Energy Technology Data Exchange (ETDEWEB)
Mesgarani, H; Parmour, P [Department of Mathematics, Shahid Rajaee University, Lavizan, Tehran (Iran, Islamic Republic of); Aghazadeh, N [Department of Applied Mathematics, Azarbaijan University of Tarbiat Moallem, Tabriz 53751 71379 (Iran, Islamic Republic of)], E-mail: hmesgarani@sru.ac.ir, E-mail: pparmour@yahoo.com, E-mail: aghazadeh@azaruniv.edu
2010-02-15
In this paper, we apply Aitken extrapolation and epsilon algorithm as acceleration technique for the solution of a weakly singular nonlinear Volterra integral equation of the second kind. In this paper, based on Tao and Yong (2006 J. Math. Anal. Appl. 324 225-37.) the integral equation is solved by Navot's quadrature formula. Also, Tao and Yong (2006) for the first time applied Richardson extrapolation to accelerating convergence for the weakly singular nonlinear Volterra integral equations of the second kind. To our knowledge, this paper may be the first attempt to apply Aitken extrapolation and epsilon algorithm for the weakly singular nonlinear Volterra integral equations of the second kind.
Zaika, Yury V.; Kostikova, Ekaterina K.
2017-11-01
One of the technological challenges for hydrogen materials science (including the ITER project) is the currently active search for structural materials with various potential applications that will have predetermined limits of hydrogen permeability. One of the experimental methods is thermal desorption spectrometry (TDS). A hydrogen-saturated sample is degassed under vacuum and monotone heating. The desorption flux is measured by mass spectrometer to determine the character of interactions of hydrogen isotopes with the solid. We are interested in such transfer parameters as the coefficients of diffusion, dissolution, desorption. The paper presents a thermal desorption functional differential equations of neutral type with integrable weak singularity and a numerical method for TDS spectrum simulation, where only integration of a nonlinear system of low order ordinary differential equations (ODE) is required. This work is supported by the Russian Foundation for Basic Research (project 15-01-00744).
Directory of Open Access Journals (Sweden)
Jing Shao
2014-01-01
Full Text Available Some new integral inequalities with weakly singular kernel for discontinuous functions are established using the method of successive iteration and properties of Mittag-Leffler function, which can be used in the qualitative analysis of the solutions to certain impulsive fractional differential systems.
Solving a Volterra integral equation with weakly singular kernel in the reproducing kernel space
Directory of Open Access Journals (Sweden)
Fazhan Geng
2010-06-01
Full Text Available In this paper, we will present a new method for a Volterra integralequation with weakly singular kernel in the reproducing kernel space. Firstly the equation is transformed into a new equivalent equation. Its exact solution is represented in the form of series in the reproducing kernel space. In the mean time, the n-term approximation $u_{n}(t$ to the exact solution $u(t$ is obtained. Some numerical examples are studied to demonstrate the accuracy of the present method. Results obtained by the method are compared with the exact solution of each example and are found to be in good agreement with each other.
Wazwaz, Abdul-Majid; Rach, Randolph; Duan, Jun-Sheng
2013-12-01
In this paper, we use the systematic modified Adomian decomposition method (ADM) and the phenomenon of the self-canceling "noise" terms for solving nonlinear weakly-singular Volterra, Fredholm, and Volterra-Fredholm integral equations. We show that the proposed approach minimizes the computation, when compared with other conventional schemes. Our results are validated by investigating several examples.
Multidimensional singular integrals and integral equations
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
Bliokh, Konstantin Yu; Niv, Avi; Kleiner, Vladimir; Hasman, Erez
2008-01-21
We describe the evolution of a paraxial electromagnetic wave characterizing by a non-uniform polarization distribution with singularities and propagating in a weakly anisotropic medium. Our approach is based on the Stokes vector evolution equation applied to a non-uniform initial polarization field. In the case of a homogeneous medium, this equation is integrated analytically. This yields a 3-dimensional distribution of the polarization parameters containing singularities, i.e. C-lines of circular polarization and L-surfaces of linear polarization. The general theory is applied to specific examples of the unfolding of a vectorial vortex in birefringent and dichroic media.
Numerical Quadrature of Periodic Singular Integral Equations
DEFF Research Database (Denmark)
Krenk, Steen
1978-01-01
This paper presents quadrature formulae for the numerical integration of a singular integral equation with Hilbert kernel. The formulae are based on trigonometric interpolation. By integration a quadrature formula for an integral with a logarithmic singularity is obtained. Finally it is demonstra......This paper presents quadrature formulae for the numerical integration of a singular integral equation with Hilbert kernel. The formulae are based on trigonometric interpolation. By integration a quadrature formula for an integral with a logarithmic singularity is obtained. Finally...... it is demonstrated how a singular integral equation with infinite support can be solved by use of the preceding formulae....
Singularity Preserving Numerical Methods for Boundary Integral Equations
Kaneko, Hideaki (Principal Investigator)
1996-01-01
In the past twelve months (May 8, 1995 - May 8, 1996), under the cooperative agreement with Division of Multidisciplinary Optimization at NASA Langley, we have accomplished the following five projects: a note on the finite element method with singular basis functions; numerical quadrature for weakly singular integrals; superconvergence of degenerate kernel method; superconvergence of the iterated collocation method for Hammersteion equations; and singularity preserving Galerkin method for Hammerstein equations with logarithmic kernel. This final report consists of five papers describing these projects. Each project is preceeded by a brief abstract.
Numerical methods for solution of singular integral equations
Boykov, I. V.
2016-01-01
This paper is devoted to overview of the authors works for numerical solution of singular integral equations (SIE), polysingular integral equations and multi-dimensional singular integral equations of the second kind. The authors investigated onsidered iterative - projective methods and parallel methods for solution of singular integral equations, polysingular integral equations and multi-dimensional singular integral equations. The paper is the second part of overview of the authors works de...
Numerical methods of computation of singular and hypersingular integrals
Directory of Open Access Journals (Sweden)
I. V. Boikov
2001-01-01
and technology one is faced with necessity of calculating different singular integrals. In analytical form calculation of singular integrals is possible only in unusual cases. Therefore approximate methods of singular integrals calculation are an active developing direction of computing in mathematics. This review is devoted to the optimal with respect to accuracy algorithms of the calculation of singular integrals with fixed singularity, Cauchy and Hilbert kernels, polysingular and many-dimensional singular integrals. The isolated section is devoted to the optimal with respect to accuracy algorithms of the calculation of the hypersingular integrals.
Shrinkage singularities of amplitudes and weak interaction cross- section asymptotic
Dolgov, A D; Okun, Lev Borisovich
1972-01-01
The so called shrinkage singularities of amplitudes caused by shrinkage of diffraction peak at asymptotically high energies are discussed given the condition that the amplitude singularities are not stronger than t/sup 2/ ln t (as is case for neutrino pair exchange diagrams) then total cross-section sigma /sub tot/ cannot increase faster at s to infinity than s/sup 1/3/. If shrinkage singularities are absent then sigma /sub tot/ cannot increase as any power of s. All the conclusions are valid, if the dispersion relations with finite number of subtractions exist at t
Algorithms for singularities and real structures of weak Del Pezzo surfaces
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.
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).
Existence of weak solutions to a nonlinear reaction-diffusion system with singular sources
Directory of Open Access Journals (Sweden)
Ida de Bonis
2017-09-01
Full Text Available We discuss the existence of a class of weak solutions to a nonlinear parabolic system of reaction-diffusion type endowed with singular production terms by reaction. The singularity is due to a potential occurrence of quenching localized to the domain boundary. The kind of quenching we have in mind is due to a twofold contribution: (i the choice of boundary conditions, modeling in our case the contact with an infinite reservoir filled with ready-to-react chemicals and (ii the use of a particular nonlinear, non-Lipschitz structure of the reaction kinetics. Our working techniques use fine energy estimates for approximating non-singular problems and uniform control on the set where singularities are localizing.
Double parton scattering singularity in one-loop integrals
Gaunt, Jonathan R.; Stirling, W. James
2011-06-01
We present a detailed study of the double parton scattering (DPS) singularity, which is a specific type of Landau singularity that can occur in certain one-loop graphs in theories with massless particles. A simple formula for the DPS singular part of a four-point diagram with arbitrary internal/external particles is derived in terms of the transverse momentum integral of a product of light cone wavefunctions with tree-level matrix elements. This is used to reproduce and explain some results for DPS singularities in box integrals that have been obtained using traditional loop integration techniques. The formula can be straightforwardly generalised to calculate the DPS singularity in loops with an arbitrary number of external particles. We use the generalised version to explain why the specific MHV and NMHV six-photon amplitudes often studied by the NLO multileg community are not divergent at the DPS singular point, and point out that whilst all NMHV amplitudes are always finite, certain MHV amplitudes do contain a DPS divergence. It is shown that our framework for calculating DPS divergences in loop diagrams is entirely consistent with the `two-parton GPD' framework of Diehl and Schafer for calculating proton-proton DPS cross sections, but is inconsistent with the `double PDF' framework of Snigirev.
Some BMO estimates for vector-valued multilinear singular integral ...
Indian Academy of Sciences (India)
In this paper, we prove some BMO end-point estimates for some vector-valued multilinear operators related to certain singular integral operators. Author Affiliations. Liu Lanzhe1. College of Mathematics and Computer, Changsha University of Science and Technology, Changsha 410077, People's Republic of China. Dates.
Mitsotakis, Dimitrios; Assylbekuly, Aydar; Zhakebaev, Dauren
2016-01-01
In this Letter we consider long capillary-gravity waves described by a fully nonlinear weakly dispersive model. First, using the phase space analysis methods we describe all possible types of localized travelling waves. Then, we especially focus on the critical regime, where the surface tension is exactly balanced by the gravity force. We show that our long wave model with a critical Bond number admits stable travelling wave solutions with a singular crest. These solutions are usually referred to in the literature as peakons or peaked solitary waves. They satisfy the usual speed-amplitude relation, which coincides with Scott-Russel's empirical formula for solitary waves, while their decay rate is the same regardless their amplitude. Moreover, they can be of depression or elevation type independent of their speed. The dynamics of these solutions are studied as well.
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.
Energy Technology Data Exchange (ETDEWEB)
Mitsotakis, Dimitrios, E-mail: dmitsot@gmail.com [Victoria University of Wellington, School of Mathematics, Statistics and Operations Research, PO Box 600, Wellington 6140 (New Zealand); Dutykh, Denys, E-mail: Denys.Dutykh@univ-savoie.fr [LAMA, UMR 5127 CNRS, Université Savoie Mont Blanc, Campus Scientifique, F-73376 Le Bourget-du-Lac Cedex (France); Assylbekuly, Aydar, E-mail: asylbekuly@mail.ru [Khoja Akhmet Yassawi International Kazakh–Turkish University, Faculty of Natural Science, Department of Mathematics, 161200 Turkestan (Kazakhstan); Zhakebayev, Dauren, E-mail: daurjaz@mail.ru [Al-Farabi Kazakh National University, Faculty of Mechanics and Mathematics, Department of Mathematical and Computer Modelling, 050000 Almaty (Kazakhstan)
2017-05-25
In this Letter we consider long capillary–gravity waves described by a fully nonlinear weakly dispersive model. First, using the phase space analysis methods we describe all possible types of localized travelling waves. Then, we especially focus on the critical regime, where the surface tension is exactly balanced by the gravity force. We show that our long wave model with a critical Bond number admits stable travelling wave solutions with a singular crest. These solutions are usually referred to in the literature as peakons or peaked solitary waves. They satisfy the usual speed-amplitude relation, which coincides with Scott–Russel's empirical formula for solitary waves, while their decay rate is the same regardless their amplitude. Moreover, they can be of depression or elevation type independent of their speed. The dynamics of these solutions are studied as well. - Highlights: • A model for long capillary–gravity weakly dispersive and fully nonlinear water waves is derived. • Shallow capillary–gravity waves are classified using phase plane analysis. • Peaked travelling waves are found in the critical regime. • The dynamics of peakons in Serre–Green–Naghdi equations is studied numerically.
Directory of Open Access Journals (Sweden)
Jin-Xiu Hu
2014-01-01
Full Text Available A new approach is presented for the numerical evaluation of arbitrary singular domain integrals. In this method, singular domain integrals are transformed into a boundary integral and a radial integral which contains singularities by using the radial integration method. The analytical elimination of singularities condensed in the radial integral formulas can be accomplished by expressing the nonsingular part of the integration kernels as a series of cubic B-spline basis functions of the distance r and using the intrinsic features of the radial integral. In the proposed method, singularities involved in the domain integrals are explicitly transformed to the boundary integrals, so no singularities exist at internal points. A few numerical examples are provided to verify the correctness and robustness of the presented method.
Singularities of n-fold integrals of the Ising class and the theory of elliptic curves
Boukraa, S.; Hassani, S.; Maillard, J.-M.; Zenine, N.
2007-09-01
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 + 4w2 = 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.
Modified Gauss rules for approximate calculation of some strongly singular integrals
Berriochoa Esnaola, Elias Manuel Maria; Cachafeiro López, María Alicia; Illán González, Jesús Ricardo; Rebollido Lorenzo, José Manuel
2013-01-01
The approach we follow consists in transforming the numerical evaluation of hyper-singular integrals into the calculation of a nearly singular integral whose mass is distributed according to a positive parameter ε. To evaluate the latter we apply a Gauss quadrature formula associated with a nearly singular weight function. It is estimated the error in terms of ε. Some numerical results are presented. Ministerio de Educación | Ref. MTM2011-22713
Mucha, Piotr B.; Peszek, Jan
2017-08-01
The Cucker-Smale flocking model belongs to a wide class of kinetic models that describe a collective motion of interacting particles that exhibit some specific tendency, e.g. to aggregate, flock or disperse. This paper examines the kinetic Cucker-Smale equation with a singular communication weight. Given a compactly supported measure as an initial datum we construct a global in time weak measure-valued solution in the space {C_{weak}(0,∞;M)} . The solution is defined as a mean-field limit of the empirical distributions of particles, the dynamics of which is governed by the Cucker-Smale particle system. The studied communication weight is {ψ(s)=|s|^{-α}} with {α \\in (0, 1/2)} . This range of singularity admits the sticking of characteristics/trajectories. The second result concerns the weak-atomic uniqueness property stating that a weak solution initiated by a finite sum of atoms, i.e. Dirac deltas in the form {m_i δ_{x_i} ⊗ δ_{v_i}} , preserves its atomic structure. Hence these coincide with unique solutions to the system of ODEs associated with the Cucker-Smale particle system.
Mucha, Piotr B.; Peszek, Jan
2018-01-01
The Cucker-Smale flocking model belongs to a wide class of kinetic models that describe a collective motion of interacting particles that exhibit some specific tendency, e.g. to aggregate, flock or disperse. This paper examines the kinetic Cucker-Smale equation with a singular communication weight. Given a compactly supported measure as an initial datum we construct a global in time weak measure-valued solution in the space {C_{weak}(0,∞M)}. The solution is defined as a mean-field limit of the empirical distributions of particles, the dynamics of which is governed by the Cucker-Smale particle system. The studied communication weight is {ψ(s)=|s|^{-α}} with {α \\in (0,1/2)}. This range of singularity admits the sticking of characteristics/trajectories. The second result concerns the weak-atomic uniqueness property stating that a weak solution initiated by a finite sum of atoms, i.e. Dirac deltas in the form {m_i δ_{x_i} ⊗ δ_{v_i}}, preserves its atomic structure. Hence these coincide with unique solutions to the system of ODEs associated with the Cucker-Smale particle system.
Multiple singular integrals and maximal operators related to homogeneous mappings
Directory of Open Access Journals (Sweden)
Feng Liu
2016-09-01
Full Text Available Abstract In this paper, we present the L p $L^{p}$ mapping properties of multiple singular integrals related to homogeneous mappings with rough kernels given by the radial function h ∈ Δ γ $h\\in\\Delta_{\\gamma}$ (or h ∈ U γ $h\\in U_{\\gamma}$ for some γ > 1 $\\gamma>1$ (or γ ≥ 1 $\\gamma\\geq1$ and the sphere function Ω ∈ L ( log + L 2 ( S m − 1 × S n − 1 $\\Omega\\in L(\\log^{+}L^{2} (S^{m-1}\\times S^{n-1}$ (or Ω ∈ L ( log + L 2 / γ ′ ( S m − 1 × S n − 1 $\\Omega\\in L(\\log^{+}L^{2/\\gamma'} (S^{m-1}\\times S^{n-1}$ . In addition, the L p $L^{p}$ bounds for the related maximal operators are also given. Our main results extend and improve some known ones.
Commutators of Singular Integral Operators Satisfying a Variant of a Lipschitz Condition
Directory of Open Access Journals (Sweden)
Pu Zhang
2014-01-01
Full Text Available Let T be a singular integral operator with its kernel satisfying |K(x-y-∑k=1ℓBk(xϕk(y|≤C|y|γ/|x-y|n+γ, |x|>2|y|>0, where Bk and ϕk (k=1,…,ℓ are appropriate functions and γ and C are positive constants. For b→=(b1,…,bm with bj∈BMO(ℝn, the multilinear commutator Tb→ generated by T and b→ is formally defined by Tb→f(x=∫ℝn∏j=1m(bj(x-bj(yK(x,yf(ydy. In this paper, the weighted Lp-boundedness and the weighted weak type LlogL estimate for the multilinear commutator Tb→ are established.
Energy Technology Data Exchange (ETDEWEB)
Chen, Ke [Univ. of Liverpool (United Kingdom)
1996-12-31
We study various preconditioning techniques for the iterative solution of boundary integral equations, and aim to provide a theory for a class of sparse preconditioners. Two related ideas are explored here: singularity separation and inverse approximation. Our preliminary conclusion is that singularity separation based preconditioners perform better than approximate inverse based while it is desirable to have both features.
On quadrature formulas for singular integral equations of the first and the second kind
DEFF Research Database (Denmark)
Krenk, Steen
1975-01-01
It is shown that by proper choice of the collocation points singular integral equations of the first and the second kind can be integrated by use of the usual Gauss-Jacobi quadrature formula. Detailed formulas are given for various values of the index....
Examples of integrable and non-integrable systems on singular symplectic manifolds
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.
Muskhelishvili, N I
2011-01-01
Singular integral equations play important roles in physics and theoretical mechanics, particularly in the areas of elasticity, aerodynamics, and unsteady aerofoil theory. They are highly effective in solving boundary problems occurring in the theory of functions of a complex variable, potential theory, the theory of elasticity, and the theory of fluid mechanics.This high-level treatment by a noted mathematician considers one-dimensional singular integral equations involving Cauchy principal values. Its coverage includes such topics as the Hölder condition, Hilbert and Riemann-Hilbert problem
PROPERTIES OF SINGULAR INTEGRAL OPERATORS Sα,β Let L2 ...
Indian Academy of Sciences (India)
18
⊥. 2 denotes the orthogonal complement of H2 in L2. Let P and Q denote the orthogonal projection of L2 onto. H2 and H2⊥ respectively. Thus P + Q = I, where I is the identity operator on L2. Let S be the singular integral operator defined by.
Nonlocal singular problem with integral condition for a second-order parabolic equation
Directory of Open Access Journals (Sweden)
Ahmed Lakhdar Marhoune
2015-03-01
Full Text Available We prove the existence and uniqueness of a strong solution for a parabolic singular equation in which we combine Dirichlet with integral boundary conditions given only on parts of the boundary. The proof uses a priori estimate and the density of the range of the operator generated by the problem considered.
Multilinear Singular and Fractional Integral Operators on Weighted Morrey Spaces
Directory of Open Access Journals (Sweden)
Hua Wang
2013-01-01
Full Text Available We will study the boundedness properties of multilinear Calderón-Zygmund operators and multilinear fractional integrals on products of weighted Morrey spaces with multiple weights.
Lukash, V N; Strokov, V N; 10.3367/UFNe.0182.201208k.0894
2012-01-01
We discuss status of the singularity problem in General Relativity and argue that the requirement that a physical solution must be completely free of singularities may be too strong. As an example, we consider properties of the integrable singularities and show that they represent light horizons separating T-regions of black and white holes. Connecting an astrophysical black hole to a white hole, they lead to a natural mechanism of generating new universes. Under favorable conditions the new universes will also contain black holes which, in their turn, will give rise to another generation of universes. In this case the cosmological evolutionary tree will continue to grow to form the "hyperverse". This scenario essentially differs from other known mechanisms, such as bounce, birth from "nothing", baby-universe scenario, etc.
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
Directory of Open Access Journals (Sweden)
Changyan Ran
2016-09-01
Full Text Available This paper presents a direct and non-singular approach based on an unscented Kalman filter (UKF for the integration of strapdown inertial navigation systems (SINSs with the aid of velocity. The state vector includes velocity and Euler angles, and the system model contains Euler angle kinematics equations. The measured velocity in the body frame is used as the filter measurement. The quaternion nonlinear equality constraint is eliminated, and the cross-noise problem is overcome. The filter model is simple and easy to apply without linearization. Data fusion is performed by an UKF, which directly estimates and outputs the navigation information. There is no need to process navigation computation and error correction separately because the navigation computation is completed synchronously during the filter time updating. In addition, the singularities are avoided with the help of the dual-Euler method. The performance of the proposed approach is verified by road test data from a land vehicle equipped with an odometer aided SINS, and a singularity turntable test is conducted using three-axis turntable test data. The results show that the proposed approach can achieve higher navigation accuracy than the commonly-used indirect approach, and the singularities can be efficiently removed as the result of dual-Euler method.
Geometries with integrable singularity -- black/white holes and astrogenic universes
Lukash, V. N.; Strokov, V. N.
2011-01-01
We briefly review the problem of generating cosmological flows of matter in GR (the genesis of universes), analyze models' shortcomings and their basic assumptions yet to be justified in physical cosmology. We propose a paradigm of cosmogenesis based on the class of spherically symmetric solutions with {\\it integrable} singularity $r=0$. They allow for geodesically complete geometries of black/white holes, which may comprise space-time regions with properties of cosmological flows.
El-Tom, M E A
1974-01-01
An arbitrarily high-order method for the approximate solution of singular Volterra integral equations of the second kind is presented. The approximate solution is a spline function of degree m, deficiency (m-1), i.e. in the continuity class C, and the method is of order m+1. For m=2 and 3 the method is modified so that the approximate solution is in C/sup 1/. Moreover, an investigation of numerical stability is given and it is shown that, while the above cited methods are numerically stable, methods using spline functions with full continuity are divergent for all m>or=3. (9 refs).
Directory of Open Access Journals (Sweden)
Ying Wang
2015-03-01
Full Text Available In this article, we study the existence of multiple positive solutions for singular semipositone boundary-value problem (BVP with integral boundary conditions on infinite intervals. By using the properties of the Green's function and the Guo-Krasnosel'skii fixed point theorem, we obtain the existence of multiple positive solutions under conditions concerning the nonlinear functions. The method in this article can be used for a large number of problems. We illustrate the validity of our results with an example in the last section.
Directory of Open Access Journals (Sweden)
Snezhana Georgieva Gocheva-Ilieva
2013-01-01
Full Text Available There are obtained integral form and recurrence representations for some Fourier series and connected with them Favard constants. The method is based on preliminary integration of Fourier series which permits to establish general recursion formulas for Favard constants. This gives the opportunity for effective summation of infinite series and calculation of some classes of multiple singular integrals by the Favard constants.
Directory of Open Access Journals (Sweden)
Uysal Gumrah
2016-01-01
Full Text Available In this paper we present some theorems concerning existence and Fatou type weighted pointwise convergence of nonlinear singular integral operators of the form: (Tλf(x=∫RKλ(t−x; f(tdt, x∈R, λ∈Λ$({T_\\lambda }f(x = \\int\\limits_R {{K_\\lambda }} (t - x;{\\rm{ }}f(tdt,{\\rm{ x}} \\in R,{\\rm{ }}\\lambda \\in \\Lambda $ where Λ ≠ ∅ is a set of non-negative indices, at a common generalized Lebesgue point of the functions f ∈ L1,ϕ (R and positive weight function φ. Here, L1,ϕ (R is the space of all measurable functions for which |fϕ|$\\left| {{f \\over \\phi }} \\right|$ is integrable on R.
Asymptotic expansions of the error for hyper-singular integrals with an interval variable
Directory of Open Access Journals (Sweden)
Chong Chen
2016-01-01
Full Text Available Abstract In this paper, we present high accuracy quadrature formulas for hyper-singular integrals ∫ a b g ( x q α ( x , t d x $\\int_{a}^{b}g(xq^{\\alpha}(x,t\\, dx$ , where q ( x , t = | x − t | $q(x,t=|x-t|$ (or x − t $x-t$ , t ∈ ( a , b $t\\in(a,b$ , and α ≤ − 1 $\\alpha\\leq-1$ (or α < − 1 $\\alpha<-1$ . If g ( x $g(x$ is 2 m + 1 $2m+1$ times differentiable on [ a , b ] $[a,b]$ , the asymptotic expansions of the error show that the convergence order is O ( h 2 μ + 1 + α $O(h^{2\\mu+1+\\alpha}$ with q ( x , t = | x − t | $q(x,t=|x-t|$ (or x − t $x-t$ for α ≤ − 1 $\\alpha\\leq-1$ (or α < − 1 $\\alpha<-1$ and α being non-integer, and the error power is O ( h η $O(h^{\\eta}$ with q ( x , t = x − t $q(x,t=x-t$ for α being integers less than −1, where η = min ( 2 μ , 2 μ + 2 + α $\\eta =\\min(2\\mu,2\\mu+2+\\alpha$ and μ = 1 , … , m $\\mu=1,\\ldots,m$ . Since the derivatives of the density function g ( x $g(x$ in the quadrature formulas can be eliminated by means of the extrapolation method, the formulas can easily be applied to solving corresponding hyper-singular boundary integral equations. The reliability and efficiency of the proposed formulas in this paper are demonstrated by some numerical examples.
Feischl, Michael; Gantner, Gregor; Haberl, Alexander; Praetorius, Dirk
2017-01-01
In a recent work (Feischl et al. in Eng Anal Bound Elem 62:141-153, 2016), we analyzed a weighted-residual error estimator for isogeometric boundary element methods in 2D and proposed an adaptive algorithm which steers the local mesh-refinement of the underlying partition as well as the multiplicity of the knots. In the present work, we give a mathematical proof that this algorithm leads to convergence even with optimal algebraic rates. Technical contributions include a novel mesh-size function which also monitors the knot multiplicity as well as inverse estimates for NURBS in fractional-order Sobolev norms.
Klaseboer, Evert; Sepehrirahnama, Shahrokh; Chan, Derek Y C
2017-08-01
The general space-time evolution of the scattering of an incident acoustic plane wave pulse by an arbitrary configuration of targets is treated by employing a recently developed non-singular boundary integral method to solve the Helmholtz equation in the frequency domain from which the space-time solution of the wave equation is obtained using the fast Fourier transform. The non-singular boundary integral solution can enforce the radiation boundary condition at infinity exactly and can account for multiple scattering effects at all spacings between scatterers without adverse effects on the numerical precision. More generally, the absence of singular kernels in the non-singular integral equation confers high numerical stability and precision for smaller numbers of degrees of freedom. The use of fast Fourier transform to obtain the time dependence is not constrained to discrete time steps and is particularly efficient for studying the response to different incident pulses by the same configuration of scatterers. The precision that can be attained using a smaller number of Fourier components is also quantified.
Energy Technology Data Exchange (ETDEWEB)
Fateev, V A [Laboratoire de Physique Mathematique, Universite Montpellier II, Pl. E. Bataillon, 34095 Montpellier (France); De Pietri, R [Dipartimento di Fisica, Universita di Parma, and INFN, Gruppo Collegato di Parma, 43100 Parma (Italy); Onofri, E [Dipartimento di Fisica, Universita di Parma, and INFN, Gruppo Collegato di Parma, 43100 Parma (Italy)
2004-11-26
A class of singular integral operators, encompassing two physically relevant cases arising in perturbative QCD and in classical fluid dynamics, is presented and analysed. It is shown that three special values of the parameters allow for an exact eigenfunction expansion; these can be associated with Riemannian symmetric spaces of rank 1 with positive, negative or vanishing curvature. For all other cases an accurate semiclassical approximation is derived, based on the identification of the operators with a peculiar Schroedinger-like operator.
FN approximation of the solution to a singular integral equation of classical reactor physics
Energy Technology Data Exchange (ETDEWEB)
Ganapol, B.D. [Department of Aerospace and Mechanical Engineering, University of Arizona, AME Building, Tucson, AZ 85721 (United States)]. E-mail: ganapol@ame.arizona.edu
2004-11-01
The iterated FN method is applied to a singular integral equation arising from a classical problem of reactor physics to determine the distribution of fissile material giving a spatially uniform flux. The FN iterations are accelerated toward convergence through the Wynn-algorithm - but first - Happy Birthday 'Fast Eddie' Larsen Why do I refer to the well known, most proper and exquisitely accomplished Edward W. Larsen as 'Fast Eddie'. Well our story begins in a small back bar room in the lobby of one of Los Alamos' finest and most luxurious hotels. Two young men were having a transport theoretic discussion while they were engaged in a serious game of pool with monetary benefits going to the winner. In addition, the two were sipping their most favorite lavation in rather large quantities - one, a short stocky man with thinning hair, was sipping to forget the cost of his recent divorce, and the other, a shorter stockier man also with thinning hair, was drinking, well because he liked to drink and it just made him silly. As they continued their transport discussion, one stocky man turned to the other and said, 'I wonder what 'Fast Eddie' Larsen would say to our transport question'. The other stocky man immediately thought the 'Fast Eddie' reference was to Paul Newman who played 'Fast Eddie', an expert at applied particle transport theory (a pool player) in the movie the Hustler and asked if indeed this was the case. The first stocky man said 'No. I call everyone with the name Ed 'Fast Eddie' ' - and that's the story of how 'Fast Eddie' Larsen got his name. Happy 60th Ed and thanks for all the great transport theory - from one of your biggest fans.
On a class of singular hyperbolic equation with a weighted integral condition
Directory of Open Access Journals (Sweden)
Said Mesloub
1999-01-01
for a class of second order singular hyperbolic equations. We prove the existence and uniqueness of a strong solution. The proof is based on a priori estimate and on the density of the range of the operator generated by the studied problem.
Directory of Open Access Journals (Sweden)
Jiqiang Jiang
2012-05-01
Full Text Available In this paper, the existence and multiplicity of positive solutions to singular fractional differential system is investigated. Sufficient conditions which guarantee the existence of positive solutions are obtained, by using a well known fixed point theorem. An example is added to illustrate the results.
Zimmerle, D.; Bernhard, R. J.
1985-01-01
An alternative method for performing singular boundary element integrals for applications in linear acoustics is discussed. The method separates the integral of the characteristic solution into a singular and nonsingular part. The singular portion is integrated with a combination of analytic and numerical techniques while the nonsingular portion is integrated with standard Gaussian quadrature. The method may be generalized to many types of subparametric elements. The integrals over elements containing the root node are considered, and the characteristic solution for linear acoustic problems are examined. The method may be generalized to most characteristic solutions.
Weak Lower Semicontinuity of Integral Functionals and Applications
Czech Academy of Sciences Publication Activity Database
Benešová, B.; Kružík, Martin
2017-01-01
Roč. 59, č. 4 (2017), s. 703-766 ISSN 0036-1445 R&D Projects: GA ČR GA14-15264S; GA ČR(CZ) GF16-34894L Grant - others:GA AV ČR(CZ) DAAD-16-14 Program:Bilaterální spolupráce Institutional support: RVO:67985556 Keywords : calculus of variations * weak lower semi-continuity Subject RIV: BA - General Mathematics Impact factor: 4.897, year: 2016 http:// library .utia.cas.cz/separaty/2017/MTR/kruzik-0481321.pdf
Integrated Urban System and Energy Consumption Model: Public and Singular Buildings
Directory of Open Access Journals (Sweden)
Rocco Papa
2014-05-01
Full Text Available The present paper illustrates the results of the first steps of a study on one aspect investigated as the preliminary step of the definition of the analysis - comprehension model of the relation between: city, buildings, and user behavior, for the reduction of energy consumption within the research project “Smart Energy Master” for the energetic governance of the territory (PON_MIUR n. pos. 04a2_00120 CUP Ricerca: E61H12000130005, at the Department of Civil, Building and Environmental Engineering - University of Naples Federico II, principal investigator prof. Carmela Gargiulo.Specifically the literary review aimed at determining if, and in what measure, the presence of public and singular buildings is present in the energy consumption estimate models, proposed by the scientific community, for the city or neighborhood scale.The difficulties in defining the weight of these singular buildings on the total energy consumption and the impossibility to define mean values that are significant for all subsets and different types as well as for each one, have forced model makers to either ignore them completely or chose a portion of this specific stock to include.
A singular ODE related to quasilinear elliptic equations
Directory of Open Access Journals (Sweden)
Luka Korkut
2000-02-01
Full Text Available We consider a quasilinear elliptic problem with the natural growth in the gradient. Existence, non-existence, uniqueness, and qualitative properties of positive solutions are obtained. We consider both weak and strong solutions. All results are based on the study of a suitable singular ODE of the first order. We also introduce a comparison principle for a class of nonlinear integral operators of Volterra type that enables to obtain uniqueness of weak solutions of the quasilinear equation.
On approximations of first integrals for a system of weakly nonlinear, coupled harmonic oscillators
Waluya, S.B.; van Horssen, W.T.
2001-01-01
In this paper a system of weakly nonlinear, coupled harmonic oscillators will be studied. It will be shown that the recently developed perturbation method based on integrating vectors can be used to approximate rst integrals and periodic solutions. To show how this perturbation method works the
Broer, H.; Hoveijn, I.; Lunter, G.; Vegter, G.
2003-01-01
The space of functions – or maps – is huge. Fortunately, many of its elements may be regarded as equivalent in a natural way, for example under right- or left-right transformations. Singularity theory studies how such equivalences foliate these spaces into a more manageable family of orbits of
Weak solvability of a hyperbolic integro-differential equation with integral condition
Directory of Open Access Journals (Sweden)
D. Belakroum
2011-06-01
Full Text Available By using the method of semidiscretization in time also called the Rothe's method, we prove the existence, uniqueness of the weak solution and its continuous dependence upon data, for an hyperbolic integro-differential equation with initial, Neumann and integral conditions.
The integral form of D = 3 Chern-Simons theories probing C{sup n}/Γ singularities
Energy Technology Data Exchange (ETDEWEB)
Fre, P. [Dipartimento di Fisica, Universita di Torino (Italy); INFN - Sezione di Torino (Italy); Arnold-Regge Center, Torino (Italy); National Research Nuclear University MEPhI, (Moscow Engineering Physics Institute), Moscow (Russian Federation); Grassi, P.A. [INFN - Sezione di Torino (Italy); Arnold-Regge Center, Torino (Italy); DISIT, Universita del Piemonte Orientale, Alessandria (Italy); Center for Gravitational Physics, Yukawa Institute for Theoretical Physics, Kyoto University (Japan)
2017-10-15
We consider D=3 supersymmetric Chern Simons gauge theories both from the point of view of their formal structure and of their applications to the AdS{sub 4}/CFT{sub 3} correspondence. From the structural view-point, we use the new formalism of integral forms in superspace that utilizes the rheonomic Lagrangians and the Picture Changing Operators, as an algorithmic tool providing the connection between different approaches to supersymmetric theories. We provide here the generalization to an arbitrary Kaehler manifold with arbitrary gauge group and arbitrary superpotential of the rheonomic lagrangian of D=3 matter coupled gauge theories constructed years ago. From the point of view of the AdS{sub 4}/CFT{sub 3} correspondence and more generally of M2-branes we emphasize the role of the Kaehler quotient data in determining the field content and the interactions of the Cherns Simons gauge theory when the transverse space to the brane is a non-compact Kaehler quotient K{sub 4} of some flat variety with respect to a suitable group. The crepant resolutions of C{sup n}/Γ singularities fall in this category. In the present paper we anticipate the general scheme how the geometrical data are to be utilized in the construction of the D=3 Chern-Simons Theory supposedly dual to the corresponding M2-brane solution. (copyright 2017 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)
Distress from Motivational Dis-integration: When Fundamental Motives Are Too Weak or Too Strong.
Cornwell, James F M; Franks, Becca; Higgins, E Tory
2016-01-01
Past research has shown that satisfying different kinds of fundamental motives contributes to well-being. More recently, advances in motivational theory have shown that z is also tied to the integration of different motives. In other words, well-being depends not only on maximizing effectiveness in satisfying specific motives, but also on ensuring that motives work together such that no individual motive is too weak or too strong. In this chapter, we review existing research to show that specific forms of psychological distress can be linked to specific types of motivational imbalance or dis-integration. Such disintegration can arise from either excessive weakness of a specific motive or the excessive strength and/or dominance of a specific motive, thereby inhibiting other motives. Possible neural correlates and avenues of intervention are discussed.
Power quality and integration of wind farms in weak grids in India
Energy Technology Data Exchange (ETDEWEB)
Soerensen, P.; Hauge Madsen, P. [Risoe National Lab., Roskilde (Denmark). Wind Energy and Atmospheric Physics Dept.; Vikkelsoe, A.; Koelbaek Jensen, K. [Danske Elvaerkers Forening Udredningsafdelingen (DEFU), Lyngby (Denmark); Fathima, K.A.; Unnikrishnan, A.K.
2000-04-01
This is the final report of a joint Danish and Indian project' Power Quality and Integration of Wind Farms in Weak Grids'. The power quality issues have been studied and analysed with the Indian conditions as a case. On the basis of meetings with Danish wind turbine industry, Indian electricity boards, nodal agencies, wind turbine industry and authorities, the critical power quality as-pects in India have been identified. Measurements on selected wind farms and wind turbines have quantified the power quality, and analyses of power quality issues, especially reactive power compensation, have been performed. Based on measurements and analyses, preliminary recommendations for grid integration of wind turbines in weak grids have been formulated. (au)
Weak convergence of the function-indexed integrated periodogram for infinite variance processes
DEFF Research Database (Denmark)
Can, Umut; Mikosch, Thomas Valentin; Samorodnitsky, Gennady
2010-01-01
), entropy conditions are needed for α ∈ [1, 2) to ensure the tightness of the sequence of integrated periodograms indexed by functions. The results of this paper are of additional interest since they provide limit results for infinite mean random quadratic forms with particular Toeplitz coefficient matrices.......In this paper, we study the weak convergence of the integrated periodogram indexed by classes of functions for linear processes with symmetric α-stable innovations. Under suitable summability conditions on the series of the Fourier coefficients of the index functions, we show that the weak limits...... constitute α-stable processes which have representations as infinite Fourier series with i.i.d. α-stable coefficients. The cases α ∈ (0, 1) and α ∈ [1, 2) are dealt with by rather different methods and under different assumptions on the classes of functions. For example, in contrast to the case α ∈ (0, 1...
Classical integrability for three-point functions: cognate structure at weak and strong couplings
Energy Technology Data Exchange (ETDEWEB)
Kazama, Yoichi [Research Center for Mathematical Physics, Rikkyo University,Toshima-ku, Tokyo 171-8501 (Japan); Quantum Hadron Physics Laboratory, RIKEN Nishina Center, Wako 351-0198 (Japan); Institute of Physics, University of Tokyo, Komaba, Meguro-ku, Tokyo 153-8902 (Japan); Komatsu, Shota [Perimeter Institute for Theoretical Physics,31 Caroline Street North, Waterloo, Ontario, N2L 2Y5 (Canada); Nishimura, Takuya [Institute of Physics, University of Tokyo, Komaba, Meguro-ku, Tokyo 153-8902 (Japan)
2016-10-10
In this paper, we develop a new method of computing three-point functions in the SU(2) sector of the N=4 super Yang-Mills theory in the semi-classical regime at weak coupling, which closely parallels the strong coupling analysis. The structure threading two disparate regimes is the so-called monodromy relation, an identity connecting the three-point functions with and without the insertion of the monodromy matrix. We shall show that this relation can be put to use directly for the semi-classical regime, where the dynamics is governed by the classical Landau-Lifshitz sigma model. Specifically, it reduces the problem to a set of functional equations, which can be solved once the analyticity in the spectral parameter space is specified. To determine the analyticity, we develop a new universal logic applicable at both weak and strong couplings. As a result, compact semi-classical formulas are obtained for a general class of three-point functions at weak coupling including the ones whose semi-classical behaviors were not known before. In addition, the new analyticity argument applied to the strong coupling analysis leads to a modification of the integration contour, producing the results consistent with the recent hexagon bootstrap approach. This modification also makes the Frolov-Tseytlin limit perfectly agree with the weak coupling form.
Power quality and integration of wind farms in weak grids in India
DEFF Research Database (Denmark)
Sørensen, Poul Ejnar; Madsen, Peter Hauge; Vikkelsø, A.
2000-01-01
This is the final report of a joint Danish and Indian project "Power Quality and Integration of Wind Farms in Weak Grids". The power quality issues have been studied and analysed with the Indian conditions as a case. On the basis of meetings with Danishwind turbine industry, Indian electricity...... boards, nodal agencies, wind turbine industry and authorities, the critical power quality as-pects in India have been identified. Measurements on selected wind farms and wind turbines have quantified the powerquality, and analyses of power quality issues, especially reactive power compensation, have been...
