High order finite volume methods for singular perturbation problems
Institute of Scientific and Technical Information of China (English)
CHEN ZhongYing; HE ChongNan; WU Bin
2008-01-01
In this paper we establish a high order finite volume method for the fourth order singular perturbation problems. In conjunction with the optimal meshes, the numerical solutions resulting from the method have optimal convergence order. Numerical experiments are presented to verify our theoretical estimates.
The theory of singular perturbations
De Jager, E M
1996-01-01
The subject of this textbook is the mathematical theory of singular perturbations, which despite its respectable history is still in a state of vigorous development. Singular perturbations of cumulative and of boundary layer type are presented. Attention has been given to composite expansions of solutions of initial and boundary value problems for ordinary and partial differential equations, linear as well as quasilinear; also turning points are discussed. The main emphasis lies on several methods of approximation for solutions of singularly perturbed differential equations and on the mathemat
High order multiplication perturbation method for singular perturbation problems
Institute of Scientific and Technical Information of China (English)
张文志; 黄培彦
2013-01-01
This paper presents a high order multiplication perturbation method for sin-gularly perturbed two-point boundary value problems with the boundary layer at one end. By the theory of singular perturbations, the singularly perturbed two-point boundary value problems are first transformed into the singularly perturbed initial value problems. With the variable coeﬃcient dimensional expanding, the non-homogeneous ordinary dif-ferential equations (ODEs) are transformed into the homogeneous ODEs, which are then solved by the high order multiplication perturbation method. Some linear and nonlinear numerical examples show that the proposed method has high precision.
Contrast structure for singular singularly perturbed boundary value problem
Institute of Scientific and Technical Information of China (English)
王爱峰; 倪明康
2014-01-01
The step-type contrast structure for a singular singularly perturbed problem is shown. By use of the method of boundary function, the formal asymptotic expansion is constructed. At the same time, based on sewing orbit smooth, the existence of the step-type solution and the uniform validity of the asymptotic expansion are proved. Finally, an example is given to demonstrate the effectiveness of the present results.
Asymptotic stability of singularly perturbed differential equations
Artstein, Zvi
2017-02-01
Asymptotic stability is examined for singularly perturbed ordinary differential equations that may not possess a natural split into fast and slow motions. Rather, the right hand side of the equation is comprised of a singularly perturbed component and a regular one. The limit dynamics consists then of Young measures, with values being invariant measures of the fast contribution, drifted by the slow one. Relations between the asymptotic stability of the perturbed system and the limit dynamics are examined, and a Lyapunov functions criterion, based on averaging, is established.
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.
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 an
Singular solution of the Liouville equation under perturbation
Kalyakin, L A
1999-01-01
Small perturbation of the Liouville equation under singular initial data is considered. An asymptotics of the singular solution is constructed by the method which is similar to Bogolubov -- Krylov one. The main object is an asymptotics of the singular lines.
hp-finite element methods for singular perturbations
Melenk, Jens M
2002-01-01
Many partial differential equations arising in practice are parameter-dependent problems that are of singularly perturbed type. Prominent examples include plate and shell models for small thickness in solid mechanics, convection-diffusion problems in fluid mechanics, and equations arising in semi-conductor device modelling. Common features of these problems are layers and, in the case of non-smooth geometries, corner singularities. Mesh design principles for the efficient approximation of both features by the hp-version of the finite element method (hp-FEM) are proposed in this volume. For a class of singularly perturbed problems on polygonal domains, robust exponential convergence of the hp-FEM based on these mesh design principles is established rigorously.
Light-Front Perturbation Without Spurious Singularities
Przeszowski, Jerzy A.; Dzimida-Chmielewska, Elżbieta; Żochowski, Jan
2016-07-01
A new form of the light front Feynman propagators is proposed. It contains no energy denominators. Instead the dependence on the longitudinal subinterval x^2_L = 2 x+ x- is explicit and a new formalism for doing the perturbative calculations is invented. These novel propagators are implemented for the one-loop effective potential and various 1-loop 2-point functions for a massive scalar field. The consistency with results for the standard covariant Feynman diagrams is obtained and no spurious singularities are encountered at all. Some remarks on the calculations with fermion and gauge fields in QED and QCD are added.
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...
Concentrating solutions of some singularly perturbed elliptic equations
Institute of Scientific and Technical Information of China (English)
2008-01-01
We study singularly perturbed elliptic equations arising from models in physics or biology, and investigate the asymptotic behavior of some special solutions. We also discuss some connections with problems arising in differential geometry.
Shock solution for quasilinear singularly perturbed Robin problem
Institute of Scientific and Technical Information of China (English)
无
2002-01-01
The shock solution for the quasilinear singularly perturbed Robin problem is considered. Under suitable conditions and using the theory of differential inequalities the existence and asymptotic behavior of the shock solution for the original boundary value problems are studied.
Hyperbolic-parabolic singular perturbations in general regions
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Berardino D'Acunto
1991-05-01
Full Text Available We consider a singular perturbations problem for the inhomogeneous damped wave equation and the inhomogeneous heat equation with moving boundary. We give rigorous and explicit estimates and show the uniform convergence.
Resonance through a Strictly Singular Perturbation.
1981-04-01
subspace of singularity with respect to H is empty. The question one now tries to answer is, if there exists a modification of the former definition...Foundations of Quantum Physics, chap. 5, sec. 3, Benjamin, London (1976). (7] J. Hadamard, Enseignement Math., 35, 5 (1936). (8) R. S. Phillips, Semi-groups
Singularly Perturbation Method Applied To Multivariable PID Controller Design
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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.
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...
A Parameter Robust Method for Singularly Perturbed Delay Differential Equations
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Erdogan Fevzi
2010-01-01
Full Text Available Uniform finite difference methods are constructed via nonstandard finite difference methods for the numerical solution of singularly perturbed quasilinear initial value problem for delay differential equations. A numerical method is constructed for this problem which involves the appropriate Bakhvalov meshes on each time subinterval. The method is shown to be uniformly convergent with respect to the perturbation parameter. A numerical example is solved using the presented method, and the computed result is compared with exact solution of the problem.
Perturbative Analysis of Spectral Singularities and Their Optical Realizations
Mostafazadeh, Ali
2012-01-01
We develop a perturbative method of computing spectral singularities of a Schreodinger operator defined by a general complex potential that vanishes outside a closed interval. These can be realized as zero-width resonances in optical gain media and correspond to a lasing effect that occurs at the threshold gain. Their time-reversed copies yield coherent perfect absorption of light that is also known as an antilaser. We use our general results to establish the exactness of the n-th order perturbation theory for an arbitrary complex potential consisting of n delta-functions, obtain an exact expression for the transfer matrix of these potentials, and examine spectral singularities of complex barrier potentials of arbitrary shape. In the context of optical spectral singularities, these correspond to inhomogeneous gain media.
A parabolic singular perturbation problem with an internal layer
Grasman, J.; Shih, S.D.
2004-01-01
A method is presented to approximate with singular perturbation methods a parabolic differential equation for the quarter plane with a discontinuity at the corner. This discontinuity gives rise to an internal layer. It is necessary to match the local solution in this layer with the one in a corner l
Robust Monotone Iterates for Nonlinear Singularly Perturbed Boundary Value Problems
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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.
THE SINGULARLY PERTURBED BOUNDARY VALUE PROBLEMS FOR SEMILINEAR ELLIPTIC EQUATION
Institute of Scientific and Technical Information of China (English)
Mo Jiaqi; Yao Jingsun
2001-01-01
The singularly perturbed boundary value problems for the semilinear elliptic equation are considered.Under suitable conditions and by using the fixed point theorem,the existence,uniqueness and asymptotic behavior of solution for the boundary value problems are studied.
Cauchy-horizon singularity inside perturbed Kerr black holes
Burko, Lior M; Zenginoǧlu, Anıl
2016-01-01
The Cauchy horizon inside a perturbed Kerr black hole develops an instability that transforms it into a curvature singularity. We solve for the linearized Weyl scalars $\\psi_0$ and $\\psi_4$ and for the curvature scalar $R_{\\alpha\\beta\\gamma\\delta}R^{\\alpha\\beta\\gamma\\delta}$ along outgoing null rays approaching the Cauchy horizon in the interior of perturbed Kerr black holes using the Teukolsky equation, and compare our results with those found in perturbation analysis. Our results corroborate the previous perturbation analysis result that at its early parts the Cauchy horizon evolves into a deformationally-weak, null, scalar-curvature singularity. We find excellent agreement for $\\psi_0(u={\\rm const},v)$, where $u,v$ are advanced and retarded times, respectively. We do find, however, that the exponential growth rate of $R_{\\alpha\\beta\\gamma\\delta}R^{\\alpha\\beta\\gamma\\delta}(u={\\rm const},v)$ approaching the singularity is dramatically slower than that found in perturbation analysis, and that the angular freq...
Singular perturbation techniques in the gravitational self-force problem
Pound, Adam
2010-01-01
Much of the progress in the gravitational self-force problem has involved the use of singular perturbation techniques. Yet the formalism underlying these techniques is not widely known. I remedy this situation by explicating the foundations and geometrical structure of singular perturbation theory in general relativity. Within that context, I sketch precise formulations of the methods used in the self-force problem: dual expansions (including matched asymptotic expansions), for which I identify precise matching conditions, one of which is a weak condition arising only when multiple coordinate systems are used; multiscale expansions, for which I provide a covariant formulation; and a self-consistent expansion with a fixed worldline, for which I provide a precise statement of the exact problem and its approximation. I then present a detailed analysis of matched asymptotic expansions as they have been utilized in calculating the self-force. Typically, the method has relied on a weak matching condition, which I s...
Composite fuzzy sliding mode control of nonlinear singularly perturbed systems.
Nagarale, Ravindrakumar M; Patre, B M
2014-05-01
This paper deals with the robust asymptotic stabilization for a class of nonlinear singularly perturbed systems using the fuzzy sliding mode control technique. In the proposed approach the original system is decomposed into two subsystems as slow and fast models by the singularly perturbed method. The composite fuzzy sliding mode controller is designed for stabilizing the full order system by combining separately designed slow and fast fuzzy sliding mode controllers. The two-time scale design approach minimizes the effect of boundary layer system on the full order system. A stability analysis allows us to provide sufficient conditions for the asymptotic stability of the full order closed-loop system. The simulation results show improved system performance of the proposed controller as compared to existing methods. The experimentation results validate the effectiveness of the proposed controller.
Aircraft pitch attitude adaptive control via singular perturbation technique
Yurkevich, V. D.
2013-12-01
The problem of aircraft pitch attitude control is treated in the presence of uncertain aerodynamics. The proposed design methodology guarantees desired pitch attitude transient performance indices by inducing of two-time-scale motions in the closed-loop system where the controller dynamics is a singular perturbation with respect to the system dynamics. The singular perturbation method is used in order to get explicit expressions for evaluation of the controller parameters. Stability of fast-motion transients for a large range of aerodynamic characteristics variations is maintained due to a high-frequency-gain online identification and gain tuning that are incorporated in the control loop. Numerical example and simulation results are presented.
CONTROLLABILITY OF ESSENTIALLY VARIOUS-SPEED SINGULARLY PERTURBED DYNAMIC SYSTEMS
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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.
On Output Feedback Multiobjective Control for Singularly Perturbed Systems
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Mehdi Ghasem Moghadam
2011-01-01
Full Text Available A new design procedure for a robust 2 and ∞ control of continuous-time singularly perturbed systems via dynamic output feedback is presented. By formulating all objectives in terms of a common Lyapunov function, the controller will be designed through solving a set of inequalities. Therefore, a dynamic output feedback controller is developed such that ∞ and 2 performance of the resulting closed-loop system is less than or equal to some prescribed value. Also, ∞ and 2 performance for a given upperbound of singular perturbation parameter ∈(0,∗] are guaranteed. It is shown that the -dependent controller is well defined for any ∈(0,∗] and can be reduced to an -independent one so long as is sufficiently small. Finally, numerical simulations are provided to validate the proposed controller. Numerical simulations coincide with the theoretical analysis.
Computational singular perturbation analysis of stochastic chemical systems with stiffness
Wang, Lijin; Han, Xiaoying; Cao, Yanzhao; Najm, Habib N.
2017-04-01
Computational singular perturbation (CSP) is a useful method for analysis, reduction, and time integration of stiff ordinary differential equation systems. It has found dominant utility, in particular, in chemical reaction systems with a large range of time scales at continuum and deterministic level. On the other hand, CSP is not directly applicable to chemical reaction systems at micro or meso-scale, where stochasticity plays an non-negligible role and thus has to be taken into account. In this work we develop a novel stochastic computational singular perturbation (SCSP) analysis and time integration framework, and associated algorithm, that can be used to not only construct accurately and efficiently the numerical solutions to stiff stochastic chemical reaction systems, but also analyze the dynamics of the reduced stochastic reaction systems. The algorithm is illustrated by an application to a benchmark stochastic differential equation model, and numerical experiments are carried out to demonstrate the effectiveness of the construction.
A Schwarz alternating procedure for singular perturbation problems
Energy Technology Data Exchange (ETDEWEB)
Garbey, M. [Universit Claude Bernard Lyon, Villeurbanne (France); Kaper, H.G. [Argonne National Lab., IL (United States)
1994-12-31
The authors show that the Schwarz alternating procedure offers a good algorithm for the numerical solution of singular perturbation problems, provided the domain decomposition is properly designed to resolve the boundary and transition layers. They give sharp estimates for the optimal position of the domain boundaries and present convergence rates of the algorithm for various second-order singular perturbation problems. The splitting of the operator is domain-dependent, and the iterative solution of each subproblem is based on a modified asymptotic expansion of the operator. They show that this asymptotic-induced method leads to a family of efficient massively parallel algorithms and report on implementation results for a turning-point problem and a combustion problem.
THIRD-ORDER NONLINEAR SINGULARLY PERTURBED BOUNDARY VALUE PROBLEM
Institute of Scientific and Technical Information of China (English)
王国灿; 金丽
2002-01-01
Third order singulary perturbed boundary value problem by means of differential inequality theories is studied. Based on the given results of second order nonlinear boundary value problem, the upper and lower solutions method of third order nonlinear boundary value problems by making use of Volterra type integral operator was established.Specific upper and lower solutions were constructed, and existence and asymptotic estimates of solutions under suitable conditions were obtained.The result shows that it seems to be new to apply these techniques to solving these kinds of third order singularly perturbed boundary value problem. An example is given to demonstrate the applications.
State feedback design for singularly perturbed system using unified approach
Institute of Scientific and Technical Information of China (English)
Chenxiao CAI; Yun ZOU; Duanjin ZHANG
2004-01-01
The state feedback design for singularly perturbed systems described in Delta operator is considered.The composite state feedback controller for slow and fast subsystems is designed by using the direct method.The obtained results can bring previous conclusions of continuous and discrete time systems into the unified Delta framework.A simulation example is presented to demonstrate the validity and efficiency of the design.
Perturbative analysis of spectral singularities and their optical realizations
Mostafazadeh, Ali; Rostamzadeh, Saber
2012-01-01
We develop a perturbative method of computing spectral singularities of a Schrodinger operator defined by a general complex potential that vanishes outside a closed interval. These can be realized as zero-width resonances in optical gain media and correspond to a lasing effect that occurs at the threshold gain. Their time-reversed copies yield coherent perfect absorption of light that is also known as antilasing. We use our general results to establish the exactness of the nth-order perturbat...
Singularly perturbed bifurcation subsystem and its application in power systems
Institute of Scientific and Technical Information of China (English)
An Yichun; Zhang Qingling; Zhu Yukun; Zhang Yan
2008-01-01
The singularly perturbed bifurcation subsystem is described,and the test conditions of subsystem persistence are deduced.By use of fast and slow reduced subsystem model,the result does not require performing nonlinear transformation.Moreover,it is shown and proved that the persistence of the periodic orbits for Hopf bifurcation in the reduced model through center manifold.Van der Pol oscillator circuit is given to illustrate the persistence of bifurcation subsystems with the full dynamic system.
Nonstationary Fronts in the Singularly Perturbed Power-Society Model
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M. G. Dmitriev
2013-01-01
Full Text Available The theory of contrasting structures in singularly perturbed boundary problems for nonlinear parabolic partial differential equations is applied to the research of formation of steady state distributions of power within the nonlinear “power-society” model. The interpretations of the solutions to the equation are presented in terms of applied model. The possibility theorem for the problem of getting the solution having some preassigned properties by means of parametric control is proved.
Bifurcation for non linear ordinary differential equations with singular perturbation
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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.
Ardema, M. D.
1979-01-01
Singular perturbation techniques are studied for dealing with singular arc problems by analyzing a relatively low-order but otherwise general system. This system encompasses many flight mechanic problems including Goddard's problem and a version of the minimum time-to-climb problem. Boundary layer solutions are constructed which are stable and reach the outer solution in a finite time. A uniformly valid composite solution is then formed from the reduced and boundary layer solutions. The value of the approximate solution is that it is relatively easy to obtain and does not involve singular arcs. To illustrate the utility of the results, the technique is used to obtain an approximate solution of a simplified version of the aircraft minimum time-to-climb problem.
Taming Landau singularities in QCD perturbation theory: The analytic approach
Stefanis, N G
2013-01-01
The aim of this topical article is to outline the fundamental ideas underlying the recently developed Fractional Analytic Perturbation Theory (FAPT) of QCD and present its main calculational tools. For this, it is first necessary to review previous methods to apply QCD perturbation theory at low spacelike momentum scales, where the influence of the Landau singularities becomes inevitable. Several concepts are considered and their limitations are pointed out. The usefulness of FAPT is discussed in terms of two characteristic hadronic quantities: the perturbatively calculable part of the pion's electromagnetic form factor in the spacelike region and the Higgs-boson decay into a b\\bar b pair in the timelike region. In the first case, the focus is on the optimization of the prediction with respect to the choice of the renormalization scheme and the dependence on the renormalization and the factorization scales. The second case serves to show that the application of FAPT to this reaction reaches already at the fou...
SINGULARLY PERTURBED MARKOV DECISION PROCESSES WITH INCLUSION OF TRANSIENT STATES
Institute of Scientific and Technical Information of China (English)
R. H. Liu; Q. Zhang; G. Yin
2001-01-01
This paper is concerned with the continuous-time Markov decision processes (MDP) having weak and strong interactions. Using a hierarchical approach, the state space of the underlying Markov chain can be decomposed into several groups of recurrent states and a group of transient states resulting in a singularly perturbed MDP formulation.Instead of solving the original problem directly, a limit problem that is much simpler to handle is derived. On the basis of the optimal solution of the limit problem, nearly optimal decisions are constructed for the original problem. The asymptotic optimality of the constructed control is obtained; the rate of convergence is ascertained.
Singular perturbation methods for nonlinear dynamic systems with time delays
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Hu, H.Y. [MOE Key Laboratory of Structure Mechanics and Control for Aircraft, Nanjing University of Aeronautics and Astronautics, 210016 Nanjing (China)], E-mail: hhyae@nuaa.edu.cn; Wang, Z.H. [MOE Key Laboratory of Structure Mechanics and Control for Aircraft, Nanjing University of Aeronautics and Astronautics, 210016 Nanjing (China)
2009-04-15
This review article surveys the recent advances in the dynamics and control of time-delay systems, with emphasis on the singular perturbation methods, such as the method of multiple scales, the method of averaging, and two newly developed methods, the energy analysis and the pseudo-oscillator analysis. Some examples are given to demonstrate the advantages of the methods. The comparisons with other methods show that these methods lead to easier computations and higher accurate prediction on the local dynamics of time-delay systems near a Hopf bifurcation.
Singular perturbation approach for control of hydraulically driven flexible manipulator
Institute of Scientific and Technical Information of China (English)
LI Guang; WU Min
2005-01-01
The hydraulic flexible manipulator system is divided into two parts: flexible arm dynamics and hydraulic servomechanism, a driving Jacobian is derived to connect these two parts. Taking hydraulic actuator force as virtual input, a singular perturbed composite model is formulated and used to design composite controllers for the flexible link, in which the slow subsystem controller dominates the trajectory tracking, and then a fast controller is designed to damp out the vibration of the flexible structure. Moreover, the backstepping technique is applied to regulate the spool position of a hydraulic valve to provide the required force. Simulation results are provided to show the effectiveness of the presented approach.
Singularly perturbed hyperbolic problems on metric graphs: asymptotics of solutions
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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.
Threshold singularities, dispersion relations and fixed-order perturbative calculations
Beneke, Martin
2016-01-01
We show how to correctly treat threshold singularities in fixed-order perturbative calculations of the electron anomalous magnetic moment and hadronic pair production processes such as top pair production. With respect to the former, we demonstrate the equivalence of the "non-perturbative", resummed treatment of the vacuum polarization contribution, whose spectral function exhibits bound state poles, with the fixed-order calculation by identifying a threshold localized term in the four-loop spectral function. In general, we find that a modification of the dispersion relation by threshold subtractions is required to make fixed-order calculations well-defined and provide the subtraction term. We then solve the apparent problem of a divergent convolution of the partonic cross section with the parton luminosity in the computation of the top pair production cross section starting from the fourth-order correction. We find that when the computation is performed in the usual way as an integral of real and virtual cor...
Institute of Scientific and Technical Information of China (English)
Jingsun Yao; Jiaqi Mo
2005-01-01
The nonlinear nonlocal singularly perturbed initial boundary value problems for reaction diffusion equations with a boundary perturbation is considered. Under suitable conditions, the outer solution of the original problem is obtained. Using the stretched variable, the composing expansion method and the expanding theory of power series the initial layer is constructed. And then using the theory of differential inequalities the asymptotic behavior of solution for the initial boundary value problems is studied. Finally the existence and uniqueness of solution for the original problem and the uniformly valid asymptotic estimation are discussed.
Sewing Connection of Step-Step Solution for Singularly Perturbed Problems
Institute of Scientific and Technical Information of China (English)
Ming Kang NI; V. I. GURMAN
2012-01-01
In view of singularly perturbed problems with complex inner layer phenomenon,including contrast structures (step-step solution and spike-type solution),corner layer behavior and right-hand side discontinuity,we carry out the process with sewing connection.The presented method of sewing connection for singularly perturbed equations is based on the two points singularly perturbed simple boundary problems.By means of sewing orbit smoothness,we get the uniformly valid solution in the whole interval.It is easy to prove the existence of solutions and deal with the high dimensional singularly perturbed problems.
Recent progress in study of singular perturbation problems
Institute of Scientific and Technical Information of China (English)
MO Jia-qi; NI Ming-kang
2009-01-01
Some results for the singular perturbation theory, methods and applications in the new century are reviewed in this paper. It could be found that in the recent decade, many approximate methods have been developed and refined, including the method of averaging, boundary layer methods, methods of matched asymptotic expansion and methods of multiple scales. An overview is given on the new work about various problems, such as the reaction diffusion, turning points, boundary layers, shock waves, stability problem, solitons, attractors, canard solution, scattering light wave and neuron network, etc. And then, a great number of applied problems are solved in applied mathematics, computational mathematics, fluid mechanics, elastic mechanics, optics, thermophysics, quantum mechanics, plasm physics, physical chemistry, analytical chemistry, epidemiology, neurology, engineering science, environment science, bionomics, atmosphere physics, ocean climate, aeronautics and astrnatics and so on, from which only some examples are extracted and described in this review.
Singularly perturbed control systems with noncompact fast variable
Nguyen, Thuong; Siconolfi, Antonio
2016-10-01
We deal with a singularly perturbed optimal control problem with slow and fast variable depending on a parameter ε. We study the asymptotics, as ε goes to 0, of the corresponding value functions, and show convergence, in the sense of weak semilimits, to sub and supersolution of a suitable limit equation containing the effective Hamiltonian. The novelty of our contribution is that no compactness condition is assumed on the fast variable. This generalization requires, in order to perform the asymptotic procedure, an accurate qualitative analysis of some auxiliary equations posed on the space of fast variable. The task is accomplished using some tools of Weak KAM theory, and in particular the notion of Aubry set.
Infrared singularities of scattering amplitudes in perturbative QCD
Energy Technology Data Exchange (ETDEWEB)
Becher, Thomas [Fermi National Accelerator Laboratory (FNAL), Batavia, IL (United States); Neubert, Matthias [Johannes Gutenberg-Universitaet Mainz, Mainz (Germany)
2013-11-01
An exact formula is derived for the infrared singularities of dimensionally regularized scattering amplitudes in massless QCD with an arbitrary number of legs, valid at any number of loops. It is based on the conjecture that the anomalous-dimension matrix of n-jet operators in soft-collinear effective theory contains only a single non-trivial color structure, whose coefficient is the cusp anomalous dimension of Wilson loops with light-like segments. Its color-diagonal part is characterized by two anomalous dimensions, which are extracted to three-loop order from known perturbative results for the quark and gluon form factors. This allows us to predict the three-loop coefficients of all 1/epsilon^k poles for an arbitrary n-parton scattering amplitudes, generalizing existing two-loop results.
Application of singular perturbation method in analyzing traffic density waves
Institute of Scientific and Technical Information of China (English)
SHEN Fei-ying; GE Hong-xia; LEI Li
2009-01-01
Car following model is one of microscopic models for describing traffic flow. Through linear stability analysis, the neutral stability lines and the critical points are obtained for the different types of car following models and two modified models. The singular perturbation method has been used to derive various nonlinear wave equations, such as the Korteweg-de-Vries (KdV) equation and the modified Korteweg-de-Vries (mKdV) equation, which could describe different density waves occurring in traffic flows under certain conditions. These density waves are mainly employed to depict the formation of traffic jams in the congested traffic flow. The general soliton solutions are given for the different types of car following models, and the results have been used to the modified models efficiently.
Embarked electrical network robust control based on singular perturbation model.
Abdeljalil Belhaj, Lamya; Ait-Ahmed, Mourad; Benkhoris, Mohamed Fouad
2014-07-01
This paper deals with an approach of modelling in view of control for embarked networks which can be described as strongly coupled multi-sources, multi-loads systems with nonlinear and badly known characteristics. This model has to be representative of the system behaviour and easy to handle for easy regulators synthesis. As a first step, each alternator is modelled and linearized around an operating point and then it is subdivided into two lower order systems according to the singular perturbation theory. RST regulators are designed for each subsystem and tested by means of a software test-bench which allows predicting network behaviour in both steady and transient states. Finally, the designed controllers are implanted on an experimental benchmark constituted by two alternators supplying loads in order to test the dynamic performances in realistic conditions.
Ultraviolet asymptotics and singular dynamics of AdS perturbations
Energy Technology Data Exchange (ETDEWEB)
Craps, Ben [Theoretische Natuurkunde, Vrije Universiteit Brussel, and The International Solvay Institutes, Pleinlaan 2, B-1050 Brussels (Belgium); Evnin, Oleg [Department of Physics, Faculty of Science, Chulalongkorn University, Thanon Phayathai, Pathumwan, Bangkok 10330 (Thailand); Theoretische Natuurkunde, Vrije Universiteit Brussel, and The International Solvay Institutes, Pleinlaan 2, B-1050 Brussels (Belgium); Vanhoof, Joris [Theoretische Natuurkunde, Vrije Universiteit Brussel, and The International Solvay Institutes, Pleinlaan 2, B-1050 Brussels (Belgium)
2015-10-12
Important insights into the dynamics of spherically symmetric AdS-scalar field perturbations can be obtained by considering a simplified time-averaged theory accurately describing perturbations of amplitude ε on time-scales of order 1/ε{sup 2}. The coefficients of the time-averaged equations are complicated expressions in terms of the AdS scalar field mode functions, which are in turn related to the Jacobi polynomials. We analyze the behavior of these coefficients for high frequency modes. The resulting asymptotics can be useful for understanding the properties of the finite-time singularity in solutions of the time-averaged theory recently reported in the literature. We highlight, in particular, the gauge dependence of this asymptotics, with respect to the two most commonly used gauges. The harsher growth of the coefficients at large frequencies in higher-dimensional AdS suggests strengthening of turbulent instabilities in higher dimensions. In the course of our derivations, we arrive at recursive relations for the coefficients of the time-averaged theory that are likely to be useful for evaluating them more efficiently in numerical simulations.
Travelling wave solutions for a singularly perturbed Burgers–KdV equation
Indian Academy of Sciences (India)
M B A Mansour
2009-11-01
This paper concerns with the existence problem of travelling wave solutions to a singularly perturbed Burgers–KdV equation. For this, we use the dynamical systems approach, specifically, the geometric singular perturbation theory and centre manifold theory. We also numerically show approximations, in particular, for kink-type waves.
1986-05-19
eary and identify by block number) We developed and applied numerical methods for singularly perturbed two-point boundary value problems and time...Numerical Methods for Singularly Perturbed Differential Equations During the period of this contract. we developed and applied numerical methods for
Singularly perturbed telegraph equations with applications in the random walk theory
Directory of Open Access Journals (Sweden)
Jacek Banasiak
1998-01-01
Full Text Available In the paper we analyze singularly perturbed telegraph systems applying the newly developed compressed asymptotic method and show that the diffusion equation is an asymptotic limit of singularly perturbed telegraph system of equations. The results are applied to the random walk theory for which the relationship between correlated and uncorrelated random walks is explained in asymptotic terms.
Institute of Scientific and Technical Information of China (English)
Wen-zhi ZHANG; Pei-yan HUANG
2014-01-01
Based on the precise integration method (PIM), a coupling technique of the high order multiplication perturbation method (HOMPM) and the reduction method is proposed to solve variable coefficient singularly perturbed two-point boundary value prob-lems (TPBVPs) with one boundary layer. First, the inhomogeneous ordinary differential equations (ODEs) are transformed into the homogeneous ODEs by variable coefficient dimensional expansion. Then, the whole interval is divided evenly, and the transfer ma-trix in each sub-interval is worked out through the HOMPM. Finally, a group of algebraic equations are given based on the relationship between the neighboring sub-intervals, which are solved by the reduction method. Numerical results show that the present method is highly efficient.
Indian Academy of Sciences (India)
J B ZHOU; J XU; J D WEI; X Q YANG
2017-04-01
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 geometric singular perturbation theory and based on the relation between solitary wave solution and homoclinic orbits of the associated ordinary differential equations, the persistence of solitary wave solutions of this equation is proved when the perturbation parameter is sufficiently small. The numerical simulations verify our theoretical analysis.
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...
Threshold singularities, dispersion relations and fixed-order perturbative calculations
Energy Technology Data Exchange (ETDEWEB)
Beneke, M.; Ruiz-Femenía, P. [Physik Department T31, Technische Universität München,James-Franck-Straße, D-85748 Garching (Germany)
2016-08-24
We show how to correctly treat threshold singularities in fixed-order perturbative calculations of the electron anomalous magnetic moment and hadronic pair production processes such as top pair production. With respect to the former, we demonstrate the equivalence of the “non-perturbative”, resummed treatment of the vacuum polarization contribution, whose spectral function exhibits bound state poles, with the fixed-order calculation by identifying a threshold localized term in the four-loop spectral function. In general, we find that a modification of the dispersion relation by threshold subtractions is required to make fixed-order calculations well-defined and provide the subtraction term. We then solve the apparent problem of a divergent convolution of the partonic cross section with the parton luminosity in the computation of the top pair production cross section starting from the fourth-order correction. We find that when the computation is performed in the usual way as an integral of real and virtual corrections over phase space at a given order in the expansion in the strong coupling, an additional contribution has to be added at N3LO.
Passive Control and ε-Bound Estimation of Singularly Perturbed Systems with Nonlinear Nonlinearities
Directory of Open Access Journals (Sweden)
Linna Zhou
2013-01-01
Full Text Available This paper considers the problems of passivity analysis and synthesis of singularly perturbed systems with nonlinear uncertainties. By a novel storage function depending on the singular perturbation parameter ε, a new method is proposed to estimate the ε-bound, such that the system is passive when the singular perturbation parameter is lower than the ε-bound. Furthermore, a controller design method is proposed to achieve a predefined ε-bound. The proposed results are shown to be less conservative than the existing ones because the adopted storage function is more general. Finally, an RLC circuit is presented to illustrate the advantages and effectiveness of the proposed methods.
