Showing papers on "Singularity published in 1995"
TL;DR: Black or reflective particles can be trapped in the dark central minimum of a doughnut laser beam produced using a high efficiency computer generated hologram to carry angular momentum transferred from the central phase singularity beam.
Abstract: Black or reflective particles can be trapped in the dark central minimum of a doughnut laser beam produced using a high efficiency computer generated hologram. Such beams carry angular momentum due to the helical wave-front structure associated with the central phase singularity even when linearly polarized. Trapped absorptive particles spin due to absorption of this angular momentum transferred from the singularity beam. The direction of spin can be reversed by changing the sign of the singularity.
1,431 citations
TL;DR: In this article, the authors considered the problem of normal forms associated with the flow on a finite-dimensional invariant manifold tangent to an invariant space for the infinitesimal generator of the linearized equation at a singularity.
406 citations
TL;DR: In this paper, a phase space appropriate to the computation of normal forms associated with the flow on a finite-dimensional invariant manifold tangent to invariant spaces for the infinitesimal generator of the linearized equation at a singularity is introduced, and adequate nonresonance conditions for the normal forms are derived.
301 citations
TL;DR: This paper analyzes the generic local bifurcations including those which are directly related to the singularity, and introduces the notion of a feasibility region, which consists of all equilibrium states that can be reached quasistatically from the current operating point without loss of local stability.
Abstract: The dynamics of a large class of physical systems such as the general power system can be represented by parameter-dependent differential-algebraic models of the form x/spl dot/=f and 0=g. Typically, such constrained models have singularities. This paper analyzes the generic local bifurcations including those which are directly related to the singularity. The notion of a feasibility region is introduced and analyzed. It consists of all equilibrium states that can be reached quasistatically from the current operating point without loss of local stability. It is shown that generically loss of stability at the feasibility boundary is caused by one of three different local bifurcations, namely the saddle-node and Hopf bifurcations and a new bifurcation called the singularity induced bifurcation which is analyzed precisely here for the first time. The latter results when an equilibrium point is at the singular surface. Under certain transversality conditions, the change in the eigenstructure of the system Jacobian at the equilibrium is established and the local dynamical structure of the trajectories near this bifurcation point is analyzed.
248 citations
TL;DR: In this article, the singularity locus of general three-degree-of-freedom planar parallel manipulators is studied and a graphical representation of these loci in the manipulator's workspace is obtained.
180 citations
01 Nov 1995
TL;DR: The taxonomy theory has been proposed as a fundamental platform for solving practical stability related problems in large constrained nonlinear systems such as the electric power system as discussed by the authors, which reveals a two-level intertwined cellular nature of the constrained system dynamics which serves as a unifying structure for analyzing nonlinear phenomena in large system models.
Abstract: This paper provides an overview of the taxonomy theory which has been proposed as a fundamental platform for solving practical stability related problems in large constrained nonlinear systems such as the electric power system. The theory reveals a two-level intertwined cellular nature of the constrained system dynamics which serves as a unifying structure, a taxonomy, for analyzing nonlinear phenomena in large system models. These broadly divide into the state space aspects (related to dynamic stability issues among others) and the parameter space aspects (connected with bifurcation phenomena among others). In the state-space formulation, the boundary of the region of attraction for the operating point is shown (under certain Morse-Smale like assumptions) to be composed of stable manifolds of certain anchors and portions of the singularity surface. Such boundary characterization provides the foundation for rigorous Lyapunov theoretic transient stability methods. In the parameter space analysis, the feasibility region which is bounded by the feasibility boundary provides a safe opening region for guaranteeing local stability at the equilibrium under slow parametric variations. The feasibility boundary where the operating point undergoes loss of local stability is characterized in the form of three principal bifurcations including a new bifurcation called the singularity induced bifurcation.
179 citations
TL;DR: In this paper, the motion of an axisymmetric column of Navier-Stokes fluid with a free surface is considered, and the asymptotic solutions of the Navier−Stokes equation are calculated, both before and after the singularity.
