zeta-gauges. Preliminary results suggest that the light-cone gauge in the Mandelstam prescription, but not in the principal value prescription, has the same renormalization property of the axial gauge

  20. 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.

  1. An Exact Solution of the Binary Singular Problem

    Directory of Open Access Journals (Sweden)

    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.

  2. The Geometry of Black Hole Singularities

    Directory of Open Access Journals (Sweden)

    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.

  3. Through the big bang: Continuing Einstein's equations beyond a cosmological singularity

    Science.gov (United States)

    Koslowski, Tim A.; Mercati, Flavio; Sloan, David

    2018-03-01

    All measurements are comparisons. The only physically accessible degrees of freedom (DOFs) are dimensionless ratios. The objective description of the universe as a whole thus predicts only how these ratios change collectively as one of them is changed. Here we develop a description for classical Bianchi IX cosmology implementing these relational principles. The objective evolution decouples from the volume and its expansion degree of freedom. We use the relational description to investigate both vacuum dominated and quiescent Bianchi IX cosmologies. In the vacuum dominated case the relational dynamical system predicts an infinite amount of change of the relational DOFs, in accordance with the well known chaotic behaviour of Bianchi IX. In the quiescent case the relational dynamical system evolves uniquely though the point where the decoupled scale DOFs predict the big bang/crunch. This is a non-trivial prediction of the relational description; the big bang/crunch is not the end of physics - it is instead a regular point of the relational evolution. Describing our solutions as spacetimes that satisfy Einstein's equations, we find that the relational dynamical system predicts two singular solutions of GR that are connected at the hypersurface of the singularity such that relational DOFs are continuous and the orientation of the spatial frame is inverted.

  4. 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.

  5. Orbital classical solutions, non-perturbative phenomena and singularity at the zero coupling constant point

    International Nuclear Information System (INIS)

    Vourdas, A.

    1982-01-01

    We try to extend previous arguments on orbital classical solutions in non-relativistic quantum mechanics to the 1/4lambda vertical stroke phi vertical stroke 4 complex relativistic field theory. The single valuedness of the Green function in the semiclassical (Planksche Konstante → 0) limit leads to a Bohr-Sommerfeld quantization. A path integral formalism for the Green functions analogous to that in non-relativistic quantum mechanics is employed and a semiclassical approach which uses our classical solutions indicates non-perturbative effects. They reflect an esub(1/lambda) singularity at the zero coupling constant point. (orig.)

  6. 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...

  7. Regular scattering patterns from near-cloaking devices and their implications for invisibility cloaking

    International Nuclear Information System (INIS)

    Kocyigit, Ilker; Liu, Hongyu; Sun, Hongpeng

    2013-01-01

    In this paper, we consider invisibility cloaking via the transformation optics approach through a ‘blow-up’ construction. An ideal cloak makes use of singular cloaking material. ‘Blow-up-a-small-region’ construction and ‘truncation-of-singularity’ construction are introduced to avoid the singular structure, however, giving only near-cloaks. The study in the literature is to develop various mechanisms in order to achieve high-accuracy approximate near-cloaking devices, and also from a practical viewpoint to nearly cloak an arbitrary content. We study the problem from a different viewpoint. It is shown that for those regularized cloaking devices, the corresponding scattering wave fields due to an incident plane wave have regular patterns. The regular patterns are both a curse and a blessing. On the one hand, the regular wave pattern betrays the location of a cloaking device which is an intrinsic defect due to the ‘blow-up’ construction, and this is particularly the case for the construction by employing a high-loss layer lining. Indeed, our numerical experiments show robust reconstructions of the location, even by implementing the phaseless cross-section data. The construction by employing a high-density layer lining shows a certain promising feature. On the other hand, it is shown that one can introduce an internal point source to produce the canceling scattering pattern to achieve a near-cloak of an arbitrary order of accuracy. (paper)

  8. 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.

  9. Singularity theory and equivariant symplectic maps

    CERN Document Server

    Bridges, Thomas J

    1993-01-01

    The monograph is a study of the local bifurcations of multiparameter symplectic maps of arbitrary dimension in the neighborhood of a fixed point.The problem is reduced to a study of critical points of an equivariant gradient bifurcation problem, using the correspondence between orbits ofa symplectic map and critical points of an action functional. New results onsingularity theory for equivariant gradient bifurcation problems are obtained and then used to classify singularities of bifurcating period-q points. Of particular interest is that a general framework for analyzing group-theoretic aspects and singularities of symplectic maps (particularly period-q points) is presented. Topics include: bifurcations when the symplectic map has spatial symmetry and a theory for the collision of multipliers near rational points with and without spatial symmetry. The monograph also includes 11 self-contained appendices each with a basic result on symplectic maps. The monograph will appeal to researchers and graduate student...

  10. Spectral singularities, biorthonormal systems and a two-parameter family of complex point interactions

    Energy Technology Data Exchange (ETDEWEB)

    Mostafazadeh, Ali [Department of Mathematics, Koc University, Rumelifeneri Yolu, 34450 Sariyer, Istanbul (Turkey); Mehri-Dehnavi, Hossein [Department of Physics, Institute for Advanced Studies in Basic Sciences, Zanjan 45195-1159 (Iran, Islamic Republic of)], E-mail: amostafazadeh@ku.edu.tr, E-mail: mehrideh@iasbs.ac.ir

    2009-03-27

    A curious feature of complex scattering potentials v(x) is the appearance of spectral singularities. We offer a quantitative description of spectral singularities that identifies them with an obstruction to the existence of a complete biorthonormal system consisting of the eigenfunctions of the Hamiltonian operator and its adjoint. We establish the equivalence of this description with the mathematicians' definition of spectral singularities for the potential v(x) = z{sub -}{delta}(x + a) + z{sub +}{delta}(x - a), where z{sub {+-}} and a are respectively complex and real parameters and {delta}(x) is the Dirac delta function. We offer a through analysis of the spectral properties of this potential and determine the regions in the space of the coupling constants z{sub {+-}} where it admits bound states and spectral singularities. In particular, we find an explicit bound on the size of certain regions in which the Hamiltonian is quasi-Hermitian and examine the consequences of imposing PT-symmetry.

  11. Spectral singularities, biorthonormal systems and a two-parameter family of complex point interactions

    International Nuclear Information System (INIS)

    Mostafazadeh, Ali; Mehri-Dehnavi, Hossein

    2009-01-01

    A curious feature of complex scattering potentials v(x) is the appearance of spectral singularities. We offer a quantitative description of spectral singularities that identifies them with an obstruction to the existence of a complete biorthonormal system consisting of the eigenfunctions of the Hamiltonian operator and its adjoint. We establish the equivalence of this description with the mathematicians' definition of spectral singularities for the potential v(x) = z - δ(x + a) + z + δ(x - a), where z ± and a are respectively complex and real parameters and δ(x) is the Dirac delta function. We offer a through analysis of the spectral properties of this potential and determine the regions in the space of the coupling constants z ± where it admits bound states and spectral singularities. In particular, we find an explicit bound on the size of certain regions in which the Hamiltonian is quasi-Hermitian and examine the consequences of imposing PT-symmetry

  12. 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.

  13. The role of self-similarity in singularities of partial differential equations

    International Nuclear Information System (INIS)

    Eggers, Jens; Fontelos, Marco A

    2009-01-01

    We survey rigorous, formal and numerical results on the formation of point-like singularities (or blow-up) for a wide range of evolution equations. We use a similarity transformation of the original equation with respect to the blow-up point, such that self-similar behaviour is mapped to the fixed point of a dynamical system. We point out that analysing the dynamics close to the fixed point is a useful way of characterizing the singularity, in that the dynamics frequently reduces to very few dimensions. As far as we are aware, examples from the literature either correspond to stable fixed points, low-dimensional centre-manifold dynamics, limit cycles or travelling waves. For each 'class' of singularity, we give detailed examples. (invited article)

  14. From Singularity Theory to Finiteness of Walrasian Equilibria

    DEFF Research Database (Denmark)

    Castro, Sofia B.S.D.; Dakhlia, Sami F.; Gothen, Peter

    The paper establishes that for an open and dense subset of smooth exchange economies, the number of Walrasian equilibria is finite. In particular, our results extend to non-regular economies; it even holds when restricted to the subset of critical ones. The proof rests on concepts from singularity...... theory....

  15. 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.

  16. 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.

  17. Higher-order glass-transition singularities in systems with short-ranged attractive potentials

    International Nuclear Information System (INIS)

    Goetze, W; Sperl, M

    2003-01-01

    Within the mode-coupling theory for the evolution of structural relaxation, the A 4 -glass-transition singularities are identified for systems of particles interacting with a hard-sphere repulsion complemented by different short-ranged potentials: Baxter's singular potential regularized by a large-wavevector cut-off, a model for the Asakura-Oosawa depletion attraction, a triangular potential, a Yukawa attraction, and a square-well potential. The regular potentials yield critical packing fractions, critical Debye-Waller factors, and critical amplitudes very close to each other. The elastic moduli and the particle localization lengths for corresponding states of the Yukawa system and the square-well system may differ by up to 20 and 10%, respectively

  18. 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

  19. 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

  20. 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.

  1. 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.

  2. Dimensional regularization in configuration space

    International Nuclear Information System (INIS)

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

    1995-09-01

    Dimensional regularization is introduced in configuration space by Fourier transforming in D-dimensions the perturbative momentum space Green functions. For this transformation, Bochner theorem is used, no extra parameters, such as those of Feynman or Bogoliubov-Shirkov are needed for convolutions. The regularized causal functions in x-space have ν-dependent moderated singularities at the origin. They can be multiplied together and Fourier transformed (Bochner) without divergence problems. The usual ultraviolet divergences appear as poles of the resultant functions of ν. Several example are discussed. (author). 9 refs

  3. Singular reduction of Nambu-Poisson manifolds

    Science.gov (United States)

    Das, Apurba

    The version of Marsden-Ratiu Poisson reduction theorem for Nambu-Poisson manifolds by a regular foliation have been studied by Ibáñez et al. In this paper, we show that this reduction procedure can be extended to the singular case. Under a suitable notion of Hamiltonian flow on the reduced space, we show that a set of Hamiltonians on a Nambu-Poisson manifold can also be reduced.

  4. 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.

  5. Numerical method of singular problems on singular integrals

    International Nuclear Information System (INIS)

    Zhao Huaiguo; Mou Zongze

    1992-02-01

    As first part on the numerical research of singular problems, a numerical method is proposed for singular integrals. It is shown that the procedure is quite powerful for solving physics calculation with singularity such as the plasma dispersion function. Useful quadrature formulas for some class of the singular integrals are derived. In general, integrals with more complex singularities can be dealt by this method easily

  6. 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

  7. An interior-point method for total variation regularized positron emission tomography image reconstruction

    Science.gov (United States)

    Bai, Bing

    2012-03-01

    There has been a lot of work on total variation (TV) regularized tomographic image reconstruction recently. Many of them use gradient-based optimization algorithms with a differentiable approximation of the TV functional. In this paper we apply TV regularization in Positron Emission Tomography (PET) image reconstruction. We reconstruct the PET image in a Bayesian framework, using Poisson noise model and TV prior functional. The original optimization problem is transformed to an equivalent problem with inequality constraints by adding auxiliary variables. Then we use an interior point method with logarithmic barrier functions to solve the constrained optimization problem. In this method, a series of points approaching the solution from inside the feasible region are found by solving a sequence of subproblems characterized by an increasing positive parameter. We use preconditioned conjugate gradient (PCG) algorithm to solve the subproblems directly. The nonnegativity constraint is enforced by bend line search. The exact expression of the TV functional is used in our calculations. Simulation results show that the algorithm converges fast and the convergence is insensitive to the values of the regularization and reconstruction parameters.

  8. 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.

  9. Point interactions of the dipole type defined through a three-parametric power regularization

    International Nuclear Information System (INIS)

    Zolotaryuk, A V

    2010-01-01

    A family of point interactions of the dipole type is studied in one dimension using a regularization by rectangles in the form of a barrier and a well separated by a finite distance. The rectangles and the distance are parametrized by a squeezing parameter ε → 0 with three powers μ, ν and τ describing the squeezing rates for the barrier, the well and the distance, respectively. This parametrization allows us to construct a whole family of point potentials of the dipole type including some other point interactions, such as e.g. δ-potentials. Varying the power τ, it is possible to obtain in the zero-range limit the following two cases: (i) the limiting δ'-potential is opaque (the conventional result obtained earlier by some authors) or (ii) this potential admits a resonant tunneling (the opposite result obtained recently by other authors). The structure of resonances (if any) also depends on a regularizing sequence. The sets of the {μ, ν, τ}-space where a non-zero (resonant or non-resonant) transmission occurs are found. For all these cases in the zero-range limit the transfer matrix is shown to be with real parameters χ and g depending on a regularizing sequence. Those cases when χ ≠ 1 and g ≠ 0 mean that the corresponding δ'-potential is accompanied by an effective δ-potential.

  10. 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.

  11. 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.)

  12. Resolution of Singularities Introduced by Hierarchical Structure in Deep Neural Networks.

    Science.gov (United States)

    Nitta, Tohru

    2017-10-01

    We present a theoretical analysis of singular points of artificial deep neural networks, resulting in providing deep neural network models having no critical points introduced by a hierarchical structure. It is considered that such deep neural network models have good nature for gradient-based optimization. First, we show that there exist a large number of critical points introduced by a hierarchical structure in deep neural networks as straight lines, depending on the number of hidden layers and the number of hidden neurons. Second, we derive a sufficient condition for deep neural networks having no critical points introduced by a hierarchical structure, which can be applied to general deep neural networks. It is also shown that the existence of critical points introduced by a hierarchical structure is determined by the rank and the regularity of weight matrices for a specific class of deep neural networks. Finally, two kinds of implementation methods of the sufficient conditions to have no critical points are provided. One is a learning algorithm that can avoid critical points introduced by the hierarchical structure during learning (called avoidant learning algorithm). The other is a neural network that does not have some critical points introduced by the hierarchical structure as an inherent property (called avoidant neural network).

  13. 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

  14. 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.

  15. Modified Differential Transform Method for Two Singular Boundary Values Problems

    Directory of Open Access Journals (Sweden)

    Yinwei Lin

    2014-01-01

    Full Text Available This paper deals with the two singular boundary values problems of second order. Two singular points are both boundary values points of the differential equation. The numerical solutions are developed by modified differential transform method (DTM for expanded point. Linear and nonlinear models are solved by this method to get more reliable and efficient numerical results. It can also solve ordinary differential equations where the traditional one fails. Besides, we give the convergence of this new method.

  16. 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.

  17. 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.

  18. 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}.

  19. Regularization of a λφ4 type tensor model, using point-splitting

    International Nuclear Information System (INIS)

    Moura Melo, W.A.; Helayel-Neto, J.A.

    1997-01-01

    The idea of using point-splitting to avoid field products in the same point was first introduced by Dirac. This splitting would be applied for example, redefining the fields present in a small vertex, at different points. More recently, Osland and Wu, in a series of papers presented used the idea as a regularization method. An generalized Lagrangian was obtained for the Qed, with interaction terms not presenting field products at the same point, exhibiting however non-locality problems. Nevertheless this fact, the authors obtained satisfactory results with this formulation, such as the Higgs mass (190 GeV) and the divergence free top quark (120 GeV). This work intends to obtain a generalized Lagrangian, modifying the original theory to avoid that the interaction terms present field products at the same point

  20. 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

  1. Point force singularities outside a drop covered with an incompressible surfactant: Image systems and their applications

    Science.gov (United States)

    Shaik, Vaseem A.; Ardekani, Arezoo M.

    2017-11-01

    In this work we derive the image flow fields for point force singularities placed outside a stationary drop covered with an insoluble, nondiffusing, and incompressible surfactant. We assume the interface to be Newtonian and use the Boussinesq-Scriven constitutive law for the interfacial stress tensor. We use this analytical solution to investigate two different problems. First, we derive the mobility matrix for two drops of arbitrary sizes covered with an incompressible surfactant. In the second example, we calculate the velocity of a swimming microorganism (modeled as a Stokes dipole) outside a drop covered with an incompressible surfactant.

  2. Shocks, singularities and oscillations in nonlinear optics and fluid mechanics

    CERN Document Server

    Santo, Daniele; Lannes, David

    2017-01-01

    The book collects the most relevant results from the INdAM Workshop "Shocks, Singularities and Oscillations in Nonlinear Optics and Fluid Mechanics" held in Rome, September 14-18, 2015. The contributions discuss recent major advances in the study of nonlinear hyperbolic systems, addressing general theoretical issues such as symmetrizability, singularities, low regularity or dispersive perturbations. It also investigates several physical phenomena where such systems are relevant, such as nonlinear optics, shock theory (stability, relaxation) and fluid mechanics (boundary layers, water waves, Euler equations, geophysical flows, etc.). It is a valuable resource for researchers in these fields. .

  3. Absence of singular continuous spectrum for certain self-adjoint operators

    International Nuclear Information System (INIS)

    Mourre, E.

    1979-01-01

    An adequate condition is given for a self-adjoint operator to show in the vinicity of a point E of its spectrum the following properties: its point spectrum is of finite size; its singular continuous spectrum is empty. In the way of new applications the absence of singular continuous spectrum is demonstrated in the following two cases: perturbations of pseudo-differential operators; Schroedinger operators of a three-body system [fr

  4. 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.

  5. 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

  6. One-loop regularization of the Polyakov string functional

    International Nuclear Information System (INIS)

    Cohen, E.; Kluberg-Stern, H.; Peschanski, R.

    1989-01-01

    The divergences of the vacuum amplitude for the bosonic Polyakov string are studied at the one-loop level in a modular invariant regularization scheme, characterized by a dimensional cutoff analogous to proper time. As a result, the singular behaviour in the cutoff is not uniform in the range of the modulus variable and this yields a control on the singularities induced by the tachyon and the dilaton. The divergences are those of a sigma model, but the coefficients of the sigma-model counter-terms are different for the sphere and the flat torus. (orig.)

  7. 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.

  8. The region interior to the event horizon of the regular Hayward black hole

    Science.gov (United States)

    Perez-Roman, Ivan; Bretón, Nora

    2018-06-01

    The Painlevé-Gullstrand coordinates allow us to explore the interior of the regular Hayward black hole. The behavior of an infalling particle in traversing the Hayward black hole is compared with the one inside the Schwarzschild and Reissner-Nordstrom singular black holes. When approaching the origin the test particle trajectories present differences depending if the center is regular or singular. The velocities of the infalling test particle into the modified Hayward black hole are analyzed as well. As compared with the normal Hayward, in the modified Hayward black hole the particle moves faster and the surface gravity is smaller.

  9. Some BMO estimates for vector-valued multilinear singular integral ...

    Indian Academy of Sciences (India)

    R. Narasimhan (Krishtel eMaging) 1461 1996 Oct 15 13:05:22

    the multilinear operator related to some singular integral operators is obtained. The main purpose of this paper is to establish the BMO end-point estimates for some vector-valued multilinear operators related to certain singular integral operators. First, let us introduce some notations [10,16]. Throughout this paper, Q = Q(x,r).

  10. Accelerated observers and the notion of singular spacetime

    Science.gov (United States)

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

    2018-03-01

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

  11. 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)

  12. 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.

  13. 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.

  14. 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.)

  15. 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)

  16. Regularization of divergent integrals

    OpenAIRE

    Felder, Giovanni; Kazhdan, David

    2016-01-01

    We study the Hadamard finite part of divergent integrals of differential forms with singularities on submanifolds. We give formulae for the dependence of the finite part on the choice of regularization and express them in terms of a suitable local residue map. The cases where the submanifold is a complex hypersurface in a complex manifold and where it is a boundary component of a manifold with boundary, arising in string perturbation theory, are treated in more detail.

  17. Kleinian singularities and the ground ring of c=1 string theory

    International Nuclear Information System (INIS)

    Ghoshal, D.; Jatkar, D.P.; Mukhi, S.

    1993-01-01

    We investigate the nature of the ground ring of c=1 string theory at the special ADE points in the c=1 moduli space associated to discrete subgroups of SU(2). The chiral ground rings at these points are shown to define the ADE series of singular varieties introduced by Klein. The non-chiral ground rings relevant to closed-string theory are 3 real dimensional singular varieties obtained as U(1) quotients of the kleinian varieties. The unbroken symmetries of the theory at these points are the volume-preserving diffeomorphisms of these varieties. The theory of kleinian singularities has a close relation to that of complex hyperKaehler surfaces, or gravitational instantons. We speculate on the relevance of these instantons and of self-dual gravity in c=1 string theory. (orig.)

  18. 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.

  19. Discrete singular convolution method for the analysis of Mindlin plates on elastic foundations

    International Nuclear Information System (INIS)

    Civalek, Omer; Acar, Mustafa Hilmi

    2007-01-01

    The method of discrete singular convolution (DSC) is used for the bending analysis of Mindlin plates on two-parameter elastic foundations for the first time. Two different realizations of singular kernels, such as the regularized Shannon's delta (RSD) kernel and Lagrange delta sequence (LDS) kernel, are selected as singular convolution to illustrate the present algorithm. The methodology and procedures are presented and bending problems of thick plates on elastic foundations are studied for different boundary conditions. The influence of foundation parameters and shear deformation on the stress resultants and deflections of the plate have been investigated. Numerical studies are performed and the DSC results are compared well with other analytical solutions and some numerical results

  20. 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

  1. Analytic Evolution of Singular Distribution Amplitudes in QCD

    Energy Technology Data Exchange (ETDEWEB)

    Tandogan Kunkel, Asli [Old Dominion Univ., Norfolk, VA (United States)

    2014-08-01

    Distribution amplitudes (DAs) are the basic functions that contain information about the quark momentum. DAs are necessary to describe hard exclusive processes in quantum chromodynamics. We describe a method of analytic evolution of DAs that have singularities such as nonzero 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 at (constant) DA, antisymmetric at DA, and then use the method for evolution of the two-photon generalized distribution amplitude. Our approach to DA evolution has advantages over the standard method of expansion in Gegenbauer polynomials [1, 2] and over a straightforward iteration of an initial distribution with evolution kernel. Expansion in Gegenbauer polynomials requires an infinite number of terms in order to accurately reproduce functions in the vicinity of singular points. Straightforward iteration of an initial distribution produces logarithmically divergent terms at each iteration. In our method the logarithmic singularities are summed from the start, which immediately produces a continuous curve. Afterwards, in order to get precise results, only one or two iterations are needed.