Directory of Open Access Journals (Sweden)
Xuemei Zhang
2014-01-01
Full Text Available This paper investigates the expression and properties of Green’s function for a second-order singular boundary value problem with integral boundary conditions and delayed argument -x′′t-atx′t+btxt=ωtft, xαt, t∈0, 1; x′0=0, x1-∫01htxtdt=0, where a∈0, 1, 0, +∞, b∈C0, 1, 0, +∞ and, ω may be singular at t=0 or/and at t=1. Furthermore, several new and more general results are obtained for the existence of positive solutions for the above problem by using Krasnosel’skii’s fixed point theorem. We discuss our problems with a delayed argument, which may concern optimization issues of some technical problems. Moreover, the approach to express the integral equation of the above problem is different from earlier approaches. Our results cover a second-order boundary value problem without deviating arguments and are compared with some recent results.
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.
Symplectic linearization of singular Lagrangian foliations in M4
Currás-Bosch, Carlos; Miranda, Eva
2003-01-01
We prove that the singular Lagrangian foliation of a 2-degree of freedom integrable Hamiltonian system, is symplectically equivalent to the linearized foliation in a neighbourhood of a non-degenerate singular orbit.
Timelike Constant Mean Curvature Surfaces with Singularities
DEFF Research Database (Denmark)
Brander, David; Svensson, Martin
2014-01-01
We use integrable systems techniques to study the singularities of timelike non-minimal constant mean curvature (CMC) surfaces in the Lorentz–Minkowski 3-space. The singularities arise at the boundary of the Birkhoff big cell of the loop group involved. We examine the behavior of the surfaces...
A depth-integrated model for weakly dispersive, turbulent, and rotational fluid flows
Kim, Dae-Hong; Lynett, Patrick J.; Socolofsky, Scott A.
A set of weakly dispersive Boussinesq-type equations, derived to include viscosity and vorticity terms in a physically consistent manner, is presented in conservative form. The model includes the approximate effects of bottom-induced turbulence, in a depth-integrated sense, as a second-order correction. Associated with this turbulence, vertical and horizontal rotational effects are captured. While the turbulence and horizontal vorticity models are simplified, a model with known physical limitations has been derived that includes the quadratic bottom friction term commonly added in an ad hoc manner to the inviscid equations. An interesting result of this derivation is that one should take care when adding such ad hoc models; it is clear from this exercise that (1) it is not necessary to do so - the terms can be included through a consistent derivation from the viscous primitive equations - and (2) one cannot properly add the quadratic bottom friction term without also adding a number of additional terms in the integrated governing equations. To solve these equations numerically, a highly accurate and stable model is developed. The numerical method uses a fourth-order MUSCL-TVD scheme to solve the leading order (shallow water) terms. For the dispersive terms, a cell averaged finite volume method is implemented. To verify the derived equations and the numerical model, four cases of verifications are given. First, solitary wave propagation is examined as a basic, yet fundamental, test of the models ability to predict dispersive and nonlinear wave propagation with minimal numerical error. Vertical velocity distributions of spatially uniform flows are compared with existing theory to investigate the effects of the newly included horizontal vorticity terms. Other test cases include comparisons with experiments that generate strong vorticity by the change of bottom bathymetry as well as by tidal jets through inlet structures. Very reasonable agreements are observed for the
Singular Isotonic Oscillator, Supersymmetry and Superintegrability
Directory of Open Access Journals (Sweden)
Ian Marquette
2012-09-01
Full Text Available In the case of a one-dimensional nonsingular Hamiltonian H and a singular supersymmetric partner H_a, the Darboux and factorization relations of supersymmetric quantum mechanics can be only formal relations. It was shown how we can construct an adequate partner by using infinite barriers placed where are located the singularities on the real axis and recover isospectrality. This method was applied to superpartners of the harmonic oscillator with one singularity. In this paper, we apply this method to the singular isotonic oscillator with two singularities on the real axis. We also applied these results to four 2D superintegrable systems with second and third-order integrals of motion obtained by Gravel for which polynomial algebras approach does not allow to obtain the energy spectrum of square integrable wavefunctions. We obtain solutions involving parabolic cylinder functions.
Stonesifer, R. B.; Atluri, S. N.
1982-01-01
The physical meaning of (Delta T)c and its applicability to creep crack growth are reviewed. Numerical evaluation of (Delta T)c and C(asterisk) is discussed with results being given for compact specimen and strip geometries. A moving crack-tip singularity, creep crack growth simulation procedure is described and demonstrated. The results of several crack growth simulation analyses indicate that creep crack growth in 304 stainless steel occurs under essentially steady-state conditions. Based on this result, a simple methodology for predicting creep crack growth behavior is summarized.
Singularity in Gravitational Collapse of Plane Symmetric Charged Vaidya Spacetime
Sharif, M
2010-01-01
We study the final outcome of gravitational collapse resulting from the plane symmetric charged Vaidya spacetime. Using the field equations, we show that the weak energy condition is always satisfied by collapsing fluid. It is found that the singularity formed is naked. The strength of singularity is also investigated by using Nolan's method. This turns out to be a strong curvature singularity in Tipler's sense and hence provides a counter example to the cosmic censorship hypothesis.
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.
Contracting singular horseshoe
Morales, C. A.; San Martín, B.
2017-11-01
We suggest a notion of hyperbolicity adapted to the geometric Rovella attractor (Robinson 2012 An Introduction to Dynamical Systems—Continuous and Discrete (Pure and Applied Undergraduate Texts vol 19) 2nd edn (Providence, RI: American Mathematical Society)) . More precisely, we call a partially hyperbolic set asymptotically sectional-hyperbolic if its singularities are hyperbolic and if its central subbundle is asymptotically sectional expanding outside the stable manifolds of the singularities. We prove that there are highly chaotic flows with Rovella-like singularities exhibiting this kind of hyperbolicity. We shall call them contracting singular horseshoes.
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...
Directory of Open Access Journals (Sweden)
Qian Lichang
2017-06-01
Full Text Available Space, time, and phase synchronization problems make weak target detection evenmore difficult in the Non-cooperative Passive Bistatic Radar (NPBR than in conventional radar systems. Therefore, a time and phase synchronization method based on direct waveform parameter estimation and a weak target detection method based on long time coherent integration of a multi-waveform is presented in this paper. First, a universal pulse extraction method based on differential sequence indexing is proposed. Second, an estimation method for the direct waveform parameters, including pulse width, pulse repetition intervals, bandwidth, carrier frequency, and arrival time, is provided. Therefore, by using the estimated waveform parameters, the NPBR time and phase synchronization can be realized. Moreover, based on the waveform parameter estimation, a weak target detection method based on the generalized Radon-Fourier transform of a multi-waveform is provided. Finally, simulation and real data experiments for verifying the effectiveness of the waveform parameter estimation and weak target detection methods are provided.
String theory and cosmological singularities
Indian Academy of Sciences (India)
time' can have a beginning or end. 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 ...
Understanding Learner Strengths and Weaknesses: Assessing Performance on an Integrated Writing Task
Sawaki, Yasuyo; Quinlan, Thomas; Lee, Yong-Won
2013-01-01
The present study examined the factor structures across features of 446 examinees' responses to a writing task that integrates reading and listening modalities as well as reading and listening comprehension items of the TOEFL iBT[R] (Internet-based test). Both human and automated scores obtained for the integrated essays were utilized. Based on a…
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.
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.
Stevens, Jan
2003-01-01
These notes deal with deformation theory of complex analytic singularities and related objects. The first part treats general theory. The central notion is that of versal deformation in several variants. The theory is developed both in an abstract way and in a concrete way suitable for computations. The second part deals with more specific problems, specially on curves and surfaces. Smoothings of singularities are the main concern. Examples are spread throughout the text.
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].
INTEGRAL and XMM-Newton observations of the weak gamma-ray burst GRB 030227
DEFF Research Database (Denmark)
Mereghetti, S.; Gotz, D.; Tiengo, A.
2003-01-01
We present International Gamma-Ray Astrophysical Laboratory ( INTEGRAL) and XMM-Newton observations of the prompt gamma-ray emission and the X-ray afterglow of GRB 030227, the first gamma-ray burst for which the quick localization obtained with the INTEGRAL Burst Alert System has led to the disco......We present International Gamma-Ray Astrophysical Laboratory ( INTEGRAL) and XMM-Newton observations of the prompt gamma-ray emission and the X-ray afterglow of GRB 030227, the first gamma-ray burst for which the quick localization obtained with the INTEGRAL Burst Alert System has led...... to the discovery of X-ray and optical afterglows. GRB 030227 had a duration of about 20 s and a peak flux of similar to1.1 photons cm(-2) s(-1) in the 20-200 keV energy range. The time-averaged spectrum can be fitted by a single power law with photon index similar to2, and we find some evidence for a hard......-to-soft spectral evolution. The X-ray afterglow has been detected starting only 8 hr after the prompt emission, with a 0.2-10 keV flux decreasing as t(-1) from 1.3 x 10(-12) to 5 x 10(-13) ergs cm(-2) s(-1). The afterglow spectrum is well described by a power law with photon index modified by a 1.94 +/- 0...
Graph-Based Weakly-Supervised Methods for Information Extraction & Integration
Talukdar, Partha Pratim
2010-01-01
The variety and complexity of potentially-related data resources available for querying--webpages, databases, data warehouses--has been growing ever more rapidly. There is a growing need to pose integrative queries "across" multiple such sources, exploiting foreign keys and other means of interlinking data to merge information from diverse…
Integrating Social Networking Tools into ESL Writing Classroom: Strengths and Weaknesses
Yunus, Melor Md; Salehi, Hadi; Chenzi, Chen
2012-01-01
With the rapid development of world and technology, English learning has become more important. Teachers frequently use teacher-centered pedagogy that leads to lack of interaction with students. This paper aims to investigate the advantages and disadvantages of integrating social networking tools into ESL writing classroom and discuss the ways to…
Directory of Open Access Journals (Sweden)
John E Fa
Full Text Available Wild animals are a primary source of protein (bushmeat for people living in or near tropical forests. Ideally, the effect of bushmeat harvests should be monitored closely by making regular estimates of offtake rate and size of stock available for exploitation. However, in practice, this is possible in very few situations because it requires both of these aspects to be readily measurable, and even in the best case, entails very considerable time and effort. As alternative, in this study, we use high-resolution, environmental favorability models for terrestrial mammals (N = 165 in Central Africa to map areas of high species richness (hot spots and hunting susceptibility. Favorability models distinguish localities with environmental conditions that favor the species' existence from those with detrimental characteristics for its presence. We develop an index for assessing Potential Hunting Sustainability (PHS of each species based on their ecological characteristics (population density, habitat breadth, rarity and vulnerability, weighted according to restrictive and permissive assumptions of how species' characteristics are combined. Species are classified into five main hunting sustainability classes using fuzzy logic. Using the accumulated favorability values of all species, and their PHS values, we finally identify weak spots, defined as high diversity regions of especial hunting vulnerability for wildlife, as well as strong spots, defined as high diversity areas of high hunting sustainability potential. Our study uses relatively simple models that employ easily obtainable data of a species' ecological characteristics to assess the impacts of hunting in tropical regions. It provides information for management by charting the geography of where species are more or less likely to be at risk of extinction from hunting.
Local Integration Accounts for Weak Selectivity of Mouse Neocortical Parvalbumin Interneurons.
Scholl, Benjamin; Pattadkal, Jagruti J; Dilly, Geoffrey A; Priebe, Nicholas J; Zemelman, Boris V
2015-07-15
Dissecting the functional roles of excitatory and inhibitory neurons in cortical circuits is a fundamental goal in neuroscience. Of particular interest are their roles in emergent cortical computations such as binocular integration in primary visual cortex (V1). We measured the binocular response selectivity of genetically defined subpopulations of excitatory and inhibitory neurons. Parvalbumin (PV+) interneurons received strong inputs from both eyes but lacked selectivity for binocular disparity. Because broad selectivity could result from heterogeneous synaptic input from neighboring neurons, we examined how individual PV+ interneuron selectivity compared to that of the local neuronal network, which is primarily composed of excitatory neurons. PV+ neurons showed functional similarity to neighboring neuronal populations over spatial distances resembling measurements of synaptic connectivity. On the other hand, excitatory neurons expressing CaMKIIα displayed no such functional similarity with the neighboring population. Our findings suggest that broad selectivity of PV+ interneurons results from nonspecific integration within local networks. VIDEO ABSTRACT. Copyright © 2015 Elsevier Inc. All rights reserved.
Blinov, Nicholas; Song, XiaoGeng; Roy, Pierre-Nicholas
2004-04-01
A path integral Monte Carlo technique suitable for the treatment of doped helium clusters with inclusion of the rotational degrees of freedom of the dopant is introduced. The extrapolation of the results to the limit of infinite Trotter number is discussed in detail. Benchmark calculations for small weakly bound (4)He(N)--OCS clusters are presented. The Monte Carlo results are compared with those of basis set calculations for the He--OCS dimer. A technique to analyze the orientational imaginary time correlation function is suggested. It allows one to obtain information regarding the effective rotational constant for a doped helium cluster based on a model for the rotational Hamiltonian. The renormalization of the effective rotational constant for (4)He(N)--OCS clusters derived from the orientational imaginary time correlation function is in good agreement with experimental results.
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
Energy Technology Data Exchange (ETDEWEB)
Bantyirga Gessesse, Belachew
2013-07-18
The impact of increased wind power on the steady state and dynamic behavior of the Ethiopian power system is the main focus of this thesis. The integration of wind power to the existing grid with conventional generators introduces new set of challenges regarding system security and operational planning, the main cause of the difference arising from the uncertainty of the primary source of energy and the response time following a disturbance. For incorporating wind turbine models into the overall dynamic model of the system and investigating the effect of wind on the dynamic behavior of the wind first models of wind turbine components were put together by reviewing the current state of the art in wind turbine modeling and control concepts. The theoretical insight thus gained was applied to the Ethiopian power system as a case study. Since the models of the installed turbines were either not available or incomplete, an alternative modeling approach based on generic models was adopted. The generic model, in addition to obviating the need for technology or manufacturer specific models, reduces the complexity the dynamic model. Using this procedure, generic dynamic models for wind farm in the system were developed. The capability of dynamic models to reproduce the dynamic response of the system has been verified by comparing simulation results obtained with a detailed and generic wind farm model. It could be shown that the generic wind turbine model is simple, but accurate enough to represent any wind turbine types or entire wind farms for power system stability analysis. The next task was the study of the effect of increased wind power level on the general behavior of the Ethiopian system. It is observed that overall the impact of wind turbines on the operational indices of the system was -as could be expected- more pronounced in the vicinity of the wind farm. But the power angle oscillation following a disturbance was observed across the whole system. Further, as a
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 19; Issue 9. Singularities in a Teacup: Good Mathematics from Bad Lenses. Rajaram Nityananda. General Article Volume 19 Issue 9 September 2014 pp 787-796. Fulltext. Click here to view fulltext PDF. Permanent link:
Pseudospherical surfaces with singularities
DEFF Research Database (Denmark)
Brander, David
2017-01-01
We study a generalization of constant Gauss curvature −1 surfaces in Euclidean 3-space, based on Lorentzian harmonic maps, that we call pseudospherical frontals. We analyse the singularities of these surfaces, dividing them into those of characteristic and non-characteristic type. We give methods...
DEFF Research Database (Denmark)
Somchaipeng, Kerawit; Sporring, Jon; Johansen, Peter
2007-01-01
We propose MultiScale Singularity Trees (MSSTs) as a structure to represent images, and we propose an algorithm for image comparison based on comparing MSSTs. The algorithm is tested on 3 public image databases and compared to 2 state-of-theart methods. We conclude that the computational complexi...
Singular Linear Differential Equations in Two Variables
Braaksma, B.L.J.; Put, M. van der
2008-01-01
The formal and analytic classification of integrable singular linear differential equations has been studied among others by R. Gerard and Y. Sibuya. We provide a simple proof of their main result, namely: For certain irregular systems in two variables there is no Stokes phenomenon, i.e. there is no
Stochastic singular optics (Conference paper)
CSIR Research Space (South Africa)
Roux, FS
2014-09-01
Full Text Available -integrals, one obtains F (x) = √ G+H 8π √ 2〈g g〉 E ( √ 2H G+H ) , (23) where E(·) is the complete elliptic integral of the second kind27 and G = 4〈gg〉(〈gxgx〉+ 〈gygy〉)− (〈gxg〉+ 〈ggx〉)2 − (〈gyg〉+ 〈ggy〉)2 (24) H = ( 16〈gg〉2 [ (〈gxgx〉 − 〈gygy〉)2 + (〈gxgy〉+ 〈gygx〉)2... (1972). [28] Freund, I. and Kessler, D., “Critical point trajectory bundles in singular wave fields,” Opt. Commun. 187, 71–90 (2001). [29] Teague, M. R., “Irradiance moments: their propagation and use for unique retrieval of phase,” J. Opt. Soc. Am. 72...
Singular potentials in quantum mechanics
Energy Technology Data Exchange (ETDEWEB)
Aguilera-Navarro, V.C. [Instituto de Fisica Teorica (IFT), Sao Paulo, SP (Brazil); Koo, E. Ley [Universidad Nacional Autonoma de Mexico, Mexico City (Mexico). Inst. de Fisica
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.
Application of the decomposition method to the solution of integral ...
African Journals Online (AJOL)
Recently Wazwaz applied it to weakly singular second-kind Volterra-type of integral equation. It is the measure of success of the above that has inspired this work. It is our contention that applying the decomposition method to integral equation with Cauchy Kernel will lead to successful result. Indeed as demonstrated in the ...
String theory and cosmological singularities
Indian Academy of Sciences (India)
Abstract. In general relativity space-like or null singularities are common: they imply that 'time' can have a beginning or end. 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 ...
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.
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...
Infinitesimal Structure of Singularities
Directory of Open Access Journals (Sweden)
Michael Heller
2017-02-01
Full Text Available Some important problems of general relativity, such as the quantisation of gravity or classical singularity problems, crucially depend on geometry on very small scales. The so-called synthetic differential geometry—a categorical counterpart of the standard differential geometry—provides a tool to penetrate infinitesimally small portions of space-time. We use this tool to show that on any “infinitesimal neighbourhood” the components of the curvature tensor are themselves infinitesimal, and construct a simplified model in which the curvature singularity disappears, owing to this effect. However, one pays a price for this result. Using topoi as a generalisation of spaces requires a weakening of arithmetic (the existence of infinitesimals and of logic (to the intuitionistic logic. Is this too high a price to pay for acquiring a new method of solving unsolved problems in physics? Without trying, we shall never know the answer.
Singularities in loop quantum cosmology.
Cailleteau, Thomas; Cardoso, Antonio; Vandersloot, Kevin; Wands, David
2008-12-19
We show that simple scalar field models can give rise to curvature singularities in the effective Friedmann dynamics of loop quantum cosmology (LQC). We find singular solutions for spatially flat Friedmann-Robertson-Walker cosmologies with a canonical scalar field and a negative exponential potential, or with a phantom scalar field and a positive potential. While LQC avoids big bang or big rip type singularities, we find sudden singularities where the Hubble rate is bounded, but the Ricci curvature scalar diverges. We conclude that the effective equations of LQC are not in themselves sufficient to avoid the occurrence of curvature singularities.
Local moduli and singularities
Laudal, Olav Arnfinn
1988-01-01
This research monograph sets out to study the notion of a local moduli suite of algebraic objects like e.g. schemes, singularities or Lie algebras and provides a framework for this. The basic idea is to work with the action of the kernel of the Kodaira-Spencer map, on the base space of a versal family. The main results are the existence, in a general context, of a local moduli suite in the category of algebraic spaces, and the proof that, generically, this moduli suite is the quotient of a canonical filtration of the base space of the versal family by the action of the Kodaira-Spencer kernel. Applied to the special case of quasihomogenous hypersurfaces, these ideas provide the framework for the proof of the existence of a coarse moduli scheme for plane curve singularities with fixed semigroup and minimal Tjurina number . An example shows that for arbitrary the corresponding moduli space is not, in general, a scheme. The book addresses mathematicians working on problems of moduli, in algebraic or in complex an...
Global existence of weak solutions to the three-dimensional Euler equations with helical symmetry
Jiu, Quansen; Li, Jun; Niu, Dongjuan
2017-05-01
In this paper, we mainly investigate the weak solutions of the three-dimensional incompressible Euler equations with helical symmetry in the whole space when the helical swirl vanishes. Specifically, we establish the global existence of weak solutions when the initial vorticity lies in L1 ∩Lp with p > 1. Our result extends the previous work [2], where the initial vorticity is compactly supported and belongs to Lp with p > 4 / 3. The key ingredient in this paper involves the explicit analysis of Biot-Savart law with helical symmetry in domain R2 × [ - π , π ] via the theories of singular integral operators and second order elliptic equations.
Identify Foot of Continental Slope by singular spectrum and fractal singularity analysis
Li, Q.; Dehler, S.
2012-04-01
Identifying the Foot of Continental Slope (FOCS) plays a critical role in the determination of exclusive economic zone (EEZ) for coastal nations. The FOCS is defined by the Law of the Sea as the point of maximum change of the slope and it is mathematically equivalent to the point which has the maximum curvature value in its vicinity. However, curvature is the second derivative and the calculation of second derivative is a high pass and noise-prone filtering procedure. Therefore, identification of FOCS with curvature analysis methods is often uncertain and erroneous because observed bathymetry profiles or interpolated raster maps commonly include high frequency noises and artifacts, observation errors, and local sharp changes. Effective low-pass filtering methods and robust FOCS indicator algorithms are highly desirable. In this approach, nonlinear singular spectral filtering and singularity FOCS-indicator methods and software tools are developed to address this requirement. The normally used Fourier domain filtering methods decompose signals into Fourier space, composed of a fixed base that depends only on the acquisition interval of the signal; the signal is required to be stationary or at least weak stationary. In contrast to that requirement, the developed singular spectral filtering method constructs orthogonal basis functions dynamically according to different signals, and it does not require the signal to be stationary or weak stationary. Furthermore, singular spectrum analysis (SSA) can assist in designing suitable filters to carefully remove high-frequency local or noise components while reserving useful global and local components according to energy distribution. Geoscientific signals, including morphological ocean bathymetry data, often demonstrate fractal or multifractal properties. With proper definition of scales in the vicinity of a certain point and related measures, it is found that 1-dimensional bathymetry profiles and 2-dimensional raster maps
Space-time singularities in Weyl manifolds
Energy Technology Data Exchange (ETDEWEB)
Lobo, I.P. [CAPES Foundation, Ministry of Education of Brazil, Brasilia (Brazil); Sapienza Universita di Roma, Dipartimento di Fisica, Rome (Italy); Barreto, A.B.; Romero, C. [Universidade Federal da Paraiba, Departamento de Fisica, C. Postal 5008, Joao Pessoa, PB (Brazil)
2015-09-15
We extend one of the Hawking-Penrose singularity theorems in general relativity to the case of some scalar-tensor gravity theories in which the scalar field has a geometrical character and space-time has the mathematical structure of a Weyl integrable space-time. We adopt an invariant formalism, so that the extended version of the theorem does not depend on a particular frame. (orig.)
Bunge, Marta
2006-01-01
The self-contained theory of certain singular coverings of toposes called complete spreads, that is presented in this volume, is a field of interest to topologists working in knot theory, as well as to various categorists. It extends the complete spreads in topology due to R. H. Fox (1957) but, unlike the classical theory, it emphasizes an unexpected connection with topos distributions in the sense of F. W. Lawvere (1983). The constructions, though often motivated by classical theories, are sometimes quite different from them. Special classes of distributions and of complete spreads, inspired respectively by functional analysis and topology, are studied. Among the former are the probability distributions; the branched coverings are singled out amongst the latter. This volume may also be used as a textbook for an advanced one-year graduate course introducing topos theory with an emphasis on geometric applications. Throughout the authors emphasize open problems. Several routine proofs are left as exercises, but...
Singular Reduction and Quantization
Meinrenken, E; Meinrenken, Eckhard; Sjamaar, Reyer
1997-01-01
Consider a compact prequantizable symplectic manifold M on which a compact Lie group G acts in a Hamiltonian fashion. The ``quantization commutes with reduction'' theorem asserts that the G-invariant part of the equivariant index of M is equal to the Riemann-Roch number of the symplectic quotient of M, provided the quotient is nonsingular. We extend this result to singular symplectic quotients, using partial desingularizations of the symplectic quotient to define its Riemann-Roch number. By similar methods we also compute multiplicities for the equivariant index of the dual of a prequantum bundle, and furthermore show that the arithmetic genus of a Hamiltonian G-manifold is invariant under symplectic reduction.
A SINGULARLY UNFEMININE PROFESSION
2016-01-01
Mary K Gaillard back to CERN to present her book and talk diversity - In 1981 Mary K Gaillard became the first woman on the physics faculty at the University of California at Berkeley. Her career as a theoretical physicist spanned the period from the inception — in the late 1960s and early 1970s — of what is now known as the Standard Model of particle physics and its experimental confirmation, culminating with the discovery of the Higgs particle in 2012. Her book A Singularly Unfeminine Profession recounts Gaillard's experiences as a woman in a very male-dominated field, while tracing the development of the Standard Model as she witnessed it and participated in it.
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 $D(\\alpha)$.
DEKOMPOSISI NILAI SINGULAR MATRIKS QUATERNION
Marda, Nurhayani
2015-01-01
Dekomposisi nilai singular matriks quaternion merupakan metode pemfaktoran matriks quaternion menjadi lebih dari satu matriks. Dalam penulisan ini, diuraikan algoritma menghitung dekomposisi nilai singular matriks quaternion. Matriks quaternion akan didekomposisi menggunakan isomorfisma matriks quaternion dan matriks kompleks. Matriks quaternion direpresentasi ke dalam bentuk matriks kompleks yang berukuran dari ukuran matriks quaternion. Dari matriks kompleks kemudian dilakukan dekomposisi ...
Loop quantum cosmology and singularities.
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.
Singularities in primate orientation maps.
Obermayer, K; Blasdel, G G
1997-04-01
We report the results of an analysis of orientation maps in primate striate cortex with focus on singularities and their distribution. Data were obtained from squirrel monkeys and macaque monkeys of different ages. We find the approximately 80% of singularities that are nearest neighbors have the opposite sign and that the spatial distribution of singularities differs significantly from a random distribution of points. We do not find evidence for consistent geometric patterns that singularities may form across the cortex. Except for a different overall alignment of orientation bands and different periods of repetition, maps obtained from different animals and different ages are found similar with respect to the measures used. Orientation maps are then compared with two different pattern models that are currently discussed in the literature: bandpass-filtered white noise, which accounts very well for the overall map structure, and the field analogy model, which specifies the orientation map by the location of singularities and their properties. The bandpass-filtered noise approach to orientation patterns correctly predicts the sign correlations between singularities and accounts for the deviations in the spatial distribution of singularities away from a random dot pattern. The field analogy model can account for the structure of certain local patches of the orientation map but not for the whole map. Neither of the models is completely satisfactory, and the structure of the orientation map remains to be fully explained.
Learning English bare singulars: Data in the L2 classroom
Directory of Open Access Journals (Sweden)
Laurel Smith Stvan
2016-09-01
Full Text Available Contrasted with the more typical English bare noun forms of mass and proper nouns, bare singular count nouns comprise a problematic set for many descriptive grammars and thus for many second language learners. Although article usage is one of the trickiest areas of English as a Second Language (ESL to master, bare noun phrases, and bare singulars in particular, are less emphasized in the English language classroom, where much of the focus is placed on learning to produce articles, not learning to exclude them. To investigate L2 sensitivity to bare singular forms, the distribution of bare and articulated NPs in corpus data is contrasted, nouns appearing most often without articles are tracked, and a survey of L2 grammaticality judgments by adult learners is gathered. Lastly, the combined results of the corpus and survey data are integrated into a lesson on the syntax and pragmatics of bare singular count nouns that is designed for the ESL classroom.
Indian Academy of Sciences (India)
2015-10-29
Oct 29, 2015 ... Abstract. In this short review, we present some applications and historical facts about the integrability detectors: Painlevé analysis, singularity confinement and algebraic entropy.
On the genericity of spacetime singularities
Indian Academy of Sciences (India)
We consider here the genericity aspects of spacetime singularities that occur in cosmology and in gravitational collapse. The singularity theorems (that predict the occurrence of singularities in general relativity) allow the singularities of gravitational collapse to be either visible to external observers or covered by an event ...
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.
El singular como diferencia divina
Directory of Open Access Journals (Sweden)
Maria Jose Binetti
2012-01-01
Full Text Available Mucho se ha hablado sobre la posición de la diferencia como motor dialéctico de la existencia singular kierkegaardiana. El pecado, el otro o el Otro fisuran la subjetividad humana y la obligan a una identidad que guardará siempre la herida. El sujeto de la escisión es, en este sentido, el existente mismo, y tal debe ser el caso si la perspectiva se concentra en la individualidad. No obstante, y desde el punto de vista especulativo, creemos que los mismos principios utilizados por Kierkegaard para explicar el dinamismo de la existencia singular nos llevan más lejos, a saber, nos conducen al absoluto mismo como sujeto último de toda alteridad, respecto del cual el singular hace la diferencia.
Self-similar singular solution of doubly singular parabolic equation with gradient absorption term
Directory of Open Access Journals (Sweden)
Shi Peihu
2006-01-01
Full Text Available We deal with the self-similar singular solution of doubly singular parabolic equation with a gradient absorption term for , and in . By shooting and phase plane methods, we prove that when there exists self-similar singular solution, while there is no any self-similar singular solution. In case of existence, the self-similar singular solution is the self-similar very singular solutions which have compact support. Moreover, the interface relation is obtained.
Directory of Open Access Journals (Sweden)
Samreen Misbah
2017-12-01
Full Text Available Purpose The purpose of this study was to conduct a strengths, weaknesses, opportunities, and threats (SWOT analysis of integrating the World Health Organization (WHO patient safety curriculum into undergraduate medical education in Pakistan. Methods A qualitative interpretive case study was conducted at Riphah International University, Islamabad, from October 2016 to June 2017. The study included 9 faculty members and 1 expert on patient safety. The interviews were audiotaped, and a thematic analysis of the transcripts was performed using NVivo software. Results Four themes were derived based on the need analysis model. The sub-themes derived from the collected data were arranged under the themes of strengths, weaknesses, opportunities, and threats, in accordance with the principles of SWOT analysis. The strengths identified were the need for a formal patient safety curriculum and its early integration into the undergraduate program. The weaknesses were faculty awareness and participation in development programs. The opportunities were an ongoing effort to develop an appropriate curriculum, to improve the current culture of healthcare, and to use the WHO curricular resource guide. The threats were attitudes towards patient safety in Pakistani culture, resistance to implementation from different levels, and the role of regulatory authorities. Conclusion The theme of patient safety needs to be incorporated early into the formal medical education curriculum, with the main goals of striving to do no harm and seeing mistakes as opportunities to learn. Faculty development activities need to be organized, and faculty members should to be encouraged to participate in them. The lack of a patient safety culture was identified as the primary reason for resistance to this initiative at many levels. The WHO curriculum, amended according to local institutional culture, can be implemented appropriately with support from the corresponding regulatory bodies.
Misbah, Samreen; Mahboob, Usman
2017-01-01
The purpose of this study was to conduct a strengths, weaknesses, opportunities, and threats (SWOT) analysis of integrating the World Health Organization (WHO) patient safety curriculum into undergraduate medical education in Pakistan. A qualitative interpretive case study was conducted at Riphah International University, Islamabad, from October 2016 to June 2017. The study included 9 faculty members and 1 expert on patient safety. The interviews were audiotaped, and a thematic analysis of the transcripts was performed using NVivo software. Four themes were derived based on the need analysis model. The sub-themes derived from the collected data were arranged under the themes of strengths, weaknesses, opportunities, and threats, in accordance with the principles of SWOT analysis. The strengths identified were the need for a formal patient safety curriculum and its early integration into the undergraduate program. The weaknesses were faculty awareness and participation in development programs. The opportunities were an ongoing effort to develop an appropriate curriculum, to improve the current culture of healthcare, and to use the WHO curricular resource guide. The threats were attitudes towards patient safety in Pakistani culture, resistance to implementation from different levels, and the role of regulatory authorities. The theme of patient safety needs to be incorporated early into the formal medical education curriculum, with the main goals of striving to do no harm and seeing mistakes as opportunities to learn. Faculty development activities need to be organized, and faculty members should to be encouraged to participate in them. The lack of a patient safety culture was identified as the primary reason for resistance to this initiative at many levels. The WHO curriculum, amended according to local institutional culture, can be implemented appropriately with support from the corresponding regulatory bodies.
Singularity Theory and its Applications
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.
Ambient cosmology and spacetime singularities
Energy Technology Data Exchange (ETDEWEB)
Antoniadis, Ignatios [Bern University, Albert Einstein Center for Fundamental Physics, Institute for Theoretical Physics, Bern (Switzerland); Ecole Polytechnique, Palaiseau (France); Cotsakis, Spiros [CERN, Theory Division, Department of Physics, Geneva 23 (Switzerland); National Technical University, School of Applied Mathematics and Physical Sciences, Athens (Greece)
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.)
Levanony, Dana
2010-01-01
We study the internal structure of a two-dimensional dilatonic evaporating black hole, based on the CGHS 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.
Energy Technology Data Exchange (ETDEWEB)
Olsson, Marcus; Nordman, Roger; Taherzadeh, Mohammad
2011-07-01
Plants for bioethanol production have been planned in several cities in Sweden, including Boraas. This report provides answers to general questions regarding how such a facility's energy demand is affected by the external integration with a heat and power plant and the internal energy integration between process units. Heat integration of a bioethanol plant means that energy is reused as much as is technically possible; this sets a practical minimum level for the energy demand of the plant. In the study, ethanol production from cellulose has been simulated using Aspen Plus. Weak acid hydrolysis and enzymatic hydrolysis have been simulated, each with 50,000 and 100,000 tonnes of ethanol per year, resulting in four simulation cases. In all cases, heat integration is evaluated using pinch analysis. The steam in the ethanol plant has been covered by steam from a heat and power plant similar to that found today in Boraas. It is important to note that the energy quotas reported here includes energy use for upgrading the residual products. This leads to lower energy quotas than would be the case if the upgrading of residuals were allocated outside of the ethanol production. The conclusions from the project are: - The steam demand of the ethanol plant leads to a reduction in both the electricity and heat production of the heat and power plant. For the weak acid hydrolysis, the electricity loss is relatively high, 26-98%, which will affect the revenue significantly. The loss of electricity production is lower for the enzymatic process: 11-47%. - The difference in decreased electricity between the theoretical case of heating the raw material and the two alternative heating cases is about a factor of two, so the design of the heating of raw material is extremely important. - The reduced heat output of the power plant can, in most cases, be balanced by the surplus heat from the ethanol plant, but to completely balance the shortage, heat over 100 deg C must be used
Boundary integral formulation for cracks at imperfect interfaces
Mishuris, G.; Piccolroaz, A.; Vellender, A.
2013-01-01
We consider an infinite bi-material plane containing a semi-infinite crack situated on a soft imperfect interface. The crack is loaded by a general asymmetrical system of forces distributed along the crack faces. On the basis of the weight function approach and the fundamental reciprocal identity, we derive the corresponding boundary integral formulation, relating physical quantities. The boundary integral equations derived in this paper in the imperfect interface setting show a weak singular...
Gravitational collapse and naked singularities
Indian Academy of Sciences (India)
Gravitational collapse is one of the most striking phenomena in gravitational physics. The cosmic censorship conjecture has provided strong motivation for research in this field. In the absence of a general proof for censorship, many examples have been proposed, in which naked singularity is the outcome of gravitational ...
Singularity: zijn wij technologisch upgradable
drs. Frans van den Reep
2013-01-01
1e alinea column: Ik wil een paar dingen kwijt over singularity en de hele horde van buitengewoon slimme mensen die daar vorm aan geven. Aanleiding hiervoor is de speech van Peter Diamandis, cofounder en chairman of the Singularty University, Nasa Research Park, Silicon Valley, die hij vorige week
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
Brane singularities and their avoidance
Antoniadis, I; klaoudatou, I
2010-01-01
The singularity structure and the corresponding asymptotic behavior of a 3-brane coupled to a scalar field or to a perfect fluid in a five-dimensional bulk is analyzed in full generality using the method of asymptotic splittings. In the case of the scalar field, it is shown that the collapse singularity at a finite distance from the brane can be avoided only at the expense of making the brane world-volume positively or negatively curved. In the case where the bulk field content is parametrized by an analogue of perfect fluid with an arbitrary equation of state P=\\gamma\\rho between the `pressure' P and the `density' \\rho, our results depend crucially on the constant fluid parameter \\gamma: (i) For \\gamma>-1/2, the flat brane solution suffers from a collapse singularity at finite distance, that disappears in the curved case. (ii) For \\gamma<-1, the singularity cannot be avoided and it becomes of the big rip type for a flat brane. (iii) For -1<\\gamma< or = -1/2, the surprising result is found that while...
Selleri, Franco
2015-01-01
Weak Relativity is an equivalent theory to Special Relativity according to Reichenbach’s definition, where the parameter epsilon equals to 0. It formulates a Neo-Lorentzian approach by replacing the Lorentz transformations with a new set named “Inertial Transformations”, thus explaining the Sagnac effect, the twin paradox and the trip from the future to the past in an easy and elegant way. The cosmic microwave background is suggested as a possible privileged reference system. Most importantly, being a theory based on experimental proofs, rather than mutual consensus, it offers a physical description of reality independent of the human observation.
Directory of Open Access Journals (Sweden)
Akira R Kinjo
Full Text Available Position-specific scoring matrices (PSSMs are useful for detecting weak homology in protein sequence analysis, and they are thought to contain some essential signatures of the protein families. In order to elucidate what kind of ingredients constitute such family-specific signatures, we apply singular value decomposition to a set of PSSMs and examine the properties of dominant right and left singular vectors. The first right singular vectors were correlated with various amino acid indices including relative mutability, amino acid composition in protein interior, hydropathy, or turn propensity, depending on proteins. A significant correlation between the first left singular vector and a measure of site conservation was observed. It is shown that the contribution of the first singular component to the PSSMs act to disfavor potentially but falsely functionally important residues at conserved sites. The second right singular vectors were highly correlated with hydrophobicity scales, and the corresponding left singular vectors with contact numbers of protein structures. It is suggested that sequence alignment with a PSSM is essentially equivalent to threading supplemented with functional information. In addition, singular vectors may be useful for analyzing and annotating the characteristics of conserved sites in protein families.
Singular solutions of contact problems and block elements
Babeshko, V. A.; Evdokimova, O. V.; Babeshko, O. M.
2017-07-01
In this work, we consider mixed problems of elasticity theory, in particular, contact problems for cases that are nontraditional. They include mixed problems with discontinuous boundary conditions in which the singularities in the behavior of contact stresses are not studied or the energy of the singularities is unbounded. An example of such mixed problems is contact problems for two rigid stamps approaching each other by rectilinear boundaries up to contact but not merging into one stamp. It has been shown that such problems, which appear in seismology, failure theory, and civil engineering, have singular components with unbounded energy and can be solved by topological methods with pointwise convergence, in particular, by the block element method. Numerical methods that are based on using the energy integral are not applicable to such problems in view of its divergence.
Singularly Perturbation Method Applied To Multivariable PID Controller Design
Directory of Open Access Journals (Sweden)
Mashitah Che Razali
2015-01-01
Full Text Available Proportional integral derivative (PID controllers are commonly used in process industries due to their simple structure and high reliability. Efficient tuning is one of the relevant issues of PID controller type. The tuning process always becomes a challenging matter especially for multivariable system and to obtain the best control tuning for different time scales system. This motivates the use of singularly perturbation method into the multivariable PID (MPID controller designs. In this work, wastewater treatment plant and Newell and Lee evaporator were considered as system case studies. Four MPID control strategies, Davison, Penttinen-Koivo, Maciejowski, and Combined methods, were applied into the systems. The singularly perturbation method based on Naidu and Jian Niu algorithms was applied into MPID control design. It was found that the singularly perturbed system obtained by Naidu method was able to maintain the system characteristic and hence was applied into the design of MPID controllers. The closed loop performance and process interactions were analyzed. It is observed that less computation time is required for singularly perturbed MPID controller compared to the conventional MPID controller. The closed loop performance shows good transient responses, low steady state error, and less process interaction when using singularly perturbed MPID controller.
Historical developments in singular perturbations
O'Malley, Robert E
2014-01-01
This engaging text describes the development of singular perturbations, including its history, accumulating literature, and its current status. While the approach of the text is sophisticated, the literature is accessible to a broad audience. A particularly valuable bonus are the historical remarks. These remarks are found throughout the manuscript. They demonstrate the growth of mathematical thinking on this topic by engineers and mathematicians. The book focuses on detailing how the various methods are to be applied. These are illustrated by a number and variety of examples. Readers are expected to have a working knowledge of elementary ordinary differential equations, including some familiarity with power series techniques, and of some advanced calculus. Dr. O'Malley has written a number of books on singular perturbations. This book has developed from many of his works in the field of perturbation theory.