Abstract: The motion of an axisymmetric column of Navier–Stokes fluid with a free surface is considered. Due to surface tension, the thickness of the fluid neck goes to zero in finite time. After the singularity, the fluid consists of two halves, which constitute a unique continuation of the Navier–Stokes equation through the singular point. The asymptotic solutions of the Navier–Stokes equation are calculated, both before and after the singularity. The solutions have scaling form, characterized by universal exponents as well as universal scaling functions, which are computed without adjustable parameters.
170 citations
TL;DR: The singularity structure of charged spherical collapse is studied by considering the evolution of the gravity-scalar field system and suggests the validity of the mass-inflation scenario.
Abstract: The singularity structure of charged spherical collapse is studied by considering the evolution of the gravity--scalar-field system. A detailed examination of the geometry at late times strongly suggests the validity of the mass-inflation scenario [E. Poisson and W. Israel, Phys. Rev. D 41, 1796 (1990)]. Although the area of the two-spheres remains finite at the Cauchy horizon, its generators are eventually focused to zero radius. Thus the null, mass-inflation singularity generally precedes a crushing $r\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0$ singularity deep inside the black hole core. This central singularity is spacelike.
145 citations
TL;DR: In this article, the authors suggest that for singular rotationally invariant closed string backgrounds which need sources for their support at the origin (in particular, for special plane waves and fundamental strings) certain trivial α′-corrections may play an important role leading to the absence of singularities in the exact solutions.
144 citations
TL;DR: In this paper, a generalized approach to the singularity analysis of mechanisms with arbitrary kinematic chains and an equal number of inputs and outputs is presented, where the instantaneous kinematics of a mechanism is described by means of a velocity equation.
Abstract: This paper presents a generalized approach to the singularity analysis of mechanisms with arbitrary kinematic chains and an equal number of inputs and outputs. The instantaneous kinematics ofa mechanism is described by means of a velocity equation, explicitly including not only the input and output velocities but also the passive-joint velocities. A precise definition of singularity of a general mechanism is provided. On the basis of the six types of singular configurations and the motion space interpretation of kinematic singularity introduced in the paper, a comprehensive singularity classification is proposed.
144 citations
TL;DR: The standard approximations of the Dyson-Schwinger equation lead to complex singularities of the fermion propagator, which is related to confinement: a confining potential leads to masslike singularities at complex momenta, and thus to the absence of a mass singularity on the real timelike axis.
Abstract: The standard approximations of the Dyson-Schwinger equation lead to complex singularities of the fermion propagator. In three-dimensional QED one can show that this phenomenon might be related to confinement: a confining potential leads to masslike singularities at complex momenta, and thus to the absence of a mass singularity on the real timelike axis. The correct treatment of the vacuum polarization is essential for the confining nature of three-dimensional QED.
TL;DR: In this article, the existence of exponentially localized structures in a (2+1)-dimensional breaking soliton equation is studied and a singularity structure analysis is carried out and it is shown that it admits the Painleve property for a specific parametric choice.
TL;DR: In this paper, a truncated Fourier series expansion for a 2π-periodic function of finite regularity is used to accurately reconstruct the corresponding function, and an algebraic equation of degree M is constructed for the M singularity locations in each period for the function in question.
Abstract: Kowledge of a truncated Fourier series expansion for a 2π-periodic function of finite regularity, which is assumed to be piecewise smooth in each period, is used to accurately reconstruct the corresponding function. An algebraic equation of degree M is constructed for the M singularity locations in each period for the function in question. The M coefficients in this algebraic equation are obtained by solving an algebraic system of M equations determined by the coefficients in the known truncated expansion. If discontinuities in the derivatives of the function are considered, in addition to discontinuities in the function itself, that algebraic system will be nonlinear with respect to the M unknown coefficients. The degree of the algebraic system will depend on the desired order of accuracy for the reconstruction, i.e., a higher degree will normally lead to a more accurate determination of the singularity locations. By solving an additional linear algebraic system for the jumps of the function and its derivatives up to the arbitrarily specified order at the calculated singularity locations, we are able to reconstruct the 2π-periodic function of finite regularity as the sum of a piecewise polynomial function and a function which is continuously differentiab1e up to the specified order
TL;DR: In this paper, a general classification of singularities for planar parallel manipulators is presented, which relies on the properties of the Jacobian matrices of the manipulator at hand.