  2. On the singular set of harmonic maps into DM-complexes

    CERN Document Server

    Daskalopoulos, Georgios

    2016-01-01

    The authors prove that the singular set of a harmonic map from a smooth Riemammian domain to a Riemannian DM-complex is of Hausdorff codimension at least two. They also explore monotonicity formulas and an order gap theorem for approximately harmonic maps. These regularity results have applications to rigidity problems examined in subsequent articles.

  3. 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.

  4. 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.)

  5. Correlation between topological structure and its properties in dynamic singular vector fields.

    Science.gov (United States)

    Vasilev, Vasyl; Soskin, Marat

    2016-04-20

    A new technique for establishment of topology measurements for static and dynamic singular vector fields is elaborated. It is based on precise measurement of the 3D landscape of ellipticity distribution for a checked singular optical field with C points on the tops of ellipticity hills. Vector fields possess three-component topology: areas with right-hand (RH) and left-hand (LH) ellipses, and delimiting those L lines as the singularities of handedness. The azimuth map of polarization ellipses is common for both RH and LH ellipses of vector fields and do not feel L lines. The strict rules were confirmed experimentally, which define the connection between the sign of underlying optical vortices and morphological parameters of upper-lying C points. Percolation phenomena explain their realization in-between singular vector fields and long duration of their chains of 103  s order.

  6. (2+1-dimensional regular black holes with nonlinear electrodynamics sources

    Directory of Open Access Journals (Sweden)

    Yun He

    2017-11-01

    Full Text Available On the basis of two requirements: the avoidance of the curvature singularity and the Maxwell theory as the weak field limit of the nonlinear electrodynamics, we find two restricted conditions on the metric function of (2+1-dimensional regular black hole in general relativity coupled with nonlinear electrodynamics sources. By the use of the two conditions, we obtain a general approach to construct (2+1-dimensional regular black holes. In this manner, we construct four (2+1-dimensional regular black holes as examples. We also study the thermodynamic properties of the regular black holes and verify the first law of black hole thermodynamics.

  7. New class of inhomogeneous cosmological perfect-fluid solutions without big-bang singularity

    Energy Technology Data Exchange (ETDEWEB)

    Senovilla, J.M.M. (Grupo de Fisica Teorica, Departamento de Fisica, Ingenieria y Radiologia Medica, Facultad de Ciencias, Universidad de Salamanca, 37008 Salmanaca (Spain))

    1990-05-07

    A new class of exact solutions to Einstein's field equations with a perfect-fluid source is presented. The solutions describe spatially inhomogeneous cosmological models and have a realistic equation of state {ital p}={rho}/3. The properties of the solutions are discussed. The most remarkable feature is the absence of an initial singularity, the curvature and matter invariants being regular and smooth everywhere. We also present an alternative interpretation of the solution as a globally regular cylindrically symmetric space-time.

  8. 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.

  9. 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.

  10. Investigation of relation between singular points and number of limit cycles for a rotor-AMBs system

    International Nuclear Information System (INIS)

    Li, J.; Tian, Y.; Zhang, W.

    2009-01-01

    The relation between singular points and the number of limit cycles is investigated for a rotor-active magnetic bearings system with time-varying stiffness and single-degree-of-freedom. The averaged equation of the system is a perturbed polynomial Hamiltonian system of degree 5. The dynamic characteristics of the unperturbed system are first analyzed for a certain parameter group. The number of limit cycles and their configurations of the perturbed system under eight different parametric groups are obtained and the influence of eight control conditions on the number of limit cycles is studied. The results obtained here will play an important leading role in the study of the properties of nonlinear dynamics and control of the rotor-active magnetic bearings system with time-varying stiffness.

  11. 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

  12. 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

  13. Cancellation of infrared and mass singularities in the thermal di-lepton rate

    International Nuclear Information System (INIS)

    Altherr, T.; Becherrawy, T.

    1989-03-01

    We give a rigorous proof that, at first order in α s , the thermal di-lepton rate is free of infrared and mass singularities. The calculation is performed for massive quarks in the real-time formalism with the n-dimensional regularization scheme. The cancellation is shown to occur within each topology

  14. NUMERICAL SOLUTION OF SINGULAR INVERSE NODAL PROBLEM BY USING CHEBYSHEV POLYNOMIALS

    OpenAIRE

    NEAMATY, ABDOLALI; YILMAZ, EMRAH; AKBARPOOR, SHAHRBANOO; DABBAGHIAN, ABDOLHADI

    2017-01-01

    In this study, we consider Sturm-Liouville problem in two cases: the first case having no singularity and the second case having a singularity at zero. Then, we calculate the eigenvalues and the nodal points and present the uniqueness theorem for the solution of the inverse problem by using a dense subset of the nodal points in two given cases. Also, we use Chebyshev polynomials of the first kind for calculating the approximate solution of the inverse nodal problem in these cases. Finally, we...

  15. Singularities of classical and quantum correlations at critical points of the Lipkin–Meshkov–Glick model in bipartitions and tripartitions of spins

    International Nuclear Information System (INIS)

    Zhang, Xiu-xing; Li, Fu-li

    2013-01-01

    By using the lowest order expansion in the number of spins, we study the classical correlation (CC) and quantum correlations (QCs) between two spin subgroups of the Lipkin–Meshkov–Glick (LMG) model in both binary and trinary decompositions of spins. In the case of bipartitions, we find that the CC and all the QCs are divergent in the same singular behavior at the critical point of the LMG model. In the case of tripartitions, however, the CC is still divergent but the QCs remain finite at the critical point. The present result shows that the CC is very robust but the QCs are much frangible to the environment disturbance.

  16. 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.

  17. The technological singularity and exponential medicine

    OpenAIRE

    Iraj Nabipour; Majid Assadi

    2016-01-01

    The "technological singularity" is forecasted to occur in 2045. It is a point when non-biological intelligence becomes more intelligent than humans and each generation of intelligent machines re-designs itself smarter. Beyond this point, there is a symbiosis between machines and humans. This co-existence will produce incredible impacts on medicine that its sparkles could be seen in healthcare industry and the future medicine since 2025. Ray Kurzweil, the great futurist, suggested th...

  18. Position difference regularity of corresponding R-wave peaks for maternal ECG components from different abdominal points

    International Nuclear Information System (INIS)

    Zhang Jie-Min; Liu Hong-Xing; Huang Xiao-Lin; Si Jun-Feng; Guan Qun; Tang Li-Ming; Liu Tie-Bing

    2014-01-01

    We collected 343 groups of abdominal electrocardiogram (ECG) data from 78 pregnant women and deleted the channels unable for experts to determine R-wave peaks from them; then, based on these filtered data, the statistics of position difference of corresponding R-wave peaks for different maternal ECG components from different points were studied. The resultant statistics showed the regularity that the position difference of corresponding maternal R-wave peaks between different abdominal points does not exceed the range of 30 ms. The regularity was also proved using the fECG data from MIT—BIH PhysioBank. Additionally, the paper applied the obtained regularity, the range of position differences of the corresponding maternal R-wave peaks, to accomplish the automatic detection of maternal R-wave peaks in the recorded all initial 343 groups of abdominal signals, including the ones with the largest fetal ECG components, and all 55 groups of ECG data from MIT—BIH PhysioBank, achieving the successful separation of the maternal ECGs. (interdisciplinary physics and related areas of science and technology)

  19. 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.)

  20. 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.)

  1. 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.

  2. Differential regularization and renormalization: a new method of calculation in quantum field theory

    International Nuclear Information System (INIS)

    Freedman, D.Z.; Johnson, K.; Latorre, J.I.

    1992-01-01

    Most primitively divergent Feynman diagrams are well defined in x-space but too singular at short distances for transformation to p-space. A new method of regularization is developed in which singular functions are written as derivatives of less singular functions which contain a logarithmic mass scale. The Fourier transform is then defined by formal integration by parts. The procedure is extended to graphs with divergent subgraphs. No explicit cutoff or counterterms are required, and the method automatically delivers renormalized amplitudes which satisfy Callan-Symanzik equations. These features are thoroughly explored in massless φ 4 theory through 3-loop order, and the method yields explicit functional forms for all amplitudes with less difficulty than conventional methods which use dimensional regularization in p-space. The procedure also appears to be compatible with gauge invariance and the chiral structure of the standard model. This aspect is tested in extensive 1-loop calculations which include the Ward identity in quantum electrodynamics, the chiral anomaly, and the background field algorithm in non-abelian gauge theories. (orig.)

  3. Singular formalism and admissible control of spacecraft with rotating flexible solar array

    Directory of Open Access Journals (Sweden)

    Lu Dongning

    2014-02-01

    Full Text Available This paper is concerned with the attitude control of a three-axis-stabilized spacecraft which consists of a central rigid body and a flexible sun-tracking solar array driven by a solar array drive assembly. Based on the linearization of the dynamics of the spacecraft and the modal identities about the flexible and rigid coupling matrices, the spacecraft attitude dynamics is reduced to a formally singular system with periodically varying parameters, which is quite different from a spacecraft with fixed appendages. In the framework of the singular control theory, the regularity and impulse-freeness of the singular system is analyzed and then admissible attitude controllers are designed by Lyapunov’s method. To improve the robustness against system uncertainties, an H∞ optimal control is designed by optimizing the H∞ norm of the system transfer function matrix. Comparative numerical experiments are performed to verify the theoretical results.

  4. Regularization strategies for hyperplane classifiers: application to cancer classification with gene expression data.

    Science.gov (United States)

    Andries, Erik; Hagstrom, Thomas; Atlas, Susan R; Willman, Cheryl

    2007-02-01

    Linear discrimination, from the point of view of numerical linear algebra, can be treated as solving an ill-posed system of linear equations. In order to generate a solution that is robust in the presence of noise, these problems require regularization. Here, we examine the ill-posedness involved in the linear discrimination of cancer gene expression data with respect to outcome and tumor subclasses. We show that a filter factor representation, based upon Singular Value Decomposition, yields insight into the numerical ill-posedness of the hyperplane-based separation when applied to gene expression data. We also show that this representation yields useful diagnostic tools for guiding the selection of classifier parameters, thus leading to improved performance.

  5. Lavrentiev regularization method for nonlinear ill-posed problems

    International Nuclear Information System (INIS)

    Kinh, Nguyen Van

    2002-10-01

    In this paper we shall be concerned with Lavientiev regularization method to reconstruct solutions x 0 of non ill-posed problems F(x)=y o , where instead of y 0 noisy data y δ is an element of X with absolut(y δ -y 0 ) ≤ δ are given and F:X→X is an accretive nonlinear operator from a real reflexive Banach space X into itself. In this regularization method solutions x α δ are obtained by solving the singularly perturbed nonlinear operator equation F(x)+α(x-x*)=y δ with some initial guess x*. Assuming certain conditions concerning the operator F and the smoothness of the element x*-x 0 we derive stability estimates which show that the accuracy of the regularized solutions is order optimal provided that the regularization parameter α has been chosen properly. (author)

  6. Finite-Time Robust H∞ Control for Uncertain Linear Continuous-Time Singular Systems with Exogenous Disturbances

    Directory of Open Access Journals (Sweden)

    Songlin Wo

    2018-01-01

    Full Text Available Singular systems arise in a great deal of domains of engineering and can be used to solve problems which are more difficult and more extensive than regular systems to solve. Therefore, in this paper, the definition of finite-time robust H∞ control for uncertain linear continuous-time singular systems is presented. The problem we address is to design a robust state feedback controller which can deal with the singular system with time-varying norm-bounded exogenous disturbance, such that the singular system is finite-time robust bounded (FTRB with disturbance attenuation γ. Sufficient conditions for the existence of solutions to this problem are obtained in terms of linear matrix equalities (LMIs. When these LMIs are feasible, the desired robust controller is given. A detailed solving method is proposed for the restricted linear matrix inequalities. Finally, examples are given to show the validity of the methodology.

  7. 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

  8. 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.

  9. 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

  10. Point-splitting as a regularization method for λφ4-type vertices: Abelian case

    International Nuclear Information System (INIS)

    Moura-Melo, Winder A.; Helayel Neto, J.A.

    1998-11-01

    We obtained regularized Abelian Lagrangians containing λφ 4 -type vertices by means of a suitable point-splitting procedure. The calculation is developed in details for a general Lagrangian, whose fields (gauge and matter ones) satisfy certain conditions. We illustrates our results by considering some special cases, such as the Abelian Higgs, the (ψ-barψ) 2 and the Avdeev-Chizov (real rank-2 antisymmetric tensor as matter fields) models. We also discuss some features of the obtained Lagrangian such as the regularity and non-locality of its new integrating terms. Moreover, the resolution of the Abelian case may teach us some useful technical aspects when dealing with the non-Abelian one. (author)

  11. Singularity of classical and quantum correlations at critical points of the Lipkin-Meshkov-Glick model in bipartition and tripartition of spins

    OpenAIRE

    Xiu-Xing, Zhang; Fu-Li, Li

    2012-01-01

    We study the classical correlation (CC) and quantum discord (QD) between two spin subgroups of the Lipkin-Meshkov-Glick (LMG) model in both binary and trinary decompositions of spins. In the case of bipartition, we find that the classical correlations and all the quantum correlations including the QD, the entanglement of formation (EoF) and the logarithmic negativity (LN) are divergent in the same singular behavior at the critical point of the LMG model. In the case of tripartition, however, ...

  12. The data singular and the data isotropic loci for affine cones

    NARCIS (Netherlands)

    Horobet, E.

    2015-01-01

    The generic number of critical points of the Euclidean distance function from a data point to a variety is called the Euclidean distance degree. The two special loci of the data points where the number of critical points is smaller then the ED degree are called the Euclidean Distance Data Singular

  13. 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.

  14. Thermodynamic formalism and circle homeophormisms with a break-type singularity

    CERN Document Server

    Dzhalilov, A A

    2002-01-01

    A renormalization group (RG) transformation on the space of circle homeomorphisms with break-type singularity point and with the rotation number $\\rho =\\genfrac{\\sqrt{5}-1}{2}$ (``golden mean'') has a unique periodic trajectory $\\{T_{1},T_{2}\\}$ with period two. For homeomorphisms $T$ which are $C^{1}-$conjugate to $T_{1}$ $($ or $T_{2})$ the behavior of Holder's exponents of singular invariant measure are studied. Limit distributions of entrance times are also studied.

  15. Spectral Stokes singularities of partially coherent radially polarized beams focused by a high numerical aperture objective

    International Nuclear Information System (INIS)

    Luo, Yamei; Lü, Baida

    2010-01-01

    The dynamic behavior of spectral Stokes singularities of partially coherent radially polarized beams focused by a high numerical aperture (NA) objective is studied by using the vectorial Debye diffraction theory and complex spectral Stokes fields. It is shown that there exist s 12 , s 23 , and s 31 singularities, as well as P (completely polarized) and U (unpolarized) singularities. The motion, pair creation and annihilation, and changes in the degree of polarization of s 12 , s 23 , and s 31 singularities, and the handedness reversal of s 12 singularities (C-points) may appear by varying a controlling parameter, such as the truncation parameter, NA, or spatial correlation length. The creation and annihilation occur for a pair of s 12 singularities with opposite topological charge but the same handedness, and for a pair of oppositely charged s 23 or s 31 singularities. The critical value of the truncation parameter, at which the pair annihilation takes place, increases as the semi-angle of the aperture lens (or, equivalently, NA) or spatial correlation length increases. The collision of an s 12 singularity with an L-line (s 3 = 0 contour) leads to a V-point, which is located at the intersection of contours of s 12 = 0 and s 23 = 0 (or s 31 = 0) and is unstable

  16. Preconditioners for regularized saddle point problems with an application for heterogeneous Darcy flow problems

    Czech Academy of Sciences Publication Activity Database

    Axelsson, Owe; Blaheta, Radim; Byczanski, Petr; Karátson, J.; Ahmad, B.

    2015-01-01

    Roč. 280, č. 280 (2015), s. 141-157 ISSN 0377-0427 R&D Projects: GA MŠk ED1.1.00/02.0070 Institutional support: RVO:68145535 Keywords : preconditioners * heterogeneous coefficients * regularized saddle point Inner–outer iterations * Darcy flow Subject RIV: BA - General Mathematics Impact factor: 1.328, year: 2015 http://www.sciencedirect.com/science/article/pii/S0377042714005238

  17. 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 $D(\\alpha)$.

  18. A direct link between the Lie group SU(3) and the singular ...

    Indian Academy of Sciences (India)

    complex variables. Our approach is constructive and shows in a precise sense how resolved. 351 ... describe this procedure first for the case n = 2 and n = 3, and then we state the result for the general case ... 3(È2,Ê). The singularity has been resolved by a process of 'blowing up' turning the singular point into a sphere.

  19. 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.

  20. 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].

  1. UV caps, IR modification of gravity, and recovery of 4D gravity in regularized braneworlds

    International Nuclear Information System (INIS)

    Kobayashi, Tsutomu

    2008-01-01

    In the context of six-dimensional conical braneworlds we consider a simple and explicit model that incorporates long-distance modification of gravity and regularization of codimension-2 singularities. To resolve the conical singularities we replace the codimension-2 branes with ringlike codimension-1 branes, filling in the interiors with regular caps. The six-dimensional Planck scale in the cap is assumed to be much greater than the bulk Planck scale, which gives rise to the effect analogous to brane-induced gravity. Weak gravity on the regularized brane is studied in the case of a sharp conical bulk. We show by a linear analysis that gravity at short distances is effectively described by the four-dimensional Brans-Dicke theory, while the higher dimensional nature of gravity emerges at long distances. The linear analysis breaks down at some intermediate scale, below which four-dimensional Einstein gravity is shown to be recovered thanks to the second-order effects of the brane bending.

  2. Construction of normal-regular decisions of Bessel typed special system

    Science.gov (United States)

    Tasmambetov, Zhaksylyk N.; Talipova, Meiramgul Zh.

    2017-09-01

    Studying a special system of differential equations in the separate production of the second order is solved by the degenerate hypergeometric function reducing to the Bessel functions of two variables. To construct a solution of this system near regular and irregular singularities, we use the method of Frobenius-Latysheva applying the concepts of rank and antirank. There is proved the basic theorem that establishes the existence of four linearly independent solutions of studying system type of Bessel. To prove the existence of normal-regular solutions we establish necessary conditions for the existence of such solutions. The existence and convergence of a normally regular solution are shown using the notion of rank and antirank.

  3. Rule-based learning of regular past tense in children with specific language impairment.

    Science.gov (United States)

    Smith-Lock, Karen M

    2015-01-01

    The treatment of children with specific language impairment was used as a means to investigate whether a single- or dual-mechanism theory best conceptualizes the acquisition of English past tense. The dual-mechanism theory proposes that regular English past-tense forms are produced via a rule-based process whereas past-tense forms of irregular verbs are stored in the lexicon. Single-mechanism theories propose that both regular and irregular past-tense verbs are stored in the lexicon. Five 5-year-olds with specific language impairment received treatment for regular past tense. The children were tested on regular past-tense production and third-person singular "s" twice before treatment and once after treatment, at eight-week intervals. Treatment consisted of one-hour play-based sessions, once weekly, for eight weeks. Crucially, treatment focused on different lexical items from those in the test. Each child demonstrated significant improvement on the untreated past-tense test items after treatment, but no improvement on the untreated third-person singular "s". Generalization to untreated past-tense verbs could not be attributed to a frequency effect or to phonological similarity of trained and tested items. It is argued that the results are consistent with a dual-mechanism theory of past-tense inflection.

  4. 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...

  5. Regularized tripartite continuous variable EPR-type states with Wigner functions and CHSH violations

    International Nuclear Information System (INIS)

    Jacobsen, Sol H; Jarvis, P D

    2008-01-01

    We consider tripartite entangled states for continuous variable systems of EPR type, which generalize the famous bipartite CV EPR states (eigenvectors of conjugate choices X 1 - X 2 , P 1 + P 2 , of the systems' relative position and total momentum variables). We give the regularized forms of such tripartite EPR states in second-quantized formulation, and derive their Wigner functions. This is directly compared with the established NOPA-like states from quantum optics. Whereas the multipartite entangled states of NOPA type have singular Wigner functions in the limit of large squeezing, r → ∞, or tanh r → 1 - (approaching the EPR states in the bipartite case), our regularized tripartite EPR states show singular behaviour not only in the approach to the EPR-type region (s → 1 in our notation), but also for an additional, auxiliary regime of the regulator (s→√2). While the s → 1 limit pertains to tripartite CV states with singular eigenstates of the relative coordinates and remaining squeezed in the total momentum, the (s→√2) limit yields singular eigenstates of the total momentum, but squeezed in the relative coordinates. Regarded as expectation values of displaced parity measurements, the tripartite Wigner functions provide the ingredients for generalized CHSH inequalities. Violations of the tripartite CHSH bound (B 3 ≤ 2) are established, with B 3 ≅2.09 in the canonical regime (s → 1 + ), as well as B 3 ≅2.32 in the auxiliary regime (s→√2 + )

  6. 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.

