Showing papers on "Singularity published in 2004"
TL;DR: In this paper, it was shown that a singularity can occur at a finite future time in an expanding Friedmann universe even when? > 0 and? + 3p > 0, and a simple condition was given which can be used to eliminate behaviour of this sort if it is judged to be unphysical.
Abstract: We show that a singularity can occur at a finite future time in an expanding Friedmann universe even when ? > 0 and ? + 3p > 0. Explicit examples are constructed and a simple condition is given which can be used to eliminate behaviour of this sort if it is judged to be unphysical.
466 citations
TL;DR: In this article, the authors studied the correlation functions of operators on the two disjoint asymptotic boundaries of the spacetime by investigating the spacelike geodesics that join the boundaries.
Abstract: We explore physics behind the horizon in eternal AdS Schwarzschild black holes. In dimension d > 3 , where the curvature grows large near the singularity, we find distinct but subtle signals of this singularity in the boundary CFT correlators. Building on previous work, we study correlation functions of operators on the two disjoint asymptotic boundaries of the spacetime by investigating the spacelike geodesics that join the boundaries. These dominate the correlators for large mass bulk fields. We show that the Penrose diagram for d > 3 is not square. As a result, the real geodesic connecting the two boundary points becomes almost null and bounces off the singularity at a finite boundary time tc≠0. If this geodesic were to dominate the correlator there would be a ``light cone" singularity at tc. However, general properties of the boundary theory rule this out. In fact, we argue that the correlator is actually dominated by a complexified geodesic, whose properties yield the large mass quasinormal mode frequencies previously found for this black hole. We find a branch cut in the correlator at small time (in the limit of large mass), arising from coincidence of three geodesics. The tc singularity, a signal of the black hole singularity, occurs on a secondary sheet of the analytically continued correlator. Its properties are computationally accessible. The tc singularity persists to all orders in the 1/m expansion, for finite α', and to all orders in gs. Certain leading nonperturbative effects can also be studied. The behavior of these boundary theory quantities near tc gives, in principle, significant information about stringy and quantum behavior in the vicinity of the black hole singularity.
344 citations
TL;DR: In this paper, the authors considered finite-time, future singularities which may occur even when strong energy condition is not violated but equation of state parameter is time-dependent, taking into account back reaction of conformal quantum fields near singularity.
339 citations
01 Jan 2004
TL;DR: In this article, the notion of non-commutative crepant resolution of a singularity was introduced and shown to exist in certain cases. And they also gave some evidence for an extension of a conjecture by Bondal and Orlov, stating that different resolutions of a Gorenstein singularity have the same derived category.
Abstract: We introduce the notion of a “non-commutative crepant” resolution of a singularity and show that it exists in certain cases. We also give some evidence for an extension of a conjecture by Bondal and Orlov, stating that different crepant resolutions of a Gorenstein singularity have the same derived category.
336 citations
TL;DR: In this paper, the authors constructed a set of extremal D1-D5-P solutions by taking appropriate limits in a known family of nonextremal 3-charge solutions.
333 citations
TL;DR: In this paper, the role of tachyon fields in cosmology as compared to the well-established use of minimally coupled scalar fields is investigated, and a specific one-parameter family of tachyonic models based on a perfect fluid mixed with a positive cosmological constant is studied.
Abstract: We study the role that tachyon fields may play in cosmology as compared to the well-established use of minimally coupled scalar fields. We first elaborate on a kind of correspondence existing between tachyons and minimally coupled scalar fields; corresponding theories give rise to the same cosmological evolution for a particular choice of the initial conditions but not for any other. This leads us to study a specific one-parameter family of tachyonic models based on a perfect fluid mixed with a positive cosmological constant. For positive values of the parameter, one needs to modify Sen's action and use the $\ensuremath{\sigma}$ process of resolution of singularities. The physics described by this model is dramatically different and much richer than that of the corresponding scalar field. For particular choices of the initial conditions, the universe, which does mimic for a long time a de Sitter--like expansion, ends up in a finite time in a special type of singularity that we call a big brake. This singularity is characterized by an infinite deceleration.