Quantum propagation across cosmological singularities
Gielen, Steffen; Turok, Neil
2017-05-01
The initial singularity is the most troubling feature of the standard cosmology, which quantum effects are hoped to resolve. In this paper, we study quantum cosmology with conformal (Weyl) invariant matter. We show that it is natural to extend the scale factor to negative values, allowing a large, collapsing universe to evolve across a quantum "bounce" into an expanding universe like ours. We compute the Feynman propagator for Friedmann-Robertson-Walker backgrounds exactly, identifying curious pathologies in the case of curved (open or closed) universes. We then include anisotropies, fixing the operator ordering of the quantum Hamiltonian by imposing covariance under field redefinitions and again finding exact solutions. We show how complex classical solutions allow one to circumvent the singularity while maintaining the validity of the semiclassical approximation. The simplest isotropic universes sit on a critical boundary, beyond which there is qualitatively different behavior, with potential for instability. Additional scalars improve the theory's stability. Finally, we study the semiclassical propagation of inhomogeneous perturbations about the flat, isotropic case, at linear and nonlinear order, showing that, at least at this level, there is no particle production across the bounce. These results form the basis for a promising new approach to quantum cosmology and the resolution of the big bang singularity.
Stringy Resolutions of Null Singularities
Energy Technology Data Exchange (ETDEWEB)
Fabinger, Michal
2003-02-06
We study string theory in supersymmetric time-dependent backgrounds. In the framework of general relativity, supersymmetry for spacetimes without flux implies the existence of a covariantly constant null vector, and a relatively simple form of the metric. As a result, the local nature of any such spacetime can be easily understood. We show that we can view any such geometry as a sequence of solutions to lower-dimensional Euclidean gravity. If we choose the lower-dimensional solutions to degenerate at some light-cone time, we obtain null singularities, which may be thought of as generalizations of the parabolic orbifold singularity. We find that in string theory, many such null singularities get repaired by {alpha}{prime}-corrections--in particular, by worldsheet instantons. As a consequence, the resulting string theory solutions do not suffer from any instability. Even though the CFT description of these solutions is not always valid, they can still be well understood after taking the effects of light D-branes into account; the breakdown of the worldsheet conformal field theory is purely gauge-theoretic, not involving strong gravitational effects.
Directory of Open Access Journals (Sweden)
Ali Al Kaissi MD, MSc
2017-01-01
Full Text Available Marked ligamentous hyperlaxity and muscle weakness/wasting associated with awkward gait are the main deficits confused with the diagnosis of myopathy. Seven children (6 boys and 1 girl with an average age of 8 years were referred to our department because of diverse forms of skeletal abnormalities. No definitive diagnosis was made, and all underwent a series of sophisticated investigations in other institutes in favor of myopathy. We applied our methodology through the clinical and radiographic phenotypes followed by targeted genotypic confirmation. Three children (2 boys and 1 girl were compatible with the diagnosis of progressive pseudorheumatoid chondrodysplasia. The genetic mutation was correlated with the WISP 3 gene actively expressed by articular chondrocytes and located on chromosome 6. Klinefelter syndrome was the diagnosis in 2 boys. Karyotyping confirmed 47,XXY (aneuploidy of Klinefelter syndrome. And 2 boys were finally diagnosed with Morquio syndrome (MPS type IV A as both showed missense mutations in the N-acetylgalactosamine-sulfate sulfatase gene. Misdiagnosis can lead to the initiation of a long list of sophisticated investigations.
Energy Technology Data Exchange (ETDEWEB)
Laverdure, N
2005-12-15
Wind energy is now an energy that can not be ignored. Because of intrinsic characteristics (scattered primary energy, generators with different technologies, use of power electronics interface), wind energy system integration in distribution grids leads to real problems in terms of impacts. With recent standard changes, it is necessary to study the possibilities of each technology of wind turbines to answer or not to these new constraints. This PhD thesis focuses on a comparison of the main present wind turbines concerning three points of discussion: energy quality, fault ride through, ancillary services (voltage and frequency). It insists on the possibilities in terms of control laws for variable speed wind turbines. (author)
Lecture notes on mean curvature flow, barriers and singular perturbations
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.
Generalized decomposition methods for singular oscillators
Energy Technology Data Exchange (ETDEWEB)
Ramos, J.I. [Room I-320-D, E. T. S. Ingenieros Industriales, Universidad de Malaga, Plaza El Ejido, s/n 29013 Malaga (Spain)], E-mail: jirs@lcc.uma.es
2009-10-30
Generalized decomposition methods based on a Volterra integral equation, the introduction of an ordering parameter and a power series expansion of the solution in terms of the ordering parameter are developed and used to determine the solution and the frequency of oscillation of a singular, nonlinear oscillator with an odd nonlinearity. It is shown that these techniques provide solutions which are free from secularities if the unknown frequency of oscillation is also expanded in power series of the ordering parameter, require that the nonlinearities be analytic functions of their arguments, and, at leading-order, provide the same frequency of oscillation as two-level iterative techniques, the homotopy perturbation method if the constants that appear in the governing equation are expanded in power series of the ordering parameter, and modified artificial parameter - Linstedt-Poincare procedures.
A new treatment of mixed virtual and real IR-singularities
Energy Technology Data Exchange (ETDEWEB)
Gluza, J. [Silesia Univ., Katowice (Poland). Dept. of Field Theory and Particle Physics, Inst. of Physics; Riemann, T. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany)
2008-01-15
We discuss the determination of the infrared singularities of massive one-loop 5-point functions with Mellin-Barnes (MB) representations. Massless internal lines may lead to poles in the {epsilon} expansion of the Feynman diagram, while unresolved massless final state particles give endpoint singularities of the phase space integrals. MB integrals are an elegant tool for their common treatment. An evaluation by taking residues leads to inverse binomial sums. (orig.)
Mathematical models with singularities a zoo of singular creatures
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.
Weak-noise limit of a piecewise-smooth stochastic differential equation
Chen, Yaming; Baule, Adrian; Touchette, Hugo; Just, Wolfram
2013-11-01
We investigate the validity and accuracy of weak-noise (saddle-point or instanton) approximations for piecewise-smooth stochastic differential equations (SDEs), taking as an illustrative example a piecewise-constant SDE, which serves as a simple model of Brownian motion with solid friction. For this model, we show that the weak-noise approximation of the path integral correctly reproduces the known propagator of the SDE at lowest order in the noise power, as well as the main features of the exact propagator with higher-order corrections, provided the singularity of the path integral associated with the nonsmooth SDE is treated with some heuristics. We also show that, as in the case of smooth SDEs, the deterministic paths of the noiseless system correctly describe the behavior of the nonsmooth SDE in the low-noise limit. Finally, we consider a smooth regularization of the piecewise-constant SDE and study to what extent this regularization can rectify some of the problems encountered when dealing with discontinuous drifts and singularities in SDEs.
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.
Overcoming Robot-Arm Joint Singularities
Barker, L. K.; Houck, J. A.
1986-01-01
Kinematic equations allow arm to pass smoothly through singular region. Report discusses mathematical singularities in equations of robotarm control. Operator commands robot arm to move in direction relative to its own axis system by specifying velocity in that direction. Velocity command then resolved into individual-joint rotational velocities in robot arm to effect motion. However, usual resolved-rate equations become singular when robot arm is straightened.
Directory of Open Access Journals (Sweden)
G. Chen
2013-07-01
Full Text Available The spatial structural characteristics of geological anomaly, including singularity and self-similarity, can be analysed using fractal or multifractal modelling. Here we apply the multifractal methods to potential fields to demonstrate that singularities can characterise geological bodies, including rock density and magnetic susceptibility. In addition to enhancing weak gravity and magnetic anomalies with respect to either strong or weak background levels, the local singularity index (α ≈ 2 can be used to delineate the edges of geological bodies. Two models were established to evaluate the effectiveness of mapping singularities for extracting weak anomalies and delineating edges of buried geological bodies. The Qikou depression of the Dagang oilfield in eastern China has been chosen as a study area for demonstrating the extraction of weak anomalies of volcanic rocks, using the singularity mapping technique to analyse complex magnetic anomalies caused by complex geological background. The results have shown that the singularities of magnetic data mapped in the paper are associated with buried volcanic rocks, which have been verified by both drilling and seismic survey, and the S–N and E–W faults in the region. The targets delineated for deeply seated faults and volcanic rocks in the Qikou depression should be further investigated for the potential application in undiscovered oil and gas reservoirs exploration.
Directory of Open Access Journals (Sweden)
Joan C. Artes
2014-07-01
Full Text Available In this work we consider the problem of classifying all configurations of singularities, both finite and infinite of quadratic differential systems, with respect to the geometric equivalence relation defined in [3]. This relation is deeper than the topological equivalence relation which does not distinguish between a focus and a node or between a strong and a weak focus or between foci of different orders. Such distinctions are however important in the production of limit cycles close to the foci in perturbations of the systems. The notion of geometric equivalence relation of configurations of singularities allows to incorporates all these important geometric features which can be expressed in purely algebraic terms. This equivalence relation is also deeper than the qualitative equivalence relation introduced in [17]. The geometric classification of all configurations of singularities, finite and infinite, of quadratic systems was initiated in [4] where the classification was done for systems with total multiplicity $m_f$ of finite singularities less than or equal to one. In this article we continue the work initiated in [4] and obtain the geometric classification of singularities, finite and infinite, for the subclass of quadratic differential systems possessing finite singularities of total multiplicity $m_f=2$. We obtain 197 geometrically distinct configurations of singularities for this family. We also give here the global bifurcation diagram of configurations of singularities, both finite and infinite, with respect to the geometric equivalence relation, for this class of systems. The bifurcation set of this diagram is algebraic. The bifurcation diagram is done in the 12-dimensional space of parameters and it is expressed in terms of polynomial invariants. The results can therefore be applied for any family of quadratic systems in this class, given in any normal form. Determining the geometric configurations of singularities for any such
Stefan-Sussmann singular foliations, singular subalgebroids and their associated sheaves
Androulidakis, Iakovos; Zambon, Marco
2016-06-01
We explain and motivate Stefan-Sussmann singular foliations, and by replacing the tangent bundle of a manifold with an arbitrary Lie algebroid, we introduce singular subalgebroids. Both notions are defined using compactly supported sections. The main results of this note are an equivalent characterization, in which the compact support condition is removed, and an explicit description of the sheaf associated to any Stefan-Sussmann singular foliation or singular subalgebroid.
Non-collision solutions for a class of planar singular Lagrangian systems
Directory of Open Access Journals (Sweden)
Morched Boughariou
2000-12-01
Full Text Available In this paper, we show the existence of non-collision periodic solutions of minimal period for a class of singular second order Hamiltonian systems in ${R}^2$ with weak forcing terms. We consider the fixed period problem and the fixed energy problem in the autonomous case.
Proton-proton bremsstrahlung cross-sections including the kinematical singularity
Mahjour-Shafiei, M.; Amir-Ahmadi, H. R.; Bacelar, J. C. S.; Castelijns, R.; Ermisch, K.; van Garderen, E. D.; Gasparic, I.; Harakeh, M. N.; Kalantar-Nayestanaki, N.; Kis, M.; Loehner, H.; Scholten, O.
Integrated cross-section data for proton-proton bremsstrahlung including the points with the phase-space singularity, which occurs close to the maximum non-coplanarity angle, are presented. A numerical integration of theoretical cross-sections is performed over the non-coplanarity angle to integrate
The Semantics of Plurals: A Defense of Singularism
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…
Directory of Open Access Journals (Sweden)
Elvio Alccinelli
2001-07-01
Full Text Available En este artículo pretendemos mostrar que le conjunto de las economías singulares, si bien pequeño desde el punto de vista de la topología y/o desde el punto de vista de la teoría de la medida, tiene importantes efectos en el desarrollo de los regímenes económicos. Es el responsable de los cambios abruptos en los estados de equilibrio y de la multiplicidad de tales estados. Permite además establecer a partir de los tipos de singularidades posibles, una partición del conjunto de economías según tenga lugar uno u otro tipo de singularidad cuya presencia o no, caracteriza el comportamiento posible de la economía en cuestión.
Singularities in linear wave propagation
Gårding, Lars
1987-01-01
These lecture notes stemming from a course given at the Nankai Institute for Mathematics, Tianjin, in 1986 center on the construction of parametrices for fundamental solutions of hyperbolic differential and pseudodifferential operators. The greater part collects and organizes known material relating to these constructions. The first chapter about constant coefficient operators concludes with the Herglotz-Petrovsky formula with applications to lacunas. The rest is devoted to non-degenerate operators. The main novelty is a simple construction of a global parametrix of a first-order hyperbolic pseudodifferential operator defined on the product of a manifold and the real line. At the end, its simplest singularities are analyzed in detail using the Petrovsky lacuna edition.
Vector fields on singular varieties
Brasselet, Jean-Paul; Suwa, Tatsuo
2009-01-01
Vector fields on manifolds play a major role in mathematics and other sciences. In particular, the Poincaré-Hopf index theorem gives rise to the theory of Chern classes, key manifold-invariants in geometry and topology. It is natural to ask what is the ‘good’ notion of the index of a vector field, and of Chern classes, if the underlying space becomes singular. The question has been explored by several authors resulting in various answers, starting with the pioneering work of M.-H. Schwartz and R. MacPherson. We present these notions in the framework of the obstruction theory and the Chern-Weil theory. The interplay between these two methods is one of the main features of the monograph.
Building Reproducible Science with Singularity Containers
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 ...
Singular multiparameter dynamic equations with distributional ...
African Journals Online (AJOL)
In this paper, we consider both singular single and several multiparameter second order dynamic equations with distributional potentials on semi-innite time scales. At rst we construct Weyl's theory for the single singular multiparameter dynamic equation with distributional potentials and we prove that the forward jump of at ...
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 delay...
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...
Quantum healing of spacetime singularities: A review
Konkowski, D. A.; Helliwell, T. M.
2018-02-01
Singularities are commonplace in general relativistic spacetimes. It is natural to hope that they might be “healed” (or resolved) by the inclusion of quantum mechanics, either in the theory itself (quantum gravity) or, more modestly, in the description of the spacetime geodesic paths used to define them. We focus here on the latter, mainly using a procedure proposed by Horowitz and Marolf to test whether singularities in broad classes of spacetimes can be resolved by replacing geodesic paths with quantum wave packets. We list the spacetime singularities that various authors have studied in this context, and distinguish those which are healed quantum mechanically (QM) from those which remain singular. Finally, we mention some alternative approaches to healing singularities.
Biclustering via Sparse Singular Value Decomposition
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.
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 literature to test nonlinear minimax algorithms, i.e., minimax design of multisection quarter-wave transformers, is shown to exhibit singularities and the reason for this is pointed out. Based on the theoretical results presented an algorithm for nonlinear minimax optimization is developed. The new algorithm...... maintains the quadratic convergence property of a recent algorithm by Madsen et al. when applied to regular problems and it is demonstrated to significantly improve the final convergence on singular problems....
One dimensional systems with singular perturbations
Energy Technology Data Exchange (ETDEWEB)
Alvarez, J J [Departamento de Informatica, E.U. de Informatica, Universidad de Valladolid, 40005 Segovia (Spain); Gadella, M; Nieto, L M [Departamento de FTAO, University of Valladolid, 47071 Valladolid (Spain); Glasser, L M [Department of Physics, Clarkson University, Potsdam, NY 13699-5820 (United States); Lara, L P, E-mail: jjalvarez@infor.uva.es, E-mail: manuelgadella1@gmail.com, E-mail: laryg@clarkson.edu, E-mail: lplara@fceia.unr.edu.ar, E-mail: luismi@metodos.fam.cie.uva.es [Departamento de Sistemas, FRRO, Zevallos 1345, Rosario (Argentina)
2011-03-01
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.
Yaşar, Emrullah; Yıldırım, Yakup; Zhou, Qin; Moshokoa, Seithuti P.; Ullah, Malik Zaka; Triki, Houria; Biswas, Anjan; Belic, Milivoj
2017-11-01
This paper obtains optical soliton solution to perturbed nonlinear Schrödinger's equation by modified simple equation method. There are four types of nonlinear fibers studied in this paper. They are Anti-cubic law, Quadratic-cubic law, Cubic-quintic-septic law and Triple-power law. Dark and singular soliton solutions are derived. Additional solutions such as singular periodic solutions also fall out of the integration scheme.
On the Spectral Singularities and Spectrality of the Hill Operator
Veliev, O. A.
2014-01-01
First we study the spectral singularity at infinity and investigate the connections of the spectral singularities and the spectrality of the Hill operator. Then we consider the spectral expansion when there is not the spectral singularity at infinity.
Formation of current singularity in a topologically constrained plasma
Energy Technology Data Exchange (ETDEWEB)
Zhou, Yao [Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States); Princeton Univ., NJ (United States). Dept. of Astrophysical Sciences; Huang, Yi-Min [Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States); Princeton Univ., NJ (United States). Dept. of Astrophysical Sciences; Qin, Hong [Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States); Princeton Univ., NJ (United States). Dept. of Astrophysical Sciences; Univ Sci & Technol China, Dept Modern Phys, Hefei 230026, Anhui, Peoples R China.; Bhattacharjee, A. [Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States); Princeton Univ., NJ (United States). Dept. of Astrophysical Sciences
2016-02-01
Recently a variational integrator for ideal magnetohydrodynamics in Lagrangian labeling has been developed. Its built-in frozen-in equation makes it optimal for studying current sheet formation. We use this scheme to study the Hahm-Kulsrud-Taylor problem, which considers the response of a 2D plasma magnetized by a sheared field under sinusoidal boundary forcing. We obtain an equilibrium solution that preserves the magnetic topology of the initial field exactly, with a fluid mapping that is non-differentiable. Unlike previous studies that examine the current density output, we identify a singular current sheet from the fluid mapping. These results are benchmarked with a constrained Grad-Shafranov solver. The same signature of current singularity can be found in other cases with more complex magnetic topologies.
Minimal solution for inconsistent singular fuzzy matrix equations
Nikuie, M.; M.K. Mirnia
2013-01-01
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 fu...
Analyticity of solutions of singular fractional differential equations
Kangro, Urve
2016-06-01
We study singular fractional differential equations in spaces of analytic functions. We reformulate the equation as a cordial Volterra integral equation of the second kind and use results from the theory of cordial Volterra integral equations. This enables us to obtain conditions under which the equation has a unique analytic solution. Note that the smooth solution in this case is unique without any initial conditions; in fact, giving initial conditions usually results in nonsmooth solution. We also consider approximate solution of these equations and prove exponential convergence of approximate solutions to the exact solution.
Spin Singularities: Clifford Kaleidoscopes and Particle Masses
Cohen, Marcus S
2009-01-01
Are particles singularities- vortex lines, tubes, or sheets in some global ocean of dark energy? We visit the zoo of Lagrangian singularities, or caustics in a spin(4,C) phase flow over compactifed Minkowsky space, and find that their varieties and energies parallel the families and masses of the elementary particles. Singularities are classified by tensor products of J Coxeter groups s generated by reflections. The multiplicity, s, is the number reflections needed to close a cycle of null zigzags: nonlinear resonances of J chiral pairs of lightlike matter spinors with (4-J) Clifford mirrors: dyads in the remaining unperturbed vacuum pairs. Using singular perturbations to "peel" phase-space singularities by orders in the vacuum intensity, we find that singular varieties with quantized mass, charge, and spin parallel the families of leptons (J=1), mesons (J=2), and hadrons (J=3). Taking the symplectic 4 form - the volume element in the 8- spinor phase space- as a natural Lagrangian, these singularities turn ou...
Mixed-Mode Oscillations Due to a Singular Hopf Bifurcation in a Forest Pest Model
DEFF Research Database (Denmark)
Brøns, Morten; Desroches, Mathieu; Krupa, Martin
2015-01-01
In a forest pest model, young trees are distinguished from old trees. The pest feeds on old trees. The pest grows on a fast scale, the young trees on an intermediate scale, and the old trees on a slow scale. A combination of a singular Hopf bifurcation and a “weak return” mechanism, characterized...... by a small change in one of the variables, determines the features of the mixed-mode oscillations. Period-doubling and saddle-node bifurcations lead to closed families (called isolas) of periodic solutions in a bifurcation corresponding to a singular Hopf bifurcation....
Causal viscous cosmology without singularities
Laciana, Carlos E
2016-01-01
An isotropic and homogeneous cosmological model with a source of dark energy is studied. That source is simulated with a viscous relativistic fluid with minimal causal correction. In this model the restrictions on the parameters coming from the following conditions are analized: a) energy density without singularities along time, b) scale factor increasing with time, c) universe accelerated at present time, d) state equation for dark energy with "w" bounded and close to -1. It is found that those conditions are satified for the following two cases. i) When the transport coefficient ({\\tau}_{{\\Pi}}), associated to the causal correction, is negative, with the aditional restriction {\\zeta}|{\\tau}_{{\\Pi}}|>2/3, where {\\zeta} is the relativistic bulk viscosity coefficient. The state equation is in the "phantom" energy sector. ii) For {\\tau}_{{\\Pi}} positive, in the "k-essence" sector. It is performed an exact calculation for the case where the equation of state is constant, finding that option (ii) is favored in r...
Cirant, Marco
2016-11-22
Here, we prove the existence of smooth solutions for mean-field games with a singular mean-field coupling; that is, a coupling in the Hamilton-Jacobi equation of the form $g(m)=-m^{-\\\\alpha}$. We consider stationary and time-dependent settings. The function $g$ is monotone, but it is not bounded from below. With the exception of the logarithmic coupling, this is the first time that MFGs whose coupling is not bounded from below is examined in the literature. This coupling arises in models where agents have a strong preference for low-density regions. Paradoxically, this causes the agents to spread and prevents the creation of solutions with a very-low density. To prove the existence of solutions, we consider an approximate problem for which the existence of smooth solutions is known. Then, we prove new a priori bounds for the solutions that show that $\\\\frac 1 m$ is bounded. Finally, using a limiting argument, we obtain the existence of solutions. The proof in the stationary case relies on a blow-up argument and in the time-dependent case on new bounds for $m^{-1}$.
From general laws to singularities.
Elkaïm, M
1985-06-01
This article comprises several sections. The first is devoted to an explanation of a number of notions stemming from work by Ilya Prigogine and others on open systems far from equilibrium. As a result of this work, I have been able to stand back from the traditional approach employed in family therapy, that of open systems at equilibrium (the theory of Ludwig von Bertalanffy). The second section describes a clinical example based on elements close to Prigogine's theories. In the third part I develop an approach that--although continuing to draw on Prigogine's work--is much more closely linked to the research I have carried out with Félix Guattari over recent years. In this part I attempt to study a level that, in my view, has too often been left outside the field of inquiry: that of couplings between "singularities" of members of the family system and the therapist. A clinical case is presented in which this "semiotic" level, as Guattari terms it, is used together with that of the "intrinsic rules" of the system. Finally, I propose a few avenues of inquiry and research on the basis of the concepts presented.
Generalizations of the Abstract Boundary singularity theorem
Whale, Ben E; Scott, Susan M
2015-01-01
The Abstract Boundary singularity theorem was first proven by Ashley and Scott. It links the existence of incomplete causal geodesics in strongly causal, maximally extended spacetimes to the existence of Abstract Boundary essential singularities, i.e., non-removable singular boundary points. We give two generalizations of this theorem: the first to continuous causal curves and the distinguishing condition, the second to locally Lipschitz curves in manifolds such that no inextendible locally Lipschitz curve is totally imprisoned. To do this we extend generalized affine parameters from $C^1$ curves to locally Lipschitz curves.
Energy Technology Data Exchange (ETDEWEB)
Collinucci, Andrés [Physique Théorique et Mathématique and International Solvay Institutes,Université Libre de Bruxelles, C.P. 231, 1050 Bruxelles (Belgium); Savelli, Raffaele [Institut de Physique Théorique, CEA Saclay,Orme de Merisiers, F-91191 Gif-surYvette (France)
2015-09-15
We propose a framework for treating F-theory directly, without resolving or deforming its singularities. This allows us to explore new sectors of gauge theories, including exotic bound states such as T-branes, in a global context. We use the mathematical framework known as Eisenbud’s matrix factorizations for hypersurface singularities. We display the usefulness of this technique by way of examples, including affine singularities of both conifold and orbifold type, as well as a class of full-fledged compact elliptically fibered Calabi-Yau fourfolds.
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...
Topology of singular fibers of differentiable maps
Saeki, Osamu
2004-01-01
The volume develops a thorough theory of singular fibers of generic differentiable maps. This is the first work that establishes the foundational framework of the global study of singular differentiable maps of negative codimension from the viewpoint of differential topology. The book contains not only a general theory, but also some explicit examples together with a number of very concrete applications. This is a very interesting subject in differential topology, since it shows a beautiful interplay between the usual theory of singularities of differentiable maps and the geometric topology of manifolds.
Singular control in minimum time spacecraft reorientation
Seywald, Hans; Kumar, Renjith R.
1991-01-01
Spacecraft reorientation is investigated numerically for an inertially symmetric rigid spacecraft with three bounded independent control torques aligned with the principal axes. The dynamical system of the spacecraft and the framework of the optimal-control problem are established in order to identify all of the potential strategies. The investigation lists bang-bang solutions and finite-order and infinite-order singular arcs, and the conditions for the finite-order singular arcs are given. Numerical examples are developed for all of the control-logic systems, and the suboptimality of the rest-to-rest maneuvers is proven for principal-axis rotations. The most efficient control technique is the singular control of infinite order, and the vector-valued singular control can be utilized in a derivative of the switching function.
ADE bundles over surfaces with ADE singularities
Chen, Yunxia; Leung, Naichung Conan
2012-01-01
Given a complex projective surface with an ADE singularity and p_{g}=0, we construct ADE bundles over it and its minimal resolution. Furthermore, we descibe their minuscule representation bundles in terms of configurations of (reducible) (-1)-curves.
Classically stable non-singular cosmological bounces
Ijjas, Anna
2016-01-01
One of the fundamental questions of theoretical cosmology is whether the universe can undergo a non-singular bounce, i.e., smoothly transit from a period of contraction to a period of expansion through violation of the null energy condition (NEC) at energies well below the Planck scale and at finite values of the scale factor such that the entire evolution remains classical. A common claim has been that a non-singular bounce either leads to ghost or gradient instabilities or a cosmological singularity. In this letter, we examine cubic Galileon theories and present a procedure for explicitly constructing examples of a non-singular cosmological bounce without encountering any pathologies and maintaining a sub-luminal sound speed for co-moving curvature modes throughout the NEC violating phase. We also discuss the relation between our procedure and earlier work.
Algunas aclaraciones acerca del conocimiento del singular.
Directory of Open Access Journals (Sweden)
Carlos Llano Cifuentes
2013-11-01
Full Text Available Llano tries to explain the main purpose of El Conocimiento del Singular, showing how the individuals about which the book is concerned are basically human individuals: people as decision makers.
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.
Comparison of sheaf cohomology and singular cohomology
Sella, Yehonatan
2016-01-01
A classic result states that on any locally contractible and paracompact topological space, singular cohomology and sheaf cohomology are isomorphic. A result by Ramanan claims that the paracompactness assumption may be removed, but Ramanan's proof in fact implicitly relies on the assumption of paracompactness and does not work in the stated generality. This paper gives a modified proof that, in fact, singular cohomology and sheaf cohomology agree on any locally contractible topological space.
Shocks and finite-time singularities in Hele-Shaw flow
Energy Technology Data Exchange (ETDEWEB)
Teodorescu, Razvan [Los Alamos National Laboratory; Wiegmann, P [UNIV OF MONTREAL; Lee, S-y [UNIV OF CHICAGO
2008-01-01
Hele-Shaw flow at vanishing surface tension is ill-defined. In finite time, the flow develops cusplike singularities. We show that the ill-defined problem admits a weak dispersive solution when singularities give rise to a graph of shock waves propagating in the viscous fluid. The graph of shocks grows and branches. Velocity and pressure jump across the shock. We formulate a few simple physical principles which single out the dispersive solution and interpret shocks as lines of decompressed fluid. We also formulate the dispersive solution in algebro-geometrical terms as an evolution of Krichever-Boutroux complex curve. We study in details the most generic (2,3) cusp singularity which gives rise to an elementary branching event. This solution is self-similar and expressed in terms of elliptic functions.
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.)
What is a Singularity in Geometrized Newtonian Gravitation?
Weatherall, James Owen
2013-01-01
I discuss singular spacetimes in the context of the geometrized formulation of Newtonian gravitation. I argue first that geodesic incompleteness is a natural criterion for when a model of geometrized Newtonian gravitation is singular, and then I show that singularities in this sense arise naturally in classical physics by stating and proving a classical version of the Raychaudhuri-Komar singularity theorem.
Liu, Y.; Xia, Q.; Cheng, Q.; Wang, X.
2013-07-01
Geo-anomalies with complex structures in the earth's crust may be defined as preferable hydrothermal ore-forming targets. The separation and explanation of anomaly from geological background have a profound influence on the analysis of geological evolution and the ore-forming process. Usually one of the key steps to identify favorable exploration targets is to determine the threshold to separate anomaly from geological background. In this paper, the singularity theory and concentration-area (C-A) fractal method was applied in determination of the threshold of geo-anomalies. According to the thresholds, four singular maps can be each divided into two segments. Each of them is correlated to the anomaly and background of the geological objects (e.g., faults, fault intersections and contacts), which reveals that the various geo-anomalies can be characterized by the singularities. The results indicate that the local singularity method can be used to identify the weak anomalies in a low background. Logistic regression model was used to combine geo-singularity maps for mineral potential mapping, which provides a useful input for further mineral exploration in the Nanling tungsten polymetallic belt, South China.
Treatment of singularities in cracked bodies
Shivakumar, K. N.; Raju, I. S.
1990-01-01
Three-dimensional finite-element analyses of middle-crack tension (M-T) and bend specimens subjected to mode I loadings were performed to study the stress singularity along the crack front. The specimen was modeled using 20-node isoparametric elements. The displacements and stresses from the analysis were used to estimate the power of singularities using a log-log regression analysis along the crack front. The analyses showed that finite-sized cracked bodies have two singular stress fields of the form rho = C sub o (theta, z) r to the -1/2 power + D sub o (theta, phi) R to the lambda rho power. The first term is the cylindrical singularity with the power -1/2 and is dominant over the middle 96 pct (for Poisson's ratio = 0.3) of the crack front and becomes nearly zero at the free surface. The second singularity is a vertex singularity with the vertex point located at the intersection of the crack front and the free surface. The second term is dominant at the free surface and becomes nearly zero away from the boundary layer. The thickness of the boundary layer depends on Poisson's ratio of the material and is independent of the specimen type. The thickness of the boundary layer varied from 0 pct to about 5 pct of the total specimen thickness as Poisson's ratio varied from 0.0 to 0.45. Because there are two singular stress fields near the free surface, the strain energy release rate (G) is an appropriate parameter to measure the severity of the crack.
FURTHER GENERALISATIONS OF THE KUMMER-SCHWARZ EQUATION: ALGEBRAIC AND SINGULARITY PROPERTIES
Directory of Open Access Journals (Sweden)
R Sinuvasan
2017-12-01
Full Text Available The Kummer–Schwarz Equation, 2y'y'''− 3(y''2 = 0, has a generalisation, (n − 1y(n−2y(n − ny(n−12 = 0, which shares many properties with the parent form in terms of symmetry and singularity. All equations of the class are integrable in closed form. Here we introduce a new class, (n+q−2y(n−2y(n −(n+q−1y(n−12 = 0, which has different integrability and singularity properties.
Energy Technology Data Exchange (ETDEWEB)
Cheng, Yanjie; Tang, Youmin; Jackson, Peter; Deng, Ziwang [University of Northern British Columbia, Department of Environmental Science and Engineering, Prince George, BC (Canada); Chen, Dake [Lamont-Doherty Earth Observatory of Columbia University, Palisades, NY (United States); State Key Laboratory of Satellite Ocean Environment Dynamics, Hangzhou (China); Zhou, Xiaobing [University of Northern British Columbia, Department of Environmental Science and Engineering, Prince George, BC (Canada); Centre for Australian Weather and Climate Research (CAWCR), Bureau of Meteorology, Melbourne, VIC (Australia)
2010-10-15
This is the second part of the 148 years (1856-2003) singular vector analysis, as an extension of part I (Cheng et al. 2009 Clim Dyn, doi:10.1007/s00382-009-0595-7), in which a fully physically based tangent linear model has been constructed for the Zebiak-Cane model LDEO5 version. In the present study, relationships between the singular values and prediction skill measures are investigated for the 148 years. Results show that at decadal/interdecadal time scales, an inverse relationship exists between the singular value (S1) and correlation-based skill measures whereas an in-phase relationship exists between the S1 and MSE-based skill measures. However, the S1 is not a good measure or predictor of prediction skill at shorter time scales such as the interannual time scale and for individual prediction. To explain these findings, S1 was decomposed into linear perturbation growth rate (L1) and linearized nonlinear perturbation growth rate (N1), which are controlled by the opposite underlying model dynamical processes (the linear warming and the nonlinear cooling). An offsetting effect was found between L1 and N1, which have opposite contributions to the S1 (i.e., S1 {approx} L1 - N1). The ''negative'' perturbation growth rate -N1 (denoted as NN1) probably is the consequence of the unrealistic nonlinear cooling in the LDEO5 model. Although the correlations of the actual prediction skill to both the L1 and the NN1 are good, their opposite signs lead to a weak relationship between S1 and actual prediction skill. Therefore, either L1 or N1/NN1 is better than S1 in measuring actual prediction skill for the LDEO5 model. (orig.)
Singularity now: using the ventricular assist device as a model for future human-robotic physiology.
Martin, Archer K
2016-04-01
In our 21 st century world, human-robotic interactions are far more complicated than Asimov predicted in 1942. The future of human-robotic interactions includes human-robotic machine hybrids with an integrated physiology, working together to achieve an enhanced level of baseline human physiological performance. This achievement can be described as a biological Singularity. I argue that this time of Singularity cannot be met by current biological technologies, and that human-robotic physiology must be integrated for the Singularity to occur. In order to conquer the challenges we face regarding human-robotic physiology, we first need to identify a working model in today's world. Once identified, this model can form the basis for the study, creation, expansion, and optimization of human-robotic hybrid physiology. In this paper, I present and defend the line of argument that currently this kind of model (proposed to be named "IshBot") can best be studied in ventricular assist devices - VAD.
Directory of Open Access Journals (Sweden)
Abid Imed
2011-01-01
Full Text Available Abstract Given Ω bounded open regular set of ℝ2 and x1, x2, ..., xm ∈ Ω, we give a sufficient condition for the problem to have a positive weak solution in Ω with u = 0 on ∂Ω, which is singular at each xi as the parameters ρ, λ > 0 tend to 0 and where f(u is dominated exponential nonlinearities functions. 2000 Mathematics Subject Classification: 35J60; 53C21; 58J05.
Singularity hypotheses a scientific and philosophical assessment
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.
Enveloping branes and brane-world singularities
Antoniadis, Ignatios; Klaoudatou, Ifigeneia
2014-01-01
The existence of envelopes is studied for systems of differential equations in connection with the method of asymptotic splittings which allows to determine the singularity structure of the solutions. The result is applied to braneworlds consisting of a 3-brane in a five-dimensional bulk, in the presence of an analog of a bulk perfect fluid parametrizing 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.
Enveloping branes and brane-world singularities.
Antoniadis, Ignatios; Cotsakis, Spiros; Klaoudatou, Ifigeneia
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.
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.)
Directory of Open Access Journals (Sweden)
Marwan Amin Kutbi
2014-01-01
weakly compatible mappings in symmetric spaces satisfying generalized (ψ,φ-contractive conditions employing the common limit range property. We furnish some interesting examples which support our main theorems. Our results generalize and extend some recent results contained in Imdad et al. (2013 to symmetric spaces. Consequently, a host of metrical common fixed theorems are generalized and improved. In the process, we also derive a fixed point theorem for four finite families of mappings which can be utilized to derive common fixed point theorems involving any number of finite mappings.
Jost-functions and attractive singular potentials
Energy Technology Data Exchange (ETDEWEB)
Arnecke, Florian; Madronero, Javier; Friedrich, Harald [Physik Department T30a, Technische Universitaet Muenchen, D-85747 Garching (Germany)
2008-07-01
We use Jost-functions to determine the leading and next-to-leading terms of the phase shifts {delta}{sub l}(k) in the case of homogeneous attractive singular potentials -1/r{sup {alpha}}, {alpha}>2, for arbitrary angular momentum l with incoming boundary conditions at small distances. The Jost-solutions are obtained by solving a Volterra-equation and a more general ansatz is used to fit the Jost-solutions to the WKB-waves in the inner region, where the WKB-approximation is accurate. A connection between the phase shifts of attractive and repulsive homogeneous singular potentials is presented.
On the genericity of spacetime singularities
Indian Academy of Sciences (India)
tant mathematical input was needed in addition to the Raychaudhuri equation. ..... ric collapse evolution from given initial data on a partial Cauchy surface S. Then ... De- pending on the initial conditions and the types of evolution of the collapse process allowed by the Einstein equations, the singularities of collapse can be ...
On the concept of spectral singularities
Indian Academy of Sciences (India)
Gusein Sh Guseinov. On the other hand, it turns out that (as A Mostafazadeh complained to the author) it is not easy to find in the literature a precise and explicit definition of the spectral singularity. Our intent in the present paper is to try to give an elementary introduction to this specific subject. We describe a definition of the.
A singularity theorem based on spatial averages
Indian Academy of Sciences (India)
Open non-rotating Universes, expanding everywhere with a non-vanishing spatial average of the matter variables, show severe geodesic incompletness in the past. Another way of stating the result is that, under the same conditions, any singularity-free model must have a vanishing spatial average of the energy density ...
A singularity theorem based on spatial averages
Indian Academy of Sciences (India)
cosmological models, but using purely spatial averages. As remarked at the end of the previous subsection, all known non-singular models were 'cosmological' in the sense that they could not describe a finite star surrounded by a surface of vanishing pressure. However, it can certainly happen that (say) the energy density ...
Singularity and Community: Levinas and Democracy
Zhao, Guoping
2016-01-01
This article explores and extends Levinas's ideas of singularity and community as multiplicity and argues that his identification of language and discourse as the means to create ethical communities provides tangible possibilities for rebuilding genuine democracy in a humane world. These ideas help us reimagine school and classroom as communities…
Diamagnetism of quantum gases with singular potentials
DEFF Research Database (Denmark)
Briet, Philippe; Cornean, Horia; Savoie, Baptiste
2010-01-01
We consider a gas of quasi-free quantum particles confined to a finite box, subjected to singular magnetic and electric fields. We prove in great generality that the finite volume grand-canonical pressure is analytic with respect to the chemical potential and the intensity of the external magneti...
Singularity Penetration with Unit Delay (SPUD
Directory of Open Access Journals (Sweden)
Timothy Sands
2018-02-01
Full Text Available This manuscript reveals both the full experimental and methodical details of a most-recent patent that demonstrates a much-desired goal of rotational maneuvers via angular exchange momentum, namely extremely high torque without mathematical singularity and accompanying loss of attitude control while the angular momentum trajectory resides in the mathematical singularity. The paper briefly reviews the most recent literature, and then gives theoretical development for implementing the new control methods described in the patent to compute a non-singular steering command to the angular momentum actuators. The theoretical developments are followed by computer simulations used to verify the theoretical computation methodology, and then laboratory experiments are used for validation on a free-floating hardware simulator. A typical 3/4 CMG array skewed at 54.73° yields 0.15H. Utilizing the proposed singularity penetration techniques, 3H momentum is achieved about yaw, 2H about roll, and 1H about pitch representing performance increases of 1900%, 1233%, and 566% respectfully.
Geometric singular perturbation theory in biological practice
Hek, G.
2010-01-01
Geometric singular perturbation theory is a useful tool in the analysis of problems with a clear separation in time scales. It uses invariant manifolds in phase space in order to understand the global structure of the phase space or to construct orbits with desired properties. This paper explains
Fault Detection in Singular Bilinear Systems
Directory of Open Access Journals (Sweden)
Sara Mansouri Nasab
2011-10-01
Full Text Available Singular systems naturally exist in many physicall and practical systems in control issues. Also, a big group of nonlinear systems which can not be estimated by linear systems are carfully estimated by bilinear systems. On the other hand, if the user in sensetive systems dose not detect the fault on time,a considerable amount of facilities and information will be damaged and destroyed; therefore,the fault detection and recognition in singular bilinear systems with unknown input disturbances and faults by using bilinear sliding mode observer, is done in this paper because of the importance that singular bilinear systems have in modeling physical systems and undesirable effect of fault on performances of systems. For this perpose, have at first singular bilinear system is decomposed, then a sliding mode observer is considered for it. More over, a method is given for fault detection and isolation base on sliding mode observer. And at the end, we have a simulation for a numeral example to illustrate the effect of given method.
Mobile communications technology: The singular factor responsible ...
African Journals Online (AJOL)
This paper investigated the factors responsible for the growth of Internet usage on the African continent. The principal finding was that increasing growth of Internet usage is also down to one singular factor: mobile communications technology. The proliferation of mobile phone usage in Africa has resulted in the sustained ...
Inverting dedevelopment: geometric singularity theory in embryology
Bookstein, Fred L.; Smith, Bradley R.