National Research Council Canada - National Science Library
Song, Changming; Li, Jina; Gao, Ran
2014-01-01
We are concerned with the singularly perturbed Boussinesq-type equation including the singularly perturbed sixth-order Boussinesq equation, which describes the bidirectional propagation of small...
Edström, Krister
1998-01-01
An initialization algorithm for the continuous states in mode switching systems is shown to give correct initial values. The mode switching systems are modeled with switched bond graphs, and the proof is based on singular perturbation theory.
Edström, Krister
1998-01-01
An initialization algorithm for the continuous states in mode switching systems is shown to give correct initial values. The mode switching systems are modeled with switched bond graphs, and the proof is based on the singular perturbation theory.
Nonlinear predator-prey singularly perturbed Robin Problems for reaction diffusion systems
Institute of Scientific and Technical Information of China (English)
莫嘉琪; 韩祥临
2003-01-01
The nonlinear predator-prey reaction diffusion systems for singularly perturbed Robin Problems are considered. Under suitable conditions, the theory of differential inequalities can be used to study the asymptotic behavior of the solution for initial boundary value problems.
Institute of Scientific and Technical Information of China (English)
莫嘉琪
2003-01-01
The nonlinear predator-prey singularly perturbed Robin initial boundary value problems for reaction diffusion systems were considered. Under suitable conditions, using theory of differential inequalities the existence and asymptotic behavior of solution for initial boundary value problems were studied.
Institute of Scientific and Technical Information of China (English)
Jia-qi Mo; Wan-tao Lin
2006-01-01
In this paper the singularly perturbed initial boundary value problems for the nonlocal reaction diffusion system are considered. Using the iteration method and the comparison theorem, the existence and its asymptotic behavior of the solution for the problem are studied.
A CLASS OF SINGULARLY PERTURBED ROBIN BOUNDARY VALUE PROBLEMS FOR SEMILINEAR ELLIPTIC EQUATION
Institute of Scientific and Technical Information of China (English)
MoJiaqi
2001-01-01
The singularly perturbed Robin boundary value problems for the semilinear elliptic equation are considered. Under suitable conditions and by using the fixed point theorem the existence ,uniqueness and asymptotic behavior of solution for the boundary value problems are studied.
QUASI-DIAGONALIZATION FOR A SINGULARLY PERTURBED DIFFERENTIAL SYSTEM WITH TWO PARAMETERS
Institute of Scientific and Technical Information of China (English)
无
2011-01-01
By two successive linear transformations,a singularly perturbed differential system with two parameters is quasi-diagonalized. The method of variation of constants and the principle of contraction map are used to prove the existence of the transformations.
A CLASS OF SINGULARLY PERTURBED INITIAL BOUNDARY PROBLEM FOR REACTION DIFFUSION EQUATION
Institute of Scientific and Technical Information of China (English)
Xie Feng
2003-01-01
The singularly perturbed initial boundary value problem for a class of reaction diffusion equation isconsidered. Under appropriate conditions, the existence-uniqueness and the asymptotic behavior of the solu-tion are showed by using the fixed-point theorem.
A SINGULARLY PERTURBED PROBLEM OF THIRD ORDER EQUATION WITH TWO PARAMETERS
Institute of Scientific and Technical Information of China (English)
无
2009-01-01
A singularly perturbed problem of third order equation with two parameters is studied. Using singular perturbation method, the structure of asymptotic solutions to the problem is discussed under three possible cases of two related small parameters. The results obtained reveal the different structures and limit behaviors of the solutions in three different cases. And in comparison with the exact solutions of the autonomous equation they are relatively perfect.
NONLINEAR SINGULARLY PERTURBED PREDATOR-PREY REACTION DIFFUSION SYSTEMS
Institute of Scientific and Technical Information of China (English)
MoJiaqi; TangRongrong
2004-01-01
A class of nonlinear predator-prey reaction diffusion systems for singularly perturbedproblems are considered. Under suitable conditions, by using theory of differential inequalitiesthe existence and asymptotic behavior of solution for initial boundary value problems arestudied.
Asymptotic Limit of a Singularly Perturbed Stationary Diffusion Equation: The Case of a Limit Cycle
Ge, Hao
2010-01-01
A limit cycle for a nonlinear ordinary differential equation has a sustained, stationary oscillation in time; Any non-trivial stationary stochastic process also exhibits stationary oscillations in time, though with randomness and a stationary probability density. A reconciliation of these two views of oscillatory dynamics has been elusive, although it becomes increasingly important in the biochemical modeling of cellular dynamics, where stochatic models based on the chemical master equation and the deterministic model based on the Law of Mass Action are routinely compared. Using a singularly perturbed stationary diffusion equation as a model for the chemical master equation with sufficiently large volume, $\\epsilon \\leftrightarrow 1/V$, we show that its stationary solution $u(\\vx)$ exhibits a clear separation of the exponentially and algebraic small contributions: $u(\\vx)=C_{\\epsilon}(\\vx) e^{-\\phi(\\vx)/\\epsilon}$, in which $\\phi(x)\\ge 0$ and $=0$ on the entire stable limit cycle. On the limit cycle, $C_0(\\vx...
Discrete approximations for singularly perturbed boundary value problems with parabolic layers
Farrell, P.A.; Hemker, P.W.; Shishkin, G.I.
1995-01-01
Singularly perturbed boundary value problems for equations of elliptic and parabolic type are studied. For small values of the perturbation parameter, parabolic boundary layers appear in these problems. If classical discretisation methods are used, the solution of the finite difference scheme and th
Wavelet-Galerkin Method for the Singular Perturbation Problem with Boundary Layers
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
A Wavelet-Galerkin method is proposed to solve the singular perturbation problem with boundary layers numerically. Because there are boundary layers in the solution of the singular perturbation problem, the approximation spaces with different scale wavelets and boundary bases are chosen. In addition, the computation of the inner integrals is transformed to an eigenvalue problem. Therefore, a high accuracy method with reasonable computation is obtained. On the other hand, there is an explicit diagonal preconditioning which makes the condition number of the stiff matrix become bounded by a constant. The error estimate of the Wavelet-Galerkin method and the analysis of the computation complexity are given. The numerical examples show that the method is feasible and effective for solving the singular perturbation problem with boundary layers numerically.
INITIAL LAYER PHENOMENA FOR A CLASS OF SINGULAR PERTURBED NONLINEAR SYSTEM WITH SLOW VARIABLES
Institute of Scientific and Technical Information of China (English)
黄蔚章; 陈育森
2004-01-01
The initial layer phenomena for a class of singular perturbed nonlinear system with slow variables are studied. By introducing stretchy variables with different quantity levels and constructing the correction term of initial layer with different "thickness", the Norder approximate expansion of perturbed solution concerning small parameter is obtained,and the "multiple layer" phenomena of perturbed solutions are revealed. Using the fixed point theorem, the existence of perturbed solution is proved, and the uniformly valid asymptotic expansion of the solutions is given as well.
Analytical methods for a selection of elliptic singular perturbation problems
Temme, N.M.
1997-01-01
We consider several model problems from a class of elliptic perturbation equations in two dimensions. The domains, the differential operators, the boundary conditions, and so on, are rather simple, and are chosen in a way that the solutions can be obtained in the form of integrals or Fourier series.
High order singular rank one perturbations of a positive operator
Dijksma, A.; Kurasov, P.; Shondin, Yu.
2005-01-01
In this paper self-adjoint realizations in Hilbert and Pontryagin spaces of the formal expression Lα = L + α〈·, φ〉φ are discussed and compared. Here L is a positive self-adjoint operator in a Hilbert space H with inner product 〈· ,·〉, α is a real parameter, and φ in the rank one perturbation is a si
Selberg zeta functions and transfer operators an experimental approach to singular perturbations
Fraczek, Markus Szymon
2017-01-01
This book presents a method for evaluating Selberg zeta functions via transfer operators for the full modular group and its congruence subgroups with characters. Studying zeros of Selberg zeta functions for character deformations allows us to access the discrete spectra and resonances of hyperbolic Laplacians under both singular and non-singular perturbations. Areas in which the theory has not yet been sufficiently developed, such as the spectral theory of transfer operators or the singular perturbation theory of hyperbolic Laplacians, will profit from the numerical experiments discussed in this book. Detailed descriptions of numerical approaches to the spectra and eigenfunctions of transfer operators and to computations of Selberg zeta functions will be of value to researchers active in analysis, while those researchers focusing more on numerical aspects will benefit from discussions of the analytic theory, in particular those concerning the transfer operator method and the spectral theory of hyperbolic spac...
CONVERGENCE RESULTS OF RUNGE-KUTTA METHODS FOR MULTIPLY-STIFF SINGULAR PERTURBATION PROBLEMS
Institute of Scientific and Technical Information of China (English)
Ai-guo Xiao
2002-01-01
The main purpose of this paper is to present some convergence results for algebraically stable Runge-Kutta methods applied to some classes of one- and two-parameter multiplystiff singular perturbation problems whose stiffness is caused by small parameters and some other factors. A numerical example confirms our results.
NON C0 NONCONFORMING ELEMENTS FOR ELLIPTIC FOURTH ORDER SINGULAR PERTURBATION PROBLEM
Institute of Scientific and Technical Information of China (English)
Shao-chun Chen; Yong-cheng Zhao; Dong-yang Shi
2005-01-01
In this paper we give a convergence theorem for non C0 nonconforming finite element to solve the elliptic fourth order singular perturbation problem. Two such kind of elements, a nine parameter triangular element and a twelve parameter rectangular element both with double set parameters, are presented. The convergence and numerical results of the two elements are given.
Bifurcations of Invariant Tori and Subharmonic Solutions of Singularly Perturbed System
Institute of Scientific and Technical Information of China (English)
Zhiyong YE; Maoan HAN
2007-01-01
This paper deals with bifurcations of subharmonic solutions and invariant tori generated from limit cycles in the fast dynamics for a nonautonomous singularly perturbed integral manifold, the conditions for the existence of invariant tori are obtained, and the saddle-node bifurcations of subharmonic solutions are studied.
Singular perturbation theory mathematical and analytical techniques with applications to engineering
Johnson, RS
2005-01-01
Written in a form that should enable the relatively inexperienced (or new) worker in the field of singular perturbation theory to learn and apply all the essential ideasDesigned as a learning tool. The numerous examples and set exercises are intended to aid this process.
SINGULARLY PERTURBED SOLUTION FOR THIRD ORDER NONLINEAR EQUATIONS WITH TWO PARAMETERS
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
A class of singularly perturbed boundary value problems for nonlinear equation of the third order with two parameters is considered. Under suitable conditions, using the theory of differential inequalities the existence and asymptotic behavior of the solution for boundary value problem are studied.
THE SINGULARLY PERTURBED BOUNDARY VALUE PROBLEMS FOR SEMILINEAR ELLIPTIC EQUATION OF HIGHER ORDER
Institute of Scientific and Technical Information of China (English)
Chen Songlin; Mo Jiaqi
2000-01-01
The singularly perturbed boundary value problems for the semilinear elliptic equation of higher order are considered. Under suitable conditions and by using the fixed point theoren the existence, uniqueness and asymp totic behavior of solution for the boundary value tproblems are studied.
Harmonic Maps to Buildings and Singular Perturbation Theory
Katzarkov, Ludmil; Pandit, Pranav; Simpson, Carlos
2013-01-01
The notion of a universal building associated with a point in the Hitchin base is introduced. This is a building equipped with a harmonic map from a Riemann surface that is initial among harmonic maps which induce the given cameral cover of the Riemann surface. In the rank one case, the universal building is the leaf space of the quadratic differential defining the point in the Hitchin base. The main conjectures of this paper are: (1) the universal building always exists; (2) the harmonic map to the universal building controls the asymptotics of the Riemann-Hilbert correspondence and the non-abelian Hodge correspondence; (3) the singularities of the universal building give rise to Spectral Networks; and (4) the universal building encodes the data of a 3d Calabi-Yau category whose space of stability conditions has a connected component that contains the Hitchin base. The main theorem establishes the existence of the universal building, conjecture (3), as well as the Riemann-Hilbert part of conjecture (2), in t...
Volume reduction through perturbative Wilson loops
Perez, Margarita Garcia; Okawa, Masanori
2016-01-01
We derive the perturbative expansion of Wilson loops to order g^4 in a SU(N) lattice gauge theory with twisted boundary conditions. Our expressions show that the thermodynamic limit is attained at infinite N for any number of lattice sites and allow to quantify the deviations from volume independence at finite large N as a function of the twist.
On Absence of Pure Singular Spectrum of Random Perturbations and in Anderson Model at Low Disorde
Grinshpun, V
2006-01-01
Absence of singular component, with probability one, in the conductivity spectra of bounded random perturbations of multidimensional finite-difference Hamiltonians, is for the first time rigorously established under certain conditions ensuring either absence of pure point, or absence of pure absolutely continuous component in the corresponding regions of spectra. The main technical tool applied is the theory of rank-one perturbations of singular spectra. The respective new result (the non-mixing property) is applied to establish existence and bounds of the (non-empty) pure absolutely continuous component in the spectrum of the Anderson model with bounded random potential in dimension 2 at low disorder. The new (1999) result implies, via the trace-class perturbation analysis, the Anderson model with the unbounded potential to have only pure point spectrum (complete system of localized wave-functions) with probability one in arbitrary dimension. The new technics, based on the resolvent reduction formula, and ex...
Computer difference scheme for a singularly perturbed convection-diffusion equation
Shishkin, G. I.
2014-08-01
The Dirichlet problem for a singularly perturbed ordinary differential convection-diffusion equation with a perturbation parameter ɛ (that takes arbitrary values from the half-open interval (0, 1]) is considered. For this problem, an approach to the construction of a numerical method based on a standard difference scheme on uniform meshes is developed in the case when the data of the grid problem include perturbations and additional perturbations are introduced in the course of the computations on a computer. In the absence of perturbations, the standard difference scheme converges at an (δ st ) rate, where δ st = (ɛ + N -1)-1 N -1 and N + 1 is the number of grid nodes; the scheme is not ɛ-uniformly well conditioned or stable to perturbations of the data. Even if the convergence of the standard scheme is theoretically proved, the actual accuracy of the computed solution in the presence of perturbations degrades with decreasing ɛ down to its complete loss for small ɛ (namely, for ɛ = (δ-2max i, j |δ a {/i j }| + δ-1 max i, j |δ b {/i j }|), where δ = δ st and δ a {/i j }, δ b {/i j } are the perturbations in the coefficients multiplying the second and first derivatives). For the boundary value problem, we construct a computer difference scheme, i.e., a computing system that consists of a standard scheme on a uniform mesh in the presence of controlled perturbations in the grid problem data and a hypothetical computer with controlled computer perturbations. The conditions on admissible perturbations in the grid problem data and on admissible computer perturbations are obtained under which the computer difference scheme converges in the maximum norm for ɛ ∈ (0, 1] at the same rate as the standard scheme in the absence of perturbations.
Optimal disturbances rejection control for singularly perturbed systems with time-delay
Institute of Scientific and Technical Information of China (English)
Zhang Baolin; Tang Gongyou; Zhao Yandong
2008-01-01
The optimal control design for singularly perturbed time-delay systems affected by external disturbances is considered. Based on the decomposition theory of singular perturbation, the system is decomposed into a fast subsystem without time-delay and a slow time-delay subsystem with disturbances. The optimal disturbances rejection control law of the slow subsystem is obtained by using the successive approximation approach (SAA) and feedforward compensation method. Further, the feedforward and feedback composite control (FFCC) law for the original problem is developed. The FFCC law consists of linear analytic terms and a time-delay compensation term which is the limit of the solution sequence of the adjoint vector equations. A disturbance observer is introduced to make the FFCC law physically realizable. Numerical examples show that the proposed algorithm is effective.
Directory of Open Access Journals (Sweden)
Vrabel Robert
2011-01-01
Full Text Available Abstract This paper deals with the existence and asymptotic behavior of the solutions to the singularly perturbed second-order nonlinear differential equations. For example, feedback control problems, such as the steady states of the thermostats, where the controllers add or remove heat, depending upon the temperature detected by the sensors in other places, can be interpreted with a second-order ordinary differential equation subject to a nonlocal four-point boundary condition. Singular perturbation problems arise in the heat transfer problems with large Peclet numbers. We show that the solutions of mathematical model, in general, start with fast transient which is the so-called boundary layer phenomenon, and after decay of this transient they remain close to the solution of reduced problem with an arising new fast transient at the end of considered interval. Our analysis relies on the method of lower and upper solutions.
Directory of Open Access Journals (Sweden)
Essam R. El-Zahar
2016-01-01
Full Text Available A reliable algorithm is presented to develop piecewise approximate analytical solutions of third- and fourth-order convection diffusion singular perturbation problems with a discontinuous source term. The algorithm is based on an asymptotic expansion approximation and Differential Transform Method (DTM. First, the original problem is transformed into a weakly coupled system of ODEs and a zero-order asymptotic expansion of the solution is constructed. Then a piecewise smooth solution of the terminal value reduced system is obtained by using DTM and imposing the continuity and smoothness conditions. The error estimate of the method is presented. The results show that the method is a reliable and convenient asymptotic semianalytical numerical method for treating high-order singular perturbation problems with a discontinuous source term.
Asymptotic solution for a class of weakly nonlinear singularly perturbed reaction diffusion problem
Institute of Scientific and Technical Information of China (English)
TANG Rong-rong
2009-01-01
Under appropriate conditions, with the perturbation method and the theory of differential inequalities, a class of weakly nonlinear singularly perturbed reaction diffusion problem is considered. The existence of solution of the original problem is proved by constructing the auxiliary functions. The uniformly valid asymptotic expansions of the solution for arbitrary mth order approximation are obtained through constructing the formal solutions of the original problem, expanding the nonlinear terms to the power in small parameter e and comparing the coefficient for the same powers of ε. Finally, an example is provided, resulting in the error of O(ε2).
A Numerical Method for a Singularly Perturbed Three-Point Boundary Value Problem
Directory of Open Access Journals (Sweden)
Musa Çakır
2010-01-01
Full Text Available The purpose of this paper is to present a uniform finite difference method for numerical solution of nonlinear singularly perturbed convection-diffusion problem with nonlocal and third type boundary conditions. The numerical method is constructed on piecewise uniform Shishkin type mesh. The method is shown to be convergent, uniformly in the diffusion parameter ε, of first order in the discrete maximum norm. Some numerical experiments illustrate in practice the result of convergence proved theoretically.
Directory of Open Access Journals (Sweden)
Leila Mebarki
2015-11-01
Full Text Available This paper is devoted to the investigation of the stability of the Weyl essential spectrum of closed densely dened linear operator A subjected to additive perturbation K such that (lambda-A-K^{-1}K or K(lambda-A-K^{-1} is a quasi-compact operator. The obtained results are used to describe the Weyl essential spectrum of singular neutron transport operator.
ORDER RESULTS OF GENERAL LINEAR METHODS FOR MULTIPLY STIFF SINGULAR PERTURBATION PROBLEMS
Institute of Scientific and Technical Information of China (English)
Si-qing Gan; Geng Sun
2002-01-01
In this paper we analyze the error behavior of general linear methods applied to some classes of one-parameter multiply stiff singularly perturbed problems. We obtain the global error estimate of algebraically and diagonally stable general linear methods. The main result of this paper can be viewed as an extension of that obtained by Xiao [13] for the case of Runge-Kutta methods.
SINGULARLY PERTURBED SEMI-LINEAR BOUNDARY VALUE PROBLEM WITH DISCONTINUOUS FUNCTION
Institute of Scientific and Technical Information of China (English)
Ding Haiyun; Ni Mingkang; Lin Wuzhong; Cao Yang
2012-01-01
A class of singularly perturbed semi-linear boundary value problems with discontinuous functions is examined in this article.Using the boundary layer function method,the asymptotic solution of such a problem is given and shown to be uniformly effective. The existence and uniqueness of the solution for the system is also proved.Numerical result is presented as an illustration to the theoretical result.
Weiya Zhang; Yongli Li; Xiaoyong Chang; Nan Wang
2014-01-01
An investigation on qualitative dynamics in a voltage-current dual-loop controlled flywheel energy storage system (FESS) operating in discharge mode is presented in this paper, providing novel insights into the effect of two-timescale characteristics on the safety and stability of energy transmission of FESS. Based on singular perturbation theory, a two-timescale approach is proposed to separate the FESS into the fast and slow subsystems. Stability analysis of the transient fixed points confi...
Uniform Convergence Analysis for Singularly Perturbed Elliptic Problems with Parabolic Layers
Institute of Scientific and Technical Information of China (English)
Jichun Li; Yitung Chen
2008-01-01
In this paper, using Lin's integral identity technique, we prove the optimal uniform convergence O(Nx-2 ln2Nx+ Ny-2 In2Ny) in the L2-norm for singularly per-turbed problems with parabolic layers. The error estimate is achieved by bilinear fi-nite elements on a Shishkin type mesh. Here Nx and Ny are the number of elements in the x- and y-directions, respectively. Numerical results are provided supporting our theoretical analysis.
Variational Iteration Method for Singular Perturbation Initial Value Problems with Delays
Directory of Open Access Journals (Sweden)
Yongxiang Zhao
2014-01-01
Full Text Available The variational iteration method (VIM is applied to solve singular perturbation initial value problems with delays (SPIVPDs. Some convergence results of VIM for solving SPIVPDs are given. The obtained sequence of iterates is based on the use of general Lagrange multipliers; the multipliers in the functionals can be identified by the variational theory. Moreover, the numerical examples show the efficiency of the method.
Relative Error Model Reduction via Time-Weighted Balanced Stochastic Singular Perturbation
DEFF Research Database (Denmark)
Tahavori, Maryamsadat; Shaker, Hamid Reza
2012-01-01
A new mixed method for relative error model reduction of linear time invariant (LTI) systems is proposed in this paper. This order reduction technique is mainly based upon time-weighted balanced stochastic model reduction method and singular perturbation model reduction technique. Compared...... by using the concept and properties of the reciprocal systems. The results are further illustrated by two practical numerical examples: a model of CD player and a model of the atmospheric storm track....
Amirkhanov, I V; Zhidkova, I E; Vasilev, S A
2000-01-01
Asymptotics of eigenfunctions and eigenvalues has been obtained for a singular perturbated relativistic analog of Schr`dinger equation. A singular convergence of asymptotic expansions of the boundary problems to degenerated problems is shown for a nonrelativistic Schr`dinger equation. The expansions obtained are in a good agreement with a numeric experiment.
Existence of localizing solutions in plasticity via the geometric singular perturbation theory
Lee, Min-Gi
2017-01-31
Shear bands are narrow zones of intense shear observed during plastic deformations of metals at high strain rates. Because they often precede rupture, their study attracted attention as a mechanism of material failure. Here, we aim to reveal the onset of localization into shear bands using a simple model from viscoplasticity. We exploit the properties of scale invariance of the model to construct a family of self-similar focusing solutions that capture the nonlinear mechanism of shear band formation. The key step is to desingularize a reduced system of singular ordinary differential equations and reduce the problem into the construction of a heteroclinic orbit for an autonomous system of three first-order equations. The associated dynamical system has fast and slow time scales, forming a singularly perturbed problem. Geometric singular perturbation theory is applied to this problem to achieve an invariant surface. The flow on the invariant surface is analyzed via the Poincaré--Bendixson theorem to construct a heteroclinic orbit.
Holographic curvature perturbations in a cosmology with a space-like singularity
Energy Technology Data Exchange (ETDEWEB)
Ferreira, Elisa G.M. [Department of Physics, McGill University,3600 University St., Montréal, QC, H3A 2T8 (Canada); Brandenberger, Robert [Department of Physics, McGill University,3600 University St., Montréal, QC, H3A 2T8 (Canada); Institute for Theoretical Studies, ETH Zürich,Clausiusstr. 47, Zürich, CH-8092 (Switzerland)
2016-07-19
We study the evolution of cosmological perturbations in an anti-de-Sitter (AdS) bulk through a cosmological singularity by mapping the dynamics onto the boundary conformal fields theory by means of the AdS/CFT correspondence. We consider a deformed AdS space-time obtained by considering a time-dependent dilaton which induces a curvature singularity in the bulk at a time which we call t=0, and which asymptotically approaches AdS both for large positive and negative times. The boundary field theory becomes free when the bulk curvature goes to infinity. Hence, the evolution of the fluctuations is under better controle on the boundary than in the bulk. To avoid unbounded particle production across the bounce it is necessary to smooth out the curvature singularity at very high curvatures. We show how the bulk cosmological perturbations can be mapped onto boundary gauge field fluctuations. We evolve the latter and compare the spectrum of fluctuations on the infrared scales relevant for cosmological observations before and after the bounce point. We find that the index of the power spectrum of fluctuations is the same before and after the bounce.
Dotti, Gustavo; Gleiser, Reinaldo J.
2009-11-01
The coupled equations for the scalar modes of the linearized Einstein equations around Schwarzschild's spacetime were reduced by Zerilli to a (1+1) wave equation \\partial ^2 \\Psi _z / \\partial t^2 + {\\cal H} \\Psi _z =0 , where {\\cal H} = -\\partial ^2 / \\partial x^2 + V(x) is the Zerilli 'Hamiltonian' and x is the tortoise radial coordinate. From its definition, for smooth metric perturbations the field Ψz is singular at rs = -6M/(ell - 1)(ell +2), with ell being the mode harmonic number. The equation Ψz obeys is also singular, since V has a second-order pole at rs. This is irrelevant to the black hole exterior stability problem, where r > 2M > 0, and rs 0, and the singularity appears in the relevant range of r (0 value of M. The relation of \\hat{\\Psi} to Ψz is provided by an intertwiner operator. The spatial pieces of the (1 + 1) wave equations that \\hat{\\Psi} and Ψz obey are related as a supersymmetric pair of quantum Hamiltonians {\\cal H} and \\hat{\\cal H} . For Mproof of the linear instability of the Schwarzschild naked singularity, by showing that a previously found unstable mode belongs to a complete basis of \\hat{\\cal H} in {\\cal D} , and thus is excitable by generic initial data. This is further illustrated by numerically solving the linearized equations for suitably chosen initial data.
Hasni, Mohd Mughti; Majid, Zanariah Abdul; Senu, Norazak; Rajalingam, Sokkalingam; Daud, Hanita; Daud, Muhamad Azlan
2016-11-01
This paper presents a four point block one-step method for solving directly boundary value problems (BVP) with Neumann boundary conditions and Singular Perturnbation BVPs. This method is formulated using Lagrange interpolating polynomial. The block method will solve the second order linear Neumann and Singular Perturbation BVPs directly without reducing it to the system of first order differential equations. This direct method will compute four points simultaneously within a block using constant step size. This method will be used together with linear shooting technique to construct the solutions. The implementation is based on the predictor and corrector formulas. Numerical results are given to show the efficiency of this method compared to the existing methods.
Institute of Scientific and Technical Information of China (English)
Ziqing Xie; Zuozheng Zhang; Zhimin Zhang
2009-01-01
In this paper,we consider the local discontinuous Galerkin method (LDG) for solving singularly perturbed convection-diffusion problems in one-and two-dimensional settings.The existence and uniqueness of the LDG solutions are verified.Numerical experiments demonstrate that it seems impossible to obtain uniform superconvergence for numerical fluxes under uniform meshes.Thanks to the implementation of two-type different anisotropic meshes,i.e.,the Shishkin and art improved grade meshes,the uniform 2p+1-order superconvergence is observed numerically for both one-dimensional and twodimensional cases.
Singular perturbation composite control of a free-floating flexible dual-arm space robot
Institute of Scientific and Technical Information of China (English)
无
2008-01-01
The Free-floating Flexible Dual-arm Space Robot is a highly nonlinear and coupled dynamics system. In this paper, the dynamic model is derived of a Free-floating Flexible Dual-arm Space Robot holding a rigid payload. Furthermore, according to the singular perturbation method, the system is separated into a slow subsystem representing rigid body motion of the robot and a fast subsystem representing the flexible link dynamics. For the slow subsystem, based on the second method of Lyapunov, using simple quanti...
Institute of Scientific and Technical Information of China (English)
Igor Boglaev; Matthew Hardy
2008-01-01
This paper presents and analyzes a monotone domain decomposition algorithm for solving nonlinear singularly perturbed reaction-diffusion problems of parabolic type.To solve the nonlinear weighted average finite difference scheme for the partial differential equation,we construct a monotone domain decomposition algorithm based on a Schwarz alternating method and a box-domain decomposition.This algorithm needs only to solve linear discrete systems at each iterative step and converges monotonically to the exact solution of the nonlinear discrete problem. The rate of convergence of the monotone domain decomposition algorithm is estimated.Numerical experiments are presented.
Relative Error Model Reduction via Time-Weighted Balanced Stochastic Singular Perturbation
DEFF Research Database (Denmark)
Tahavori, Maryamsadat; Shaker, Hamid Reza
2012-01-01
A new mixed method for relative error model reduction of linear time invariant (LTI) systems is proposed in this paper. This order reduction technique is mainly based upon time-weighted balanced stochastic model reduction method and singular perturbation model reduction technique. Compared...... to the other analogous counterparts, the proposed method shows to provide more accurate results in terms of time weighted norms when applied to the practical examples. It is shown that important properties of the time-weighted stochastic balanced reduction technique are extended to the mixed reduction method...
Fuzzy Controllers for Nonaffine-in-Control Singularly Perturbed Switched Systems
Directory of Open Access Journals (Sweden)
Linna Zhou
2015-01-01
Full Text Available This paper investigates the problem of fuzzy controller design for nonaffine-in-control singularly perturbed switched systems (NCSPSSs. First, the NCSPSS is approximated by Takagi-Sugeno (T-S models which include not only state but also control variables in the premise part of the rules. Then, a dynamic state feedback controller design method is proposed in terms of linear matrix inequalities. Under the controller, stability bound estimation problem of the closed-loop system is solved. Finally, an example is given to show the feasibility and effectiveness of the obtained methods.
A Singular Perturbation Based Midcourse Guidance Law for Realistic Air-to-Air Engagement
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M Manickavasagam
2016-12-01
Full Text Available In this study, a singular perturbation based technique is used for synthesis and analysis of a near optimal midcourse guidance law for realistic air-to-air engagement. After designing the proposed midcourse guidance law using three dimensional point mass formulation it has been validated through detailed realistic six degrees of freedom simulation. During terminal phase only proportional navigation guidance have been used. The calculation of optimal altitude in present guidance law has been carried out using Newton’s method, which needs generally one iteration for convergence and suitable for real-time implementation. Extended Kalman filter based estimator has been used for obtaining evader kinetic information from both radar and seeker noisy measurements available during midcourse and terminal guidance. The data link look angle constraint due to hardware limitation which affects the performance of midcourse guidance has also been incorporated in guidance law design. Robustness of complete simulation has been carried out through Monte Carlo studies. Extension of launch boundary due to singular perturbation over proportional navigation guidance at a given altitude for a typical engagement has also been reported.
Roul, Pradip; Warbhe, Ujwal
2017-08-01
The classical homotopy perturbation method proposed by J. H. He, Comput. Methods Appl. Mech. Eng. 178, 257 (1999) is useful for obtaining the approximate solutions for a wide class of nonlinear problems in terms of series with easily calculable components. However, in some cases, it has been found that this method results in slowly convergent series. To overcome the shortcoming, we present a new reliable algorithm called the domain decomposition homotopy perturbation method (DDHPM) to solve a class of singular two-point boundary value problems with Neumann and Robin-type boundary conditions arising in various physical models. Five numerical examples are presented to demonstrate the accuracy and applicability of our method, including thermal explosion, oxygen-diffusion in a spherical cell and heat conduction through a solid with heat generation. A comparison is made between the proposed technique and other existing seminumerical or numerical techniques. Numerical results reveal that only two or three iterations lead to high accuracy of the solution and this newly improved technique introduces a powerful improvement for solving nonlinear singular boundary value problems (SBVPs).
