Showing papers on "Singularity published in 2000"
TL;DR: In this article, the authors consider F/M/Type IIA theory compactified to four, three, or two dimensions on a Calabi-Yau fourfold, and study the behavior near an isolated singularity in the presence of appropriate fluxes and branes.
1,516 citations
TL;DR: The transition from a liquid to a glass in colloidal suspensions of particles interacting through a hard core plus an attractive square-well potential is studied within the mode-coupling-theory framework and shows stretching of huge dynamical windows, in particular logarithmic time dependence.
Abstract: The transition from a liquid to a glass in colloidal suspensions of particles interacting through a hard core plus an attractive square-well potential is studied within the mode-coupling-theory framework. When the width of the attractive potential is much shorter than the hard-core diameter, a reentrant behavior of the liquid-glass line and a glass-glass-transition line are found in the temperature-density plane of the model. For small well-width values, the glass-glass-transition line terminates in a third-order bifurcation point, i.e., in a A3 (cusp) singularity. On increasing the square-well width, the glass-glass line disappears, giving rise to a fourth-order A4 (swallow-tail) singularity at a critical well width. Close to the A3 and A4 singularities the decay of the density correlators shows stretching of huge dynamical windows, in particular logarithmic time dependence.
340 citations
TL;DR: In this paper, a method for treating the coordinate singularity whereby singular coordinates are redefined so that data are differentiated smoothly through the pole, and avoiding placing a grid point directly at the pole is proposed.
313 citations
TL;DR: In this article, fractional branes in N = 2 orbifold and N = 1 conifold theories were studied and the resulting solutions were given by holomorphic functions and the field-theoretic beta-function was simply reproduced.
304 citations
TL;DR: This paper reports a theoretical and experimental study of the generation of a singularity by inertial focusing, in which no break-up of the fluid surface occurs, and predicts that the surface profiles should be describable by a single universal exponent.
Abstract: Finite-time singularities—local divergences in the amplitude or gradient of a physical observable at a particular time—occur in a diverse range of physical systems. Examples include singularities capable of damaging optical fibres and lasers in nonlinear optical systems1, and gravitational singularities2 associated with black holes. In fluid systems, the formation of finite-time singularities cause spray and air-bubble entrainment3, processes which influence air–sea interaction on a global scale4,5. Singularities driven by surface tension have been studied in the break-up of pendant drops6,7,8,9 and liquid sheets10,11,12. Here we report a theoretical and experimental study of the generation of a singularity by inertial focusing, in which no break-up of the fluid surface occurs. Inertial forces cause a collapse of the surface that leads to jet formation; our analysis, which includes surface tension effects, predicts that the surface profiles should be describable by a single universal exponent. These theoretical predictions correlate closely with our experimental measurements of a collapsing surface singularity. The solution can be generalized to apply to a broad class of singular phenomena.
232 citations
TL;DR: In this paper, the singularity of the eigenfunctions in the Lax representation of soliton equation with self-consistent sources (SESCS) is treated to determine the evolution of scattering data.
Abstract: In contrast with the soliton equations, the evolution of the eigenfunctions in the Lax representation of soliton equation with self-consistent sources (SESCS) possesses singularity. We present a general method to treat the singularity to determine the evolution of scattering data. The AKNS hierarchy with self-consistent sources, the MKdV hierarchy with self-consistent sources, the nonlinear Schrodinger equation hierarchy with self-consistent sources, the Kaup–Newell hierarchy with self-consistent sources and the derivative nonlinear Schrodinger equation hierarchy with self-consistent sources are integrated directly by using the inverse scattering method. The N soliton solutions for some SESCS are presented. It is shown that the insertion of a source may cause the variation of the velocity of soliton. This approach can be applied to all other (1+1)-dimensional soliton hierarchies.
204 citations
TL;DR: In this paper, a multipole approximation for the linear scaling local second-order Moller-Plesset perturbation theory (MP2) method is presented, which is based on a splitting of the Coulomb operator into two terms.
Abstract: A novel multipole approximation for the linear scaling local second-order Moller–Plesset perturbation theory (MP2) method is presented, which is based on a splitting of the Coulomb operator into two terms. The first one contains the singularity and is rapidly decaying with increasing distance. It is treated by a conventional two-electron transformation, where the rapid decay leads to significant savings. The second term is long range, but nonsingular and can therefore be approximated by a multipole expansion. Reliability, accuracy, and efficiency of this method are demonstrated by an extensive benchmark study. It is shown that the goal to further improve the efficiency of the existing linear scaling local MP2 algorithm has been achieved. Moreover, the new method is a promising starting point for future developments, such as coupling of MP2 with density functional theory.
202 citations
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TL;DR: In this paper, the authors considered N = 1 supersymmetric renormalization group flows of N = 4 Yang-Mills theory from the perspective of ten-dimensional IIB supergravity.