2000-10-01
The diffeomorphism model so useful in the biomathematics of normal morphological variability and disease is inappropriate for applications in embryogenesis, where whole coordinate patches are created out of single points. For this application we need a suitable algebra for the creation of something from nothing in a carefully organized geometry: a formalism for parameterizing discrete nondifferentiabilities of invertible functions on Rk, k $GTR 1. One easy way to begin is via the inverse of the development map - call it the dedevelopment map, the deformation backwards in time. Extrapolated, this map will inevitably have singularities at which its derivative is zero. When the dedevelopment map is inverted to face forward in time, the singularities become appropriately isolated infinities of derivative. We have recently introduced growth visualizations via extrapolations to the isolated singularities at which only one directional derivative is zero. Maps inverse to these create new coordinate patches directionally rather than radically. The most generic singularity that suits this purpose is the crease f(x,y) equals (x,x2y+y3), which has already been applied in morphometrics for the description of focal morphogenetic phenomena. We apply it to embryogenesis in the form of its analytic inverse, and demonstrate its power using a priceless new data set of mouse embryos imaged in 3D by micro-MR with voxels smaller than 100micrometers 3.
Classical resolution of singularities in dilaton cosmologies
Bergshoeff, EA; Collinucci, A; Roest, D; Russo, JG; Townsend, PK
2005-01-01
For models of dilaton gravity with a possible exponential potential, such as the tensor-scalar sector of ITA supergravity, we show how cosmological solutions correspond to trajectories in a 2D Milne space (parametrized by the dilaton and the scale factor). Cosmological singularities correspond to
Resolving curvature singularities in holomorphic gravity
Mantz, C.L.M.; Prokopec, T.|info:eu-repo/dai/nl/326113398
2011-01-01
We formulate a holomorphic theory of gravity and study how the holomorphy symmetry alters the two most important singular solutions of general relativity: black holes and cosmology. We show that typical observers (freely) falling into a holomorphic black hole do not encounter a curvature
Balder, E.J.
1984-01-01
This note presents a new, quick approach to existence results without convexity conditions for optimal control problems with singular components in the sense of [11.], 438–485). Starting from the resolvent kernel representation of the solutions of a linear integral equation, a version of Fatou's
Entanglement and area laws in weakly correlated gaussian states
Matera, Juan Mauricio; Rossignoli, Raúl Dante; Canosa, Norma B.
2012-01-01
We examine the evaluation of entanglement measures in weakly correlated gaussian states. It is shown that they can be expressed in terms of the singular values of a particular block of the generalized contraction matrix. This result enables to obtain in a simple way asymptotic expressions and related area laws for the entanglement entropy of bipartitions in pure states, as well as for the logarithmic negativity associated with bipartitions and also pairs of arbitrary subsystems. As illustrati...
Directory of Open Access Journals (Sweden)
Marwan Abukhaled
2013-01-01
Full Text Available The variational iteration method is applied to solve a class of nonlinear singular boundary value problems that arise in physiology. The process of the method, which produces solutions in terms of convergent series, is explained. The Lagrange multipliers needed to construct the correctional functional are found in terms of the exponential integral and Whittaker functions. The method easily overcomes the obstacle of singularities. Examples will be presented to test the method and compare it to other existing methods in order to confirm fast convergence and significant accuracy.
Positive solutions for higher order singular p-Laplacian boundary ...
Indian Academy of Sciences (India)
This paper investigates 2 m − t h ( m ≥ 2 ) order singular -Laplacian boundary value problems, and obtains the necessary and sufficient conditions for existence of positive solutions for sublinear 2-th order singular -Laplacian BVPs on closed interval.
São Carlos Workshop on Real and Complex Singularities
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.
Singularities and the geometry of spacetime
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
Constructing Current Singularity in a 3D Line-tied Plasma
Zhou, Yao; Huang, Yi-Min; Qin, Hong; Bhattacharjee, A.
2018-01-01
We revisit Parker’s conjecture of current singularity formation in 3D line-tied plasmas using a recently developed numerical method, variational integration for ideal magnetohydrodynamics in Lagrangian labeling. With the frozen-in equation built-in, the method is free of artificial reconnection, and hence it is arguably an optimal tool for studying current singularity formation. Using this method, the formation of current singularity has previously been confirmed in the Hahm–Kulsrud–Taylor problem in 2D. In this paper, we extend this problem to 3D line-tied geometry. The linear solution, which is singular in 2D, is found to be smooth for arbitrary system length. However, with finite amplitude, the linear solution can become pathological when the system is sufficiently long. The nonlinear solutions turn out to be smooth for short systems. Nonetheless, the scaling of peak current density versus system length suggests that the nonlinear solution may become singular at finite length. With the results in hand, we can neither confirm nor rule out this possibility conclusively, since we cannot obtain solutions with system length near the extrapolated critical value.
7 CFR 61.1 - Words in singular form.
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...
7 CFR 46.1 - Words in singular form.
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...
7 CFR 900.1 - Words in the singular form.
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...
Positive solutions for higher order singular p-Laplacian boundary ...
Indian Academy of Sciences (India)
of positive solutions for sublinear 2m-th order singular p-Laplacian BVPs on closed interval. Keywords. Positive solution; singular BVPs; sufficient and necessary conditions; p-Laplacian equations. 1. Introduction. In this paper, we are concerned with higher order singular p-Laplacian boundary value problems. ⎧. ⎨. ⎩.
On the Theory of Multilinear Singular Operators with Rough Kernels on the Weighted Morrey Spaces
Directory of Open Access Journals (Sweden)
Sha He
2016-01-01
Full Text Available We study some multilinear operators with rough kernels. For the multilinear fractional integral operators TΩ,αA and the multilinear fractional maximal integral operators MΩ,αA, we obtain their boundedness on weighted Morrey spaces with two weights Lp,κ(u,v when DγA∈Λ˙β (|γ|=m-1 or DγA∈BMO (|γ|=m-1. For the multilinear singular integral operators TΩA and the multilinear maximal singular integral operators MΩA, we show they are bounded on weighted Morrey spaces with two weights Lp,κ(u,v if DγA∈Λ˙β (|γ|=m-1 and bounded on weighted Morrey spaces with one weight Lp,κ(w if DγA∈BMO (|γ|=m-1 for m=1,2.
Singularity analysis of frequency density of isotop age data
Cheng, Qiuming
2017-04-01
Frequency distribution (histogram) calculated on the basis of igneous and detrital zircon U-Pb ages has been commonly utilized to interpret the age (range) of magmatic events. The temporal properties of this type of data have also been integrated with other types of isotope data (e.g., neodymium, hafnium, and oxygen) to describe the high magmatic addition rate (MAR) caused by plate subduction. Major peaks are identified to determine pulses of high-volume magmatic flare-ups related to subduction. In this paper, power-law models are applied to analyze these age peaks. The strong singularities of these models indicate that magmatic flare ups might be related to nonlinear phenomena of plate subduction including but being not limited to phase transition, self-organized criticality and multiplicative cascade processes. The case studies chosen for methodology validation include an igneous zircon U-Pb datasets from Gangdese arc, a orogen related to the India-Asia collision and from the Coastal Batholith related to east pacific plate subduction. It was found that the age density around peaks ca 51-50 Ma in both datasets can be fitted by power-law functions with the age interval about 30 - 40 Myr. The positive singularities of the age peaks estimated by these power-law models suggest that these age peaks might be related to magmatic flare-ups caused by multiplicative cascade and self-organized criticality tectonic processes.
Spectral asymptotics for nonsmooth singular Green operators
DEFF Research Database (Denmark)
Grubb, Gerd
2014-01-01
Singular Green operators G appear typically as boundary correction terms in resolvents for elliptic boundary value problems on a domain Ω ⊂ ℝ n , and more generally they appear in the calculus of pseudodifferential boundary problems. In particular, the boundary term in a Krein resolvent formula......) are known. We show that (*) holds when G is a general selfadjoint nonnegative singular Green operator with symbol merely Hölder continuous in x. We also show (*) with t = 2 for the boundary term in the Krein resolvent formula comparing the Dirichlet and a Neumann-type problem for a strongly elliptic...... second-order differential operator (not necessarily selfadjoint) with coefficients in for some q > n....
Image compression using singular value decomposition
Swathi, H. R.; Sohini, Shah; Surbhi; Gopichand, G.
2017-11-01
We often need to transmit and store the images in many applications. Smaller the image, less is the cost associated with transmission and storage. So we often need to apply data compression techniques to reduce the storage space consumed by the image. One approach is to apply Singular Value Decomposition (SVD) on the image matrix. In this method, digital image is given to SVD. SVD refactors the given digital image into three matrices. Singular values are used to refactor the image and at the end of this process, image is represented with smaller set of values, hence reducing the storage space required by the image. Goal here is to achieve the image compression while preserving the important features which describe the original image. SVD can be adapted to any arbitrary, square, reversible and non-reversible matrix of m × n size. Compression ratio and Mean Square Error is used as performance metrics.
Symmetries and singularities of the Szekeres system
Energy Technology Data Exchange (ETDEWEB)
Paliathanasis, Andronikos, E-mail: anpaliat@phys.uoa.gr [Instituto de Ciencias Físicas y Matemáticas, Universidad Austral de Chile, Valdivia (Chile); Institute of Systems Science, Durban University of Technology, POB 1334, Durban 4000 (South Africa); Leach, P.G.L., E-mail: leach.peter@ucy.ac.cy [Department of Mathematics and Institute of Systems Science, Research and Postgraduate Support, Durban University of Technology, POB 1334, Durban 4000 (South Africa); School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Private Bag X54001, Durban 4000 (South Africa)
2017-04-18
Highlights: • Lagrangian formalism of the Szekeres system. • Symmetries and conservation laws for the silent universe. • Comparison of stability analysis of special solutions with the Laurent expansion provided by the singularity analysis. - Abstract: The Szekeres system is studied with two methods for the determination of conservation laws. Specifically we apply the theory of group invariant transformations and the method of singularity analysis. We show that the Szekeres system admits a Lagrangian and the conservation laws that we find can be derived by the application of Noether's theorem. The stability for the special solutions of the Szekeres system is studied and it is related with the Left or Right Painlevé Series which describes the expansions.
The Singularity May Never Be Near
Walsh, Toby
2016-01-01
There is both much optimism 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 intelligent species star...
Superlinear singular fractional boundary-value problems
Directory of Open Access Journals (Sweden)
Imed Bachar
2016-04-01
Full Text Available In this article, we study the superlinear fractional boundary-value problem $$\\displaylines{ D^{\\alpha }u(x =u(xg(x,u(x,\\quad 00$. The function $g(x,u\\in C((0,1\\times [ 0,\\infty ,[0,\\infty$ that may be singular at x=0 and x=1 is required to satisfy convenient hypotheses to be stated later.
Critical singular problems on unbounded domains
Directory of Open Access Journals (Sweden)
D. C. de Morais Filho
2005-01-01
Full Text Available We present some results of existence for the following problem: −Δu=a(xg(u+u|u|2∗−2, x∈ℝN(N≥3, u∈D1,2(ℝN, where the function a is a sign-changing function with a singularity at the origin and g has growth up to the Sobolev critical exponent 2∗=2N/(N−2.
Cosmological Solutions of Supergravity in Singular Spaces
Brax, P; Brax, Ph.
2001-01-01
We study brane-world solutions of five-dimensional supergravity in singular spaces. We exhibit a self-tuned four-dimensional cosmological constant when five-dimensional supergravity is broken by an arbitrary tension on the brane-world. The brane-world metric is of the FRW type corresponding to a cosmological constant $\\Omega_{\\Lambda}={5/7}$ and an equation of state $\\omega=-{5/7}$ which are consistent with experiment.
Zemlyanova, A. Y.
2013-03-08
A problem of an interface crack between two semi-planes made out of different materials under an action of an in-plane loading of general tensile-shear type is treated in a semi-analytical manner with the help of Dirichlet-to-Neumann mappings. The boundaries of the crack and the interface between semi-planes are subjected to a curvature-dependent surface tension. The resulting system of six singular integro-differential equations is reduced to the system of three Fredholm equations. It is shown that the introduction of the curvature-dependent surface tension eliminates both classical integrable power singularity of the order 1/2 and an oscillating singularity present in a classical linear elasticity solutions. The numerical results are obtained by solving the original system of singular integro-differential equations by approximating unknown functions with Taylor polynomials. © 2013 The Author.
Spinfoams near a classical curvature singularity
Han, Muxin; Zhang, Mingyi
2016-11-01
We apply the technique of the spinfoam to study space-time, which, classically, contains a curvature singularity. We derive from the full covariant loop quantum gravity (LQG) that the region near curvature singularity has to be of the strong quantum gravity effect. We show that the spinfoam configuration describing the near-singularity region has to be of small spins j , in order that its contribution to the full spinfoam amplitude is nontrivial. The spinfoams in low and high-curvature regions of space-time may be viewed as in two different phases of covariant LQG. There should be a phase transition as space-time described by the spinfoam becomes more and more curved. A candidate of the order parameter is proposed for understanding the phase transition. Moreover, we also analyze the spin-spin correlation function of the spinfoam and show the correlation is of long range in the low-curvature phase. This work is a first step toward understanding the physics of black hole and early Universe from the full covariant LQG theory.
WEAK GORENSTEIN GLOBAL DIMENSION
Bennis, Driss
2010-01-01
In this paper, we investigate the weak Gorenstein global dimensions. We are mainly interested in studying the problem when the left and right weak Gorenstein global dimensions coincide. We first show, for GF-closed rings, that the left and right weak Gorenstein global dimensions are equal when they are finite. Then, we prove that the same equality holds for any two-sided coherent ring. We conclude the paper with some examples and a brief discussion of the scope and limits of our results.
Singular inflation from generalized equation of state fluids
Nojiri, S; Oikonomou, V K
2015-01-01
We study models with a generalized inhomogeneous equation of state fluids, in the context of singular inflation, focusing to so-called Type IV singular evolution. In the simplest case, this cosmological fluid is described by an equation of state with constant $w$, and therefore a direct modification of this constant $w$ fluid, is achieved by using a generalized form of an equation of state. We investigate from which models with generalized phenomenological equation of state, a Type IV singular inflation can be generated and what the phenomenological implications of this singularity would be. We support our results with illustrative examples and we also study the impact of the Type IV singularities on the slow-roll parameters and on the observational inflationary indices, showing the consistency with Planck mission results. The unification of singular inflation with singular dark energy era for specific generalized fluids is also proposed.
Singular inflation from generalized equation of state fluids
Energy Technology Data Exchange (ETDEWEB)
Nojiri, S., E-mail: nojiri@gravity.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, S.D., E-mail: odintsov@ieec.uab.es [Institut de Ciencies de lEspai (IEEC-CSIC), Campus UAB, Carrer de Can Magrans, s/n, 08193 Cerdanyola del Valles, Barcelona (Spain); ICREA, Passeig Lluîs Companys, 23, 08010 Barcelona (Spain); National Research Tomsk State University, 634050 Tomsk (Russian Federation); Tomsk State Pedagogical University, 634061 Tomsk (Russian Federation); Oikonomou, V.K., E-mail: v.k.oikonomou1979@gmail.com [Department of Theoretical Physics, Aristotle University of Thessaloniki, 54124 Thessaloniki (Greece); National Research Tomsk State University, 634050 Tomsk (Russian Federation); Tomsk State Pedagogical University, 634061 Tomsk (Russian Federation)
2015-07-30
We study models with a generalized inhomogeneous equation of state fluids, in the context of singular inflation, focusing to so-called Type IV singular evolution. In the simplest case, this cosmological fluid is described by an equation of state with constant w, and therefore a direct modification of this constant w fluid is achieved by using a generalized form of an equation of state. We investigate from which models with generalized phenomenological equation of state, a Type IV singular inflation can be generated and what the phenomenological implications of this singularity would be. We support our results with illustrative examples and we also study the impact of the Type IV singularities on the slow-roll parameters and on the observational inflationary indices, showing the consistency with Planck mission results. The unification of singular inflation with singular dark energy era for specific generalized fluids is also proposed.
H(infinity) filtering for fuzzy singularly perturbed systems.
Yang, Guang-Hong; Dong, Jiuxiang
2008-10-01
This paper considers the problem of designing H(infinity) filters for fuzzy singularly perturbed systems with the consideration of improving the bound of singular-perturbation parameter epsilon. First, a linear-matrix-inequality (LMI)-based approach is presented for simultaneously designing the bound of the singularly perturbed parameter epsilon, and H(infinity) filters for a fuzzy singularly perturbed system. When the bound of singularly perturbed parameter epsilon is not under consideration, the result reduces to an LMI-based design method for H(infinity) filtering of fuzzy singularly perturbed systems. Furthermore, a method is given for evaluating the upper bound of singularly perturbed parameter subject to the constraint that the considered system is to be with a prescribed H(infinity) performance bound, and the upper bound can be obtained by solving a generalized eigenvalue problem. Finally, numerical examples are given to illustrate the effectiveness of the proposed methods.
Directory of Open Access Journals (Sweden)
Giuliano Dall'O'
2013-11-01
Full Text Available Owners and municipalities face the choice to renovate or rebuild buildings in order to improve energy efficiency and sustainability. The process of upgrading the existing building stock can be supported by land management tools, i.e., municipal energy plans (MEP or sustainable building codes (BC, that municipalities use to plan, check and monitor actions taken. Many local and regional authorities are involved in the Covenant of Mayors supported by the European Union (EU: the sustainable energy action plan (SEAP is the key document in which the Covenant signatory outlines how it intends to reach CO2 reduction target by 2020. Sustainability at the urban scale is also supported by voluntary certification schemes such as Leadership in Energy and Environmental Design (LEED® for neighbourhood development proposed by the United States Green Building Council (USGBC, Building Research Establishment Environmental Assessment Method (BREEAM Communities proposed by UK Building Research Establishment (BRE and Comprehensive Assessment System for Built Environment Efficiency (CASBEE for Urban Development proposed by the Japan GreenBuild Council. The fact that there are so many tools to manage urban sustainability is positive, but what happens when multiple tools are applied to the same territory? Overlap, redundancy, and conflicts in management may be critical elements. The purpose of this article is to analyze these critical issues, highlighting the elements of integration and possible synergies for effective management of sustainability at the local level.
Lee, T. D.
1970-07-01
While the phenomenon of beta-decay was discovered near the end of the last century, the notion that the weak interaction forms a separate field of physical forces evolved rather gradually. This became clear only after the experimental discoveries of other weak reactions such as muon-decay, muon-capture, etc., and the theoretical observation that all these reactions can be described by approximately the same coupling constant, thus giving rise to the notion of a universal weak interaction. Only then did one slowly recognize that the weak interaction force forms an independent field, perhaps on the same footing as the gravitational force, the electromagnetic force, and the strong nuclear and sub-nuclear forces.
Less singular quasicrystals: The case of low codimensions
Jagannathan, A.
2001-10-01
We consider a set of tilings proposed recently as d-dimensional generalizations of the Fibonacci chain, by Vidal and Mosseri. These tilings have a particularly simple theoretical description, making them appealing candidates for analytical solutions for electronic properties. Given their self-similar geometry, one could expect that the tight-binding spectra of these tilings might possess the characteristically singular features of well-known quasiperiodic systems such as the Penrose or the octagonal tilings. We show here, by a numerical study of statistical properties of the tight-binding spectra that these tilings fall rather in an intermediate category between the crystal and the quasicrystal, i.e., in a class of almost integrable models. This is certainly a consequence of the low codimension of the tilings.
Chuang, S. Y.; Chang, F. H.; Bell, J. R.
Consideration is given to the development of a weak bond screening system which is based on the utilization of a high power ultrasonic (HPU) technique. The instrumentation of the prototype bond strength screening system is described, and the adhesively bonded specimens used in the system developmental effort are detailed. Test results obtained from these specimens are presented in terms of bond strength and level of high power ultrasound irradiation. The following observations were made: (1) for Al/Al specimens, 2.6 sec of HPU irradiation will screen weak bond conditions due to improper preparation of bonding surfaces; (2) for composite/composite specimens, 2.0 sec of HPU irradiation will disrupt weak bonds due to under-cured conditions; (3) for Al honeycomb core with composite skin structure, 3.5 sec of HPU irradiation will disrupt weak bonds due to bad adhesive or oils contamination of bonding surfaces; and (4) for Nomex honeycomb with Al skin structure, 1.3 sec of HPU irradiation will disrupt weak bonds due to bad adhesive.
The Singularity May Never Be Near
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”...
Singularities, horizons, firewalls, and local conformal symmetry
Hooft, Gerard 't
2015-01-01
The Einstein-Hilbert theory of gravity can be rephrased by focusing on local conformal symmetry as an exact, but spontaneously broken symmetry of nature. The conformal component of the metric field is then treated as a dilaton field with only renormalizable interactions. This imposes constraints on the theory, which can also be viewed as demanding regularity of the action as the dilaton field variable tends to 0. In other words, we have constraints on the small distance behaviour. Our procedure appears to turn a black hole into a regular, topologically trivial soliton without singularities, horizons of firewalls, but many questions remain.
On the singular solutions of nonlinear singular partial differential equations I
Tahara, Hidetoshi
2001-01-01
Let us consider the following nonlinear singular partial differential equation: $(t\\partial_{t})^{m}u=F(t,x,\\{(t\\partial_{t})^{j}\\partial_{x}^{\\alpha}u\\}_{j+|\\alpha|\\leq m,j0$ . Clearly $\\mathscr{S}_{log}\\supset \\mathscr{S}_{+}$ . The paper gives a sufficient condition for $\\mathscr{S}_{log}=\\mathscr{S}_{+}$ to be valid.
DEFF Research Database (Denmark)
Lukas, Manuel; Hillebrand, Eric
Relations between economic variables can often not be exploited for forecasting, suggesting that predictors are weak in the sense that estimation uncertainty is larger than bias from ignoring the relation. In this paper, we propose a novel bagging predictor designed for such weak predictor...... variables. The predictor is based on a test for finitesample predictive ability. Our predictor shrinks the OLS estimate not to zero, but towards the null of the test which equates squared bias with estimation variance. We derive the asymptotic distribution and show that the predictor can substantially lower...
On the Reduction of Singularly-Perturbed Linear Differential Systems
Barkatou, Moulay; Maddah, Suzy S.; Abbas, Hassan
2014-01-01
In this article, we recover singularly-perturbed linear differential systems from their turning points and reduce the rank of the singularity in the parameter to its minimal integer value. Our treatment is Moser-based; that is to say it is based on the reduction criterion introduced for linear singular differential systems by Moser. Such algorithms have proved their utility in the symbolic resolution of the systems of linear functional equations, giving rise to the package ISOLDE, as well as ...
Big-Rip, Sudden Future, and other exotic singularities in the universe
Dabrowski, Mariusz P
2016-01-01
We discuss exotic singularities in the evolution of the universe motivated by the progress of observations in cosmology. Among them there are: Big-Rip (BR), Sudden Future Singularities (SFS), Generalized Sudden Future Singularities (GSFS), Finite Density Singularities (FD), type III, and type IV singularities. We relate some of these singularities with higher-order characteristics of expansion such as jerk and snap. We also discuss the behaviour of pointlike objects and classical strings on the approach to these singularities.
Electricity consumption forecasting using singular spectrum analysis
Directory of Open Access Journals (Sweden)
Moisés Lima de Menezes
2015-01-01
Full Text Available El Análisis Espectral Singular (AES es una técnica no paramétrica que permite la descomposición de una serie de tiempo en una componente de señal y otra de ruido. De este modo, AES es una técnica útil para la extracción de la tendencia, la suavización y el filtro una serie de tiempo. En este artículo se investiga el efecto sobre el desempeño los modelos de Holt-Winters y de Box & Jenkins al ser aplicados a una serie de tiempo filtrada por AES. Tres diferentes metodologías son evaluadas con el enfoque de AES: Análisis de Componentes Principales (ACP, análisis de conglomerados y análisis gráfico de vectores singulares. Con el fin de ilustrar y comparar dichas metodologías, en este trabajo también se presentaron los principales resultados de un experimento computacional para el consumo residencial mensual de electricidad en Brasil.
Combining transcriptional datasets using the generalized singular value decomposition
Directory of Open Access Journals (Sweden)
Burton Rachel A
2008-08-01
Full Text Available Abstract Background Both microarrays and quantitative real-time PCR are convenient tools for studying the transcriptional levels of genes. The former is preferable for large scale studies while the latter is a more targeted technique. Because of platform-dependent systematic effects, simple comparisons or merging of datasets obtained by these technologies are difficult, even though they may often be desirable. These difficulties are exacerbated if there is only partial overlap between the experimental conditions and genes probed in the two datasets. Results We show here that the generalized singular value decomposition provides a practical tool for merging a small, targeted dataset obtained by quantitative real-time PCR of specific genes with a much larger microarray dataset. The technique permits, for the first time, the identification of genes present in only one dataset co-expressed with a target gene present exclusively in the other dataset, even when experimental conditions for the two datasets are not identical. With the rapidly increasing number of publically available large scale microarray datasets the latter is frequently the case. The method enables us to discover putative candidate genes involved in the biosynthesis of the (1,3;1,4-β-D-glucan polysaccharide found in plant cell walls. Conclusion We show that the generalized singular value decomposition provides a viable tool for a combined analysis of two gene expression datasets with only partial overlap of both gene sets and experimental conditions. We illustrate how the decomposition can be optimized self-consistently by using a judicious choice of genes to define it. The ability of the technique to seamlessly define a concept of "co-expression" across both datasets provides an avenue for meaningful data integration. We believe that it will prove to be particularly useful for exploiting large, publicly available, microarray datasets for species with unsequenced genomes by
Propagation of the Lissajous singularity dipole in free space
Chen, Haitao; Gao, Zenghui; Zou, Xuefang; Xiao, Xi; Wang, Fanhou; Yang, Huajun
2014-01-01
The propagation properties of a pair of Lissajous singularities with opposite singularity indexes called the Lissajous singularity dipole (LSD) in free space are studied analytically and illustrated numerically. It is shown that the motion, creation, annihilation and change in the degree of polarization of the LSD, and change in the shape of Lissajous figures take place by suitably varying the waist width, off-axis distance or propagation distance. In particular, the creation and shift to infinity of a single Lissajous singularity may appear. A comparison with the free-space propagation of an optical vortex dipole and a C-dipole is also made.
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.
Turlay, René
1979-01-01
In this review of charged weak currents the author concentrates on inclusive high energy neutrino physics. The authors discusses the general structure of charged currents, new results on total cross- sections, the Callan-Gross relation, antiquark distributions, scaling violations and tests of QCD. A very short summary on multilepton physics is given. (44 refs).
DEFF Research Database (Denmark)
Kohlenbach, Ulrich Wilhelm
2002-01-01
We show that the so-called weak Markov's principle (WMP) which states that every pseudo-positive real number is positive is underivable in E-HA + AC. Since allows one to formalize (atl eastl arge parts of) Bishop's constructive mathematics, this makes it unlikely that WMP can be proved within...
Ardema, M. D.; Yang, L.
1985-01-01
A method of solving the boundary-layer equations that arise in singular-perturbation analysis of flightpath optimization problems is presented. The method is based on Picard iterations of the integrated form of the equations and does not require iteration to find unknown boundary conditions. As an example, the method is used to develop a solution algorithm for the zero-order boundary-layer equations of the aircraft minimum-time-to-climb problem.
Zhao, Ming; Jia, Xiaodong
2017-09-01
Singular value decomposition (SVD), as an effective signal denoising tool, has been attracting considerable attention in recent years. The basic idea behind SVD denoising is to preserve the singular components (SCs) with significant singular values. However, it is shown that the singular values mainly reflect the energy of decomposed SCs, therefore traditional SVD denoising approaches are essentially energy-based, which tend to highlight the high-energy regular components in the measured signal, while ignoring the weak feature caused by early fault. To overcome this issue, a reweighted singular value decomposition (RSVD) strategy is proposed for signal denoising and weak feature enhancement. In this work, a novel information index called periodic modulation intensity is introduced to quantify the diagnostic information in a mechanical signal. With this index, the decomposed SCs can be evaluated and sorted according to their information levels, rather than energy. Based on that, a truncated linear weighting function is proposed to control the contribution of each SC in the reconstruction of the denoised signal. In this way, some weak but informative SCs could be highlighted effectively. The advantages of RSVD over traditional approaches are demonstrated by both simulated signals and real vibration/acoustic data from a two-stage gearbox as well as train bearings. The results demonstrate that the proposed method can successfully extract the weak fault feature even in the presence of heavy noise and ambient interferences.
Examples of Naked Singularity Formation in Higher-Dimensional Einstein-Vacuum Spacetimes
An, Xinliang; Zhang, Xuefeng
2018-02-01
The vacuum Einstein equations in 5+1 dimensions are shown to admit solutions describing naked singularity formation in gravitational collapse from nonsingular asymptotically locally flat initial data that contain no trapped surface. We present a class of specific examples with topology $\\mathbb{R}^{3+1} \\times S^2$. Thanks to the Kaluza-Klein dimensional reduction, these examples are constructed by lifting continuously self-similar solutions of the 4-dimensional Einstein-scalar field system with a negative exponential potential. The latter solutions are obtained by solving a 3-dimensional autonomous system of first-order ordinary differential equations with a combined analytic and numerical approach. Their existence provides a new test-bed for weak cosmic censorship in higher-dimensional gravity. In addition, we point out that a similar attempt of lifting Christodoulou's naked singularity solutions of massless scalar fields fails to capture formation of naked singularities in 4+1 dimensions, due to a diverging Kretschmann scalar in the initial data.
A vida singular de um jovem militante
Directory of Open Access Journals (Sweden)
Áurea Maria Guimarães
2012-01-01
Full Text Available Esse artigo é fruto de uma pesquisa realizada no período de 2007 a 2010, junto a jovens militantes da cidade de Campinas, com o objetivo de compreender as diferentes maneiras que conduziam esses jovens tanto a reproduzir um modelo de vida quanto a criar outras possibilidades de militância na relação com esse modelo. Entre as histórias orais de vida narradas por jovens que militavam em diferentes grupos ou instituições, escolhi a vida de Biula, representante do movimento estudantil secundarista, procurando evidenciar que a singularidade desta vida, como também e a de outros jovens, estava conectada à problematização que faziam no interior de certas práticas, histórica e culturalmente constituídas, possibilitando a criação de novas formas de subjetivação nas quais se modificava a experiência que tinham deles mesmos na relação com os seus heróis ou modelos de referência. Palavras-chave: história oral – transcriação – heróis – resistência - processos de singularização. THE SINGULAR LIFE OF A YOUNG MILITANT ABSTRACT This article is the result of a research carried out from 2007 to 2010 with young militants in the city of Campinas, aiming to understand the different ways which conducted these youngsters to both reproduce a life model and create other possibilities of militancy in the relationship with this model. Among oral stories narrated by young militants from different groups or institutions, I have chosen the life of Biula, a representative of the secondary students’ movement, trying to show that the singularity of this life and other youngsters’ lives was connected to the problematization they promoted within certain practices, historically and culturally built, thus enabling the creation of new subjectification modes in which the experience they had of themselves in the relationship with their heroes or reference models has changed. Key words: oral history - transcreation – heroes
Rhodes, J. D.; Bennett, D. P.; Kaiser, N.
2001-12-01
Weak lensing by large-scale structure (cosmic shear) provides an opportunity to directly observe the dark matter in the universe. Current ground-based and space-based surveys have demonstrated the efficacy of this technique in determining the mass distribution and thus placing constraints on cosmological parameters such as Ω m, σ 8, and the bias parameter b. Current surveys have been hampered by the comparatively low resolution of ground-based telescopes and the small field of view of HST. To make significant progress in this field, wide field space-based surveys are needed. The Galactic Exoplanet Survey Telescope (GEST) will be able to provide 500- 1000 sqare degrees with a resolution of better than 0.2 arcseconds in multiple filters. This will make it an ideal instrument for a weak lensing survey.
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.
Singular Optimal Controls of Rocket Motion (Survey)
Kiforenko, B. N.
2017-05-01
Survey of modern state and discussion of problems of the perfection of methods of investigation of variational problems with a focus on mechanics of space flight are presented. The main attention is paid to the enhancement of the methods of solving of variational problems of rocket motion in the gravitational fields, including rocket motion in the atmosphere. These problems are directly connected with the permanently actual problem of the practical astronautics to increase the payload that is orbited by the carrier rockets in the circumplanetary orbits. An analysis of modern approaches to solving the problems of control of rockets and spacecraft motion on the trajectories with singular arcs that are optimal for the motion of the variable mass body in the medium with resistance is given. The presented results for some maneuvers can serve as an information source for decision making on designing promising rocket and space technology
On transformation to the singularly perturbed system
Bykov, V.
2011-01-01
A rapid progress in hard- and software development of computational facilities as well as in numerical methods has increased the role of numerical simulations in the quantitative system analysis of many engineering problems. At the same time, the system complexity (in terms of dimensionality and non-linearity) has grown considerably increasing demand for automatic methods of analysis of qualitative system behavior. For instance, nowadays, definition of key system parameters controlling the system dynamics and finding critical regimes automatically have become crucial issue of numerical system analysis. In the present paper a transformation to the Singularly Perturbed System (SPS) as a main theoretical framework to cope with the complexity and high dimensionality will be discussed in detail. Both simple but famous and meaningful model example of Van der Pol oscillator and an example of application to numerical analysis of chemical kinetics mechanisms will be used to show the potential of the suggested framework.
Spectral singularities and zero energy bound states
Energy Technology Data Exchange (ETDEWEB)
Heiss, W.D. [National Institute for Theoretical Physics, Stellenbosch Institute for Advanced Study, and Institute of Theoretical Physics, University of Stellenbosch, 7602 Matieland (South Africa); Nazmitdinov, R.G. [Department de Fisica, Universitat de les Illes Balears, E-07122 Palma de Mallorca (Spain); Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, 141980 Dubna (Russian Federation)
2011-08-15
Single particle scattering around zero energy is re-analysed in view of recent experiments with ultra-cold atoms, nano-structures and nuclei far from the stability valley. For non-zero orbital angular momentum the low energy scattering cross section exhibits dramatic changes depending on the occurrence of either a near resonance or a bound state or the situation in between, that is a bound state at zero energy. Such state is singular in that it has an infinite scattering length, behaves for the eigenvalues but not for the eigenfunctions as an exceptional point and has no pole in the scattering function. These results should be observable whenever the interaction or scattering length can be controlled. (authors)
Pure-Connection Gravity and Anisotropic Singularities
Krasnov, Kirill; Shtanov, Yuri
2018-01-01
In four space-time dimensions, there exists a special infinite-parameter family of chiral modified gravity theories. They are most properly described by a connection field, with space-time metric being a secondary and derived concept. All these theories have the same number of degrees of freedom as general relativity, which is the only parity-invariant member of this family. Modifications of general relativity can be arranged so as to become important in regions with large curvature. In this paper we review how a certain simple modification of this sort can resolve the Schwarzschild black-hole and Kasner anisotropic singularities of general relativity. In the corresponding solutions, the fundamental connection field is regular in space-time.
Energy Technology Data Exchange (ETDEWEB)
Suzuki, M.
1988-04-01
Dynamical mechanism of composite W and Z is studied in a 1/N field theory model with four-fermion interactions in which global weak SU(2) symmetry is broken explicitly by electromagnetic interaction. Issues involved in such a model are discussed in detail. Deviation from gauge coupling due to compositeness and higher order loop corrections are examined to show that this class of models are consistent not only theoretically but also experimentally.
Horizonless, singularity-free, compact shells satisfying NEC
Shankar, Karthik H.
2017-02-01
Gravitational collapse singularities are undesirable, yet inevitable to a large extent in General Relativity. When matter satisfying null energy condition (NEC) collapses to the extent a closed trapped surface is formed, a singularity is inevitable according to Penrose's singularity theorem. Since positive mass vacuum solutions are generally black holes with trapped surfaces inside the event horizon, matter cannot collapse to an arbitrarily small size without generating a singularity. However, in modified theories of gravity where positive mass vacuum solutions are naked singularities with no trapped surfaces, it is reasonable to expect that matter can collapse to an arbitrarily small size without generating a singularity. Here we examine this possibility in the context of a modified theory of gravity with torsion in an extra dimension. We study singularity-free static shell solutions to evaluate the validity of NEC on the shell. We find that with sufficiently high pressure, matter can be collapsed to arbitrarily small size without violating NEC and without producing a singularity.
Reliable finite element methods for self-adjoint singular perturbation ...
African Journals Online (AJOL)
It is well known that the standard finite element method based on the space Vh of continuous piecewise linear functions is not reliable in solving singular perturbation problems. It is also known that the solution of a two-point boundaryvalue singular perturbation problem admits a decomposition into a regular part and a finite ...
Stability of naked singularity arising in gravitational collapse of Type ...
Indian Academy of Sciences (India)
to choose the velocity function and rest of the initial data so that the end state of collapse is either a black hole (BH) or a naked singularity (NS). This result is significant for two reasons: (1) It produces a substantially 'big' initial data set which under gravitational collapse results into a naked singularity. (2) Type I matter fields.
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. Therefor...
A robust and secure watermarking scheme based on singular ...
Indian Academy of Sciences (India)
In this work, we propose a blind watermarking scheme based on the discrete wavelet transform (DWT) and singular value decomposition (SVD). Singular values (SV's) of high frequency (HH) band are used to optimize perceptual transparency and robustness constraints. Although most of the SVD-based schemes prove to ...
Solitary wave solution to a singularly perturbed generalized Gardner ...
Indian Academy of Sciences (India)
2017-03-24
Mar 24, 2017 ... Abstract. This paper is concerned with the existence of travelling wave solutions to a singularly perturbed gen- eralized Gardner equation with nonlinear terms of any order. By using geometric singular perturbation theory and based on the relation between solitary wave solution and homoclinic orbits of the ...
Some Characterizations of Dirac Type Singularity of Monopoles
Mochizuki, Takuro; Yoshino, Masaki
2017-12-01
We study singular monopoles on open subsets in the 3-dimensional Euclidean space. We give two characterizations of Dirac type singularities. One is given in terms of the growth order of the norms of sections which are invariant by the scattering map. The other is given in terms of the growth order of the norms of the Higgs fields.
A numerical method for solving singular De`s
Energy Technology Data Exchange (ETDEWEB)
Mahaver, W.T.
1996-12-31
A numerical method is developed for solving singular differential equations using steepest descent based on weighted Sobolev gradients. The method is demonstrated on a variety of first and second order problems, including linear constrained, unconstrained, and partially constrained first order problems, a nonlinear first order problem with irregular singularity, and two second order variational problems.
Stability of naked singularity arising in gravitational collapse of Type ...
Indian Academy of Sciences (India)
We further prove that the occurrence of such a naked singularity is stable with respect to small changes in the initial data. We remark that though the initial data leading to both black hole (BH) and naked singularity (NS) form a `big' subset of the true initial data set, their occurrence is not generic. The terms `stability' and ...
The Metaphysics and Epistemology of Singular Terms | Borg ...
African Journals Online (AJOL)
Can we draw apart questions of what it is to be a singular term (a metaphysical issue) from questions about how we tell when some expression is a singular term (an epistemological matter)? Prima facie, it might seem we can't: language, as a man-made edifice, might seem to prohibit such a distinction, and, indeed, some ...
Singularity is the future of ICT research | Osuagwu | West African ...
African Journals Online (AJOL)
Proponents of the singularity call the event an "intelligence explosion" which is a key factor of the Singularity where super-intelligence design successive generations of increasingly powerful minds. The originator of the term – Vernor Vinge - and popularized by Ray Kurzwei has proposed that Artificial Intelligence, human ...
On spherically symmetric singularity-free models in relativistic ...
Indian Academy of Sciences (India)
These observations led to the search of spherically symmetric singularity-free cosmo- logical models with a perfect fluid source characterized by isotropic pressure This search resulted in construction of two spherically symmetric singularity-free relativistic cosmo- logical models, describing universes filled with non-adiabatic ...
A Note on Inclusion Intervals of Matrix Singular Values
Directory of Open Access Journals (Sweden)
Shu-Yu Cui
2012-01-01
Full Text Available We establish an inclusion relation between two known inclusion intervals of matrix singular values in some special case. In addition, based on the use of positive scale vectors, a known inclusion interval of matrix singular values is also improved.
Complexity, Analysis and Control of Singular Biological Systems
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 ...
The structure of singularities in nonlocal transport equations
Energy Technology Data Exchange (ETDEWEB)
Hoz, F de la [Departamento de Matematica Aplicada, Universidad del PaIs Vasco-Euskal Herriko Unibertsitatea, Escuela Universitaria de IngenierIa Tecnica Industrial, Plaza de la Casilla 3, 48012 Bilbao (Spain); Fontelos, M A [Instituto de Matematicas y Fisica Fundamental, Consejo Superior de Investigaciones CientIficas, C/Serrano 123, 28006 Madrid (Spain)
2008-05-09
We describe the structure of solutions developing singularities in the form of cusps in finite time in nonlocal transport equations of the family: {theta}{sub t}-{delta}({theta}H({theta})){sub x}-(1-{delta})H({theta}){theta}{sub x}=0, 0<={delta}<=1, where H represents the Hilbert transform. Equations of this type appear in various contexts: evolution of vortex sheets, models for quasi-geostrophic equation and evolution equations for order parameters. Equation (1) was studied, and the existence of singularities developing in finite time was proved. The structure of such singularities was, nevertheless, not described. In this paper, we will describe the geometry of the solution in the neighborhood of the singularity once it develops and the (self-similar) way in which it is approached as t {yields} t{sub 0}, where t{sub 0} is the singular time.