  7. Bounded Perturbation Regularization for Linear Least Squares Estimation

    KAUST Repository

    Ballal, Tarig

    2017-10-18

    This paper addresses the problem of selecting the regularization parameter for linear least-squares estimation. We propose a new technique called bounded perturbation regularization (BPR). In the proposed BPR method, a perturbation with a bounded norm is allowed into the linear transformation matrix to improve the singular-value structure. Following this, the problem is formulated as a min-max optimization problem. Next, the min-max problem is converted to an equivalent minimization problem to estimate the unknown vector quantity. The solution of the minimization problem is shown to converge to that of the ℓ2 -regularized least squares problem, with the unknown regularizer related to the norm bound of the introduced perturbation through a nonlinear constraint. A procedure is proposed that combines the constraint equation with the mean squared error (MSE) criterion to develop an approximately optimal regularization parameter selection algorithm. Both direct and indirect applications of the proposed method are considered. Comparisons with different Tikhonov regularization parameter selection methods, as well as with other relevant methods, are carried out. Numerical results demonstrate that the proposed method provides significant improvement over state-of-the-art methods.

  8. 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.

  9. Regularization of absorber or doorway states in heavy-particle collisions

    International Nuclear Information System (INIS)

    Errea, L.F.; Riera, A.; Sanchez, P.

    1994-01-01

    We present a unified theoretical basis of the recently proposed regularization method of absorber or doorway states. The theory is applicable to the close-coupling solutions of time-dependent Schroedinger equations corresponding to Hamiltonians containing singular terms and with a partial continuum spectrum. The presentation and illustration are restricted to the treatment of atomic collisions. (author)

  10. Robust Guaranteed Cost Observer Design for Singular Markovian Jump Time-Delay Systems with Generally Incomplete Transition Probability

    Directory of Open Access Journals (Sweden)

    Yanbo Li

    2014-01-01

    Full Text Available This paper is devoted to the investigation of the design of robust guaranteed cost observer for a class of linear singular Markovian jump time-delay systems with generally incomplete transition probability. In this singular model, each transition rate can be completely unknown or only its estimate value is known. Based on stability theory of stochastic differential equations and linear matrix inequality (LMI technique, we design an observer to ensure that, for all uncertainties, the resulting augmented system is regular, impulse free, and robust stochastically stable with the proposed guaranteed cost performance. Finally, a convex optimization problem with LMI constraints is formulated to design the suboptimal guaranteed cost filters for linear singular Markovian jump time-delay systems with generally incomplete transition probability.

  11. 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

  12. Regularization Techniques for Linear Least-Squares Problems

    KAUST Repository

    Suliman, Mohamed

    2016-04-01

    Linear estimation is a fundamental branch of signal processing that deals with estimating the values of parameters from a corrupted measured data. Throughout the years, several optimization criteria have been used to achieve this task. The most astonishing attempt among theses is the linear least-squares. Although this criterion enjoyed a wide popularity in many areas due to its attractive properties, it appeared to suffer from some shortcomings. Alternative optimization criteria, as a result, have been proposed. These new criteria allowed, in one way or another, the incorporation of further prior information to the desired problem. Among theses alternative criteria is the regularized least-squares (RLS). In this thesis, we propose two new algorithms to find the regularization parameter for linear least-squares problems. In the constrained perturbation regularization algorithm (COPRA) for random matrices and COPRA for linear discrete ill-posed problems, an artificial perturbation matrix with a bounded norm is forced into the model matrix. This perturbation is introduced to enhance the singular value structure of the matrix. As a result, the new modified model is expected to provide a better stabilize substantial solution when used to estimate the original signal through minimizing the worst-case residual error function. Unlike many other regularization algorithms that go in search of minimizing the estimated data error, the two new proposed algorithms are developed mainly to select the artifcial perturbation bound and the regularization parameter in a way that approximately minimizes the mean-squared error (MSE) between the original signal and its estimate under various conditions. The first proposed COPRA method is developed mainly to estimate the regularization parameter when the measurement matrix is complex Gaussian, with centered unit variance (standard), and independent and identically distributed (i.i.d.) entries. Furthermore, the second proposed COPRA

  13. Leading singularities and off-shell conformal integrals

    Energy Technology Data Exchange (ETDEWEB)

    Drummond, James; Duhr, Claude; Eden, Burkhard; Heslop, Paul; Pennington, Jeffrey; Smirnov, Vladimir A.

    2013-08-29

    The three-loop four-point function of stress-tensor multiplets in N=4 super Yang-Mills theory contains two so far unknown, off-shell, conformal integrals, in addition to the known, ladder-type integrals. In our paper we evaluate the unknown integrals, thus obtaining the three-loop correlation function analytically. The integrals have the generic structure of rational functions multiplied by (multiple) polylogarithms. We use the idea of leading singularities to obtain the rational coefficients, the symbol — with an appropriate ansatz for its structure — as a means of characterising multiple polylogarithms, and the technique of asymptotic expansion of Feynman integrals to obtain the integrals in certain limits. The limiting behaviour uniquely fixes the symbols of the integrals, which we then lift to find the corresponding polylogarithmic functions. The final formulae are numerically confirmed. Furthermore, we develop techniques that can be applied more generally, and we illustrate this by analytically evaluating one of the integrals contributing to the same four-point function at four loops. This example shows a connection between the leading singularities and the entries of the symbol.

  14. 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)

  15. Complex singularities of the critical potential in the large-N limit

    International Nuclear Information System (INIS)

    Meurice, Y.

    2003-01-01

    We show with two numerical examples that the conventional expansion in powers of the field for the critical potential of 3-dimensional O(N) models in the large-N limit does not converge for values of φ 2 larger than some critical value. This can be explained by the existence of conjugated branch points in the complex φ 2 plane. Pade approximants [L+3/L] for the critical potential apparently converge at large φ 2 . This allows high-precision calculation of the fixed point in a more suitable set of coordinates. We argue that the singularities are generic and not an artifact of the large-N limit. We show that ignoring these singularities may lead to inaccurate approximations

  16. Constrained Perturbation Regularization Approach for Signal Estimation Using Random Matrix Theory

    KAUST Repository

    Suliman, Mohamed Abdalla Elhag

    2016-10-06

    In this work, we propose a new regularization approach for linear least-squares problems with random matrices. In the proposed constrained perturbation regularization approach, an artificial perturbation matrix with a bounded norm is forced into the system model matrix. This perturbation is introduced to improve the singular-value structure of the model matrix and, hence, the solution of the estimation problem. Relying on the randomness of the model matrix, a number of deterministic equivalents from random matrix theory are applied to derive the near-optimum regularizer that minimizes the mean-squared error of the estimator. Simulation results demonstrate that the proposed approach outperforms a set of benchmark regularization methods for various estimated signal characteristics. In addition, simulations show that our approach is robust in the presence of model uncertainty.

  17. Regularization of plurisubharmonic functions with a net of good points

    OpenAIRE

    Li, Long

    2017-01-01

    The purpose of this article is to present a new regularization technique of quasi-plurisubharmoinc functions on a compact Kaehler manifold. The idea is to regularize the function on local coordinate balls first, and then glue each piece together. Therefore, all the higher order terms in the complex Hessian of this regularization vanish at the center of each coordinate ball, and all the centers build a delta-net of the manifold eventually.

  18. The initial value problem for linearized gravitational perturbations of the Schwarzschild naked singularity

    Energy Technology Data Exchange (ETDEWEB)

    Dotti, Gustavo; Gleiser, Reinaldo J [Facultad de Matematica, AstronomIa y Fisica (FaMAF), Universidad Nacional de Cordoba, Ciudad Universitaria, 5000 Cordoba (Argentina)

    2009-11-07

    The coupled equations for the scalar modes of the linearized Einstein equations around Schwarzschild's spacetime were reduced by Zerilli to a (1+1) wave equation partial deriv{sup 2}PSI{sub z} /partial derivt{sup 2} +HPSI{sub z} =0, where H= -partial deriv{sup 2} /partial derivx{sup 2} + V(x) is the Zerilli 'Hamiltonian' and x is the tortoise radial coordinate. From its definition, for smooth metric perturbations the field PSI{sub z} is singular at r{sub s} = -6M/(l - 1)(l +2), with l being the mode harmonic number. The equation PSI{sub z} obeys is also singular, since V has a second-order pole at r{sub s}. This is irrelevant to the black hole exterior stability problem, where r > 2M > 0, and r{sub s} < 0, but it introduces a non-trivial problem in the naked singular case where M < 0, then r{sub s} > 0, and the singularity appears in the relevant range of r (0 < r < infinity). We solve this problem by developing a new approach to the evolution of the even mode, based on a new gauge invariant function, PSI-circumflex, that is a regular function of the metric perturbation for any value of M. The relation of PSI-circumflex to PSI{sub z} is provided by an intertwiner operator. The spatial pieces of the (1 + 1) wave equations that PSI-circumflex and PSI{sub z} obey are related as a supersymmetric pair of quantum Hamiltonians H and H-circumflex. For M < 0,H-circumflex has a regular potential and a unique self-adjoint extension in a domain D defined by a physically motivated boundary condition at r = 0. This allows us to address the issue of evolution of gravitational perturbations in this non-globally hyperbolic background. This formulation is used to complete the proof of the linear instability of the Schwarzschild naked singularity, by showing that a previously found unstable mode belongs to a complete basis of H-circumflex in D, and thus is excitable by generic initial data. This is further illustrated by numerically solving the linearized equations for

  19. 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

  20. 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.)

  1. Quantum transitions through cosmological singularities

    Energy Technology Data Exchange (ETDEWEB)

    Bramberger, Sebastian F.; Lehners, Jean-Luc [Max Planck Institute for Gravitational Physics (Albert Einstein Institute), 14476 Potsdam-Golm (Germany); Hertog, Thomas; Vreys, Yannick, E-mail: sebastian.bramberger@aei.mpg.de, E-mail: thomas.hertog@kuleuven.be, E-mail: jlehners@aei.mpg.de, E-mail: yannick.vreys@kuleuven.be [Institute for Theoretical Physics, KU Leuven, 3001 Leuven (Belgium)

    2017-07-01

    In a quantum theory of cosmology spacetime behaves classically only in limited patches of the configuration space on which the wave function of the universe is defined. Quantum transitions can connect classical evolution in different patches. Working in the saddle point approximation and in minisuperspace we compute quantum transitions connecting inflationary histories across a de Sitter like throat or a singularity. This supplies probabilities for how an inflating universe, when evolved backwards, transitions and branches into an ensemble of histories on the opposite side of a quantum bounce. Generalising our analysis to scalar potentials with negative regions we identify saddle points describing a quantum transition between a classically contracting, crunching ekpyrotic phase and an inflationary universe.

  2. Quantum transitions through cosmological singularities

    International Nuclear Information System (INIS)

    Bramberger, Sebastian F.; Lehners, Jean-Luc; Hertog, Thomas; Vreys, Yannick

    2017-01-01

    In a quantum theory of cosmology spacetime behaves classically only in limited patches of the configuration space on which the wave function of the universe is defined. Quantum transitions can connect classical evolution in different patches. Working in the saddle point approximation and in minisuperspace we compute quantum transitions connecting inflationary histories across a de Sitter like throat or a singularity. This supplies probabilities for how an inflating universe, when evolved backwards, transitions and branches into an ensemble of histories on the opposite side of a quantum bounce. Generalising our analysis to scalar potentials with negative regions we identify saddle points describing a quantum transition between a classically contracting, crunching ekpyrotic phase and an inflationary universe.

  3. 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...

  4. A Schwarz alternating procedure for singular perturbation problems

    Energy Technology Data Exchange (ETDEWEB)

    Garbey, M. [Universit Claude Bernard Lyon, Villeurbanne (France); Kaper, H.G. [Argonne National Lab., IL (United States)

    1994-12-31

    The authors show that the Schwarz alternating procedure offers a good algorithm for the numerical solution of singular perturbation problems, provided the domain decomposition is properly designed to resolve the boundary and transition layers. They give sharp estimates for the optimal position of the domain boundaries and present convergence rates of the algorithm for various second-order singular perturbation problems. The splitting of the operator is domain-dependent, and the iterative solution of each subproblem is based on a modified asymptotic expansion of the operator. They show that this asymptotic-induced method leads to a family of efficient massively parallel algorithms and report on implementation results for a turning-point problem and a combustion problem.

  5. Symmetric periodic orbits near a heteroclinic loop formed by two singular points and their invariant manifolds of dimension 1 and 2

    International Nuclear Information System (INIS)

    Corbera, Montserrat; Llibre, Jaume; Perez-Chavela, Ernesto

    2006-01-01

    In this paper we consider vector fields in R 3 that are invariant under a suitable symmetry and that possess a 'generalized heteroclinic loop' L formed by two singular points (e + and e - ) and their invariant manifolds: one of dimension 2 (a sphere minus the points e + and e - ) and one of dimension 1 (the open diameter of the sphere having endpoints e + and e - ). In particular, we analyse the dynamics of the vector field near the heteroclinic loop L by means of a convenient Poincar? map, and we prove the existence of infinitely many symmetric periodic orbits near L. We also study two families of vector fields satisfying this dynamics. The first one is a class of quadratic polynomial vector fields in R 3 , and the second one is the charged rhomboidal four-body problem

  6. 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.

  7. On singularities of lattice varieties

    OpenAIRE

    Mukherjee, Himadri

    2013-01-01

    Toric varieties associated with distributive lattices arise as a fibre of a flat degeneration of a Schubert variety in a minuscule. The singular locus of these varieties has been studied by various authors. In this article we prove that the number of diamonds incident on a lattice point $\\a$ in a product of chain lattices is more than or equal to the codimension of the lattice. Using this we also show that the lattice varieties associated with product of chain lattices is smooth.

  8. 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)

  9. 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

  10. Singular perturbations with boundary conditions and the Casimir effect in the half space

    Science.gov (United States)

    Albeverio, S.; Cognola, G.; Spreafico, M.; Zerbini, S.

    2010-06-01

    We study the self-adjoint extensions of a class of nonmaximal multiplication operators with boundary conditions. We show that these extensions correspond to singular rank 1 perturbations (in the sense of Albeverio and Kurasov [Singular Perturbations of Differential Operaters (Cambridge University Press, Cambridge, 2000)]) of the Laplace operator, namely, the formal Laplacian with a singular delta potential, on the half space. This construction is the appropriate setting to describe the Casimir effect related to a massless scalar field in the flat space-time with an infinite conducting plate and in the presence of a pointlike "impurity." We use the relative zeta determinant (as defined in the works of Müller ["Relative zeta functions, relative determinants and scattering theory," Commun. Math. Phys. 192, 309 (1998)] and Spreafico and Zerbini ["Finite temperature quantum field theory on noncompact domains and application to delta interactions," Rep. Math. Phys. 63, 163 (2009)]) in order to regularize the partition function of this model. We study the analytic extension of the associated relative zeta function, and we present explicit results for the partition function and for the Casimir force.

  11. Can static regular black holes form from gravitational collapse?

    International Nuclear Information System (INIS)

    Zhang, Yiyang; Zhu, Yiwei; Modesto, Leonardo; Bambi, Cosimo

    2015-01-01

    Starting from the Oppenheimer-Snyder model, we know how in classical general relativity the gravitational collapse of matter forms a black hole with a central spacetime singularity. It is widely believed that the singularity must be removed by quantum-gravity effects. Some static quantum-inspired singularity-free black hole solutions have been proposed in the literature, but when one considers simple examples of gravitational collapse the classical singularity is replaced by a bounce, after which the collapsing matter expands for ever. We may expect three possible explanations: (i) the static regular black hole solutions are not physical, in the sense that they cannot be realized in Nature, (ii) the final product of the collapse is not unique, but it depends on the initial conditions, or (iii) boundary effects play an important role and our simple models miss important physics. In the latter case, after proper adjustment, the bouncing solution would approach the static one. We argue that the ''correct answer'' may be related to the appearance of a ghost state in de Sitter spacetimes with super Planckian mass. Our black holes have indeed a de Sitter core and the ghost would make these configurations unstable. Therefore we believe that these black hole static solutions represent the transient phase of a gravitational collapse but never survive as asymptotic states. (orig.)

  12. Algorithms for singularities and real structures of weak Del Pezzo surfaces

    KAUST Repository

    Lubbes, Niels

    2014-08-01

    In this paper, we consider the classification of singularities [P. Du Val, On isolated singularities of surfaces which do not affect the conditions of adjunction. I, II, III, Proc. Camb. Philos. Soc. 30 (1934) 453-491] and real structures [C. T. C. Wall, Real forms of smooth del Pezzo surfaces, J. Reine Angew. Math. 1987(375/376) (1987) 47-66, ISSN 0075-4102] of weak Del Pezzo surfaces from an algorithmic point of view. It is well-known that the singularities of weak Del Pezzo surfaces correspond to root subsystems. We present an algorithm which computes the classification of these root subsystems. We represent equivalence classes of root subsystems by unique labels. These labels allow us to construct examples of weak Del Pezzo surfaces with the corresponding singularity configuration. Equivalence classes of real structures of weak Del Pezzo surfaces are also represented by root subsystems. We present an algorithm which computes the classification of real structures. This leads to an alternative proof of the known classification for Del Pezzo surfaces and extends this classification to singular weak Del Pezzo surfaces. As an application we classify families of real conics on cyclides. © World Scientific Publishing Company.

  13. 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.

  14. Class of regular bouncing cosmologies

    Science.gov (United States)

    Vasilić, Milovan

    2017-06-01

    In this paper, I construct a class of everywhere regular geometric sigma models that possess bouncing solutions. Precisely, I show that every bouncing metric can be made a solution of such a model. My previous attempt to do so by employing one scalar field has failed due to the appearance of harmful singularities near the bounce. In this work, I use four scalar fields to construct a class of geometric sigma models which are free of singularities. The models within the class are parametrized by their background geometries. I prove that, whatever background is chosen, the dynamics of its small perturbations is classically stable on the whole time axis. Contrary to what one expects from the structure of the initial Lagrangian, the physics of background fluctuations is found to carry two tensor, two vector, and two scalar degrees of freedom. The graviton mass, which naturally appears in these models, is shown to be several orders of magnitude smaller than its experimental bound. I provide three simple examples to demonstrate how this is done in practice. In particular, I show that graviton mass can be made arbitrarily small.

  15. Identifying secondary series for stepwise common singular spectrum ...

    African Journals Online (AJOL)

    Abstract. Common singular spectrum analysis is a technique which can be used to forecast a pri- mary time series by using the information from a secondary series. Not all secondary series, however, provide useful information. A first contribution in this paper is to point out the properties which a secondary series should ...

  16. Regularization scheme dependence of virtual corrections to DY and DIS

    International Nuclear Information System (INIS)

    Khalafi, F.; Landshoff, P.V.

    1981-01-01

    One loop virtual corrections to the quark photon vertex are calculated under various assumptions and their sensitivity to the manner in which infra-red and mass singularities are regularized is studied. A method based on the use of Mellin-transforms in the Feynman parametric space is developed and shown to be convenient in calculating virtual diagrams beyond the leading logarithm in perturbative QCD. (orig.)

  17. Image deblurring using a perturbation-basec regularization approach

    KAUST Repository

    Alanazi, Abdulrahman

    2017-11-02

    The image restoration problem deals with images in which information has been degraded by blur or noise. In this work, we present a new method for image deblurring by solving a regularized linear least-squares problem. In the proposed method, a synthetic perturbation matrix with a bounded norm is forced into the discrete ill-conditioned model matrix. This perturbation is added to enhance the singular-value structure of the matrix and hence to provide an improved solution. A method is proposed to find a near-optimal value of the regularization parameter for the proposed approach. To reduce the computational complexity, we present a technique based on the bootstrapping method to estimate the regularization parameter for both low and high-resolution images. Experimental results on the image deblurring problem are presented. Comparisons are made with three benchmark methods and the results demonstrate that the proposed method clearly outperforms the other methods in terms of both the output PSNR and SSIM values.

  18. Image deblurring using a perturbation-basec regularization approach

    KAUST Repository

    Alanazi, Abdulrahman; Ballal, Tarig; Masood, Mudassir; Al-Naffouri, Tareq Y.

    2017-01-01

    The image restoration problem deals with images in which information has been degraded by blur or noise. In this work, we present a new method for image deblurring by solving a regularized linear least-squares problem. In the proposed method, a synthetic perturbation matrix with a bounded norm is forced into the discrete ill-conditioned model matrix. This perturbation is added to enhance the singular-value structure of the matrix and hence to provide an improved solution. A method is proposed to find a near-optimal value of the regularization parameter for the proposed approach. To reduce the computational complexity, we present a technique based on the bootstrapping method to estimate the regularization parameter for both low and high-resolution images. Experimental results on the image deblurring problem are presented. Comparisons are made with three benchmark methods and the results demonstrate that the proposed method clearly outperforms the other methods in terms of both the output PSNR and SSIM values.

  19. 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

  20. 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.

  1. Scaled lattice fermion fields, stability bounds, and regularity

    Science.gov (United States)

    O'Carroll, Michael; Faria da Veiga, Paulo A.