Towards the Right Hamiltonian for Singular Perturbations via Regularization and Extension Theory
Neidhardt, Hagen; Zagrebnov, Valentin
For singular potentials in quantum mechanics it can happen that the Schrödinger operator is not esssentially self-adjoint on a natural domain, i.e., each self-adjoint extension is a candidate for the right physical Hamiltonian. Traditional way to single out this Hamiltonian is the removing cut-offs for regularizing potential. Connecting regularization and extension theory we develop an abstract operator method to treat the problem of the right Hamiltonian. We show that, using the notion of the maximal (with respect to the perturbation) Friedrichs extension of unperturbed operator, one can classify the above problem as wellposed or ill-posed depending on intersection of the quadratic form domain of perturbation and deficiency subspace corresponding to restriction of unperturbed operator to stability domain. If this intersection is trivial, then the right Hamiltonian is unique: it coincides with the form sum of perturbation and the Friedrich extension of the unperturbed operator restricted to the stability domain. Otherwise it is not unique: the family of “right Hamiltonians” can be described in terms of symmetric extensions reducing the ill-posed problem to the well-posed problem.
Directory of Open Access Journals (Sweden)
Juing-Shian Chiou
2013-01-01
Full Text Available This paper presents a novel and general approach, which is based on the composite control method, to synthesize the controller and observer-based state feedback to stabilize the singularly perturbed time-delay systems. First, the equivalent models of the original systems and the subsystems reduced via singular perturbation techniques are derived. Through these equivalent models, approximation of the stabilization and observer design for the original systems can be achieved through separate analyses for the slow and fast subsystems via a transformation of block diagonalization.
SUPERCONVERGENCE OF DG METHOD FOR ONE-DIMENSIONAL SINGULARLY PERTURBED PROBLEMS
Institute of Scientific and Technical Information of China (English)
Ziqing Xie; Zhimin Zhang
2007-01-01
The convergence and superconvergence properties of the discontinuous Galerkin (DG) method for a singularly perturbed model problem in one-dimensional setting are studied.By applying the DG method with appropriately chosen numerical traces, the existence and uniqueness of the DG solution, the optimal order L2 error bounds, and 2p+1-order superconvergence of the numerical traces are established. The numerical results indicate that the DG method does not produce any oscillation even under the uniform mesh. Numerical experiments demonstrate that, under the uniform mesh, it seems impossible to obtain the uniform superconvergence of the numerical traces. Nevertheless, thanks to the implementation of the so-called Shishkin-type mesh, the uniform 2p + 1-order superconvergence is observed numerically.
On bifurcation delay: An alternative approach using Geometric Singular Perturbation Theory
Hsu, Ting-Hao
2017-02-01
To explain the phenomenon of bifurcation delay, which occurs in planar systems of the form x ˙ = ɛf (x , z , ɛ), z ˙ = g (x , z , ɛ) z, where f (x , 0 , 0) > 0 and g (x , 0 , 0) changes sign at least once on the x-axis, we use the Exchange Lemma in Geometric Singular Perturbation Theory to track the limiting behavior of the solutions. Using the trick of extending dimension to overcome the degeneracy at the turning point, we show that the limiting attracting and repulsion points are given by the well-known entry-exit function, and the minimum of z on the trajectory is of order exp (- 1 / ɛ). Also we prove smoothness of the return map up to arbitrary finite order in ɛ.
Neuro-Sliding-Mode Control of Flexible-Link Manipulators Based on Singularly Perturbed Model
Institute of Scientific and Technical Information of China (English)
ZHANG Yu; YANG Tangwen; SUN Zengqi
2009-01-01
A neuro-sliding-mode control (NSMC) strategy was developed to handle the complex nonlinear dynamics and model uncertainties of flexible-link manipulators. A composite controller was designed based on a singularly perturbed model of flexible-link manipulators when the rigid motion and flexible motion are decoupled. The NSMC is employed to control the slow subsystem to track a desired trajectory with a traditional sliding mode controller to stabilize the fast subsystem which represents the link vibrations. A stability analysis of the flexible modes is also given. Simulations confirm that the NSMC performs better than the tra-ditional sliding-mode control for controlling flexible-link manipulators. The control strategy not only gives good tracking performance for the joint angle, but also effectively suppresses endpoint vibrations. The simulations also show that the control strategy has a strong self-adaptive ability for controlling manipulators with different parameters.
Energy Technology Data Exchange (ETDEWEB)
Reinhardt, Hans-Juergen, E-mail: reinhardt@mathematik.uni-siegen.de [Department of Mathematics, University of Siegen, Emmy-Noether-Campus, Walter-Flex-Str. 3, D-57072 Siegen (Germany)
2011-04-01
In this paper singularly perturbed parabolic initial-boundary value problems are considered which, in addition, are illposed. The latter means that at one end of the 1-d spatial domain two conditions (for the solution and its spatial derivative) are given while on the other end the corresponding quantities are to be determined. It is well-known that such problems are illposed in the mathematical sense. Here, in addition, boundary layers may occur which make the problems more difficult. For relatively simple examples numerical experiments have been carried out and numerical results are shown. The Conjugate Gradient Methods is used to find the desired quantities iteratively. It will be explained what has to be done in any iteration step. A regularisation is performed by means of discretization and by determining an optimal final iteration step via a stopping rule.
Directory of Open Access Journals (Sweden)
Wenzhen Chen
2013-01-01
Full Text Available The singularly perturbed method (SPM is proposed to obtain the analytical solution for the delayed supercritical process of nuclear reactor with temperature feedback and small step reactivity inserted. The relation between the reactivity and time is derived. Also, the neutron density (or power and the average density of delayed neutron precursors as the function of reactivity are presented. The variations of neutron density (or power and temperature with time are calculated and plotted and compared with those by accurate solution and other analytical methods. It is shown that the results by the SPM are valid and accurate in the large range and the SPM is simpler than those in the previous literature.
Singular perturbation composite control of a free-floating flexible dual-arm space robot
Institute of Scientific and Technical Information of China (English)
Luo Zhanwu; Wang Congqing
2008-01-01
The Free-floating Flexible Dual-arm Space Robot is a highly nonlinear and coupled dynamics system. In this paper, the dynamic model is derived of a Free-floating Flexible Dual-arm Space Robot holding a rigid payload. Furthermore, according to the singular perturbation method, the system is separated into a slow subsystem representing rigid body motion of the robot and a fast subsystem representing the flexible link dynamics. For the slow subsystem, based on the second method of Lyapunov, using simple quantitative bounds on the model uncertainties, a robust tracking controller design is used during the trajectory tracking phase. The optimal control method is designed in the fast subsystem to guarantee the exponential stability. With the combination of the two above, the system can track the expected trajectory accurately, even though with uncertainty in model parameters, and its flexible vibration gets suppressed, too. Finally, some simulation tests have been conducted to verify the effectiveness of the proposed methods.
On Singular Perturbations of Flexible and Variable-Speed Wind Turbines
Directory of Open Access Journals (Sweden)
R. Oulad Ben Zarouala
2012-01-01
Full Text Available A model for the mechanical dynamics of a wind turbine is developed, which is the composition of three physical mechanisms: flexion, torsion, and rotational dynamics. A first contribution is the identification of the essential physical parameters that provide a time-scale separation of these three mechanisms. Under the assumption of singular perturbations the time-scale separation allows to work with a reduced model of order one. This reduction has been essential for the control of this system allowing to control designers to take into account only the reduced-order model. A second contribution consists in employing a measurement of the fore-aft nacelle acceleration with the reduced model, together with a Kalman filter to estimate the flexible DOFs of the system (tower and average blade deflection. The successful approach is tested on high-order nonlinear aeroelastic simulator (FAST.
An evaluation of parallel multigrid as a solver and a preconditioner for singular perturbed problems
Energy Technology Data Exchange (ETDEWEB)
Oosterlee, C.W. [Inst. for Algorithms and Scientific Computing, Sankt Augustin (Germany); Washio, T. [C& C Research Lab., Sankt Augustin (Germany)
1996-12-31
In this paper we try to achieve h-independent convergence with preconditioned GMRES and BiCGSTAB for 2D singular perturbed equations. Three recently developed multigrid methods are adopted as a preconditioner. They are also used as solution methods in order to compare the performance of the methods as solvers and as preconditioners. Two of the multigrid methods differ only in the transfer operators. One uses standard matrix- dependent prolongation operators from. The second uses {open_quotes}upwind{close_quotes} prolongation operators, developed. Both employ the Galerkin coarse grid approximation and an alternating zebra line Gauss-Seidel smoother. The third method is based on the block LU decomposition of a matrix and on an approximate Schur complement. This multigrid variant is presented in. All three multigrid algorithms are algebraic methods.
Singular perturbations and time scales in the design of digital flight control systems
Naidu, Desineni S.; Price, Douglas B.
1988-01-01
The results are presented of application of the methodology of Singular Perturbations and Time Scales (SPATS) to the control of digital flight systems. A block diagonalization method is described to decouple a full order, two time (slow and fast) scale, discrete control system into reduced order slow and fast subsystems. Basic properties and numerical aspects of the method are discussed. A composite, closed-loop, suboptimal control system is constructed as the sum of the slow and fast optimal feedback controls. The application of this technique to an aircraft model shows close agreement between the exact solutions and the decoupled (or composite) solutions. The main advantage of the method is the considerable reduction in the overall computational requirements for the evaluation of optimal guidance and control laws. The significance of the results is that it can be used for real time, onboard simulation. A brief survey is also presented of digital flight systems.
反应扩散方程的奇摄动%SINGULAR PERTURBATION FOR REACTION DIFFUSION EQUATIONS
Institute of Scientific and Technical Information of China (English)
莫嘉琪; 王辉; 朱江
2003-01-01
The singularly perturbed initial boundary value problems for reaction diffusion equations are considered. Under suitable conditions and by using the theory of differential inequality, the asymptotic behavior of solution for initial boundary value problems are studied, where the reduced problems possess two intersecting solutions.
奇摄动非线性边值问题%THE SINGULARLY PERTURBED NONLINEAR BOUNDARY VALUE PROBLEMS
Institute of Scientific and Technical Information of China (English)
莫嘉琪
2000-01-01
The singularly perturbed nonlinear boundary value problems are considered.Using the stretched variable and the method of boundary layer correction,the formal asymptotic expansion of solution is obtained.And then the uniform validity of solution is proved by using the differential inequalities.
Directory of Open Access Journals (Sweden)
Linfei Nie
2013-04-01
Full Text Available In this article, a singular perturbation is introduced to analyze the global asymptotic stability of positive equilibria of ratio-dependent predator-prey models with stage structure for the prey. We prove theoretical results and show numerically that the proposed approach is feasible and efficient.
Institute of Scientific and Technical Information of China (English)
王琴; 段梦兰; 李海明; 张庆元
2013-01-01
The maximum bending moment or curvature in the neighborhood of the touch down point (TDP) and the maximum tension at the top are two key parameters to be controlled during deepwater J-lay installation in order to ensure the safety of the pipe-laying operation and the normal operation of the pipelines. In this paper, the non-linear governing differential equation for getting the two parameters during J-lay installation is proposed and solved by use of singular perturbation technique, from which the asymptotic expression of stiffened catenary is obtained and the theoretical expression of its static geometric configuration as well as axial tension and bending moment is derived. Finite element results are applied to verify this method. Parametric investigation is conducted to analyze the influences of the seabed slope, unit weight, flexural stiffness, water depth, and the pipe-laying tower angle on the maximum tension and moment of pipeline by this method, and the results show how to control the installation process by changing individual parameters.
Averaging and Linear Programming in Some Singularly Perturbed Problems of Optimal Control
Energy Technology Data Exchange (ETDEWEB)
Gaitsgory, Vladimir, E-mail: vladimir.gaitsgory@mq.edu.au [Macquarie University, Department of Mathematics (Australia); Rossomakhine, Sergey, E-mail: serguei.rossomakhine@flinders.edu.au [Flinders University, Flinders Mathematical Sciences Laboratory, School of Computer Science, Engineering and Mathematics (Australia)
2015-04-15
The paper aims at the development of an apparatus for analysis and construction of near optimal solutions of singularly perturbed (SP) optimal controls problems (that is, problems of optimal control of SP systems) considered on the infinite time horizon. We mostly focus on problems with time discounting criteria but a possibility of the extension of results to periodic optimization problems is discussed as well. Our consideration is based on earlier results on averaging of SP control systems and on linear programming formulations of optimal control problems. The idea that we exploit is to first asymptotically approximate a given problem of optimal control of the SP system by a certain averaged optimal control problem, then reformulate this averaged problem as an infinite-dimensional linear programming (LP) problem, and then approximate the latter by semi-infinite LP problems. We show that the optimal solution of these semi-infinite LP problems and their duals (that can be found with the help of a modification of an available LP software) allow one to construct near optimal controls of the SP system. We demonstrate the construction with two numerical examples.
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Weiya Zhang
2014-01-01
Full Text Available An investigation on qualitative dynamics in a voltage-current dual-loop controlled flywheel energy storage system (FESS operating in discharge mode is presented in this paper, providing novel insights into the effect of two-timescale characteristics on the safety and stability of energy transmission of FESS. Based on singular perturbation theory, a two-timescale approach is proposed to separate the FESS into the fast and slow subsystems. Stability analysis of the transient fixed points confirms the effects of systemic parameters on FESS’s dynamics and indicates that the FESS shifts from the spiking state to the quiescent state when the slow variable crosses the bifurcation point of the fast subsystem. Mechanism analysis reveals that the root cause of the qualitative dynamics is the voltage instability of the FESS. Moreover, the feasibility boundaries of key parameters are derived, and application requirements of the proposed approach are also discussed, guiding the extension of the approach to engineering applications and solving the dynamics analysis problem to some extent at a theoretical analysis level. Constant voltage discharge experiment is performed based on the FESS test bench built in Key Laboratory of Smart Grid of Ministry of Education, Tianjin University, which validates the theoretical results.
Composite control of a class of nonlinear singularly perturbed discrete-time systems via D-SDRE
Zhang, Yan; Subbaram Naidu, D.; Cai, Chenxiao; Zou, Yun
2016-08-01
In this paper, the regulation problem of a class of nonlinear singularly perturbed discrete-time systems is investigated. Using the theory of singular perturbations and time scales, the nonlinear system is decoupled into reduced-order slow and fast (boundary layer) subsystems. Then, a composite controller consisting of two sub-controllers for the slow and fast subsystems is developed using the discrete-time state-dependent Riccati equation (D-SDRE). It is proved that the equilibrium point of the original closed-loop system with a composite controller is locally asymptotically stable. Moreover, the region of attraction of the closed-loop system is estimated by using linear matrix inequality. One example is given to illustrate the effectiveness of the results obtained.
Faye, Ibrahima; Seck, Diaraf
2009-01-01
In this paper we build models for short-term, mean-term and long-term dynamics of dune and megariple morphodynamics. They are models that are degenerated parabolic equations which are, moreover, singularly perturbed. We, then give an existence and uniqueness result for the short-term and mean-term models. This result is based on a time-space periodic solution existence result for degenerated parabolic equation that we set out. Finally the short-term model is homogenized.
Singularly Perturbed Elliptic Problems in the Case of Exchange of Stabilities
Butuzov, V. F.; Nefedov, N. N.; Schneider, K. R.
2001-01-01
We consider the singularly perturbed boundary value problem (Eɛ) ɛ2 Δu=f(u, x, ɛ) for x∈D, {∂u}/{∂n}-λ(x) u=0 for x∈Γ where D⊂R2 is an open bounded simply connected region with smooth boundary Γ, ɛ is a small positive parameter and ∂/∂n is the derivative along the inner normal of Γ. We assume that the degenerate problem (E0) f(u, x, 0)=0 has two solutions ϕ1(x) and ϕ2(x) intersecting in an smooth Jordan curve C located in D such that fu(ϕi(x), x, 0) changes its sign on C for i=1, 2 (exchange of stabilities). By means of the method of asymptotic lower and upper solutions we prove that for sufficiently small ɛ, problem (Eɛ) has at least one solution u(x, ɛ) satisfying α(x, ɛ)⩽u(x, ɛ)⩽β(x, ɛ) where the upper and lower solutions β(x, ɛ) and α(x, ɛ) respectively fulfil β(x, ɛ)-α(x, ɛ)=O(ɛ) for x in a δ-neighborhood of C where δ is any fixed positive number sufficiently small, while β(x, ɛ)-α(x, ɛ)=O(ɛ) for x∈DDδ. In case that f does not depend on ɛ these estimates can be improved. Applying this result to a special reaction system in a nonhomogeneous medium we prove that the reaction rate exhibits a spatial jumping behavior.
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Alberto Lastra
2012-01-01
in the complex domain which generalizes a previous result by Malek in (2011. First, we construct solutions defined in open q-spirals to the origin. By means of a q-Gevrey version of Malgrange-Sibuya theorem we show the existence of a formal power series in the perturbation parameter which turns out to be the q-Gevrey asymptotic expansion (of certain type of the actual solutions.
Quantifying Volume Changing Perturbations in a Wave Chaotic System
Taddese, Biniyam Tesfaye; Moglie, Franco; Antonsen, Thomas M; Ott, Edward; Anlage, Steven M
2012-01-01
A sensor was developed to quantitatively measure perturbations which change the volume of a wave chaotic cavity while leaving its shape intact. The sensors work in the time domain by using either scattering fidelity of the transmitted signals or the classical analog of the Loschmidt echo. The sensors were tested experimentally by inducing volume changing perturbations to a one cubic meter pseudo-integrable, real-world cavity. Perturbations which caused a volume change that is as small as 54 parts in a million were quantitatively measured. These results were obtained by using electromagnetic waves with a wavelength of about $5cm$, therefore, the sensor is sensitive to extreme sub-wavelength changes of the boundaries of a cavity. The experimental results were compared with Finite Difference Time Domain (FDTD) simulation results, and good agreement was found. Furthermore, the sensor was tested using a frequency domain approach on a numerical model of the star graph, which is a representative wave chaotic system....
Mohamed, Firdawati binti; Karim, Mohamad Faisal bin Abd
2015-10-01
Modelling physical problems in mathematical form yields the governing equations that may be linear or nonlinear for known and unknown boundaries. The exact solution for those equations may or may not be obtained easily. Hence we seek an analytical approximation solution in terms of asymptotic expansion. In this study, we focus on a singular perturbation in second order ordinary differential equations. Solutions to several perturbed ordinary differential equations are obtained in terms of asymptotic expansion. The aim of this work is to find an approximate analytical solution using the classical method of matched asymptotic expansion (MMAE). The Mathematica computer algebra system is used to perform the algebraic computations. The details procedures will be discussed and the underlying concepts and principles of the MMAE will be clarified. Perturbation problem for linear equation that occurs at one boundary and two boundary layers are discussed. Approximate analytical solution obtained for both cases are illustrated by graph using selected parameter by showing the outer, inner and composite solution separately. Then, the composite solution will be compare to the exact solution to show their accuracy by graph. By comparison, MMAE is found to be one of the best methods to solve singular perturbation problems in second order ordinary differential equation since the results obtained are very close to the exact solution.
Bighamian, Ramin; Hahn, Jin-Oh
2014-01-01
Arterial pulse pressure has been widely used as surrogate of stroke volume, for example, in the guidance of fluid therapy. However, recent experimental investigations suggest that arterial pulse pressure is not linearly proportional to stroke volume. However, mechanisms underlying the relation between the two have not been clearly understood. The goal of this study was to elucidate how arterial pulse pressure and stroke volume respond to a perturbation in the left ventricular blood volume based on a systematic mathematical analysis. Both our mathematical analysis and experimental data showed that the relative change in arterial pulse pressure due to a left ventricular blood volume perturbation was consistently smaller than the corresponding relative change in stroke volume, due to the nonlinear left ventricular pressure-volume relation during diastole that reduces the sensitivity of arterial pulse pressure to perturbations in the left ventricular blood volume. Therefore, arterial pulse pressure must be used with care when used as surrogate of stroke volume in guiding fluid therapy.
Institute of Scientific and Technical Information of China (English)
JIANG Zhina; MU Mu
2009-01-01
The authors apply the technique of conditional nonlinear optimal perturbations (CNOPs) as a means of providing initial perturbations for ensemble forecasting by using a barotropic quasi-gcostrophic (QG) model in a perfect-model scenario. Ensemble forecasts for the medium range (14 days) are made from the initial states perturbed by CNOPs and singular vectors (SVs). 13 different cases have been chosen when analysis error is a kind of fast growing error. Our experiments show that the introduction of CNOP provides better forecast skill than the SV method. Moreover, the spread-skill relationship reveals that the ensemble samples in which the first SV is replaced by CNOP appear supcrior to those obtained by SVs from day 6 to day 14. Rank diagrams are adopted to compare the new method with the SV approach. The results illustrate that the introduction of CNOP has higher reliability for medium-range ensemble forecasts.
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
On the basis of singular perturbation theory, a composite controlapproach is proposed for constrained flexible manipulators in this paper. The dynamics equation of a constrained two-link flexible manipulator is divided into slow-subsystem and fast-subsystem. Based on the adaptive theory, the slow controller is designed. For the fast subsystem, a robust optimal controller is presented. Under the slow time scale and the fast time scale, a composite control strategy is constructed. Some results of numerical simulations are presented to show the effectiveness of this design procedure.
Institute of Scientific and Technical Information of China (English)
Grigory I. Shishkin
2008-01-01
A boundary value problem is considered for a singularly perturbed parabolic convection-diffusion equation; we construct a finite difference scheme on a priori (se-quentially) adapted meshes and study its convergence. The scheme on a priori adapted meshes is constructed using a majorant function for the singular component of the discrete solution, which allows us to find a priori a subdomain where the computed solution requires a further improvement. This subdomain is defined by the perturbation parameter ε, the step-size of a uniform mesh in x, and also by the required accuracy of the discrete solution and the prescribed number of refinement iterations K for im-proving the solution. To solve the discrete problems aimed at the improvement of the solution, we use uniform meshes on the subdomains. The error of the numerical so-lution depends weakly on the parameter ε. The scheme converges almost ε-uniformly, precisely, under the condition N-1 = o(ev), where N denotes the number of nodes in the spatial mesh, and the value v=v(K) can be chosen arbitrarily small for suitable K.
Reconstructing the cosmic Horseshoe gravitational lens using the singular perturbative approach
Alard, C
2016-01-01
The cosmic horseshoe gravitational lens is analyzed using the perturbative approach. The two first order perturbative fields are expanded in Fourier series. The source is reconstructed using a fine adaptive grid. The expansion of the fields at order 2 produces a higher value of the chi-square. Expanding at order 3 provides a very significant improvement, while order 4 does not bring a significant improvement over order 3. The presence of the order 3 terms is not a consequence of limiting the perturbative expansion to the first order. The amplitude and signs of the third order terms are recovered by including the contribution of the other group members. This analysis demonstrates that the fine details of the potential of the lens could be recovered independently of any assumptions by using the perturbative approach.
Reconstructing the cosmic Horseshoe gravitational lens using the singular perturbative approach.
Alard, C.
2017-01-01
The reconstruction of the cosmic horseshoe gravitational lens using the perturbative method reveals the presence of significant third order terms. The presence of these higher order terms is apparent in the numerical expansion of the perturbative fields in Fourier series. The expansion of the fields at order 2 produces a higher value of the chi-square. Expanding at order 3 provides a very significant improvement, while order 4 does not bring a significant improvement over order 3. The presence of the order 3 terms is not a consequence of limiting the perturbative expansion to the first order. The amplitude and signs of the third order terms are recovered by including the contribution of the other group members. This analysis demonstrates that the fine details of the potential of the lens could be recovered independently of any initial assumptions by using the perturbative approach.
Directory of Open Access Journals (Sweden)
Andrei Perjan
2009-07-01
Full Text Available We study the behavior of solutions to perturbed second order abstract evolution equations in Hilbert spaces, when the small parameter, multiplying the second order time derivative, converges to zero.
Energy integral of the Stokes flow in a singularly perturbed exterior domain
Directory of Open Access Journals (Sweden)
Matteo Dalla Riva
2012-01-01
Full Text Available We consider a pair of domains \\(\\Omega ^b\\ and \\(\\Omega ^s\\ in \\(\\mathbb{R}^n\\ and we assume that the closure of \\(\\Omega ^b\\ does not intersect the closure of \\(\\epsilon \\Omega ^s\\ for \\(\\epsilon \\in (0,\\epsilon _0\\. Then for a fixed \\(\\epsilon \\in (0,\\epsilon_0\\ we consider a boundary value problem in \\(\\mathbb{R}^n \\setminus (\\Omega ^b \\cup \\epsilon \\Omega ^s\\ which describes the steady state Stokes flow of an incompressible viscous fluid past a body occupying the domain \\(\\Omega ^b\\ and past a small impurity occupying the domain \\(\\epsilon \\Omega ^s\\. The unknown of the problem are the velocity field \\(u\\ and the pressure field \\(p\\, and we impose the value of the velocity field \\(u\\ on the boundary both of the body and of the impurity. We assume that the boundary velocity on the impurity displays an arbitrarily strong singularity when \\(\\epsilon\\ tends to 0. The goal is to understand the behaviour of the strain energy of \\( (u, p\\ for \\(\\epsilon\\ small and positive. The methods developed aim at representing the limiting behaviour in terms of analytic maps and possibly singular but completely known functions of \\(\\epsilon\\, such as \\(\\epsilon ^{-1}\\, \\(\\log \\epsilon\\.
Analytical methods for an elliptic singular perturbation problem In a circle
Temme, N.M.
2007-01-01
We consider an elliptic perturbation problem in a circle by using the analytical solution that is given by a Fourier series with coefficients in terms of modified Bessel functions. By using saddle point methods we construct asymptotic approximations with respect to a small parameter. In particular
Analytical methods for an elliptic singular perturbation problem in a circle
Temme, N.M.
2006-01-01
We consider an elliptic perturbation problem in a circle by using the analytical solution that is given by a Fourier series with coefficients in terms of modified Bessel functions. By using saddle point methods we construct asymptotic approximations with respect to a small parameter. In particular w
Wang, Chengwen; Quan, Long; Zhang, Shijie; Meng, Hongjun; Lan, Yuan
2017-03-01
Hydraulic servomechanism is the typical mechanical/hydraulic double-dynamics coupling system with the high stiffness control and mismatched uncertainties input problems, which hinder direct applications of many advanced control approaches in the hydraulic servo fields. In this paper, by introducing the singular value perturbation theory, the original double-dynamics coupling model of the hydraulic servomechanism was reduced to a integral chain system. So that, the popular ADRC (active disturbance rejection control) technology could be directly applied to the reduced system. In addition, the high stiffness control and mismatched uncertainties input problems are avoided. The validity of the simplified model is analyzed and proven theoretically. The standard linear ADRC algorithm is then developed based on the obtained reduced-order model. Extensive comparative co-simulations and experiments are carried out to illustrate the effectiveness of the proposed method.
Robust Control of Uncertain Markov Jump Singularly Perturbed Systems%Markov跳变线性奇异摄动系统鲁棒H∞控制
Institute of Scientific and Technical Information of China (English)
刘华平; 孙富春; 李春文; 孙增圻
2005-01-01
In this paper, we study the robust control for uncertain Markov jump linear singularly perturbed systems (MJLSPS), whose transition probability matrix is unknown. An improved heuristic algorithm is proposed to solve the nonlinear matrix inequalities. The results of this paper can apply not only to standard, but also to nonstandard MJLSPS. Moreover, the proposed approach is independent of the perturbation parameter and therefore avoids the ill-conditioned numerical problems.
Shishkin, G. I.; Shishkina, L. P.
2009-05-01
The boundary value problem for the singularly perturbed reaction-diffusion parabolic equation in a ball in the case of spherical symmetry is considered. The derivatives with respect to the radial variable appearing in the equation are written in divergent form. The third kind boundary condition, which admits the Dirichlet and Neumann conditions, is specified on the boundary of the domain. The Laplace operator in the differential equation involves a perturbation parameter ɛ2, where ɛ takes arbitrary values in the half-open interval (0, 1]. When ɛ → 0, the solution of such a problem has a parabolic boundary layer in a neighborhood of the boundary. Using the integro-interpolational method and the condensing grid technique, conservative finite difference schemes on flux grids are constructed that converge ɛ-uniformly at a rate of O( N -2ln2 N + N {0/-1}), where N + 1 and N 0 + 1 are the numbers of the mesh points in the radial and time variables, respectively.
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
@@Suppose Rn, n = 2,3 be a smooth bounded domain, we consider the perturbed Navier-Stokes equationequation ut - ut - u + (u )u + p = F, in ,equationequation div u = 0, in ,equationequation u = 0, on .equation The study of this equation for = 0 has a long and richhistory. In the two-dimensional case, the study is very successful and it iswell known that the solutions of the equation define a C0-semigroupS(t): t 0 inthe space H = PL2() (where P is the projection onto the space ofdivergence-free vector fields) and which has a global attractor A0 on H(see ［1］). But, in the three-dimensional case, things are quitedifference, although some progress has been made recently,there are many problems still open, i.e., the global regularity of thesolutions and the existence of the global attractors (see ［1--7］ andthe references therein). The machanical background ofthe equation in the case of > 0 can be found in ［8］
PERTURBATION FINITE VOLUME METHOD FOR CONVECTIVE-DIFFUSION INTEGRAL EQUATION
Institute of Scientific and Technical Information of China (English)
GAO Zhi; YANG Guowei
2004-01-01
A perturbation finite volume (PFV) method for the convective-diffusion integral equation is developed in this paper. The PFV scheme is an upwind and mixed scheme using any higher-order interpolation and second-order integration approximations, with the least nodes similar to the standard three-point schemes, that is, the number of the nodes needed is equal to unity plus the face-number of the control volume. For instance, in the two-dimensional (2-D) case, only four nodes for the triangle grids and five nodes for the Cartesian grids are utilized, respectively. The PFV scheme is applied on a number of 1-D linear and nonlinear problems, 2-D and 3-D flow model equations. Comparing with other standard three-point schemes, the PFV scheme has much smaller numerical diffusion than the first-order upwind scheme (UDS). Its numerical accuracies are also higher than the second-order central scheme (CDS), the power-law scheme (PLS) and QUICK scheme.
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Wu Zuozhu
2013-01-01
Full Text Available A criterion based on the computational singular perturbation (CSP method is proposed in order to determine the number of quasi-steady state (QSS species. This criterion is employed for the reduction of a detailed chemical kinetics mechanism for the oxidation of dimethyl ether (DME, involving 55 species and 290 reactions, leading to a 20 steps reduced mechanism which involves 26 species. A software package, named I-CSP, was developed to make the reduction process algorithmic. Input to the I-CSP includes (i the detailed mechanism, (ii the numerical solution of the problem for a specific set of operating conditions, (iii the number of quasi steady state (QSS species. The resulting reduced mechanism was validated both in homogenous reactor, including auto-ignition and PSR, over a wide range of pressures and equivalence ratios, and in a one-dimensional, unstretched, premixed, laminar steady DME/Air flame. Comparison of the results calculated with the detailed and the reduced mechanisms shows excellent agreement in the case of homogenous reactor, but discrepancies can be observed in the case of the premixed laminar flame.
Institute of Scientific and Technical Information of China (English)
R. Mythili Priyadharshini; N. Ramanujam
2009-01-01
In this paper, a singularly perturbed Robin type boundary value problem for second-order ordinary differential equation with discontinuous convection coefficient and source term is considered. A robust-layer-resolving numerical method is proposed. An e-uniform global error estimate for the numerical solution and also to the numerical derivative are established. Numerical results are presented, which are in agreement with the theoretical predictions.AMS subject classifications: 65L10, CR G1.7
Institute of Scientific and Technical Information of China (English)
莫嘉琪
2006-01-01
A class of nonlinear nonlocal singularly perturbed Robin initial boundary value problems for reaction diffusion equations with boundary perturbation is considered. Under suitable conditions, firstly, the outer solution of the original problem is obtained; secondly, by using the stretched variable, the composing expansion method and the expanding theory of power series, the initial layer is constructed; and finally,by using the theory of differential inequalities the asymptotic behavior of solutions for initial boundary value problems is studied, and including some relational inequalities the existence and uniqueness of solutions for the original problem and the uniformly valid asymptotic estimation are discussed.