324 citations
TL;DR: This work investigates the applicability of a mesoscale modeling approach, lattice Boltzmann simulations, to the problem of contact line motion in one and two component, two phase fluids and shows that the contact line singularity is overcome by evaporation or condensation near the contact lines.
Abstract: We investigate the applicability of a mesoscale modeling approach, lattice Boltzmann simulations, to the problem of contact line motion in one and two component, two phase fluids. In this, the first of two papers, we consider liquid-gas systems. Careful implementation of the thermodynamic boundary condition allows us to fix the static contact angle in the simulations. We then consider the behavior of a sheared interface. We show that the contact line singularity is overcome by evaporation or condensation near the contact line which is driven by the curvature of the diffuse interface. An analytic approximation is derived for the angular position of a sheared interface.
274 citations
TL;DR: Experimental and numerical techniques allowed us to predict and verify the existence of a robust phase singularity in the spatial coherence function when a vortex is present.
Abstract: Experimental and numerical techniques allowed us to predict and verify the existence of a robust phase singularity in the spatial coherence function when a vortex is present. Though observed in the optical domain, this phenomenon may occur in any partially coherent vortex wave.
249 citations
TL;DR: Time-resolved optical Kerr effect measurements are reported that unambiguously demonstrate that the structural relaxation of liquid and weakly supercooled water follows the behaviour predicted by simple mode-coupling theory, supporting the interpretation of the singularity as a purely dynamical transition.
Abstract: Water has many kinetic and thermodynamic properties that exhibit an anomalous dependence on temperature, in particular in the supercooled phase. These anomalies have long been interpreted in terms of underlying structural causes, and their experimental characterization points to the existence of a singularity at a temperature of about 225 K. Further insights into the nature and origin of this singularity might be gained by completely characterizing the structural relaxation in supercooled water. But until now, such a characterization has only been realized in simulations that agree with the predictions of simple mode-coupling theory; unambiguous experimental support for this surprising conclusion is, however, not yet available. Here we report time-resolved optical Kerr effect measurements that unambiguously demonstrate that the structural relaxation of liquid and weakly supercooled water follows the behaviour predicted by simple mode-coupling theory. Our findings thus support the interpretation of the singularity as a purely dynamical transition. That is, the anomalous behaviour of weakly supercooled water can be explained using a fully dynamic model and without needing to invoke a thermodynamic origin. In this regard, water behaves like many other, normal molecular liquids that are fragile glass-formers.
240 citations
TL;DR: The contact line singularity is overcome by diffusion which is effective over a length scale L about the contact line and derive a scaling form for the dependence of L on system parameters.
Abstract: We investigate the applicability of a mesoscale modeling approach, lattice Boltzmann simulations, to the problem of contact line motion in one- and two-component two phase fluids. In this, the second of two papers, we consider binary systems. We show that the contact line singularity is overcome by diffusion which is effective over a length scale L about the contact line and derive a scaling form for the dependence of L on system parameters.
210 citations
TL;DR: In this article, a time-independent nonlinear Schrodinger equation with an attractive inverse square potential and a nonautonomous nonlinearity whose power is the critical Sobolev exponent is studied.
Abstract: We study a time-independent nonlinear Schrodinger equation with an attractive inverse square potential and a nonautonomous nonlinearity whose power is the critical Sobolev exponent. The problem shares a strong resemblance with the prescribed scalar curvature problem on the standard sphere. Particular attention is paid to the blow-up possibilities, i.e. the critical points at infinity of the corresponding variational problem. Due to the strong singularity in the potential, some new phenomenon appear. A complete existence result is obtained in dimension 4 using a detailed analysis of the gradient flow lines.
TL;DR: In this article, the authors present a general form for the solution of an expanding general-relativistic Friedmann universe that encounters a singularity at finite future time, where the singularity occurs in the material pressure and acceleration whilst the scale factor, expansion rate and material density remain finite and the strong energy condition holds.