    2018-02-01

    We consider locally gauge-invariant lattice quantum field theory models with locally scaled Wilson-Fermi fields in d = 1, 2, 3, 4 spacetime dimensions. The use of scaled fermions preserves Osterwalder-Seiler positivity and the spectral content of the models (the decay rates of correlations are unchanged in the infinite lattice). In addition, it also results in less singular, more regular behavior in the continuum limit. Precisely, we treat general fermionic gauge and purely fermionic lattice models in an imaginary-time functional integral formulation. Starting with a hypercubic finite lattice Λ ⊂(aZ ) d, a ∈ (0, 1], and considering the partition function of non-Abelian and Abelian gauge models (the free fermion case is included) neglecting the pure gauge interactions, we obtain stability bounds uniformly in the lattice spacing a ∈ (0, 1]. These bounds imply, at least in the subsequential sense, the existence of the thermodynamic (Λ ↗ (aZ ) d) and the continuum (a ↘ 0) limits. Specializing to the U(1) gauge group, the known non-intersecting loop expansion for the d = 2 partition function is extended to d = 3 and the thermodynamic limit of the free energy is shown to exist with a bound independent of a ∈ (0, 1]. In the case of scaled free Fermi fields (corresponding to a trivial gauge group with only the identity element), spectral representations are obtained for the partition function, free energy, and correlations. The thermodynamic and continuum limits of the free fermion free energy are shown to exist. The thermodynamic limit of n-point correlations also exist with bounds independent of the point locations and a ∈ (0, 1], and with no n! dependence. Also, a time-zero Hilbert-Fock space is constructed, as well as time-zero, spatially pointwise scaled fermion creation operators which are shown to be norm bounded uniformly in a ∈ (0, 1]. The use of our scaled fields since the beginning allows us to extract and isolate the singularities of the free

  2. 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

  3. 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

  4. Bianchi I cosmology in the presence of a causally regularized viscous fluid

    Energy Technology Data Exchange (ETDEWEB)

    Montani, Giovanni [ENEA, FSN-FUSPHY-TSM, R.C. Frascati, Frascati (Italy); Universita degli Studi di Roma ' ' La Sapienza' ' , Dipartimento di Fisica, Rome (Italy); Venanzi, Marta [Universita degli Studi di Roma ' ' La Sapienza' ' , Dipartimento di Fisica, Rome (Italy); University of Southampton, Department of Physics and Astronomy, Southampton (United Kingdom)

    2017-07-15

    We analyze the dynamics of a Bianchi I cosmology in the presence of a viscous fluid, causally regularized according to the Lichnerowicz approach. We show how the effect induced by shear viscosity is still able to produce a matter creation phenomenon, meaning that also in the regularized theory we address, the Universe is emerging from a singularity with a vanishing energy density value. We discuss the structure of the singularity in the isotropic limit, when bulk viscosity is the only retained contribution. We see that, as far as viscosity is not a dominant effect, the dynamics of the isotropic Universe possesses the usual non-viscous power-law behaviour but in correspondence to an effective equation of state, depending on the bulk viscosity coefficient. Finally, we show that, in the limit of a strong non-thermodynamical equilibrium of the Universe mimicked by a dominant contribution of the effective viscous pressure, a power-law inflation behaviour of the Universe appears, the cosmological horizons are removed and a significant amount of entropy is produced. (orig.)

  5. Fuzzy Stochastic Optimal Guaranteed Cost Control of Bio-Economic Singular Markovian Jump Systems.

    Science.gov (United States)

    Li, Li; Zhang, Qingling; Zhu, Baoyan

    2015-11-01

    This paper establishes a bio-economic singular Markovian jump model by considering the price of the commodity as a Markov chain. The controller is designed for this system such that its biomass achieves the specified range with the least cost in a finite-time. Firstly, this system is described by Takagi-Sugeno fuzzy model. Secondly, a new design method of fuzzy state-feedback controllers is presented to ensure not only the regularity, nonimpulse, and stochastic singular finite-time boundedness of this kind of systems, but also an upper bound achieved for the cost function in the form of strict linear matrix inequalities. Finally, two examples including a practical example of eel seedling breeding are given to illustrate the merit and usability of the approach proposed in this paper.

  6. Stochastic analytic regularization

    International Nuclear Information System (INIS)

    Alfaro, J.

    1984-07-01

    Stochastic regularization is reexamined, pointing out a restriction on its use due to a new type of divergence which is not present in the unregulated theory. Furthermore, we introduce a new form of stochastic regularization which permits the use of a minimal subtraction scheme to define the renormalized Green functions. (author)

  7. Plane waves with weak singularities

    International Nuclear Information System (INIS)

    David, Justin R.

    2003-03-01

    We study a class of time dependent solutions of the vacuum Einstein equations which are plane waves with weak null singularities. This singularity is weak in the sense that though the tidal forces diverge at the singularity, the rate of divergence is such that the distortion suffered by a freely falling observer remains finite. Among such weak singular plane waves there is a sub-class which does not exhibit large back reaction in the presence of test scalar probes. String propagation in these backgrounds is smooth and there is a natural way to continue the metric beyond the singularity. This continued metric admits string propagation without the string becoming infinitely excited. We construct a one parameter family of smooth metrics which are at a finite distance in the space of metrics from the extended metric and a well defined operator in the string sigma model which resolves the singularity. (author)

  8. Hindmarsh–Rose model: Close and far to the singular limit

    Energy Technology Data Exchange (ETDEWEB)

    Barrio, Roberto, E-mail: rbarrio@unizar.es [Departamento de Matemática Aplicada and IUMA, University of Zaragoza, E-50009 Zaragoza (Spain); Computational Dynamics group, University of Zaragoza, E-50009 Zaragoza (Spain); Ibáñez, Santiago, E-mail: mesa@uniovi.es [Departamento de Matemáticas, University of Oviedo, E-33007 Oviedo (Spain); Pérez, Lucía, E-mail: lpcuadrado@gmail.com [Departamento de Matemáticas, University of Oviedo, E-33007 Oviedo (Spain)

    2017-02-12

    Dynamics arising in the Hindmarsh–Rose model are considered from a novel perspective. We study qualitative changes that occur as the time scale of the slow variable increases taking the system far from the slow-fast scenario. We see how the structure of spike-adding still persists far from the singular case but the geometry of the bifurcations changes notably. Particular attention is paid to changes in the shape of the homoclinic bifurcation curves and the disappearance of Inclination-Flip codimension-two points. These transformations seem to be linked to the way in which the spike-adding takes place, the changing from fold/hom to fold/Hopf bursting behavior and also with the way in which the chaotic regions evolve as the time scale of the slow variable increases. - Highlights: • Dynamics arising in the Hindmarsh–Rose model are considered close and far to the singular limit. • The structure of spike-adding still persists far from the singular case but the geometry of the bifurcations changes notably. • The homoclinic bifurcation curves change their shape and some codimension-two points (Inclination-Flip) disappear. • The changes in the homoclinic curves are correlated with adjustments in the spike-adding process and in the chaotic regions.

  9. 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.)

  10. Efficiently enclosing the compact binary parameter space by singular-value decomposition

    International Nuclear Information System (INIS)

    Cannon, Kipp; Hanna, Chad; Keppel, Drew

    2011-01-01

    Gravitational-wave searches for the merger of compact binaries use matched filtering as the method of detecting signals and estimating parameters. Such searches construct a fine mesh of filters covering a signal parameter space at high density. Previously it has been shown that singular-value decomposition can reduce the effective number of filters required to search the data. Here we study how the basis provided by the singular-value decomposition changes dimension as a function of template-bank density. We will demonstrate that it is sufficient to use the basis provided by the singular-value decomposition of a low-density bank to accurately reconstruct arbitrary points within the boundaries of the template bank. Since this technique is purely numerical, it may have applications to interpolating the space of numerical relativity waveforms.

  11. 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.

  12. 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.

  13. 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.

  14. 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

  15. Regular black holes: electrically charged solutions, Reissner-Nordstroem outside a De Sitter core

    Energy Technology Data Exchange (ETDEWEB)

    Lemos, Jose P.S. [Universidade Tecnica de Lisboa (CENTRA/IST/UTL) (Portugal). Instituto Superior Tecnico. Centro Multidisciplinar de Astrofisica; Zanchin, Vilson T. [Universidade Federal do ABC (UFABC), Santo Andre, SP (Brazil). Centro de Ciencias Naturais e Humanas

    2011-07-01

    Full text: The understanding of the inside of a black hole is of crucial importance in order to have the correct picture of a black hole as a whole. The singularities that lurk inside of the usual black hole solutions are things to avoid. Their substitution by a regular part is of great interest, the process generating regular black holes. In the present work regular black hole solutions are found within general relativity coupled to Maxwell's electromagnetism and charged matter. We show that there are objects which correspond to regular charged black holes, whose interior region is de Sitter, whose exterior region is Reissner-Nordstroem, and the boundary between both regions is made of an electrically charged spherically symmetric coat. There are several solutions: the regular nonextremal black holes with a null matter boundary, the regular nonextremal black holes with a timelike matter boundary, the regular extremal black holes with a timelike matter boundary, and the regular overcharged stars with a timelike matter boundary. The main physical and geometrical properties of such charged regular solutions are analyzed. (author)

  16. 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.

  17. Online co-regularized algorithms

    NARCIS (Netherlands)

    Ruijter, T. de; Tsivtsivadze, E.; Heskes, T.

    2012-01-01

    We propose an online co-regularized learning algorithm for classification and regression tasks. We demonstrate that by sequentially co-regularizing prediction functions on unlabeled data points, our algorithm provides improved performance in comparison to supervised methods on several UCI benchmarks

  18. Multidimensional singular integrals and integral equations

    CERN Document Server

    Mikhlin, Solomon Grigorievich; Stark, M; Ulam, S

    1965-01-01

    Multidimensional Singular Integrals and Integral Equations presents the results of the theory of multidimensional singular integrals and of equations containing such integrals. Emphasis is on singular integrals taken over Euclidean space or in the closed manifold of Liapounov and equations containing such integrals. This volume is comprised of eight chapters and begins with an overview of some theorems on linear equations in Banach spaces, followed by a discussion on the simplest properties of multidimensional singular integrals. Subsequent chapters deal with compounding of singular integrals

  19. Homogeneous Solutions of Stationary Navier-Stokes Equations with Isolated Singularities on the Unit Sphere. I. One Singularity

    Science.gov (United States)

    Li, Li; Li, YanYan; Yan, Xukai

    2018-03-01

    We classify all (-1)-homogeneous axisymmetric no-swirl solutions of incompressible stationary Navier-Stokes equations in three dimension which are smooth on the unit sphere minus the south pole, parameterize them as a two dimensional surface with boundary, and analyze their pressure profiles near the north pole. Then we prove that there is a curve of (-1)-homogeneous axisymmetric solutions with nonzero swirl, having the same smoothness property, emanating from every point of the interior and one part of the boundary of the solution surface. Moreover we prove that there is no such curve of solutions for any point on the other part of the boundary. We also establish asymptotic expansions for every (-1)-homogeneous axisymmetric solutions in a neighborhood of the singular point on the unit sphere.

  20. 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.

  1. 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.

  2. Optimal Tikhonov Regularization in Finite-Frequency Tomography

    Science.gov (United States)

    Fang, Y.; Yao, Z.; Zhou, Y.

    2017-12-01

    The last decade has witnessed a progressive transition in seismic tomography from ray theory to finite-frequency theory which overcomes the resolution limit of the high-frequency approximation in ray theory. In addition to approximations in wave propagation physics, a main difference between ray-theoretical tomography and finite-frequency tomography is the sparseness of the associated sensitivity matrix. It is well known that seismic tomographic problems are ill-posed and regularizations such as damping and smoothing are often applied to analyze the tradeoff between data misfit and model uncertainty. The regularizations depend on the structure of the matrix as well as noise level of the data. Cross-validation has been used to constrain data uncertainties in body-wave finite-frequency inversions when measurements at multiple frequencies are available to invert for a common structure. In this study, we explore an optimal Tikhonov regularization in surface-wave phase-velocity tomography based on minimization of an empirical Bayes risk function using theoretical training datasets. We exploit the structure of the sensitivity matrix in the framework of singular value decomposition (SVD) which also allows for the calculation of complete resolution matrix. We compare the optimal Tikhonov regularization in finite-frequency tomography with traditional tradeo-off analysis using surface wave dispersion measurements from global as well as regional studies.

  3. 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

  4. Imaging a non-singular rotating black hole at the center of the Galaxy

    Science.gov (United States)

    Lamy, F.; Gourgoulhon, E.; Paumard, T.; Vincent, F. H.

    2018-06-01

    We show that the rotating generalization of Hayward’s non-singular black hole previously studied in the literature is geodesically incomplete, and that its straightforward extension leads to a singular spacetime. We present another extension, which is devoid of any curvature singularity. The obtained metric depends on three parameters and, depending on their values, yields an event horizon or not. These two regimes, named respectively regular rotating Hayward black hole and naked rotating wormhole, are studied both numerically and analytically. In preparation for the upcoming results of the Event Horizon Telescope, the images of an accretion torus around Sgr A*, the supermassive object at the center of the Galaxy, are computed. These images contain, even in the absence of a horizon, a central faint region which bears a resemblance to the shadow of Kerr black holes and emphasizes the difficulty of claiming the existence of an event horizon from the analysis of strong-field images. The frequencies of the co- and contra-rotating orbits at the innermost stable circular orbit (ISCO) in this geometry are also computed, in the hope that quasi-periodic oscillations may permit to compare this model with Kerr’s black hole on observational grounds.

  5. 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

  6. Singularities of n-fold integrals of the Ising class and the theory of elliptic curves

    International Nuclear Information System (INIS)

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

    2007-01-01

    We introduce some multiple integrals that are expected to have the same singularities as the singularities of the n-particle contributions χ (n) to the susceptibility of the square lattice Ising model. We find the Fuchsian linear differential equation satisfied by these multiple integrals for n = 1, 2, 3, 4 and only modulo some primes for n = 5 and 6, thus providing a large set of (possible) new singularities of χ (n) . We discuss the singularity structure for these multiple integrals by solving the Landau conditions. We find that the singularities of the associated ODEs identify (up to n = 6) with the leading pinch Landau singularities. The second remarkable obtained feature is that the singularities of the ODEs associated with the multiple integrals reduce to the singularities of the ODEs associated with a finite number of one-dimensional integrals. Among the singularities found, we underline the fact that the quadratic polynomial condition 1 + 3w + 4w 2 = 0, that occurs in the linear differential equation of χ (3) , actually corresponds to a remarkable property of selected elliptic curves, namely the occurrence of complex multiplication. The interpretation of complex multiplication for elliptic curves as complex fixed points of the selected generators of the renormalization group, namely isogenies of elliptic curves, is sketched. Most of the other singularities occurring in our multiple integrals are not related to complex multiplication situations, suggesting an interpretation in terms of (motivic) mathematical structures beyond the theory of elliptic curves

  7. An Existence Principle for Nonlocal Difference Boundary Value Problems with φ-Laplacian and Its Application to Singular Problems

    Directory of Open Access Journals (Sweden)

    Svatoslav Stanêk

    2008-03-01

    Full Text Available The paper presents an existence principle for solving a large class of nonlocal regular discrete boundary value problems with the φ-Laplacian. Applications of the existence principle to singular discrete problems are given.

  8. 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.

  9. 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.

  10. The Singularity May Never Be Near

    OpenAIRE

    Walsh, Toby

    2017-01-01

    There is both much optimisim and pessimism around artificial intelligence (AI) today. The optimists are investing millions of dollars, and even in some cases billions of dollars into AI. The pessimists, on the other hand, predict that AI will end many things: jobs, warfare, and even the human race. Both the optimists and the pessimists often appeal to the idea of a technological singularity, a point in time where machine intelligence starts to run away, and a new, more in- telligent “species”...

  11. 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)].

  12. Numerical solution of singularity-perturbed two-point boundary-value problems

    International Nuclear Information System (INIS)

    Masenge, R.W.P.

    1993-07-01

    Physical processes which involve transportation of slowly diffusing substances in a fast-flowing medium are mathematically modelled by so-called singularly-perturbed second order convection diffusion differential equations in which the convective first order terms dominate over the diffusive second order terms. In general, analytical solutions of such equations are characterized by having sharp solution fronts in some sections of the interior and/or the boundary of the domain of solution. The presence of these (usually very narrow) layer regions in the solution domain makes the task of globally approximating such solutions by standard numerical techniques very difficult. In this expository paper we use a simple one-dimensional prototype problem as a vehicle for analysing the nature of the numerical approximation difficulties involved. In the sequel we present, without detailed derivation, two practical numerical schemes which succeed in varying degrees in numerically resolving the layer of the solution to the prototype problem. (author). 3 refs, 1 fig., 1 tab

  13. Singular perturbations of empty Robertson-Walker cosmologies

    International Nuclear Information System (INIS)

    Newman, R.P.A.C.

    1979-02-01

    An investigation is presented which concerns a class of cosmological models defined by McVittie (1931): the universe is envisaged as a set of galaxies, idealised as point particles, which provide singular perturbations of Robertson-Walker cosmologies. The perturbations are considered only to first order in the gravitational coupling constant (8πG)/c 2 . Attention will only be given to such perturbations of empty Robertson-Walker cosmologies. Chapter 1 summarises the observational support for the type of model employed and for the smallness of the quantities to be used as perturbation coefficients. Chapter 2 provides the prerequisite analysis of Robertson-Walker cosmologies. Perturbations of empty Robertson-Walker cosmologies of non-vanishing cosmical constant are considered in general in Chapter 3. The structure of McVittie's singularly perturbed Robertson-Walker cosmologies are considered in detail in Chapter 4. The remaining chapters seek to investigate them further by way of their optical properties. Chapter 5 provides the necessary theory of geometric optics with particular regard to the intensity and distortion of a beam of light, and Chapter 6 applies this theory to the McVittie cosmologies. Chapter 7 sees the definition of an averaging procedure which leads to expressions for the intensity and distortion of a typical beam of light from a point source. (author)

  14. 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.

  15. 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.

  16. Hybrid direct and iterative solvers for h refined grids with singularities

    KAUST Repository

    Paszyński, Maciej R.; Paszyńska, Anna; Dalcin, Lisandro; Calo, Victor M.

    2015-01-01

    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

  17. Regular black holes in Einstein-Gauss-Bonnet gravity

    Science.gov (United States)

    Ghosh, Sushant G.; Singh, Dharm Veer; Maharaj, Sunil D.

    2018-05-01

    Einstein-Gauss-Bonnet theory, a natural generalization of general relativity to a higher dimension, admits a static spherically symmetric black hole which was obtained by Boulware and Deser. This black hole is similar to its general relativity counterpart with a curvature singularity at r =0 . We present an exact 5D regular black hole metric, with parameter (k >0 ), that interpolates between the Boulware-Deser black hole (k =0 ) and the Wiltshire charged black hole (r ≫k ). Owing to the appearance of the exponential correction factor (e-k /r2), responsible for regularizing the metric, the thermodynamical quantities are modified, and it is demonstrated that the Hawking-Page phase transition is achievable. The heat capacity diverges at a critical radius r =rC, where incidentally the temperature is maximum. Thus, we have a regular black hole with Cauchy and event horizons, and evaporation leads to a thermodynamically stable double-horizon black hole remnant with vanishing temperature. The entropy does not satisfy the usual exact horizon area result of general relativity.

  18. Bardeen regular black hole with an electric source

    Science.gov (United States)

    Rodrigues, Manuel E.; Silva, Marcos V. de S.

    2018-06-01

    If some energy conditions on the stress-energy tensor are violated, is possible construct regular black holes in General Relativity and in alternative theories of gravity. This type of solution has horizons but does not present singularities. The first regular black hole was presented by Bardeen and can be obtained from Einstein equations in the presence of an electromagnetic field. E. Ayon-Beato and A. Garcia reinterpreted the Bardeen metric as a magnetic solution of General Relativity coupled to a nonlinear electrodynamics. In this work, we show that the Bardeen model may also be interpreted as a solution of Einstein equations in the presence of an electric source, whose electric field does not behave as a Coulomb field. We analyzed the asymptotic forms of the Lagrangian for the electric case and also analyzed the energy conditions.

  19. Singularities of Type-Q ABS Equations

    Directory of Open Access Journals (Sweden)

    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.

  20. 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.

  1. Symmetry generators in singular theories

    International Nuclear Information System (INIS)

    Lavrov, P.M.; Tyutin, I.V.

    1989-01-01

    It is proved that in the singular nondegenerate theories any symmetry of the lagrangian under non-point transformations of lagrangian variables with the open (in the general case) algebra in the hamiltonian approach generates corresponding transformations of canonical variables the generator of which is the Noether charge with respect to the Dirac brackets. On the surface of all constraints these transformations leave the hamiltonian invariant and the algebra of the Noether charges is closed. As a consequence it is shown that the nilpotent BRST charge operator always exists in gauge theories of the general form (if possible anomalies are not taken into account)

  2. Topological dynamics of optical singularities in speckle-fields induced by photorefractive scattering in a LiNbO3 : Fe crystal

    International Nuclear Information System (INIS)

    Vasil'ev, Vasilii I; Soskin, M S

    2013-01-01

    A natural singular dynamics of elliptically polarised speckle-fields induced by the 'optical damage' effect in a photorefractive crystal of lithium niobate by a passing beam of a helium — neon laser is studied by the developed methods of singular optics. For the polarisation singularities (C points), a new class of chain reactions, namely, singular chain reactions are discovered and studied. It is shown that they obey the topological charge and sum Poincare index conservation laws. In addition, they exist for all the time of crystal irradiation. They consist of a series of interlocking chains, where singularity pairs arising in a chain annihilate with singularities from neighbouring independently created chains. Less often singular 'loop' reactions are observed where arising pairs of singularities annihilate after reversible transformations in within the boundaries of a single speckle. The type of a singular reaction is determined by a topology and dynamics of the speckles, in which the reactions are developing. (laser optics 2012)

  3. Regularity of optimal transport maps on multiple products of spheres

    OpenAIRE

    Figalli, Alessio; Kim, Young-Heon; McCann, Robert J.