Plasma physics and environmental perturbation laboratory. Volume 1: Executive summary
1973-01-01
Space physics and plasma physics experiments that can be performed from the space shuttle were identified. Potential experiment concepts were analyzed to derive requirements for a spaceborne experiment facility. The laboratory, known as the Plasma Physics and Environmental Perturbation Laboratory consists of a 33-foot pallet of instruments connected to a 25-foot pressurized control module. Two 50-meter booms, two subsatellites, a high power transmitter, a multipurpose accelerator array, a set of deployable canisters, and a gimbaled instrument platform are the primary systems deployed from the pallet. The pressurized module contains all the control and display equipment required to conduct the experiments, and life support and power subsystems.
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Chi-Chang Wang
2013-09-01
Full Text Available This paper seeks to use the proposed residual correction method in coordination with the monotone iterative technique to obtain upper and lower approximate solutions of singularly perturbed non-linear boundary value problems. First, the monotonicity of a non-linear differential equation is reinforced using the monotone iterative technique, then the cubic-spline method is applied to discretize and convert the differential equation into the mathematical programming problems of an inequation, and finally based on the residual correction concept, complex constraint solution problems are transformed into simpler questions of equational iteration. As verified by the four examples given in this paper, the method proposed hereof can be utilized to fast obtain the upper and lower solutions of questions of this kind, and to easily identify the error range between mean approximate solutions and exact solutions.
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
. The singularly perturbed Robin boundary value problems for the semilinear elliptic equation are considered.Under suitable conditions and by using the fixed point theorem the existence,uniqueness and asymptotic behavior of solution for the boundary value problems are studied.Received:2000-10-07.
Institute of Scientific and Technical Information of China (English)
Linghai Zhang
2004-01-01
We establish the exponential stability of fast traveling pulse solutions to nonlinear singularly perturbedsystems of integral di.erential equations arising from neuronal networks. It has been proved that exponentialstability of these orbits is equivalent to linear stability. Let L be the linear di.erential operator obtainedby linearizing the nonlinear system about its fast pulse, and let σ(L) be the spectrum of L. The linearizedstability criterion says that if max{Reλ: λ∈σ(L), λ ≠ 0} ≤ .D, for some positive constant D, and λ = 0 is asimple eigenvalue of L(ε), then the stability follows immediately (see [13] and [37]). Therefore, to establish theexponential stability of the fast pulse, it su.ces to investigate the spectrum of the operator L. It is relativelyeasy to .nd the continuous spectrum, but it is very di.cult to .nd the isolated spectrum. The real part ofthe continuous spectrum has a uniformly negative upper bound, hence it causes no threat to the stability. Itremains to see if the isolated spectrum is safe.Eigenvalue functions (see [14] and [35,36]) have been a powerful tool to study the isolated spectrum of the associatedlinear di.erential operators because the zeros of the eigenvalue functions coincide with the eigenvaluesof the operators. There have been some known methods to de.ne eigenvalue functions for nonlinear systems ofreaction di.usion equations and for nonlinear dispersive wave equations. But for integral di.erential equations,we have to use di.erent ideas to construct eigenvalue functions. We will use the method of variation of parametersto construct the eigenvalue functions in the complex plane C. By analyzing the eigenvalue functions, we.nd that there are no nonzero eigenvalues of L in {λ∈ C: Reλ≥ .D} for the fast traveling pulse. Moreoverλ = 0 is simple. This implies that the exponential stability of the fast orbits is true.
Singularities and Closed String Tachyons
Silverstein, E
2006-01-01
A basic problem in gravitational physics is the resolution of spacetime singularities where general relativity breaks down. The simplest such singularities are conical singularities arising from orbifold identifications of flat space, and the most challenging are spacelike singularities inside black holes (and in cosmology). Topology changing processes also require evolution through classically singular spacetimes. I briefly review how a phase of closed string tachyon condensate replaces, and helps to resolve, basic singularities of each of these types. Finally I discuss some interesting features of singularities arising in the small volume limit of compact negatively curved spaces and the emerging zoology of spacelike singularities.
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...
Beljadid, Abdelaziz; Mohammadian, Abdolmajid; Qiblawey, Hazim
2016-10-01
The discretization of the shallow water system on unstructured grids can lead to spurious modes which usually can affect accuracy and/or cause stability problems. This paper introduces a new approach for stability analysis of unstructured linear finite volume schemes for linear shallow water equations with the Coriolis Effect using spectra, pseudospectra, and singular value decomposition. The discrete operator of the scheme is the principal parameter used in the analysis. It is shown that unstructured grids have a large influence on operator normality. In some cases the eigenvectors of the operator can be far from orthogonal, which leads to amplification of solutions and/or stability problems. Large amplifications of the solution can be observed, even for discrete operators which respect the condition of asymptotic stability, and in some cases even for Lax-Richtmyer stable methods. The pseudospectra are shown to be efficient for the verification of stability of finite volume methods for linear shallow water equations. In some cases, the singular value decomposition is employed for further analysis in order to provide more information about the existence of unstable modes. The results of the analysis can be helpful in choosing the type of mesh, the appropriate placements of the variables of the system on the grid, and the suitable discretization method which is stable for a wide range of modes.
Institute of Scientific and Technical Information of China (English)
李惠芳; 包立平
2015-01-01
A stochastic volatility model for a class of electricity Asian option pricing problem is discussed in this paper .The volatility of the model adopts the fast stochastic volatility mean reversion model .By using Feynman-Kac's formula , it turns out the Black-Scholes model in which the risky asserts of electricity Asian option prices .The asymptotic solution to its Black-Scholes equation with the singular perturbation method is obtained .%讨论了一类电力亚式期权定价问题的随机波动率模型，其中随机波动率采用了快速均值回归的随机波动率模型。通过Feynman-Kac公式，得出了风险资产电力亚式期权价格所应满足的Black-Sholes模型，运用奇摄动渐近展开方法，得到了Black-Sholes方程的渐近解。
Bobodzhanov, A. A.; Safonov, V. F.
2016-04-01
We consider an algorithm for constructing asymptotic solutions regularized in the sense of Lomov (see [1], [2]). We show that such problems can be reduced to integro-differential equations with inverse time. But in contrast to known papers devoted to this topic (see, for example, [3]), in this paper we study a fundamentally new case, which is characterized by the absence, in the differential part, of a linear operator that isolates, in the asymptotics of the solution, constituents described by boundary functions and by the fact that the integral operator has kernel with diagonal degeneration of high order. Furthermore, the spectrum of the regularization operator A(t) (see below) may contain purely imaginary eigenvalues, which causes difficulties in the application of the methods of construction of asymptotic solutions proposed in the monograph [3]. Based on an analysis of the principal term of the asymptotics, we isolate a class of inhomogeneities and initial data for which the exact solution of the original problem tends to the limit solution (as \\varepsilon\\to+0) on the entire time interval under consideration, also including a boundary-layer zone (that is, we solve the so-called initialization problem). The paper is of a theoretical nature and is designed to lead to a greater understanding of the problems in the theory of singular perturbations. There may be applications in various applied areas where models described by integro-differential equations are used (for example, in elasticity theory, the theory of electrical circuits, and so on).
Ju, Jinyong; Li, Wei; Wang, Yuqiao; Fan, Mengbao; Yang, Xuefeng
2016-01-01
Effective feedback control requires all state variable information of the system. However, in the translational flexible-link manipulator (TFM) system, it is unrealistic to measure the vibration signals and their time derivative of any points of the TFM by infinite sensors. With the rigid-flexible coupling between the global motion of the rigid base and the elastic vibration of the flexible-link manipulator considered, a two-time scale virtual sensor, which includes the speed observer and the vibration observer, is designed to achieve the estimation for the vibration signals and their time derivative of the TFM, as well as the speed observer and the vibration observer are separately designed for the slow and fast subsystems, which are decomposed from the dynamic model of the TFM by the singular perturbation. Additionally, based on the linear-quadratic differential games, the observer gains of the two-time scale virtual sensor are optimized, which aims to minimize the estimation error while keeping the observer stable. Finally, the numerical calculation and experiment verify the efficiency of the designed two-time scale virtual sensor. PMID:27801840
Ju, Jinyong; Li, Wei; Wang, Yuqiao; Fan, Mengbao; Yang, Xuefeng
2016-10-28
Effective feedback control requires all state variable information of the system. However, in the translational flexible-link manipulator (TFM) system, it is unrealistic to measure the vibration signals and their time derivative of any points of the TFM by infinite sensors. With the rigid-flexible coupling between the global motion of the rigid base and the elastic vibration of the flexible-link manipulator considered, a two-time scale virtual sensor, which includes the speed observer and the vibration observer, is designed to achieve the estimation for the vibration signals and their time derivative of the TFM, as well as the speed observer and the vibration observer are separately designed for the slow and fast subsystems, which are decomposed from the dynamic model of the TFM by the singular perturbation. Additionally, based on the linear-quadratic differential games, the observer gains of the two-time scale virtual sensor are optimized, which aims to minimize the estimation error while keeping the observer stable. Finally, the numerical calculation and experiment verify the efficiency of the designed two-time scale virtual sensor.
Ullmann, R Thomas; Ullmann, G Matthias
2011-01-27
We present a generalized free energy perturbation theory that is inspired by Monte Carlo techniques and based on a microstate description of a transformation between two states of a physical system. It is shown that the present free energy perturbation theory stated by the Zwanzig equation follows as a special case of our theory. Our method uses a stochastic mapping of the end states that associates a given microstate from one ensemble with a microstate from the adjacent ensemble according to a probability distribution. In contrast, previous free energy perturbation methods use a static, deterministic mapping that associates fixed pairs of microstates from the two ensembles. The advantages of our approach are that end states of differing configuration space volume can be treated easily also in the case of discrete configuration spaces and that the method does not require the potentially cumbersome search for an optimal deterministic mapping. The application of our theory is illustrated by some example problems. We discuss practical applications for which our findings could be relevant and point out perspectives for further development of the free energy perturbation theory.
Neural Excitability and Singular Bifurcations.
De Maesschalck, Peter; Wechselberger, Martin
2015-12-01
We discuss the notion of excitability in 2D slow/fast neural models from a geometric singular perturbation theory point of view. We focus on the inherent singular nature of slow/fast neural models and define excitability via singular bifurcations. In particular, we show that type I excitability is associated with a novel singular Bogdanov-Takens/SNIC bifurcation while type II excitability is associated with a singular Andronov-Hopf bifurcation. In both cases, canards play an important role in the understanding of the unfolding of these singular bifurcation structures. We also explain the transition between the two excitability types and highlight all bifurcations involved, thus providing a complete analysis of excitability based on geometric singular perturbation theory.
The volume conjecture, perturbative knot invariants, and recursion relations for topological strings
Dijkgraaf, Robbert; Fuji, Hiroyuki; Manabe, Masahide
2011-08-01
We study the relation between perturbative knot invariants and the free energies defined by topological string theory on the character variety of the knot. Such a correspondence between SL(2;C) Chern-Simons gauge theory and the topological open string theory was proposed earlier on the basis of the volume conjecture and AJ conjecture. In this paper we discuss this correspondence beyond the subleading order in the perturbative expansion on both sides. In the computation of the perturbative invariants for the hyperbolic 3-manifold, we adopt the state integral model for the hyperbolic knots, and the factorized AJ conjecture for the torus knots. On the other hand, we iteratively compute the free energies on the character variety using the Eynard-Orantin topological recursion relation. We discuss the correspondence for the figure eight knot complement and the once punctured torus bundle over S with the monodromy LR up to the fifth order. For the torus knots, we find trivial the recursion relations on both sides.
The volume conjecture, perturbative knot invariants, and recursion relations for topological strings
Energy Technology Data Exchange (ETDEWEB)
Dijkgraaf, Robbert, E-mail: r.h.dijkgraaf@uva.n [Institute for Theoretical Physics and KdV Institute for Mathematics, University of Amsterdam, Spui 21, 1012 WX Amsterdam (Netherlands); Fuji, Hiroyuki, E-mail: fuji@th.phys.nagoya-u.ac.j [Department of Physics, Nagoya University, Nagoya 464-8602 (Japan); Manabe, Masahide, E-mail: d07002p@math.nagoya-u.ac.j [Graduate School of Mathematics, Nagoya University, Nagoya 464-8602 (Japan)
2011-08-01
We study the relation between perturbative knot invariants and the free energies defined by topological string theory on the character variety of the knot. Such a correspondence between SL(2;C) Chern-Simons gauge theory and the topological open string theory was proposed earlier on the basis of the volume conjecture and AJ conjecture. In this paper we discuss this correspondence beyond the subleading order in the perturbative expansion on both sides. In the computation of the perturbative invariants for the hyperbolic 3-manifold, we adopt the state integral model for the hyperbolic knots, and the factorized AJ conjecture for the torus knots. On the other hand, we iteratively compute the free energies on the character variety using the Eynard-Orantin topological recursion relation. We discuss the correspondence for the figure eight knot complement and the once punctured torus bundle over S{sup 1} with the monodromy L{sup 2}R up to the fifth order. For the torus knots, we find trivial the recursion relations on both sides.
The Volume Conjecture, Perturbative Knot Invariants, and Recursion Relations for Topological Strings
Dijkgraaf, Robbert; Manabe, Masahide
2010-01-01
We study the relation between perturbative knot invariants and the free energies defined by topological string theory on the character variety of the knot. Such a correspondence between SL(2;C) Chern-Simons gauge theory and the topological open string theory was proposed earlier on the basis of the volume conjecture and AJ conjecture. In this paper we discuss this correspondence beyond the subleading order in the perturbative expansion on both sides. In the computation of the perturbative invariants for the hyperbolic 3-manifold, we adopt the state integral model for the hyperbolic knots, and the factorized AJ conjecture for the torus knots. On the other hand, we iteratively compute the free energies on the character variety using the Eynard-Orantin topological recursion relation. We check the correspondence for the figure eight knot complement and the once punctured torus bundle over S^1 with the holonomy L^2R up to the fourth order. For the torus knots, we find trivial the recursion relations on both sides.
Halyo, Edi
2009-01-01
We describe solitons that live on the world--volumes of D5 branes wrapped on deformed $A_2$ singularities fibered over $C(x)$. We show that monopoles are D3 branes wrapped on a node of the deformed singularity and stretched along $C(x)$. F and D--term strings are D3 branes wrapped on a node of a singularity that is deformed and resolved respectively. Domain walls require deformed $A_3$ singularities and correspond to D5 branes wrapped on a node and stretched along $C(x)$.
Sasmita, Yoga; Darmawan, Gumgum
2017-08-01
This research aims to evaluate the performance of forecasting by Fourier Series Analysis (FSA) and Singular Spectrum Analysis (SSA) which are more explorative and not requiring parametric assumption. Those methods are applied to predicting the volume of motorcycle sales in Indonesia from January 2005 to December 2016 (monthly). Both models are suitable for seasonal and trend component data. Technically, FSA defines time domain as the result of trend and seasonal component in different frequencies which is difficult to identify in the time domain analysis. With the hidden period is 2,918 ≈ 3 and significant model order is 3, FSA model is used to predict testing data. Meanwhile, SSA has two main processes, decomposition and reconstruction. SSA decomposes the time series data into different components. The reconstruction process starts with grouping the decomposition result based on similarity period of each component in trajectory matrix. With the optimum of window length (L = 53) and grouping effect (r = 4), SSA predicting testing data. Forecasting accuracy evaluation is done based on Mean Absolute Percentage Error (MAPE), Mean Absolute Error (MAE) and Root Mean Square Error (RMSE). The result shows that in the next 12 month, SSA has MAPE = 13.54 percent, MAE = 61,168.43 and RMSE = 75,244.92 and FSA has MAPE = 28.19 percent, MAE = 119,718.43 and RMSE = 142,511.17. Therefore, to predict volume of motorcycle sales in the next period should use SSA method which has better performance based on its accuracy.
Directory of Open Access Journals (Sweden)
Antonio SANDU
2016-12-01
Full Text Available We are at a point in the creative evolution of humanity in which we can see the dawn of a new type of consciousness and of self-awareness that would provoke humanity to a redefinition of itself: Artificial Intelligence. The moment of the emergence of self-aware artificial intelligence, whose computing capacity exceeds the human power is defined as Technological Singularity. The volume Filosofia singularităţii. Creierul global, o etică a gândirii fără om [Philosophy of singularity. Global brain, an ethics of thinking without the human] published by Eikon Publishing House in 2016, is a first attempt in philosophy and the Romanian culture of philosophizing on the technology of artificial intelligence, with particular reference to the technological singularity.
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.
Sitohang, Yosep Oktavianus; Darmawan, Gumgum
2017-08-01
This research attempts to compare between two forecasting models in time series analysis for predicting the sales volume of motorcycle in Indonesia. The first forecasting model used in this paper is Autoregressive Fractionally Integrated Moving Average (ARFIMA). ARFIMA can handle non-stationary data and has a better performance than ARIMA in forecasting accuracy on long memory data. This is because the fractional difference parameter can explain correlation structure in data that has short memory, long memory, and even both structures simultaneously. The second forecasting model is Singular spectrum analysis (SSA). The advantage of the technique is that it is able to decompose time series data into the classic components i.e. trend, cyclical, seasonal and noise components. This makes the forecasting accuracy of this technique significantly better. Furthermore, SSA is a model-free technique, so it is likely to have a very wide range in its application. Selection of the best model is based on the value of the lowest MAPE. Based on the calculation, it is obtained the best model for ARFIMA is ARFIMA (3, d = 0, 63, 0) with MAPE value of 22.95 percent. For SSA with a window length of 53 and 4 group of reconstructed data, resulting MAPE value of 13.57 percent. Based on these results it is concluded that SSA produces better forecasting accuracy.
Correlators of left charges and weak operators in finite volume chiral perturbation theory
Hernández, Pilar; Laine, Mikko
2003-01-01
We compute the two-point correlator between left-handed flavour charges, and the three-point correlator between two left-handed charges and one strangeness violating DeltaI = 3/2 weak operator, at next-to-leading order in finite volume SU(3)L × SU(3)R chiral perturbation theory, in the so-called epsilon-regime. Matching these results with the corresponding lattice measurements would in principle allow to extract the pion decay constant F, and the effective chiral theory parameter g27, which determines the Delta I = 3/2 amplitude of the weak decays K to pipi as well as the kaon mixing parameter BK in the chiral limit. We repeat the calculations in the replica formulation of quenched chiral perturbation theory, finding only mild modifications. In particular, a properly chosen ratio of the three-point and two-point functions is shown to be identical in the full and quenched theories at this order.
Volume and expansivity changes of micelle formation measured by pressure perturbation calorimetry.
Fan, Helen Y; Nazari, Mozhgan; Chowdhury, Saria; Heerklotz, Heiko
2011-03-01
We present the application of pressure perturbation calorimetry (PPC) as a new method for the volumetric characterization of the micelle formation of surfactants. The evaluation is realized by a global fit of PPC curves at different surfactant concentration ranging, if possible, from below to far above the CMC. It is based on the knowledge of the temperature dependence of the CMC, which can for example be characterized by isothermal titration calorimetry. We demonstrate the new approach for decyl-β-maltopyranoside (DM). It shows a strong volume increase upon micelle formation of 16 ± 2.5 mL/mol (+4%) at 25 °C, and changes with temperature by -0.1 mL/(mol K). The apparent molar expansivity (E(S)) decreases upon micelle formation from 0.44 to 0.31 mL/(mol K) at 25 °C. Surprisingly, the temperature dependence of the expansivity of DM in solution (as compared with that of maltose) does not agree with the principal behavior described for polar (E(S)(T) decreasing) and hydrophobic (E(S)(T) increasing) solutes or moieties before. The results are discussed in terms of changes in hydration of the molecules and internal packing of the micelles and compared with the volumetric effects of transitions of proteins, DNA, lipids, and polymers.
Elitzur, Shmuel; Rabinovici, Eliezer; Elitzur, Shmuel; Giveon, Amit; Rabinovici, Eliezer
2003-01-01
Big bang/crunch curvature singularities in exact CFT string backgrounds can be removed by turning on gauge fields. This is described within a family of {SL(2)xSU(2)xU(1)_x}/{U(1)xU(1)} quotient CFTs. Uncharged incoming wavefunctions from the ``whiskers'' of the extended universe can be fully reflected if and only if a big bang/crunch curvature singularity, from which they are scattered, exists. Extended BTZ-like singularities remain as long as U(1)_x is compact.
Belinski, V
2009-01-01
The talk at international conference in honor of Ya. B. Zeldovich 95th Anniversary, Minsk, Belarus, April 2009. The talk represents a review of the old results and contemporary development on the problem of cosmological singularity.
Geometric Hamiltonian structures and perturbation theory
Energy Technology Data Exchange (ETDEWEB)
Omohundro, S.
1984-08-01
We have been engaged in a program of investigating the Hamiltonian structure of the various perturbation theories used in practice. We describe the geometry of a Hamiltonian structure for non-singular perturbation theory applied to Hamiltonian systems on symplectic manifolds and the connection with singular perturbation techniques based on the method of averaging.
Abelian Vortices with Singularities
Baptista, J M
2012-01-01
Let L --> X be a complex line bundle over a compact connected Riemann surface. We consider the abelian vortex equations on L when the metric on the surface has finitely many point degeneracies or conical singularities and the line bundle has parabolic structure. These conditions appear naturally in the study of vortex configurations with constraints, or configurations invariant under the action of a finite group. We first show that the moduli space of singular vortex solutions is the same as in the regular case. Then we compute the total volume and total scalar curvature of the moduli space singular vortex solutions. These numbers differ from the case of regular vortices by a very natural term. Finally we exhibit explicit non-trivial vortex solutions over the thrice punctured hyperbolic sphere.
Valley Singularities and Baryon Number Violation
Provero, P
1994-01-01
We consider the valley--method computation of the inclusive cross section of baryon number violating processes in the Standard Model. We show that any physically correct model of the valley action should present a singularity in the saddle point valley parameters as functions of the energy of the process. This singularity prevents the saddle point configuration from collapsing into the perturbative vacuum.
Chiral Perturbation Theory at Finite Volume and/or with Twisted Boundary Conditions
Bijnens, Johan
2016-01-01
In this talk we discuss a number of ChPT calculations relevant for lattice QCD. These include the finite volume corrections at two-loop order for masses and decay constants. The second part is about hadronic vacuum polarization where we present the two-loop ChPT estimate for the disconnected and strange quark contributions. We also present the finite volume corrections at two-loop order. The final part is the one-loop finite volume with twisted boundary conditions contribution to $f_+(q^2)$ and the full $K_{\\ell3}$ amplitude
Pindza, Edson; Maré, Eben
2017-03-01
A modified discrete singular convolution method is proposed. The method is based on the single (SE) and double (DE) exponential transformation to speed up the convergence of the existing methods. Numerical computations are performed on a wide variety of singular boundary value and singular perturbed problems in one and two dimensions. The obtained results from discrete singular convolution methods based on single and double exponential transformations are compared with each other, and with the existing methods too. Numerical results confirm that these methods are considerably efficient and accurate in solving singular and regular problems. Moreover, the method can be applied to a wide class of nonlinear partial differential equations.
Institute of Scientific and Technical Information of China (English)
耿发展
2015-01-01
A numerical method is proposed for solving singularly perturbed turning point problems exhibiting twin boundary layers based on the reproducing kernel method. Firstly, the original problem is reformulated as a new boundary value problem whose solution does not change rapidly via a proper transformation. Then the repro?ducing kernel method is employed to solve the boundary value new problem. Numerical results show that the present method can provide very accurate analytical approximate solutions.%基于再生核理论,提出了求解具有两个边界层的奇异摄动转向点问题的数值方法. 首先通过一个合适的变量变换,把原问题转化成不再具有边界层的边值问题,转化后的边值问题通过再生核方法进行求解,数值算例的结果表明该方法是有效的.
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.
Perturbative results for two and three particle threshold energies in finite volume
Hansen, Maxwell T
2016-01-01
We calculate the energy of the state closest to threshold for two and three identical, spinless particles confined to a cubic spatial volume with periodic boundary conditions and with zero total momentum in the finite-volume frame. The calculation is performed in relativistic quantum field theory with particles coupled via a $\\lambda \\phi^4$ interaction, and we work through order $\\lambda^3$. The energy shifts begin at ${\\cal O}(1/L^3)$, and we keep subleading terms proportional to $1/L^4$, $1/L^5$ and $1/L^6$. These terms allow a non-trivial check of the results obtained from quantization conditions that hold for arbitrary interactions, namely that of L\\"uscher for two particles and our recently developed formalism for three particles. We also compare to previously obtained results based on non-relativistic quantum mechanics.
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
Stable computation of generalized singular values
Energy Technology Data Exchange (ETDEWEB)
Drmac, Z.; Jessup, E.R. [Univ. of Colorado, Boulder, CO (United States)
1996-12-31
We study floating-point computation of the generalized singular value decomposition (GSVD) of a general matrix pair (A, B), where A and B are real matrices with the same numbers of columns. The GSVD is a powerful analytical and computational tool. For instance, the GSVD is an implicit way to solve the generalized symmetric eigenvalue problem Kx = {lambda}Mx, where K = A{sup {tau}}A and M = B{sup {tau}}B. Our goal is to develop stable numerical algorithms for the GSVD that are capable of computing the singular value approximations with the high relative accuracy that the perturbation theory says is possible. We assume that the singular values are well-determined by the data, i.e., that small relative perturbations {delta}A and {delta}B (pointwise rounding errors, for example) cause in each singular value {sigma} of (A, B) only a small relative perturbation {vert_bar}{delta}{sigma}{vert_bar}/{sigma}.
Holley-Bockelmann, Kelly; Sinha, Manodeep
2012-01-01
We explore structure formation in the dark ages ($z\\sim 30-6$) using two well-known methods for initializing cosmological $N$-body simulations. Overall, both the Zel'dovich approximation (\\za) and second order Lagrangian perturbation theory (\\lpt) are known to produce accurate present-day dark matter halo mass functions. However, since the \\lpt method drives more rapid evolution of dense regions, it increases the occurrence of rare massive objects -- an effect that is most pronounced at high redshift. We find that \\lpt produces more halos that could harbor Population III stars and their black hole remnants, and they produce them earlier. Although the differences between the \\lpt and \\za mass functions are nearly erased by $z=6$, this small boost to the number and mass of black holes more than doubles the reionized volume of the early Universe. We discuss the implications for reionization and massive black hole growth.
Homogeneous spacelike singularities inside spherical black holes
Burko, L M
1997-01-01
Recent numerical simulations have found that the Cauchy horizon inside spherical charged black holes, when perturbed nonlinearly by a self-gravitating, minimally-coupled, massless, spherically-symmetric scalar field, turns into a null weak singularity which focuses monotonically to $r=0$ at late times, where the singularity becomes spacelike. Our main objective is to study this spacelike singularity. We study analytically the spherically-symmetric Einstein-Maxwell-scalar equations asymptotically near the singularity. We obtain a series-expansion solution for the metric functions and for the scalar field near $r=0$ under the simplifying assumption of homogeneity. Namely, we neglect spatial derivatives and keep only temporal derivatives. We find that there indeed exists a generic spacelike singularity solution for these equations (in the sense that the solution depends on enough free parameters), with similar properties to those found in the numerical simulations. This singularity is strong in the Tipler sense,...
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.
Topological resolution of gauge theory singularities
Saracco, Fabio; Torroba, Gonzalo
2013-01-01
Some gauge theories with Coulomb branches exhibit singularities in perturbation theory, which are usually resolved by nonperturbative physics. In string theory this corresponds to the resolution of timelike singularities near the core of orientifold planes by effects from F or M theory. We propose a new mechanism for resolving Coulomb branch singularities in three dimensional gauge theories, based on Chern-Simons interactions. This is illustrated in a supersymmetric SU(2) Yang-Mills-Chern-Simons theory. We calculate the one loop corrections to the Coulomb branch of this theory and find a result that interpolates smoothly between the high energy metric (that would exhibit the singularity) and a regular singularity-free low energy result. We suggest possible applications to singularity resolution in string theory and speculate a relationship to a similar phenomenon for the orientifold six-plane in massive IIA supergravity.
On Type I Singularities in Ricci flow
Enders, Joerg; Topping, Peter M
2010-01-01
We define several notions of singular set for Type I Ricci flows and show that they all coincide. In order to do this, we prove that blow-ups around singular points converge to nontrivial gradient shrinking solitons, thus extending work of Naber. As a by-product we conclude that the volume of a finite-volume singular set vanishes at the singular time. We also define a notion of density for Type I Ricci flows and use it to prove a regularity theorem reminiscent of White's partial regularity result for mean curvature flow.
Energy Technology Data Exchange (ETDEWEB)
Butz, T. [Leipzig Univ. (Germany). Faculty of Physics and Earth Sciences
2012-07-01
Various TiO{sub 2} nanomaterials with primary particle sizes well below 10 nm and TiO{sub 2} nanotubes with the anatase structure were studied via the nuclear quadrupole interaction (NQI) of {sup 44}Ti(EC){sup 44}Sc by time differential perturbed angular correlation. In general two different NQIs were observed, the lower one attributed to the volume fraction because of the similarity to bulk values and the higher one to probes closest to the surface. Rather broad distributions of the strength of the interaction were observed which were different for nominally identical particles, contrary to the axial symmetry which is preserved to a very large extent. These distributions are interpreted as disorder arising from surface tension. These complications affect the interaction between these nanomaterials with biological systems and the environment and render toxicological assessments problematic. Dissolution studies in a synthetic body fluid mimicking blood plasma at 37 C for 4 weeks exhibited a very low solubility, but surprisingly slight changes in the volume fraction, probably due to surface adsorbates. (orig.)
Nonexplicit Singular Perturbations and Interconnected Systems.
1982-09-01
34 Econometrica, Vol. 29, pp. 111-138, 1963. 47. A. N. Michel and R. K. Miller, Qualitative Analysis of Large Scale Dynamical Systems, Academic Press...Illinois, 1977. 100 56. N. R. Sandell , Jr., P. Varaiya, M. Athans, and M. G. Safonov, "Survey of Decentralized Control Methods for Large Scale Systems
Nonlinear singular vectors and nonlinear singular values
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
A novel concept of nonlinear singular vector and nonlinear singular value is introduced, which is a natural generalization of the classical linear singular vector and linear singular value to the nonlinear category. The optimization problem related to the determination of nonlinear singular vectors and singular values is formulated. The general idea of this approach is demonstrated by a simple two-dimensional quasigeostrophic model in the atmospheric and oceanic sciences. The advantage and its applications of the new method to the predictability, ensemble forecast and finite-time nonlinear instability are discussed. This paper makes a necessary preparation for further theoretical and numerical investigations.
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...
Singularity analysis: theory and further developments
Cheng, Qiuming
2015-04-01
Since the concept of singularity and local singularity analysis method (LSA) were originally proposed by the author for characterizing the nonlinear property of hydrothermal mineralization processes, the local singularity analysis technique has been successfully applied for identification of geochemical and geophysical anomalies related to various types of mineral deposits. It has also been shown that the singularity is the generic property of singular geo-processes which result in anomalous amounts of energy release or material accumulation within a narrow spatial-temporal interval. In the current paper we introduce several new developments about singularity analysis. First is a new concept of 'fractal density' which describes the singularity of complex phenomena of fractal nature. While the ordinary density possesses a unit of ratio of mass and volume (e.g. g/cm3, kg/m3) or ratio of energy over volume or time (e.g. J/cm3, w/L3, w/s), the fractal density has a unit of ratio of mass over fractal set or energy over fractal set (e.g. g/cmα, kg/mα, J/ mα, w/Lα, where α can be a non-integer). For the matter with fractal density (a non-integer α), the ordinary density of the phenomena (mass or energy) no longer exists and depicts singularity. We demonstrate that most of extreme geo-processes occurred in the earth crust originated from cascade earth dynamics (mental convection, plate tectonics, orogeny and weathering etc) may cause fractal density of mass accumulation or energy release. The examples to be used to demonstrate the concepts of fractal density and singularity are earthquakes, floods, volcanos, hurricanes, heat flow over oceanic ridge, hydrothermal mineralization in orogenic belt, and anomalies in regolith over mine caused by ore and toxic elements vertical migration. Other developments of singularity theory and methodologies including singular Kriging and singularity weights of evidence model for information integration will also be introduced.