Abstract: We present a general form for the solution of an expanding general-relativistic Friedmann universe that encounters a singularity at finite future time. The singularity occurs in the material pressure and acceleration whilst the scale factor, expansion rate and material density remain finite and the strong energy condition holds. We also show that the same phenomenon occurs, but under different conditions, for Friedmann universes in gravity theories arising from the variation of an action that is an arbitrary analytic function of the scalar curvature.
TL;DR: In this article, the authors established a correspondence between integrable connections with irregular singularities, and Higgs bundles such that the Higgs field is meromorphic with poles of any order.
Abstract: On a complex curve, we establish a correspondence between integrable connections with irregular singularities, and Higgs bundles such that the Higgs field is meromorphic with poles of any order. Moduli spaces of these objects are obtained with fixed generic polar parts at each singularity, which amounts to fixing a coadjoint orbit of the group
TL;DR: In this paper, the singularity problem inherent in redundant single-gimbal control moment gyro (CMG) systems is examined and the physical and mathematical properties of singularities, singular gimbal angles, singular momentum surfaces, null motion manifolds, and degenerate null motions are investigated.
Abstract: The singularity problem inherent in redundant single-gimbal control moment gyro (CMG) systems is examined. It is intended to provide a comprehensive mathematical treatment of the CMG singularity problem, expanding upon the previous work by Margulies, Aubrun, and Bedrossian. However, particular emphasis is placed on characterizing and visualizing the physical as well as mathematical nature of the singularities, singular gimbal angles, singular momentum surfaces, null motion manifolds, and degenerate null motions. The mathematical framework for characterizing the geometric property of singular surfaces is also established by applying the surface theory of differential geometry. Two and three parallel single-gimbal CMG configurations and a typical pyramid array of four single-gimbal CMGs (including a special case of 90-deg skew angle) are examined in detail to illustrate the various concepts and approaches useful for characterizing and visualizing the CMG singularities.
TL;DR: In this article, the authors consider the singularities that occur in linear elastostatics and present several interpretations of these singularities, such as the singularity coefficient or stress intensity factor.
Abstract: This review article has two parts, published in separate issues of this journal, which consider the stress singularities that occur in linear elastostatics. In the present Part I, after a brief review of the singularities that attend concentrated loads, attention is focused on the singularities that occur away from such loading, and primarily on 2D configurations. A number of examples of these singularities are given in the Introduction. For all of these examples, it is absolutely essential that the presence of singularities at least be recognized if the stress fields are to be used in attempts to ensure structural integrity. Given an appreciation of a stress singularity’s occurrence, there are two options open to the stress analyst if the stress analysis is to actually be used. First, to try and improve the modeling so that the singularity is removed and physically sensible stresses result. Second, to try and interpret singularities that persist in a physically meaningful way. Section 2 of the paper reviews avenues available for the removal of stress singularities. At this time, further research is needed to effect the removal of all singularities. Section 3 of the paper reviews possible interpretations of singularities. At this time, interpretations using the singularity coefficient, or stress intensity factor, would appear to be the best available. To implement an approach using stress intensity factors in a general context, two types of companion analysis are usually required: analytical asymptotics to characterize local singular fields; and numerical analysis to capture participation in global configurations. Section 4 of the paper reviews both types of analysis. At this time, methods for both are fairly well developed. Studies in the literature which actually effect asymptotic analyses of specific singular configurations will be considered in Part II of this review article. The present Part I has 182 references. @DOI: 10.1115/1.1762503#
TL;DR: In this article, a matrix function solution for the scaled boundary finite-element equation in statics is presented, which is numerically stable for multiple or near-multiple eigenvalues as it is based on real Schur decomposition Power functions, logarithmic functions and their transitions as occurring in fracture mechanics, composites and two-dimensional unbounded domains, are represented semi-analytically.
TL;DR: In this paper, the authors present a general form for the solution of an expanding general-relativistic Friedmann universe that encounters a singularity at finite future time, where the singularity occurs in the material pressure and acceleration whilst the scale factor, expansion rate and material density remain finite and the strong energy condition holds.