The Notion of 'Singularity' in the Work of Gilles Deleuze
DEFF Research Database (Denmark)
Borum, Peter
2017-01-01
In Deleuze, singularity replaces generality in the economy of thought. A Deleuzian singularity is an event, but the notion comprises the effectuation of the event into form. The triptych émission–distribution–répartition itself distributes the dimensions of the passage from form-giving event...... to topological morphology. The Deleuzian concept of intensity allows thinking both pre-individuality and the rhizomatic connection of singularities on the metaphysical surface of structure. Reflections upon the philosophy of differential calculus allow for a coherent scaffolding reaching from pre......-individual intensity to specific individuality, in the passage from transcendental genesis to empirical morphogenesis. But if singularity as event is intensive, singularity as determinant of morphology – and hence, of structural metastability – is not. Although the differential scaffolding covers both intensive...
Infinite derivative gravity: non-singular cosmology & blackhole solutions
Mazumdar, A.
Both Einstein’s theory of General Relativity and Newton’s theory of gravity possess a short distance and small time scale catastrophe. The blackhole singularity and cosmological Big Bang singularity problems highlight that current theories of gravity are incomplete description at early times and small distances. I will discuss how one can potentially resolve these fundamental problems at a classical level and quantum level. In particular, I will discuss infinite derivative theories of gravity, where gravitational interactions become weaker in the ultraviolet, and therefore resolving some of the classical singularities, such as Big Bang and Schwarzschild singularity for compact non-singular objects with mass up to 1025 grams. In this lecture, I will discuss quantum aspects of infinite derivative gravity and discuss few aspects which can make the theory asymptotically free in the UV.
Workshop on Singularities in Geometry, Topology, Foliations and Dynamics
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.
DEFF Research Database (Denmark)
Haagerup, Uffe; Knudby, Søren
2015-01-01
The weak Haagerup property for locally compact groups and the weak Haagerup constant were recently introduced by the second author [27]. The weak Haagerup property is weaker than both weak amenability introduced by Cowling and the first author [9] and the Haagerup property introduced by Connes [6......] and Choda [5]. In this paper, it is shown that a connected simple Lie group G has the weak Haagerup property if and only if the real rank of G is zero or one. Hence for connected simple Lie groups the weak Haagerup property coincides with weak amenability. Moreover, it turns out that for connected simple...... Lie groups the weak Haagerup constant coincides with the weak amenability constant, although this is not true for locally compact groups in general. It is also shown that the semidirect product R2 × SL(2,R) does not have the weak Haagerup property....
Political corruption and weak state
Directory of Open Access Journals (Sweden)
Stojiljković Zoran
2013-01-01
Full Text Available The author starts from the hypothesis that it is essential for the countries of the region to critically assess the synergy established between systemic, political corruption and a selectively weak, “devious” nature of the state. Moreover, the key dilemma is whether the expanded practice of political rent seeking supports the conclusion that the root of all corruption is in the very existence of the state - particularly in excessive, selective and deforming state interventions and benefits that create a fertile ground for corruption? The author argues that the destructive combination of weak government and rampant political corruption is based on scattered state intervention, while also rule the parties cartel in the executive branch subordinate to parliament, the judiciary and the police. Corrupt exchange takes place with the absence of strong institutional framework and the precise rules of the political and electoral games, control of public finances and effective political and anti-monopoly legislation and practice included. Exit from the current situation can be seen in the realization of effective anticorruption strategy that integrates preventive and repressive measures and activities and lead to the establishment of principles of good governance. [Projekat Ministarstva nauke Republike Srbije, br. 179076: Politički identitet Srbije u regionalnom i globalnom kontekstu
Cultural capital: strengths, weaknesses and two advancements
van de Werfhorst, H.G.
2010-01-01
In this paper I discuss two weaknesses in Bourdieu’s work on cultural capital, both of which are related to his integration of the multidimensional nature of social space in different domains of life: social mobility, lifestyle differentiation, and political orientation. First, there is an anomaly
Energy Technology Data Exchange (ETDEWEB)
Cheng, Yanjie; Tang, Youmin; Jackson, Peter [University of Northern British Columbia, Environmental Science and Engineering, Prince George, BC (Canada); Zhou, Xiaobing [University of Northern British Columbia, Environmental Science and Engineering, Prince George, BC (Canada); Centre for Australian Weather and Climate Research (CAWCR), Bureau of Meteorology, Melbourne, VIC (Australia); Chen, Dake [Lamont-Doherty Earth Observatory of Columbia University, Palisades, NY (United States); State Key Laboratory of Satellite Ocean Environment Dynamics, Hangzhou (China)
2010-10-15
In this study, singular vector analysis was performed for the period from 1856 to 2003 using the latest Zebiak-Cane model version LDEO5. The singular vector, representing the optimal growth pattern of initial perturbations/errors, was obtained by perturbing the constructed tangent linear model of the Zebiak-Cane model. Variations in the singular vector and singular value, as a function of initial time, season, ENSO states, and optimal period, were investigated. Emphasis was placed on exploring relative roles of linear and nonlinear processes in the optimal perturbation growth of ENSO, and deriving statistically robust conclusions using long-term singular vector analysis. It was found that the first singular vector is dominated by a west-east dipole spanning most of the equatorial Pacific, with one center located in the east and the other in the central Pacific. Singular vectors are less sensitive to initial conditions, i.e., independence of seasons and decades; while singular values exhibit a strong sensitivity to initial conditions. The dynamical diagnosis shows that the total linear and nonlinear heating terms play opposite roles in controlling the optimal perturbation growth, and that the linear optimal perturbation is more than twice as large as the nonlinear one. The total linear heating causes a warming effect and controls two positive perturbation growth regions: one in the central Pacific and the other in the eastern Pacific; whereas the total linearized nonlinear advection brings a cooling effect controlling the negative perturbation growth in the central Pacific. (orig.)
Measurement of weak radioactivity
Theodorsson , P
1996-01-01
This book is intended for scientists engaged in the measurement of weak alpha, beta, and gamma active samples; in health physics, environmental control, nuclear geophysics, tracer work, radiocarbon dating etc. It describes the underlying principles of radiation measurement and the detectors used. It also covers the sources of background, analyzes their effect on the detector and discusses economic ways to reduce the background. The most important types of low-level counting systems and the measurement of some of the more important radioisotopes are described here. In cases where more than one type can be used, the selection of the most suitable system is shown.
Jolley, Sarah E; Bunnell, Aaron E; Hough, Catherine L
2016-11-01
Survivorship after critical illness is an increasingly important health-care concern as ICU use continues to increase while ICU mortality is decreasing. Survivors of critical illness experience marked disability and impairments in physical and cognitive function that persist for years after their initial ICU stay. Newfound impairment is associated with increased health-care costs and use, reductions in health-related quality of life, and prolonged unemployment. Weakness, critical illness neuropathy and/or myopathy, and muscle atrophy are common in patients who are critically ill, with up to 80% of patients admitted to the ICU developing some form of neuromuscular dysfunction. ICU-acquired weakness (ICUAW) is associated with longer durations of mechanical ventilation and hospitalization, along with greater functional impairment for survivors. Although there is increasing recognition of ICUAW as a clinical entity, significant knowledge gaps exist concerning identifying patients at high risk for its development and understanding its role in long-term outcomes after critical illness. This review addresses the epidemiologic and pathophysiologic aspects of ICUAW; highlights the diagnostic challenges associated with its diagnosis in patients who are critically ill; and proposes, to our knowledge, a novel strategy for identifying ICUAW. Copyright © 2016 American College of Chest Physicians. Published by Elsevier Inc. All rights reserved.
Nonplanar on-shell diagrams and leading singularities of scattering amplitudes
Energy Technology Data Exchange (ETDEWEB)
Chen, Baoyi; Cheung, Yeuk-Kwan E.; Li, Yunxuan; Xie, Ruofei; Xin, Yuan [Nanjing University, Department of Physics, Nanjing (China); Chen, Gang [Zhejiang Normal University, Department of Physics, Jinhua, Zhejiang (China); Nanjing University, Department of Physics, Nanjing (China)
2017-02-15
Bipartite on-shell diagrams are the latest tool in constructing scattering amplitudes. In this paper we prove that a Britto-Cachazo-Feng-Witten (BCFW) decomposable on-shell diagram process a rational top form if and only if the algebraic ideal comprised the geometrical constraints are shifted linearly during successive BCFW integrations. With a proper geometric interpretation of the constraints in the Grassmannian manifold, the rational top form integration contours can thus be obtained, and understood, in a straightforward way. All rational top form integrands of arbitrary higher loops leading singularities can therefore be derived recursively, as long as the corresponding on-shell diagram is BCFW decomposable. (orig.)
Singular Dimensions of theN= 2 Superconformal Algebras. I
Dörrzapf, Matthias; Gato-Rivera, Beatriz
Verma modules of superconfomal algebras can have singular vector spaces with dimensions greater than 1. Following a method developed for the Virasoro algebra by Kent, we introduce the concept of adapted orderings on superconformal algebras. We prove several general results on the ordering kernels associated to the adapted orderings and show that the size of an ordering kernel implies an upper limit for the dimension of a singular vector space. We apply this method to the topological N= 2 algebra and obtain the maximal dimensions of the singular vector spaces in the topological Verma modules: 0, 1, 2 or 3 depending on the type of Verma module and the type of singular vector. As a consequence we prove the conjecture of Gato-Rivera and Rosado on the possible existing types of topological singular vectors (4 in chiral Verma modules and 29 in complete Verma modules). Interestingly, we have found two-dimensional spaces of singular vectors at level 1. Finally, by using the topological twists and the spectral flows, we also obtain the maximal dimensions of the singular vector spaces for the Neveu-Schwarz N= 2 algebra (0, 1 or 2) and for the Ramond N= 2 algebra (0, 1, 2 or 3).
Boundary singularities produced by the motion of soap films.
Goldstein, Raymond E; McTavish, James; Moffatt, H Keith; Pesci, Adriana I
2014-06-10
Recent work has shown that a Möbius strip soap film rendered unstable by deforming its frame changes topology to that of a disk through a "neck-pinching" boundary singularity. This behavior is unlike that of the catenoid, which transitions to two disks through a bulk singularity. It is not yet understood whether the type of singularity is generally a consequence of the surface topology, nor how this dependence could arise from an equation of motion for the surface. To address these questions we investigate experimentally, computationally, and theoretically the route to singularities of soap films with different topologies, including a family of punctured Klein bottles. We show that the location of singularities (bulk or boundary) may depend on the path of the boundary deformation. In the unstable regime the driving force for soap-film motion is the mean curvature. Thus, the narrowest part of the neck, associated with the shortest nontrivial closed geodesic of the surface, has the highest curvature and is the fastest moving. Just before onset of the instability there exists on the stable surface the shortest closed geodesic, which is the initial condition for evolution of the neck's geodesics, all of which have the same topological relationship to the frame. We make the plausible conjectures that if the initial geodesic is linked to the boundary, then the singularity will occur at the boundary, whereas if the two are unlinked initially, then the singularity will occur in the bulk. Numerical study of mean curvature flows and experiments support these conjectures.
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.
Belkina, T. A.; Konyukhova, N. B.; Kurochkin, S. V.
2016-01-01
Previous and new results are used to compare two mathematical insurance models with identical insurance company strategies in a financial market, namely, when the entire current surplus or its constant fraction is invested in risky assets (stocks), while the rest of the surplus is invested in a risk-free asset (bank account). Model I is the classical Cramér-Lundberg risk model with an exponential claim size distribution. Model II is a modification of the classical risk model (risk process with stochastic premiums) with exponential distributions of claim and premium sizes. For the survival probability of an insurance company over infinite time (as a function of its initial surplus), there arise singular problems for second-order linear integrodifferential equations (IDEs) defined on a semiinfinite interval and having nonintegrable singularities at zero: model I leads to a singular constrained initial value problem for an IDE with a Volterra integral operator, while II model leads to a more complicated nonlocal constrained problem for an IDE with a non-Volterra integral operator. A brief overview of previous results for these two problems depending on several positive parameters is given, and new results are presented. Additional results are concerned with the formulation, analysis, and numerical study of "degenerate" problems for both models, i.e., problems in which some of the IDE parameters vanish; moreover, passages to the limit with respect to the parameters through which we proceed from the original problems to the degenerate ones are singular for small and/or large argument values. Such problems are of mathematical and practical interest in themselves. Along with insurance models without investment, they describe the case of surplus completely invested in risk-free assets, as well as some noninsurance models of surplus dynamics, for example, charity-type models.
Singular limits in thermodynamics of viscous fluids
Feireisl, Eduard
2017-01-01
This book is about singular limits of systems of partial differential equations governing the motion of thermally conducting compressible viscous fluids. "The main aim is to provide mathematically rigorous arguments how to get from the compressible Navier-Stokes-Fourier system several less complex systems of partial differential equations used e.g. in meteorology or astrophysics. However, the book contains also a detailed introduction to the modelling in mechanics and thermodynamics of fluids from the viewpoint of continuum physics. The book is very interesting and important. It can be recommended not only to specialists in the field, but it can also be used for doctoral students and young researches who want to start to work in the mathematical theory of compressible fluids and their asymptotic limits." Milan Pokorný (zbMATH) "This book is of the highest quality from every point of view. It presents, in a unified way, recent research material of fundament al importance. It is self-contained, thanks to Chapt...
Singular perturbation in the physical sciences
Neu, John C
2015-01-01
This book is the testimony of a physical scientist whose language is singular perturbation analysis. Classical mathematical notions, such as matched asymptotic expansions, projections of large dynamical systems onto small center manifolds, and modulation theory of oscillations based either on multiple scales or on averaging/transformation theory, are included. The narratives of these topics are carried by physical examples: Let's say that the moment when we "see" how a mathematical pattern fits a physical problem is like "hitting the ball." Yes, we want to hit the ball. But a powerful stroke includes the follow-through. One intention of this book is to discern in the structure and/or solutions of the equations their geometric and physical content. Through analysis, we come to sense directly the shape and feel of phenomena. The book is structured into a main text of fundamental ideas and a subtext of problems with detailed solutions. Roughly speaking, the former is the initial contact between mathematics and p...
Interior tomography with continuous singular value decomposition.
Jin, Xin; Katsevich, Alexander; Yu, Hengyong; Wang, Ge; Li, Liang; Chen, Zhiqiang
2012-11-01
The long-standing interior problem has important mathematical and practical implications. The recently developed interior tomography methods have produced encouraging results. A particular scenario for theoretically exact interior reconstruction from truncated projections is that there is a known sub-region in the ROI. In this paper, we improve a novel continuous singular value decomposition (SVD) method for interior reconstruction assuming a known sub-region. First, two sets of orthogonal eigen-functions are calculated for the Hilbert and image spaces respectively. Then, after the interior Hilbert data are calculated from projection data through the ROI, they are projected onto the eigen-functions in the Hilbert space, and an interior image is recovered by a linear combination of the eigen-functions with the resulting coefficients. Finally, the interior image is compensated for the ambiguity due to the null space utilizing the prior sub-region knowledge. Experiments with simulated and real data demonstrate the advantages of our approach relative to the POCS type interior reconstructions.
Singular Value Decomposition and Ligand Binding Analysis
Directory of Open Access Journals (Sweden)
André Luiz Galo
2013-01-01
Full Text Available Singular values decomposition (SVD is one of the most important computations in linear algebra because of its vast application for data analysis. It is particularly useful for resolving problems involving least-squares minimization, the determination of matrix rank, and the solution of certain problems involving Euclidean norms. Such problems arise in the spectral analysis of ligand binding to macromolecule. Here, we present a spectral data analysis method using SVD (SVD analysis and nonlinear fitting to determine the binding characteristics of intercalating drugs to DNA. This methodology reduces noise and identifies distinct spectral species similar to traditional principal component analysis as well as fitting nonlinear binding parameters. We applied SVD analysis to investigate the interaction of actinomycin D and daunomycin with native DNA. This methodology does not require prior knowledge of ligand molar extinction coefficients (free and bound, which potentially limits binding analysis. Data are acquired simply by reconstructing the experimental data and by adjusting the product of deconvoluted matrices and the matrix of model coefficients determined by the Scatchard and McGee and von Hippel equation.
Electrochemical etching of sharp tips for STM reveals singularity
DEFF Research Database (Denmark)
Quaade, Ulrich; Oddershede, Lene
2002-01-01
Electrochemical etching of metal wires is widely used to produce atomically sharp tips for use in scanning tunneling microscopy (STM). In this letter we uncover the existence of a finite-time singularity in the process: Several of the physical parameters describing the system exhibit scaling...... towards and away from a particular singular point in time, exactly the time at which the wire breaks. The obtained scaling exponents coincide with exponents reported from other singular dynamical systems. The results also provide knowledge of how to control STM tip properties on the nano-scale....
On the singular perturbations for fractional differential equation.
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.
A Singularity Avoidance Steering Law Based on the Minimization Technique
Directory of Open Access Journals (Sweden)
Hwa-Suk Oh
2006-12-01
Full Text Available Geometric singularity problems are principle difficulties of single-gimbal control moment gyros in spacecraft attitude control. To overcome these singularities, many steering logics have been studied. In this paper, a new null motion steering law is suggested, which is based on the minimization of the directional components of output torque with respect to the required torque. The suggested steering law has been simulated and verified to work well around several critical singular points which have been classified as testing points of avoidance algorithm in previous literatures.
Kaplan, L
1998-01-01
We examine the consequences of classical ergodicity for the localization properties of individual quantum eigenstates in the classical limit. We note that the well known Schnirelman result is a weaker form of quantum ergodicity than the one implied by random matrix theory. This suggests the possibility of systems with non-gaussian random eigenstates which are nonetheless ergodic in the sense of Schnirelman and lead to ergodic transport in the classical limit. These we call "weakly quantum ergodic.'' Indeed for a class of "slow ergodic" classical systems, it is found that each eigenstate becomes localized to an ever decreasing fraction of the available state space, in the semiclassical limit. Nevertheless, each eigenstate in this limit covers phase space evenly on any classical scale, and long-time transport properties betwen individual quantum states remain ergodic due to the diffractive effects which dominate quantum phase space exploration.
Some Properties of Solutions to Weakly Hypoelliptic Equations
Directory of Open Access Journals (Sweden)
Christian Bär
2013-01-01
Full Text Available A linear different operator L is called weakly hypoelliptic if any local solution u of Lu=0 is smooth. We allow for systems, that is, the coefficients may be matrices, not necessarily of square size. This is a huge class of important operators which coverall elliptic, overdetermined elliptic, subelliptic, and parabolic equations. We extend several classical theorems from complex analysis to solutions of any weakly hypoelliptic equation: the Montel theorem providing convergent subsequences, the Vitali theorem ensuring convergence of a given sequence, and Riemann's first removable singularity theorem. In the case of constant coefficients, we show that Liouville's theorem holds, any bounded solution must be constant, and any Lp-solution must vanish.
Renormalization Group in the uniqueness region weak Gibbsianity and convergence.
Bertini, L; Olivieri, E
2004-01-01
We analyze the block averaging transformation applied to lattice gas models with short range interaction in the uniqueness region below the critical temperature. %We discuss the %Gibbs property of the renormalized measure and the convergence of %renormalized potential under iteration of the map. We prove weak Gibbsianity of the renormalized measure and convergence of the renormalized potential in a weak sense. Since we are arbitrarily close to the coexistence region we have a diverging characteristic length of the system: the correlation length or the critical length for metastability, or both. Thus, to perturbatively treat the problem we have to use a scale--adapted expansion. Moreover, such a model below the critical temperature resembles a disordered system in presence of Griffiths' singularity. Then the cluster expansion that we use must be graded with its minimal scale length diverging when the coexistence line is approached.
Numerical Integral of Resistance Coefficients in Diffusion
Zhang, Q. S.
2017-01-01
The resistance coefficients in the screened Coulomb potential of stellar plasma are evaluated to high accuracy. I have analyzed the possible singularities in the integral of scattering angle. There are possible singularities in the case of an attractive potential. This may result in a problem for the numerical integral. In order to avoid the problem, I have used a proper scheme, e.g., splitting into many subintervals where the width of each subinterval is determined by the variation of the integrand, to calculate the scattering angle. The collision integrals are calculated by using Romberg’s method, therefore the accuracy is high (I.e., ˜10-12). The results of collision integrals and their derivatives for -7 ≤ ψ ≤ 5 are listed. By using Hermite polynomial interpolation from those data, the collision integrals can be obtained with an accuracy of 10-10. For very weakly coupled plasma (ψ ≥ 4.5), analytical fittings for collision integrals are available with an accuracy of 10-11. I have compared the final results of resistance coefficients with other works and found that, for a repulsive potential, the results are basically the same as others’ for an attractive potential, the results in cases of intermediate and strong coupling show significant differences. The resulting resistance coefficients are tested in the solar model. Comparing with the widely used models of Cox et al. and Thoul et al., the resistance coefficients in the screened Coulomb potential lead to a slightly weaker effect in the solar model, which is contrary to the expectation of attempts to solve the solar abundance problem.
Borcherds Forms and Generalizations of Singular Moduli
Schofer, Jarad
2006-01-01
We give a factorization of averages of Borcherds forms over CM points associated to a quadratic form of signature (n,2). As a consequence of this result, we are able to state a theorem like that of Gross and Zagier about which primes can occur in this factorization. One remarkable phenomenon we observe is that the regularized theta lift of a weakly holomorphic modular form is always finite.
Singularities of robot mechanisms numerical computation and avoidance path planning
Bohigas, Oriol; Ros, Lluís
2017-01-01
This book presents the singular configurations associated with a robot mechanism, together with robust methods for their computation, interpretation, and avoidance path planning. Having such methods is essential as singularities generally pose problems to the normal operation of a robot, but also determine the workspaces and motion impediments of its underlying mechanical structure. A distinctive feature of this volume is that the methods are applicable to nonredundant mechanisms of general architecture, defined by planar or spatial kinematic chains interconnected in an arbitrary way. Moreover, singularities are interpreted as silhouettes of the configuration space when seen from the input or output spaces. This leads to a powerful image that explains the consequences of traversing singular configurations, and all the rich information that can be extracted from them. The problems are solved by means of effective branch-and-prune and numerical continuation methods that are of independent interest in themselves...
Quantum gravitational collapse: non-singularity and non-locality
Greenwood, Eric; Stojkovic, Dejan
2008-06-01
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.
Loop quantum cosmology and the fate of cosmological singularities
Singh, Parampreet
2015-01-01
Singularities in general relativity such as the big bang and big crunch, and exotic singularities such as the big rip are the boundaries of the classical spacetimes. These events are marked by a divergence in the curvature invariants and the breakdown of the geodesic evolution. Recent progress on implementing techniques of loop quantum gravity to cosmological models reveals that such singularities may be generically resolved because of the quantum gravitational effects. Due to the quantum geometry, which replaces the classical differential geometry at the Planck scale, the big bang is replaced by a big bounce without any assumptions on the matter content or any fine tuning. In this manuscript, we discuss some of the main features of this approach and the results on the generic resolution of singularities for the isotropic as well as anisotropic models. Using effective spacetime description of the quantum theory, we show the way quantum gravitational effects lead to the universal bounds on the energy density, ...
Stability Analysis and Design for Nonlinear Singular Systems
Yang, Chunyu; Zhou, Linna
2013-01-01
Singular systems which are also referred to as descriptor systems, semi-state systems, differential- algebraic systems or generalized state-space systems have attracted much attention because of their extensive applications in the Leontief dynamic model, electrical and mechanical models, etc. This monograph presented up-to-date research developments and references on stability analysis and design of nonlinear singular systems. It investigated the problems of practical stability, strongly absolute stability, input-state stability and observer design for nonlinear singular systems and the problems of absolute stability and multi-objective control for nonlinear singularly perturbed systems by using Lyapunov stability theory, comparison principle, S-procedure and linear matrix inequality (LMI), etc. Practical stability, being quite different from stability in the sense of Lyapunov, is a significant performance specification from an engineering point of view. The basic concepts and results on practical stability f...
The geometry of resonance tongues : a singularity theory approach
Broer, Hendrik; Golubitsky, Martin; Vegter, Gert
Resonance tongues and their boundaries are studied for nondegenerate and (certain) degenerate Hopf bifurcations of maps using singularity theory methods of equivariant contact equivalence and universal unfoldings. We recover the standard theory of tongues (the nondegencrate case) in a
On singular solutions of a magnetohydrodynamic nonlinear boundary layer equation
Mohammed Guedda; Abdelilah Gmira; Mohammed Benlahsen
2007-01-01
This paper concerns the singular solutions of the equation $$ f''' +kappa ff''-eta {f'}^2 = 0, $$ where $eta < 0$ and $kappa = 0$ or 1. This equation arises when modelling heat transfer past a vertical flat plate embedded in a saturated porous medium with an applied magnetic field. After suitable normalization, $f'$ represents the velocity parallel to the surface or the non-dimensional fluid temperature. Our interest is in solutions which develop a singularity at some point (t...
Kurzweil's Singularity as a part of Evo-SETI Theory
Maccone, Claudio
2017-03-01
Ray Kurzweil's famous 2006 book "The Singularity Is Near" predicted that the Singularity (i.e. computers taking over humans) would occur around the year 2045. In this paper we prove that Kurzweil's prediction is in agreement with the "Evo-SETI" (Evolution and SETI)" mathematical model that this author has developed over the last five years in a series of mathematical papers published in both Acta Astronautica and the International Journal of Astrobiology.
Classical resolution of black hole singularities via wormholes
Energy Technology Data Exchange (ETDEWEB)
Olmo, Gonzalo J. [Universidad de Valencia, Departamento de Fisica Teorica and IFIC, Centro Mixto Universidad de Valencia-CSIC, Valencia (Spain); Universidade Federal da Paraiba, Departamento de Fisica, Joao Pessoa, Paraiba (Brazil); Rubiera-Garcia, D. [Universidade de Lisboa, Faculdade de Ciencias, Instituto de Astrofisica e Ciencias do Espaco, Lisbon (Portugal); Fudan University, Department of Physics, Center for Field Theory and Particle Physics, Shanghai (China); Sanchez-Puente, A. [Universidad de Valencia, Departamento de Fisica Teorica and IFIC, Centro Mixto Universidad de Valencia-CSIC, Valencia (Spain)
2016-03-15
In certain extensions of General Relativity, wormholes generated by spherically symmetric electric fields can resolve black hole singularities without necessarily removing curvature divergences. This is shown by studying geodesic completeness, the behavior of time-like congruences going through the divergent region, and by means of scattering of waves off the wormhole. This provides an example of the logical independence between curvature divergences and space-time singularities, concepts very often identified with each other in the literature. (orig.)
A singular value sensitivity approach to robust eigenstructure assignment
DEFF Research Database (Denmark)
Søgaard-Andersen, Per; Trostmann, Erik; Conrad, Finn
1986-01-01
A design technique for improving the feedback properties of multivariable state feedback systems designed using eigenstructure assignment is presented. Based on a singular value analysis of the feedback properties a design parameter adjustment procedure is outlined. This procedure allows for the ......A design technique for improving the feedback properties of multivariable state feedback systems designed using eigenstructure assignment is presented. Based on a singular value analysis of the feedback properties a design parameter adjustment procedure is outlined. This procedure allows...
Analysis and design of nonlinear resonances via singularity theory
Cirillo, G I; Kerschen, G; Sepulchre, R
2016-01-01
Bifurcation theory and continuation methods are well-established tools for the analysis of nonlinear mechanical systems subject to periodic forcing. We illustrate the added value and the complementary information provided by singularity theory with one distinguished parameter. While tracking bifurcations reveals the qualitative changes in the behaviour, tracking singularities reveals how structural changes are themselves organised in parameter space. The complementarity of that information is demonstrated in the analysis of detached resonance curves in a two-degree-of-freedom system.
Wormholes as a cure for black hole singularities
Olmo, Gonzalo J; Sanchez-Puente, Antonio
2016-01-01
Using exactly solvable models, it is shown that black hole singularities in different electrically charged configurations can be cured. Our solutions describe black hole space-times with a wormhole giving structure to the otherwise point-like singularity. We show that geodesic completeness is satisfied despite the existence of curvature divergences at the wormhole throat. In some cases, physical observers can go through the wormhole and in other cases the throat lies at an infinite affine distance.
Stability of Schwarzschild singularity in non-local gravity
Calcagni, Gianluca; Modesto, Leonardo
2017-10-01
In a previous work, it was shown that all Ricci-flat spacetimes are exact solutions for a large class of non-local gravitational theories. Here we prove that, for a subclass of non-local theories, the Schwarzschild singularity is stable under linear perturbations. Thus, non-locality may be not enough to cure all the singularities of general relativity. Finally, we show that the Schwarzschild solution can be generated by the gravitational collapse of a thin shell of radiation.
Resolving the Schwarzschild singularity in both classic and quantum gravity
Zeng, Ding-fang
2017-01-01
The Schwarzschild singularity's resolution has key values in cracking the key mysteries related with black holes, the origin of their horizon entropy and the information missing puzzle involved in their evaporations. We provide in this work the general dynamic inner metric of collapsing stars with horizons and with non-trivial radial mass distributions. We find that static central singularities are not the final state of the system. Instead, the final state of the system is a periodically zer...
On the singular values decoupling in the Singular Spectrum Analysis of volcanic tremor at Stromboli
Directory of Open Access Journals (Sweden)
R. Carniel
2006-01-01
Full Text Available The well known strombolian activity at Stromboli volcano is occasionally interrupted by rarer episodes of paroxysmal activity which can lead to considerable hazard for Stromboli inhabitants and tourists. On 5 April 2003 a powerful explosion, which can be compared in size with the latest one of 1930, covered with bombs a good part of the normally tourist-accessible summit area. This explosion was not forecasted, although the island was by then effectively monitored by a dense deployment of instruments. After having tackled in a previous paper the problem of highlighting the timescale of preparation of this event, we investigate here the possibility of highlighting precursors in the volcanic tremor continuously recorded by a short period summit seismic station. We show that a promising candidate is found by examining the degree of coupling between successive singular values that result from the Singular Spectrum Analysis of the raw seismic data. We suggest therefore that possible anomalies in the time evolution of this parameter could be indicators of volcano instability to be taken into account e.g. in a bayesian eruptive scenario evaluator. Obviously, further (and possibly forward testing on other cases is needed to confirm the usefulness of this parameter.
DEFF Research Database (Denmark)
Emerek, Ruth
2004-01-01
Bidraget diskuterer de forskellige intergrationsopfattelse i Danmark - og hvad der kan forstås ved vellykket integration......Bidraget diskuterer de forskellige intergrationsopfattelse i Danmark - og hvad der kan forstås ved vellykket integration...
Analysis of singular interface stresses in dissimilar material joints for plasma facing components
You, J. H.; Bolt, H.
2001-10-01
Duplex joint structures are typical material combinations for the actively cooled plasma facing components of fusion devices. The structural integrity under the incident heat loads from the plasma is one of the most crucial issues in the technology of these components. The most critical domain in a duplex joint component is the free surface edge of the bond interface between heterogeneous materials. This is due to the fact that the thermal stress usually shows a singular intensification in this region. If the plasma facing armour tile consists of a brittle material, the existence of the stress singularity can be a direct cause of failure. The present work introduces a comprehensive analytical tool to estimate the impact of the stress singularity for duplex PFC design and quantifies the relative stress intensification in various materials joints by use of a model formulated by Munz and Yang. Several candidate material combinations of plasma facing armour and metallic heat sink are analysed and the results are compared with each other.
Interacting realization of cosmological singularities with variable vacuum energy
Chimento, Luis P
2015-01-01
We examine an interacting dark matter--variable vacuum energy model for a spatially flat Friedmann-Roberston-Walker spacetime, focusing on the appearance of cosmological singularities such as \\emph{big rip, big brake, big freeze}, and \\emph{ big separation} along with abrupt events (\\emph{infinite $\\gamma$- singularity} and \\emph{new w-singularity}) at late times. We introduce a phenomenological interaction which has a nonlinear dependence on the total energy density of the dark sector and its derivative, solve exactly the source equation for the model and find the energy density as function of the scale factor as well as the time dependence of the approximate scale factor in the neighborhood of the singularities. We describe the main characteristics of these singularities by exploring the type of interaction that makes them possible along with behavior of dark components near them. We apply the geometric Tipler and Kr\\'olak method for determining the fate of time-like geodesic curves around the singularities...
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.
Wave regularity in curve integrable spacetimes
Sanchez, Yafet Sanchez
2015-01-01
The idea of defining a gravitational singularity as an obstruction to the dynamical evolution of a test field (described by a PDE) rather than the dynamical evolution of a particle (described by a geodesics) is explored. In particular, the concept of wave regularity is introduced which serves to show that the classical singularities in curve integrable spacetimes do not interrupt the well-posedness of the wave equation. The techniques used also provide arguments that can be extended to establish when a classically singular spacetime remains singular in a semi-classical picture.
Gómez Rodríguez, Rafael Ángel
2014-01-01
To say that someone possesses integrity is to claim that that person is almost predictable about responses to specific situations, that he or she can prudentially judge and to act correctly. There is a closed interrelationship between integrity and autonomy, and the autonomy rests on the deeper moral claim of all humans to integrity of the person. Integrity has two senses of significance for medical ethic: one sense refers to the integrity of the person in the bodily, psychosocial and intellectual elements; and in the second sense, the integrity is the virtue. Another facet of integrity of the person is la integrity of values we cherish and espouse. The physician must be a person of integrity if the integrity of the patient is to be safeguarded. The autonomy has reduced the violations in the past, but the character and virtues of the physician are the ultimate safeguard of autonomy of patient. A field very important in medicine is the scientific research. It is the character of the investigator that determines the moral quality of research. The problem arises when legitimate self-interests are replaced by selfish, particularly when human subjects are involved. The final safeguard of moral quality of research is the character and conscience of the investigator. Teaching must be relevant in the scientific field, but the most effective way to teach virtue ethics is through the example of the a respected scientist.
Weak separation limit of a two-component Bose-Einstein condensate
Directory of Open Access Journals (Sweden)
Christos Sourdis
2018-01-01
Full Text Available This paper studies of the behaviour of the wave functions of a two-component Bose-Einstein condensate in the case of weak segregation. This amounts to the study of the asymptotic behaviour of a heteroclinic connection in a conservative Hamiltonian system of two coupled second order ODE's, as the strength of the coupling tends to its infimum. For this purpose, we apply geometric singular perturbation theory.
Weak Measurement and Quantum Correlation
Indian Academy of Sciences (India)
Arun Kumar Pati
The concept of the weak measurements, for the first time, was introduced by Aharonov et al.1. Quantum state is preselected in |ψi〉 and allowed to interact weakly with apparatus. Measurement strength can be tuned and for “small g(t)” it is called 'weak measurement'. With postselection in |ψf 〉, apparatus state is shifted by an ...
Inflationary Cosmology Leading to a Soft Type Singularity
Brevik, I; Timoshkin, A V
2016-01-01
A remarkable property of modern cosmology is that it allows for a special case of symmetry, consisting in the possibility of describing the early-time acceleration (inflation) and the late-time acceleration using the same theoretical framework. In this paper we consider various cosmological models corresponding to a generalized form for the equation of state for the fluid in a flat Friedmann -Robertson-Walker universe, emphasizing cases where the so-called type IV singular inflation is encountered in the future. This is a soft (non-crushing) kind of singularity. Parameter values for an inhomogeneous equation of state leading to singular inflation are obtained. We present models for which there are two type IV singularities, the first corresponding to the end of the inflationary era and the second to a late time event. We also study the correspondence between the theoretical slow-roll parameters leading to type IV singular inflation and the recent results observed by the Planck satellite.
Milnor fiber boundary of a non-isolated surface singularity
Némethi, András
2012-01-01
In the study of algebraic/analytic varieties a key aspect is the description of the invariants of their singularities. This book targets the challenging non-isolated case. Let f be a complex analytic hypersurface germ in three variables whose zero set has a 1-dimensional singular locus. We develop an explicit procedure and algorithm that describe the boundary M of the Milnor fiber of f as an oriented plumbed 3-manifold. This method also provides the characteristic polynomial of the algebraic monodromy. We then determine the multiplicity system of the open book decomposition of M cut out by the argument of g for any complex analytic germ g such that the pair (f,g) is an ICIS. Moreover, the horizontal and vertical monodromies of the transversal type singularities associated with the singular locus of f and of the ICIS (f,g) are also described. The theory is supported by a substantial amount of examples, including homogeneous and composed singularities and suspensions. The properties peculiar to M are also empha...
On Smooth Time-Dependent Orbifolds and Null Singularities
Energy Technology Data Exchange (ETDEWEB)
Fabinger, Michel
2002-08-08
We study string theory on a non-singular time-dependent orbifold of flat space. The orbifold group, which involves only space-like identifications, is obtained by a combined action of a null Lorentz transformation and a constant shift in an extra direction. In the limit where the shift goes to zero, the geometry of this orbifold reproduces an orbifold with a light-like singularity, which was recently studied by Liu, Moore and Seiberg (hep-th/0204168). We find that the backreaction on the geometry due to a test particle can be made arbitrarily small, and that there are scattering processes which can be studied in the approximation of a constant background. We quantize strings on this orbifold and calculate the torus partition function. We construct a basis of states on the smooth orbifold whose tree level string interactions are nonsingular. We discuss the existence of physical modes in the singular orbifold which resolve the singularity. We also describe another way of making the singular orbifold smooth which involves a sandwich pp-wave.
Dynamics of learning near singularities in radial basis function networks.
Wei, Haikun; Amari, Shun-Ichi
2008-09-01
The radial basis function (RBF) networks are one of the most widely used models for function approximation in the regression problem. In the learning paradigm, the best approximation is recursively or iteratively searched for based on observed data (teacher signals). One encounters difficulties in such a process when two component basis functions become identical, or when the magnitude of one component becomes null. In this case, the number of the components reduces by one, and then the reduced component recovers as the learning process proceeds further, provided such a component is necessary for the best approximation. Strange behaviors, especially the plateau phenomena, have been observed in dynamics of learning when such reduction occurs. There exist singularities in the space of parameters, and the above reduction takes place at the singular regions. This paper focuses on a detailed analysis of the dynamical behaviors of learning near the overlap and elimination singularities in RBF networks, based on the averaged learning equation that is applicable to both on-line and batch mode learning. We analyze the stability on the overlap singularity by solving the eigenvalues of the Hessian explicitly. Based on the stability analysis, we plot the analytical dynamic vector fields near the singularity, which are then compared to those real trajectories obtained by a numeric method. We also confirm the existence of the plateaus in both batch and on-line learning by simulation.
Fermi condensation near van Hove singularities within the Hubbard model on the triangular lattice.
Yudin, Dmitry; Hirschmeier, Daniel; Hafermann, Hartmut; Eriksson, Olle; Lichtenstein, Alexander I; Katsnelson, Mikhail I
2014-02-21
The proximity of the Fermi surface to van Hove singularities drastically enhances interaction effects and leads to essentially new physics. In this work we address the formation of flat bands ("Fermi condensation") within the Hubbard model on the triangular lattice and provide a detailed analysis from an analytical and numerical perspective. To describe the effect we consider both weak-coupling and strong-coupling approaches, namely the renormalization group and dual fermion methods. It is shown that the band flattening is driven by correlations and is well pronounced even at sufficiently high temperatures, of the order of 0.1-0.2 of the hopping parameter. The effect can therefore be probed in experiments with ultracold fermions in optical lattices.
Multiple Metaphors for a Singular Idea.
Cairns, Robert B.
1991-01-01
Evaluates the epigenetic landscape metaphor in light of behavioral development. Cites two common errors in integrated models of behavior and biology: (1) fixing behavior as structure, thereby robbing it of dynamics and plasticity; and (2) assuming that a single optimal trajectory applies to development of organisms or systems. (BC)
Gharekhan, Anita H.; Rath, Dhaitri; Oza, Ashok N.; Pradhan, Asima; Sureshkumar, M. B.; Panigrahi, Prasanta K.
2009-02-01
A systematic investigation of the fluorescence characteristics of normal and cancerous human breast tissues is carried out, using laser and lamp as excitation sources. It is found that earlier observed subtle differences between these two tissue types in the wavelet domain are absent, when lamp is used as excitation source. However, singular value decomposition of the average spectral profile in the wavelet domain yields strong correlation for the cancer tissues in the 580-750 nm regimes indicating weak fluorophore activity in this wavelength range.
Evans, J. D.; Palhares Junior, I. L.; Oishi, C. M.
2017-12-01
We characterise the stress singularity of the Oldroyd-B, Phan-Thien-Tanner (PTT), and Giesekus viscoelastic models in steady planar stick-slip flows. For both PTT and Giesekus models in the presence of a solvent viscosity, the asymptotics show that the velocity field is Newtonian dominated near to the singularity at the join of the stick and slip surfaces. Polymer stress boundary layers are present at both the stick and slip surfaces. By integrating along streamlines, we verify the polymer stress behavior of r-4/11 for PTT and r-5/16 for Giesekus, where r is the radial distance from the singularity. These asymptotic results for PTT and Giesekus do not hold in the limit of vanishing quadratic stress terms for Oldroyd-B. However, we can consider the Oldroyd-B model in the fixed kinematics of a prescribed Newtonian velocity field. In contrast to PTT and Giesekus, this is not the correct balance for the momentum equation but does allow insight into the behavior of the Oldroyd-B equations near the singularity. A three-region asymptotic structure is again apparent with now a polymer stress singularity of r-4/5. The high Weissenberg boundary layer equations are found to manifest themselves at the stick surface and are of thickness r3/2. At the slip surface, dominant balance between the upper convected stress and rate-of-strain terms gives a slip boundary layer of thickness r2. The solution of the slip boundary layer shows that the polymer stress is now singular along the slip surface. These results are supported through numerical integration along streamlines of the Oldroyd-B equations in a Newtonian velocity field. The Oldroyd-B model thus extends the point singularity at the join of the stick and slip surfaces to the whole of slip surface. As such, it does not have a physically meaningful solution in a Newtonian velocity field. We would expect a similar stress behavior for this model in the true viscoelastic velocity field.