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.
Exact invariants and adiabatic invariants of the singular Lagrange system
Institute of Scientific and Technical Information of China (English)
陈向炜; 李彦敏
2003-01-01
Based on the theory of symmetries and conserved quantities of the singular Lagrange system,the perturbations to the symmetries and adiabatic invariants of the singular Lagrange systems are discussed.Firstly,the concept of higher-order adiabatic invariants of the singular Lagrange system is proposed.Then,the conditions for the existence of the exact invariants and adiabatic invariants are proved,and their forms are given.Finally,an example is presented to illustrate these results.
Statistical analysis of effective singular values in matrix rank determination
Konstantinides, Konstantinos; Yao, Kung
1988-01-01
A major problem in using SVD (singular-value decomposition) as a tool in determining the effective rank of a perturbed matrix is that of distinguishing between significantly small and significantly large singular values to the end, conference regions are derived for the perturbed singular values of matrices with noisy observation data. The analysis is based on the theories of perturbations of singular values and statistical significance test. Threshold bounds for perturbation due to finite-precision and i.i.d. random models are evaluated. In random models, the threshold bounds depend on the dimension of the matrix, the noisy variance, and predefined statistical level of significance. Results applied to the problem of determining the effective order of a linear autoregressive system from the approximate rank of a sample autocorrelation matrix are considered. Various numerical examples illustrating the usefulness of these bounds and comparisons to other previously known approaches are given.
Non-Singular Bouncing Cosmology: Consistency of the Effective Description
Koehn, Michael; Ovrut, Burt
2015-01-01
We explicitly confirm that spatially flat non-singular bouncing cosmologies make sense as effective theories. The presence of a non-singular bounce in a spatially flat universe implies a temporary violation of the null energy condition, which can be achieved through a phase of ghost condensation. We calculate the scale of strong coupling and demonstrate that the ghost-condensate bounce remains trustworthy throughout, and that all perturbation modes within the regime of validity of the effective description remain under control. For this purpose we require the perturbed action up to third order in perturbations, which we calculate in both flat and co-moving gauge -- since these two gauges allow us to highlight different physical aspects. Our conclusion is that there exist healthy descriptions of non-singular bouncing cosmologies providing a viable resolution of the big-bang singularities in cosmological models. Our results also suggest a variant of ekpyrotic cosmology, in which entropy perturbations are genera...
Bali, Gunnar S; Pineda, Antonio
2014-01-01
Using numerical stochastic perturbation theory, we determine the first 35 infinite volume coefficients of the perturbative expansion in powers of the strong coupling constant $\\alpha$ of the plaquette in SU(3) gluodynamics. These coefficients are obtained in lattice regularization with the standard Wilson gauge action. The on-set of the dominance of the dimension four renormalon associated to the gluon condensate is clearly observed. We determine the normalization of the corresponding singularity in the Borel plane and convert this into the $\\overline{\\mathrm{MS}}$ scheme. We also comment on the impact of the renormalon on non-perturbative determinations of the gluon condensate.
Mariwalla, K H
2002-01-01
Basis and limitations of singularity theorems for Gravity are examined. As singularity is a critical situation in course of time, study of time paths, in full generality of Equivalence principle, provides two mechanisms to prevent singularity. Resolution of singular Time translation generators into space of its orbits, and essential higher dimensions for Relativistic particle interactions has facets to resolve any real singularity problem. Conceptually, these varied viewpoints have a common denominator: arbitrariness in the definition of `energy' intrinsic to the space of operation in each case, so as to render absence of singularity a tautology for self-consistency of the systems.
Resolution of quantum singularities
Konkowski, Deborah; Helliwell, Thomas
2017-01-01
A review of quantum singularities in static and conformally static spacetimes is given. A spacetime is said to be quantum mechanically non-singular if a quantum wave packet does not feel, in some sense, the presence of a singularity; mathematically, this means that the wave operator is essentially self-adjoint on the space of square integrable functions. Spacetimes with classical mild singularities (quasiregular ones) to spacetimes with classical strong curvature singularities have been tested. Here we discuss the similarities and differences between classical singularities that are healed quantum mechanically and those that are not. Possible extensions of the mathematical technique to more physically realistic spacetimes are discussed.
The Singular Behavior of Jet Substructure Observables
Larkoski, Andrew J
2016-01-01
Jet substructure observables play a central role at the Large Hadron Collider for identifying the boosted hadronic decay products of electroweak scale resonances. The complete description of these observables requires understanding both the limit in which hard substructure is resolved, as well as the limit of a jet with a single hard core. In this paper we study in detail the perturbative structure of two prominent jet substructure observables, $N$-subjettiness and the energy correlation functions, as measured on background QCD jets. In particular, we focus on the distinction between the limits in which two-prong structure is resolved or unresolved. Depending on the choice of subjet axes, we demonstrate that at fixed order, $N$-subjettiness can manifest myriad behaviors in the unresolved region: smooth tails, end-point singularities, or singularities in the physical region. The energy correlation functions, by contrast, only have non-singular perturbative tails extending to the end point. We discuss the effec...
Renormalization of singular potentials and power counting
Long, B.; van Koick, U.; van Kolck, U.
2008-01-01
We use a toy model to illustrate how to build effective theories for singular potentials. We consider a central attractive 1/r(2) potential perturbed by a 1/r(4) correction. The power-counting rule, an important ingredient of effective theory, is established by seeking the minimum set of short-range
Hybrid singular systems of differential equations
Institute of Scientific and Technical Information of China (English)
殷刚; 张纪峰
2002-01-01
This work develops hybrid models for large-scale singular differential system and analyzestheir asymptotic properties. To take into consideration the discrete shifts in regime across whichthe behavior of the corresponding dynamic systems is markedly different, our goals are to develophybrid systems in which continuous dynamics are intertwined with discrete events under random-jumpdisturbances and to reduce complexity of large-scale singular systems via singularly perturbed Markovchains. To reduce the complexity of large-scale hybrid singular systems, two-time scale is used in theformulation. Under general assumptions, limit behavior of the underlying system is examined. Usingweak convergence methods, it is shown that the systems can be approximated by limit systems inwhich the coefficients are averaged out with respect to the quasi-stationary distributions. Since thelimit systems have fewer states, the complexity is much reduced.
Singular solutions of a singular differential equation
Directory of Open Access Journals (Sweden)
Naito Manabu
2000-01-01
Full Text Available An attempt is made to study the problem of existence of singular solutions to singular differential equations of the type which have never been touched in the literature. Here and are positive constants and is a positive continuous function on . A solution with initial conditions given at is called singular if it ceases to exist at some finite point . Remarkably enough, it is observed that the equation may admit, in addition to a usual blowing-up singular solution, a completely new type of singular solution with the property that Such a solution is named a black hole solution in view of its specific behavior at . It is shown in particular that there does exist a situation in which all solutions of are black hole solutions.
On exceptional quotient singularities
Cheltsov, Ivan; Shramov, Constantin
2011-01-01
We study exceptional quotient singularities. In particular, we prove an exceptionality criterion in terms of the $\\alpha$-invariant of Tian, and utilize it to classify four-dimensional and five-dimensional exceptional quotient singularities.
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.
Gratton, Steven
2010-01-01
In this paper we present a path integral formulation of stochastic inflation, in which volume weighting can easily be implemented. With an in-depth study of inflation in a quartic potential, we investigate how the inflaton evolves and how inflation typically ends both with and without volume weighting. Perhaps unexpectedly, complex histories sometimes emerge with volume weighting. The reward for this excursion into the complex plane is an insight into how volume-weighted inflation both loses memory of initial conditions and ends via slow-roll. The slow-roll end of inflation mitigates certain "Youngness Paradox"-type criticisms of the volume-weighted paradigm. Thus it is perhaps time to rehabilitate proper time volume weighting as a viable measure for answering at least some interesting cosmological questions.
Institute of Scientific and Technical Information of China (English)
陈志勇; 陈力
2015-01-01
为解决载体位姿无控柔性关节空间双臂机器人系统在外部干扰、未知载荷参数影响下关节运动控制问题，提出奇异摄动增广鲁棒自适应 PD 复合控制方法。以柔性关节空间双臂欠驱动式机器人及关节电机动力学子方程为设计基础，借助柔性补偿奇异摄动技术建立系统奇异摄动修正模型；针对系统外部干扰确界未知、载荷参数未知工况，为柔性关节空间双臂机器人设计由快变状态反馈控制、增广鲁棒自适应 PD 慢变控制组合而成的复合控制规律。仿真结果证实，所提奇异摄动增广鲁棒自适应 PD 复合控制方法可有效消除系统关节柔性、未知外部干扰及载荷参数影响，确保空间双臂机器人能精确执行预期关节运动任务。%To solve the joint movement control problem of a flexible-joint dual-arm space robot system with an uncontrolled base under the effects of external disturbances and unknown load parameters,a singular perturbation augmented robust adaptive PD composite control method was proposed.On the basis of the under-actuated robot dynamic sub-equations and joint motor dynamic sub-equations,a singular perturbation correction model of robot system was established by using the flexibility compensating singular perturbation technique.Then,a composite control integrating the fast varying state feedback control and the augmented robust adaptive PD slowly varying control were designed for the flexible-joint dual-arm space robot with unknown upper bound external disturbances and unknown load parameters.The simulation results confirm that the influences of the joint flexibility,unknown external disturbances and unknown load parameters can be eliminated effectively by the presented control method,and the desired joint movement of dual-arm space robot can be achieved accurately.
Conformal window and Landau singularities
Grunberg, G
2001-01-01
A physical characterization of Landau singularities is emphasized, which should trace the lower boundary N_f^* of the conformal window in QCD and supersymmetric QCD. A natural way to disentangle ``perturbative'' from ``non-perturbative'' contributions below N_f^* is suggested. Assuming an infrared fixed point is present in the perturbative part of the QCD coupling even in some range below N_f^* leads to the condition gamma(N_f^*)=1, where gamma is the critical exponent. Using the Banks-Zaks expansion, one gets 4
Brumby, Paul E.; Haslam, Andrew J.; de Miguel, Enrique; Jackson, George
2011-01-01
An efficient and versatile method to calculate the components of the pressure tensor for hard-body fluids of generic shape from the perspective of molecular simulation is presented. After due consideration of all the possible repulsive contributions exerted by molecules upon their surroundings during an anisotropic system expansion, it is observed that such a volume change can, for non-spherical molecules, give rise to configurations where overlaps occur. This feature of anisotropic molecules has to be taken into account rigorously as it can lead to discrepancies in the calculation of tensorial contributions to the pressure. Using the condition of detailed balance as a basis, a perturbation method developed for spherical molecules has been extended so that it is applicable to non-spherical and non-convex molecules. From a series of 'ghost' anisotropic volume perturbations the residual contribution to the components of the pressure tensor may be accurately calculated. Comparisons are made with prior methods and, where relevant, results are evaluated against existing data. For inhomogeneous systems this method provides a particularly convenient route to the calculation of the interfacial tension (surface free energy) from molecular simulations.
Singular stochastic differential equations
Cherny, Alexander S
2005-01-01
The authors introduce, in this research monograph on stochastic differential equations, a class of points termed isolated singular points. Stochastic differential equations possessing such points (called singular stochastic differential equations here) arise often in theory and in applications. However, known conditions for the existence and uniqueness of a solution typically fail for such equations. The book concentrates on the study of the existence, the uniqueness, and, what is most important, on the qualitative behaviour of solutions of singular stochastic differential equations. This is done by providing a qualitative classification of isolated singular points, into 48 possible types.
Energy Technology Data Exchange (ETDEWEB)
2016-04-12
Singularity is a container solution designed to facilitate mobility of compute across systems and HPC infrastructures. It does this by creating minimal containers that are defined by a specfile and files from the host system are used to build the container. The resulting container can then be launched by any Linux computer with Singularity installed regardless if the programs inside the container are present on the target system, or if they are a different version, or even incompatible versions. Singularity achieves extreme portability without sacrificing usability thus solving the need of mobility of compute. Singularity containers can be executed within a normal/standard command line process flow.
Vaz, C; Vaz, Cenalo; Witten, Louis
1995-01-01
A naked singularity is formed by the collapse of a Sine-Gordon soliton in 1+1 dimensional dilaton gravity with a negative cosmological constant. We examine the quantum stress tensor resulting from the formation of the singularity. Consistent boundary conditions require that the incoming soliton is accompanied by a flux of incoming radiation across past null infinity, but neglecting the back reaction of the spacetime leads to the absurd conclusion that the total energy entering the system by the time the observer is able to receive information from the singularity is infinite. We conclude that the back reaction must prevent the formation of the naked singularity.
On singular and sincerely singular compact patterns
Rosenau, Philip; Zilburg, Alon
2016-08-01
A third order dispersive equation ut +(um)x +1/b[ua∇2ub]x = 0 is used to explore two very different classes of compact patterns. In the first, the prevailing singularity at the edge induces traveling compactons, solitary waves with a compact support. In the second, the singularity induced at the perimeter of the initial excitation, entraps the dynamics within the domain's interior (nonetheless, certain very singular excitations may escape it). Here, overlapping compactons undergo interaction which may result in an interchange of their positions, or form other structures, all confined within their initial support. We conjecture, and affirm it empirically, that whenever the system admits more than one type of compactons, only the least singular compactons may be evolutionary. The entrapment due to singularities is also unfolded and confirmed numerically in a class of diffusive equations ut =uk∇2un with k > 1 and n > 0 with excitations entrapped within their initial support observed to converge toward a space-time separable structure. A similar effect is also found in a class of nonlinear Klein-Gordon Equations.
Milnor open books of links of some rational surface singularities
Özbağcı, Burak; Bhupal, Mohan
2011-01-01
Pacific Journal of Mathematics MILNOR OPEN BOOKS OF LINKS OF SOME RATIONAL SURFACE SINGULARITIES MOHAN BHUPAL AND BURAK OZBAGCI Volume 254 No. 1 November 2011 PACIFIC JOURNAL OF MATHEMATICS Vol. 254, No. 1, 2011 MILNOR OPEN BOOKS OF LINKS OF SOME RATIONAL SURFACE SINGULARITIES MOHAN BHUPAL AND BURAK OZBAGCI We determine Legendrian surgery diagrams for the canonical contact struc-tures of links of rational surface singularities that are also small Seifert...
Fernández-Jambrina, L
2015-01-01
In this talk we would like to analyse the appearance of singularities in FLRW cosmological models which evolve close to w=-1, where w is the barotropic index of the universe. We relate small terms in cosmological time around w=-1 with the correspondent scale factor of the universe and check for the formation of singularities.
Halyo, Edi
2009-01-01
We describe domain walls that live on $A_2$ and $A_3$ singularities. The walls are BPS if the singularity is resolved and non--BPS if it is deformed and fibered. We show that these domain walls may interpolate between vacua that support monopoles and/or vortices.
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...
Singularity theory for W-algebra potentials
Gaite, J C
1993-01-01
The Landau potentials of $W_3$-algebra models are analyzed with algebraic-geometric methods. The number of ground states and the number of independent perturbations of every potential coincide and can be computed. This number agrees with the structure of ground states obtained in a previous paper, namely, as the phase structure of the IRF models of Jimbo et al. The singularities associated to these potentials are identified.
Singular Continuous Spectrum for Singular Potentials
Jitomirskaya, Svetlana; Yang, Fan
2017-05-01
We prove that Schrödinger operators with meromorphic potentials {(H_{α,θ}u)_n=u_{n+1}+u_{n-1}+ g(θ+nα)/f(θ+nα) u_n} have purely singular continuous spectrum on the set {{E: L(E) operator. Preprint, 2015) for the almost Mathieu operator to the general family of meromorphic potentials.
Beane, Silas R; Vuorinen, Aleksi
2009-01-01
We present a new formulation of effective field theory for nucleon-nucleon (NN) interactions which treats pion interactions perturbatively, and we offer evidence that the expansion converges satisfactorily to third order in the expansion, which we have computed analytically for s and d wave NN scattering. Starting with the Kaplan-Savage-Wise (KSW) expansion about the nontrivial fixed point corresponding to infinite NN scattering length, we cure the convergence problems with that theory by summing to all orders the singular short distance part of the pion tensor interaction. This method makes possible a host of high precision analytic few-body calculations in nuclear physics.
Resonance Van Hove singularities in wave kinetics
Shi, Yi-Kang; Eyink, Gregory L.
2016-10-01
Wave kinetic theory has been developed to describe the statistical dynamics of weakly nonlinear, dispersive waves. However, we show that systems which are generally dispersive can have resonant sets of wave modes with identical group velocities, leading to a local breakdown of dispersivity. This shows up as a geometric singularity of the resonant manifold and possibly as an infinite phase measure in the collision integral. Such singularities occur widely for classical wave systems, including acoustical waves, Rossby waves, helical waves in rotating fluids, light waves in nonlinear optics and also in quantum transport, e.g. kinetics of electron-hole excitations (matter waves) in graphene. These singularities are the exact analogue of the critical points found by Van Hove in 1953 for phonon dispersion relations in crystals. The importance of these singularities in wave kinetics depends on the dimension of phase space D =(N - 2) d (d physical space dimension, N the number of waves in resonance) and the degree of degeneracy δ of the critical points. Following Van Hove, we show that non-degenerate singularities lead to finite phase measures for D > 2 but produce divergences when D ≤ 2 and possible breakdown of wave kinetics if the collision integral itself becomes too large (or even infinite). Similar divergences and possible breakdown can occur for degenerate singularities, when D - δ ≤ 2, as we find for several physical examples, including electron-hole kinetics in graphene. When the standard kinetic equation breaks down, then one must develop a new singular wave kinetics. We discuss approaches from pioneering 1971 work of Newell & Aucoin on multi-scale perturbation theory for acoustic waves and field-theoretic methods based on exact Schwinger-Dyson integral equations for the wave dynamics.
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 magnetic...
Global existence for a singular Gierer-Meinhardt system
Chen, Shaohua; Salmaniw, Yurij; Xu, Runzhang
2017-02-01
This paper is concerned with existence results for a singular Gierer-Meinhardt system subject to zero Dirichlet boundary conditions, which originally arose in studies of pattern-formation in biology. The mathematical difficulties are that the system becomes singular near the boundary and it lacks a variational structure. We use a functional method to obtain both upper and lower bounds for the perturbed system and then use Sobolev embedding theorem to prove the existence of a pair of positive solutions under suitable conditions. This method is first used in a singular parabolic system and is completely different than the traditional methods of sub and super solutions.
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.
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.
Singularities in Speckled Speckle
Freund, Isaac
2007-01-01
Speckle patterns produced by random optical fields with two (or more) widely different correlation lengths exhibit speckle spots that are themselves highly speckled. Using computer simulations and analytic theory we present results for the point singularities of speckled speckle fields: optical vortices in scalar (one polarization component) fields; C points in vector (two polarization component) fields. In single correlation length fields both types of singularities tend to be more{}-or{}-less uniformly distributed. In contrast, the singularity structure of speckled speckle is anomalous: for some sets of source parameters vortices and C points tend to form widely separated giant clusters, for other parameter sets these singularities tend to form chains that surround large empty regions. The critical point statistics of speckled speckle is also anomalous. In scalar (vector) single correlation length fields phase (azimuthal) extrema are always outnumbered by vortices (C points). In contrast, in speckled speckl...
Complex singularities and PDEs
Caflisch, R E; Sammartino, M; Sciacca, V
2015-01-01
In this paper we give a review on the computational methods used to characterize the complex singularities developed by some relevant PDEs. We begin by reviewing the singularity tracking method based on the analysis of the Fourier spectrum. We then introduce other methods generally used to detect the hidden singularities. In particular we show some applications of the Pad\\'e approximation, of the Kida method, and of Borel-Polya method. We apply these techniques to the study of the singularity formation of some nonlinear dispersive and dissipative one dimensional PDE of the 2D Prandtl equation, of the 2D KP equation, and to Navier-Stokes equation for high Reynolds number incompressible flows in the case of interaction with rigid boundaries.
Singularity methods for magnetohydrodynamics
Directory of Open Access Journals (Sweden)
A. D. Alawneh
1986-01-01
Full Text Available Singular solutions for linearized MHD equations based on Oseen approximations have been obtained such as Oseenslet. Oseenrotlet, mass source, etc. By suitably distributing these singular solutions along the axes of symmetry of an axially symmetric bodies, we derive the approximate values for the velocity fields, the force and the momentum for the case of translational and rotational motions of such bodies in a steady flow of an incompressible viscous and magnetized fluid.
Generic singularity studies revisited
Barrow, John D.; Tipler, Frank J.
1981-04-01
We comment on a reply by Belinskii, Khalatnikov and Lifshitz to our analysis of their conclusions regarding the general structure of space-time singularities. We support our contention that it is impossible to provide a reliable analysis of the evolution of a general (or stable) solution with local techniques in a synchronous coordinate system having a simultaneous physical singularity. Work supported in part by the National Science Foundation under grant number PHY 78-26592.
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.
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.
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].
Kozma, Gady
2012-01-01
We proved earlier that every measurable function on the circle, after a uniformly small perturbation, can be written as a power series (i.e. a series of exponentials with positive frequencies), which converges almost everywhere. Here we show that this result is basically sharp: the perturbation cannot be made smooth or even H\\"older. We discuss also a similar problem for perturbations with lacunary spectrum.
Automorphic forms with singularities on Grassmannians
Borcherds, R E
1996-01-01
We construct some families of automorphic forms on Grassmannians which have singularities along smaller sub Grassmannians, using a version of the theta correspondence extended to modular forms with poles at cusps. Some of the applications are as follows. We construct families of holomorphic automorphic forms which can be written as infinite products, which give many new examples of generalized Kac-Moody superalgebras. We extend the Shimura and Maass-Gritsenko correspondences to modular forms with singularities. We prove some congruences satisfied by the theta functions of positive definite lattices, and find a sufficient condition for a Lorentzian lattice to have a reflection group with a finite volume fundamental domain. We give some examples suggesting that these automorphic forms with singularities are related to Donaldson polynomials and to mirror symmetry for K3 surfaces.
Singular Continuous Spectrum for Singular Potentials
Jitomirskaya, Svetlana; Yang, Fan
2017-01-01
We prove that Schrödinger operators with meromorphic potentials {(H_{α,θ}u)_n=u_{n+1}+u_{n-1}+ g(θ+nα)/f(θ+nα) u_n} have purely singular continuous spectrum on the set {{E: L(E) Lyapunov exponent. This extends results of Jitomirskaya and Liu (Arithmetic spectral transitions for the Maryland model. CPAM, to appear) for the Maryland model and of Avila,You and Zhou (Sharp Phase transitions for the almost Mathieu operator. Preprint, 2015) for the almost Mathieu operator to the general family of meromorphic potentials.
Some aspects of singular interactions in condensed Fermi systems
Stamp, P. C. E.
1993-02-01
This article gives a fairly detailed survey of some of the problems raised when the interaction energy f^{σ σ'}_{k k'} between 2 fermionic quasiparticles (in 2 dimensions) is singular when |k-k'|to 0. Before dealing with singular interactions, it is shown how a non-singular f^{σ σ'}_{k k'} leads to a 2-dimensional Fermi liquid theory, which is internally consistent, at least as far as its infrared properties are concerned. The quasiparticle properties are calculated in detail. The question of whether singular interactions arise for the dilute Fermi gas, with short-range repulsive interactions, is investigated perturbatively. One finds a weak singularity in f^{σ σ'}_{k k'}, when the dimensionality D = 2, but it does not destabilize the Fermi liquid. A more sophisticated analysis is then given, to all orders in the interaction, using the Lippman-Schwinger equation as well as a phase shift analysis for a finite box. The conclusion is that any breakdown of Fermi liquid theory must come from non-perturbative effects. An examination is then made of some of the consequences arising if a singular interaction is introduced — the form proposed by Anderson is used as an example. A hierarchy of singular terms arise in all quantities — this is shown for the self-energy, and also the 3 point and 4 point scattering functions. These may be summed in a perfectly consistent manner. Most attention is given to the particle-hole channel, since it appears to lead to results different from those of Anderson. Nevertheless it appears that it is possible to derive a sensible theory starting from a singular effective Hamiltonian — although Fermi Liquid theory breaks down, all fermionic quantities may be calculated consistently. Finally, the effect of a magnetic field (which cuts off the infrared divergences) is investigated, and the de Haas-van Alphen amplitude calculated, for such a singular Fermionic system.
On adiabatic perturbations in the ekpyrotic scenario
Linde, A.; Mukhanov, V.; Vikman, A.
2010-02-01
In a recent paper, Khoury and Steinhardt proposed a way to generate adiabatic cosmological perturbations with a nearly flat spectrum in a contracting Universe. To produce these perturbations they used a regime in which the equation of state exponentially rapidly changed during a short time interval. Leaving aside the singularity problem and the difficult question about the possibility to transmit these perturbations from a contracting Universe to the expanding phase, we will show that the methods used in Khoury are inapplicable for the description of the cosmological evolution and of the process of generation of perturbations in this scenario.
On adiabatic perturbations in the ekpyrotic scenario
Linde, A; Vikman, A
2009-01-01
In a recent paper arXiv:0910.2230, Khoury and Steinhardt proposed a way to generate adiabatic cosmological perturbations with a nearly flat spectrum in a contracting Universe. To produce these perturbations they used a regime in which the equation of state exponentially rapidly changed during a short time interval. Leaving aside the singularity problem and the difficult question about the possibility to transmit these perturbations from a contracting Universe to the expanding phase, we will show that the methods used in arXiv:0910.2230 are inapplicable for the description of the cosmological evolution and of the process of generation of perturbations in this scenario.
Perturbative spacetimes from Yang-Mills theory
Luna, Andrés; Nicholson, Isobel; Ochirov, Alexander; O'Connell, Donal; Westerberg, Niclas; White, Chris D.
2017-04-12
The double copy relates scattering amplitudes in gauge and gravity theories. In this paper, we expand the scope of the double copy to construct spacetime metrics through a systematic perturbative expansion. The perturbative procedure is based on direct calculation in Yang-Mills theory, followed by squaring the numerator of certain perturbative diagrams as specified by the double-copy algorithm. The simplest spherically symmetric, stationary spacetime from the point of view of this procedure is a particular member of the Janis-Newman-Winicour family of naked singularities. Our work paves the way for applications of the double copy to physically interesting problems such as perturbative black-hole scattering.
Perturbative spacetimes from Yang-Mills theory
Luna, Andres; Nicholson, Isobel; Ochirov, Alexander; O'Connell, Donal; Westerberg, Niclas; White, Chris D.
2016-01-01
The double copy relates scattering amplitudes in gauge and gravity theories. In this paper, we expand the scope of the double copy to construct spacetime metrics through a systematic perturbative expansion. The perturbative procedure is based on direct calculation in Yang-Mills theory, followed by squaring the numerator of certain perturbative diagrams as specified by the double-copy algorithm. The simplest spherically symmetric, stationary spacetime from the point of view of this procedure is a particular member of the Janis-Newman-Winicour family of naked singularities. Our work paves the way for applications of the double copy to physically interesting problems such as perturbative black-hole scattering.
Classical dynamics of the Bianchi IX model: space-like and time-like singularity cases
Parnovsky, S L
2016-01-01
We present the comparison of the dynamics of the vacuum Bianchi IX model near the space-like and time-like singularities. In both cases there exist oscillatory type solutions with diverging asymptotically curvature invariants. The dynamics of the time-like singularity case includes additionally the singular solutions with diverging volume density, but vanishing curvature invariants. Our numerical results are consistent with qualitative analytical considerations underlying finding the generic singular solutions to general relativity.
Gil, José J; José, Ignacio San
2015-01-01
Singular Mueller matrices play an important role in polarization algebra and have peculiar properties that stem from the fact that either the medium exhibits maximum diattenuation and/or polarizance, or because its associated canonical depolarizer has the property of fully randomizing, the circular component (at least) of the states of polarization of light incident on it. The formal reasons for which the Mueller matrix M of a given medium is singular are systematically investigated, analyzed and interpreted in the framework of the serial decompositions and the characteristic ellipsoids of M. The analysis allows for a general classification and geometric representation of singular Mueller matrices, of potential usefulness to experimentalists dealing with such media.
Strength and genericity of singularities in Tolman-Bondi-de Sitter collapse
Gonçalves, S M C V
2001-01-01
We study the curvature strength and visibility of the central singularity arising in Tolman-Bondi-de Sitter collapse. We find that the singularity is visible and Tipler strong along an infinite number of timelike geodesics, independently of the initial data, and thus stable against perturbations of the latter.
Classification of singular points in polarization field of CMB and eigenvectors of Stokes matrix
Dolgov, A D; Novikov, D I; Novikov, I D
1998-01-01
Analysis of the singularities of the polarization field of CMB, where polarization is equal to zero, is presented. It is found that the classification of the singular points differs from the usual three types known in the ordinary differential equations. The new statistical properties of polarization field are discussed, and new methods to detect the presence of primordial tensor perturbations are indicated.
Big brake singularity is accommodated as an exotic quintessence field
Chimento, Luis P
2015-01-01
We describe a big brake singularity in terms of a modified Chaplygin gas equation of state $p=(\\ga_{m}-1)\\rho+\\al\\ga_{m}\\rho^{-n}$, accommodate this late-time event as an exotic quintessence model obtained from an energy-momentum tensor, and focus on the cosmological behaviour of the exotic field, its kinetic energy and the potential energy. At background level, the exotic field does not blow-up whereas its kinetic energy and potential both grow without limit near the future singularity. We evaluate the classical stability of this background solution by examining the scalar perturbations of the metric along with the inclusion of entropy perturbation in the perturbed pressure. Within the Newtonian gauge, the gravitational field approaches to a constant near the singularity plus additional regular terms. When the perturbed exotic field is associated with $\\al>0$, the perturbed pressure and contrast density both diverge whereas the perturbed exotic field and the divergence of exotic field's velocity go to zero e...
Singularities of invariant connections
Energy Technology Data Exchange (ETDEWEB)
Amores, A.M. (Universidad Complutense, Madrid (Spain)); Gutierrez, M. (Universidad Politecnica, Madrid (Spain))
1992-12-01
A reductive homogeneous space M = P/G is considered, endowed with an invariant connection, i.e., such that all left translations of M induced by members of P preserve it. The authors study the set of singularities of such connections giving sufficient conditions for it to be empty, or, in other cases, familities of b-incomplete curves converging to singularities. A full description of the b-completion of a connection with M = R[sup m] (or a quotient of it) is given with information on its topology. 5 refs.
Propagation of singularities for Schr\\"odinger equations with modestly long range type potentials
2013-01-01
In a previous paper by the second author, we discussed a characterization of the microlocal singularities for solutions to Schr\\"odinger equations with long range type perturbations, using solutions to a Hamilton-Jacobi equation. In this paper we show that we may use Dollard type approximate solutions to the Hamilton-Jacobi equation if the perturbation satisfies somewhat stronger conditions. As applications, we describe the propagation of microlocal singularities for $e^{itH_0}e^{-itH}$ when ...
Singularity-free cosmological solutions of the superstring effective action
Energy Technology Data Exchange (ETDEWEB)
Antoniadis, I. (Ecole Polytechnique, 91 - Palaiseau (France). Centre de Physique Theorique); Rizos, J. (Ecole Polytechnique, 91 - Palaiseau (France). Centre de Physique Theorique); Tamvakis, K. (Ioannina Univ. (Greece). Dept. of Physics)
1994-03-07
We study the cosmological solutions of the one-loop corrected superstring effective action, in a Friedmann-Robertson-Walker background, and in the presence of the dilaton and modulus fields. A particularly interesting class of solutions is found which avoid the initial singularity and are consistent with the perturbative treatment of the effective action. (orig.)