    2010-01-01

    This article addresses regularity of optimal transport maps for cost="squared distance" on Riemannian manifolds that are products of arbitrarily many round spheres with arbitrary sizes and dimensions. Such manifolds are known to be non-negatively cross-curved [KM2]. Under boundedness and non-vanishing assumptions on the transfered source and target densities we show that optimal maps stay away from the cut-locus (where the cost exhibits singularity), and obtain injectivity and continuity of o...

  4. 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.

  5. Algorithms for singularities and real structures of weak Del Pezzo surfaces

    KAUST Repository

    Lubbes, Niels

    2014-01-01

    . Wall, Real forms of smooth del Pezzo surfaces, J. Reine Angew. Math. 1987(375/376) (1987) 47-66, ISSN 0075-4102] of weak Del Pezzo surfaces from an algorithmic point of view. It is well-known that the singularities of weak Del Pezzo surfaces correspond

  6. The Semantics of Plurals: A Defense of Singularism

    Science.gov (United States)

    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…

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

    Directory of Open Access Journals (Sweden)

    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.

  8. Infrared singularities of scattering amplitudes in perturbative QCD

    Energy Technology Data Exchange (ETDEWEB)

    Becher, Thomas [Fermi National Accelerator Laboratory (FNAL), Batavia, IL (United States); Neubert, Matthias [Johannes Gutenberg-Universitaet Mainz, Mainz (Germany)

    2013-11-01

    An exact formula is derived for the infrared singularities of dimensionally regularized scattering amplitudes in massless QCD with an arbitrary number of legs, valid at any number of loops. It is based on the conjecture that the anomalous-dimension matrix of n-jet operators in soft-collinear effective theory contains only a single non-trivial color structure, whose coefficient is the cusp anomalous dimension of Wilson loops with light-like segments. Its color-diagonal part is characterized by two anomalous dimensions, which are extracted to three-loop order from known perturbative results for the quark and gluon form factors. This allows us to predict the three-loop coefficients of all 1/epsilon^k poles for an arbitrary n-parton scattering amplitudes, generalizing existing two-loop results.

  9. 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.)

  10. Multiple positive solutions of nonlinear singular m-point boundary value problem for second-order dynamic equations with sign changing coefficients on time scales

    Directory of Open Access Journals (Sweden)

    Fuyi Xu

    2010-04-01

    \\end{array}\\right.$$ where $1\\leq k\\leq s\\leq m-2, a_i, b_i\\in(0,+\\infty$ with $0<\\sum_{i=1}^{k}b_{i}-\\sum_{i=k+1}^{s}b_{i}<1, 0<\\sum_{i=1}^{m-2}a_{i}<1, 0<\\xi_1<\\xi_2<\\cdots<\\xi_{m-2}<\\rho(T$, $f\\in C( [0,+\\infty,[0,+\\infty$, $a(t$ may be singular at $t=0$. We show that there exist two positive solutions by using two different fixed point theorems respectively. As an application, some examples are included to illustrate the main results. In particular, our criteria extend and improve some known results.

  11. Singularity theory and N = 2 superconformal field theories

    International Nuclear Information System (INIS)

    Warner, N.P.

    1989-01-01

    The N = 2 superconformal field theories that appear at the fixed points of the renormalization group flows of Landau-Ginsburg models are discussed. Some of the techniques of singularity theory are employed to deduce properties of these superconformal theories. These ideas are then used to deduce the relationship between Calabi-Yau compactifications and tensored discrete series models. The chiral rings of general N = 2 superconformal theories are also described. 14 refs

  12. Perturbation-Based Regularization for Signal Estimation in Linear Discrete Ill-posed Problems

    KAUST Repository

    Suliman, Mohamed Abdalla Elhag; Ballal, Tarig; Al-Naffouri, Tareq Y.

    2016-01-01

    Estimating the values of unknown parameters from corrupted measured data faces a lot of challenges in ill-posed problems. In such problems, many fundamental estimation methods fail to provide a meaningful stabilized solution. In this work, we propose a new regularization approach and a new regularization parameter selection approach for linear least-squares discrete ill-posed problems. The proposed approach is based on enhancing the singular-value structure of the ill-posed model matrix to acquire a better solution. Unlike many other regularization algorithms that seek to minimize the estimated data error, the proposed approach is developed to minimize the mean-squared error of the estimator which is the objective in many typical estimation scenarios. The performance of the proposed approach is demonstrated by applying it to a large set of real-world discrete ill-posed problems. Simulation results demonstrate that the proposed approach outperforms a set of benchmark regularization methods in most cases. In addition, the approach also enjoys the lowest runtime and offers the highest level of robustness amongst all the tested benchmark regularization methods.

  13. Perturbation-Based Regularization for Signal Estimation in Linear Discrete Ill-posed Problems

    KAUST Repository

    Suliman, Mohamed Abdalla Elhag

    2016-11-29

    Estimating the values of unknown parameters from corrupted measured data faces a lot of challenges in ill-posed problems. In such problems, many fundamental estimation methods fail to provide a meaningful stabilized solution. In this work, we propose a new regularization approach and a new regularization parameter selection approach for linear least-squares discrete ill-posed problems. The proposed approach is based on enhancing the singular-value structure of the ill-posed model matrix to acquire a better solution. Unlike many other regularization algorithms that seek to minimize the estimated data error, the proposed approach is developed to minimize the mean-squared error of the estimator which is the objective in many typical estimation scenarios. The performance of the proposed approach is demonstrated by applying it to a large set of real-world discrete ill-posed problems. Simulation results demonstrate that the proposed approach outperforms a set of benchmark regularization methods in most cases. In addition, the approach also enjoys the lowest runtime and offers the highest level of robustness amongst all the tested benchmark regularization methods.

  14. The Motion of Point Particles in Curved Spacetime

    Directory of Open Access Journals (Sweden)

    Eric Poisson

    2011-09-01

    Full Text Available This review is concerned with the motion of a point scalar charge, a point electric charge, and a point mass in a specified background spacetime. In each of the three cases the particle produces a field that behaves as outgoing radiation in the wave zone, and therefore removes energy from the particle. In the near zone the field acts on the particle and gives rise to a self-force that prevents the particle from moving on a geodesic of the background spacetime. The self-force contains both conservative and dissipative terms, and the latter are responsible for the radiation reaction. The work done by the self-force matches the energy radiated away by the particle. The field's action on the particle is difficult to calculate because of its singular nature: the field diverges at the position of the particle. But it is possible to isolate the field's singular part and show that it exerts no force on the particle -- its only effect is to contribute to the particle's inertia. What remains after subtraction is a regular field that is fully responsible for the self-force. Because this field satisfies a homogeneous wave equation, it can be thought of as a free field that interacts with the particle; it is this interaction that gives rise to the self-force. The mathematical tools required to derive the equations of motion of a point scalar charge, a point electric charge, and a point mass in a specified background spacetime are developed here from scratch. The review begins with a discussion of the basic theory of bitensors (Part I. It then applies the theory to the construction of convenient coordinate systems to chart a neighbourhood of the particle's word line (Part II. It continues with a thorough discussion of Green's functions in curved spacetime (Part III. The review presents a detailed derivation of each of the three equations of motion (Part IV. Because the notion of a point mass is problematic in general relativity, the review concludes (Part V

  15. A study of the application of singular perturbation theory. [development of a real time algorithm for optimal three dimensional aircraft maneuvers

    Science.gov (United States)

    Mehra, R. K.; Washburn, R. B.; Sajan, S.; Carroll, J. V.

    1979-01-01

    A hierarchical real time algorithm for optimal three dimensional control of aircraft is described. Systematic methods are developed for real time computation of nonlinear feedback controls by means of singular perturbation theory. The results are applied to a six state, three control variable, point mass model of an F-4 aircraft. Nonlinear feedback laws are presented for computing the optimal control of throttle, bank angle, and angle of attack. Real Time capability is assessed on a TI 9900 microcomputer. The breakdown of the singular perturbation approximation near the terminal point is examined Continuation methods are examined to obtain exact optimal trajectories starting from the singular perturbation solutions.

  16. 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.

  17. A Jacobi-Davidson type method for the generalized singular value problem

    NARCIS (Netherlands)

    Hochstenbach, M.E.

    2009-01-01

    We discuss a new method for the iterative computation of some of the generalized singular values and vectors of a large sparse matrix. Our starting point is the augmented matrix formulation of the GSVD. The subspace expansion is performed by (approximately) solving a Jacobi–Davidson type correction

  18. Minimal solution for inconsistent singular fuzzy matrix equations

    Directory of Open Access Journals (Sweden)

    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.

  19. A spin-liquid with pinch-line singularities on the pyrochlore lattice.

    Science.gov (United States)

    Benton, Owen; Jaubert, L D C; Yan, Han; Shannon, Nic

    2016-05-26

    The mathematics of gauge theories lies behind many of the most profound advances in physics in the past 200 years, from Maxwell's theory of electromagnetism to Einstein's theory of general relativity. More recently it has become clear that gauge theories also emerge in condensed matter, a prime example being the spin-ice materials which host an emergent electromagnetic gauge field. In spin-ice, the underlying gauge structure is revealed by the presence of pinch-point singularities in neutron-scattering measurements. Here we report the discovery of a spin-liquid where the low-temperature physics is naturally described by the fluctuations of a tensor field with a continuous gauge freedom. This gauge structure underpins an unusual form of spin correlations, giving rise to pinch-line singularities: line-like analogues of the pinch points observed in spin-ice. Remarkably, these features may already have been observed in the pyrochlore material Tb2Ti2O7.

  20. 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.

  1. An examination of the concept of driving point receptance

    Science.gov (United States)

    Sheng, X.; He, Y.; Zhong, T.

    2018-04-01

    In the field of vibration, driving point receptance is a well-established and widely applied concept. However, as demonstrated in this paper, when a driving point receptance is calculated using the finite element (FE) method with solid elements, it does not converge as the FE mesh becomes finer, suggesting that there is a singularity. Hence, the concept of driving point receptance deserves a rigorous examination. In this paper, it is firstly shown that, for a point harmonic force applied on the surface of an elastic half-space, the Boussinesq formula can be applied to calculate the displacement amplitude of the surface if the response point is sufficiently close to the load. Secondly, by applying the Betti reciprocal theorem, it is shown that the displacement of an elastic body near a point harmonic force can be decomposed into two parts, with the first one being the displacement of an elastic half-space. This decomposition is useful, since it provides a solid basis for the introduction of a contact spring between a wheel and a rail in interaction. However, according to the Boussinesq formula, this decomposition also leads to the conclusion that a driving point receptance is infinite (singular), and would be undefinable. Nevertheless, driving point receptances have been calculated using different methods. Since the singularity identified in this paper was not appreciated, no account was given to the singularity in these calculations. Thus, the validity of these calculation methods must be examined. This constructs the third part of the paper. As the final development of the paper, the above decomposition is utilised to define and determine driving point receptances required for dealing with wheel/rail interactions.

  2. Converting point-wise nuclear cross sections to pole representation using regularized vector fitting

    Science.gov (United States)

    Peng, Xingjie; Ducru, Pablo; Liu, Shichang; Forget, Benoit; Liang, Jingang; Smith, Kord

    2018-03-01

    Direct Doppler broadening of nuclear cross sections in Monte Carlo codes has been widely sought for coupled reactor simulations. One recent approach proposed analytical broadening using a pole representation of the commonly used resonance models and the introduction of a local windowing scheme to improve performance (Hwang, 1987; Forget et al., 2014; Josey et al., 2015, 2016). This pole representation has been achieved in the past by converting resonance parameters in the evaluation nuclear data library into poles and residues. However, cross sections of some isotopes are only provided as point-wise data in ENDF/B-VII.1 library. To convert these isotopes to pole representation, a recent approach has been proposed using the relaxed vector fitting (RVF) algorithm (Gustavsen and Semlyen, 1999; Gustavsen, 2006; Liu et al., 2018). This approach however needs to specify ahead of time the number of poles. This article addresses this issue by adding a poles and residues filtering step to the RVF procedure. This regularized VF (ReV-Fit) algorithm is shown to efficiently converge the poles close to the physical ones, eliminating most of the superfluous poles, and thus enabling the conversion of point-wise nuclear cross sections.

  3. A well-posed numerical method to track isolated conformal map singularities in Hele-Shaw flow

    International Nuclear Information System (INIS)

    Baker, G.; Siegel, M.; Tanveer, S.

    1995-01-01

    We present a new numerical method for calculating an evolving 2D Hele-Shaw interface when surface tension effects are neglected. In the case where the flow is directed from the less viscous fluid into the more viscous fluid, the motion of the interface is ill-posed; small deviations in the initial condition will produce significant changes in the ensuing motion. The situation is disastrous for numerical computation, as small roundoff errors can quickly lead to large inaccuracies in the computed solution. Our method of computation is most easily formulated using a conformal map from the fluid domain into a unit disk. The method relies on analytically continuing the initial data and equations of motion into the region exterior to the disk, where the evolution problem becomes well-posed. The equations are then numerically solved in the extended domain. The presence of singularities in the conformal map outside of the disk introduces specific structures along the fluid interface. Our method can explicitly track the location of isolated pole and branch point singularities, allowing us to draw connections between the development of interfacial patterns and the motion of singularities as they approach the unit disk. In particular, we are able to relate physical features such as finger shape, side-branch formation, and competition between fingers to the nature and location of the singularities. The usefulness of this method in studying the formation of topological singularities (self-intersections of the interface) is also pointed out. 47 refs., 10 figs., 1 tab

  4. Gravitational lensing and ghost images in the regular Bardeen no-horizon spacetimes

    International Nuclear Information System (INIS)

    Schee, Jan; Stuchlík, Zdeněk

    2015-01-01

    We study deflection of light rays and gravitational lensing in the regular Bardeen no-horizon spacetimes. Flatness of these spacetimes in the central region implies existence of interesting optical effects related to photons crossing the gravitational field of the no-horizon spacetimes with low impact parameters. These effects occur due to existence of a critical impact parameter giving maximal deflection of light rays in the Bardeen no-horizon spacetimes. We give the critical impact parameter in dependence on the specific charge of the spacetimes, and discuss 'ghost' direct and indirect images of Keplerian discs, generated by photons with low impact parameters. The ghost direct images can occur only for large inclination angles of distant observers, while ghost indirect images can occur also for small inclination angles. We determine the range of the frequency shift of photons generating the ghost images and determine distribution of the frequency shift across these images. We compare them to those of the standard direct images of the Keplerian discs. The difference of the ranges of the frequency shift on the ghost and direct images could serve as a quantitative measure of the Bardeen no-horizon spacetimes. The regions of the Keplerian discs giving the ghost images are determined in dependence on the specific charge of the no-horizon spacetimes. For comparison we construct direct and indirect (ordinary and ghost) images of Keplerian discs around Reissner-Nördström naked singularities demonstrating a clear qualitative difference to the ghost direct images in the regular Bardeen no-horizon spacetimes. The optical effects related to the low impact parameter photons thus give clear signature of the regular Bardeen no-horizon spacetimes, as no similar phenomena could occur in the black hole or naked singularity spacetimes. Similar direct ghost images have to occur in any regular no-horizon spacetimes having nearly flat central region

  5. A singular position-dependent mass particle in an infinite potential well

    International Nuclear Information System (INIS)

    Mustafa, Omar; Mazharimousavi, S. Habib

    2009-01-01

    An unusual singular position-dependent-mass particle in an infinite potential well is considered. The corresponding Hamiltonian is mapped through a point-canonical-transformation and an explicit correspondence between the target Hamiltonian and a Poeschl-Teller type reference Hamiltonian is obtained. New ordering ambiguity parametric setting are suggested

  6. 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.

  7. Collocation methods for the solution of eigenvalue problems for singular ordinary differential equations

    Directory of Open Access Journals (Sweden)

    Winfried Auzinger

    2006-01-01

    Full Text Available We demonstrate that eigenvalue problems for ordinary differential equations can be recast in a formulation suitable for the solution by polynomial collocation. It is shown that the well-posedness of the two formulations is equivalent in the regular as well as in the singular case. Thus, a collocation code equipped with asymptotically correct error estimation and adaptive mesh selection can be successfully applied to compute the eigenvalues and eigenfunctions efficiently and with reliable control of the accuracy. Numerical examples illustrate this claim.

  8. Integral equations of the first kind, inverse problems and regularization: a crash course

    International Nuclear Information System (INIS)

    Groetsch, C W

    2007-01-01

    This paper is an expository survey of the basic theory of regularization for Fredholm integral equations of the first kind and related background material on inverse problems. We begin with an historical introduction to the field of integral equations of the first kind, with special emphasis on model inverse problems that lead to such equations. The basic theory of linear Fredholm equations of the first kind, paying particular attention to E. Schmidt's singular function analysis, Picard's existence criterion, and the Moore-Penrose theory of generalized inverses is outlined. The fundamentals of the theory of Tikhonov regularization are then treated and a collection of exercises and a bibliography are provided

  9. The Poisson equation in axisymmetric domains with conical points

    International Nuclear Information System (INIS)

    Nkemzi, B.

    2003-01-01

    This paper analyzes the application of the Fourier-finite-element method (FFEM) for the resolution of the Derichlet problem for the Poisson equation -Δu-circumflex = f-circumflex in axisymmetric domains Ω-circumflex subset of R 3 with conical points on the rotation axis. The FFEM combines the approximate Fourier method with respect to one space direction with the finite element method for the approximate calculation of the Fourier coefficients of the solution. Here, the influence of the conical points on the regularity of the Fourier coefficients of the solution is analyzed and the asymptotic behaviour of the coefficients near the conical points is described by some singularity functions and treated numerically by mesh grading in the two-dimensional meridian of Ω-circumflex. It is proved that for f-circumflex in L 2 (Ω-circumflex), the rate of convergence of the combined approximations in the Sobolev space W 2 1 (Ω-circumflex) is of the order O(h + N -1 ), where h and N represent, respectively, the parameters of the finite-element- and the Fourier-approximation, with h → 0 and n → ∞. (author)

  10. Singular Value Decomposition Method to Determine Distance Distributions in Pulsed Dipolar Electron Spin Resonance.

    Science.gov (United States)

    Srivastava, Madhur; Freed, Jack H

    2017-11-16

    Regularization is often utilized to elicit the desired physical results from experimental data. The recent development of a denoising procedure yielding about 2 orders of magnitude in improvement in SNR obviates the need for regularization, which achieves a compromise between canceling effects of noise and obtaining an estimate of the desired physical results. We show how singular value decomposition (SVD) can be employed directly on the denoised data, using pulse dipolar electron spin resonance experiments as an example. Such experiments are useful in measuring distances and their distributions, P(r) between spin labels on proteins. In noise-free model cases exact results are obtained, but even a small amount of noise (e.g., SNR = 850 after denoising) corrupts the solution. We develop criteria that precisely determine an optimum approximate solution, which can readily be automated. This method is applicable to any signal that is currently processed with regularization of its SVD analysis.

  11. Classical Liouville action on the sphere with three hyperbolic singularities

    Energy Technology Data Exchange (ETDEWEB)

    Hadasz, Leszek E-mail: hadasz@th.if.uj.edu.pl; Jaskolski, Zbigniew E-mail: jask@ift.uniwroc.pl

    2004-08-30

    The classical solution to the Liouville equation in the case of three hyperbolic singularities of its energy-momentum tensor is derived and analyzed. The recently proposed classical Liouville action is explicitly calculated in this case. The result agrees with the classical limit of the three-point function in the DOZZ solution of the quantum Liouville theory.

  12. Classical Liouville action on the sphere with three hyperbolic singularities

    Science.gov (United States)

    Hadasz, Leszek; Jaskólski, Zbigniew

    2004-08-01

    The classical solution to the Liouville equation in the case of three hyperbolic singularities of its energy-momentum tensor is derived and analyzed. The recently proposed classical Liouville action is explicitly calculated in this case. The result agrees with the classical limit of the three-point function in the DOZZ solution of the quantum Liouville theory.

  13. Classical Liouville action on the sphere with three hyperbolic singularities

    International Nuclear Information System (INIS)

    Hadasz, Leszek; Jaskolski, Zbigniew

    2004-01-01

    The classical solution to the Liouville equation in the case of three hyperbolic singularities of its energy-momentum tensor is derived and analyzed. The recently proposed classical Liouville action is explicitly calculated in this case. The result agrees with the classical limit of the three-point function in the DOZZ solution of the quantum Liouville theory

  14. Mechanical quadrature method as applied to singular integral equations with logarithmic singularity on the right-hand side

    Science.gov (United States)

    Amirjanyan, A. A.; Sahakyan, A. V.

    2017-08-01

    A singular integral equation with a Cauchy kernel and a logarithmic singularity on its righthand side is considered on a finite interval. An algorithm is proposed for the numerical solution of this equation. The contact elasticity problem of a П-shaped rigid punch indented into a half-plane is solved in the case of a uniform hydrostatic pressure occurring under the punch, which leads to a logarithmic singularity at an endpoint of the integration interval. The numerical solution of this problem shows the efficiency of the proposed approach and suggests that the singularity has to be taken into account in solving the equation.