Abstract: We present a general form for the solution of an expanding general-relativistic Friedmann universe that encounters a singularity at finite future time. The singularity occurs in the material pressure and acceleration whilst the scale factor, expansion rate and material density remain finite and the strong energy condition holds. We also show that the same phenomenon occurs, but under different conditions, for Friedmann universes in gravity theories arising from the variation of an action that is an arbitrary analytic function of the scalar curvature.
TL;DR: In this article, a quantization of the corresponding Hamiltonian constraints is presented and shown to lead to a locally stable, non-singular evolution compatible with almost classical behaviour at large volume.
Abstract: Homogeneous cosmological models with non-vanishing intrinsic curvature require a special treatment when they are quantized with loop quantum cosmological methods. Guidance from the full theory which is lost in this context can be replaced by two criteria for an acceptable quantization, admissibility of a continuum approximation and local stability. A quantization of the corresponding Hamiltonian constraints is presented and shown to lead to a locally stable, non-singular evolution compatible with almost classical behaviour at large volume. As an application, the Bianchi IX model and its modified behaviour close to its classical singularity is explored.
TL;DR: In this paper, it was shown that any resolution X of an isolated cyclic quotient singularity admits a complete scalar-flat Kahler metric of negative scalar curvature.
Abstract: This paper is concerned with the construction of special metrics on non-compact 4-manifolds which arise as resolutions of complex orbifold singularities. Our study is close in spirit to the construction of the hyperkahler gravitational instantons, but we focus on a different class of singularities. We show that any resolution X of an isolated cyclic quotient singularity admits a complete scalar-flat Kahler metric (which is hyperkahler if and only if K
X
is trivial), and that if K
X
is strictly nef, then X also admits a complete (non-Kahler) self-dual Einstein metric of negative scalar curvature. In particular, complete self-dual Einstein metrics are constructed on simply-connected non-compact 4-manifolds with arbitrary second Betti number. Deformations of these self-dual Einstein metrics are also constructed: they come in families parameterized, roughly speaking, by free functions of one real variable. All the metrics constructed here are toric (that is, the isometry group contains a 2-torus) and are essentially explicit. The key to the construction is the remarkable fact that toric self-dual Einstein metrics are given quite generally in terms of linear partial differential equations on the hyperbolic plane.
TL;DR: In this article, an exact solution to the Friedmann equations with a string inspired phantom scalar matter field is constructed and the absence of the Big Rip singularity is shown explicitly; the model is stable with respect to small fluctuations of the initial conditions and special deviations of the form of the potential.
Abstract: An exact solution to the Friedmann equations with a string inspired phantom scalar matter field is constructed and the absence of the "Big Rip" singularity is shown explicitly. The notable features of the concerned model are a ghost sign of the kinetic term and a special polynomial form of the effective tachyon potential. The constructed solution is stable with respect to small fluctuations of the initial conditions and special deviations of the form of the potential.
TL;DR: In this article, the singularity in vacuum spacetimes has been studied and it is shown that it is spacelike and, as it is approached, the spacetime dynamics becomes local and oscillatory.
Abstract: Numerical simulations of the approach to the singularity in vacuum spacetimes are presented here. The spacetimes examined have no symmetries and can be regarded as representing the general behavior of singularities. It is found that the singularity is spacelike and that, as it is approached, the spacetime dynamics becomes local and oscillatory.
TL;DR: An iterative method to compute singular points at any given parameter value and is implemented into voltage stability toolbox and simulations results are presented for a 5-bus and IEEE 118-bus systems.