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TL;DR: In this paper, a self-dual non-critical string appears in Type IIB superstring theory at points in the moduli space where the Type IIA theory has extended gauge symmetry.
Abstract: Three subjects are considered here: a self-dual non-critical string that appears in Type IIB superstring theory at points in ${\rm K3}$ moduli space where the Type IIA theory has extended gauge symmetry; a conformal field theory singularity at such points which may signal quantum effects that persist even at weak coupling; and the rich dynamics of the real world under compactification, which may be relevant to some attempts to explain the vanishing of the cosmological constant.
TL;DR: Non-equilibrium noise in the transmission current through barriers in 1-D Luttinger liquids and in the tunneling current between edges of fractional quantum Hall liquids is studied and it is shown that contributions from terms of order higher than the dipole-dipole interaction should only affect the strength of the $|\omega|$ singularity.
Abstract: We study non-equilibrium noise in the transmission current through barriers in 1-D Luttinger liquids and in the tunneling current between edges of fractional quantum Hall liquids. The distribution of tunneling events through narrow barriers can be described by a Coulomb gas lying in the time axis along a Keldysh (or non-equilibrium) contour. The charges tend to reorganize as a dipole gas, which we use to describe the tunneling statistics. Intra-dipole correlations contribute to the high-frequency ``Josephson'' noise, which has an algebraic singularity at $\omega=e^*V/\hbar$, whereas inter-dipole correlations are responsible for the low-frequency noise. Inter-dipole interactions give a $1/t^2$ correlation between the tunneling events that results in a $|\omega|$ singularity in the noise spectrum. We present a diagrammatic technique to calculate the correlations in perturbation theory, and show that contributions from terms of order higher than the dipole-dipole interaction should only affect the strength of the $|\omega|$ singularity, but its form should remain $\sim |\omega|$ to all orders in perturbation theory.
TL;DR: In this paper, an equation of state for a fluid of hard disks is proposed: Z=[1−2η+η + 2η0−1/(η/η 0)2]−1.
Abstract: An equation of state for a fluid of hard disks is proposed: Z=[1−2η+(2η0−1)(η/η0)2]−1. The exact fit of the second virial coefficient and the existence of a single pole singularity at the close‐packing fraction η0 are the only requirements imposed on its construction. A comparison of the prediction of virial coefficients and of the values of the compressibility factor Z with those stemming out of other known equations of state is made. The overall performance of this very simple equation of state is quite satisfactory.
TL;DR: In this paper, a new geometric approach is proposed to stabilize spin-axis stabilization of a spacecraft with only two control torques on the unactuated axis, whose state is defined on the sphere.
TL;DR: In this paper, the authors examined the effect of fluid loss to the formation modelled by the Carter leak-off mechanism and showed that there is always a region immediately adjacent to the fluid front where the solution is dominated by fluid loss.
Abstract: This paper extends previous work on self-similar analytical solutions for a hydraulically driven fracture propagating in a solid which is in a state of plane strain In particular, we examine the effect of fluid loss to the formation modelled by the Carter leak-off mechanism Our main new results are asymptotic solutions for arbitrary rock permeability; it is shown how these may be represented by an expansion whose leading term is the near-tip solution in the high permeability limit This term gives an integrable singularity in the near-tip fluid pressure which is slightly stronger than the singularity which arises in the impermeable case; it follows that there is always a region immediately adjacent to the fluid front where the solution is dominated by fluid loss Our most important conclusion for applications is that the solution in the practical case of intermediate permeability may be constructed as a series which starts from the loss dominated limit We also provide a detailed comparison of our predictions with results from a numerical model which includes a fluid lag zone The results are found to be in good agreement in all of the various permeability regimes
TL;DR: In this article, the authors suggest that for singular rotationally invariant closed string backgrounds which need sources for their support at the origin (in particular, for special plane waves and fundamental strings) certain ''trivial'' \a-corrections may play an important role eliminating the singularities in the exact solutions.