  15. Critical and Griffiths-McCoy singularities in quantum Ising spin glasses on d -dimensional hypercubic lattices: A series expansion study

    Science.gov (United States)

    Singh, R. R. P.; Young, A. P.

    2017-08-01

    We study the ±J transverse-field Ising spin-glass model at zero temperature on d -dimensional hypercubic lattices and in the Sherrington-Kirkpatrick (SK) model, by series expansions around the strong-field limit. In the SK model and in high dimensions our calculated critical properties are in excellent agreement with the exact mean-field results, surprisingly even down to dimension d =6 , which is below the upper critical dimension of d =8 . In contrast, at lower dimensions we find a rich singular behavior consisting of critical and Griffiths-McCoy singularities. The divergence of the equal-time structure factor allows us to locate the critical coupling where the correlation length diverges, implying the onset of a thermodynamic phase transition. We find that the spin-glass susceptibility as well as various power moments of the local susceptibility become singular in the paramagnetic phase before the critical point. Griffiths-McCoy singularities are very strong in two dimensions but decrease rapidly as the dimension increases. We present evidence that high enough powers of the local susceptibility may become singular at the pure-system critical point.

  16. Regular expression containment

    DEFF Research Database (Denmark)

    Henglein, Fritz; Nielsen, Lasse

    2011-01-01

    We present a new sound and complete axiomatization of regular expression containment. It consists of the conventional axiomatiza- tion of concatenation, alternation, empty set and (the singleton set containing) the empty string as an idempotent semiring, the fixed- point rule E* = 1 + E × E......* for Kleene-star, and a general coin- duction rule as the only additional rule. Our axiomatization gives rise to a natural computational inter- pretation of regular expressions as simple types that represent parse trees, and of containment proofs as coercions. This gives the axiom- atization a Curry......-Howard-style constructive interpretation: Con- tainment proofs do not only certify a language-theoretic contain- ment, but, under our computational interpretation, constructively transform a membership proof of a string in one regular expres- sion into a membership proof of the same string in another regular expression. We...

  17. Forty Necessary and Sufficient Conditions for Regularity of Interval Matrices: A survey

    Czech Academy of Sciences Publication Activity Database

    Rohn, Jiří

    2009-01-01

    Roč. 18, - (2009), s. 500-512 E-ISSN 1081-3810 R&D Projects: GA ČR GA201/09/1957; GA ČR GC201/08/J020 Institutional research plan: CEZ:AV0Z10300504 Keywords : interval matrix * regularity * singularity * necessary and sufficient condition * algorithm Subject RIV: BA - General Mathematics Impact factor: 0.892, year: 2009 http://www.math.technion.ac.il/iic/ ela / ela -articles/articles/vol18_pp500-512.pdf

  18. Regularization parameter estimation for underdetermined problems by the χ 2 principle with application to 2D focusing gravity inversion

    International Nuclear Information System (INIS)

    Vatankhah, Saeed; Ardestani, Vahid E; Renaut, Rosemary A

    2014-01-01

    The χ 2 principle generalizes the Morozov discrepancy principle to the augmented residual of the Tikhonov regularized least squares problem. For weighting of the data fidelity by a known Gaussian noise distribution on the measured data, when the stabilizing, or regularization, term is considered to be weighted by unknown inverse covariance information on the model parameters, the minimum of the Tikhonov functional becomes a random variable that follows a χ 2 -distribution with m+p−n degrees of freedom for the model matrix G of size m×n, m⩾n, and regularizer L of size p × n. Then, a Newton root-finding algorithm, employing the generalized singular value decomposition, or singular value decomposition when L = I, can be used to find the regularization parameter α. Here the result and algorithm are extended to the underdetermined case, m 2 algorithms when m 2 and unbiased predictive risk estimator of the regularization parameter are used for the first time in this context. For a simulated underdetermined data set with noise, these regularization parameter estimation methods, as well as the generalized cross validation method, are contrasted with the use of the L-curve and the Morozov discrepancy principle. Experiments demonstrate the efficiency and robustness of the χ 2 principle and unbiased predictive risk estimator, moreover showing that the L-curve and Morozov discrepancy principle are outperformed in general by the other three techniques. Furthermore, the minimum support stabilizer is of general use for the χ 2 principle when implemented without the desirable knowledge of the mean value of the model. (paper)

  19. Error estimates in projective solutions of the radon equation

    International Nuclear Information System (INIS)

    Lubuma, M.S.

    1991-04-01

    The model Radon equation is the integral equation of the second kind defined by the interior limits of the electrostatic double layer potential relative to a curve with one angular point and characterized by the non compactness of the operator with respect to the maximum norm. It is shown that the solution to this equation is decomposable into a regular part and a finite linear combination of intrinsic singular functions. The maximal regularity of the solution and explicit formulae for the coefficients of the singular functions are given. The regularity permits to specify how slow the convergence of the classical projection method is, while the above mentioned formulae lead to modified projection methods of the Dual Singular Function Method type, with better approximations for the solution and for the coefficients of singularities. (author). 23 refs

  20. 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)

  1. 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

  2. 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.

  3. The technological singularity and exponential medicine

    Directory of Open Access Journals (Sweden)

    Iraj Nabipour

    2016-01-01

    Full Text Available The "technological singularity" is forecasted to occur in 2045. It is a point when non-biological intelligence becomes more intelligent than humans and each generation of intelligent machines re-designs itself smarter. Beyond this point, there is a symbiosis between machines and humans. This co-existence will produce incredible impacts on medicine that its sparkles could be seen in healthcare industry and the future medicine since 2025. Ray Kurzweil, the great futurist, suggested that three revolutions in science and technology consisting genetic and molecular science, nanotechnology, and robotic (artificial intelligence provided an exponential growth rate for medicine. The "exponential medicine" is going to create more disruptive technologies in healthcare industry. The exponential medicine shifts the paradigm of medical philosophy and produces significant impacts on the healthcare system and patient-physician relationship.   

  4. Numerical solver of the time-dependent Schroedinger equation with Coulomb singularities

    International Nuclear Information System (INIS)

    Gordon, Ariel; Jirauschek, Christian; Kaertner, Franz X.

    2006-01-01

    This paper addresses a very fundamental and important problem in the numerical analysis of atomic and molecular systems: How to discretize Hamiltonians with divergent potential terms, such as Coulomb singularities. At the point of a Coulomb singularity, the wave function cannot be described by a Taylor series expansion, which results in problems when standard discretization schemes are used. We propose using the known asymptotic form of the wave function near the singularity instead of the (nonexistent) Taylor series. This principle, namely discretization by asymptotic behavior correspondence (ABC), is employed in this paper for obtaining grid-discretizations for the Coulomb potential in Cartesian, cylindrical and spherical coordinate systems. We show that computations with the ABC discretization are faster and more precise than with a naive discretization by orders of magnitude. The ABC discretization is well suited for the standard numerical time propagators, such as the Crank-Nicholson, Peaceman-Rachford, and leapfrog schemes. We use the latter, since it is faster and has the same order of accuracy. The leapfrog scheme is generalized to allow absorbing potentials at the grid boundaries

  5. 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.)

  6. 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.)

  7. New singularities in nonrelativistic coupled channel scattering. II. Fourth order

    International Nuclear Information System (INIS)

    Khuri, N.N.; Tsun Wu, T.

    1997-01-01

    We consider a two-channel nonrelativistic potential scattering problem, and study perturbation theory in fourth order for the forward amplitude. The main result is that the new singularity demonstrated in second order in the preceding paper I also occurs at the same point in fourth order. Its strength is again that of a pole. copyright 1997 The American Physical Society

  8. String wave function across a Kasner singularity

    International Nuclear Information System (INIS)

    Copeland, Edmund J.; Niz, Gustavo; Turok, Neil

    2010-01-01

    A collision of orbifold planes in 11 dimensions has been proposed as an explanation of the hot big bang. When the two planes are close to each other, the winding membranes become the lightest modes of the theory, and can be effectively described in terms of fundamental strings in a ten-dimensional background. Near the brane collision, the 11-dimensional metric is a Euclidean space times a 1+1-dimensional Milne universe. However, one may expect small perturbations to lead into a more general Kasner background. In this paper we extend the previous classical analysis of winding membranes to Kasner backgrounds, and using the Hamiltonian equations, solve for the wave function of loops with circular symmetry. The evolution across the singularity is regular, and explained in terms of the excitement of higher oscillation modes. We also show there is finite particle production and unitarity is preserved.

  9. An adaptive surface filter for airborne laser scanning point clouds by means of regularization and bending energy

    Science.gov (United States)

    Hu, Han; Ding, Yulin; Zhu, Qing; Wu, Bo; Lin, Hui; Du, Zhiqiang; Zhang, Yeting; Zhang, Yunsheng

    2014-06-01

    The filtering of point clouds is a ubiquitous task in the processing of airborne laser scanning (ALS) data; however, such filtering processes are difficult because of the complex configuration of the terrain features. The classical filtering algorithms rely on the cautious tuning of parameters to handle various landforms. To address the challenge posed by the bundling of different terrain features into a single dataset and to surmount the sensitivity of the parameters, in this study, we propose an adaptive surface filter (ASF) for the classification of ALS point clouds. Based on the principle that the threshold should vary in accordance to the terrain smoothness, the ASF embeds bending energy, which quantitatively depicts the local terrain structure to self-adapt the filter threshold automatically. The ASF employs a step factor to control the data pyramid scheme in which the processing window sizes are reduced progressively, and the ASF gradually interpolates thin plate spline surfaces toward the ground with regularization to handle noise. Using the progressive densification strategy, regularization and self-adaption, both performance improvement and resilience to parameter tuning are achieved. When tested against the benchmark datasets provided by ISPRS, the ASF performs the best in comparison with all other filtering methods, yielding an average total error of 2.85% when optimized and 3.67% when using the same parameter set.

  10. Accreting fluids onto regular black holes via Hamiltonian approach

    Energy Technology Data Exchange (ETDEWEB)

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

    2017-08-15

    We investigate the accretion of test fluids onto regular black holes such as Kehagias-Sfetsos black holes and regular black holes with Dagum distribution function. We analyze the accretion process when different test fluids are falling onto these regular black holes. The accreting fluid is being classified through the equation of state according to the features of regular black holes. The behavior of fluid flow and the existence of sonic points is being checked for these regular black holes. It is noted that the three-velocity depends on critical points and the equation of state parameter on phase space. (orig.)

  11. Piercing the water surface with a blade: Singularities of the contact line

    Energy Technology Data Exchange (ETDEWEB)

    Alimov, Mars M. [Kazan Federal University, Kazan 420008 (Russian Federation); Kornev, Konstantin G. [Department of Materials Science & Engineering, Clemson University, Clemson, South Carolina 29634 (United States)

    2016-01-15

    An external meniscus on a narrow blade with a slit-like cross section is studied using the hodograph formulation of the Laplace nonlinear equation of capillarity. On narrow blades, the menisci are mostly shaped by the wetting and capillary forces; gravity plays a secondary role. To describe a meniscus in this asymptotic case, the model of Alimov and Kornev [“Meniscus on a shaped fibre: Singularities and hodograph formulation,” Proc. R. Soc. A 470, 20140113 (2014)] has been employed. It is shown that at the sharp edges of the blade, the contact line makes a jump. In the wetting case, the contact line sitting at each side of the blade is lifted above the points where the meniscus first meets the blade edges. In the non-wetting case, the contact line is lowered below these points. The contours of the constant height emanating from the blade edges generate unusual singularities with infinite curvatures at some points at the blade edges. The meniscus forms a unique surface made of two mirror-symmetric sheets fused together. Each sheet is supported by the contact line sitting at each side of the blade.

  12. Piercing the water surface with a blade: Singularities of the contact line

    International Nuclear Information System (INIS)

    Alimov, Mars M.; Kornev, Konstantin G.

    2016-01-01

    An external meniscus on a narrow blade with a slit-like cross section is studied using the hodograph formulation of the Laplace nonlinear equation of capillarity. On narrow blades, the menisci are mostly shaped by the wetting and capillary forces; gravity plays a secondary role. To describe a meniscus in this asymptotic case, the model of Alimov and Kornev [“Meniscus on a shaped fibre: Singularities and hodograph formulation,” Proc. R. Soc. A 470, 20140113 (2014)] has been employed. It is shown that at the sharp edges of the blade, the contact line makes a jump. In the wetting case, the contact line sitting at each side of the blade is lifted above the points where the meniscus first meets the blade edges. In the non-wetting case, the contact line is lowered below these points. The contours of the constant height emanating from the blade edges generate unusual singularities with infinite curvatures at some points at the blade edges. The meniscus forms a unique surface made of two mirror-symmetric sheets fused together. Each sheet is supported by the contact line sitting at each side of the blade

  13. 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

  14. Regular black holes from semi-classical down to Planckian size

    Science.gov (United States)

    Spallucci, Euro; Smailagic, Anais

    In this paper, we review various models of curvature singularity free black holes (BHs). In the first part of the review, we describe semi-classical solutions of the Einstein equations which, however, contains a “quantum” input through the matter source. We start by reviewing the early model by Bardeen where the metric is regularized by-hand through a short-distance cutoff, which is justified in terms of nonlinear electro-dynamical effects. This toy-model is useful to point-out the common features shared by all regular semi-classical black holes. Then, we solve Einstein equations with a Gaussian source encoding the quantum spread of an elementary particle. We identify, the a priori arbitrary, Gaussian width with the Compton wavelength of the quantum particle. This Compton-Gauss model leads to the estimate of a terminal density that a gravitationally collapsed object can achieve. We identify this density to be the Planck density, and reformulate the Gaussian model assuming this as its peak density. All these models, are physically reliable as long as the BH mass is big enough with respect to the Planck mass. In the truly Planckian regime, the semi-classical approximation breaks down. In this case, a fully quantum BH description is needed. In the last part of this paper, we propose a nongeometrical quantum model of Planckian BHs implementing the Holographic Principle and realizing the “classicalization” scenario recently introduced by Dvali and collaborators. The classical relation between the mass and radius of the BH emerges only in the classical limit, far away from the Planck scale.

  15. 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

  16. Multi-Label Classification by Semi-Supervised Singular Value Decomposition.

    Science.gov (United States)

    Jing, Liping; Shen, Chenyang; Yang, Liu; Yu, Jian; Ng, Michael K

    2017-10-01

    Multi-label problems arise in various domains, including automatic multimedia data categorization, and have generated significant interest in computer vision and machine learning community. However, existing methods do not adequately address two key challenges: exploiting correlations between labels and making up for the lack of labelled data or even missing labelled data. In this paper, we proposed to use a semi-supervised singular value decomposition (SVD) to handle these two challenges. The proposed model takes advantage of the nuclear norm regularization on the SVD to effectively capture the label correlations. Meanwhile, it introduces manifold regularization on mapping to capture the intrinsic structure among data, which provides a good way to reduce the required labelled data with improving the classification performance. Furthermore, we designed an efficient algorithm to solve the proposed model based on the alternating direction method of multipliers, and thus, it can efficiently deal with large-scale data sets. Experimental results for synthetic and real-world multimedia data sets demonstrate that the proposed method can exploit the label correlations and obtain promising and better label prediction results than the state-of-the-art methods.

  17. A Differential Quadrature Procedure with Regularization of the Dirac-delta Function for Numerical Solution of Moving Load Problem

    Directory of Open Access Journals (Sweden)

    S. A. Eftekhari

    Full Text Available AbstractThe differential quadrature method (DQM is one of the most elegant and efficient methods for the numerical solution of partial differential equations arising in engineering and applied sciences. It is simple to use and also straightforward to implement. However, the DQM is well-known to have some difficulty when applied to partial differential equations involving singular functions like the Dirac-delta function. This is caused by the fact that the Dirac-delta function cannot be directly discretized by the DQM. To overcome this difficulty, this paper presents a simple differential quadrature procedure in which the Dirac-delta function is replaced by regularized smooth functions. By regularizing the Dirac-delta function, such singular function is treated as non-singular functions and can be easily and directly discretized using the DQM. To demonstrate the applicability and reliability of the proposed method, it is applied here to solve some moving load problems of beams and rectangular plates, where the location of the moving load is described by a time-dependent Dirac-delta function. The results generated by the proposed method are compared with analytical and numerical results available in the literature. Numerical results reveal that the proposed method can be used as an efficient tool for dynamic analysis of beam- and plate-type structures traversed by moving dynamic loads.

  18. Inverse electrocardiographic transformations: dependence on the number of epicardial regions and body surface data points.

    Science.gov (United States)

    Johnston, P R; Walker, S J; Hyttinen, J A; Kilpatrick, D

    1994-04-01

    The inverse problem of electrocardiography, the computation of epicardial potentials from body surface potentials, is influenced by the desired resolution on the epicardium, the number of recording points on the body surface, and the method of limiting the inversion process. To examine the role of these variables in the computation of the inverse transform, Tikhonov's zero-order regularization and singular value decomposition (SVD) have been used to invert the forward transfer matrix. The inverses have been compared in a data-independent manner using the resolution and the noise amplification as endpoints. Sets of 32, 50, 192, and 384 leads were chosen as sets of body surface data, and 26, 50, 74, and 98 regions were chosen to represent the epicardium. The resolution and noise were both improved by using a greater number of electrodes on the body surface. When 60% of the singular values are retained, the results show a trade-off between noise and resolution, with typical maximal epicardial noise levels of less than 0.5% of maximum epicardial potentials for 26 epicardial regions, 2.5% for 50 epicardial regions, 7.5% for 74 epicardial regions, and 50% for 98 epicardial regions. As the number of epicardial regions is increased, the regularization technique effectively fixes the noise amplification but markedly decreases the resolution, whereas SVD results in an increase in noise and a moderate decrease in resolution. Overall the regularization technique performs slightly better than SVD in the noise-resolution relationship. There is a region at the posterior of the heart that was poorly resolved regardless of the number of regions chosen. The variance of the resolution was such as to suggest the use of variable-size epicardial regions based on the resolution.

  19. 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

  20. Quantum dress for a naked singularity

    Directory of Open Access Journals (Sweden)

    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.

  1. Regularization Techniques for ECG Imaging during Atrial Fibrillation: a Computational Study

    Directory of Open Access Journals (Sweden)

    Carlos Figuera

    2016-10-01

    Full Text Available The inverse problem of electrocardiography is usually analyzed during stationary rhythms. However, the performance of the regularization methods under fibrillatory conditions has not been fully studied. In this work, we assessed different regularization techniques during atrial fibrillation (AF for estimating four target parameters, namely, epicardial potentials, dominant frequency (DF, phase maps, and singularity point (SP location. We use a realistic mathematical model of atria and torso anatomy with three different electrical activity patterns (i.e. sinus rhythm, simple AF and complex AF. Body surface potentials (BSP were simulated using Boundary Element Method and corrupted with white Gaussian noise of different powers. Noisy BSPs were used to obtain the epicardial potentials on the atrial surface, using fourteen different regularization techniques. DF, phase maps and SP location were computed from estimated epicardial potentials. Inverse solutions were evaluated using a set of performance metrics adapted to each clinical target. For the case of SP location, an assessment methodology based on the spatial mass function of the SP location and four spatial error metrics was proposed. The role of the regularization parameter for Tikhonov-based methods, and the effect of noise level and imperfections in the knowledge of the transfer matrix were also addressed. Results showed that the Bayes maximum-a-posteriori method clearly outperforms the rest of the techniques but requires a priori information about the epicardial potentials. Among the purely non-invasive techniques, Tikhonov-based methods performed as well as more complex techniques in realistic fibrillatory conditions, with a slight gain between 0.02 and 0.2 in terms of the correlation coefficient. Also, the use of a constant regularization parameter may be advisable since the performance was similar to that obtained with a variable parameter (indeed there was no difference for the zero

  2. 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.

  3. Three symmetric positive solutions of fourth-order singular nonlocal boundary value problems

    Directory of Open Access Journals (Sweden)

    Fuyi Xu

    2011-12-01

    Full Text Available In this paper, we study the existence of three positive solutions of fourth-order singular nonlocal boundary value problems. We show that there exist triple symmetric positive solutions by using Leggett-Williams fixed-point theorem. The conclusions in this paper essentially extend and improve some known results.

  4. 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.

  5. Resonant tunnelling through short-range singular potentials

    International Nuclear Information System (INIS)

    Zolotaryuk, A V; Christiansen, P L; Iermakova, S V

    2007-01-01

    A three-parameter family of point interactions constructed from sequences of symmetric barrier-well-barrier and well-barrier-well rectangles is studied in the limit, when the rectangles are squeezed to zero width but the barrier height and the well depth become infinite (the zero-range limit). The limiting generalized potentials are referred to as the second derivative of Dirac's delta function ±λδ-prime(x) with a renormalized coupling constant λ > 0 or simply as ±δ-prime-like point interactions. As a result, a whole family of self-adjoint extensions of the one-dimensional Schroedinger operator is shown to exist, which results in full and partial resonant tunnelling through this class of singular potentials. The resonant tunnelling occurs for countable sets of interaction strength values in the λ-space which are the roots of several transcendental equations. The comparison with the previous results for δ'-like point interactions is also discussed

  6. 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.

  7. An industrial robot singular trajectories planning based on graphs and neural networks

    Science.gov (United States)

    Łęgowski, Adrian; Niezabitowski, Michał

    2016-06-01

    Singular trajectories are rarely used because of issues during realization. A method of planning trajectories for given set of points in task space with use of graphs and neural networks is presented. In every desired point the inverse kinematics problem is solved in order to derive all possible solutions. A graph of solutions is made. The shortest path is determined to define required nodes in joint space. Neural networks are used to define the path between these nodes.