Abstract: In this paper, we present an efficient algorithm to compute singular points and singularity-induced bifurcation points of differential-algebraic equations for a multimachine power-system model. Power systems are often modeled as a set of differential-algebraic equations (DAE) whose algebraic part brings singularity issues into dynamic stability assessment of power systems. Roughly speaking, the singular points are points that satisfy the algebraic equations, but at which the vector field is not defined. In terms of power-system dynamics, around singular points, the generator angles (the natural states variables) are not defined as a graph of the load bus variables (the algebraic variables). Thus, the causal requirement of the DAE model breaks down and it cannot predict system behavior. Singular points constitute important organizing elements of power-system DAE models. This paper proposes an iterative method to compute singular points at any given parameter value. With a lemma presented in this paper, we are also able to locate singularity induced bifurcation points upon identifying the singular points. The proposed method is implemented into voltage stability toolbox and simulations results are presented for a 5-bus and IEEE 118-bus systems.
TL;DR: In this article, the authors investigated flat surfaces in hyperbolic 3-space with admissible singularities, called flat fronts, and showed that all the ends are embedded, and gave new examples for which equality holds.
Abstract: We investigate flat surfaces in hyperbolic 3-space with admissible singularities, called flat fronts An Osserman-type inequality for complete flat fronts is shown When equality holds in this inequality, we show that all the ends are embedded, and give new examples for which equality holds
10 Oct 2004
TL;DR: This work presents an approach for monitoring the positions of vector field singularities and related structural changes in time-dependent datasets, and applies the presented algorithm to CFD datasets to illustrate its purpose.
Abstract: In this paper, we present an approach for monitoring the positions of vector field singularities and related structural changes in time-dependent datasets. The concept of singularity index is discussed and extended from the well-understood planar case to the more intricate three-dimensional setting. Assuming a tetrahedral grid with linear interpolation in space and time, vector field singularities obey rules imposed by fundamental invariants (Poincare index), which we use as a basis for an efficient tracking algorithm. We apply the presented algorithm to CFD datasets to illustrate its purpose. We examine structures that exhibit topological variations with time and describe some of the insight gained with our method. Examples are given that show a correlation in the evolution of physical quantities that play a role in vortex breakdown.
TL;DR: In this article, the authors explore what information from behind the horizon of the bulk black hole geometry can be found in boundary CFT correlators, and they argue that the correlators contain distinct, albeit subtle, signals of the black hole singularity.
Abstract: We present a short review of hep-th/0306170. In the context of AdS/CFT correspondence, we explore what information from behind the horizon of the bulk black hole geometry can be found in boundary CFT correlators. In particular, we argue that the CFT correlators contain distinct, albeit subtle, signals of the black hole singularity.
TL;DR: In this paper, the singularity loci of a 3-SPS parallel manipulator with three identical limbs made of spherical + prismatic + spherical joints are derived, and a passive spherical joint connecting a moving platform to a fixed base.
TL;DR: In this paper, the authors put forward a stricter and more complete theory of degrees of freedom for mechanisms, especially for the complex spatial mechanisms, which may not be solved correctly with traditional theories, and they also pointed out that it is more appropriate to calculate the DOF of the mechanism with an output member rather than that of the whole mechanism.
TL;DR: The scaled Schrödinger equation is proposed and the related principles are constructed, and a general method of calculating the exact wave functions of atoms and molecules in analytical forms is constructed.
Abstract: We propose the scaled Schr\"odinger equation and the related principles, and construct a general method of calculating the exact wave functions of atoms and molecules in analytical forms. The nuclear and electron singularity problems no longer occur. Test applications to hydrogen atom, helium atom, and hydrogen molecule are satisfactory, implying a high potentiality of the proposed method.
TL;DR: In this paper, the Nariai field equations with cosmological constant are analyzed for a static, spherically symmetric perfect fluid having constant density and five new global solutions are described.
Abstract: Einstein's field equations with cosmological constant are analysed for a static, spherically symmetric perfect fluid having constant density. Five new global solutions are described. One of these solutions has the Nariai solution joined on as an exterior field. Another solution describes a decreasing pressure model with exterior Schwarzschild-de Sitter spacetime having decreasing group orbits at the boundary. Two further types generalise the Einstein static universe. The other new solution is unphysical, it is an increasing pressure model with a geometric singularity.