Singular perturbations introduction to system order reduction methods with applications
Shchepakina, Elena; Mortell, Michael P
2014-01-01
These lecture notes provide a fresh approach to investigating singularly perturbed systems using asymptotic and geometrical techniques. It gives many examples and step-by-step techniques, which will help beginners move to a more advanced level. Singularly perturbed systems appear naturally in the modelling of many processes that are characterized by slow and fast motions simultaneously, for example, in fluid dynamics and nonlinear mechanics. This book’s approach consists in separating out the slow motions of the system under investigation. The result is a reduced differential system of lesser order. However, it inherits the essential elements of the qualitative behaviour of the original system. Singular Perturbations differs from other literature on the subject due to its methods and wide range of applications. It is a valuable reference for specialists in the areas of applied mathematics, engineering, physics, biology, as well as advanced undergraduates for the earlier parts of the book, and graduate stude...
Solving the relative Lambert's problem and accounting for its singularities
Wen, Changxuan; Zhao, Yushan; Li, Baojun; Shi, Peng
2014-04-01
A novel approach based on Lagrange's time equation and differential orbital elements is developed to solve the relative Lambert's problem for circular reference orbits. Compared with the conventional Clohessy-Wiltshire equation, the proposed method directly obtains differences of orbital elements between a transfer orbit and a reference orbit. This advantage enables us to account for singularities that occur in the relative Lambert's problem. The solved relative velocities depend on the five differential orbital elements. Accordingly, singularities can be attributed to any significant change in the semi-major axis, eccentricity, or orbital plane. Furthermore, appropriately adjusting initial and final relative positions eliminates some singularities. A numerical simulation based on the classic Lambert's formula for a rendezvous mission in closed range demonstrates the analytical results.
Symposium on Singularities, Representation of Algebras, and Vector Bundles
Trautmann, Günther
1987-01-01
It is well known that there are close relations between classes of singularities and representation theory via the McKay correspondence and between representation theory and vector bundles on projective spaces via the Bernstein-Gelfand-Gelfand construction. These relations however cannot be considered to be either completely understood or fully exploited. These proceedings document recent developments in the area. The questions and methods of representation theory have applications to singularities and to vector bundles. Representation theory itself, which had primarily developed its methods for Artinian algebras, starts to investigate algebras of higher dimension partly because of these applications. Future research in representation theory may be spurred by the classification of singularities and the highly developed theory of moduli for vector bundles. The volume contains 3 survey articles on the 3 main topics mentioned, stressing their interrelationships, as well as original research papers.
Singular structure of magnetic islands resulting from reconnection
Jemella, B. D.; Drake, J. F.; Shay, M. A.
2004-12-01
Magnetic island equilibria resulting from reconnection in magnetohydrodynamic (MHD) simulations are explored in a two-dimensional slab geometry. Magnetic islands are evolved to finite amplitude with a nonzero resistivity. The resistivity and flows are then set to zero and the system is allowed to relax toward equilibrium. A y-type singular current layer in the equilibrium state is identified for all but systems with the smallest values of the tearing mode stability parameter Δ'. It is shown that the length of the equilibrium y line tracks the length of the Sweet-Parker current layer that develops during reconnection. This suggests that the formation of Sweet-Parker current layers during magnetic reconnection in the resistive MHD model is a consequence of the presence of a singularity in post-reconnection state. A threshold in Δ' for singular behavior is also identified.
Two-scale approach to oscillatory singularly perturbed transport equations
Frénod, Emmanuel
2017-01-01
This book presents the classical results of the two-scale convergence theory and explains – using several figures – why it works. It then shows how to use this theory to homogenize ordinary differential equations with oscillating coefficients as well as oscillatory singularly perturbed ordinary differential equations. In addition, it explores the homogenization of hyperbolic partial differential equations with oscillating coefficients and linear oscillatory singularly perturbed hyperbolic partial differential equations. Further, it introduces readers to the two-scale numerical methods that can be built from the previous approaches to solve oscillatory singularly perturbed transport equations (ODE and hyperbolic PDE) and demonstrates how they can be used efficiently. This book appeals to master’s and PhD students interested in homogenization and numerics, as well as to the Iter community.
Non singular promises from Born-Infeld gravity
Fiorini, Franco
2013-01-01
Born-Infeld determinantal gravity formulated in Weitzenbock spacetime is discussed in the context of Friedmann-Robertson-Walker cosmologies. It is shown how the standard model Big Bang singularity is absent in certain spatially flat FRW spacetimes, where the high energy regime is characterized by a de Sitter inflationary stage of geometrical character, i.e., without the presence of the inflaton field. This taming of the initial singularity is also achieved for some spatially curved FRW manifolds where the singularity is replaced by a de Sitter stage or a Big Bounce of the scale factor depending on certain combinations of free parameters appearing in the action. Unlike other Born-Infeld like theories in vogue, the one here presented is also capable of deforming vacuum General Relativistic solutions.
PT -symmetric spectral singularity and negative-frequency resonance
Pendharker, Sarang; Guo, Yu; Khosravi, Farhad; Jacob, Zubin
2017-03-01
Vacuum consists of a bath of balanced and symmetric positive- and negative-frequency fluctuations. Media in relative motion or accelerated observers can break this symmetry and preferentially amplify negative-frequency modes as in quantum Cherenkov radiation and Unruh radiation. Here, we show the existence of a universal negative-frequency-momentum mirror symmetry in the relativistic Lorentzian transformation for electromagnetic waves. We show the connection of our discovered symmetry to parity-time (PT ) symmetry in moving media and the resulting spectral singularity in vacuum fluctuation-related effects. We prove that this spectral singularity can occur in the case of two metallic plates in relative motion interacting through positive- and negative-frequency plasmonic fluctuations (negative-frequency resonance). Our work paves the way for understanding the role of PT -symmetric spectral singularities in amplifying fluctuations and motivates the search for PT symmetry in novel photonic systems.
Image Fakery Detection Based on Singular Value Decomposition
Directory of Open Access Journals (Sweden)
T. Basaruddin
2009-11-01
Full Text Available The growing of image processing technology nowadays make it easier for user to modify and fake the images. Image fakery is a process to manipulate part or whole areas of image either in it content or context with the help of digital image processing techniques. Image fakery is barely unrecognizable because the fake image is looking so natural. Yet by using the numerical computation technique it is able to detect the evidence of fake image. This research is successfully applied the singular value decomposition method to detect image fakery. The image preprocessing algorithm prior to the detection process yields two vectors orthogonal to the singular value vector which are important to detect fake image. The result of experiment to images in several conditions successfully detects the fake images with threshold value 0.2. Singular value decomposition-based detection of image fakery can be used to investigate fake image modified from original image accurately.
Curved singular beams for three-dimensional particle manipulation.
Zhao, Juanying; Chremmos, Ioannis D; Song, Daohong; Christodoulides, Demetrios N; Efremidis, Nikolaos K; Chen, Zhigang
2015-07-13
For decades, singular beams carrying angular momentum have been a topic of considerable interest. Their intriguing applications are ubiquitous in a variety of fields, ranging from optical manipulation to photon entanglement, and from microscopy and coronagraphy to free-space communications, detection of rotating black holes, and even relativistic electrons and strong-field physics. In most applications, however, singular beams travel naturally along a straight line, expanding during linear propagation or breaking up in nonlinear media. Here, we design and demonstrate diffraction-resisting singular beams that travel along arbitrary trajectories in space. These curved beams not only maintain an invariant dark "hole" in the center but also preserve their angular momentum, exhibiting combined features of optical vortex, Bessel, and Airy beams. Furthermore, we observe three-dimensional spiraling of microparticles driven by such fine-shaped dynamical beams. Our findings may open up new avenues for shaped light in various applications.
Free energy of singular sticky-sphere clusters
Kallus, Yoav
2016-01-01
Networks of particles connected by springs model many condensed-matter systems, from colloids interacting with a short-range potential, to complex fluids near jamming, to self-assembled lattices, to origami-inspired materials. Under small thermal fluctuations the vibrational entropy of a ground state is given by the harmonic approximation if it has no zero-frequency modes, yet such "singular" states are at the epicenter of many interesting behaviors in the systems above. To account for singularities we consider a finite cluster of $N$ spherical particles and solve for the partition function in the sticky limit where the pairwise interaction is strong and short ranged. Although the partition function diverges for singular clusters in the limit, the asymptotic contribution can be calculated and depends on only two parameters, characterizing the depth and range of the potential. The result holds for clusters that are second-order rigid, a geometric characterization that describes all known ground-state (rigid) s...
Identity and singularity: Metastability and morphogenesis in light of Deleuze
Directory of Open Access Journals (Sweden)
Barison Marcello
2015-01-01
Full Text Available The question of life is inextricably connected with the problem of identification and with the fact that each identification process includes the acquisition of a form. Nevertheless, it appears that at the biological level, that is, for what concerns a morphogenetic description of the status of the living being, the term singularity comes into play right there where you would expect to get into the notion of identity. According to Christian De Duve, the organic form has no identity, but it expresses - and is an expression of - a singularity. Given these observations, this is the object of the paper: to explain in a clear and consistent way how these terms - namely identity and singularity - differ and whether it is possible to ground their distinction in a coherent theoretical manner.
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.
Harnack's Inequality for Degenerate and Singular Parabolic Equations
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
Fatigue crack shape prediction based on the stress singularity exponent
Czech Academy of Sciences Publication Activity Database
Hutař, Pavel; Ševčík, Martin; Náhlík, Luboš; Knésl, Zdeněk
488-489, č. 1 (2012), s. 178-181 ISSN 1013-9826. [International Conference on Fracture and Damage Mechanics - FDM 2011 /10./. Dubrovník, 19.09.2011-21.09.2011] R&D Projects: GA ČR GA101/09/0867 Grant - others:GA AV ČR(CZ) M100420901 Institutional research plan: CEZ:AV0Z2041904 Keywords : stress singularity exponent * crack front curvature * vertex singularity * free surface effect Subject RIV: JL - Materials Fatigue, Friction Mechanics
Gauge invariance properties and singularity cancellations in a modified PQCD
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.
On singular solutions of a magnetohydrodynamic nonlinear boundary layer equation
Directory of Open Access Journals (Sweden)
Mohammed Guedda
2007-05-01
Full Text Available This paper concerns the singular solutions of the equation $$ f''' +kappa ff''-eta {f'}^2 = 0, $$ where $eta < 0$ and $kappa = 0$ or 1. This equation arises when modelling heat transfer past a vertical flat plate embedded in a saturated porous medium with an applied magnetic field. After suitable normalization, $f'$ represents the velocity parallel to the surface or the non-dimensional fluid temperature. Our interest is in solutions which develop a singularity at some point (the blow-up point. In particular, we shall examine in detail the behavior of $f$ near the blow-up point.
Entanglement entropy for singular surfaces in hyperscaling violating theories
Energy Technology Data Exchange (ETDEWEB)
Alishahiha, Mohsen [School of Physics, Institute for Research in Fundamental Sciences (IPM),P.O. Box 19395-5531, Tehran (Iran, Islamic Republic of); Astaneh, Amin Faraji [School of Particles and Accelerators, Institute for Research in Fundamental Sciences (IPM),P.O. Box 19395-5531, Tehran (Iran, Islamic Republic of); Fonda, Piermarco [SISSA and INFN,via Bonomea 265, 34136, Trieste (Italy); Omidi, Farzad [School of Astronomy, Institute for Research in Fundamental Sciences (IPM),P.O. Box 19395-5531, Tehran (Iran, Islamic Republic of)
2015-09-24
We study the holographic entanglement entropy for singular surfaces in theories described holographically by hyperscaling violating backgrounds. We consider singular surfaces consisting of cones or creases in diverse dimensions. The structure of UV divergences of entanglement entropy exhibits new logarithmic terms whose coefficients, being cut-off independent, could be used to define new central charges in the nearly smooth limit. We also show that there is a relation between these central charges and the one appearing in the two-point function of the energy-momentum tensor. Finally we examine how this relation is affected by considering higher-curvature terms in the gravitational action.
Shocks, singularities and oscillations in nonlinear optics and fluid mechanics
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. .
La reputación corporativa de entidades singulares
Grandi, Elisa
2016-01-01
1. Conceptualizar la Reputación Corporativa. 2. Identificar las Dimensiones de la Reputación Corporativa. 3. Explicar los beneficios de la Reputación. 4. Señalar las dimensiones de la reputación que son importantes en las Entidades Singulares. 5. Estudiar las características de las entidades sin ánimo de lucro. 6. Estudiar las características de las entidades sigulares. 7. Analizar la reputación corporativa de la entidades singulares Facultad de Ciencias de la Empresa Universidad Polité...
Stability of Schwarzschild singularity in non-local gravity
Directory of Open Access Journals (Sweden)
Gianluca Calcagni
2017-10-01
Full Text Available In a previous work, it was shown that all Ricci-flat spacetimes are exact solutions for a large class of non-local gravitational theories. Here we prove that, for a subclass of non-local theories, the Schwarzschild singularity is stable under linear perturbations. Thus, non-locality may be not enough to cure all the singularities of general relativity. Finally, we show that the Schwarzschild solution can be generated by the gravitational collapse of a thin shell of radiation.
Singularity theory and some problems of functional analysis
1992-01-01
The emergence of singularity theory marks the return of mathematics to the study of the simplest analytical objects: functions, graphs, curves, surfaces. The modern singularity theory for smooth mappings, which is currently undergoing intensive development, can be thought of as a crossroad where the most abstract topics (such as algebraic and differential geometry and topology, complex analysis, invariant theory, and Lie group theory) meet the most applied topics (such as dynamical systems, mathematical physics, geometrical optics, mathematical economics, and control theory). The papers in thi
Phase transition in the singularity spectrum of an intermingled basin
Ishikawa, Hiromi G.; Horita, Takehiko
2017-09-01
A two-dimensional piecewise linear mapping is introduced as a solvable model to characterize the multifractal structure of an intermingled basin. To this end, we make use of the multifractal formalism and introduce a partition function. The singularity spectrum, which characterizes local scaling property of the intermingled basin, is then determined. We have found that if the system is not symmetric, the singularity spectrum of either basin shows a phase transition, corresponding to the existence of two phases the orbits experience in the system, i.e., local one governed by the chaotic motions on the chaotic attractor, and the other global one reflecting nonhyperbolic motions characteristic of the intermingled basin.
Ações singulares em um projeto plural/Singular actions in a plural project
Directory of Open Access Journals (Sweden)
Maria Ângela de Melo Pinheiro
2006-01-01
Full Text Available Este artigo apresenta a produção escrita de uma das professoras da EMEF Padre Francisco Silva que participa do Projeto “Escola Singular, Ações Plurais”, uma parceria dessa escola pública municipal de Campinas com a UNICAMP.O artigo vem relatar os diferentes níveis de participação da professora nos diversos espaços que freqüenta e nos quais atua como professora e pesquisadora. Um desses espaços é o GT (Grupo de Trabalho que consiste em reuniões semanais para estudo, onde se dá o levantamento de temas de interesse do grupo, seguido de discussão e aprofundamento dos mesmos. Um outro espaço é o subgrupo “Interdisciplinaridade”, formado por alguns professores de 5ª a 8ª séries, que tem por objetivo a busca de fundamentação teórica sobre este tema, além da utilização do espaço/tempo das reuniões para planejar e avaliar as práticas de sala de aula, na busca de um trabalho interdisciplinar. This article shows the writing production of one of the teachers from school “Padre Francisco Silva”, that participates of the project “Singular school: plural actions”, a partnership from this public municipal school from Campinas with Unicamp. The article comes to relate the different participation levels of the teacher at the diversify spaces where she frequents and participates as a professor and ressearcher. One of these spaces is the GT (Workgroup, in portuguese Grupo de Trabalho, that consists in weekly study reunions, when is made the apointing of the themes of interest for the group, followed by the discussion of it. Another space is the “Interdisciplinary” subgroup, formed by some fifth and eight grades teachers, that have as objective the search for theoric fundamentation, besides the utilization of the space/time at the reunion to plan and validate the classroom practics, at the search for interdisciplinarity work.
Non Singular Origin of the Universe and its Present Vacuum Energy Density
Guendelman, E I
2011-01-01
We consider a non singular origin for the Universe starting from an Einstein static Universe, the so called "emergent universe" scenario, in the framework of a theory which uses two volume elements $\\sqrt{-{g}}d^{4}x$ and $\\Phi d^{4}x$, where $\\Phi $ is a metric independent density, used as an additional measure of integration. Also curvature, curvature square terms and for scale invariance a dilaton field $\\phi$ are considered in the action. The first order formalism is applied. The integration of the equations of motion associated with the new measure gives rise to the spontaneous symmetry breaking (S.S.B) of scale invariance (S.I.). After S.S.B. of S.I., it is found that a non trivial potential for the dilaton is generated. In the Einstein frame we also add a cosmological term that parametrizes the zero point fluctuations. The resulting effective potential for the dilaton contains two flat regions, for $\\phi \\rightarrow \\infty$ relevant for the non singular origin of the Universe, followed by an inflationa...
Singular value decomposition-based reconstruction algorithm for seismic traveltime tomography.
Song, L P; Zhang, S Y
1999-01-01
A reconstruction method is given for seismic transmission traveltime tomography. The method is implemented via the combinations of singular value decomposition, appropriate weighting matrices, and variable regularization parameter. The problem is scaled through the weighting matrices so that the singular spectrum is normalized. Matching the normalized singular values, a regularization parameter varies within the interval [0, 1], and linearly increases with singular value index from a small, initial value rather than a fixed one to eliminate the impacts of smaller singular values' components. The experimental results show that the proposed method is superior to the ordinary singular value decomposition (SVD) methods such as truncated SVD and Tikhonov regularization.
Energy Technology Data Exchange (ETDEWEB)
Eisenbart, Constanze (ed.) [Forschungsstaette der Evangelischen Studiengemeinschaft (FEST), Heidelberg (Germany)
2012-07-01
The book contains the following contributions: Why do we talk about the atomic age? The language of the atomic myth - comments to a protestant debate. Nuclear singularity between fiction and reality. Only one can get through: military singularity of nuclear weapons. Physical singularity of nuclear weapons. Nuclear weapons test and fall-out. Quantitative disarmament and qualitative rearmament. Do mini nukes neutralize the singularity? The vulnerability of the industrial society by the nuclear electromagnetic momentum. Nuclear weapons as national status symbol - the example of India. The general regulations of international laws and the singularity of nuclear weapons. The construction of normative singularity - development and change of the nuclear taboo.
Resisting Weakness of the Will.
Levy, Neil
2011-01-01
I develop an account of weakness of the will that is driven by experimental evidence from cognitive and social psychology. I will argue that this account demonstrates that there is no such thing as weakness of the will: no psychological kind corresponds to it. Instead, weakness of the will ought to be understood as depletion of System II resources. Neither the explanatory purposes of psychology nor our practical purposes as agents are well-served by retaining the concept. I therefore suggest that we ought to jettison it, in favour of the vocabulary and concepts of cognitive psychology.
Weak Coupling Phases future directions
Rosner, Jonathan L.
2003-01-01
Recent results obtained from B decays on the phases of weak couplings described by the Cabibbo-Kobayashi-Maskawa (CKM) matrix are discussed, with particular emphasis on $\\alpha$ and $\\gamma = \\pi - \\beta - \\alpha$.
Uniqueness of singular solution of semilinear elliptic equation
Indian Academy of Sciences (India)
Information Science, Henan University, Kaifeng 475004, People's Republic of China. E-mail: laibaishun@henu.edu.cn ... Keywords. Nonhomogeneous semilinear elliptic equation; positive solutions; asymptotic behavior; singular solutions. 1. Introduction. In this paper, we study the elliptic equation u + K(|x|)up + μf (|x|) = 0,.
Transitions of the Multi-Scale Singularity Trees
DEFF Research Database (Denmark)
Somchaipeng, Kerawit; Sporring, Jon; Kreiborg, Sven
2005-01-01
Multi-Scale Singularity Trees(MSSTs) [10] are multi-scale image descriptors aimed at representing the deep structures of images. Changes in images are directly translated to changes in the deep structures; therefore transitions in MSSTs. Because MSSTs can be used to represent the deep structure o...
A generalized Dirichlet distribution accounting for singularities of the variables
DEFF Research Database (Denmark)
Lewy, Peter
1996-01-01
A multivariate generalized Dirichlet distribution has been formulated for the case where the stochastic variables are allowed to have singularities at 0 and 1. Small sample properties of the estimates of moments of the variables based on maximum likelihood estimates of the parameters have been co...
New criteria to detect singularities in experimental incompressible flows
Kuzzay, Denis; Martins, Fabio J W A; Faranda, Davide; Foucaut, Jean-Marc; Daviaud, François; Dubrulle, Bérengère
2016-01-01
We introduce two new singularity detection criteria based on the work of Duchon-Robert (DR) [J. Duchon and R. Robert, Nonlinearity, 13, 249 (2000)], and Eyink [G.L. Eyink, Phys. Rev. E, 74 (2006)] which allow for the local detection of singularities with scaling exponent $h\\leqslant1/2$ in experimental flows, using PIV measurements. We show that in order to detect such singularities, one does not need to have access to the whole velocity field inside a volume but can instead look for them from stereoscopic particle image velocimetry (SPIV) data on a plane. We discuss the link with the Beale-Kato-Majda (BKM) [J.T. Beale, T. Kato, A. Majda, Commun. Math. Phys., 94, 61 (1984)] criterion, based on the blowup of vorticity, which applies to singularities of Navier-Stokes equations. We illustrate our discussion using tomographic PIV data obtained inside a high Reynolds number flow generated inside the boundary layer of a wind tunnel. In such a case, BKM and DR criteria are well correlated with each other.
Faddeev–Jackiw quantization of non-autonomous singular systems
Energy Technology Data Exchange (ETDEWEB)
Belhadi, Zahir [Laboratoire de physique théorique, Faculté des sciences exactes, Université de Bejaia, 06000 Bejaia (Algeria); Equipe BioPhyStat, ICPMB, IF CNRS N 2843, Université de Lorraine, 57070 Metz Cedex (France); Bérard, Alain [Equipe BioPhyStat, ICPMB, IF CNRS N 2843, Université de Lorraine, 57070 Metz Cedex (France); Mohrbach, Hervé, E-mail: herve.mohrbach@univ-lorraine.fr [Equipe BioPhyStat, ICPMB, IF CNRS N 2843, Université de Lorraine, 57070 Metz Cedex (France)
2016-10-07
We extend the quantization à la Faddeev–Jackiw for non-autonomous singular systems. This leads to a generalization of the Schrödinger equation for those systems. The method is exemplified by the quantization of the damped harmonic oscillator and the relativistic particle in an external electromagnetic field.
Singular spectrum analysis, Harmonic regression and El-Nino effect ...
Indian Academy of Sciences (India)
42
1. Singular spectrum analysis, Harmonic regression and El-Nino effect on total ozone (1979-93) over India and surrounding regions. Chandramadhab Pal cmpmagra@gmail.com. Department of Physics, Ramakrishna Mission Vidyamandira, Belurmath, Howrah 711202, W.B.,. India. Abstract: The Total Ozone Mapping ...
Fourth order compact finite difference method for solving singularly ...
African Journals Online (AJOL)
A numerical method based on finite difference scheme with uniform mesh is presented for solving singularly perturbed two-point boundary value problems of 1D reaction-diffusion equations. First, the derivatives of the given differential equation is replaced by the finite difference approximations and then, solved by using ...
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...
Singularity free non-rotating cosmological solutions for perfect fluids ...
Indian Academy of Sciences (India)
It is an attempt to explore non-singular cosmological solutions with non-rotating perfect ﬂuids with =kρ. The investigation strongly indicates that there is no solution of the above type other than already known. It is hoped that this result may be rigorously proved in future.
On self-adjointness of singular Floquet Hamiltonians
DEFF Research Database (Denmark)
Duclos, Pierre; Jensen, Arne
2010-01-01
Schrödinger equations with time-dependent interactions are studied. We investigate how to define the Floquet Hamiltonian as a self-adjoint operator, when the interaction is singular in time or space. Using these results we establish the existence of a bounded propagator, by applying a result given...
Spatial Behaviour of Singularities in Fractal- and Gaussian Speckle Fields
DEFF Research Database (Denmark)
Angelsky, Oleg V.; Maksimyak, Alexander P.; Maksimyak, Peter P.
2009-01-01
Peculiarities of the spatial behaviour of the dislocation lines resulting from scattering of coherent radiation from random and fractal rough surfaces are studied. The technique of optical correlation is proposed for diagnostics of phase singularities in a complex speckle field by comparing...
Priapism after a Singular Dose of Chlorpromazine | Suleekwe ...
African Journals Online (AJOL)
A case of priapism in a young Nigerian man following a singular dose of chlorpromazine is presented. Complete detumescence was achieved with needle aspiration and adrenaline infiltration. Potency was retained. A review of relevant literature is done. Key words: Priapism, Chlorpromazine, Needle aspiration.
Do sewn up singularities falsify the Palatini cosmology?
Energy Technology Data Exchange (ETDEWEB)
Szydlowski, Marek [Astronomical Observatory, Jagiellonian University, Krakow (Poland); Mark Kac Complex Systems Research Centre, Jagiellonian University, Krakow (Poland); Stachowski, Aleksander [Astronomical Observatory, Jagiellonian University, Krakow (Poland); Borowiec, Andrzej [University of Wroclaw, Institute for Theoretical Physics, Wroclaw (Poland); Wojnar, Aneta [University of Wroclaw, Institute for Theoretical Physics, Wroclaw (Poland); Universita di Napoli Federico II, Complesso Universitario di Monte S. Angelo, Dipartimento di Fisica, Naples (Italy)
2016-10-15
We investigate further (cf. Borowiec et al. JCAP 1601(01):040, 2016) the Starobinsky cosmological model R + γR{sup 2} in the Palatini formalism with a Chaplygin gas and baryonic matter as a source in the context of singularities. The dynamics reduces to the 2D sewn dynamical system of a Newtonian type (a piece-wise-smooth dynamical system). We demonstrate that the presence of a sewn up freeze singularity (glued freeze type singularities) for the positive γ is, in this case, a generic feature of the early evolution of the universe. It is demonstrated that γ equal zero is a bifurcation parameter and the dynamics qualitatively changes as the γ sign is changing. On the other side for the case of negative γ instead of the big bang the sudden bounce singularity of a finite scale factor does appear and there is a generic class of bouncing solutions. While the Ω{sub γ} > 0 is favored by data only very small values of Ω{sub γ} parameter are allowed if we require agreement with the ΛCDM model. From the statistical analysis of astronomical observations, we deduce that the case of only very small negative values of Ω{sub γ} cannot be rejected. Therefore, observation data favor the universe without the ghost states (f{sup '}(R) > 0) and tachyons (f''(R) > 0). (orig.)
Non-perturbative string theories and singular surfaces
Energy Technology Data Exchange (ETDEWEB)
Bochicchio, M. (Rome-1 Univ. (Italy). Dipt. di Fisica Istituto Nazionale di Fisica Nucleare, Rome (Italy))
1990-08-23
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 {epsilon} is introduced and the approximate genus is defined as half the number of connected regions covered by punctures of radius {epsilon}. 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.).
Solitary wave solution to a singularly perturbed generalized Gardner ...
Indian Academy of Sciences (India)
This paper is concerned with the existence of travelling wave solutions to a singularly perturbed generalized Gardner equation with nonlinear terms of any order. By using ... X Q YANG1. Nonlinear Scientific Research Center, Faculty of Science, Jiangsu University, Zhenjiang, Jiangsu, 212013, People's Republic of China ...
Discrete singular convolution for the generalized variable-coefficient ...
African Journals Online (AJOL)
Numerical solutions of the generalized variable-coefficient Korteweg-de Vries equation are obtained using a discrete singular convolution and a fourth order singly diagonally implicit Runge-Kutta method for space and time discretisation, respectively. The theoretical convergence of the proposed method is rigorously ...
Robust Monotone Iterates for Nonlinear Singularly Perturbed Boundary Value Problems
Directory of Open Access Journals (Sweden)
Boglaev Igor
2009-01-01
Full Text Available This paper is concerned with solving nonlinear singularly perturbed boundary value problems. Robust monotone iterates for solving nonlinear difference scheme are constructed. Uniform convergence of the monotone methods is investigated, and convergence rates are estimated. Numerical experiments complement the theoretical results.
Quantum jump from singularity to outside of black hole
Energy Technology Data Exchange (ETDEWEB)
Dündar, Furkan Semih [Physics and Mathematics Departments, Sakarya University, 54050, Sakarya (Turkey); Hajian, Kamal [School of Physics, Institute for Research in Fundamental Sciences, P.O. Box 19395-5531, Tehran (Iran, Islamic Republic of); Department of Physics, Sharif University of Technology, P.O. Box 11365-8639, Tehran (Iran, Islamic Republic of)
2016-02-26
Considering the role of black hole singularity in quantum evolution, a resolution to the firewall paradox is presented. It is emphasized that if an observer has the singularity as a part of his spacetime, then the semi-classical evolution would be non-unitary as viewed by him. Specifically, a free-falling observer inside the black hole would have a Hilbert space with non-unitary evolution; a quantum jump for particles encountering the singularity to outside of the horizon as late Hawking radiations. The non-unitarity in the jump resembles the one in collapse of wave function, but preserves entanglements. Accordingly, we elaborate the first postulate of black hole complementarity: freely falling observers who pass through the event horizon would have non-unitary evolution, while it does not have physically measurable effects for them. Besides, no information would be lost in the singularity. Taking the modified picture into account, the firewall paradox can be resolved, respecting No Drama. A by-product of our modification is that roughly half of the entropy of the black hole is released close to the end of evaporation in the shape of very hot Hawking radiation.
Numerical method for singularly perturbed delay parabolic partial differential equations
Directory of Open Access Journals (Sweden)
Wang Yulan
2017-01-01
Full Text Available The barycentric interpolation collocation method is discussed in this paper, which is not valid for singularly perturbed delay partial differential equations. A modified version is proposed to overcome this disadvantage. Two numerical examples are provided to show the effectiveness of the present method.
Singularity free non-rotating cosmological solutions for perfect fluids ...
Indian Academy of Sciences (India)
Singularity free cosmological solutions of the type stated in the title known so far are of a very special class and have the following characteristics: (a) The space time is cylindrically symmetric. (b) In case the metric is diagonal, the μ's are of the form μ = a function of time multiplied by a function of the radial coordinate.
Brane singularities and their avoidance in a fluid bulk
Antoniadis, Ignatios; Klaoudatou, Ifigeneia
2010-01-01
Using the method of asymptotic splittings, the possible singularity structures and the corresponding asymptotic behavior of a 3-brane in a five-dimensional bulk are classified, in the case where the bulk field content is parametrized by an analog of perfect fluid with an arbitrary equation of state $P=\\gamma\\rho$ between the `pressure' $P$ and the `density' $\\rho$. In this analogy with homogeneous cosmologies, the time is replaced by the extra coordinate transverse to the 3-brane, whose world-volume can have an arbitrary constant curvature. The results depend crucially on the constant parameter $\\gamma$: (i) For $\\gamma>-1/2$, the flat brane solution suffers from a collapse singularity at finite distance, that disappears in the curved case. (ii) For $\\gamma<-1$, the singularity cannot be avoided and it becomes of the type big rip for a flat brane. (iii) For $-1<\\gamma\\le -1/2$, the surprising result is found that while the curved brane solution is singular, the flat brane is not, opening the possibility...
Fitted-Stable Finite Difference Method for Singularly Perturbed Two ...
African Journals Online (AJOL)
A fitted-stable central difference method is presented for solving singularly perturbed two point boundary value problems with the boundary layer at one end (left or right) of the interval. A fitting factor is introduced in second order stable central difference scheme (SCD Method) and its value is obtained using the theory of ...
Propagation of singularities for linearised hybrid data impedance tomography
DEFF Research Database (Denmark)
Bal, Guillaume; Hoffmann, Kristoffer; Knudsen, Kim
2017-01-01
For a general formulation of linearised hybrid inverse problems in impedance tomography, the qualitative properties of the solutions are analysed. Using an appropriate scalar pseudo-differential formulation, the problems are shown to permit propagating singularities under certain non-elliptic con...
Frobenius 3-Folds via Singular Flat 3-Webs
Directory of Open Access Journals (Sweden)
Sergey I. Agafonov
2012-10-01
Full Text Available We give a geometric interpretation of weighted homogeneous solutions to the associativity equation in terms of the web theory and construct a massive Frobenius 3-fold germ via a singular 3-web germ satisfying the following conditions: 1 the web germ admits at least one infinitesimal symmetry, 2 the Chern connection form is holomorphic, 3 the curvature form vanishes identically.
Frobenius 3-Folds via Singular Flat 3-Webs
Agafonov, Sergey I.
2012-10-01
We give a geometric interpretation of weighted homogeneous solutions to the associativity equation in terms of the web theory and construct a massive Frobenius 3-fold germ via a singular 3-web germ satisfying the following conditions: 1) the web germ admits at least one infinitesimal symmetry, 2) the Chern connection form is holomorphic, 3) the curvature form vanishes identically.
Weakly compact operators and interpolation
Maligranda, Lech
1992-01-01
The class of weakly compact operators is, as well as the class of compact operators, a fundamental operator ideal. They were investigated strongly in the last twenty years. In this survey, we have collected and ordered some of this (partly very new) knowledge. We have also included some comments, remarks and examples. The class of weakly compact operators is, as well as the class of compact operators, a fundamental operator ideal. They were investigated strongly in the last twenty years. I...
Weak interactions of elementary particles
Okun, Lev Borisovich
1965-01-01
International Series of Monographs in Natural Philosophy, Volume 5: Weak Interaction of Elementary Particles focuses on the composition, properties, and reactions of elementary particles and high energies. The book first discusses elementary particles. Concerns include isotopic invariance in the Sakata model; conservation of fundamental particles; scheme of isomultiplets in the Sakata model; universal, unitary-symmetric strong interaction; and universal weak interaction. The text also focuses on spinors, amplitudes, and currents. Wave function, calculation of traces, five bilinear covariants,
Acute muscular weakness in children
Directory of Open Access Journals (Sweden)
Ricardo Pablo Javier Erazo Torricelli
Full Text Available ABSTRACT Acute muscle weakness in children is a pediatric emergency. During the diagnostic approach, it is crucial to obtain a detailed case history, including: onset of weakness, history of associated febrile states, ingestion of toxic substances/toxins, immunizations, and family history. Neurological examination must be meticulous as well. In this review, we describe the most common diseases related to acute muscle weakness, grouped into the site of origin (from the upper motor neuron to the motor unit. Early detection of hyperCKemia may lead to a myositis diagnosis, and hypokalemia points to the diagnosis of periodic paralysis. Ophthalmoparesis, ptosis and bulbar signs are suggestive of myasthenia gravis or botulism. Distal weakness and hyporeflexia are clinical features of Guillain-Barré syndrome, the most frequent cause of acute muscle weakness. If all studies are normal, a psychogenic cause should be considered. Finding the etiology of acute muscle weakness is essential to execute treatment in a timely manner, improving the prognosis of affected children.
Precision metrology using weak measurements.
Zhang, Lijian; Datta, Animesh; Walmsley, Ian A
2015-05-29
Weak values and measurements have been proposed as a means to achieve dramatic enhancements in metrology based on the greatly increased range of possible measurement outcomes. Unfortunately, the very large values of measurement outcomes occur with highly suppressed probabilities. This raises three vital questions in weak-measurement-based metrology. Namely, (Q1) Does postselection enhance the measurement precision? (Q2) Does weak measurement offer better precision than strong measurement? (Q3) Is it possible to beat the standard quantum limit or to achieve the Heisenberg limit with weak measurement using only classical resources? We analyze these questions for two prototypical, and generic, measurement protocols and show that while the answers to the first two questions are negative for both protocols, the answer to the last is affirmative for measurements with phase-space interactions, and negative for configuration space interactions. Our results, particularly the ability of weak measurements to perform at par with strong measurements in some cases, are instructive for the design of weak-measurement-based protocols for quantum metrology.
Perfect fluid tori orbiting Kehagias-Sfetsos naked singularities
Stuchlík, Z.; Pugliese, D.; Schee, J.; Kučáková, H.
2015-09-01
We construct perfect fluid tori in the field of the Kehagias-Sfetsos (K-S) naked singularities. These are spherically symmetric vacuum solutions of the modified Hořava quantum gravity, characterized by a dimensionless parameter ω M^2, combining the gravitational mass parameter M of the spacetime with the Hořava parameter ω reflecting the role of the quantum corrections. In dependence on the value of ω M^2, the K-S naked singularities demonstrate a variety of qualitatively different behavior of their circular geodesics that is fully reflected in the properties of the toroidal structures, demonstrating clear distinction to the properties of the torii in the Schwarzschild spacetimes. In all of the K-S naked singularity spacetimes the tori are located above an "antigravity" sphere where matter can stay in a stable equilibrium position, which is relevant for the stability of the orbiting fluid toroidal accretion structures. The signature of the K-S naked singularity is given by the properties of marginally stable tori orbiting with the uniform distribution of the specific angular momentum of the fluid, l= const. In the K-S naked singularity spacetimes with ω M^2 > 0.2811, doubled tori with the same l= const can exist; mass transfer between the outer torus and the inner one is possible under appropriate conditions, while only outflow to the outer space is allowed in complementary conditions. In the K-S spacetimes with ω M^2 < 0.2811, accretion from cusped perfect fluid tori is not possible due to the non-existence of unstable circular geodesics.
Smith, D J; Gaffney, E A; Blake, J R
2007-07-01
We discuss in detail techniques for modelling flows due to finite and infinite arrays of beating cilia. An efficient technique, based on concepts from previous 'singularity models' is described, that is accurate in both near and far-fields. Cilia are modelled as curved slender ellipsoidal bodies by distributing Stokeslet and potential source dipole singularities along their centrelines, leading to an integral equation that can be solved using a simple and efficient discretisation. The computed velocity on the cilium surface is found to compare favourably with the boundary condition. We then present results for two topics of current interest in biology. 1) We present the first theoretical results showing the mechanism by which rotating embryonic nodal cilia produce a leftward flow by a 'posterior tilt,' and track particle motion in an array of three simulated nodal cilia. We find that, contrary to recent suggestions, there is no continuous layer of negative fluid transport close to the ciliated boundary. The mean leftward particle transport is found to be just over 1 mum/s, within experimentally measured ranges. We also discuss the accuracy of models that represent the action of cilia by steady rotlet arrays, in particular, confirming the importance of image systems in the boundary in establishing the far-field fluid transport. Future modelling may lead to understanding of the mechanisms by which morphogen gradients or mechanosensing cilia convert a directional flow to asymmetric gene expression. 2) We develop a more complex and detailed model of flow patterns in the periciliary layer of the airway surface liquid. Our results confirm that shear flow of the mucous layer drives a significant volume of periciliary liquid in the direction of mucus transport even during the recovery stroke of the cilia. Finally, we discuss the advantages and disadvantages of the singularity technique and outline future theoretical and experimental developments required to apply this
Detection of weak frequency jumps for GNSS onboard clocks.
Huang, Xinming; Gong, Hang; Ou, Gang
2014-05-01
In this paper, a weak frequency jump detection method is developed for onboard clocks in global navigation satellite systems (GNSS). A Kalman filter is employed to facilitate the onboard real-time processing of atomic clock measurements, whose N-step prediction residuals are used to construct the weak frequency jump detector. Numerical simulations show that the method can successfully detect weak frequency jumps. The detection method proposed in this paper is helpful for autonomous integrity monitoring of GNSS satellite clocks, and can also be applied to other frequency anomalies with an appropriately modified detector.
Quantum discord with weak measurements
Energy Technology Data Exchange (ETDEWEB)
Singh, Uttam, E-mail: uttamsingh@hri.res.in; Pati, Arun Kumar, E-mail: akpati@hri.res.in
2014-04-15
Weak measurements cause small change to quantum states, thereby opening up the possibility of new ways of manipulating and controlling quantum systems. We ask, can weak measurements reveal more quantum correlation in a composite quantum state? We prove that the weak measurement induced quantum discord, called as the “super quantum discord”, is always larger than the quantum discord captured by the strong measurement. Moreover, we prove the monotonicity of the super quantum discord as a function of the measurement strength and in the limit of strong projective measurement the super quantum discord becomes the normal quantum discord. We find that unlike the normal discord, for pure entangled states, the super quantum discord can exceed the quantum entanglement. Our results provide new insights on the nature of quantum correlation and suggest that the notion of quantum correlation is not only observer dependent but also depends on how weakly one perturbs the composite system. We illustrate the key results for pure as well as mixed entangled states. -- Highlights: •Introduced the role of weak measurements in quantifying quantum correlation. •We have introduced the notion of the super quantum discord (SQD). •For pure entangled state, we show that the SQD exceeds the entanglement entropy. •This shows that quantum correlation depends not only on observer but also on measurement strength.