Abstract: We consider N = 1 supersymmetric renormalization group flows of N = 4 Yang-Mills theory from the perspective of ten-dimensional IIB supergravity. We explicitly construct
the complete ten-dimensional lift of the flow in which exactly one chiral superfield becomes massive (the LS flow). We also examine the ten-dimensional metric and dilaton configurations for the “super-QCD” flow (the GPPZ flow) in which all chiral superfields become massive. We show that the latter flow generically gives rise to a dielectric 7-brane in the infra-red, but the solution contains a singularity that may be interpreted as a “duality averaged” ring distribution of 5-branes wrapped on S_2. At special values of the parameters the singularity simplifies to a pair of S-dual branes with (p, q) charge (1,±1).
199 citations
TL;DR: In this article, the category of coherent sheaves on the minimal resolution of the Kleinian singularity associated to a finite subgroup G of SL(2) was derived and applied to the Euler-characteristic version of the Hall algebra.
Abstract: We describe the derived category of coherent sheaves on the minimal resolution of the Kleinian singularity associated to a finite subgroup G of SL(2). Then, we give an application to the Euler-characteristic version of the Hall algebra of the category of coherent sheaves on an algebraic surface.
191 citations
TL;DR: This paper presents an algorithm based on analytical expressions of the determinant of the Jacobian matrix, using two different approaches, namely, linear decomposition and cofactor expansion, to assess the effect of the architecture parameters on the nature of the singularity loci of the Gough-Stewart platform.
Abstract: In this paper, the singularity loci of the Gough-Stewart platform are studied and a graphical representation of these loci in the manipulator’s workspace is obtained. The algorithm presented is based on analytical expressions of the determinant of the Jacobian matrix, using two different approaches, namely, linear decomposition and cofactor expansion. The first approach is used to assess the effect of the architecture parameters on the nature of the singularity loci, while the second approach leads to a significant reduction of the computational complexity of the determinant. It is shown that, for a given orientation of the platform, the singularity locus in the Cartesian space is represented by a polynomial of degree three. Moreover, this polynomial equation is applied to several simplified Gough-Stewart architectures and it is shown that the expression is reduced when the base of the mechanism is coplanar and for other special geometries. A comparison with the results obtained using Grassmann geometry i...
189 citations
TL;DR: In this article, it was shown that the general solution near a spacelike singularity of the Einstein-dilaton-p-form field equations relevant to superstring theories exhibits an oscillatory behavior of the Belinskii-Khalatnikov-Lifshitz type.
Abstract: It is shown that the general solution near a spacelike singularity of the Einstein-dilaton- p-form field equations relevant to superstring theories and M theory exhibits an oscillatory behavior of the Belinskii-Khalatnikov-Lifshitz type. String dualities play a significant role in the analysis.
TL;DR: In this article, the authors investigated field theories on the world volume of a D3-brane transverse to partial resolutions of a Z 3 × Z 3 Calabi-Yau threefold quotient singularity.
01 Mar 2000
TL;DR: It is shown that the general solution near a spacelike singularity of the Einstein-dilaton- p-form field equations relevant to superstring theories and M theory exhibits an oscillatory behavior of the Belinskii-Khalatnikov-Lifshitz type.
Abstract: It is shown that the general solution near a spacelike singularity of the Einstein-dilaton- p-form field equations relevant to superstring theories and M theory exhibits an oscillatory behavior of the Belinskii-Khalatnikov-Lifshitz type. String dualities play a significant role in the analysis.
TL;DR: In this article, the authors give a new proof, avoiding case-by-case analysis, of a theorem of Y. Ito and I. Nakamura which provides a module-theoretic interpretation of the bijection between the irreducible components of the exceptional fibre for a Kleinian singularity, and the nontrivial simple modules for the corresponding finite subgroup of SL.
Abstract: We give a new proof, avoiding case-by-case analysis, of a theorem of Y. Ito and I. Nakamura which provides a module-theoretic interpretation of the bijection between the irreducible components of the exceptional fibre for a Kleinian singularity, and the nontrivial simple modules for the corresponding finite subgroup of SL (2, [inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="01i" /]). Our proof uses a classification of certain cyclic modules for preprojective algebras.
TL;DR: In this paper, a method based on the method of moment was proposed to solve the volume integral equation using tetrahedral (3-D) and triangular (2D) elements.
Abstract: We present a formalism based on the method of moment to solve the volume integral equation using tetrahedral (3-D) and triangular (2-D) elements. We introduce a regularization scheme to handle the strong singularity of the Green's tensor. This regularization scheme is extended to neighboring elements, which dramatically improves the accuracy and the convergence of the technique. Scattering by high-permittivity scatterers, like semiconductors, can be accurately computed. Furthermore, plasmon-polariton resonances in dispersive materials can also be reproduced.