Abstract: We suggest that for singular rotationally invariant closed string backgrounds which need sources for their support at the origin (in particular, for special plane waves and fundamental strings) certain `trivial' \a'-corrections (which are usually ignored since in the absence of sources they can be eliminated by a field redefinition) may play an important role eliminating the singularities in the exact solutions. These corrections effectively regularize the source delta-function at the \a'-scale. We demonstrate that similar smearing of the singularity of the leading-order point-source solution indeed takes place in the open string theory.
01 Oct 1995
TL;DR: This analysis first derive the Jacobian matrix and then shows its six columns can be viewed as zero-pitch wrenches acting on the top platform and how line geometry and rank determining geometric constructions can be used to obtain all configuration singularities.
Abstract: Force-reflected teleoperation with in-parallel devices are gaining prominence in robotics applications. Although their development has been limited primarily to Stewart-platform type devices, many other in-parallel hand controllers hold promise for force-reflected manipulation. One factor prohibiting a full exploration involves their singularity analyses-use of conventional rank determining methods are overly complicated. Singularity analysis complications arise because the Jacobian matrix has several functionally dependent variables. In this analysis, we first derive the Jacobian matrix and then show its six columns can be viewed as zero-pitch wrenches (lines) acting on the top platform. We then show how line geometry and rank determining geometric constructions can be used to obtain all configuration singularities. >
TL;DR: In this paper, the authors considered the multidimensional cosmological model describing the evolution of n Einstein spaces in the presence of a multicomponent perfect fluid and the dynamics of the model near the singularity were reduced to a billiard on the (n-1)-dimensional Lobachevsky space.
Abstract: The multidimensional cosmological model describing the evolution of n Einstein spaces is considered in the presence of a multicomponent perfect fluid. When certain restrictions on the parameters of the model are imposed, the dynamics of the model near the singularity are reduced to a billiard on the (n-1)-dimensional Lobachevsky space . The geometrical criterion for the finiteness of the billiard volume and its compactness is suggested. This criterion reduces the problem to the problem of illumination of an (n-2)-dimensional sphere by point-like sources. Some generalizations of the considered scheme (including scalar field and quantum generalizations) are considered.
TL;DR: The relation between the pole quark mass and the MS-renormalized mass is governed by an infrared renormalon singularity, which leads to an ambiguity of order ΛQCD in the definition of the pole mass as discussed by the authors.
TL;DR: The links between a recently developped long wavelength iteration scheme of Einstein's equations, the Belinski Khalatnikov Lifchitz (BKL) general solution near a singularity and the antinewtonian scheme of Tomita's are clarified.
Abstract: We analyze the behavior of a very inhomogeneous spacetime near the singularity by using the recently developed long wavelength iteration scheme of Einstein's equations. Near the singularity, the local anisotropy cannot be neglected and we give the first order and third order solutions for any perfect fluid adiabatic index. We also clarify the links between a recently developed long wavelength iteration scheme of Einstein's equations, the Belinski-Khalatnikov-Lifschitz (BKL) general solution near a singularity and the anti-Newtonian scheme of Tomita's. We determine the regimes when the long wavelength or anti-Newtonian scheme is directly applicable and show how it can otherwise be implemented to yield the BKL oscillatory approach to a spacetime singularity.
TL;DR: It is shown that the Kerr princi-pal null congruence retains its property to be geodesic and shearfree, however, the axidilatonic Kerr solution is not algebraicallyspecial.