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...
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...
Supersymmetry in singular spaces
Bergshoeff, E; Kallosh, R; Van Proeyen, A
2000-01-01
We develop the concept of supersymmetry in singular spaces, apply it in an example for 3-branes in D = 5 and comment on 8-branes in D = 10. The new construction has an interpretation that the brane is a sink for the flux and requires adding to the standard supergravity a (D - 1)-form field and a sup
Supersymmetry in singular spaces
Bergshoeff, E; Kallosh, R; Van Proeyen, A
2000-01-01
We develop the concept of supersymmetry in singular spaces, apply it in an example for 3-branes in D = 5 and comment on 8-branes in D = 10. The new construction has an interpretation that the brane is a sink for the flux and requires adding to the standard supergravity a (D - 1)-form field and a
Supersymmetry in Singular Spaces
Bergshoeff, E. A.; Kallosh, R.; Proeyen, A. van
2000-01-01
Published in: J. High Energy Phys. 10 (2000) 033 citations recorded in [Science Citation Index] Abstract: We develop the concept of supersymmetry in singular spaces, apply it in an example for 3-branes in D=5 and comment on 8-branes in D=10. The new construction has an interpretation that the brane
Pseudospherical surfaces with singularities
DEFF Research Database (Denmark)
Brander, David
2016-01-01
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...
Szydlowski, Marek; Borowiec, Andrzej; Wojnar, Aneta
2015-01-01
We investigate modified gravity cosmological model $f(R)=R+\\gamma R^2$ in Palatini formalism. We consider the universe filled with the Chaplygin gas and baryonic matter. The dynamics is reduced to the 2D sewn dynamical system of a Newtonian type. For this aim we use dynamical system theory. We classify all evolutional paths in the model as well as trajectories in the phase space. We demonstrate that the presence of a degenerate freeze singularity (glued freeze type singularities) is a generic feature of early evolution of the universe. We point out that a degenerate type III of singularity can be considered as an endogenous model of inflation between the matter dominating epoch and the dark energy phase. We also investigate cosmological models with negative $\\gamma$. It is demonstrated that $\\gamma$ equal zero is a bifurcation parameter and dynamics qualitatively changes in comparison to positive $\\gamma$. Instead of the big bang the sudden singularity appears and there is a generic class of bouncing solution...
Institute of Scientific and Technical Information of China (English)
Yu-tong LI; Yu-xin WANG; Shuang-xia PAN; Rui-qin GUO
2008-01-01
The singular points of a 6-SPS Stewart platform are distributed on the multi-dimensional singularity hypersurface in the task-space,which divides the workspace of the manipulator into several singularity-free regions.Because of the motion un-certainty at singular points,while the manipulator traverses this kind of hypersurface from one singularity-free region to another,its motion cannot be predetermined.In this paper,a detailed approach for the manipulator to traverse the singularity hypersurface with its non-persistent configuration is presented.First,the singular point transfer disturbance and the pose disturbance,which make the perturbed singular point transfer horizontally and vertically,respectively,arc constructed.Through applying these dis-turbances into the input parameters within the maximum loss control domain,the perturbed persistent configuration is transformed into its corresponding non-persistent one.Under the action of the disturbances,the manipulator can traverse the singularity hy-persurface from one singularity-free region to another with a desired configuration.
Quantum effects near future singularities
Barrow, John D; Dito, Giuseppe; Fabris, Julio C; Houndjo, Mahouton J S
2012-01-01
General relativity allows a variety of future singularities to occur in the evolution of the universe. At these future singularities, the universe will end in a singular state after a finite proper time and geometrical invariants of the space time will diverge. One question that naturally arises with respect to these cosmological scenarios is the following: can quantum effects lead to the avoidance of these future singularities? We analyze this problem considering massless and conformally coupled scalar fields in an isotropic and homogeneous background leading to future singularities. It is shown that near strong, big rip-type singularities, with violation of the energy conditions, the quantum effects are very important, while near some milder classes of singularity like the sudden singularity, which preserve the energy conditions, quantum effects are irrelevant.
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.
Approximation by Multivariate Singular Integrals
Anastassiou, George A
2011-01-01
Approximation by Multivariate Singular Integrals is the first monograph to illustrate the approximation of multivariate singular integrals to the identity-unit operator. The basic approximation properties of the general multivariate singular integral operators is presented quantitatively, particularly special cases such as the multivariate Picard, Gauss-Weierstrass, Poisson-Cauchy and trigonometric singular integral operators are examined thoroughly. This book studies the rate of convergence of these operators to the unit operator as well as the related simultaneous approximation. The last cha
String theory and cosmological singularities
Indian Academy of Sciences (India)
Sumit R Das
2007-07-01
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 singularities which may lead to an understanding of these in the standard framework of time evolution in quantum mechanics. In this article, we describe some of these approaches.
Can we see naked singularities?
Deshingkar, Shrirang S.
2007-01-01
We study singularities which can form in a spherically symmetric gravitational collapse of a general matter field obeying weak energy condition. We show that no energy can reach an outside observer from a null naked singularity. That means they will not be a serious threat to the Cosmic Censorship Conjecture (CCC). For the timelike naked singularities, where only the central shell gets singular, the redshift is always finite and they can in principle, carry energy to a faraway observer. Hence...
Random perturbations of nonlinear parabolic systems
Beck, Lisa
2011-01-01
Several aspects of regularity theory for parabolic systems are investigated under the effect of random perturbations. The deterministic theory, when strict parabolicity is assumed, presents both classes of systems where all weak solutions are in fact more regular, and examples of systems with weak solutions which develop singularities in finite time. Our main result is the extension of a regularity result due to Kalita to the stochastic case. Concerning the examples with singular solutions (outside the setting of Kalita's regularity result), we do not know whether stochastic noise may prevent the emergence of singularities, as it happens for easier PDEs. We can only prove that, for a linear stochastic parabolic system with coefficients outside the previous regularity theory, the expected value of the solution is not singular.
Singularity avoidance in the hybrid quantization of the Gowdy model
Tarrío, Paula; Marugán, Guillermo A Mena
2013-01-01
One of the most remarkable phenomena in Loop Quantum Cosmology is that, at least for homogeneous cosmological models, the Big Bang is replaced with a Big Bounce that connects our universe with a previous branch without passing through a cosmological singularity. The goal of this work is to study the existence of singularities in Loop Quantum Cosmology including inhomogeneities and check whether the behavior obtained in the purely homogeneous setting continues to be valid. With this aim, we focus our attention on the three-torus Gowdy cosmologies with linearly polarized gravitational waves and use effective dynamics to carry out the analysis. For this model, we prove that all the potential cosmological singularities are avoided, generalizing the results about resolution of singularities to this scenario with inhomogeneities. We also demonstrate that, if a bounce in the (Bianchi background) volume occurs, the inhomogeneities increase the value of this volume at the bounce with respect to its counterpart in the ...
Compact Variables and Singular Fields in QCD
Lenz, F; Lenz, Frieder; Woerlen, Stefan
2000-01-01
Subject of our investigations is QCD formulated in terms of physical degrees of freedom. Starting from the Faddeev-Popov procedure, the canonical formulation of QCD is derived for static gauges. Particular emphasis is put on obstructions occurring when implementing gauge conditions and on the concomitant emergence of compact variables and singular fields. A detailed analysis of non-perturbative dynamics associated with such exceptional field configurations within Coulomb- and axial gauge is described. We present evidence that compact variables generate confinement-like phenomena in both gauges and point out the deficiencies in achieving a satisfactory non-perturbative treatment concerning all variables. Gauge fixed formulations are shown to constitute also a useful framework for phenomenological studies. Phenomenological insights into the dynamics of Polyakov loops and monopoles in confined and deconfined phases are presented within axial gauge QCD
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.
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.
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 complexity...... of our algorithm only allows for the comparison of small trees, and that the results of our method are comparable with state-of-the-art using much fewer parameters for image representation....
Wheeler-DeWitt quantization and singularities
Falciano, Felipe Tovar; Struyve, Ward
2015-01-01
We consider a Bohmian approach to the Wheeler-DeWitt quantization of the Friedmann-Lemaitre-Robertson-Walker model and investigate the question whether or not there are singularities, in the sense that the universe reaches zero volume. We find that for generic wave functions (i.e., non-classical wave functions), there is a non-zero probability for a trajectory to be non-singular. This should be contrasted to the consistent histories approach for which it was recently shown by Craig and Singh that there is always a singularity. This result illustrates that the question of singularities depends much on which version of quantum theory one adopts. This was already pointed out by Pinto-Neto et al., albeit with a different Bohmian approach. Our current Bohmian approach agrees with the consistent histories approach by Craig and Singh for single-time histories, unlike the one studied earlier by Pinto-Neto et al. Although the trajectories are usually different in the two Bohmian approach, their qualitative behavior is...
Long term behaviour of singularly perturbed parabolic degenerated equation
Directory of Open Access Journals (Sweden)
Ibrahima Faye
2016-12-01
Full Text Available In this paper we consider models built in [4] for short-term, mean-term and long-term morphodynamics of dunes and megariples. We give an existence and uniqueness result for long term dynamics of dunes. This result is based on a periodic-in-time-and-space solution existence result for degenerated parabolic equation that we set out. Finally the mean-term and long-term models are homogenized.
Asymptotics of a singularly perturbed GUE partition function
Mezzadri, F
2010-01-01
We study the double scaling asymptotic limit for large matrix dimension N of the partition function of the unitary ensemble with weight exp(-z^2/2x^2 + t/x - x^2/2). We derive the asymptotics of the partition function when z and t are of O(N^(-1/2)). Our results are obtained using the Deift-Zhou steepest descent method and are expressed in terms of a solution of a fourth order nonlinear differential equation. We also compute the asymptotic limit of such a solution when zN^(1/2) -> 0. The behavior of this solution, together with fact that the partition function is an odd function in the variable t, allows us to reduce such a fourth order differential equation into a second order nonlinear ODE.
Singularly perturbed Burger-Huxley equation: Analytical solution ...
African Journals Online (AJOL)
user
Keywords: Burger-Huxley equation, iteration method, analytical solution, ... dynamics, chemical kinetics and mathematical biology (Albowitz and Clarkson, ... numbers, Navier-Stokes flows with large Reynolds numbers, chemical reactor theory, ...
Long term behaviour of singularly perturbed parabolic degenerated equation
Faye, Ibrahima; Seck, Diaraf
2011-01-01
In this paper we consider models for short-term, mean-term and long-term morphodynamics of dunes and megariples. We give an existence and uniqueness result for long term dynamics of dunes. This result is based on a time-space periodic solution existence result for degenerated parabolic equation that we set out. Finally the mean-term and long-term models are homogenized.
Stability of S-brane singular solutions and expansion of the universe
Mochizuki, Riuji
2012-01-01
We investigate stability of single S-brane singular solutions obtained in our previous papers. A stable perturbative solution exists for each of them, while an unstable one exists only if the dilaton field does not depend on time. We apply these perturbative solutions to inflation and late-time acceleration of expansion of the universe.
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. .
Quantum Singularity of Quasiregular Spacetimes
Konkowski, Deborah A.; Helliwell, Thomas M.
2001-04-01
A quasiregular spacetime is a spacetime with a classical quasiregular singularity, the mildest form of true singularity [G.F.R. Ellis and B.G. Schmidt, Gen. Rel. Grav. 8, 915 (1977)]. The definition of G.T. Horowitz and D. Marolf [Phys. Rev. D52, 5670 (1995)] for a quantum-mechanically singular spacetime is one in which the spatial-derivative operator in the Klein-Gordon equation for a massive scalar field is not essentially self-adjoint. In such a quantum-mechanically singular spacetime, the time evolution of a quantum test particle is not uniquely determined. Horowitz and Marolf showed that a two-dimensional spacetime with a classical conical singularity (i.e., a two-dimensional quasiregular singularity) is also quantum-mechanically singular. Here we show that a class of static quasiregular spacetimes possessing disclinations and dislocations [R.A.Puntigam and H.H. Soleng , Class. Quantum Grav. 14, 1129 (1997)] is quantum-mechanically singular, since the scalar wave operator is not essentially self-adjoint. These spacetimes include an idealized cosmic string spacetime, i.e., a four-dimensional spacetime with conical singularity, and a Galtsov/Letelier/Tod spacetime featuring a screw dislocation [K.P. Tod, Class. Quantum Grav. 11, 1331 (1994); D.V. Galtsov and P.S. Letelier, Phys. Rev. D47, 4273 (1993)]. In addition, we show that the definition of quantum-mechanically singular spacetimes can be extended to include Maxwell and Dirac fields.
Scalar and tensor perturbations in loop quantum cosmology: High-order corrections
Zhu, Tao; Cleaver, Gerald; Kirsten, Klaus; Sheng, Qin; Wu, Qiang
2015-01-01
Loop quantum cosmology (LQC) provides promising resolutions to the trans-Planckian issue and initial singularity arising in the inflationary models of general relativity. In general, due to different quantization approaches, LQC involves two types of quantum corrections, the holonomy and inverse-volume, to both of the cosmological background evolution and perturbations. In this paper, using {\\em the third-order uniform asymptotic approximations}, we derive explicitly the observational quantities of the slow-roll inflation in the framework of LQC with these quantum corrections. We calculate the power spectra, spectral indices, and running of the spectral indices for both scalar and tensor perturbations, whereby the tensor-to-scalar ratio is obtained. We expand all the observables at the time when the inflationary mode crosses the Hubble horizon. As the upper error bounds for the uniform asymptotic approximation at the third-order are $\\lesssim 0.15\\%$, these results represent the most accurate results obtained...
Perturbative quantum chromodynamics
1989-01-01
This book will be of great interest to advanced students and researchers in the area of high energy theoretical physics. Being the most complete and updated review volume on Perturbative QCD, it serves as an extremely useful textbook or reference book. Some of the reviews in this volume are the best that have been written on the subject anywhere. Contents: Factorization of Hard Processes in QCD (J C Collins, D E Soper & G Sterman); Exclusive Processes in Quantum Chromodynamics (S J Brodsky & G P Lepage); Coherence and Physics of QCD Jets (Yu L Dokshitzer, V A Khoze & S I Troyan); Pomeron in Qu
Dilatonic effects near naked singularities
Morris, J R
2011-01-01
Static spherically symmetric solutions of 4d Brans-Dicke theory include a set of naked singularity solutions. Dilatonic effects near the naked singularities result in either a shielding or an antishielding effect from intruding massive test particles. One result is that for a portion of the solution parameter space, no communication between the singularity and a distant observer is possible via massive particle exchanges. Kaluza-Klein gravity is considered as a special case.
How Does Naked Singularity Look?
Nakao, Ken-ichi; Kobayashi, Naoki; Ishihara, Hideki
2002-01-01
There are non-radial null geodesics emanating from the shell focusing singularity formed at the symmetric center in a spherically symmetric dust collapse. In this article, assuming the self-similarity in the region filled with the dust fluid, we study these singular null geodesics in detail. We see the time evolution of the angular diameter of the central naked singularity and show that it might be bounded above by the value corresponding to the circular null geodesic in the Schwarzschild spa...
Cosmological perturbations through a simple bounce
Allen, L E
2004-01-01
We present a detailed study of a simple scalar field model that yields non-singular cosmological solutions. We study both the qualitative dynamics of the homogeneous and isotropic background and the evolution of inhomogeneous linear perturbations. We calculate the spectrum of perturbations generated on super-Hubble scales during the collapse phase from initial vacuum fluctuations on small scales and then evolve these numerically through the bounce. We show there is a gauge that remains well-defined throughout the bounce, even though other commonly used gauges break down. We show that the comoving curvature perturbation calculated during the collapse phase provides a good estimate of the resulting large scale adiabatic perturbation in the expanding phase while the Bardeen metric potential is dominated by what becomes a decaying mode after the bounce. We show that a power-law collapse phase with scale factor proportional $(-t)^{2/3}$ can yield a scale-invariant spectrum of adiabatic scalar perturbations in the ...
Eikonal perturbation theory in photoionization
Cajiao Vélez, F.; Krajewska, K.; Kamiński, J. Z.
2016-02-01
The eikonal perturbation theory is formulated and applied to photoionization by strong laser pulses. A special emphasis is put on the first order approximation with respect to the binding potential, which is known as the generalized eikonal approximation [2015 Phys. Rev. A 91 053417]. The ordinary eikonal approximation and its domain of applicability is derived from the generalized eikonal approximation. While the former approach is singular for the electron trajectories which return to the potential center, the generalized eikonal avoids this problem. This property makes it a promising tool for further investigations of rescattering and high-order harmonic generation processes.
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...
Directory of Open Access Journals (Sweden)
Lv Xuezhe
2010-01-01
Full Text Available Abstract The existence and uniqueness of positive solution is obtained for the singular second-order -point boundary value problem for , , , where , , are constants, and can have singularities for and/or and for . The main tool is the perturbation technique and Schauder fixed point theorem.
Legchenko, Anatoly; Comte, Jean-Christophe; Ofterdinger, Ulrich; Vouillamoz, Jean-Michel; Lawson, Fabrice Messan Amen; Walsh, John
2017-09-01
We propose a simple and robust approach for investigating uncertainty in the results of inversion in geophysics. We apply this approach to inversion of Surface Nuclear Magnetic Resonance (SNMR) data, which is also known as Magnetic Resonance Sounding (MRS). Solution of this inverse problem is known to be non-unique. We inverse MRS data using the well-known Tikhonov regularization method, which provides an optimal solution as a trade-off between the stability and accuracy. Then, we perturb this model by random values and compute the fitting error for the perturbed models. The magnitude of these perturbations is limited by the uncertainty estimated with the singular value decomposition (SVD) and taking into account experimental errors. We use 106 perturbed models and show that the large majority of these models, which have all the water content within the variations given by the SVD estimate, do not fit data with an acceptable accuracy. Thus, we may limit the solution space by only the equivalent inverse models that fit data with the accuracy close to that of the initial inverse model. For representing inversion results, we use three equivalent solutions instead of the only one: the ;best; solution given by the regularization or other inversion technic and the extreme variations of this solution corresponding to the equivalent models with the minimum and the maximum volume of water. For demonstrating our approach, we use synthetic data sets and experimental data acquired in the framework of investigation of a hard rock aquifer in the Ireland (County Donegal).
Nonspherical perturbations of critical collapse and cosmic censorship
Gundlach, C
1998-01-01
Numerical simulations have shown that, in general relativity with various kinds of matter, initial data that form a naked singularity have codimension one within spherical symmetry. The singularity is approached through a self-similar spacetime which is the same for all initial data and even for universality classes of matter models. The codimension is one because this critical solution has precisely one perturbation mode that grows towards the singularity (and which must be suppressed by fine-tuning). Here we go beyond spherical symmetry. For a perfect fluid with equation of state p = (1/3) rho we construct the spherically symmetric critical solution and examine its linear perturbations, both spherical and non-spherical. We find only the one spherical growing mode already known, while all nonspherical modes decay. This means that naked singularities, for this matter model at least, have codimension one in a region of the space of initial data.
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.
Entanglement Entropy for Singular Surfaces
Myers, Robert C
2012-01-01
We study entanglement entropy for regions with a singular boundary in higher dimensions using the AdS/CFT correspondence and find that various singularities make new universal contributions. When the boundary CFT has an even spacetime dimension, we find that the entanglement entropy of a conical surface contains a term quadratic in the logarithm of the UV cut-off. In four dimensions, the coefficient of this contribution is proportional to the central charge 'c'. A conical singularity in an odd number of spacetime dimensions contributes a term proportional to the logarithm of the UV cut-off. We also study the entanglement entropy for various boundary surfaces with extended singularities. In these cases, similar universal terms may appear depending on the dimension and curvature of the singular locus.
Gover, A. Rod; Waldron, Andrew
2017-09-01
We develop a universal distributional calculus for regulated volumes of metrics that are suitably singular along hypersurfaces. When the hypersurface is a conformal infinity we give simple integrated distribution expressions for the divergences and anomaly of the regulated volume functional valid for any choice of regulator. For closed hypersurfaces or conformally compact geometries, methods from a previously developed boundary calculus for conformally compact manifolds can be applied to give explicit holographic formulæ for the divergences and anomaly expressed as hypersurface integrals over local quantities (the method also extends to non-closed hypersurfaces). The resulting anomaly does not depend on any particular choice of regulator, while the regulator dependence of the divergences is precisely captured by these formulæ. Conformal hypersurface invariants can be studied by demanding that the singular metric obey, smoothly and formally to a suitable order, a Yamabe type problem with boundary data along the conformal infinity. We prove that the volume anomaly for these singular Yamabe solutions is a conformally invariant integral of a local Q-curvature that generalizes the Branson Q-curvature by including data of the embedding. In each dimension this canonically defines a higher dimensional generalization of the Willmore energy/rigid string action. Recently, Graham proved that the first variation of the volume anomaly recovers the density obstructing smooth solutions to this singular Yamabe problem; we give a new proof of this result employing our boundary calculus. Physical applications of our results include studies of quantum corrections to entanglement entropies.
Naked singularities are not singular in distorted gravity
Energy Technology Data Exchange (ETDEWEB)
Garattini, Remo, E-mail: Remo.Garattini@unibg.it [Università degli Studi di Bergamo, Facoltà di Ingegneria, Viale Marconi 5, 24044 Dalmine (Bergamo) (Italy); I.N.F.N. – sezione di Milano, Milan (Italy); Majumder, Barun, E-mail: barunbasanta@iitgn.ac.in [Indian Institute of Technology Gandhinagar, Ahmedabad, Gujarat 382424 (India)
2014-07-15
We compute the Zero Point Energy (ZPE) induced by a naked singularity with the help of a reformulation of the Wheeler–DeWitt equation. A variational approach is used for the calculation with Gaussian Trial Wave Functionals. The one loop contribution of the graviton to the ZPE is extracted keeping under control the UltraViolet divergences by means of a distorted gravitational field. Two examples of distortion are taken under consideration: Gravity's Rainbow and Noncommutative Geometry. Surprisingly, we find that the ZPE is no more singular when we approach the singularity.
Cosmological perturbations in mimetic matter model
Matsumoto, Jiro; Sushkov, Sergey V
2015-01-01
We investigate the cosmological evolution of mimetic matter model with arbitrary scalar potential. The cosmological reconstruction is explicitly done for different choices of potential. The cases that mimetic matter model shows the evolution as Cold Dark Matter(CDM), wCDM model, dark matter and dark energy with dynamical $Om(z)$ or phantom dark energy with phantom-non-phantom crossing are presented in detail. The cosmological perturbations for such evolution are studied in mimetic matter model. For instance, the evolution behavior of the matter density contrast which is different from usual one, i.e. $\\ddot \\delta + 2 H \\dot \\delta - \\kappa ^2 \\rho \\delta /2 = 0$ is investigated. The possibility of peculiar evolution of $\\delta$ in the model under consideration is shown. Special attention is paid to the behavior of matter density contrast near to future singularity where decay of perturbations may occur much earlier the singularity.
Ghost and singularity free theories of gravity
Buoninfante, L; Mazumdar, A
2016-01-01
Albert Einstein's General Relativity (GR) from 1916 has become the widely accepted theory of gravity and been tested observationally to a very high precision at different scales of energy and distance. At the same time, there still remain important questions to resolve. The presence of cosmological and black hole singularities are examples of problems at the classical level which strongly suggest the incompleteness of GR at short distances (high energy). Furthermore, at the quantum level GR is not UV complete, namely it is not perturbatively renormalizable. These two kind of questions, classical and quantum, could be closely related as both concern short-distance (high energy) physics. Most of the work try to solve these problems modifying GR by considering finite higher order derivative terms. Fourth Order Gravity, for example, turns out to be renormalizable, but at the same time it introduces ghost. To avoid both UV divergence and presence of ghost one could consider an infinite set of higher derivative ter...
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.
BOUNDEDNESS OF MAXIMAL SINGULAR INTEGRALS
Institute of Scientific and Technical Information of China (English)
CHEN JIECHENG; ZHU XIANGRONG
2005-01-01
The authors study the singular integrals under the Hormander condition and the measure not satisfying the doubling condition. At first, if the corresponding singular integral is bounded from L2 to itseff, it is proved that the maximal singu lar integral is bounded from L∞ to RBMO except that it is infinite μ-a.e. on Rd. A sufficient condition and a necessary condition such that the maximal singular integral is bounded from L2 to itself are also obtained. There is a small gap between the two conditions.
Perturbation theory for solitons in optical fibers
Kaup, D. J.
1990-11-01
Using a singular perturbation expansion, we study the evolution of a Raman loss compensated soliton in an optical fiber. Our analytical results agree quite well with the numerical results of Mollenauer, Gordon, and Islam [IEEE J. Quantum Electron. QE-22, 157 (1986)]. However, there are some differences in that our theory predicts an additional structure that was only partially seen in the numerical calculations. Our analytical results do give a quite good qualitative and quantitative check of the numerical results.
Alien calculus and non perturbative effects in Quantum Field Theory
Bellon, Marc P.
2016-12-01
In many domains of physics, methods for dealing with non-perturbative aspects are required. Here, I want to argue that a good approach for this is to work on the Borel transforms of the quantities of interest, the singularities of which give non-perturbative contributions. These singularities in many cases can be largely determined by using the alien calculus developed by Jean Écalle. My main example will be the two point function of a massless theory given as a solution of a renormalization group equation.
Combined perturbation bounds:Ⅱ.Polar decompositions
Institute of Scientific and Technical Information of China (English)
2007-01-01
In this paper,we study the perturbation bounds for the polar decomposition A=QH where Q is unitary and H is Hermitian.The optimal （asymptotic） bounds obtained in previous works for the unitary factor,the Hermitian factor and singular values of A areσr2||ΔQ||F2≤||ΔA||F2, 1/2||ΔH||F2≤||ΔA||F2 and ||Δ∑||F2≤||ΔA||F2,respectively,where∑=diag（σ1,σ2,...,σr,0,...,0） is the singular value matrix of A andσr denotes the smallest nonzero singular value.Here we present some new combined （asymptotic） perturbation boundsσr2||ΔQ||F2+1/2||ΔH||F2≤||ΔA||F2 andσr2||ΔQ||F2+||Δ∑||F2≤||ΔA||F2 which are optimal for each factor.Some corresponding absolute perturbation bounds are also given.
Segmentation of singularity maps in the context of soil porosity
Martin-Sotoca, Juan J.; Saa-Requejo, Antonio; Grau, Juan; Tarquis, Ana M.
2016-04-01
Geochemical exploration have found with increasingly interests and benefits of using fractal (power-law) models to characterize geochemical distribution, including concentration-area (C-A) model (Cheng et al., 1994; Cheng, 2012) and concentration-volume (C-V) model (Afzal et al., 2011) just to name a few examples. These methods are based on the singularity maps of a measure that at each point define areas with self-similar properties that are shown in power-law relationships in Concentration-Area plots (C-A method). The C-A method together with the singularity map ("Singularity-CA" method) define thresholds that can be applied to segment the map. Recently, the "Singularity-CA" method has been applied to binarize 2D grayscale Computed Tomography (CT) soil images (Martin-Sotoca et al, 2015). Unlike image segmentation based on global thresholding methods, the "Singularity-CA" method allows to quantify the local scaling property of the grayscale value map in the space domain and determinate the intensity of local singularities. It can be used as a high-pass-filter technique to enhance high frequency patterns usually regarded as anomalies when applied to maps. In this work we will put special attention on how to select the singularity thresholds in the C-A plot to segment the image. We will compare two methods: 1) cross point of linear regressions and 2) Wavelets Transform Modulus Maxima (WTMM) singularity function detection. REFERENCES Cheng, Q., Agterberg, F. P. and Ballantyne, S. B. (1994). The separation of geochemical anomalies from background by fractal methods. Journal of Geochemical Exploration, 51, 109-130. Cheng, Q. (2012). Singularity theory and methods for mapping geochemical anomalies caused by buried sources and for predicting undiscovered mineral deposits in covered areas. Journal of Geochemical Exploration, 122, 55-70. Afzal, P., Fadakar Alghalandis, Y., Khakzad, A., Moarefvand, P. and Rashidnejad Omran, N. (2011) Delineation of mineralization zones in
Gravitational collapse and naked singularities
Indian Academy of Sciences (India)
Tomohiro Harada
2004-10-01
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 collapse. Recent developments have revealed that there are examples of naked singularity formation in the collapse of physically reasonable matter fields, although the stability of these examples is still uncertain. We propose the concept of `effective naked singularities', which will be quite helpful because general relativity has limitation in its application at the high-energy end. The appearance of naked singularities is not detestable but can open a window for the new physics of strongly curved space-times.
Holographic signatures of cosmological singularities.
Engelhardt, Netta; Hertog, Thomas; Horowitz, Gary T
2014-09-19
To gain insight into the quantum nature of cosmological singularities, we study anisotropic Kasner solutions in gauge-gravity duality. The dual description of the bulk evolution towards the singularity involves N=4 super Yang-Mills theory on the expanding branch of deformed de Sitter space and is well defined. We compute two-point correlators of Yang-Mills operators of large dimensions using spacelike geodesics anchored on the boundary. The correlators show a strong signature of the singularity around horizon scales and decay at large boundary separation at different rates in different directions. More generally, the boundary evolution exhibits a process of particle creation similar to that in inflation. This leads us to conjecture that information on the quantum nature of cosmological singularities is encoded in long-wavelength features of the boundary wave function.
Penrose Limits and Spacetime Singularities
Blau, Matthias; O'Loughlin, M; Papadopoulos, G; Blau, Matthias; Borunda, Monica; Loughlin, Martin O'; Papadopoulos, George
2003-01-01
We give a covariant characterisation of the Penrose plane wave limit: the plane wave profile matrix $A(u)$ is the restriction of the null geodesic deviation matrix (curvature tensor) of the original spacetime metric to the null geodesic, evaluated in a comoving frame. We also consider the Penrose limits of spacetime singularities and show that for a large class of black hole, cosmological and null singularities (of Szekeres-Iyers ``power-law type''), including those of the FRW and Schwarzschild metrics, the result is a singular homogeneous plane wave with profile $A(u)\\sim u^{-2}$, the scale invariance of the latter reflecting the power-law behaviour of the singularities.
Dual geometries and spacetime singularities
Quirós, I
2000-01-01
The concept of geometrical duality is disscused in the context of Brans-Dicke theory and extended to general relativity. It is shown, in some generic cases, that spacetime singularities that arise in usual Riemannian general relativity, may be avoided in its dual representation: Weyl-like general relativity, thus providing a singularity-free picture of the World that is physicaly equivalent to the canonical general relativistic one.
Polarization singularity anisotropy: determining monstardom
Dennis, Mark R
2008-01-01
C points, that is isolated points of circular polarization in transverse fields of varying polarization, are classified morphologically into three distinct types, known as lemons, stars and monstars. These morphologies are interpreted here according to two natural parameters associated with the singularity, namely the anisotropy of the C point, and the polarization azimuth on the anisotropy axis. In addition to providing insight into singularity morphology, this observation applies to the densities of the various morphologies in isotropic random polarization speckle fields.
Singular traces theory and applications
Sukochev, Fedor; Zanin, Dmitriy
2012-01-01
This text is the first complete study and monograph dedicated to singular traces. For mathematical readers the text offers, due to Nigel Kalton's contribution, a complete theory of traces on symmetrically normed ideals of compact operators. For mathematical physicists and other users of Connes' noncommutative geometry the text offers a complete reference to Dixmier traces and the deeper mathematical features of singular traces. An application section explores the consequences of these features, which previously were not discussed in general texts on noncommutative geometry.