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

    Science.gov (United States)

    Stuchlík, Zdeněk; Schee, Jan

    2015-12-01

    In this paper, we study circular geodesic motion of test particles and photons in the Bardeen and Ayon-Beato-Garcia (ABG) geometry describing spherically symmetric regular black-hole or no-horizon spacetimes. While the Bardeen geometry is not exact solution of Einstein's equations, the ABG spacetime is related to self-gravitating charged sources governed by Einstein's gravity and nonlinear electrodynamics. They both are characterized by the mass parameter m and the charge parameter g. We demonstrate that in similarity to the Reissner-Nordstrom (RN) naked singularity spacetimes an antigravity static sphere should exist in all the no-horizon Bardeen and ABG solutions that can be surrounded by a Keplerian accretion disc. However, contrary to the RN naked singularity spacetimes, the ABG no-horizon spacetimes with parameter g/m > 2 can contain also an additional inner Keplerian disc hidden under the static antigravity sphere. Properties of the geodesic structure are reflected by simple observationally relevant optical phenomena. We give silhouette of the regular black-hole and no-horizon spacetimes, and profiled spectral lines generated by Keplerian rings radiating at a fixed frequency and located in strong gravity region at or nearby the marginally stable circular geodesics. We demonstrate that the profiled spectral lines related to the regular black-holes are qualitatively similar to those of the Schwarzschild black-holes, giving only small quantitative differences. On the other hand, the regular no-horizon spacetimes give clear qualitative signatures of their presence while compared to the Schwarschild spacetimes. Moreover, it is possible to distinguish the Bardeen and ABG no-horizon spacetimes, if the inclination angle to the observer is known.

  9. 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.

  10. The three-point function in split dimensional regularization in the Coulomb gauge

    International Nuclear Information System (INIS)

    Leibbrandt, G.

    1998-01-01

    We use a gauge-invariant regularization procedure, called split dimensional regularization, to evaluate the quark self-energy Σ(p) and quark-quark-gluon vertex function Λ μ (p',p) in the Coulomb gauge, ∇-vector.A - vectora=0. The technique of split dimensional regularization was designed to regulate Coulomb-gauge Feynman integrals in non-Abelian theories. The technique which is based on two complex regulating parameters, ω and σ, is shown to generate a well-defined set of Coulomb-gauge integrals. A major component of this project deals with the evaluation of four-propagator and five-propagator Coulomb integrals, some of which are non-local. It is further argued that the standard one-loop BRST identity relating Σ and Λ μ , should by rights be replaced by a more general BRST identity which contains two additional contributions from ghost vertex diagrams. Despite the appearance of non-local Coulomb integrals, both Σ and Λ μ are local functions which satisfy the appropriate BRST identity. Application of split dimensional regularization to two-loop energy integrals is briefly discussed. (orig.)

  11. 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

  12. 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.

  13. ``All that Matter ... in One Big Bang ...'', &Other Cosmological Singularities

    Science.gov (United States)

    Elizalde, Emilio

    2018-02-01

    The first part of this paper contains a brief description of the beginnings of modern cosmology, which, the author will argue, was most likely born in the Year 1912. Some of the pieces of evidence presented here have emerged from recent research in the history of science, and are not usually shared with the general audiences in popular science books. In special, the issue of the correct formulation of the original Big Bang concept, according to the precise words of Fred Hoyle, is discussed. Too often, this point is very deficiently explained (when not just misleadingly) in most of the available generalist literature. Other frequent uses of the same words, Big Bang, as to name the initial singularity of the cosmos, and also whole cosmological models, are then addressed, as evolutions of its original meaning. Quantum and inflationary additions to the celebrated singularity theorems by Penrose, Geroch, Hawking and others led to subsequent results by Borde, Guth and Vilenkin. And corresponding corrections to the Einstein field equations have originated, in particular, $R^2$, $f(R)$, and scalar-tensor gravities, giving rise to a plethora of new singularities. For completeness, an updated table with a classification of the same is given.

  14. The critical singularities of water and its significance in the hydrothermal mineralization of uranium

    International Nuclear Information System (INIS)

    Hu Baoqun; Lv Guxian; Wang Fangzheng; Sun Zhanxue; Zhu Peng

    2008-01-01

    Water is the main composition of the geo-fiuid. With the changes of temperature and pressure, its phases and physicochemical properties will vary and the critical singularity occur at the critical point of second-order phase transition. These changes of water will enormously affect the hydrothermal mineralizations. This paper has introduced the types and characteristics of water phase transitions, studied the phase transitions of water in the lithosphere and showed the critical singularity of water with the example of the isobaric heat capacity. The conclusions are as follow: (1) the critical singularities of water are the most obvious as the temperature and pressure near to the critical constants of water; (2) Because the temperature changes with the pressure according to the thermal curve in the lithosphere, it is difficult to find a place where the temperature and pressure can be at the critical constants at same time except the coupling effect of the hydrothermal processes, intermediate-acidic magmatism and faulting; (3) To the hydrothermal mineralization, the significances of water's critical singularities at least include the sharp variation of solubility and instantaneous high pressure to conduct the deposit of ore-forming materials and fault formation. (authors)

  15. 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.)

  16. Connection conditions and the spectral family under singular potentials 03.65.Ge Solutions of wave equations: bound states; 03.65.-w Quantum mechanics;

    CERN Document Server

    Tsutsui, I; Cheon, T

    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 sup 2 vertical bar x vertical bar and the harmonic oscillator with square inverse potential V(x)=(m omega sup 2 /2)x sup 2 +g/x sup 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 ...

  17. Simple rules for the signature and singularity structure of the multiparticle amplitudes

    International Nuclear Information System (INIS)

    Buras, A.J.

    1975-08-01

    It is shown that the representation of the 2→N amplitude in the multiregge limit which exhibits signature factors and singularity structure allowed by the Stoimann relations can be reproduced by means of few simple rules. The rules are illustrated on several examples and their importance in the Reggeon Calculus are pointed out. (Auth.)

  18. 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...

  19. Multilinear Graph Embedding: Representation and Regularization for Images.

    Science.gov (United States)

    Chen, Yi-Lei; Hsu, Chiou-Ting

    2014-02-01

    Given a set of images, finding a compact and discriminative representation is still a big challenge especially when multiple latent factors are hidden in the way of data generation. To represent multifactor images, although multilinear models are widely used to parameterize the data, most methods are based on high-order singular value decomposition (HOSVD), which preserves global statistics but interprets local variations inadequately. To this end, we propose a novel method, called multilinear graph embedding (MGE), as well as its kernelization MKGE to leverage the manifold learning techniques into multilinear models. Our method theoretically links the linear, nonlinear, and multilinear dimensionality reduction. We also show that the supervised MGE encodes informative image priors for image regularization, provided that an image is represented as a high-order tensor. From our experiments on face and gait recognition, the superior performance demonstrates that MGE better represents multifactor images than classic methods, including HOSVD and its variants. In addition, the significant improvement in image (or tensor) completion validates the potential of MGE for image regularization.

  20. Potential profile near singularity point in kinetic Tonks-Langmuir discharges as a function of the ion sources temperature

    Science.gov (United States)

    Kos, L.; Tskhakaya, D. D.; Jelić, N.

    2011-05-01

    A plasma-sheath transition analysis requires a reliable mathematical expression for the plasma potential profile Φ(x) near the sheath edge xs in the limit ɛ ≡λD/ℓ =0 (where λD is the Debye length and ℓ is a proper characteristic length of the discharge). Such expressions have been explicitly calculated for the fluid model and the singular (cold ion source) kinetic model, where exact analytic solutions for plasma equation (ɛ =0) are known, but not for the regular (warm ion source) kinetic model, where no analytic solution of the plasma equation has ever been obtained. For the latter case, Riemann [J. Phys. D: Appl. Phys. 24, 493 (1991)] only predicted a general formula assuming relatively high ion-source temperatures, i.e., much higher than the plasma-sheath potential drop. Riemann's formula, however, according to him, never was confirmed in explicit solutions of particular models (e.g., that of Bissell and Johnson [Phys. Fluids 30, 779 (1987)] and Scheuer and Emmert [Phys. Fluids 31, 3645 (1988)]) since "the accuracy of the classical solutions is not sufficient to analyze the sheath vicinity" [Riemann, in Proceedings of the 62nd Annual Gaseous Electronic Conference, APS Meeting Abstracts, Vol. 54 (APS, 2009)]. Therefore, for many years, there has been a need for explicit calculation that might confirm the Riemann's general formula regarding the potential profile at the sheath edge in the cases of regular very warm ion sources. Fortunately, now we are able to achieve a very high accuracy of results [see, e.g., Kos et al., Phys. Plasmas 16, 093503 (2009)]. We perform this task by using both the analytic and the numerical method with explicit Maxwellian and "water-bag" ion source velocity distributions. We find the potential profile near the plasma-sheath edge in the whole range of ion source temperatures of general interest to plasma physics, from zero to "practical infinity." While within limits of "very low" and "relatively high" ion source temperatures

  1. A regularized vortex-particle mesh method for large eddy simulation

    DEFF Research Database (Denmark)

    Spietz, Henrik Juul; Walther, Jens Honore; Hejlesen, Mads Mølholm

    We present recent developments of the remeshed vortex particle-mesh method for simulating incompressible fluid flow. The presented method relies on a parallel higher-order FFT based solver for the Poisson equation. Arbitrary high order is achieved through regularization of singular Green’s function...... solutions to the Poisson equation and recently we have derived novel high order solutions for a mixture of open and periodic domains. With this approach the simulated variables may formally be viewed as the approximate solution to the filtered Navier Stokes equations, hence we use the method for Large Eddy...

  2. 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

  3. 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

  4. 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...

  5. 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...

  6. Coulomb singularities in scattering wave functions of spin-orbit-coupled states

    International Nuclear Information System (INIS)

    Bogdanski, P.; Ouerdane, H.

    2011-01-01

    We report on our analysis of the Coulomb singularity problem in the frame of the coupled channel scattering theory including spin-orbit interaction. We assume that the coupling between the partial wave components involves orbital angular momenta such that Δl= 0, ±2. In these conditions, the two radial functions, components of a partial wave associated to two values of the angular momentum l, satisfy a system of two second-order ordinary differential equations. We examine the difficulties arising in the analysis of the behavior of the regular solutions near the origin because of this coupling. First, we demonstrate that for a singularity of the first kind in the potential, one of the solutions is not amenable to a power series expansion. The use of the Lippmann-Schwinger equations confirms this fact: a logarithmic divergence arises at the second iteration. To overcome this difficulty, we introduce two auxilliary functions which, together with the two radial functions, satisfy a system of four first-order differential equations. The reduction of the order of the differential system enables us to use a matrix-based approach, which generalizes the standard Frobenius method. We illustrate our analysis with numerical calculations of coupled scattering wave functions in a solid-state system.

  7. Positive solutions of boundary value problem for singular positone and semi-positone third-order difference equations

    Directory of Open Access Journals (Sweden)

    Gai Gongqi

    2011-01-01

    Full Text Available Abstract This article studies the boundary value problems for the third-order nonlinear singular difference equations Δ 3 u ( i - 2 + λ a ( i f ( i , u ( i = 0 , i ∈ [ 2 , T + 2 ] , satisfying five kinds of different boundary value conditions. This article shows the existence of positive solutions for positone and semi-positone type. The nonlinear term may be singular. Two examples are also given to illustrate the main results. The arguments are based upon fixed point theorems in a cone. MSC [2008]: 34B15; 39A10.

  8. Evaluation of three Monte Carlo estimation schemes for flux at a point

    International Nuclear Information System (INIS)

    Kalli, H.J.; Cashwell, E.D.

    1977-09-01

    Three Monte Carlo estimation schemes were studied to avoid the difficulties caused by the (1/r 2 ) singularity in the expression of the normal next-event estimator (NEE) for the flux at a point. A new, fast, once-more collided flux estimator (OMCFE) scheme, based on a very simple probability density function (p.d.f.) of the distance to collision in the selection of the intermediate collision points, is proposed. This kind of p.d.f. of the collision distance is used in two nonanalog schemes using the NEE. In these two schemes, which have principal similarities to some schemes proposed earlier in the literature, the (1/r 2 ) singularity is canceled by incorporating the singularity into the p.d.f. of the collision points. This is achieved by playing a suitable nonanalog game in the neighborhood of the detector points. The three schemes were tested in a monoenergetic, homogeneous infinite-medium problem, then were evaluated in a point-cross-section problem by using the Monte Carlo code MCNG. 10 figures

  9. 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...

  10. 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.

  11. Numerical Solutions of Singularly Perturbed Reaction Diffusion Equation with Sobolev Gradients

    Directory of Open Access Journals (Sweden)

    Nauman Raza

    2013-01-01

    Full Text Available Critical points related to the singular perturbed reaction diffusion models are calculated using weighted Sobolev gradient method in finite element setting. Performance of different Sobolev gradients has been discussed for varying diffusion coefficient values. A comparison is shown between the weighted and unweighted Sobolev gradients in two and three dimensions. The superiority of the method is also demonstrated by showing comparison with Newton's method.

  12. An analysis method for fatigue crack initiation on geometrical singularities

    International Nuclear Information System (INIS)

    Amzallag, C.; Bernard, J.L.; Pellissier-Tanon, A.; Vassal, J.M.

    1982-05-01

    For studying the significance of defects a promising point of view is to separate fatigue crack initiation and propagation. Comparing the works done on these two stages it appears that relatively few has been done on the first one. This presentation shows how this stage can be evaluated by using appropriate criteria. The validation of a criterion through experimental data obtained on actual and simulated singularities for different specimen geometries is presented

  13. 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.

  14. 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.

  15. Solution of Point Reactor Neutron Kinetics Equations with Temperature Feedback by Singularly Perturbed Method

    Directory of Open Access Journals (Sweden)

    Wenzhen Chen

    2013-01-01

    Full Text Available The singularly perturbed method (SPM is proposed to obtain the analytical solution for the delayed supercritical process of nuclear reactor with temperature feedback and small step reactivity inserted. The relation between the reactivity and time is derived. Also, the neutron density (or power and the average density of delayed neutron precursors as the function of reactivity are presented. The variations of neutron density (or power and temperature with time are calculated and plotted and compared with those by accurate solution and other analytical methods. It is shown that the results by the SPM are valid and accurate in the large range and the SPM is simpler than those in the previous literature.

  16. 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.

  17. Gravitational field of massive point particle in general relativity

    International Nuclear Information System (INIS)

    Fiziev, P.P.

    2003-10-01

    Using various gauges of the radial coordinate we give a description of the static spherically symmetric space-times with point singularity at the center and vacuum outside the singularity. We show that in general relativity (GR) there exist infinitely many such solutions to the Einstein equations which are physically different and only some of them describe the gravitational field of a single massive point particle. In particular, we show that the widespread Hilbert's form of Schwarzschild solution does not solve the Einstein equations with a massive point particle's stress-energy tensor. Novel normal coordinates for the field and a new physical class of gauges are proposed, in this way achieving a correct description of a point mass source in GR. We also introduce a gravitational mass defect of a point particle and determine the dependence of the solutions on this mass defect. In addition we give invariant characteristics of the physically and geometrically different classes of spherically symmetric static space-times created by one point mass. (author)

  18. 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

  19. 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.

  20. 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.

  1. Quantum critical singularities in two-dimensional metallic XY ferromagnets

    Science.gov (United States)

    Varma, Chandra M.; Gannon, W. J.; Aronson, M. C.; Rodriguez-Rivera, J. A.; Qiu, Y.

    2018-02-01

    An important problem in contemporary physics concerns quantum-critical fluctuations in metals. A scaling function for the momentum, frequency, temperature, and magnetic field dependence of the correlation function near a 2D-ferromagnetic quantum-critical point (QCP) is constructed, and its singularities are determined by comparing to the recent calculations of the correlation functions of the dissipative quantum XY model (DQXY). The calculations are motivated by the measured properties of the metallic compound YFe2Al10 , which is a realization of the DQXY model in 2D. The frequency, temperature, and magnetic field dependence of the scaling function as well as the singularities measured in the experiments are given by the theory without adjustable exponents. The same model is applicable to the superconductor-insulator transitions, classes of metallic AFM-QCPs, and as fluctuations of the loop-current ordered state in hole-doped cuprates. The results presented here lend credence to the solution found for the 2D-DQXY model and its applications in understanding quantum-critical properties of diverse systems.

  2. The three-point function in split dimensional regularization in the Coulomb gauge

    CERN Document Server

    Leibbrandt, G

    1998-01-01

    We use a gauge-invariant regularization procedure, called ``split dimensional regularization'', to evaluate the quark self-energy $\\Sigma (p)$ and quark-quark-gluon vertex function $\\Lambda_\\mu (p^\\prime,p)$ in the Coulomb gauge, $\\vec{\\bigtriangledown}\\cdot\\vec{A}^a = 0$. The technique of split dimensional regularization was designed to regulate Coulomb-gauge Feynman integrals in non-Abelian theories. The technique which is based on two complex regulating parameters, $\\omega$ and $\\sigma$, is shown to generate a well-defined set of Coulomb-gauge integrals. A major component of this project deals with the evaluation of four-propagator and five-propagator Coulomb integrals, some of which are nonlocal. It is further argued that the standard one-loop BRST identity relating $\\Sigma$ and $\\Lambda_\\mu$, should by rights be replaced by a more general BRST identity which contains two additional contributions from ghost vertex diagrams. Despite the appearance of nonlocal Coulomb integrals, both $\\Sigma$ and $\\Lambda_\\...

  3. Theory of motion for monopole-dipole singularities of classical Yang-Mills-Higgs fields. I. Laws of motion

    International Nuclear Information System (INIS)

    Drechsler, W.; Havas, P.; Rosenblum, A.

    1984-01-01

    In two recent papers, the general form of the laws of motion for point particles which are multipole sources of the classical coupled Yang-Mills-Higgs fields was determined by Havas, and for the special case of monopole singularities of a Yang-Mills field an iteration procedure was developed by Drechsler and Rosenblum to obtain the equations of motion of mass points, i.e., the laws of motion including the explicit form of the fields of all interacting particles. In this paper we give a detailed derivation of the laws of motion of monopole-dipole singularities of the coupled Yang-Mills-Higgs fields for point particles with mass and spin, following a procedure first applied by Mathisson and developed by Havas. To obtain the equations of motion, a systematic approximation method is developed in the following paper for the solution of the nonlinear field equations and determination of the fields entering the laws of motion found here to any given order in the coupling constant g

  4. 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

  5. Hierarchical regular small-world networks

    International Nuclear Information System (INIS)

    Boettcher, Stefan; Goncalves, Bruno; Guclu, Hasan

    2008-01-01

    Two new networks are introduced that resemble small-world properties. These networks are recursively constructed but retain a fixed, regular degree. They possess a unique one-dimensional lattice backbone overlaid by a hierarchical sequence of long-distance links, mixing real-space and small-world features. Both networks, one 3-regular and the other 4-regular, lead to distinct behaviors, as revealed by renormalization group studies. The 3-regular network is planar, has a diameter growing as √N with system size N, and leads to super-diffusion with an exact, anomalous exponent d w = 1.306..., but possesses only a trivial fixed point T c = 0 for the Ising ferromagnet. In turn, the 4-regular network is non-planar, has a diameter growing as ∼2 √(log 2 N 2 ) , exhibits 'ballistic' diffusion (d w = 1), and a non-trivial ferromagnetic transition, T c > 0. It suggests that the 3-regular network is still quite 'geometric', while the 4-regular network qualifies as a true small world with mean-field properties. As an engineering application we discuss synchronization of processors on these networks. (fast track communication)

  6. Regularization dependence on phase diagram in Nambu–Jona-Lasinio model

    International Nuclear Information System (INIS)

    Kohyama, H.; Kimura, D.; Inagaki, T.

    2015-01-01

    We study the regularization dependence on meson properties and the phase diagram of quark matter by using the two flavor Nambu–Jona-Lasinio model. The model also has the parameter dependence in each regularization, so we explicitly give the model parameters for some sets of the input observables, then investigate its effect on the phase diagram. We find that the location or the existence of the critical end point highly depends on the regularization methods and the model parameters. Then we think that regularization and parameters are carefully considered when one investigates the QCD critical end point in the effective model studies

  7. 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)

  8. 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.

  9. 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.

  10. 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.

  11. 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 ...

  12. 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.)

  13. 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)

  14. 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.

  15. 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

  16. Cyclic multiverses

    Science.gov (United States)

    Marosek, Konrad; Dąbrowski, Mariusz P.; Balcerzak, Adam

    2016-09-01

    Using the idea of regularization of singularities due to the variability of the fundamental constants in cosmology we study the cyclic universe models. We find two models of oscillating and non-singular mass density and pressure (`non-singular' bounce) regularized by varying gravitational constant G despite the scale factor evolution is oscillating and having sharp turning points (`singular' bounce). Both violating (big-bang) and non-violating (phantom) null energy condition models appear. Then, we extend this idea on to the multiverse containing cyclic individual universes with either growing or decreasing entropy though leaving the net entropy constant. In order to get an insight into the key idea, we consider the doubleverse with the same geometrical evolution of the two `parallel' universes with their physical evolution [physical coupling constants c(t) and G(t)] being different. An interesting point is that there is a possibility to exchange the universes at the point of maximum expansion - the fact which was already noticed in quantum cosmology. Similar scenario is also possible within the framework of Brans-Dicke theory where varying G(t) is replaced by the dynamical Brans-Dicke field φ(t) though these theories are slightly different.