01 Oct 2000
TL;DR: In this article, a simplification of plane, turbulent vector fields is achieved by merging critical points within a prescribed radius into higher order critical points, which can be used for analysis on different scales.
Abstract: Topology analysis of plane, turbulent vector fields results in visual clutter caused by critical points indicating vortices of finer and finer scales. A simplification can be achieved by merging critical points within a prescribed radius into higher order critical points. After building clusters containing the singularities to merge, the method generates a piecewise linear representation of the vector field in each cluster containing only one (higher order) singularity. Any visualization method can be applied to the result after this process. Using different maximal distances for the critical points to be merged results in a hierarchy of simplified vector fields that can be used for analysis on different scales.
TL;DR: In this paper, the authors survey pure Yang-Mills theory on the noncommutative torus, including Feynman rules and BRS symmetry, and show that the theory is ultraviolet divergent.
Abstract: Using standard field theoretical techniques, we survey pure Yang–Mills theory on the noncommutative torus, including Feynman rules and BRS symmetry. Although in general free of any infrared singularity, the theory is ultraviolet divergent. Because of an invariant regularization scheme, this theory turns out to be renormalizable and the detailed computation of the one-loop counterterms is given, leading to an asymptotically free theory. Besides, it turns out that nonplanar diagrams are overall convergent when θ is irrational.
TL;DR: A method for computing a nearly singular integral, such as a double layer potential due to sources on a curve in the plane, evaluated at a point near the curve, to regularize the singularity and obtain a preliminary value from a standard quadrature rule.
Abstract: We develop a method for computing a nearly singular integral, such as a double layer potential due to sources on a curve in the plane, evaluated at a point near the curve. The approach is to regularize the singularity and obtain a preliminary value from a standard quadrature rule. Then we add corrections for the errors due to smoothing and discretization, which are found by asymptotic analysis. We prove an error estimate for the corrected value, uniform with respect to the point of evaluation. One application is a simple method for solving the Dirichlet problem for Laplace's equation on a grid covering an irregular region in the plane, similar to an earlier method of A. Mayo [SIAM J. Sci. Statist. Comput., 6 (1985), pp. 144--157]. This approach could also be used to compute the pressure gradient due to a force on a moving boundary in an incompressible fluid. Computational examples are given for the double layer potential and for the Dirichlet problem.
TL;DR: In this article, it was shown that there is an obstruction to decoupling the time-space noncommutativity scale from that of the string fuzziness scale, and that this censorship may be string-theory's way of protecting the causality and unitarity structure.
TL;DR: In this article, a detailed study in the semi-classical regime h of microlocal properties of systems of two commuting operators Ph Ph such that the joint principal symbol p p p has a special kind of singularity called a focusfocus singularity was presented.
Abstract: We present a detailed study in the semi
classical regime h of microlocal properties of systems of two commuting h
pseudo
dierential operators Ph Ph such that the joint principal symbol p p p has a special kind of singularity called a focusfocus singularity Typical examples include the quantum spherical pendulum or the quantum Champagne
bottle In the spirit of Colin de Verdiere and Parisse we show that such systems have a universal behavior described by singular quantization conditions of Bohr
Sommerfeld type
These conditions are used to give a precise description of the joint spectrum of such systems including the phenomenon of quantum monodromy and dierent formulations of the counting function for the joint eigenvalues close to the singularity in which a logarithm of the semi
classical constant h appears Thanks to numerical computations done by MS Child for the case of the Champagne bottle we are able to accurately illustrate our statements
TL;DR: In this article, a smooth G-invariant Riemannian Einstein metric is obtained in a tubular neighbourhood around a singular orbit, provided that the representations of the principal isotropy group on the tangent and the normal space of the singular orbit Q have no common sub-representations.
Abstract: The PDE Ric(g) = λ · g for a Riemannian Einstein metric g on a smooth manifold M becomes an ODE if we require g to be invariant under a Lie group G acting properly on M with principal orbits of codimension one. A singular orbit of the G-action gives a singularity of this ODE. Generically, an equation with such type of singularity has no smooth solution at the singularity. However, in our case, the very geometric nature of the equation makes it solvable. More precisely, we obtain a smooth G-invariant Einstein metric (with any Einstein constant λ) in a tubular neighbourhood around a singular orbit Q ⊂ M for any prescribed G-invariant metric gQ and second fundamental form LQ on Q, provided that the following technical condition is satisfied (which is very often the case): the representations of the principal isotropy group on the tangent and the normal space of the singular orbit Q have no common sub-representations. This Einstein metric is not uniquely determined by the initial data gQ and LQ; in fact, one may prescribe initial derivatives of higher degree, and examples show that this degree can be arbitrarily high. The proof involves a blend of ODE techniques and representation theory of the principal and singular isotropy groups.