Dynkin graphs and quadrilateral singularities
Urabe, Tohsuke
1993-01-01
The study of hypersurface quadrilateral singularities can be reduced to the study of elliptic K3 surfaces with a singular fiber of type I * 0 (superscript *, subscript 0), and therefore these notes consider, besides the topics of the title, such K3 surfaces too. The combinations of rational double points that can occur on fibers in the semi-universal deformations of quadrilateral singularities are examined, to show that the possible combinations can be described by a certain law from the viewpoint of Dynkin graphs. This is equivalent to saying that the possible combinations of singular fibers in elliptic K3 surfaces with a singular fiber of type I * 0 (superscript *, subscript 0) can be described by a certain law using classical Dynkin graphs appearing in the theory of semi-simple Lie groups. Further, a similar description for thecombination of singularities on plane sextic curves is given. Standard knowledge of algebraic geometry at the level of graduate students is expected. A new method based on graphs wil...
Complex curves and non-perturbative effects in c=1 string theory
Alexandrov, S
2004-01-01
We investigate a complex curve in the $c=1$ string theory which provides a geometric interpretation for different kinds of D-branes. The curve is constructed for a theory perturbed by a tachyon potential using its matrix model formulation. The perturbation removes the degeneracy of the non-perturbed curve and allows to identify its singularities with ZZ branes. Also, using the constructed curve, we find non-perturbative corrections to the free energy and elucidate their CFT origin.
SINGULAR INTEGRALS ALONG SURFACES ON PRODUCT DOMAINS
Institute of Scientific and Technical Information of China (English)
Hussain Al-Qassem
2004-01-01
In this paper, we study the mapping properties of singular integral operator along surfaces of revolution. We prove Lp bounds (1 ＜ p ＜∞) for such singular integral operators as well as for their corresponding maximal truncated singular integrals if the singular kernels are allowed to be in certain block spaces.
A New Type of Singularity Theorem
Senovilla, José M M
2007-01-01
A new type of singularity theorem, based on spatial averages of physical quantities, is presented and discussed. Alternatively, the results inform us of when a spacetime can be singularity-free. This theorem provides a decisive observational difference between singular and non-singular, globally hyperbolic, open cosmological models.
DEFF Research Database (Denmark)
Kristiansen, Kristian Uldall; Hogan, S. J.
2015-01-01
In this paper we use the blowup method of Dumortier and Roussarie, in the formulation due to Krupa and Szmolyan, to study the regularization of singularities of piecewise smooth dynamical systems in R3. Using the regularization method of Sotomayor and Teixeira, we first demonstrate the power of our...... approach by considering the case of a fold line. We quickly extend a main result of Reves and Seara in a simple manner. Then, for the two-fold singularity, we show that the regularized system only fully retains the features of the singular canards in the piecewise smooth system in the cases when...... the sliding region does not include a full sector of singular canards. In particular, we show that every locally unique primary singular canard persists the regularizing perturbation. For the case of a sector of primary singular canards, we show that the regularized system contains a canard, provided...
Negative Point Mass Singularities in General Relativity
Robbins, Nicholas
2010-01-01
First we review the definition of a negative point mass singularity. Then we examine the gravitational lensing effects of these singularities in isolation and with shear and convergence from continuous matter. We review the Inverse Mean Curvature Flow and use this flow to prove some new results about the mass of a singularity, the ADM mass of the manifold, and the capacity of the singularity. We describe some particular examples of these singularities that exhibit additional symmetries.
On the Milnor fibers of sandwiched singularities
Nemethi, Andras; Popescu-Pampu, Patrick
2009-01-01
The sandwiched surface singularities are those rational surface singularities which dominate birationally smooth surface singularities. de Jong and van Straten showed that one can reduce the study of the deformations of a sandwiched surface singularity to the study of deformations of a 1-dimensional object, a so-called decorated plane curve singularity. In particular, the Milnor fibers corresponding to their various smoothing components may be reconstructed up to diffeomorphisms from those de...
On the genericity of spacetime singularities
Indian Academy of Sciences (India)
Pankaj S Joshi
2007-07-01
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 horizon of gravity. It is shown that the visible singularities that develop as final states of spherical collapse are generic. Some consequences of this fact are discussed.
A quantitative analysis of singular inflation with scalar-tensor and modified gravity
Nojiri, S; Oikonomou, V K
2015-01-01
We provide a detailed quantitative description of singular inflation. Its close analogy with finite-time future singularity which is associated to dark energy era is described. Calling and classifying the singularities of such inflation as finite-time cosmological singularities we investigate their occurrence, with special emphasis on the Type IV singularity. The study is performed in the context of a general non-canonical scalar-tensor theory. In addition, the impact of finite time singularities on the slow-roll parameters is also investigated. Particularly, we study three cases, in which the singularity occurs during the inflationary era, at the end, and also we study the case that the singularity occurs much more later than inflation ends. Using the obtained slow-roll parameters, for each case, we calculate explicitly the spectral index of primordial curvature perturbations $n_s$, the associated running of the spectral index $a_s$ and of the scalar-to-tensor ratio $r$ and compare the resulting values to th...
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.
Spacetime Singularities in Quantum Gravity
Minassian, Eric A.
2000-04-01
Recent advances in 2+1 dimensional quantum gravity have provided tools to study the effects of quantization of spacetime on black hole and big bang/big crunch type singularities. I investigate effects of quantization of spacetime on singularities of the 2+1 dimensional BTZ black hole and the 2+1 dimensional torus universe. Hosoya has considered the BTZ black hole, and using a "quantum generalized affine parameter" (QGAP), has shown that, for some specific paths, quantum effects "smear" the singularities. Using gaussian wave functions as generic wave functions, I found that, for both BTZ black hole and the torus universe, there are families of paths that still reach the singularities with a finite QGAP, suggesting that singularities persist in quantum gravity. More realistic calculations, using modular invariant wave functions of Carlip and Nelson for the torus universe, offer further support for this conclusion. Currently work is in progress to study more realistic quantum gravity effects for BTZ black holes and other spacetime models.
Singular solutions of doubly singular parabolic equations with absorption
Directory of Open Access Journals (Sweden)
Yuanwei Qi
2000-11-01
Full Text Available In this paper we study a doubly singular parabolic equation with absorption, $$ u_t = hbox{ m div} ( |abla u^m|^{p-2}abla u^m -u^q $$ with $m>0$, $p>1$, $m(p-11$. We give a complete classification of solutions, which we call singular, that are non-negative, non-trivial, continuous in ${mathbb R}^n imes [0, inftybackslash{(0,0} $, and satisfy $u(x,0=0$ for all $xeq 0$. Applications of similar but simpler equations show that these solutions are very important in the study of intermediate asymptotic behavior of general solutions.
Pfister, Gerhard; Schulze, Mathias
2017-01-01
This book arose from a conference on “Singularities and Computer Algebra” which was held at the Pfalz-Akademie Lambrecht in June 2015 in honor of Gert-Martin Greuel’s 70th birthday. This unique volume presents a collection of recent original research by some of the leading figures in singularity theory on a broad range of topics including topological and algebraic aspects, classification problems, deformation theory and resolution of singularities. At the same time, the articles highlight a variety of techniques, ranging from theoretical methods to practical tools from computer algebra. Greuel himself made major contributions to the development of both singularity theory and computer algebra. With Gerhard Pfister and Hans Schönemann, he developed the computer algebra system SINGULAR, which has since become the computational tool of choice for many singularity theorists. The book addresses researchers whose work involves singularity theory and computer algebra from the PhD to expert level.
Sudakov Safety in Perturbative QCD
Larkoski, Andrew J; Thaler, Jesse
2015-01-01
Traditional calculations in perturbative quantum chromodynamics (pQCD) are based on an order-by-order expansion in the strong coupling $\\alpha_s$. Observables that are calculable in this way are known as "safe". Recently, a class of unsafe observables was discovered that do not have a valid $\\alpha_s$ expansion but are nevertheless calculable in pQCD using all-orders resummation. These observables are called "Sudakov safe" since singularities at each $\\alpha_s$ order are regulated by an all-orders Sudakov form factor. In this letter, we give a concrete definition of Sudakov safety based on conditional probability distributions, and we study a one-parameter family of momentum sharing observables that interpolate between the safe and unsafe regimes. The boundary between these regimes is particularly interesting, as the resulting distribution can be understood as the ultraviolet fixed point of a generalized fragmentation function, yielding a leading behavior that is independent of $\\alpha_s$.
Initial conditions for cosmological perturbations
Ashtekar, Abhay
2016-01-01
Penrose proposed that the big bang singularity should be constrained by requiring that the Weyl curvature vanishes there. The idea behind this past hypothesis is attractive because it constrains the initial conditions for the universe in geometric terms and is not confined to a specific early universe paradigm. However, the precise statement of Penrose's hypothesis is tied to classical space-times and furthermore restricts only the gravitational degrees of freedom. These are encapsulated only in the tensor modes of the commonly used cosmological perturbation theory. Drawing inspiration from the underlying idea, we propose a quantum generalization of Penrose's hypothesis using the Planck regime in place of the big bang, and simultaneously incorporating tensor as well as scalar modes. Initial conditions selected by this generalization constrain the universe to be as homogeneous and isotropic in the Planck regime \\emph{as permitted by the Heisenberg uncertainty relations}.
Brane-like singularities with no brane
Energy Technology Data Exchange (ETDEWEB)
Yurov, A.V., E-mail: artyom_yurov@mail.r [I. Kant Russian State University, Theoretical Physics Department, Al. Nevsky St. 14, Kaliningrad 236041 (Russian Federation)
2010-05-17
We use a method of linearization to study the emergence of the future cosmological singularity characterized by finite value of the cosmological radius. We uncover such singularities that keep Hubble parameter finite while making all higher derivatives of the scale factor (starting out from the a) diverge as the cosmological singularity is approached. Since such singularities has been obtained before in the brane world model we name them the 'brane-like' singularities. These singularities can occur during the expanding phase in usual Friedmann universe filled with both a self-acting, minimally coupled scalar field and a homogeneous tachyon field. We discover a new type of finite-time, future singularity which is different from type I-IV cosmological singularities in that it has the scale factor, pressure and density finite and nonzero. The generalization of w-singularity is obtained as well.
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.
Cosmological density perturbations from perturbed couplings
Tsujikawa, S
2003-01-01
The density perturbations generated when the inflaton decay rate is perturbed by a light scalar field $\\chi$ are studied. By explicitly solving the perturbation equations for the system of two scalar fields and radiation, we show that even in low energy-scale inflation nearly scale-invariant spectra of scalar perturbations with an amplitude set by observations are obtained through the conversion of $\\chi$ fluctuations into adiabatic density perturbations. We demonstrate that the spectra depend on the average decay rate of the inflaton & on the inflaton fluctuations. We then apply this new mechanism to string cosmologies & generalized Einstein theories and discuss the conditions under which scale-invariant spectra are possible.
Naked singularities as particle accelerators
Patil, Mandar; 10.1103/PhysRevD.82.104049
2010-01-01
We investigate here the particle acceleration by naked singularities to arbitrarily high center of mass energies. Recently it has been suggested that black holes could be used as particle accelerators to probe the Planck scale physics. We show that the naked singularities serve the same purpose and probably would do better than their black hole counterparts. We focus on the scenario of a self-similar gravitational collapse starting from a regular initial data, leading to the formation of a globally naked singularity. It is seen that when particles moving along timelike geodesics interact and collide near the Cauchy horizon, the energy of collision in the center of mass frame will be arbitrarily high, thus offering a window to Planck scale physics.
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.
Infrared singularities in QCD amplitudes
Gardi, Einan
2009-01-01
We review recent progress in determining the infrared singularity structure of on-shell scattering amplitudes in massless gauge theories. We present a simple ansatz where soft singularities of any scattering amplitude of massless partons, to any loop order, are written as a sum over colour dipoles, governed by the cusp anomalous dimension. We explain how this formula was obtained, as the simplest solution to a newly-derived set of equations constraining the singularity structure to all orders. We emphasize the physical ideas underlying this derivation: the factorization of soft and collinear modes, the special properties of soft gluon interactions, and the notion of the cusp anomaly. Finally, we briefly discuss potential multi-loop contributions going beyond the sum-over-dipoles formula, which cannot be excluded at present.
Singular Integrals with Bilinear Phases
Institute of Scientific and Technical Information of China (English)
Elena PRESTINI
2006-01-01
We prove the boundedness from Lp(T2) to itself, 1 ＜ p ＜∞, of highly oscillatory singular integrals Sf(x, y) presenting singularities of the kind of the double Hilbert transform on a non-rectangular domain of integration, roughly speaking, defined by |y′| ＞ | x′|, and presenting phases λ(Ax + By) with 0 ≤ A, B ≤ 1 and λ≥ 0. The norms of these oscillatory singular integrals are proved to be independent of all parameters A, B and λ involved. Our method extends to a more general family of phases. These results are relevant to problems of almost everywhere convergence of double Fourier and Walsh series.
Big-Bounce with Finite-time Singularity: The $F(R)$ Gravity Description
Odintsov, S D
2015-01-01
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 the singular ...
Ambient cosmology and spacetime singularities
Antoniadis, Ignatios
2015-01-01
We present a new approach to the issues of spacetime singularities and cosmic censorship in general relativity. This is based on the idea that standard 4-dimensional spacetime is the conformal infinity of an ambient metric for the 5-dimensional Einstein equations with fluid sources. We then find that the existence of spacetime singularities in four dimensions is constrained by asymptotic properties of the ambient 5-metric, while the non-degeneracy of the latter crucially depends on cosmic censorship holding on the boundary.
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.)
Okulov, A Yu
2009-01-01
The interaction of the two counter-propagating ultrashort laser pulses of a picosecond duration with a singular wavefronts in the thin slice of the underdense plasma is considered. It is shown that ion-acoustic wave excited via Brillouin three-wave resonance by corkscrew interference pattern acts as a rotating solenoid generating kilogauss quasi-static magnetic fields. The orbital angular momentum carried by light is imprinted into an ion-acoustic liquid. The exact analytical configurations for an ion-acoustic wave current and magnetic field are given for a general class of a paraxial singular beams with an integer topological charges. The range of experimentally accessible parameters is evaluated.
Converting entropy to curvature perturbations after a cosmic bounce
Energy Technology Data Exchange (ETDEWEB)
Fertig, Angelika; Lehners, Jean-Luc; Mallwitz, Enno; Wilson-Ewing, Edward [Max Planck Institute for Gravitational Physics, Albert Einstein Institute,14476 Potsdam-Golm (Germany)
2016-10-04
We study two-field bouncing cosmologies in which primordial perturbations are created in either an ekpyrotic or a matter-dominated contraction phase. We use a non-singular ghost condensate bounce model to follow the perturbations through the bounce into the expanding phase of the universe. In contrast to the adiabatic perturbations, which on large scales are conserved across the bounce, entropy perturbations can grow significantly during the bounce phase. If they are converted into adiabatic/curvature perturbations after the bounce, they typically form the dominant contribution to the observed temperature fluctuations in the microwave background, which can have several beneficial implications. For ekpyrotic models, this mechanism loosens the constraints on the amplitude of the ekpyrotic potential while naturally suppressing the intrinsic amount of non-Gaussianity. For matter bounce models, the mechanism amplifies the scalar perturbations compared to the associated primordial gravitational waves.
Converting entropy to curvature perturbations after a cosmic bounce
Fertig, Angelika; Mallwitz, Enno; Wilson-Ewing, Edward
2016-01-01
We study two-field bouncing cosmologies in which primordial perturbations are created in either an ekpyrotic or a matter-dominated contraction phase. We use a non-singular ghost condensate bounce model to follow the perturbations through the bounce into the expanding phase of the universe. In contrast to the adiabatic perturbations, which on large scales are conserved across the bounce, entropy perturbations can grow significantly during the bounce phase. If they are converted into adiabatic/curvature perturbations after the bounce, they typically form the dominant contribution to the observed temperature fluctuations in the microwave background, which can have several beneficial implications. For ekpyrotic models, this mechanism loosens the constraints on the amplitude of the ekpyrotic potential while naturally suppressing the intrinsic amount of non-Gaussianity. For matter bounce models, the mechanism amplifies the scalar perturbations compared to the associated primordial gravitational waves.
Correlation energy for elementary bosons: Physics of the singularity
Shiau, Shiue-Yuan; Combescot, Monique; Chang, Yia-Chung
2016-04-01
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.
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.
Electrostatic fields without singularities: Theory and algorithms
Energy Technology Data Exchange (ETDEWEB)
Pellegrini, M. [Instituto di Matematica Computazionale del CNR, Pisa (Italy)
1996-12-31
We consider the following problem which arises in the computation of electrostatic fields. We are given two convex disjoint simplicies S{sub 1} and S{sub 2} in 3-space, of volume respectively V{sub 1} and V{sub 2}, with a uniform charge density respectively p{sub 1} and p{sub 2}. We want to compute the electrostatic force F{sub 12} acting on the two simplicies. We describe a Monte Carlo method that computes an approximation F{prime}{sub 12} of F{sub 12} such that, with probability 1 - {delta}, the absolute approximation error is {parallel}F{sub 12} - F{prime}{sub 12}{parallel} {le} {epsilon}p{sub 1} V{sub 1}p{sub 2} V{sub 2}, for any {epsilon} > 0. The approximation is computed in time O({epsilon}{sup -2} log {delta}{sup -1}) in the real-RAM model. We do not make use of any additional assumption, in particular, on the minimum distance between the two objects. The method is very simple, practical, and easy to extend to non-convex polyhedra. This result is obtained using a new interpretation of the electrostatic field, based on integral geometry, which eliminates the singularities present in traditional definitions of the electrostatic force and electrostatic potential. A singularity-free expression of the electrostatic force, beside its elegance, has the beneficial effect of making the derived algorithms more robust against numerical errors.
PERSISTENT HOMOCLINIC ORBITS FOR A PERTURBED CUBIC-QUINTIC NONLINEAR SCHRODINGER EQUATION
Institute of Scientific and Technical Information of China (English)
郭柏灵; 陈翰林
2002-01-01
In this paper, the existence of homoclinic orbits, for a perturbed cubicquintic nonlinear Schrodinger equation with even periodic boundary conditions, under the generalized parameters conditions is established. More specifically, we combine geometric singular perturbation theory with Melnikov analysis and integrable theory to prove the persistence of homoclinic orbits.
Singularity: Raychaudhuri equation once again
Indian Academy of Sciences (India)
Naresh Dadhich
2007-07-01
I first recount Raychaudhuri's deep involvement with the singularity problem in general relativity. I then argue that precisely the same situation has arisen today in loop quantum cosmology as obtained when Raychaudhuri discovered his celebrated equation. We thus need a new analogue of the Raychaudhuri equation in quantum gravity.
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
Lightlike singularities in compactified supergravity
Baal, P. van; Bais, F.A.
1983-01-01
We discuss the (causal) structure of a recently found black hole solution of compatified d = 11 supergravity. It is shown that the singularity is in fact lightlike and coincides with the horizon. Consequences are that the Hawking temperature is undetermined and that there is no other universe connec
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 i
Lightlike singularities in compactified supergravity
Baal, P. van; Bais, F.A.
1983-01-01
We discuss the (causal) structure of a recently found black hole solution of compatified d = 11 supergravity. It is shown that the singularity is in fact lightlike and coincides with the horizon. Consequences are that the Hawking temperature is undetermined and that there is no other universe connec
Singularities in Speckled Speckle: Screening
Kessler, David A
2008-01-01
We study screening of optical singularities in random optical fields with two widely different length scales. We call the speckle patterns generated by such fields speckled speckle, because the major speckle spots in the pattern are themselves highly speckled. We study combinations of fields whose components exhibit short- and long-range correlations, and find unusual forms of screening.
Singularity: zijn wij technologisch upgradable
Reep, Frans van der
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 i
On the concept of spectral singularities
Indian Academy of Sciences (India)
Gusein Sh Guseinov
2009-09-01
In this paper, we discuss the concept of spectral singularities for non-Hermitian Hamiltonians. We exihibit spectral singularities of some well-known concrete Hamiltonians with complex-valued coefficients.
Singular Soliton Operators and Indefinite Metrics
Grinevich, P. G.; Novikov, S. P.
2011-01-01
The singular real second order 1D Schrodinger operators are considered here with such potentials that all local solutions near singularities to the eigenvalue problem are meromorphic for all values of the spectral parameter. All algebro-geometrical or "singular finite-gap" potentials satisfy to this condition. A Spectral Theory is constructed here for the periodic and rapidly decreasing cases in the special classes of functions with singularities and indefinite inner product. It has a finite ...
Free string evolution across plane wave singularities
Craps, Ben; Evnin, Oleg
2009-01-01
In these proceedings, we summarize our studies of free string propagation in (near-)singular scale-invariant plane wave geometries. We analyze the singular limit of the evolution for the center-of-mass motion and all excited string modes. The requirement that the entire excitation energy of the string should be finite excludes consistent propagation across the singularity, in case no dimensionful scales are introduced at the singular locus (in an otherwise scale-invariant space-time).
Singular integral on bounded strictly pseudoconvex domain
Institute of Scientific and Technical Information of China (English)
GONG Ding-dong
2008-01-01
Kytmanov and Myslivets gave a special Cauchy principal value of the singular integral on the bounded strictly pseudoconvex domain with smooth boundary. By means of this Cauchy integral principal value, the corresponding singular integral and a composition formula are obtained. This composition formula is quite different from usual ones in form. As an application, the corresponding singular integral equation and the system of singular integral equations are discussed as well.
Eigenvalues of singular differential operators by finite difference methods. II.
Baxley, J. V.
1972-01-01
Note is made of an earlier paper which defined finite difference operators for the Hilbert space L2(m), and gave the eigenvalues for these operators. The present work examines eigenvalues for higher order singular differential operators by using finite difference methods. The two self-adjoint operators investigated are defined by a particular value in the same Hilbert space, L2(m), and are strictly positive with compact inverses. A class of finite difference operators is considered, with the idea of application to the theory of Toeplitz matrices. The approximating operators consist of a good approximation plus a perturbing operator.
Renormalized Volumes with Boundary
Gover, A Rod
2016-01-01
We develop a general regulated volume expansion for the volume of a manifold with boundary whose measure is suitably singular along a separating hypersurface. The expansion is shown to have a regulator independent anomaly term and a renormalized volume term given by the primitive of an associated anomaly operator. These results apply to a wide range of structures. We detail applications in the setting of measures derived from a conformally singular metric. In particular, we show that the anomaly generates invariant (Q-curvature, transgression)-type pairs for hypersurfaces with boundary. For the special case of anomalies coming from the volume enclosed by a minimal hypersurface ending on the boundary of a Poincare--Einstein structure, this result recovers Branson's Q-curvature and corresponding transgression. When the singular metric solves a boundary version of the constant scalar curvature Yamabe problem, the anomaly gives generalized Willmore energy functionals for hypersurfaces with boundary. Our approach ...
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...
Third-Body Perturbation Using a Single Averaged Model: Application in Nonsingular Variables
Directory of Open Access Journals (Sweden)
Carlos Renato Huaura Solórzano
2007-01-01
Full Text Available The Lagrange's planetary equations written in terms of the classical orbital elements have the disadvantage of singularities in eccentricity and inclination. These singularities are due to the mathematical model used and do not have physical reasons. In this paper, we studied the third-body perturbation using a single averaged model in nonsingular variables. The goal is to develop a semianalytical study of the perturbation caused in a spacecraft by a third body using a single averaged model to eliminate short-period terms caused by the motion of the spacecraft. This is valid if no resonance occurs with the moon or the sun. Several plots show the time histories of the Keplerian elements of equatorial and circular orbits, which are the situations with singularities. In this paper, the expansions are limited only to second order in eccentricity and for the ratio of the semimajor axis of the perturbing and perturbed bodies and to the fourth order for the inclination.
Singularities from colliding plane gravitational waves
Tipler, Frank J.
1980-12-01
A simple geometrical argument is given which shows that a collision between two plane gravitational waves must result in singularities. The argument suggests that these singularities are a peculiar feature of plane waves, because singularities are also a consequence of a collision between self-gravitating plane waves of other fields with arbitrarily small energy density.
Singularities from colliding plane gravitational waves
Energy Technology Data Exchange (ETDEWEB)
Tipler, F.J.
1980-12-15
A simple geometrical argument is given which shows that a collision between two plane gravitational waves must result in singularities. The argument suggests that these singularities are a peculiar feature of plane waves, because singularities are also a consequence of a collision between self-gravitating plane waves of other fields with arbitrarily small energy density.
Singularity development and supersymmetry in holography
Buchel, Alex
2017-08-01
We study the effects of supersymmetry on singularity development scenario in holography presented in [1] (BBL). We argue that the singularity persists in a supersymmetric extension of the BBL model. The challenge remains to find a string theory embedding of the singularity mechanism.
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 demonstrated how a singular integral equation with infinite support can be solved by use of the preceding formulae....
Evolution of cosmological perturbations in a stage dominated by an oscillatory scalar field
Kodama, H; Kodama, Hideo; Hamazaki, Takashi
1996-01-01
In the investigation of the evolution of cosmological perturbations in inflationary universe models the behavior of perturbations during the reheating stage is the most unclear point. In particular in the early reheating phase in which a rapidly oscillating scalar field dominates the energy density, the behavior of perturbations is not known well because their evolution equation expressed in terms of the curvature perturbation becomes singular. In this paper it is shown that in spite of this singular behavior of the evolution equation the Bardeen parameter stays constant in a good accuracy during this stage for superhorizon-scale perturbations except for a sequence of negligibly short intervals around the zero points of the time derivative of the scalar field. This justifies the conventional formula relating the amplitudes of quantum fluctuations during inflation and those of adiabatic perturbations at horizon crossing in the Friedmann stage, except for possible corrections produced by the energy transfer fro...
Double perturbation series in the differential equations of enzyme kinetics
Fraser, Simon J.
1998-07-01
The connection between combined singular and ordinary perturbation methods and slow-manifold theory is discussed using the Michaelis-Menten model of enzyme catalysis as an example. This two-step mechanism is described by a planar system of ordinary differential equations (ODEs) with a fast transient and a slow "steady-state" decay mode. The systems of scaled nonlinear ODEs for this mechanism contain a singular (η) and an ordinary (ɛ) perturbation parameter: η multiplies the velocity component of the fast variable and dominates the fast-mode perturbation series; ɛ controls the decay toward equilibrium and dominates the slow-mode perturbation series. However, higher order terms in both series contain η and ɛ. Finite series expansions partially decouple the system of ODEs into fast-mode and slow-mode ODEs; infinite series expansions completely decouple these ODEs. Correspondingly, any slow-mode ODE approximately describes motion on M, the linelike slow manifold of the system, and in the infinite series limit this description is exact. Thus the perturbation treatment and the slow-manifold picture of the system are closely related. The functional equation for M is solved automatically with the manipulative language MAPLE. The formal η and ɛ single perturbation expansions for the slow mode yield the same double (η,ɛ) perturbation series expressions to given order. Generalizations of this procedure are discussed.
Singularities formation, structure, and propagation
Eggers, J
2015-01-01
Many key phenomena in physics and engineering are described as singularities in the solutions to the differential equations describing them. Examples covered thoroughly in this book include the formation of drops and bubbles, the propagation of a crack and the formation of a shock in a gas. Aimed at a broad audience, this book provides the mathematical tools for understanding singularities and explains the many common features in their mathematical structure. Part I introduces the main concepts and techniques, using the most elementary mathematics possible so that it can be followed by readers with only a general background in differential equations. Parts II and III require more specialised methods of partial differential equations, complex analysis and asymptotic techniques. The book may be used for advanced fluid mechanics courses and as a complement to a general course on applied partial differential equations.
Energy conditions and spacetime singularities
Energy Technology Data Exchange (ETDEWEB)
Tipler, F.J.
1978-05-15
In this paper, a number of theorems are proven which collectively show that singularities will occur in spacetime under weaker energy conditions than the strong energy condition. In particular, the Penrose theorem, which uses only the weak energy condition but which applies only to open universes, is extended to all closed universes which have a Cauchy surface whose universal covering manifold is not a three-sphere. Furthermore, it is shown that the strong energy condition in the Hawking-Penrose theorem can be replaced by the weak energy condition and the assumption that the strong energy condition holds only on the average. In addition, it is demonstrated that if the Universe is closed, then the existence of singularities follows from the averaged strong energy condition alone. It is argued that any globally hyperbolic spacetime which satisfies the weak energy condition and which contains a black hole must be null geodesically incomplete.
Singularities in fully developed turbulence
Energy Technology Data Exchange (ETDEWEB)
Shivamoggi, Bhimsen K., E-mail: bhimsen.shivamoggi@ucf.edu
2015-09-18
Phenomenological arguments are used to explore finite-time singularity (FTS) development in different physical fully-developed turbulence (FDT) situations. Effects of spatial intermittency and fluid compressibility in three-dimensional (3D) FDT and the role of the divorticity amplification mechanism in two-dimensional (2D) FDT and quasi-geostrophic FDT and the advection–diffusion mechanism in magnetohydrodynamic turbulence are considered to provide physical insights into the FTS development in variant cascade physics situations. The quasi-geostrophic FDT results connect with the 2D FDT results in the barotropic limit while they connect with 3D FDT results in the baroclinic limit and hence apparently provide a bridge between 2D and 3D. - Highlights: • Finite-time singularity development in turbulence situations is phenomenologically explored. • Spatial intermittency and compressibility effects are investigated. • Quasi-geostrophic turbulence is shown to provide a bridge between two-dimensional and three-dimensional cases.
Cosmological perturbations on the Phantom brane
Bag, Satadru; Shtanov, Yuri; Sahni, Varun
2016-01-01
We obtain a closed system of equations for scalar perturbations in a multi-component braneworld. Our braneworld possesses a phantom-like equation of state at late times, $w_{\\rm eff} < -1$, but no big-rip future singularity. In addition to matter and radiation, the braneworld possesses a new effective degree of freedom - the 'Weyl fluid' or 'dark radiation'. Setting initial conditions on super-Hubble spatial scales at the epoch of radiation domination, we evolve perturbations of radiation, pressureless matter and the Weyl fluid until the present epoch. We observe a gradual decrease in the amplitude of the Weyl-fluid perturbations after Hubble-radius crossing, which results in a negligible effect of the Weyl fluid on the evolution of matter perturbations on spatial scales relevant for structure formation. Consequently, the quasi-static approximation of Koyama and Maartens provides a good fit to the exact results during the matter-dominated epoch. We find that the late-time growth of density perturbations on...
Large Field Cutoffs Make Perturbative Series Converge
Meurice, Y
2002-01-01
For lambda phi^4 problems, convergent perturbative series can be obtained by cutting off the large field configurations. The modified series converge to values exponentially close to the exact ones. For lambda larger than some critical value, the method outperforms Pade approximants and Borel summations. We discuss some aspects of the semi-classical methods used to calculate the modified Feynman rules and estimate the error associated with the procedure. We provide a simple numerical example where the procedure works despite the fact that the Borel sum has singularities on the positive real axis.
Large field cutoffs make perturbative series converge
Meurice, Yannick
2002-03-01
For λφ 4 problems, convergent perturbative series can be obtained by cutting off the large field configurations. The modified series converge to values exponentially close to the exact ones. For λ larger than some critical value, the method outperforms Padé approximants and Borel summations. We discuss some aspects of the semi-classical methods used to calculate the modified Feynman rules and estimate the error associated with the procedure. We provide a simple numerical example where the procedure works despite the fact that the Borel sum has singularities on the positive real axis.
Ortiz, Néstor; Sarbach, Olivier; Zannias, Thomas
2015-08-01
We analyze the redshift suffered by photons originating from an external source, traversing a collapsing dust cloud, and finally being received by an asymptotic observer. In addition, we study the shadow that the collapsing cloud casts on the sky of the asymptotic observer. We find that the resulting redshift and properties of the shadow depend crucially on whether the final outcome of the complete gravitational collapse is a black hole or a naked singularity. In the black hole case, the shadow is due to the high redshift acquired by the photons as they approach the event horizon, implying that their energy is gradually redshifted toward zero within a few crossing times associated with the event horizon radius. In contrast to this, a naked singularity not only absorbs photons originating from the source, but it also emits infinitely redshifted photons with and without angular momenta. This emission introduces an abrupt cutoff in the frequency shift of the photons detected in directions close to the radial one, and it is responsible for the shadow masking the source in the naked singularity case. Furthermore, even though the shadow forms and begins to grow immediately after the observer crosses the Cauchy horizon, it takes many more crossing times than in the black hole case for the source to be occulted from the observer's eyes. We discuss possible implications of our results for testing the weak cosmic censorship hypothesis. Even though at late times the image of the source perceived by the observer looks the same in both cases, the dynamical formation of the shadow and the redshift images has distinct features and time scales in the black hole versus the naked singularity case. For stellar collapse, these time scales seem to be too short to be resolved with existing technology. However, our results may be relevant for the collapse of seeds leading to supermassive black holes.