  17. 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)

  18. Hamilton-Jacobi theorems for regular reducible Hamiltonian systems on a cotangent bundle

    Science.gov (United States)

    Wang, Hong

    2017-09-01

    In this paper, some of formulations of Hamilton-Jacobi equations for Hamiltonian system and regular reduced Hamiltonian systems are given. At first, an important lemma is proved, and it is a modification for the corresponding result of Abraham and Marsden (1978), such that we can prove two types of geometric Hamilton-Jacobi theorem for a Hamiltonian system on the cotangent bundle of a configuration manifold, by using the symplectic form and dynamical vector field. Then these results are generalized to the regular reducible Hamiltonian system with symmetry and momentum map, by using the reduced symplectic form and the reduced dynamical vector field. The Hamilton-Jacobi theorems are proved and two types of Hamilton-Jacobi equations, for the regular point reduced Hamiltonian system and the regular orbit reduced Hamiltonian system, are obtained. As an application of the theoretical results, the regular point reducible Hamiltonian system on a Lie group is considered, and two types of Lie-Poisson Hamilton-Jacobi equation for the regular point reduced system are given. In particular, the Type I and Type II of Lie-Poisson Hamilton-Jacobi equations for the regular point reduced rigid body and heavy top systems are shown, respectively.

  19. 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

  20. 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

  1. Criteria for the singularity of a pairwise l1-distance matrix and their generalizations

    International Nuclear Information System (INIS)

    D'yakonov, Alexander G

    2012-01-01

    We study the singularity problem for the pairwise distance matrix of a system of points, as well as generalizations of this problem that are connected with applications to interpolation theory and with an algebraic approach to recognition problems. We obtain necessary and sufficient conditions on a system under which the dimension of the range space of polynomials of bounded degree over the columns of the distance matrix is less than the number of points in the system.

  2. 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).

  3. 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)

  4. The Conical Singularity and Quantum Corrections to Entropy of Black Hole

    International Nuclear Information System (INIS)

    Solodukhin, S.N.

    1994-01-01

    It is well known that at the temperature different from the Hawking temperature there appears a conical singularity in the Euclidean classical solution of gravitational equations. The method of regularizing the cone by regular surface is used to determine the curvature tensors for such metrics. It allows to calculate the one-loop matter effective action and the corresponding one-loop quantum corrections to the entropy in the framework of the path integral approach of Gibbons and Hawking. The two-dimensional and four-dimensional cases are considered. The entropy of the Rindler space is shown to be divergent logarithmically in two dimensions and quadratically in four dimensions. It corresponds to the results obtained earlier. For the eternal 2D black hole we observe finite, dependent on the mass, correction to the entropy. The entropy of the 4D Schwarzschild black hole is shown to possess an additional (in comparison to the 4D Rindler space) logarithmically divergent correction which does not vanish in the limit of infinite mass of the black hole. We argue that infinities of the entropy in four dimensions are renormalized with the renormalization of the gravitational coupling. (author). 35 refs

  5. Geometric perspective on singularity resolution and uniqueness in loop quantum cosmology

    International Nuclear Information System (INIS)

    Corichi, Alejandro; Singh, Parampreet

    2009-01-01

    We reexamine the issue of singularity resolution in homogeneous loop quantum cosmology from the perspective of geometrical entities such as expansion rate and the shear scalar. These quantities are very reliable measures of the properties of spacetime and can be defined not only at the classical and effective level, but also at an operator level in the quantum theory. From their behavior in the effective constraint surface and in the effective loop quantum spacetime, we show that one can severely restrict the ambiguities in regularization of the quantum constraint and rule out unphysical choices. We analyze this in the flat isotropic model and the Bianchi-I spacetimes. In the former case we show that the expansion rate is absolutely bounded only for the so-called improved quantization, a result which synergizes with uniqueness of this quantization as proved earlier. Surprisingly, for the Bianchi-I spacetime, we show that out of the available choices, the expansion rate and shear are bounded for only one regularization of the quantum constraint. It turns out that only for this choice, the theory exhibits quantum gravity corrections at a unique scale, and is physically viable.

  6. 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.

  7. 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

  8. 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 ...

  9. 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.

  10. 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.

  11. A singular one-parameter family of solutions in cubic superstring field theory

    Energy Technology Data Exchange (ETDEWEB)

    Arroyo, E. Aldo [Centro de Ciências Naturais e Humanas, Universidade Federal do ABC, Santo André, 09210-170 São Paulo, SP (Brazil)

    2016-05-03

    Performing a gauge transformation of a simple identity-like solution of superstring field theory, we construct a one-parameter family of solutions, and by evaluating the energy associated to this family, we show that for most of the values of the parameter the solution represents the tachyon vacuum, except for two isolated singular points where the solution becomes the perturbative vacuum and the half brane solution.

  12. 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

  13. 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.

  14. Singularities of the transmission coefficient and anomalous scattering by a dielectric slab

    Science.gov (United States)

    Shestopalov, Yury

    2018-03-01

    We prove the existence and describe the distribution on the complex plane of the singularities, resonant states (RSs), of the transmission coefficient in the problem of the plane wave scattering by a parallel-plate dielectric slab in free space. It is shown that the transmission coefficient has isolated poles all with nonzero imaginary parts that form countable sets in the complex plane of the refraction index or permittivity of the slab with the only accumulation point at infinity. The transmission coefficient never vanishes and anomalous scattering, when its modulus exceeds unity, occurs at arbitrarily small loss of the dielectric filling the layer. These results are extended to the cases of scattering by arbitrary multi-layer parallel-plane media. Connections are established between RSs, spectral singularities, eigenvalues of the associated Sturm-Liouville problems on the line, and zeros of the corresponding Jost function.

  15. 7 CFR 1200.50 - 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. 1200.50 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...

  16. 7 CFR 900.1 - 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. 900.1 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...

  17. 7 CFR 900.100 - 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. 900.100 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...

  18. 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...

  19. 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

  20. 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.)

  1. On Absence of Pure Singular Spectrum of Random Perturbations and in Anderson Model at Low Disorde

    CERN Document Server

    Grinshpun, V

    2006-01-01

    Absence of singular component, with probability one, in the conductivity spectra of bounded random perturbations of multidimensional finite-difference Hamiltonians, is for the first time rigorously established under certain conditions ensuring either absence of pure point, or absence of pure absolutely continuous component in the corresponding regions of spectra. The main technical tool applied is the theory of rank-one perturbations of singular spectra. The respective new result (the non-mixing property) is applied to establish existence and bounds of the (non-empty) pure absolutely continuous component in the spectrum of the Anderson model with bounded random potential in dimension 2 at low disorder. The new (1999) result implies, via the trace-class perturbation analysis, the Anderson model with the unbounded potential to have only pure point spectrum (complete system of localized wave-functions) with probability one in arbitrary dimension. The new technics, based on the resolvent reduction formula, and ex...

  2. 7 CFR 900.20 - 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. 900.20 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...

  3. 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...

  4. Structure-Based Low-Rank Model With Graph Nuclear Norm Regularization for Noise Removal.

    Science.gov (United States)

    Ge, Qi; Jing, Xiao-Yuan; Wu, Fei; Wei, Zhi-Hui; Xiao, Liang; Shao, Wen-Ze; Yue, Dong; Li, Hai-Bo

    2017-07-01

    Nonlocal image representation methods, including group-based sparse coding and block-matching 3-D filtering, have shown their great performance in application to low-level tasks. The nonlocal prior is extracted from each group consisting of patches with similar intensities. Grouping patches based on intensity similarity, however, gives rise to disturbance and inaccuracy in estimation of the true images. To address this problem, we propose a structure-based low-rank model with graph nuclear norm regularization. We exploit the local manifold structure inside a patch and group the patches by the distance metric of manifold structure. With the manifold structure information, a graph nuclear norm regularization is established and incorporated into a low-rank approximation model. We then prove that the graph-based regularization is equivalent to a weighted nuclear norm and the proposed model can be solved by a weighted singular-value thresholding algorithm. Extensive experiments on additive white Gaussian noise removal and mixed noise removal demonstrate that the proposed method achieves a better performance than several state-of-the-art algorithms.

  5. 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)

  6. 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.

  7. 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)

  8. Singular value decomposition analysis of a photoacoustic imaging system and 3D imaging at 0.7 FPS.

    Science.gov (United States)

    Roumeliotis, Michael B; Stodilka, Robert Z; Anastasio, Mark A; Ng, Eldon; Carson, Jeffrey J L

    2011-07-04

    Photoacoustic imaging is a non-ionizing imaging modality that provides contrast consistent with optical imaging techniques while the resolution and penetration depth is similar to ultrasound techniques. In a previous publication [Opt. Express 18, 11406 (2010)], a technique was introduced to experimentally acquire the imaging operator for a photoacoustic imaging system. While this was an important foundation for future work, we have recently improved the experimental procedure allowing for a more densely populated imaging operator to be acquired. Subsets of the imaging operator were produced by varying the transducer count as well as the measurement space temporal sampling rate. Examination of the matrix rank and the effect of contributing object space singular vectors to image reconstruction were performed. For a PAI system collecting only limited data projections, matrix rank increased linearly with transducer count and measurement space temporal sampling rate. Image reconstruction using a regularized pseudoinverse of the imaging operator was performed on photoacoustic signals from a point source, line source, and an array of point sources derived from the imaging operator. As expected, image quality increased for each object with increasing transducer count and measurement space temporal sampling rate. Using the same approach, but on experimentally sampled photoacoustic signals from a moving point-like source, acquisition, data transfer, reconstruction and image display took 1.4 s using one laser pulse per 3D frame. With relatively simple hardware improvements to data transfer and computation speed, our current imaging results imply that acquisition and display of 3D photoacoustic images at laser repetition rates of 10Hz is easily achieved.

  9. The focal boundary value problem for strongly singular higher-order nonlinear functional-differential equations

    Czech Academy of Sciences Publication Activity Database

    Mukhigulashvili, Sulkhan; Půža, B.

    2015-01-01

    Roč. 2015, January (2015), s. 17 ISSN 1687-2770 Institutional support: RVO:67985840 Keywords : higher order nonlinear functional-differential equations * two-point right-focal boundary value problem * strong singularity Subject RIV: BA - General Mathematics Impact factor: 0.642, year: 2015 http://link.springer.com/article/10.1186%2Fs13661-014-0277-1

  10. 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.)

  11. Singularity in the positive Hall coeffcient near pre-onset temperatures in high-Tc superconductors

    Science.gov (United States)

    Vezzoli, G. C.; Chen, M. F.; Craver, F.; Moon, B. M.; Safari, A.; Burke, T.; Stanley, W.

    1990-10-01

    Hall measurements using continuous extremely slow cooling and reheating rates as well as employing eqiulibrium point-by-point conventional techniques reveals a clear anomally in RH at pre-onset temperatures near Tc in polycrystalline samples Y1Ba2Cu3O7 and Bi2Sr2Ca2Cu3O10. The anomaly has the appearance of a singularity of Dirac-delta function which parallels earlier work on La1-xSrxCuO4. Recent single crystal work on the Bi-containing high-Tc superconductor is in accord with a clearcut anomaly. The singularity is tentatively interpreted to be associated (upon cooling) with initially the removal of positive holes from the hopping conduction system of the normal state such as from the increased concentration of bound virtual excitons due to increased exciton and hole lifetimes at low temperature. Subsequently the formation of Cooper pairs by mediation from these centers (bound-holes) and/or bound excitons) may cause an ionization of these bound virtual excitons thereby re-introducing holes and electrons into the conduction system at Tc.

  12. A local-to-global singularity theorem for quantum field theory on curved space-time

    International Nuclear Information System (INIS)

    Radzikowski, M.J.; York Univ.

    1996-01-01

    We prove that if a reference two-point distribution of positive type on a time orientable curved space-time (CST) satisfies a certain condition on its wave front set (the ''class P M,g condition'') and if any other two-point distribution (i) is of positive type, (ii) has the same antisymmetric part as the reference modulo smooth function and (iii) has the same local singularity structure, then it has the same global singularity structure. In the proof we use a smoothing, positivity-preserving pseudo-differential operator the support of whose symbol is restricted to a certain conic region which depends on the wave front set of the reference state. This local-to-global theorem, together with results published elsewhere, leads to a verification of a conjecture by Kay that for quasi-free states of the Klein-Gordon quantum field on a globally hyperbolic CST, the local Hadamard condition implies the global Hadamard condition. A counterexample to the local-to-global theorem on a strip in Minkowski space is given when the class P M,g condition is not assumed. (orig.)

  13. 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...

  14. Triple Positive Solutions of a Nonlocal Boundary Value Problem for Singular Differential Equations with p-Laplacian

    Directory of Open Access Journals (Sweden)

    Jufang Wang

    2013-01-01

    Full Text Available We establish the existence of triple positive solutions of an m-point boundary value problem for the nonlinear singular second-order differential equations of mixed type with a p-Laplacian operator by Leggett-William fixed point theorem. At last, we give an example to demonstrate the use of the main result of this paper. The conclusions in this paper essentially extend and improve the known results.

  15. Fibonacci-regularization method for solving Cauchy integral equations of the first kind

    Directory of Open Access Journals (Sweden)

    Mohammad Ali Fariborzi Araghi

    2017-09-01

    Full Text Available In this paper, a novel scheme is proposed to solve the first kind Cauchy integral equation over a finite interval. For this purpose, the regularization method is considered. Then, the collocation method with Fibonacci base function is applied to solve the obtained second kind singular integral equation. Also, the error estimate of the proposed scheme is discussed. Finally, some sample Cauchy integral equations stem from the theory of airfoils in fluid mechanics are presented and solved to illustrate the importance and applicability of the given algorithm. The tables in the examples show the efficiency of the method.

  16. 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

  17. Orbital Maneuvers for Spacecrafts Travelling to/from the Lagrangian Points

    Science.gov (United States)

    Bertachini, A.

    ) Guess a final regularized time f and integrate the regularized equations of motion from 0 = 0 until f; iii) Check the final position rf obtained from the numerical integration with the prescribed final position and the final real time with the specified time of flight. If there is an agreement (difference less than a specified error allowed) the solution is found and the process can stop here. If there is no agreement, an increment in the initial guessed velocity Vi and in the guessed final regularized time is made and the process goes back to step i). The method used to find the increment in the guessed variables is the standard gradient method, as described in Press et. al., 1989. The routines available in this reference are also used in this research with minor modifications. After that this algorithm is implemented, the Lambert's three-body problem between the Earth and the Lagrangian points is solved for several values of the time of flight. Since the regularized system is used to solve this problem, there is no need to specify the final position of M3 as lying in an primary's parking orbit (to avoid the singularity). Then, to make a comparison with previous papers (Broucke, 1979 and Prado, 1996) the centre of the primary is used as the final position for M3. The results are organized in plots of the energy and the initial flight path angle (the control to be used) in the rotating frame against the time of flight. The definition of the angle is such that the zero is in the "x" axis, (pointing to the positive direction) and it increases in the counter-clock-wise sense. This problem, as well as the Lambert's original version, has two solutions for a given transfer time: one in the counter-clock-wise direction and one in the clock-wise direction in the inertial frame. In this paper, emphasis is given in finding the families with the smallest possible energy (and velocity), although many other families do exist. Broucke, R., (1979) Travelling Between the Lagrange

  18. Criteria for the singularity of a pairwise l{sub 1}-distance matrix and their generalizations

    Energy Technology Data Exchange (ETDEWEB)

    D' yakonov, Alexander G [M. V. Lomonosov Moscow State University, Faculty of Computational Mathematics and Cybernetics, Moscow (Russian Federation)

    2012-06-30

    We study the singularity problem for the pairwise distance matrix of a system of points, as well as generalizations of this problem that are connected with applications to interpolation theory and with an algebraic approach to recognition problems. We obtain necessary and sufficient conditions on a system under which the dimension of the range space of polynomials of bounded degree over the columns of the distance matrix is less than the number of points in the system.

  19. 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...

  20. A regularized vortex-particle mesh method for large eddy simulation

    Science.gov (United States)

    Spietz, H. J.; Walther, J. H.; Hejlesen, M. M.

    2017-11-01

    We present recent developments of the remeshed vortex particle-mesh method for simulating incompressible fluid flow. The presented method relies on a parallel higher-order FFT based solver for the Poisson equation. Arbitrary high order is achieved through regularization of singular Green's function solutions to the Poisson equation and recently we have derived novel high order solutions for a mixture of open and periodic domains. With this approach the simulated variables may formally be viewed as the approximate solution to the filtered Navier Stokes equations, hence we use the method for Large Eddy Simulation by including a dynamic subfilter-scale model based on test-filters compatible with the aforementioned regularization functions. Further the subfilter-scale model uses Lagrangian averaging, which is a natural candidate in light of the Lagrangian nature of vortex particle methods. A multiresolution variation of the method is applied to simulate the benchmark problem of the flow past a square cylinder at Re = 22000 and the obtained results are compared to results from the literature.

  1. A toy MCT model for multiple glass transitions: Double swallow tail singularity

    Energy Technology Data Exchange (ETDEWEB)

    Ryzhov, V.N. [Institute for High Pressure Physics, Russian Academy of Sciences, Troitsk 142190, Moscow region (Russian Federation); Moscow Institute of Physics and Technology, 141700 Moscow (Russian Federation); Tareyeva, E.E. [Institute for High Pressure Physics, Russian Academy of Sciences, Troitsk 142190, Moscow region (Russian Federation)

    2014-11-07

    We propose a toy model to describe in the frame of Mode Coupling Theory multiple glass transitions. The model is based on the postulated simple form for static structure factor as a sum of two delta-functions. This form makes it possible to solve the MCT equations in almost analytical way. The phase diagram is governed by two swallow tails resulting from two A{sub 4} singularities and includes liquid–glass transition and multiple glasses. The diagram has much in common with those of binary and quasibinary systems. - Highlights: • A simple toy model is proposed for description of glass–glass transitions. • The static structure factor of the model has the form of a sum of delta-functions. • The phase diagram contains A{sub 4} bifurcation singularities and A{sub 3} end points. • The results can be applied for the qualitative description of quasibinary systems.

  2. Application of Littlewood-Paley decomposition to the regularity of Boltzmann type kinetic equations

    International Nuclear Information System (INIS)

    EL Safadi, M.

    2007-03-01

    We study the regularity of kinetic equations of Boltzmann type.We use essentially Littlewood-Paley method from harmonic analysis, consisting mainly in working with dyadics annulus. We shall mainly concern with the homogeneous case, where the solution f(t,x,v) depends only on the time t and on the velocities v, while working with realistic and singular cross-sections (non cutoff). In the first part, we study the particular case of Maxwellian molecules. Under this hypothesis, the structure of the Boltzmann operator and his Fourier transform write in a simple form. We show a global C ∞ regularity. Then, we deal with the case of general cross-sections with 'hard potential'. We are interested in the Landau equation which is limit equation to the Boltzmann equation, taking in account grazing collisions. We prove that any weak solution belongs to Schwartz space S. We demonstrate also a similar regularity for the case of Boltzmann equation. Let us note that our method applies directly for all dimensions, and proofs are often simpler compared to other previous ones. Finally, we finish with Boltzmann-Dirac equation. In particular, we adapt the result of regularity obtained in Alexandre, Desvillettes, Wennberg and Villani work, using the dissipation rate connected with Boltzmann-Dirac equation. (author)

  3. 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

  4. 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...

  5. Matrix models, Argyres-Douglas singularities and double scaling limits

    International Nuclear Information System (INIS)

    Bertoldi, Gaetano

    2003-01-01

    We construct an N = 1 theory with gauge group U(nN) and degree n+1 tree level superpotential whose matrix model spectral curve develops an Argyres-Douglas singularity. The calculation of the tension of domain walls in the U(nN) theory shows that the standard large-N expansion breaks down at the Argyres-Douglas points, with tension that scales as a fractional power of N. Nevertheless, it is possible to define appropriate double scaling limits which are conjectured to yield the tension of 2-branes in the resulting N = 1 four dimensional non-critical string theories as proposed by Ferrari. (author)

  6. 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.

  7. 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.

  8. 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.

  9. Existence of Positive Solutions to Singular -Laplacian General Dirichlet Boundary Value Problems with Sign Changing Nonlinearity

    Directory of Open Access Journals (Sweden)

    Qiying Wei

    2009-01-01

    Full Text Available By using the well-known Schauder fixed point theorem and upper and lower solution method, we present some existence criteria for positive solution of an -point singular -Laplacian dynamic equation on time scales with the sign changing nonlinearity. These results are new even for the corresponding differential (=ℝ and difference equations (=ℤ, as well as in general time scales setting. As an application, an example is given to illustrate the results.

  10. 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)

  11. 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.

  12. 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.

  13. 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

  14. 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.

  15. 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.

  16. 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.

  17. UNFOLDED REGULAR AND SEMI-REGULAR POLYHEDRA

    Directory of Open Access Journals (Sweden)

    IONIŢĂ Elena

    2015-06-01

    Full Text Available This paper proposes a presentation unfolding regular and semi-regular polyhedra. Regular polyhedra are convex polyhedra whose faces are regular and equal polygons, with the same number of sides, and whose polyhedral angles are also regular and equal. Semi-regular polyhedra are convex polyhedra with regular polygon faces, several types and equal solid angles of the same type. A net of a polyhedron is a collection of edges in the plane which are the unfolded edges of the solid. Modeling and unfolding Platonic and Arhimediene polyhedra will be using 3dsMAX program. This paper is intended as an example of descriptive geometry applications.

  18. 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

  19. 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

  20. 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