TL;DR: In this article, the authors study massive one-loop integrals with arbitrary powers of propagators in general dimension D and construct a template solution valid for all n which allows them to obtain a representation of the graph in terms of a finite sum of generalised hypergeometric functions with m + q − 1 variables.
TL;DR: It is shown that viscous dissipation in the thin layer of air between the disk and the table is sufficient to account for the observed abruptness of the settling process, during which, paradoxically, Ω increases without limit.
Abstract: Air viscosity makes the rolling speed of a disk go up as its energy goes down. It is a fact of common experience that if a circular disk (for example, a penny) is spun upon a table, then ultimately it comes to rest quite abruptly, the final stage of motion being characterized by a shudder and a whirring sound of rapidly increasing frequency. As the disk rolls on its rim, the point P of rolling contact describes a circle with angular velocity Ω. In the classical (non-dissipative) theory1, Ω is constant and the motion persists forever, in stark conflict with observation. Here I show that viscous dissipation in the thin layer of air between the disk and the table is sufficient to account for the observed abruptness of the settling process, during which, paradoxically, Ω increases without limit. I analyse the nature of this ‘finite-time singularity’, and show how it must be resolved.
TL;DR: In this paper, the authors examined the coupled electromechanical behavior of a thin piezoceramic actuator embedded in or bonded to an elastic medium under inplane mechanical and electrical loadings.
TL;DR: In this article, the authors present static solutions of the 5-dimensional Einstein equations in the brane-world scenario by using two different approaches for the stabilization of the extra dimension.
TL;DR: In this paper, the authors studied numerically a class of stretched solutions of the three-dimensional Euler and Navier-Stokes equations identified by Gibbon, Fokas, and Doering (1999).
Abstract: We study numerically a class of stretched solutions of the three-dimensional Euler and Navier–Stokes equations identified by Gibbon, Fokas, and Doering (1999). Pseudo-spectral computations of a Euler flow starting from a simple smooth initial condition suggests a breakdown in finite time. Moreover, this singularity apparently persists in the Navier–Stokes case. Independent evidence for the existence of a singularity is given by a Taylor series expansion in time. The mechanism underlying the formation of this singularity is the two-dimensionalization of the vorticity vector under strong compression; that is, the intensification of the azimuthal components associated with the diminishing of the axial component. It is suggested that the hollowing of the vortex accompanying this phenomenon may have some relevance to studies in vortex breakdown.
TL;DR: In this article, the authors considered a multidimensional model describing the cosmological evolution of n Einstein spaces in the theory with l scalar fields and forms, and the dynamics of the model near the singularity was reduced to a billiard on the (N− 1)-dimensional Lobachevsky space HN−1, N=n+l.
Abstract: Multidimensional model describing the cosmological evolution of n Einstein spaces in the theory with l scalar fields and forms is considered. When electromagnetic composite p-brane ansatz is adopted, and certain restrictions on the parameters of the model are imposed, the dynamics of the model near the singularity is reduced to a billiard on the (N−1)-dimensional Lobachevsky space HN−1, N=n+l. The geometrical criterion for the finiteness of the billiard volume and its compactness is used. This criterion reduces the problem to the problem of illumination of (N−2)-dimensional sphere SN−2 by pointlike sources. Some examples with billiards of finite volume and hence oscillating behavior near the singularity are considered. Among them examples with square and triangle two-dimensional billiards (e.g., that of the Bianchi-IX model) and a four-dimensional billiard in “truncated” D=11 supergravity model (without the Chern–Simons term) are considered. It is shown that the inclusion of the Chern–Simons term destroys...
TL;DR: In this article, a survey of treatments for singularity problems of elliptic equations of polygons is provided, where the authors take the Laplace equation on polygons as an example, and choose Motz's problem as a benchmark of singularity problem.
TL;DR: A remarkable product formula for the integrand of the two-dimensional Ising model susceptibility expansion coefficients (2n ) for temperatures T less than the critical T c is shown in this paper.
Abstract: A remarkable product formula first derived by Palmer and Tracy (1981 Adv. Appl. Math. 2 329) for the integrand of the two-dimensional Ising model susceptibility expansion coefficients (2n ) for temperatures T less than the critical T c is shown to apply equally for (2n +1) for T >T c and agrees with formulae derived by Yamada (1984 Prog. Theor. Phys. 71 1416). This new representation simplifies the derivation of the results in the original paper of this title (1999 J. Phys. A: Math. Gen. 32 3889) to the extent that the leading series behaviour and the singularity structure can be deduced almost by inspection. The derivation of series is also simplified and I show, using extended series and knowledge of the singularity structure, that there is now unambiguous evidence for correction to scaling terms in the susceptibility beyond those inferred from a nonlinear scaling field analysis.