How crosscutting weak ties are established : The case of Muslims in Europe
Damstra, A.; Tillie, J.
2016-01-01
Building on the work of Granovetter [1973. “The Strength of Weak Ties.” American Journal of Sociology 78 (6): 1360–1380.], weak ties are assumed to play a vital role in processes of integration. In this paper, the focus lies on weak ties that cut across ethnic boundaries, connecting Muslim
Essential Spectral Singularities and the Spectral Expansion for the Hill Operator
Veliev, O. A.
2015-01-01
In this paper we investigate the spectral expansion for the one-dimensional Schrodinger operator with a periodic complex-valued potential. For this we consider in detail the spectral singularities and introduce new concepts as essential spectral singularities and singular quasimomenta.
Big bounce with finite-time singularity: The F(R) gravity description
Odintsov, S. D.; Oikonomou, V. K.
An alternative to the Big Bang cosmologies is obtained by the Big Bounce cosmologies. In this paper, we study a bounce cosmology with a Type IV singularity occurring at the bouncing point in the context of F(R) modified gravity. We investigate the evolution of the Hubble radius and we examine the issue of primordial cosmological perturbations in detail. As we demonstrate, for the singular bounce, the primordial perturbations originating from the cosmological era near the bounce do not produce a scale-invariant spectrum and also the short wavelength modes after these exit the horizon, do not freeze, but grow linearly with time. After presenting the cosmological perturbations study, we discuss the viability of the singular bounce model, and our results indicate that the singular bounce must be combined with another cosmological scenario, or should be modified appropriately, in order that it leads to a viable cosmology. The study of the slow-roll parameters leads to the same result indicating that the singular bounce theory is unstable at the singularity point for certain values of the parameters. We also conformally transform the Jordan frame singular bounce, and as we demonstrate, the Einstein frame metric leads to a Big Rip singularity. Therefore, the Type IV singularity in the Jordan frame becomes a Big Rip singularity in the Einstein frame. Finally, we briefly study a generalized singular cosmological model, which contains two Type IV singularities, with quite appealing features.
Warping the Weak Gravity Conjecture
Directory of Open Access Journals (Sweden)
Karta Kooner
2016-08-01
Full Text Available The Weak Gravity Conjecture, if valid, rules out simple models of Natural Inflation by restricting their axion decay constant to be sub-Planckian. We revisit stringy attempts to realise Natural Inflation, with a single open string axionic inflaton from a probe D-brane in a warped throat. We show that warped geometries can allow the requisite super-Planckian axion decay constant to be achieved, within the supergravity approximation and consistently with the Weak Gravity Conjecture. Preliminary estimates of the brane backreaction suggest that the probe approximation may be under control. However, there is a tension between large axion decay constant and high string scale, where the requisite high string scale is difficult to achieve in all attempts to realise large field inflation using perturbative string theory. We comment on the Generalized Weak Gravity Conjecture in the light of our results.
Singular effective slip length for longitudinal flow over a dense bubble mattress
Schnitzer, Ory
2016-01-01
We consider the effective hydrophobicity of a Cassie-state liquid above a periodically grooved surface, with trapped shear-free bubbles protruding between no-slip ridges at a pi/2 contact angle. Specifically, we carry out a singular-perturbation analysis in the limit where the bubbles are closely separated, finding the effective slip length for longitudinal flow along the the ridges as a[pi*sqrt(a/d) - 2.53 + o(1)], a being the bubble radius and d the width of the no-slip segments; the square-root divergence with a/d highlights the strong hydrophobic character of this configuration. The leading singular term follows from a local analysis of the gap regions between the bubbles, together with general matching considerations and a global relation linking the applied shear, the protrusion geometry, and the variation of the flow speed transverse to the no-slip ridges. The corrective constant term is found as an integral quantity of the leading-order "outer" problem, where the bubbles appear to be touching. We find...
Cosmological singularity theorems and splitting theorems for N-Bakry-Émery spacetimes
Energy Technology Data Exchange (ETDEWEB)
Woolgar, Eric, E-mail: ewoolgar@ualberta.ca [Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta T6G 2G1 (Canada); Wylie, William, E-mail: wwylie@syr.edu [215 Carnegie Building, Department of Mathematics, Syracuse University, Syracuse, New York 13244 (United States)
2016-02-15
We study Lorentzian manifolds with a weight function such that the N-Bakry-Émery tensor is bounded below. Such spacetimes arise in the physics of scalar-tensor gravitation theories, including Brans-Dicke theory, theories with Kaluza-Klein dimensional reduction, and low-energy approximations to string theory. In the “pure Bakry-Émery” N = ∞ case with f uniformly bounded above and initial data suitably bounded, cosmological-type singularity theorems are known, as are splitting theorems which determine the geometry of timelike geodesically complete spacetimes for which the bound on the initial data is borderline violated. We extend these results in a number of ways. We are able to extend the singularity theorems to finite N-values N ∈ (n, ∞) and N ∈ (−∞, 1]. In the N ∈ (n, ∞) case, no bound on f is required, while for N ∈ (−∞, 1] and N = ∞, we are able to replace the boundedness of f by a weaker condition on the integral of f along future-inextendible timelike geodesics. The splitting theorems extend similarly, but when N = 1, the splitting is only that of a warped product for all cases considered. A similar limited loss of rigidity has been observed in a prior work on the N-Bakry-Émery curvature in Riemannian signature when N = 1 and appears to be a general feature.
Removal of singularity in radial Langmuir probe models for non-zero ion temperature
Regodón, Guillermo Fernando; Fernández Palop, José Ignacio; Tejero-del-Caz, Antonio; Díaz-Cabrera, Juan Manuel; Carmona-Cabezas, Rafael; Ballesteros, Jerónimo
2017-10-01
We solve a radial theoretical model that describes the ion sheath around a cylindrical Langmuir probe with finite non-zero ion temperature in which singularity in an a priori unknown point prevents direct integration. The singularity appears naturally in fluid models when the velocity of the ions reaches the local ion speed of sound. The solutions are smooth and continuous and are valid from the plasma to the probe with no need for asymptotic matching. The solutions that we present are valid for any value of the positive ion to electron temperature ratio and for any constant polytropic coefficient. The model is numerically solved to obtain the electric potential and the ion population density profiles for any given positive ion current collected by the probe. The ion-current to probe-voltage characteristic curves and the Sonin plot are calculated in order to use the results of the model in plasma diagnosis. The proposed methodology is adaptable to other geometries and in the presence of other presheath mechanisms.
Weakly nonlinear electrophoresis of a highly charged colloidal particle
Schnitzer, Ory; Zeyde, Roman; Yavneh, Irad; Yariv, Ehud
2013-05-01
At large zeta potentials, surface conduction becomes appreciable in thin-double-layer electrokinetic transport. In the linear weak-field regime, where this effect is quantified by the Dukhin number, it is manifested in non-Smoluchowski electrophoretic mobilities. In this paper we go beyond linear response, employing the recently derived macroscale model of Schnitzer and Yariv ["Macroscale description of electrokinetic flows at large zeta potentials: Nonlinear surface conduction," Phys. Rev. E 86, 021503 (2012), 10.1103/PhysRevE.86.021503] as the infrastructure for a weakly nonlinear analysis of spherical-particle electrophoresis. A straightforward perturbation in the field strength is frustrated by the failure to satisfy the far-field conditions, representing a non-uniformity of the weak-field approximation at large distances away from the particle, where salt advection becomes comparable to diffusion. This is remedied using inner-outer asymptotic expansions in the spirit of Acrivos and Taylor ["Heat and mass transfer from single spheres in Stokes flow," Phys. Fluids 5, 387 (1962), 10.1063/1.1706630], with the inner region representing the particle neighborhood and the outer region corresponding to distances scaling inversely with the field magnitude. This singular scheme furnishes an asymptotic correction to the electrophoretic velocity, proportional to the applied field cubed, which embodies a host of nonlinear mechanisms unfamiliar from linear electrokinetic theories. These include the effect of induced zeta-potential inhomogeneity, animated by concentration polarization, on electro-osmosis and diffuso-osmosis; bulk advection of salt; nonuniform bulk conductivity; Coulomb body forces acting on bulk volumetric charge; and the nonzero electrostatic force exerted upon the otherwise screened particle-layer system. A numerical solution of the macroscale model validates our weakly nonlinear analysis.
Cosmology and the weak interaction
Energy Technology Data Exchange (ETDEWEB)
Schramm, D.N. (Fermi National Accelerator Lab., Batavia, IL (USA)):(Chicago Univ., IL (USA))
1989-12-01
The weak interaction plays a critical role in modern Big Bang cosmology. This review will emphasize two of its most publicized cosmological connections: Big Bang nucleosynthesis and Dark Matter. The first of these is connected to the cosmological prediction of Neutrino Flavours, N{sub {nu}} {approximately} 3 which is now being confirmed at SLC and LEP. The second is interrelated to the whole problem of galaxy and structure formation in the universe. This review will demonstrate the role of the weak interaction both for dark matter candidates and for the problem of generating seeds to form structure. 87 refs., 3 figs., 5 tabs.
Nonlinear waves and weak turbulence
Zakharov, V E
1997-01-01
This book is a collection of papers on dynamical and statistical theory of nonlinear wave propagation in dispersive conservative media. Emphasis is on waves on the surface of an ideal fluid and on Rossby waves in the atmosphere. Although the book deals mainly with weakly nonlinear waves, it is more than simply a description of standard perturbation techniques. The goal is to show that the theory of weakly interacting waves is naturally related to such areas of mathematics as Diophantine equations, differential geometry of waves, Poincaré normal forms, and the inverse scattering method.
Correlation energy for elementary bosons: Physics of the singularity
Energy Technology Data Exchange (ETDEWEB)
Shiau, Shiue-Yuan, E-mail: syshiau@mail.ncku.edu.tw [Department of Physics, National Cheng Kung University, Tainan, 701, Taiwan (China); Combescot, Monique [Institut des NanoSciences de Paris, Université Pierre et Marie Curie, CNRS, 4 place Jussieu, 75005 Paris (France); Chang, Yia-Chung, E-mail: yiachang@gate.sinica.edu.tw [Research Center for Applied Sciences, Academia Sinica, Taipei, 115, Taiwan (China); Department of Physics, National Cheng Kung University, Tainan, 701, Taiwan (China)
2016-04-15
We propose a compact perturbative approach that reveals the physical origin of the singularity occurring in the density dependence of correlation energy: like fermions, elementary bosons have a singular correlation energy which comes from the accumulation, through Feynman “bubble” diagrams, of the same non-zero momentum transfer excitations from the free particle ground state, that is, the Fermi sea for fermions and the Bose–Einstein condensate for bosons. This understanding paves the way toward deriving the correlation energy of composite bosons like atomic dimers and semiconductor excitons, by suggesting Shiva diagrams that have similarity with Feynman “bubble” diagrams, the previous elementary boson approaches, which hide this physics, being inappropriate to do so.
Biplot and Singular Value Decomposition Macros for Excel©
Directory of Open Access Journals (Sweden)
Ilya A. Lipkovich
2002-06-01
Full Text Available The biplot display is a graph of row and column markers obtained from data that forms a two-way table. The markers are calculated from the singular value decomposition of the data matrix. The biplot display may be used with many multivariate methods to display relationships between variables and objects. It is commonly used in ecological applications to plot relationships between species and sites. This paper describes a set of Excel macros that may be used to draw a biplot display based on results from principal components analysis, correspondence analysis, canonical discriminant analysis, metric multidimensional scaling, redundancy analysis, canonical correlation analysis or canonical correspondence analysis. The macros allow for a variety of transformations of the data prior to the singular value decomposition and scaling of the markers following the decomposition.
An omnidirectional retroreflector based on the transmutation of dielectric singularities.
Ma, Yun Gui; Ong, C K; Tyc, Tomás; Leonhardt, Ulf
2009-08-01
Transformation optics is a concept used in some metamaterials to guide light on a predetermined path. In this approach, the materials implement coordinate transformations on electromagnetic waves to create the illusion that the waves are propagating through a virtual space. Transforming space by appropriately designed materials makes devices possible that have been deemed impossible. In particular, transformation optics has led to the demonstration of invisibility cloaking for microwaves, surface plasmons and infrared light. Here, on the basis of transformation optics, we implement a microwave device that would normally require a dielectric singularity, an infinity in the refractive index. To fabricate such a device, we transmute a dielectric singularity in virtual space into a mere topological defect in a real metamaterial. In particular, we demonstrate an omnidirectional retroreflector, a device for faithfully reflecting images and for creating high visibility from all directions. Our method is robust, potentially broadband and could also be applied to visible light using similar techniques.
Multiscale singular value manifold for rotating machinery fault diagnosis
Energy Technology Data Exchange (ETDEWEB)
Feng, Yi; Lu, BaoChun; Zhang, Deng Feng [School of Mechanical Engineering, Nanjing University of Science and Technology,Nanjing (United States)
2017-01-15
Time-frequency distribution of vibration signal can be considered as an image that contains more information than signal in time domain. Manifold learning is a novel theory for image recognition that can be also applied to rotating machinery fault pattern recognition based on time-frequency distributions. However, the vibration signal of rotating machinery in fault condition contains cyclical transient impulses with different phrases which are detrimental to image recognition for time-frequency distribution. To eliminate the effects of phase differences and extract the inherent features of time-frequency distributions, a multiscale singular value manifold method is proposed. The obtained low-dimensional multiscale singular value manifold features can reveal the differences of different fault patterns and they are applicable to classification and diagnosis. Experimental verification proves that the performance of the proposed method is superior in rotating machinery fault diagnosis.
An omnidirectional retroreflector based on the transmutation of dielectric singularities
Ma, Yun Gui; Ong, C. K.; Tyc, Tomáš; Leonhardt, Ulf
2009-08-01
Transformation optics is a concept used in some metamaterials to guide light on a predetermined path. In this approach, the materials implement coordinate transformations on electromagnetic waves to create the illusion that the waves are propagating through a virtual space. Transforming space by appropriately designed materials makes devices possible that have been deemed impossible. In particular, transformation optics has led to the demonstration of invisibility cloaking for microwaves, surface plasmons and infrared light. Here, on the basis of transformation optics, we implement a microwave device that would normally require a dielectric singularity, an infinity in the refractive index. To fabricate such a device, we transmute a dielectric singularity in virtual space into a mere topological defect in a real metamaterial. In particular, we demonstrate an omnidirectional retroreflector, a device for faithfully reflecting images and for creating high visibility from all directions. Our method is robust, potentially broadband and could also be applied to visible light using similar techniques.
CONTROLLABILITY OF ESSENTIALLY VARIOUS-SPEED SINGULARLY PERTURBED DYNAMIC SYSTEMS
Directory of Open Access Journals (Sweden)
T. Kopeikina
2013-01-01
Full Text Available The paper considers the controllability problem of essentially various-speed singularly perturbed dynamic system consisting of three subsystems of different dimensions, containing a small parameter to a variable degree as a multiplier for derivatives. A method for studying complete and relative controllability of such systems has been proposed in the paper. The method is based on investigation of a controllability matrix rank. The matrix is composed of solution components of algebraic recurrent equations, which are drawn directly in accordance with the studied system of differential equations. The obtained effective algebraic conditions of controllability, expressed through parameters of the investigated system are obtained are illustrated by the case of essentially various-speed singularly perturbed dynamic system of fifth order with rational powers of small parameter.
Towards realistic string vacua from branes at singularities
Conlon, Joseph P; Quevedo, Fernando
2009-01-01
We report on progress towards constructing string models incorporating both realistic D-brane matter content and full moduli stabilisation with dynamical low-scale supersymmetry breaking. The general framework is that of local D-brane models embedded into the LARGE volume approach to moduli stabilisation. We review quiver theories on del Pezzo n (dP_n) singularities including both D3 and D7 branes. We provide supersymmetric examples with three quark/lepton families and the gauge symmetries of the Standard, Left-Right Symmetric, Pati-Salam and Trinification models, without unwanted chiral exotics. We describe how the singularity structure leads to family symmetries governing the Yukawa couplings which can give mass hierarchies among the different generations. We outline how these models can be embedded into compact Calabi-Yau compactifications with LARGE volume moduli stabilisation, and state the minimal conditions for this to be possible. We study the general structure of soft supersymmetry breaking. At the s...
Highly efficient singular surface plasmon generation by achiral apertures
Jiang, Quanbo; Bellessa, Joel; Huant, Serge; Genet, Cyriaque; Drezet, Aurélien
2016-01-01
We report a highly efficient generation of singular surface plasmon (SP) field by an achiral plasmonic structure consisting of $\\Lambda$-shaped apertures. Our quantitative analysis based on leakage radiation microscopy (LRM) demonstrates that the induced spin-orbit coupling can be tuned by adjusting the apex angle of the $\\Lambda$-shaped aperture. Specifically, the array of $\\Lambda$-shaped apertures with the apex angle $60^\\circ$ is shown to give rise to the directional coupling efficiency. The ring of $\\Lambda$-shaped apertures with the apex angle $60^\\circ$ realized to generate the maximum extinction ratio (ER=11) for the SP singularities between two different polarization states. This result provides a more efficient way for developing SP focusing and SP vortex in the field of nanophotonics such as optical tweezers.
Stabilization of fractional-order singular uncertain systems.
Ji, Yude; Qiu, Jiqing
2015-05-01
This paper focuses on the state and static output feedback stabilization for fractional-order singular (FOS) uncertain linear systems with the fractional commensurate order 0controllers that guarantee the stability of resulting closed-loop control systems. First, the sufficient conditions for robust asymptotical stability of the closed-loop control systems are presented. Next, based on the matrix׳s singular value decomposition (SVD) and linear matrix inequality (LMI) technics, some new results in the form of LMI are developed to the state and static output feedback controller synthesis for the FOS systems. Finally, three numerical examples are given to illustrate the effectiveness of the proposed design methods. Copyright © 2014 ISA. Published by Elsevier Ltd. All rights reserved.
Surface singularities of nanorod laden droplets in magnetic field
Kornev, Konstantin; Tokarev, Alexander; Lee, Wah-Keat
2013-11-01
Magnetic nanorods are attractive materials enabling assembly, ordering, control, and reconfiguration of different magnetic lattices within milliseconds in milliTesla magnetic fields. In this talk we will show a new physical principle of self-assembly of magnetic nanorods into singular cusps at the droplet surface. These singularities can be formed on demand not deforming the entire droplets by taking advantage of the magneto-static interactions between nanorods in non-uniform magnetic field. Using X-ray phase contrast imaging and scaling analysis we will explain the behavior of magnetic nematics and their interactions with the droplet surface. The authors are grateful for the financial support of the National Science Foundation through Grant EFRI 0937985, and of the Air Force Office of Scientific Research through Grant FA9550-12-1-0459.
S-matrix singularities and CFT correlation functions
Cardona, Carlos; Huang, Yu-tin
2017-08-01
In this note, we explore the correspondence between four-dimensional flat space S-matrix and two-dimensional CFT proposed by Pasterski et al. We demonstrate that the factorisation singularities of an n-point cubic diagram reproduces the AdS Witten diagrams if mass conservation is imposed at each vertex. Such configuration arises naturally if we consider the 4-dimensional S-matrix as a compactified massless 5-dimensional theory. This identification allows us to rewrite the massless S-matrix in the CHY formulation, where the factorisation singularities are re-interpreted as factorisation limits of a Riemann sphere. In this light, the map is recast into a form of 2 d/2 d correspondence.
Asymptotically AdS spacetimes with a timelike Kasner singularity
Energy Technology Data Exchange (ETDEWEB)
Ren, Jie [Racah Institute of Physics, The Hebrew University of Jerusalem, Jerusalem 91904 (Israel)
2016-07-21
Exact solutions to Einstein’s equations for holographic models are presented and studied. The IR geometry has a timelike cousin of the Kasner singularity, which is the less generic case of the BKL (Belinski-Khalatnikov-Lifshitz) singularity, and the UV is asymptotically AdS. This solution describes a holographic RG flow between them. The solution’s appearance is an interpolation between the planar AdS black hole and the AdS soliton. The causality constraint is always satisfied. The entanglement entropy and Wilson loops are discussed. The boundary condition for the current-current correlation function and the Laplacian in the IR is examined. There is no infalling wave in the IR, but instead, there is a normalizable solution in the IR. In a special case, a hyperscaling-violating geometry is obtained after a dimensional reduction.
Weak characteristic information extraction from early fault of wind turbine generator gearbox
Xu, Xiaoli; Liu, Xiuli
2017-09-01
Given the weak early degradation characteristic information during early fault evolution in gearbox of wind turbine generator, traditional singular value decomposition (SVD)-based denoising may result in loss of useful information. A weak characteristic information extraction based on μ-SVD and local mean decomposition (LMD) is developed to address this problem. The basic principle of the method is as follows: Determine the denoising order based on cumulative contribution rate, perform signal reconstruction, extract and subject the noisy part of signal to LMD and μ-SVD denoising, and obtain denoised signal through superposition. Experimental results show that this method can significantly weaken signal noise, effectively extract the weak characteristic information of early fault, and facilitate the early fault warning and dynamic predictive maintenance.
Integrability and the conformal field theory of the Higgs branch
Energy Technology Data Exchange (ETDEWEB)
Sax, Olof Ohlsson [Theoretical Physics, The Blackett Laboratory, Imperial College,London, SW7 2AZ (United Kingdom); Sfondrini, Alessandro [Institut für Mathematik und Institut für Physik, Humboldt-Universität zu Berlin, IRIS Gebäude,Zum Grossen Windkanal 6, Berlin, 12489 (Germany); Bogdan, Stefański Jr. [Centre for Mathematical Science, City University London,Northampton Square, London, EC1V 0HB (United Kingdom)
2015-06-16
In the context of the AdS{sub 3}/CFT{sub 2} correspondence, we investigate the Higgs branch CFT{sub 2}. Witten showed that states localised near the small instanton singularity can be described in terms of vector multiplet variables. This theory has a planar, weak-coupling limit, in which anomalous dimensions of single-trace composite operators can be calculated. At one loop, the calculation reduces to finding the spectrum of a spin-chain with nearest-neighbour interactions. This CFT{sub 2} spin-chain matches precisely the one that was previously found as the weak-coupling limit of the integrable system describing the AdS{sub 3} side of the duality. We compute the one-loop dilatation operator in a non-trivial compact subsector and show that it corresponds to an integrable spin-chain Hamiltonian. This provides the first direct evidence of integrability on the CFT{sub 2} side of the correspondence.
Biplot and Singular Value Decomposition Macros for Excel©
Eric P. Smith; Ilya Lipkovich
2002-01-01
The biplot display is a graph of row and column markers obtained from data that forms a two-way table. The markers are calculated from the singular value decomposition of the data matrix. The biplot display may be used with many multivariate methods to display relationships between variables and objects. It is commonly used in ecological applications to plot relationships between species and sites. This paper describes a set of Excel macros that may be used to draw a biplot display based ...
Dyslexia singular brain; Le singulier cerveau des dyslexiques
Energy Technology Data Exchange (ETDEWEB)
Habis, M.; Robichon, F. [Centre Hospitalier Universitaire de la Timone, 13 - Marseille (France); Demonet, J.F. [Centre Hospitalier Universitaire la Grave, 31 - Toulouse (France)
1996-07-01
Of late ten years, neurologists are studying the brain of the dyslectics. The cerebral imagery (NMR imaging, positron computed tomography) has allowed to confirm the anatomical particularities discovered by some of them: asymmetry default of cerebral hemispheres, size abnormally large of the white substance mass which connect the two hemispheres. The functional imagery, when visualizing this singular brain at work, allows to understand why it labors to reading. (O.M.). 4 refs.
Singular divergence instability thresholds of kinematically constrained circulatory systems
Energy Technology Data Exchange (ETDEWEB)
Kirillov, O.N., E-mail: o.kirillov@hzdr.de [Magnetohydrodynamics Division, Helmholtz-Zentrum Dresden-Rossendorf, P.O. Box 510119, D-01314 Dresden (Germany); Challamel, N. [University of South Brittany, LIMATB, Lorient (France); Darve, F. [Laboratoire Sols Solides Structures, UJF-INPG-CNRS, Grenoble (France); Lerbet, J. [IBISC, Universite d' Evry Val d' Essone, 40 Rue Pelvoux, CE 1455 Courcouronnes, 91020 Evry Cedex (France); Nicot, F. [Cemagref, Unite de Recherche Erosion Torrentielle Neige et Avalanches, Grenoble (France)
2014-01-10
Static instability or divergence threshold of both potential and circulatory systems with kinematic constraints depends singularly on the constraints' coefficients. Particularly, the critical buckling load of the kinematically constrained Ziegler's pendulum as a function of two coefficients of the constraint is given by the Plücker conoid of degree n=2. This simple mechanical model exhibits a structural instability similar to that responsible for the Velikhov–Chandrasekhar paradox in the theory of magnetorotational instability.
The quest for transformational leadership and brand singularity
Wilson, Jonathan A.J.
2014-01-01
Whether that transformational leader is a person, brand, organization, or nation – I argue that the same blueprint applies to all. A further challenge occurs when trying to\\ud widen the net in order to galvanize several streams of leadership and innovation to achieve collective singularity. This article contains some of my musings.\\ud \\ud In everyday conversations, the terms Manager and Leader seem to be used interchangeably. Also, over the past thirty years or so the term Transformational ha...
The structure and singularities of quotient arc complexes
DEFF Research Database (Denmark)
Penner, Robert
2008-01-01
A well-known combinatorial fact is that the simplicial complex consisting of disjointly embedded chords in a convex planar polygon is a sphere. For any surface F with non-empty boundary, there is an analogous complex QA(F) consisting of equivalence classes of arcs in F connecting a given finite s...... with a related quotient arc complex in the punctured case with no boundary. Namely, the essential singularities of the natural cellular compactification of Riemann's moduli space can be described....
Adaptive Control of the Chaotic System via Singular System Approach
Directory of Open Access Journals (Sweden)
Yudong Li
2014-01-01
Full Text Available This paper deals with the control problem of the chaotic system subject to disturbance. The sliding mode surface is designed by singular system approach, and sufficient condition for convergence is given. Then, the adaptive sliding mode controller is designed to make the state arrive at the sliding mode surface in finite time. Finally, Lorenz system is considered as an example to show the effectiveness of the proposed method.
Singularity-free gravitational collapse and asymptotic safety
Torres, Ramón
2014-06-01
A general class of quantum improved stellar models with interiors composed of non-interacting (dust) particles is obtained and analyzed in a framework compatible with asymptotic safety. First, the effective exterior, based on the Quantum Einstein Gravity approach to asymptotic safety is presented and, second, its effective compatible dust interiors are deduced. The resulting stellar models appear to be devoid of shell-focusing singularities.
Singular-value demodulation of phase-shifted holograms.
Lopes, Fernando; Atlan, Michael
2015-06-01
We report on phase-shifted holographic interferogram demodulation by singular-value decomposition. Numerical processing of optically acquired interferograms over several modulation periods was performed in two steps: (1) rendering of off-axis complex-valued holograms by Fresnel transformation of the interferograms; and (2) eigenvalue spectrum assessment of the lag-covariance matrix of hologram pixels. Experimental results in low-light recording conditions were compared with demodulation by Fourier analysis, in the presence of random phase drifts.
Bifurcation for non linear ordinary differential equations with singular perturbation
Directory of Open Access Journals (Sweden)
Safia Acher Spitalier
2016-10-01
Full Text Available We study a family of singularly perturbed ODEs with one parameter and compare their solutions to the ones of the corresponding reduced equations. The interesting characteristic here is that the reduced equations have more than one solution for a given set of initial conditions. Then we consider how those solutions are organized for different values of the parameter. The bifurcation associated to this situation is studied using a minimal set of tools from non standard analysis.
Positive solutions of singular boundary value problem of negative ...
Indian Academy of Sciences (India)
R. Narasimhan (Krishtel eMaging) 1461 1996 Oct 15 13:05:22
may be singular at t = 0,t = 1. When λ 0, [6] shows the existence and uniqueness to (1) and (2) in the case of β = δ = 0 by means of the shooting method. For the following problem u + p(t)u−λ(t) + q(t)u−m(t) = 0, 0
Topological Field Theory of the Initial Singularity of Space-Time
Bogdanoff, I
2000-01-01
Here we suggest a possible resolution of the initial space-time singularity. In this novel approach, the initial singularity of space-time corresponds to a 0 size singular gravitational instanton, characterised by a Riemannian metric configuration (++++) in dimension D = 4. Associated with the 0 scale of space-time, the initial singularity is thus not considered in terms of divergences of physical fields but can be resolved in terms of topological field symmetries and associated invariants (in particular the first Donaldson invariant ). In this perspective, we here introduce a new topological invariant, associated with 0 scale, of the form Z = Tr (-1)s which we call "singularity invariant".
Propagation of the Lissajous singularity dipole emergent from non-paraxial polychromatic beams
Haitao, Chen; Gao, Zenghui; Wang, Wanqing
2017-06-01
The propagation of the Lissajous singularity dipole (LSD) emergent from the non-paraxial polychromatic beams is studied. It is found that the handedness reversal of Lissajous singularities, the change in the shape of Lissajous figures, as well as the creation and annihilation of the LSD may take place by varying the propagation distance, off-axis parameter, wavelength, or amplitude factor. Comparing with the LSD emergent from paraxial polychromatic beams, the output field of non-paraxial polychromatic beams is more complicated, which results in some richer dynamic behaviors of Lissajous singularities, such as more Lissajous singularities and no vanishing of a single Lissajous singularity at the plane z>0.
Submanifolds weakly associated with graphs
Indian Academy of Sciences (India)
Sci. (Math. Sci.) Vol. 119, No. 3, June 2009, pp. 297–318. © Printed in India. Submanifolds weakly associated with graphs. A CARRIAZO, L M FERN ´ANDEZ and A RODRÍGUEZ-HIDALGO. Department of Geometry and Topology, Faculty of Mathematics, University of Sevilla,. Apartado de Correos 1160, 41080-Sevilla, Spain.
Beam splitting on weak illumination.
Snyder, A W; Buryak, A V; Mitchell, D J
1998-01-01
We demonstrate, in both two and three dimensions, how a self-guided beam in a non-Kerr medium is split into two beams on weak illumination. We also provide an elegant physical explanation that predicts the universal character of the observed phenomenon. Possible applications of our findings to guiding light with light are also discussed.
Thomys, Janus; Zhang, Xiaohong
2013-01-01
We describe weak-BCC-algebras (also called BZ-algebras) in which the condition (x∗y)∗z = (x∗z)∗y is satisfied only in the case when elements x, y belong to the same branch. We also characterize ideals, nilradicals, and nilpotent elements of such algebras. PMID:24311983
Voltage Weak DC Distribution Grids
Hailu, T.G.; Mackay, L.J.; Ramirez Elizondo, L.M.; Ferreira, J.A.
2017-01-01
This paper describes the behavior of voltage weak DC distribution systems. These systems have relatively small system capacitance. The size of system capacitance, which stores energy, has a considerable effect on the value of fault currents, control complexity, and system reliability. A number of
Watermarking scheme based on singular value decomposition and homomorphic transform
Verma, Deval; Aggarwal, A. K.; Agarwal, Himanshu
2017-10-01
A semi-blind watermarking scheme based on singular-value-decomposition (SVD) and homomorphic transform is pro-posed. This scheme ensures the digital security of an eight bit gray scale image by inserting an invisible eight bit gray scale wa-termark into it. The key approach of the scheme is to apply the homomorphic transform on the host image to obtain its reflectance component. The watermark is embedded into the singular values that are obtained by applying the singular value decomposition on the reflectance component. Peak-signal-to-noise-ratio (PSNR), normalized-correlation-coefficient (NCC) and mean-structural-similarity-index-measure (MSSIM) are used to evaluate the performance of the scheme. Invisibility of watermark is ensured by visual inspection and high value of PSNR of watermarked images. Presence of watermark is ensured by visual inspection and high values of NCC and MSSIM of extracted watermarks. Robustness of the scheme is verified by high values of NCC and MSSIM for attacked watermarked images.
Schrodinger formalism, black hole horizons, and singularity behavior
Wang, John E.; Greenwood, Eric; Stojkovic, Dejan
2009-12-01
The Gauss-Codazzi method is used to discuss the gravitational collapse of a charged Reisner-Nordström domain wall. We solve the classical equations of motion of a thin charged shell moving under the influence of its own gravitational field and show that a form of cosmic censorship applies. If the charge of the collapsing shell is greater than its mass, then the collapse does not form a black hole. Instead, after reaching some minimal radius, the shell bounces back. The Schrödinger canonical formalism is used to quantize the motion of the charged shell. The limits near the horizon and near the singularity are explored. Near the horizon, the Schrödinger equation describing evolution of the collapsing shell takes the form of the massive wave equation with a position dependent mass. The outgoing and incoming modes of the solution are related by the Bogolubov transformation which precisely gives the Hawking temperature. Near the classical singularity, the Schrödinger equation becomes nonlocal, but the wave function describing the system is nonsingular. This indicates that while quantum effects may be able to remove the classical singularity, it may also introduce some new effects.
Towards realistic string vacua from branes at singularities
Conlon, Joseph P.; Maharana, Anshuman; Quevedo, Fernando
2009-05-01
We report on progress towards constructing string models incorporating both realistic D-brane matter content and moduli stabilisation with dynamical low-scale supersymmetry breaking. The general framework is that of local D-brane models embedded into the LARGE volume approach to moduli stabilisation. We review quiver theories on del Pezzo n (dPn) singularities including both D3 and D7 branes. We provide supersymmetric examples with three quark/lepton families and the gauge symmetries of the Standard, Left-Right Symmetric, Pati-Salam and Trinification models, without unwanted chiral exotics. We describe how the singularity structure leads to family symmetries governing the Yukawa couplings which may give mass hierarchies among the different generations. We outline how these models can be embedded into compact Calabi-Yau compactifications with LARGE volume moduli stabilisation, and state the minimal conditions for this to be possible. We study the general structure of soft supersymmetry breaking. At the singularity all leading order contributions to the soft terms (both gravity- and anomaly-mediation) vanish. We enumerate subleading contributions and estimate their magnitude. We also describe model-independent physical implications of this scenario. These include the masses of anomalous and non-anomalous U(1)'s and the generic existence of a new hyperweak force under which leptons and/or quarks could be charged. We propose that such a gauge boson could be responsible for the ghost muon anomaly recently found at the Tevatron's CDF detector.
Naked singularity explosion in higher-dimensional dust collapse
Shimano, Masahiro
2013-01-01
In the context of the large extra dimensions or TeV-scale gravity, it has been argued that an effective naked singularity, called the visible border of spacetime, would be generated by high-energy particle collisions. Motivated by this interesting possibility, we investigate a particle creation by a naked singularity in general dimensions, adopting a spherically symmetric self-similar dust collapse as the simple model of a naked singularity formation. The power and energy of the particle emission behave in two distinct ways depending on a parameter in the model. In a generic case, the emission power is proportional to the quadratic inverse of the remaining time to the Cauchy horizon, which has been known for the four-dimensional case in the literature. On the other hand, in a degenerate case the emission power is proportional to the quartic inverse of the remaining time to the Cauchy horizon, and depends on the total mass of a dust fluid in spite that the central region of the collapse is scale-free due to th...
Weak fault detection and health degradation monitoring using customized standard multiwavelets
Yuan, Jing; Wang, Yu; Peng, Yizhen; Wei, Chenjun
2017-09-01
Due to the nonobvious symptoms contaminated by a large amount of background noise, it is challenging to beforehand detect and predictively monitor the weak faults for machinery security assurance. Multiwavelets can act as adaptive non-stationary signal processing tools, potentially viable for weak fault diagnosis. However, the signal-based multiwavelets suffer from such problems as the imperfect properties missing the crucial orthogonality, the decomposition distortion impossibly reflecting the relationships between the faults and signatures, the single objective optimization and independence for fault prognostic. Thus, customized standard multiwavelets are proposed for weak fault detection and health degradation monitoring, especially the weak fault signature quantitative identification. First, the flexible standard multiwavelets are designed using the construction method derived from scalar wavelets, seizing the desired properties for accurate detection of weak faults and avoiding the distortion issue for feature quantitative identification. Second, the multi-objective optimization combined three dimensionless indicators of the normalized energy entropy, normalized singular entropy and kurtosis index is introduced to the evaluation criterions, and benefits for selecting the potential best basis functions for weak faults without the influence of the variable working condition. Third, an ensemble health indicator fused by the kurtosis index, impulse index and clearance index of the original signal along with the normalized energy entropy and normalized singular entropy by the customized standard multiwavelets is achieved using Mahalanobis distance to continuously monitor the health condition and track the performance degradation. Finally, three experimental case studies are implemented to demonstrate the feasibility and effectiveness of the proposed method. The results show that the proposed method can quantitatively identify the fault signature of a slight rub on
Competing weak localization and weak antilocalization in ultrathin topological insulators.
Lang, Murong; He, Liang; Kou, Xufeng; Upadhyaya, Pramey; Fan, Yabin; Chu, Hao; Jiang, Ying; Bardarson, Jens H; Jiang, Wanjun; Choi, Eun Sang; Wang, Yong; Yeh, Nai-Chang; Moore, Joel; Wang, Kang L
2013-01-09
We demonstrate evidence of a surface gap opening in topological insulator (TI) thin films of (Bi(0.57)Sb(0.43))(2)Te(3) below six quintuple layers through transport and scanning tunneling spectroscopy measurements. By effective tuning the Fermi level via gate-voltage control, we unveil a striking competition between weak localization and weak antilocalization at low magnetic fields in nonmagnetic ultrathin films, possibly owing to the change of the net Berry phase. Furthermore, when the Fermi level is swept into the surface gap of ultrathin samples, the overall unitary behaviors are revealed at higher magnetic fields, which are in contrast to the pure WAL signals obtained in thicker films. Our findings show an exotic phenomenon characterizing the gapped TI surface states and point to the future realization of quantum spin Hall effect and dissipationless TI-based applications.
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.
Singularity confinement for a class of m-th order difference equations of combinatorics.
Adler, Mark; van Moerbeke, Pierre; Vanhaecke, Pol
2008-03-28
In a recent publication, it was shown that a large class of integrals over the unitary group U(n) satisfy nonlinear, non-autonomous difference equations over n, involving a finite number of steps; special cases are generating functions appearing in questions of the longest increasing subsequences in random permutations and words. The main result of the paper states that these difference equations have the discrete Painlevé property; roughly speaking, this means that after a finite number of steps the solution to these difference equations may develop a pole (Laurent solution), depending on the maximal number of free parameters, and immediately after be finite again ("singularity confinement"). The technique used in the proof is based on an intimate relationship between the difference equations (discrete time) and the Toeplitz lattice (continuous time differential equations); the point is that the Painlevé property for the discrete relations is inherited from the Painlevé property of the (continuous) Toeplitz lattice.
Approximate series solution of nonlinear singular boundary value problems arising in physiology.
Singh, Randhir; Kumar, Jitendra; Nelakanti, Gnaneshwar
2014-01-01
We introduce an efficient recursive scheme based on Adomian decomposition method (ADM) for solving nonlinear singular boundary value problems. This approach is based on a modification of the ADM; here we use all the boundary conditions to derive an integral equation before establishing the recursive scheme for the solution components. In fact, we develop the recursive scheme without any undetermined coefficients while computing the solution components. Unlike the classical ADM, the proposed method avoids solving a sequence of nonlinear algebraic or transcendental equations for the undetermined coefficients. The approximate solution is obtained in the form of series with easily calculable components. The uniqueness of the solution is discussed. The convergence and error analysis of the proposed method are also established. The accuracy and reliability of the proposed method are examined by four numerical examples.
Singular inverse square potential in coordinate space with a minimal length
Bouaziz, Djamil; Birkandan, Tolga
2017-12-01
The problem of a particle of mass m in the field of the inverse-square potential α /r2 is studied in quantum mechanics with a generalized uncertainty principle, characterized by the existence of a minimal length. Using the coordinate representation, for a specific form of the generalized uncertainty relation, we solve the deformed Schrödinger equation analytically in terms of confluent Heun functions. We explicitly show the regularizing effect of the minimal length on the singularity of the potential. We discuss the problem of bound states in detail and we derive an expression for the energy spectrum in a natural way from the square integrability condition; the results are in complete agreement with the literature.
Optimal Weak Lensing Skewness Measurements
Zhang, Tong-Jie; Pen, Ue-Li; Zhang, Pengjie; Dubinski, John
2003-01-01
Weak lensing measurements are entering a precision era to statistically map the distribution of matter in the universe. The most common measurement has been of the variance of the projected surface density of matter, which corresponds to the induced correlation in alignments of background galaxies. This measurement of the fluctuations is insensitive to the total mass content, like using waves on the ocean to measure its depths. But when the depth is shallow as happens near a beach, waves beco...
Weak neutral-current interactions
Energy Technology Data Exchange (ETDEWEB)
Barnett, R.M.
1978-08-01
The roles of each type of experiment in establishing uniquely the values of the the neutral-current couplings of u and d quarks are analyzed together with their implications for gauge models of the weak and electromagnetic interactions. An analysis of the neutral-current couplings of electrons and of the data based on the assumption that only one Z/sup 0/ boson exists is given. Also a model-independent analysis of parity violation experiments is discussed. 85 references. (JFP)
[Muscle weakness in cerebral palsy].