Abstract: Gravity Research Group, Nuclear Safety InstituteRussian Academy of Sciences, B.Tulskaya 52, 113191 Moscow, RussiaAbstractThe Kerr solution to axidilaton gravity is analyzed in theDebney–Kerr–Schild formalism. It is shown that the Kerr princi-pal null congruence retains its property to be geodesic and shearfree, however, the axidilatonic Kerr solution is not algebraicallyspecial. A limiting form of this solution is considered near thering-like Kerr singularity. This limiting solution coincides withthe field of fundamental heterotic string obtained by Sen [2, 3].
TL;DR: In this paper, a detailed characterization of vortex structures on the basis of previously proposed two eigenvalue problems associated with vorticity is given. And the role of the pressure Hessian in vortex dynamics, especially in connection with a possible singularity is highlighted.
Abstract: Three‐dimensional Euler equations are studied numerically and analytically to characterize intense vortex stretching in an inviscid fluid. Emphasis is put on the nonlocal effects stemming from the pressure term. The purpose of this paper is twofold. One is to give numerically a detailed characterization of vortex structures on the basis of previously proposed two eigenvalue problems associated with vorticity. The other is to give some mathematical analyses which highlight the role of the pressure Hessian in vortex dynamics, especially in connection with a possible singularity. Also discussed are the differences in local and global (possible) blowups. The blowup problem is not directly discussed by the present numerics at moderate resolution.
TL;DR: A manipulability measure is introduced into the visual tracking objective function, providing an elegant and robust technique for deriving a control law that visually tracks objects while accounting for the configuration of the manipulator.
Abstract: An eye-in-hand system visually tracking objects can fail when the manipulator encounters a kinematic singularity or a joint limit. A solution to this problem is presented in which objects are visua...
TL;DR: A finite element formulation based on the work of Yarnada and Okumura 14 is presented to determine the order of singularity and angular variation of the stress and displacement fields surrounding a singular point on a free edge of anisotropic materials as discussed by the authors.
Abstract: A finite element formulation based on the work of Yarnada and Okumura 14 is presented to determine the order of singularity and angular variation of the stress and displacement fields surrounding a singular point on a free edge of anisotropic materials. Emphasis is placed on the computational aspects of this method when applied to configurations including fully bonded multi-material junctions intersecting a free edge as well as materials containing cracks intersecting a free edge. The study shows that the singularity of the three-dimensional stress field may be accurately determined with a relatively small number of elements only when a proper level of numerical integration is used. The method is applied to isotropic and orthotropic materials with a crack intersecting a free edge and an anisotropic three-material junction intersecting a free edge. The efficiency and accuracy of the method indicates it could be used to develop a numerical solution for the singular field that could in turn be used to create free-edge enriched finite elements.
TL;DR: In this article, the authors give the local classification of solution curves of binary differential equations at points at which the discriminant function b2-ac has a Morse singularity, and discuss the formal reduction of such equations to some normal form.
Abstract: In this paper we give the local classification of solution curves of binary differential equations a(x,y)dy2+2b(x,y)dxdy+c(x,y)dx2=0 at points at which the discriminant function b2-ac has a Morse singularity. We also discuss the formal reduction of such equations to some normal form. The results determine the topological structure of asymptotic curves on a smooth surface with a flat umbilic, the principal curves at general umbilics, and asymptotic curves at cross-cap points of an otherwise smooth surface.
TL;DR: Using a combination of numerical and analytic techniques it is shown that there are two classes of solutions, which includes both black holes and naked singularities with a critical evolution interpolating between these two extremes.
Abstract: Homothetic scalar field collapse is considered in this article. By making a suitable choice of variables the equations are reduced to an autonomous system. Then using a combination of numerical and analytic techniques it is shown that there are two classes of solutions. The first consists of solutions with a nonsingular origin in which the scalar field collapses and disperses again. There is a singularity at one point of these solutions; however, it is not visible to observers at a finite radius. The second class of solutions includes both black holes and naked singularities with a critical evolution (which is neither) interpolating between these two extremes. The properties of these solutions are discussed in detail. The paper also contains some speculation about the significance of self-similarity in recent numerical studies.