Givon, Uri
2009-01-01
Over the last two decades, muscle weakness has been shown to be a major component of cerebral palsy (CP) pathology. Caused by multiple etiologies including variations in the muscle fiber type, pathologic motor unit function, co-contraction of agonists and antagonists, and muscle size and rigidity, weakness interferes with function and leads to limited function and participation. Muscle strength was found to be associated with walking ability and with functional scales. Children with CP were found to be weaker than typically developing children, and differences were found with respect to muscle groups in children with CP. Muscle weakness should be evaluated as objectively as possible to improve the quality of diagnosis and treatment. Manual muscle testing is not sufficient for evaluation, and instrumented muscle testing is validated in CP. Muscle strengthening is an important part of treatment of CP. Several methods of strengthening have been described. Muscle lengthening and other spasticity-modifying therapies have been shown to have a positive effect on muscle strength. Children who participated in muscle strengthening programs had a better quality of life and improved function.
Multilinear integral operators and mean oscillation
Indian Academy of Sciences (India)
In this paper, the boundedness properties for some multilinear operators related to certain integral operators from Lebesgue spaces to Orlicz spaces are obtained. The operators include Calderón–Zygmund singular integral operator, fractional integral operator, Littlewood–Paley operator and Marcinkiewicz operator.
LoCuSS: Subaru Weak Lensing Study of 30 Galaxy Clusters
Okabe, Nobuhiro; Takada, Masahiro; Umetsu, Keiichi; Futamase, Toshifumi; Smith, Graham P.
2010-06-01
We use high-quality Subaru/Suprime-Cam imaging data to conduct a detailed weak lensing study of the distribution of dark matter in a sample of 30 X-ray luminous galaxy clusters at 0.15 ≤ z ≤ 0.3. A weak lensing signal is detected at high statistical significance in each cluster, the total signal-to-noise ratio of the detections ranging from 5 to 13. Comparing spherical models to the tangential distortion profiles of the clusters individually, we are unable to discriminate statistically between a singular isothermal sphere (SIS) and Navarro, Frenk, and White (NFW) models. However, when the tangential distortion profiles are combined and then models are fitted to the stacked profile, the SIS model is rejected at 6σ and 11σ, respectively, for low (Mvir 6 × 1014h-1Modot) mass bins. We also used individual cluster NFW model fits to investigate the relationship between the cluster mass and the concentration, finding that the concentration (cvir) decreases with increasing cluster mass (Mvir). The best-fit cvir-Mvir relation is: cvir(Mvir) = 8.75+4.13-2.89 × (Mvir/1014h-1Modot)-α with α≍0.40±0.19: i.e., a non-zero slope is detected at 2σ significance. This relation gives a concentration of cvir = 3.48+1.65-1.15 for clusters with Mvir = 1015h-1Modot, which is inconsistent at 4σ significance with the values of cvir ˜ 10 reported for strong-lensing-selected clusters. We have found that the measurement error on the cluster mass is smaller at higher over-densities, Δ ≃ 500-2000, than at the virial over-density, Δvir ≃ 110; typical fractional errors at Δ ≃ 500-2000 are improved to σ(MΔ)/MΔ ≃ 0.1-0.2 compared with 0.2-0.3 at Δvir. Furthermore, comparing the 3D spherical mass with the 2D cylinder mass, obtained from the aperture mass method at a given aperture radius, θΔ, reveals M2D(<θΔ)/M3D (
Completely continuous and weakly completely continuous abstract ...
Indian Academy of Sciences (India)
if the operator ρa of right multiplication by a is compact (weakly compact, respectively). An algebra A is called right completely continuous (right weakly completely continuous) if any element a ∈ A is right completely continuous (right weakly completely con- tinuous, respectively). Left completely continuous (left weakly ...
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.
Enhancing reproducibility in scientific computing: Metrics and registry for Singularity containers.
Sochat, Vanessa V; 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.
Do weak global stresses synchronize earthquakes?
Bendick, R.; Bilham, R.
2017-08-01
Insofar as slip in an earthquake is related to the strain accumulated near a fault since a previous earthquake, and this process repeats many times, the earthquake cycle approximates an autonomous oscillator. Its asymmetric slow accumulation of strain and rapid release is quite unlike the harmonic motion of a pendulum and need not be time predictable, but still resembles a class of repeating systems known as integrate-and-fire oscillators, whose behavior has been shown to demonstrate a remarkable ability to synchronize to either external or self-organized forcing. Given sufficient time and even very weak physical coupling, the phases of sets of such oscillators, with similar though not necessarily identical period, approach each other. Topological and time series analyses presented here demonstrate that earthquakes worldwide show evidence of such synchronization. Though numerous studies demonstrate that the composite temporal distribution of major earthquakes in the instrumental record is indistinguishable from random, the additional consideration of event renewal interval serves to identify earthquake groupings suggestive of synchronization that are absent in synthetic catalogs. We envisage the weak forces responsible for clustering originate from lithospheric strain induced by seismicity itself, by finite strains over teleseismic distances, or by other sources of lithospheric loading such as Earth's variable rotation. For example, quasi-periodic maxima in rotational deceleration are accompanied by increased global seismicity at multidecadal intervals.
A Weak Convergence to Hermite Process by Martingale Differences
Directory of Open Access Journals (Sweden)
Xichao Sun
2014-01-01
Full Text Available We consider the weak convergence to general Hermite process ZH,k of order k with index H. By applying martingale differences we construct a sequence {ZH,kn , n=1,2,…} of multiple Wiener-Itô stochastic integrals such that it converges in distribution to the Hermite process ZH,k.
Protecting weak measurements against systematic errors
Pang, Shengshi; Alonso, Jose Raul Gonzalez; Brun, Todd A.; Jordan, Andrew N.
2016-01-01
In this work, we consider the systematic error of quantum metrology by weak measurements under decoherence. We derive the systematic error of maximum likelihood estimation in general to the first-order approximation of a small deviation in the probability distribution, and study the robustness of standard weak measurement and postselected weak measurements against systematic errors. We show that, with a large weak value, the systematic error of a postselected weak measurement when the probe u...
Gossip and Distributed Kalman Filtering: Weak Consensus Under Weak Detectability
Kar, Soummya; Moura, José M. F.
2011-04-01
The paper presents the gossip interactive Kalman filter (GIKF) for distributed Kalman filtering for networked systems and sensor networks, where inter-sensor communication and observations occur at the same time-scale. The communication among sensors is random; each sensor occasionally exchanges its filtering state information with a neighbor depending on the availability of the appropriate network link. We show that under a weak distributed detectability condition: 1. the GIKF error process remains stochastically bounded, irrespective of the instability properties of the random process dynamics; and 2. the network achieves \\emph{weak consensus}, i.e., the conditional estimation error covariance at a (uniformly) randomly selected sensor converges in distribution to a unique invariant measure on the space of positive semi-definite matrices (independent of the initial state.) To prove these results, we interpret the filtered states (estimates and error covariances) at each node in the GIKF as stochastic particles with local interactions. We analyze the asymptotic properties of the error process by studying as a random dynamical system the associated switched (random) Riccati equation, the switching being dictated by a non-stationary Markov chain on the network graph.
Prevalence of superficial siderosis following singular, acute aneurysmal subarachnoid hemorrhage
Energy Technology Data Exchange (ETDEWEB)
Lummel, N.; Bochmann, K. [Ludwig-Maximilian-University, Department of Neuroradiology, Klinikum Grosshadern, Munich (Germany); Bernau, C. [Leibniz-Rechenzentrum, Munich (Germany); Thon, N. [Ludwig-Maximilian-University, Department of Neurosurgery, Klinikum Grosshadern, Munich (Germany); Linn, J. [Technical University, Department of Neuroradiology, Klinikum Dresden, Dresden (Germany)
2015-04-01
Superficial siderosis is presumably a consequence of recurrent bleeding into the subarachnoid space. The objective of this study was to assess the prevalence of superficial siderosis after singular, aneurysmal subarachnoid hemorrhage (SAH) in the long term. We retrospectively identified all patients who presented with a singular, acute, aneurysmal SAH at our institution between 2010 and 2013 and in whom a magnetic resonance imaging (MRI) including T2*-weighted imaging was available at least 4 months after the acute bleeding event. MRI scans were judged concerning the presence and distribution of superficial siderosis. Influence of clinical data, Fisher grade, localization, and cause of SAH as well as the impact of neurosurgical interventions on the occurrence of superficial siderosis was tested. Seventy-two patients with a total of 117 MRIs were included. Mean delay between SAH and the last available MRI was 47.4 months (range 4-129). SAH was Fisher grade 1 in 2 cases, 2 in 4 cases, 3 in 10 cases, and 4 in 56 cases. Superficial siderosis was detected in 39 patients (54.2 %). In all patients with more than one MRI scan, localization and distribution of superficial siderosis did not change over time. Older age (p = 0.02) and higher degree of SAH (p = 0.03) were significantly associated with the development of superficial siderosis. Superficial siderosis develops in approximately half of patients after singular, aneurysmal SAH and might be more common in patients with an older age and a greater amount of blood. However, additional factors must play a role in whether a patient is prone to develop superficial siderosis or not. (orig.)
Motion Control of a Quadrotor Aircraft via Singular Perturbations
Directory of Open Access Journals (Sweden)
Salvador González-Vázquez
2013-10-01
Full Text Available In this paper, a new motion controller for a quadrotor aircraft is introduced. A reformulation of the control inputs of the dynamic model is discussed and then the control algorithm is given in a constructive form. The stability proof of the state space origin of the overall closed-loop system relies on the theory of singularly perturbed systems. Numerical simulations corroborate the viability of the proposed control scheme and the conclusions concerning stability. A set of simulations under practical conditions is also presented, where the system is affected by different types of disturbances and nonlinearities such as noise and actuator saturation.
Finite time singularities in a class of hydrodynamic models
DEFF Research Database (Denmark)
Ruban, V.P.; Podolsky, D.I.; Juul Rasmussen, J.
2001-01-01
solution is performed for a pair of antiparallel vortex filaments and an analog of the Crow instability is found at small wave numbers. A local approximate Hamiltonian is obtained for the nonlinear long-scale dynamics of this system. Self-similar solutions of the corresponding equations are found......), a finite value of alpha results in a finite energy for a singular, frozen-in vortex filament. This property allows us to study the dynamics of such filaments without the necessity of a regularization procedure for short length scales. The linear analysis of small symmetrical deviations from a stationary...
Singularly perturbed hyperbolic problems on metric graphs: asymptotics of solutions
Directory of Open Access Journals (Sweden)
Golovaty Yuriy
2017-04-01
Full Text Available We are interested in the evolution phenomena on star-like networks composed of several branches which vary considerably in physical properties. The initial boundary value problem for singularly perturbed hyperbolic differential equation on a metric graph is studied. The hyperbolic equation becomes degenerate on a part of the graph as a small parameter goes to zero. In addition, the rates of degeneration may differ in different edges of the graph. Using the boundary layer method the complete asymptotic expansions of solutions are constructed and justified.
Raychaudhuri equation and singularity theorems in Finsler spacetimes
Minguzzi, E
2015-01-01
The Raychaudhuri equation and its consequences for chronality are studied in the context of Finsler spacetimes. It is proved that all the notable singularity theorems of Lorentzian geometry extend to the Finslerian domain, e.g. Hawking's, Penrose's, Hawking and Penrose's, Geroch's, Gannon's, Tipler's, Kriele's, Topological Censorship's, and so on. It is argued that all the notable results in causality theory connected to achronal sets, future sets, domains of dependence, limit curve theorems, length functional, Lorentzian distance, geodesic connectedness, extend to the Finslerian domain. Results concerning the spacetime asymptotic structure and horizons differentiability are also included.
Model averaging and dimension selection for the singular value decomposition
Hoff, Peter D.
2006-01-01
Many multivariate data analysis techniques for an $m\\times n$ matrix $\\m Y$ are related to the model $\\m Y = \\m M +\\m E$, where $\\m Y$ is an $m\\times n$ matrix of full rank and $\\m M$ is an unobserved mean matrix of rank $K< (m\\wedge n)$. Typically the rank of $\\m M$ is estimated in a heuristic way and then the least-squares estimate of $\\m M$ is obtained via the singular value decomposition of $\\m Y$, yielding an estimate that can have a very high variance. In this paper we suggest a model-b...
Numerical simulation of singularly perturbed differential equation with small shift
Arora, Geeta; Kaur, Mandeep
2017-07-01
In the present paper, perturbed singular differential equations of second order with small shift are treated for their numerical simulation. These equations arise in the mathematical models for the study of neuronal behavior and their basic activities. Collocation method is used to solve these boundary value problems using modified B-spline basis functions. To partition the domain the piecewise uniform mesh-shiskhin mesh is generated that generate more partitions near the boundary region. The study targets on the impact of small parameters on the solution. To confirm the coherence of the method test problems are presented and conduct of solution of the problem with the time lag parameter is shown.
Dark and singular optical solitons perturbation with fractional temporal evolution
Younis, Muhammad; ur Rehman, Hamood; Rizvi, Syed Tahir Raza; Mahmood, Syed Amer
2017-04-01
The article studies the dynamics of dark, singular, combined optical solitons and many other periodic solutions to fractional temporal perturbed nonlinear Schrödinger equation in nonlinear optics. The fractional extended Fan sub-equation method is first time used for any fractional temporal nonlinear Schrödinger equation. The solutions are of qualitatively different nature, depending on the five parameters. The constraint conditions, for the existence of the solitons, are also listed. Moreover a couple of other solutions known as combined soliton and combined periodic solution, fall out as a by product in limiting cases.
Complete Controllability of Linear Fractional Differential Systems with Singularity
Directory of Open Access Journals (Sweden)
Qun Huang
2015-01-01
Full Text Available This paper is concerned with the controllability of a class of linear fractional differential systems with singularity. The method which is used to deal with the fast subsystem N·cD0,tαx2(t=x2(t+B2u(t and y2(t=C2x2(t is an improvement of the known ones. Based on the movement orbit of the state equation, we obtain several controllability criteria which are sufficient and necessary.
Resolving the sign ambiguity in the singular value decomposition.
Energy Technology Data Exchange (ETDEWEB)
Bro, Rasmus (University of Copenhagen, Frederiksberg C, Denmark); Acar, Evrim (Rensselaer Polytechnic Institute, Troy, NY); Kolda, Tamara Gibson
2007-10-01
Many modern data analysis methods involve computing a matrix singular value decomposition (SVD) or eigenvalue decomposition (EVD). Principal components analysis is the time-honored example, but more recent applications include latent semantic indexing, hypertext induced topic selection (HITS), clustering, classification, etc. Though the SVD and EVD are well-established and can be computed via state-of-the-art algorithms, it is not commonly mentioned that there is an intrinsic sign indeterminacy that can significantly impact the conclusions and interpretations drawn from their results. Here we provide a solution to the sign ambiguity problem and show how it leads to more sensible solutions.
Singular limit analysis of a model for earthquake faulting
DEFF Research Database (Denmark)
Bossolini, Elena; Brøns, Morten; Kristiansen, Kristian Uldall
2017-01-01
In this paper we consider the one dimensional spring-block model describing earthquake faulting. By using geometric singular perturbation theory and the blow-up method we provide a detailed description of the periodicity of the earthquake episodes. In particular, the limit cycles arise from...... of the blow-up method to recover the hyperbolicity. This enables the identification of a new attracting manifold that organises the dynamics at infinity. This in turn leads to the formulation of a conjecture on the behaviour of the limit cycles as the time-scale separation increases. We provide the basic...
Total graph of a module with respect to singular submodule
Directory of Open Access Journals (Sweden)
Jituparna Goswami
2016-07-01
Full Text Available Let R be a commutative ring with unity and M be an R-module. We introduce the total graph of a module M with respect to singular submodule Z(M of M as an undirected graph T(Γ(M with vertex set as M and any two distinct vertices x and y are adjacent if and only if x+y∈Z(M. We investigate some properties of the total graph T(Γ(M and its induced subgraphs Z(Γ(M and Z¯(Γ(M. In some aspects, we have noticed some sort of finiteness.
Analysis and design of singular Markovian jump systems
Wang, Guoliang; Yan, Xinggang
2014-01-01
This monograph is an up-to-date presentation of the analysis and design of singular Markovian jump systems (SMJSs) in which the transition rate matrix of the underlying systems is generally uncertain, partially unknown and designed. The problems addressed include stability, stabilization, H∞ control and filtering, observer design, and adaptive control. applications of Markov process are investigated by using Lyapunov theory, linear matrix inequalities (LMIs), S-procedure and the stochastic Barbalat's Lemma, among other techniques.Features of the book include:·???????? study of the stability pr
Simple singularities and N = 2 supersymmetric Yang-Mills theory
Klemm, A D; Theisen, Stefan J; Yankielowicz, Shimon; Klemm, A; Lerche, W; Theisen, S
1995-01-01
We present a first step towards generalizing the work of Seiberg and Witten on N=2 supersymmetric Yang-Mills theory to arbitrary gauge groups. Specifically, we propose a particular sequence of hyperelliptic genus n-1 Riemann surfaces to underly the quantum moduli space of SU(n) N=2 supersymmetric gauge theory. These curves have an obvious generalization to arbitrary simply laced gauge groups, which involves the A-D-E type simple singularities. To support our proposal, we argue that the monodromy in the semiclassical regime is correctly reproduced. We also give some remarks on a possible relation to string theory.
Exact solutions to relativistic singular fractional power potentials
Agboola, Davids; Zhang, Yao-Zhong
2013-12-01
We present (exact) solutions of the Dirac equation with equally mixed interactions for a single fermion bounded by the family of fractional power singular potentials. Closed-form expressions as well as numerical values for the energies were obtained. The wave functions and the allowed values of the potential parameters for the first two members of the family are obtained in terms of a set of algebraic equations. The non-relativistic limit is also discussed and using the Hellmann-Feynmann theorem, some useful expectation values are obtained.
The Singular Universe and the Reality of Time
Mangabeira Unger, Roberto; Smolin, Lee
2015-01-01
Introduction; Part I. Roberto Mangabeira Unger: 1. The science of the one universe in time; 2. The context and consequences of the argument; 3. The singular existence of the universe; 4. The inclusive reality of time; 5. The mutability of the laws of nature; 6. The selective realism of mathematics; Part II. Lee Smolin: 1. Cosmology in crisis; 2. Principles for a cosmological theory; 3. The setting: the puzzles of contemporary cosmology; 4. Hypotheses for a new cosmology; 5. Mathematics; 6. Approaches to solving the metalaw dilemma; 7. Implications of temporal naturalism for philosophy of mind; 8. An agenda for science; 9. Concluding remarks; A note concerning disagreements between our views.
Orientifolds of warped throats from toric Calabi-Yau singularities
Energy Technology Data Exchange (ETDEWEB)
Retolaza, Ander [Instituto de Física Teórica UAM-CSIC, C/ Nicolás Cabrera 13-15, Campus de Cantoblanco, Madrid, 28049 (Spain); Departamento de Física Teórica, Universidad Autónoma de Madrid,Campus de Cantoblanco, Madrid, 28049 (Spain); Uranga, Angel [Instituto de Física Teórica UAM-CSIC, C/ Nicolás Cabrera 13-15, Campus de Cantoblanco, Madrid, 28049 (Spain)
2016-07-28
We study the complex deformations of orientifolds of D3-branes at toric CY singularities, using their description in terms of dimer diagrams. We describe orientifold quotients that have fixed lines or fixed points in the dimer, and characterize the possibilities to deform them in terms of the behaviour of zig-zag paths under the orientifold symmetry. The resulting models are holographic duals to warped throats with orientifold planes. Our systematic construction provides a general class of configurations which includes models recently appeared in the context of de Sitter uplift by nilpotent goldstino or dynamical supersymmetry breaking.
Singular perturbation analysis of AOTV related trajectory optimization problems
Calise, Anthony J.
1986-01-01
The problem of aeroassisted orbital plane change is discussed. This maneuver requires the use of three impulses - one to deorbit, one to reorbit and one to recircularize at the new orbit. The orbit plane change is effected entirely in the atmosphere through the use of lift and bank angle control. For circular orbits of nearly equal radii, it can be shown that the fuel consumption is minimized by minimizing the energy loss in the atmospheric portion of the trajectory. The research explores the use of singular perturbation theory to develop an optimal guidance law for the atmospheric portion.
Guendelman, Eduardo; Labrana, Pedro
2013-01-01
We consider a non-singular origin for the Universe starting from an Einstein static Universe, the so called "emergent universe" scenario, in the framework of a theory which uses two volume elements $\\sqrt{-{g}}d^{4}x$ and $\\Phi d^{4}x$, where $\\Phi $ is a metric independent density, used as an additional measure of integration. Also curvature, curvature square terms and for scale invariance a dilaton field $\\phi$ are considered in the action. The first order formalism is applied. The integrat...
Abakar, A.; Meunier, G.; Coulomb, J.-L.; Zgainski, F.-X.
2001-04-01
The 3D modeling of thin structures by the finite element method leads to a high number of elements or elements of bad quality, which yields to badly conditioned problems. For the thin plates, shell formulations have been used by several authors. In the case of thin wires, we use a model of unmeshed conductor in which the current is unknown. Physics characteristics: resistance, inductance are integrated in the circuit equation. This article presents a method that extracts the inductance computation which introduced a singularity in the case of thin wires.
Donskykh, G. I.; Ryabov, M. I.; Sukharev, A. I.; Aller, M.
2014-01-01
We investigated the monitoring data of extragalactic source BL Lac. This monitoring was held withUniversityofMichigan26-meter radio telescope. To study flux density of extragalactic source BL Lac at frequencies of 14.5, 8 and 4.8 GHz, the wavelet analysis and singular spectrum analysis were used. Calculating the integral wavelet spectra allowed revealing long-term components (~7-8 years) and short-term components (~ 1-4 years) in BL Lac. Studying of VLBI radio maps (by the program Mojave) ...
Weak polyelectrolytes in Confined Geometries
Whitmer, Jonathan K.; Rathee, Vikramjit S.; Sikora, Benjamin
Crucial to the behavior of recently designed charge-rejection and mosaic membranes are the conformations of polyelectrolyte brushes and oligomeric grafts used to control the membranes' surface charge. The use of pH-tunable weak polyelectrolytes with associative interactions enables fine tuning of material transport properties. Here, we apply constant-pH molecular dynamics along with free energy sampling algorithms to understand the subtle tug-of-war between pH, salt concentrations, and solvation forces in confined systems, and determine how each of these effects alters transport within the system. We further discuss the implications of our findings for the design of electrolyte separation membranes.
Algebraic method for constructing singular steady solitary waves: A case study
Clamond, Didier; Galligo, André
2016-01-01
This article describes the use of algebraic methods in a phase plane analysis of ordinary differential equations. The method is illustrated by the study of capillary-gravity steady surface waves propagating in shallow water. We consider the (fully nonlinear, weakly dispersive) Serre-Green-Naghdi equations with surface tension, because it provides a tractable model that, in the same time, is not too simple so the interest of the method can be emphasised. In particular, we analyse a special class of solutions, the solitary waves, which play an important role in many fields of Physics. In capillary-gravity regime, there are two kinds of localised infinitely smooth travelling wave solutions -- solitary waves of elevation and of depression. However, if we allow the solitary waves to have an angular point, the "zoology" of solutions becomes much richer and the main goal of this study is to provide a complete classification of such singular localised solutions using the methods of the effective Algebraic Geometry.
Split-and-Combine Singular Value Decomposition for Large-Scale Matrix
Directory of Open Access Journals (Sweden)
Jengnan Tzeng
2013-01-01
Full Text Available The singular value decomposition (SVD is a fundamental matrix decomposition in linear algebra. It is widely applied in many modern techniques, for example, high- dimensional data visualization, dimension reduction, data mining, latent semantic analysis, and so forth. Although the SVD plays an essential role in these fields, its apparent weakness is the order three computational cost. This order three computational cost makes many modern applications infeasible, especially when the scale of the data is huge and growing. Therefore, it is imperative to develop a fast SVD method in modern era. If the rank of matrix is much smaller than the matrix size, there are already some fast SVD approaches. In this paper, we focus on this case but with the additional condition that the data is considerably huge to be stored as a matrix form. We will demonstrate that this fast SVD result is sufficiently accurate, and most importantly it can be derived immediately. Using this fast method, many infeasible modern techniques based on the SVD will become viable.
The method of rigged spaces in singular perturbation theory of self-adjoint operators
Koshmanenko, Volodymyr; Koshmanenko, Nataliia
2016-01-01
This monograph presents the newly developed method of rigged Hilbert spaces as a modern approach in singular perturbation theory. A key notion of this approach is the Lax-Berezansky triple of Hilbert spaces embedded one into another, which specifies the well-known Gelfand topological triple. All kinds of singular interactions described by potentials supported on small sets (like the Dirac δ-potentials, fractals, singular measures, high degree super-singular expressions) admit a rigorous treatment only in terms of the equipped spaces and their scales. The main idea of the method is to use singular perturbations to change inner products in the starting rigged space, and the construction of the perturbed operator by the Berezansky canonical isomorphism (which connects the positive and negative spaces from a new rigged triplet). The approach combines three powerful tools of functional analysis based on the Birman-Krein-Vishik theory of self-adjoint extensions of symmetric operators, the theory of singular quadra...
Weak lensing and cosmological investigation
Acquaviva, V
2005-01-01
In the last few years the scientific community has been dealing with the challenging issue of identifying the dark energy component. We regard weak gravitational lensing as a brand new, and extremely important, tool for cosmological investigation in this field. In fact, the features imprinted on the cosmic microwave background radiation by the lensing from the intervening distribution of matter represent a pretty unbiased estimator, and can thus be used for putting constraints on different dark energy models. This is true in particular for the magnetic-type B-modes of CMB polarization, whose unlensed spectrum at large multipoles (l approximately=1000) is very small even in presence of an amount of gravitational waves as large as currently allowed by the experiments: therefore, on these scales the lensing phenomenon is the only responsible for the observed power, and this signal turns out to be a faithful tracer of the dark energy dynamics. We first recall the formal apparatus of the weak lensing in extended t...
Directory of Open Access Journals (Sweden)
Eliana Henriques de Brito
1990-01-01
Full Text Available In continuing from previous papers, where we studied the existence and uniqueness of the global solution and its asymptotic behavior as time t goes to infinity, we now search for a time-periodic weak solution u(t for the equation whose weak formulation in a Hilbert space H isddt(u′,v+δ(u′,v+αb(u,v+βa(u,v+(G(u,v=(h,vwhere: ′=d/dt; (′ is the inner product in H; b(u,v, a(u,v are given forms on subspaces U⊂W, respectively, of H; δ>0, α≥0, β≥0 are constants and α+β>0; G is the Gateaux derivative of a convex functional J:V⊂H→[0,∞ for V=U, when α>0 and V=W when α=0, hence β>0; v is a test function in V; h is a given function of t with values in H.
Singularities in Structural Optimization of the Ziegler Pendulum
Directory of Open Access Journals (Sweden)
O. N. Kirillov
2011-01-01
Full Text Available Structural optimization of non-conservative systems with respect to stability criteria is a research area with important applications in fluid-structure interactions, friction-induced instabilities, and civil engineering. In contrast to optimization of conservative systems where rigorously proven optimal solutions in buckling problems have been found, for nonconservative optimization problems only numerically optimized designs have been reported. The proof of optimality in non-conservative optimization problems is a mathematical challenge related to multiple eigenvalues, singularities in the stability domain, and non-convexity of the merit functional. We present here a study of optimal mass distribution in a classical Ziegler pendulum where local and global extrema can be found explicitly. In particular, for the undamped case, the two maxima of the critical flutter load correspond to a vanishing mass either in a joint or at the free end of the pendulum; in the minimum, the ratio of the masses is equal to the ratio of the stiffness coefficients. The role of the singularities on the stability boundary in the optimization is highlighted, and an extension to the damped case as well as to the case of higher degrees of freedom is discussed.
Scaling and singularity characteristics of solar wind and magnetospheric fluctuations
Directory of Open Access Journals (Sweden)
Z. Vörös
2002-01-01
Full Text Available Preliminary results are presented which suggest that scaling and singularity characteristics of solar wind and ground-based magnetic fluctuations appear to be a significant component in the solar wind-magnetosphere interaction processes. Of key importance is the intermittence of the "magnetic turbulence" as seen in ground-based and solar wind magnetic data. The methods used in this paper (estimation of flatness and multifractal spectra are commonly used in the studies of fluid or MHD turbulence. The results show that single observatory characteristics of magnetic fluctuations are different from those of the multi-observatory AE-index. In both data sets, however, the influence of the solar wind fluctuations is recognizable. The correlation between the scaling/singularity features of solar wind magnetic fluctuations and the corresponding geomagnetic response is demonstrated in a number of cases. The results are also discussed in terms of patchy reconnection processes in the magnetopause and forced and/or self-organized criticality (F/SOC of internal magnetosphere dynamics.
3-Form Cosmology: Phantom Behaviour, Singularities and Interactions
Directory of Open Access Journals (Sweden)
João Morais
2017-03-01
Full Text Available The latest cosmological observations by the Planck collaboration (and combined with others are compatible with a phantom-like behaviour ( w < − 1 for the dark energy equation of state that drives the current acceleration of the Universe. With this mindset, we look into models where dark energy is described by a 3-form field minimally coupled to gravity. When compared to a scalar field, these models have the advantage of more naturally accommodating a cosmological-constant and phantom-like behaviours. We show how the latter happens for a fairly general class of positive-valued potentials, and through a dynamical system approach, we find that in such cases the 3-form field leads the Universe into a Little Sibling of the Big Rip singular event into the future. In this work, we explore the possibility of avoiding such singularity via an interaction in the dark sector between cold dark matter and the 3-form field. For the kind of interactions considered, we deduce a condition for replacing the LSBR by a late time de Sitter phase. For specific examples of interactions that meet this condition, we look for distinctive imprints in the statefinder hierarchy { S 3 ( 1 ; S 4 ( 1 } , { S 3 ( 1 ; S 5 ( 1 } , and in the growth rate of matter, ϵ ( z , through the composite null diagnostic (CND.
Spatialization of social process vs singular object of architecture
Directory of Open Access Journals (Sweden)
Lujak Mihailo
2010-01-01
Full Text Available The fundamental subject of this research is spatialization of social process in the period of modernism manifested through transformation and/or change in meaning of space under a variety of social processes without changing the physical structure of space. These changes in meaning represent the specificity of development in space under the influence of the said social processes, which in this case is Yugoslav modernism, resulting in the creation of a singular object of architecture specific of a certain environment. These processes have been researched in the residential complex of Block 19a in New Belgrade, designed by architects Milan Lojanica, Predrag Cagić, and Borivoje Jovanović, and constructed between 1975 and 1982. The basic objective of this paper is to establish crucial causes for this complex to be considered the landmark in the designing practice of the time in Yugoslavia through research and critical analysis of the residential complex of Block 19a, and to try and determine the importance and potential influence in further architectural development in the period following its construction. In other words, the basic objective of this paper is to establish whether residential complex Block 19a represents a singular object of architecture in Yugoslavia/Serbia.
Resolving the Schwarzschild singularity in both classic and quantum gravity
Zeng, Ding-fang
2017-04-01
The Schwarzschild singularity's resolution has key values in cracking the key mysteries related with black holes, the origin of their horizon entropy and the information missing puzzle involved in their evaporations. We provide in this work the general dynamic inner metric of collapsing stars with horizons and with non-trivial radial mass distributions. We find that static central singularities are not the final state of the system. Instead, the final state of the system is a periodically zero-cross breathing ball. Through 3+1 decomposed general relativity and its quantum formulation, we establish a functional Schrödinger equation controlling the micro-state of this breathing ball and show that, the system configuration with all the matter concentrating on the central point is not the unique eigen-energy-density solution. Using a Bohr-Sommerfield like ;orbital; quantisation assumption, we show that for each black hole of horizon radius rh, there are about e rh2/#x2113;pl 2 allowable eigen-energy-density profiles. This naturally leads to physic interpretations for the micro-origin of horizon entropy, as well as solutions to the information missing puzzle involved in Hawking radiations.
Obstruction of black hole singularity by quantum field theory effects
Energy Technology Data Exchange (ETDEWEB)
Abedi, Jahed; Arfaei, Hessamaddin [Department of Physics, Sharif University of Technology,P.O. Box 11155-9161, Tehran, Irany (Iran, Islamic Republic of); School of Particles and Accelerators, Institute for Research in Fundamental Sciences (IPM),P.O. Box 19395-5531, Tehran (Iran, Islamic Republic of)
2016-03-21
We consider the back reaction of the energy due to quantum fluctuation of the background fields considering the trace anomaly for Schwarzschild black hole. It is shown that it will result in modification of the horizon and also formation of an inner horizon. We show that the process of collapse of a thin shell stops before formation of the singularity at a radius slightly smaller than the inner horizon at the order of (c{sub A}(M/(M{sub p}))){sup 1/3}l{sub p}. After the collapse stops the reverse process takes place. Thus we demonstrate that without turning on quantum gravity and just through the effects the coupling of field to gravity as trace anomaly of quantum fluctuations the formation of the singularity through collapse is obstructed. An important consequence of our work is existence of an extremal solution with zero temperature and a mass which is lower bound for the Schwazschild solution. This solution is also the asymptotic final stable state after Hawking radiation.
Dynamic structure function of some singular Fermi liquids
Varma, Chandra M.
2017-08-01
The density correlations of some singular Fermi liquids with anomalous properties such as resistivity varying linearly with T at low temperatures and a T logT contribution to the entropy and thermopower are expected to be quite different from that in Landau Fermi liquids. A possible statistical mechanical model for the quantum-critical fluctuations in diverse systems with such properties is the 2D dissipative quantum XY model. Exact relations between the density correlations and singular irreducible vertices due to coupling of fermions to the topological excitations of the 2D dissipative quantum XY model are used to derive results which have become measurable only recently because of advances in experimental techniques. The density correlations are unusual at all momenta q and energy ω , from the hydrodynamic limit to that for large momenta and energy. The hydrodynamic limit together with the continuity equation gives the linear in T resistivity. The density correlations are almost independent of frequency up to a high-frequency cutoff for qZ B≳q ≫ω /vF ; qZ B is the Brillouin zone boundary and vF is the Fermi velocity. The results should be applicable to loop-current quantum criticality in cuprates, and to 2D Fe-based compounds near their antiferromagnetic quantum criticality. The relation of the results to the temperature and frequency dependent conductivity and to Raman response is also discussed.
Resolving the Schwarzschild singularity in both classic and quantum gravity
Directory of Open Access Journals (Sweden)
Ding-fang Zeng
2017-04-01
Full Text Available The Schwarzschild singularity's resolution has key values in cracking the key mysteries related with black holes, the origin of their horizon entropy and the information missing puzzle involved in their evaporations. We provide in this work the general dynamic inner metric of collapsing stars with horizons and with non-trivial radial mass distributions. We find that static central singularities are not the final state of the system. Instead, the final state of the system is a periodically zero-cross breathing ball. Through 3+1 decomposed general relativity and its quantum formulation, we establish a functional Schrödinger equation controlling the micro-state of this breathing ball and show that, the system configuration with all the matter concentrating on the central point is not the unique eigen-energy-density solution. Using a Bohr–Sommerfield like “orbital” quantisation assumption, we show that for each black hole of horizon radius rh, there are about erh2/ℓpl2 allowable eigen-energy-density profiles. This naturally leads to physic interpretations for the micro-origin of horizon entropy, as well as solutions to the information missing puzzle involved in Hawking radiations.
Can van Hove singularities be observed in relativistic heavy-ion ...
Indian Academy of Sciences (India)
Keywords. Perturbative quantum chromodynamics; hard thermal loop; gluon condensate; quark–gluon plasma; dispersion relation; collective modes; van Hove singularity; relativistic heavy-ion collisions.
Dynamical singularities for complex initial conditions and the motion at a real separatrix.
Shnerb, Tamar; Kay, K G
2006-04-01
This work investigates singularities occurring at finite real times in the classical dynamics of one-dimensional double-well systems with complex initial conditions. The objective is to understand the relationship between these singularities and the behavior of the systems for real initial conditions. An analytical treatment establishes that the dynamics of a quartic double well system possesses a doubly infinite sequence of singularities. These are associated with initial conditions that converge to those for the real separatrix as the singularity time becomes infinite. This confluence of singularities is shown to lead to the unstable behavior that characterizes the real motion at the separatrix. Numerical calculations confirm the existence of a large number of singularities converging to the separatrix for this and two additional double-well systems. The approach of singularities to the real axis is of particular interest since such behavior has been related to the formation of chaos in nonintegrable systems. The properties of the singular trajectories which cause this convergence to the separatrix are identified. The hyperbolic fixed point corresponding to the potential energy maximum, responsible for the characteristic motion at a separatrix, also plays a critical role in the formation of the complex singularities by delaying trajectories and then deflecting them into asymptotic regions of space from where they are directly repelled to infinity in a finite time.
Commutators of integral operators with variable kernels on Hardy ...
Indian Academy of Sciences (India)
is interpreted in the sense of Cauchy principal value. In addition, we assume that (x,z) satisfies the cancellation condition,. ∫. Sn−1. (x,z )dσ (z ) = 0, for all x ∈ Rn. (1.2). Then T ,0 is the singular integral with variable kernel, and we simply write it as T . The. Lp-boundedness of the singular integral operator with variable ...
Weak transitions in lattice QCD
Energy Technology Data Exchange (ETDEWEB)
Maturana, G.
1984-01-01
Some techniques to calculate the effects of the strong interactions on the matrix elements of weak processes are described. The lattice formulation of Quantum Chromodynamics is used to account for the low energy gluons, and the corresponding numerical methods are explained. The high energy contributions are included in effective lagrangians and the problem of matching the different scales related to the renormalization of the operators and wavefunctions is also discussed. The ..delta..l = 1/2 enhancement rule and the K/sup 0/-anti-K/sup 0/ are used to illustrate these techniques and the results of a numerical calculation is reported. The values obtained are very encouraging and they certainly show good qualitative agreement with the experimental values. The emphasis is on general techniques, and in particular, several improvements to this particular calculation are proposed.
Strengths, weaknesses, opportunities and threats
DEFF Research Database (Denmark)
Bull, Joseph William; Jobstvogt, N.; Böhnke-Henrichs, A.
2016-01-01
The ecosystem services concept (ES) is becoming a cornerstone of contemporary sustainability thought. Challenges with this concept and its applications are well documented, but have not yet been systematically assessed alongside strengths and external factors that influence uptake. Such an assess......The ecosystem services concept (ES) is becoming a cornerstone of contemporary sustainability thought. Challenges with this concept and its applications are well documented, but have not yet been systematically assessed alongside strengths and external factors that influence uptake....... Such an assessment could form the basis for improving ES thinking, further embedding it into environmental decisions and management.The Young Ecosystem Services Specialists (YESS) completed a Strengths-Weaknesses-Opportunities-Threats (SWOT) analysis of ES through YESS member surveys. Strengths include the approach...
Fault zone fabric and fault weakness
Collettini, C.; Niemeijer, A.; Viti, C.; Marone, C.
2009-01-01
Geological and geophysical evidence suggests that some crustal faults are weak1–6 compared to laboratory measurements of frictional strength7. Explanations for fault weakness include the presence of weak minerals4, high fluid pressures within the fault core8,9 and dynamic processes such as
Weakly distributive modules. Applications to supplement submodules
Indian Academy of Sciences (India)
Abstract. In this paper, we define and study weakly distributive modules as a proper generalization of distributive modules. We prove that, weakly distributive supplemented modules are amply supplemented. In a weakly distributive supplemented module every submodule has a unique coclosure. This generalizes a result of ...
Directory of Open Access Journals (Sweden)
Zeyad Al-Zhour
2016-06-01
Full Text Available In this paper, we generalize the time-varying descriptor systems to the case of fractional order in matrix forms. Moreover, we present the general exact solutions of the linear singular and non-singular matrix fractional time-varying descriptor systems with constant coefficient matrices in Caputo sense by using a new attractive method. Finally, two illustrated examples are also given to show our new approach.
The Effect of Weak Collisions on the Plasma Wave Echo
Black, Carrie; Germaschewski, Kai; Ng, C. S.; Bhattacharjee, Amitava
2008-11-01
It has been shown recently that weak collisions, which are a singular perturbation on the collisionless Vlasov equation, have a profound effect on the underlying spectrum for linear plasma waves by eliminating the Case-Van Kampen continuous spectrum and replacing it with a complete class of discrete eigenmodes [C.S. Ng, A. Bhattacharjee, F. Skiff, Phys. Rev. Lett. 83, 1974 (1999); 92, 065002 (2004).]. This discovery has important consequences for the regime of validity of C. H. Su and C. Oberman's classical theory [Phys. Rev. Lett. 20, 427 (1968)] on the collisional decay of plasma wave echoes. Using a fully nonlinear one-dimensional Vlasov-Poisson system solver including the Lenard-Bernstein collision operator, we have studied the effects of collisions on the echoes. We have identified the Su-Oberman regime on intermediate time scales. The long-time asymptotics of the system and its relation to the complete set of discrete eigenmodes found by Ng, Bhattacharjee and Skiff will be discussed.