Singularities in Speckled Speckle: Statistics
Freund, Isaac
2008-01-01
Random optical fields with two widely different correlation lengths generate far field speckle spots that are themselves highly speckled. We call such patterns speckled speckle, and study their critical points (singularities and stationary points) using analytical theory and computer simulations. We find anomalous spatial arrangements of the critical points and orders of magnitude anomalies in their relative number densities, and in the densities of the associated zero crossings.
Singularity Problem in Teleparallel Dark Energy Models
Geng, Chao-Qiang; Lee, Chung-Chi
2013-01-01
We study the singularity problem in teleparallel dark energy models. A future singularity may occur due to the non-minimal coupling of the dark energy scalar field to teleparallel gravity that effectively changes the gravitational coupling strength and can even make it diverge. This singularity may be avoided by a binding-type self-potential that keeps the scalar field away from the singularity point. For demonstration we analyze the model with a quadratic potential and show how the (non)occurrence of the singularity depends on the initial conditions and the steepness of the potential, both of which affect the competition between the self-interaction and the non-minimal coupling. To examine the capability of the binding-type potential to fit observational data and meanwhile to avoid the singularity, we perform the data fitting for this model and show that the observationally viable region up to the $3\\sigma$ confidence level is free of the future singularity.
On the Milnor fibers of sandwiched singularities
Nemethi, Andras
2009-01-01
The sandwiched surface singularities are those rational surface singularities which dominate birationally smooth surface singularities. de Jong and van Straten showed that one can reduce the study of the deformations of a sandwiched surface singularity to the study of deformations of a 1-dimensional object, a so-called decorated plane curve singularity. In particular, the Milnor fibers corresponding to their various smoothing components may be reconstructed up to diffeomorphisms from those deformations of associated decorated curves which have only ordinary singularities. Part of the topology of such a deformation is encoded in the incidence matrix between the irreducible components of the deformed curve and the points which decorate it, well-defined up to permutations of columns. Extending a previous theorem ofours, which treated the case of cyclic quotient singularities, we show that the Milnor fibers which correspond to deformations whose incidence matrices are different up to permutations of columns are n...
Non-singular dislocation fields
Energy Technology Data Exchange (ETDEWEB)
Aifantis, Elias C, E-mail: mom@mom.gen.auth.gr [Laboratory of Mechanics and Materials, Faculty of Engineering, Aristotle University of Thessaloniki, GR-54124, Thessaloniki (Greece); Center for Mechanics of Materials, Michigan Technological University, Houghton MI 49931 (United States)
2009-07-15
Non-singular solutions for dislocation and disclination fields have recently been obtained by the author and his co-workers by using a robust model of gradient elasticity theory. These solutions, whose form is simple and easy to implement, are obtained by reducing the gradient elasticity problem to a corresponding linear elasticity boundary value problem through the solutions of an inhomogeneous Helmholtz equation where the source term is the classical singular solution. The Laplacian in the Helmholtz equation, involving the extra gradient coefficient, produces a new term in the gradient solution which asymptotically approaches the negative of the classical elasticity solution on the dislocation line. Thus, the singularity is eliminated and an arbitrary estimate of the dislocation core size introduced in classical theory, is not required. These predictions are tested against atomistic calculations and their implications to various dislocation related configurations are discussed. Due to the simple and elegant form of these solutions, it is hoped that they will be useful in discrete dislocation dynamics simulations.
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.
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.
Non-singular bounce transitions in the multiverse
Energy Technology Data Exchange (ETDEWEB)
Garriga, Jaume [Departament de Fisica Fonamental i Institut de Ciencies del Cosmos, Universitat de Barcelona, Marti i Franques, 1, 08028, Barcelona (Spain); Vilenkin, Alexander; Zhang, Jun, E-mail: jaume.garriga@ub.edu, E-mail: vilenkin@cosmos.phy.tufts.edu, E-mail: jun.zhang@tufts.edu [Institute of Cosmology, Department of Physics and Astronomy, Tufts University, Medford, MA 02155 (United States)
2013-11-01
According to classical GR, negative-energy (AdS) bubbles in the multiverse terminate in big crunch singularities. It has been conjectured, however, that the fundamental theory may resolve these singularities and replace them by non-singular bounces. Here we explore possible dynamics of such bounces using a simple modification of the Friedmann equation, which ensures that the scale factor bounces when the matter density reaches some critical value ρ{sub c}. This is combined with a simple scalar field 'landscape', where the energy barriers between different vacua are small compared to ρ{sub c}. We find that the bounce typically results in a transition to another vacuum, with a scalar field displacement Δφ ∼ 1 in Planck units. If the new vacuum is AdS, we have another bounce, and so on, until the field finally transits to a positive-energy (de Sitter) vacuum. We also consider perturbations about the homogeneous solution and discuss some of their amplification mechanisms (e.g., tachyonic instability and parametric resonance). For a generic potential, these mechanisms are much less efficient than in models of slow-roll inflation. But the amplification may still be strong enough to cause the bubble to fragment into a mosaic of different vacua.
Brane World Cosmological Perturbations
Casali, A G; Wang, B; Casali, Adenauer G.; Abdalla, Elcio; Wang, Bin
2004-01-01
We consider a brane world and its gravitational linear perturbations. We present a general solution of the perturbations in the bulk and find the complete perturbed junction conditions for generic brane dynamics. We also prove that (spin 2) gravitational waves in the great majority of cases can only arise in connection with a non-vanishing anisotropic stress. This has far reaching consequences for inflation in the brane world. Moreover, contrary to the case of the radion, perturbations are stable.
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.
Singular layers for transmission problems in thin shallow shell theory: Rigid junction case
Merabet, Ismail; Chacha, D. A.; Nicaise, S.
2010-02-01
In this Note we study two-dimensional transmission problems for the linear Koiter's model of an elastic multi-structure composed of two thin shallow shells. This work enters in the framework of singular perturbation of problems depending on a small parameter ɛ. The formal limit problem fails to give a solution satisfying all boundary and transmission conditions; it gives only the outer solution. Both in the case of regular or singular loadings, we derive a limit problem which allows us to determine the inner solution explicitly.
High frequency quasi-normal modes for black-holes with generic singularities
Das, Saurya; Shankaranarayanan, S.
2004-01-01
We compute the high frequency quasi-normal modes (QNM) for scalar perturbations of spherically symmetric single horizon black-holes in $(D+2)$-space-time dimensions with generic curvature singularities and having metrics of the form $ds^2 = \\eta x^p (dy^2-dx^2) + x^q d\\O_D^2$ near the singularity $x=0$. The real part of the QN frequencies is shown to be proportional to $\\log \\le[ 1 + 2\\cos \\le(\\p \\le[ qD -2 \\ri]/2 \\ri) \\ri]$ where the constant of proportionality is equal to the Hawking temper...
A Short Review of Time Dependent Solutions and Space-like Singularities in String Theory
Energy Technology Data Exchange (ETDEWEB)
Berkooz, Micha [Department of Particle Physics, Weizmann Institute of Science, Rehovot 76100 (Israel)], E-mail: micha.berkooz@weizmann.ac.il; Reichmann, Dori [Department of Particle Physics, Weizmann Institute of Science, Rehovot 76100 (Israel)], E-mail: dor.reichmann@weizmann.ac.il
2007-09-15
These lecture notes provide a short review of the status of time dependent backgrounds in String theory, and in particular those that contain space-like singularities. Despite considerable efforts, we do not have yet a full and compelling picture of such backgrounds. We review some of the various attempts to understand these singularities via generalizations of the BKL dynamics, using worldsheet methods and using non-perturbative tools such as the AdS/CFT correspondence and M(atrix) theory. These lecture notes are based on talks given at Cargese 06 and the dead-sea conference 06.
A Short Review of Time Dependent Solutions and Space-like Singularities in String Theory
Berkooz, Micha
2007-01-01
These lecture notes provide a short review of the status of time dependent backgrounds in String theory, and in particular those that contain space-like singularities. Despite considerable efforts, we do not have yet a full and compelling picture of such backgrounds. We review some of the various attempts to understand these singularities via generalizations of the BKL dynamics, using worldsheet methods and using non-perturbative tools such as the AdS/CFT correspondence and M(atrix) theory. These lecture notes are based on talks given at Cargese 06 and the dead-sea conference 06.
Dimensional Mutation and Spacelike Singularities
Silverstein, E
2006-01-01
I argue that critical string theory on a Riemann surface of genus $h >> 1$ crosses over, when the surface approaches the string scale in size, to a background of supercritical string theory with effective central charge as large as $2h$. Concrete evidence for this proposal is provided by the high energy density of states (realized on the Riemann surface side by strings wrapping nontrivial elements of the fundamental group) and by a linear sigma model which at large $h$ approximates the time evolution through the initial transition. This suggests that cosmological singularities arising in negatively curved FRW backgrounds may be replaced by a phase of supercritical string theory.
Multichannel framework for singular quantum mechanics
Energy Technology Data Exchange (ETDEWEB)
Camblong, Horacio E., E-mail: camblong@usfca.edu [Department of Physics and Astronomy, University of San Francisco, San Francisco, CA 94117-1080 (United States); Epele, Luis N., E-mail: epele@fisica.unlp.edu.ar [Laboratorio de Física Teórica, Departamento de Física, IFLP, CONICET, Facultad de Ciencias Exactas, Universidad Nacional de La Plata, C.C. 67–1900 La Plata (Argentina); Fanchiotti, Huner, E-mail: huner@fisica.unlp.edu.ar [Laboratorio de Física Teórica, Departamento de Física, IFLP, CONICET, Facultad de Ciencias Exactas, Universidad Nacional de La Plata, C.C. 67–1900 La Plata (Argentina); García Canal, Carlos A., E-mail: garcia@fisica.unlp.edu.ar [Laboratorio de Física Teórica, Departamento de Física, IFLP, CONICET, Facultad de Ciencias Exactas, Universidad Nacional de La Plata, C.C. 67–1900 La Plata (Argentina); Ordóñez, Carlos R., E-mail: ordonez@uh.edu [Department of Physics, University of Houston, Houston, TX 77204-5506 (United States)
2014-01-15
A multichannel S-matrix framework for singular quantum mechanics (SQM) subsumes the renormalization and self-adjoint extension methods and resolves its boundary-condition ambiguities. In addition to the standard channel accessible to a distant (“asymptotic”) observer, one supplementary channel opens up at each coordinate singularity, where local outgoing and ingoing singularity waves coexist. The channels are linked by a fully unitary S-matrix, which governs all possible scenarios, including cases with an apparent nonunitary behavior as viewed from asymptotic distances. -- Highlights: •A multichannel framework is proposed for singular quantum mechanics and analogues. •The framework unifies several established approaches for singular potentials. •Singular points are treated as new scattering channels. •Nonunitary asymptotic behavior is subsumed in a unitary multichannel S-matrix. •Conformal quantum mechanics and the inverse quartic potential are highlighted.
Weyl Anomaly and Initial Singularity Crossing
Awad, Adel
2015-01-01
We consider the role of quantum effects, mainly, Weyl anomaly in modifying FLRW model singular behavior at early times. Weyl anomaly corrections to FLRW models have been considered in the past, here we reconsider this model and show the following: The singularity of this model is weak according to Tipler and Krolak, therefore, the spacetime might admit a geodesic extension. Weyl anomaly corrections changes the nature of the initial singularity from a big bang singularity to a sudden singularity. The two branches of solutions consistent with the semiclassical treatment form a disconnected manifold. Joining these two parts at the singularity provides us with a $C^1$ extension to nonspacelike geodesics and leaves the spacetime geodesically complete. Using Gauss-Codazzi equations one can derive generalized junction conditions for this higher-derivative gravity. The extended spacetime obeys Friedmann and Raychaudhuri equations and the junction conditions. The junction does not generate Dirac delta functions in mat...
Conformal anomaly around the sudden singularity
Houndjo, S J M
2010-01-01
Quantum effects due to particle creation on a classical sudden singularity have been investigated in a previous work. The conclusion was that quantum effects do not lead to the avoidance nor the modification of the sudden future singularity. In this paper, we investigate quantum corrections coming from conformal anomaly near the sudden future singularity. We conclude that when the equation of state is chosen to be $p=-\\rho-A\\rho^\\alpha$, the conformal anomaly can transform the sudden singularity in the singularity of type III for any $\\alpha> 1/2$ and in the singularity of the type I (the big rip) or the big crunch for $1/2<\\alpha<3/2$.
Conformal anomaly around the sudden singularity
Houndjo, S. J. M.
2010-10-01
Quantum effects due to particle creation on a classical sudden singularity have been investigated in a previous work. The conclusion was that quantum effects do not lead to the avoidance nor the modification of the sudden future singularity. In this paper, we investigate quantum corrections coming from conformal anomaly near the sudden future singularity. We conclude that when the equation of state is chosen to be p=-ρ-Aρα, the conformal anomaly can transform the sudden singularity into the singularity of type III for any α>1/2 and into the singularity of the type I (the big rip) or the big crunch for 1/2<α<3/2.
The geometry of warped product singularities
Stoica, Ovidiu Cristinel
In this article, the degenerate warped products of singular semi-Riemannian manifolds are studied. They were used recently by the author to handle singularities occurring in General Relativity, in black holes and at the big-bang. One main result presented here is that a degenerate warped product of semi-regular semi-Riemannian manifolds with the warping function satisfying a certain condition is a semi-regular semi-Riemannian manifold. The connection and the Riemann curvature of the warped product are expressed in terms of those of the factor manifolds. Examples of singular semi-Riemannian manifolds which are semi-regular are constructed as warped products. Applications include cosmological models and black holes solutions with semi-regular singularities. Such singularities are compatible with a certain reformulation of the Einstein equation, which in addition holds at semi-regular singularities too.
Singularity Analysis of Geometric Constraint Systems
Institute of Scientific and Technical Information of China (English)
彭小波; 陈立平; 周凡利; 周济
2002-01-01
Singularity analysis is an important subject of the geometric constraint sat-isfaction problem. In this paper, three kinds of singularities are described and corresponding identification methods are presented for both under-constrained systems and over-constrained systems. Another special but common singularity for under-constrained geometric systems, pseudo-singularity, is analyzed. Pseudo-singularity is caused by a variety of constraint match ing of under-constrained systems and can be removed by improving constraint distribution. To avoid pseudo-singularity and decide redundant constraints adaptively, a differentiation algo rithm is proposed in the paper. Its correctness and efficiency have been validated through its practical applications in a 2D/3D geometric constraint solver CBA.
String spectra near some null cosmological singularities
Madhu, Kallingalthodi
2009-01-01
We construct cosmological spacetimes with null Kasner-like singularities as purely gravitational solutions with no other background fields turned on. These can be recast as anisotropic plane-wave spacetimes by coordinate transformations. We analyse string quantization to find the spectrum of string modes in these backgrounds. The classical string modes can be solved for exactly in these time-dependent backgrounds, which enables a detailed study of the near singularity string spectrum, (time-dependent) oscillator masses and wavefunctions. We find that for low lying string modes(finite oscillation number), the classical near-singularity string mode functions are non-divergent for various families of singularities. Furthermore, for any infinitesimal regularization of the vicinity of the singularity, we find a tower of string modes of ultra-high oscillation number which propagate essentially freely in the background. The resulting picture suggests that string interactions are non-negligible near the singularity.
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.
Precursory singularities in spherical gravitational collapse
Lake, Kayll
1992-05-01
General conditions are developed for the formation of naked precursory ('shell-focusing') singularities in spherical gravitational collapse. These singularities owe their nakedness to the fact that the gravitational potential fails to be single valued prior to the onset of a true gravitational singularity. It is argued that they do not violate the spirit of cosmic censorship. Rather, they may well be an essentially generic feature of relativistic gravitational collapse.
Quantum dress for a naked singularity
Casals, Marc; Fabbri, Alessandro; Martínez, Cristián; Zanelli, Jorge
2016-09-01
We investigate semiclassical backreaction on a conical naked singularity space-time with a negative cosmological constant in (2 + 1)-dimensions. In particular, we calculate the renormalized quantum stress-energy tensor for a conformally coupled scalar field on such naked singularity space-time. We then obtain the backreacted metric via the semiclassical Einstein equations. We show that, in the regime where the semiclassical approximation can be trusted, backreaction dresses the naked singularity with an event horizon, thus enforcing (weak) cosmic censorship.
Connections Between Singular Control and Optimal Switching
Guo, Xin; Tomecek, Pascal
2007-01-01
This paper builds a new theoretical connection between singular control of finite variation and optimal switching problems. This correspondence provides a novel method for solving high-dimensional singular control problems, and enables us to extend the theory of reversible investment: sufficient conditions are derived for the existence of optimal controls and for the regularity of value functions. Consequently, our regularity result links singular controls and Dynkin games through sequential ...
Discrete equations and the singular manifold method
Estévez, P G
1999-01-01
The Painleve expansion for the second Painleve equation (PII) and fourth Painleve equation (PIV) have two branches. The singular manifold method therefore requires two singular manifolds. The double singular manifold method is used to derive Miura transformations from PII and PIV to modified Painleve type equations for which auto-Backlund transformations are obtained. These auto-Backlund transformations can be used to obtain discrete equations.
Quantum dress for a naked singularity
Casals, Marc; Martínez, Cristián; Zanelli, Jorge
2016-01-01
We investigate semiclassical backreaction on a conical naked singularity space-time with a negative cosmological constant in (2+1)-dimensions. In particular, we calculate the renormalized quantum stress-energy tensor for a conformally coupled scalar field on such naked singularity space-time. We then obtain the backreacted metric via the semiclassical Einstein equations. We show that, in the regime where the semiclassical approximation can be trusted, backreaction dresses the naked singularity with an event horizon, thus enforcing cosmic censorship.
A singularity theorem based on spatial averages
Indian Academy of Sciences (India)
J M M Senovilla
2007-07-01
Inspired by Raychaudhuri's work, and using the equation named after him as a basic ingredient, a new singularity theorem is proved. 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 (and other physical variables). This is very satisfactory and provides a clear decisive difference between singular and non-singular cosmologies.
On curves on sandwiched surface singularities
Fernandez-Sanchez, Jesus
2007-01-01
Fixed a point O on a non-singular surface S and a complete mO-primary ideal I in its local ring, the curves on the surface X obtained by blowing-up I are studied in terms of the base points of I. Criteria for the principality of these curves are obtained. New formulas for their multiplicity, intersection numbers and order of singularity at the singularities of X are given. The semigroup of branches going through a sandwiched singularity is effectively determined, too.
Three-qutrit entanglement and simple singularities
Holweck, Frédéric; Jaffali, Hamza
2016-11-01
In this paper, we use singularity theory to study the entanglement nature of pure three-qutrit systems. We first consider the algebraic variety X of separable three-qutrit states within the projective Hilbert space {{P}}({ H })={{{P}}}26. Given a quantum pure state | \\varphi > \\in {{P}}({ H }) we define the X φ -hypersuface by cutting X with a hyperplane H φ defined by the linear form ranges over the stochastic local operation and classical communication entanglement classes, the ‘worst’ possible singular X φ -hypersuface with isolated singularities, has a unique singular point of type D 4.
Generalised hyperbolicity in spacetimes with singular submanifolds
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 this paper we obtain general conditions under which the wave equation is well-posed in spacetimes with weak singularities in which the singularity is concentrated in a submanifold. In particular, the results can be applied to spacetimes with shell-crossing singularities, surface layers and generalised cosmic strings.
Singularities of slice regular functions
Stoppato, Caterina
2010-01-01
Beginning in 2006, G. Gentili and D.C. Struppa developed a theory of regular quaternionic functions with properties that recall classical results in complex analysis. For instance, in each Euclidean ball centered at 0 the set of regular functions coincides with that of quaternionic power series converging in the same ball. In 2009 the author proposed a classification of singularities of regular functions as removable, essential or as poles and studied poles by constructing the ring of quotients. In that article, not only the statements, but also the proving techniques were confined to the special case of balls centered at 0. In a subsequent paper, F. Colombo, G. Gentili, I. Sabadini and D.C. Struppa (2009) identified a larger class of domains, on which the theory of regular functions is natural and not limited to quaternionic power series. The present article studies singularities in this new context, beginning with the construction of the ring of quotients and of Laurent-type expansions at points other than ...
Perturbative Degrees of Freedom in Loop Quantum Gravity: Anisotropies
Bojowald, M; Morales-Tecotl, H A; Bojowald, Martin; Hernandez, Hector H.; Morales-Tecotl, Hugo A
2006-01-01
The relation between an isotropic and an anisotropic model in loop quantum cosmology is discussed in detail, comparing the strict symmetry reduction with a perturbative implementation of symmetry. While the latter cannot be done in a canonical manner, it allows to consider the dynamics including the role of small non-symmetric degrees of freedom for the symmetric evolution. This serves as a model for the general situation of perturbative degrees of freedom in a background independent quantization such as loop quantum gravity, and for the more complicated addition of perturbative inhomogeneities. While being crucial for cosmological phenomenology, it is shown that perturbative non-symmetric degrees of freedom do not allow definitive conclusions for the singularity issue and in such a situation could even lead to wrong claims.
Automated Lattice Perturbation Theory
Energy Technology Data Exchange (ETDEWEB)
Monahan, Christopher
2014-11-01
I review recent developments in automated lattice perturbation theory. Starting with an overview of lattice perturbation theory, I focus on the three automation packages currently "on the market": HiPPy/HPsrc, Pastor and PhySyCAl. I highlight some recent applications of these methods, particularly in B physics. In the final section I briefly discuss the related, but distinct, approach of numerical stochastic perturbation theory.
Perturbative tests of non-perturbative counting
Dabholkar, Atish; Gomes, João
2010-03-01
We observe that a class of quarter-BPS dyons in mathcal{N} = 4 theories with charge vector ( Q, P) and with nontrivial values of the arithmetic duality invariant I := gcd( Q∧ P) are nonperturbative in one frame but perturbative in another frame. This observation suggests a test of the recently computed nonperturbative partition functions for dyons with nontrivial values of the arithmetic invariant. For all values of I, we show that the nonperturbative counting yields vanishing indexed degeneracy for this class of states everywhere in the moduli space in precise agreement with the perturbative result.
Generalized Supersymmetric Perturbation Theory
Institute of Scientific and Technical Information of China (English)
B. G(o)n(ǖ)l
2004-01-01
@@ Using the basic ingredient of supersymmetry, a simple alternative approach is developed to perturbation theory in one-dimensional non-relativistic quantum mechanics. The formulae for the energy shifts and wavefunctions do not involve tedious calculations which appear in the available perturbation theories. The model applicable in the same form to both the ground state and excited bound states, unlike the recently introduced supersymmetric perturbation technique which, together with other approaches based on logarithmic perturbation theory, are involved within the more general framework of the present formalism.
Density matrix perturbation theory.
Niklasson, Anders M N; Challacombe, Matt
2004-05-14
An orbital-free quantum perturbation theory is proposed. It gives the response of the density matrix upon variation of the Hamiltonian by quadratically convergent recursions based on perturbed projections. The technique allows treatment of embedded quantum subsystems with a computational cost scaling linearly with the size of the perturbed region, O(N(pert.)), and as O(1) with the total system size. The method allows efficient high order perturbation expansions, as demonstrated with an example involving a 10th order expansion. Density matrix analogs of Wigner's 2n+1 rule are also presented.
Constraints on Stress Components at the Internal Singular Point of an Elastic Compound Structure
Pestrenin, V. M.; Pestrenina, I. V.
2017-03-01
The classical analytical and numerical methods for investigating the stress-strain state (SSS) in the vicinity of a singular point consider the point as a mathematical one (having no linear dimensions). The reliability of the solution obtained by such methods is valid only outside a small vicinity of the singular point, because the macroscopic equations become incorrect and microscopic ones have to be used to describe the SSS in this vicinity. Also, it is impossible to set constraint or to formulate solutions in stress-strain terms for a mathematical point. These problems do not arise if the singular point is identified with the representative volume of material of the structure studied. In authors' opinion, this approach is consistent with the postulates of continuum mechanics. In this case, the formulation of constraints at a singular point and their investigation becomes an independent problem of mechanics for bodies with singularities. This method was used to explore constraints at an internal singular point (representative volume) of a compound wedge and a compound rib. It is shown that, in addition to the constraints given in the classical approach, there are also constraints depending on the macroscopic parameters of constituent materials. These constraints turn the problems of deformable bodies with an internal singular point into nonclassical ones. Combinations of material parameters determine the number of additional constraints and the critical stress state at the singular point. Results of this research can be used in the mechanics of composite materials and fracture mechanics and in studying stress concentrations in composite structural elements.
Energy Technology Data Exchange (ETDEWEB)
Biswas, Tirthabir [Department of Physics, St. Cloud State University, St. Cloud, MN 56301 U.S.A (United States); Koivisto, Tomi [Institute for Theoretical Physics and Spinoza Institute, Postbus 80.195, 3508 TD Utrecht (Netherlands); Mazumdar, Anupam, E-mail: tbiswas@loyno.edu, E-mail: T.S.Koivisto@uu.nl, E-mail: a.mazumdar@lancaster.ac.uk [Physics Department, Lancaster University, Lancaster, LA1 4YB (United Kingdom)
2010-11-01
One of the greatest problems of standard cosmology is the Big Bang singularity. Previously it has been shown that non-local ghostfree higher-derivative modifications of Einstein gravity in the ultra-violet regime can admit non-singular bouncing solutions. In this paper we study in more details the dynamical properties of the equations of motion for these theories of gravity in presence of positive and negative cosmological constants and radiation. We find stable inflationary attractor solutions in the presence of a positive cosmological constant which renders inflation geodesically complete, while in the presence of a negative cosmological constant a cyclic universe emerges. We also provide an algorithm for tracking the super-Hubble perturbations during the bounce and show that the bouncing solutions are free from any perturbative instability.
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 at ...
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...
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...
On non-singular inhomogeneous cosmological models
Fernández-Jambrina, L
2009-01-01
In this talk we would like to review recent results on non-singular cosmological models. It has been recently shown that among stiff perfect fluid inhomogeneous spacetimes the absence of singularities is more common than it was expected in the literature. We would like to generalize these results and apply them to other matter sources.
Singularities inside non-Abelian black holes
Gal'tsov, D. V.; Donets, E. E.; Zotov, M. Yu.
1997-01-01
Singularities inside static spherically symmetric black holes in the SU(2) Einstein-Yang-Mills and Einstein-Yang-Mills-dilaton theories are investigated. Analytical formulas are presented describing oscillatory and power law metric behavior near spacelike singularities in generic solutions.
Twisting singular solutions of Bethe's equations
Nepomechie, Rafael I
2014-01-01
The Bethe equations for the periodic XXX and XXZ spin chains admit singular solutions, for which the corresponding eigenvalues and eigenvectors are ill-defined. We use a twist regularization to derive conditions for such singular solutions to be physical, in which case they correspond to genuine eigenvalues and eigenvectors of the Hamiltonian.
Quantum fields and "Big Rip" expansion singularities
Calderon, H; Calderon, Hector; Hiscock, William A.
2005-01-01
The effects of quantized conformally invariant massless fields on the evolution of cosmological models containing a ``Big Rip'' future expansion singularity are examined. Quantized scalar, spinor, and vector fields are found to strengthen the accelerating expansion of such models as they approach the expansion singularity.
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...
An extension theorem for conformal gauge singularities
Tod, Paul
2007-01-01
We analyse conformal gauge, or isotropic, singularities in cosmological models in general relativity. Using the calculus of tractors, we find conditions in terms of tractor curvature for a local extension of the conformal structure through a cosmological singularity and prove a local extension theorem.
Correlation singularities in partially coherent electromagnetic beams
Raghunathan, S.B.; Schouten, H.F.; Visser, T.D.
2012-01-01
We demonstrate that coherence vortices, singularities of the correlation function, generally occur in partially coherent electromagnetic beams. In successive cross sections of Gaussian Schell-model beams, their locus is found to be a closed string. These coherence singularities have implications for
Resolving curvature singularities in holomorphic gravity
Mantz, C.L.M.; Prokopec, T.
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 singularity
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...
Singular surfaces in the open field line region of a diverted tokamak
Energy Technology Data Exchange (ETDEWEB)
Reiman, A.
1995-05-01
The structure of the open field lines of a slightly nonaxisymmetric, poloidally diverted tokamak is explored by numerical integration of the field line equations for a simple model field. In practice, the nonaxisymmetry could be produced self-consistently by the nonlinear evolution of a free-boundary MHD mode, or it could be produced by field errors, or it could be imposed externally by design. In the presence of a nonaxisymmetric perturbation, the tokamak is shown to develop open field line regions of differing topology separated by singular surfaces. It is argued that the singular surfaces can be expected to play a role analogous to that of rational toroidal flux surfaces, in terms of constraining ideal MHD perturbations and thus constraining the free-energy that can be tapped by ideal MHD instabilities. The possibility of active control of free-boundary instabilities by means of currents driven on the open singular surfaces, which are directly accessible from the divertor plates, is discussed. Also discussed is the possibility of early detection of imminent disruptions through localized measurement of the singular surface currents.
Generalized Strong Curvature Singularities and Cosmic Censorship
Rudnicki, W; Kondracki, W
2002-01-01
A new definition of a strong curvature singularity is proposed. This definition is motivated by the definitions given by Tipler and Krolak, but is significantly different and more general. All causal geodesics terminating at these new singularities, which we call generalized strong curvature singularities, are classified into three possible types; the classification is based on certain relations between the curvature strength of the singularities and the causal structure in their neighborhood. A cosmic censorship theorem is formulated and proved which shows that only one class of generalized strong curvature singularities, corresponding to a single type of geodesics according to our classification, can be naked. Implications of this result for the cosmic censorship hypothesis are indicated.
Singularities in gravitational collapse with radial pressure
Gonçalves, S M C V; Goncalves, Sergio M. C. V.; Jhingan, Sanjay
2001-01-01
We analyze spherical dust collapse with non-vanishing radial pressure, $\\Pi$, and vanishing tangential stresses. Considering a barotropic equation of state, $\\Pi=\\gamma\\rho$, we obtain an analytical solution in closed form---which is exact for $\\gamma=-1,0$, and approximate otherwise---near the center of symmetry (where the curvature singularity forms). We study the formation, visibility, and curvature strength of singularities in the resulting spacetime. We find that visible, Tipler strong singularities can develop from generic initial data. Radial pressure alters the spectrum of possible endstates for collapse, increasing the parameter space region that contains no visible singularities, but cannot by itself prevent the formation of visible singularities for sufficiently low values of the energy density. Known results from pressureless dust are recovered in the $\\gamma=0$ limit.
Are loop quantum cosmos never singular?
Singh, Parampreet
2009-01-01
A unified treatment of all known types of singularities for flat, isotropic and homogeneous spacetimes in the framework of loop quantum cosmology (LQC) is presented. These include bangs, crunches and all future singularities. Using effective spacetime description we perform a model independent general analysis of the properties of curvature, behavior of geodesics and strength of singularities. For illustration purposes a phenomenological model based analysis is also performed. We show that all values of the scale factor at which a strong singularity may occur are excluded from the effective loop quantum spacetime. Further, if the evolution leads to either a vanishing or divergent scale factor then the loop quantum universe is asymptotically deSitter in that regime. We also show that there exist a class of sudden extremal events, which includes a recently discussed possibility, for which the curvature or its derivatives will always diverge. Such events however turn out to be harmless weak curvature singulariti...
On non-singular GRADELA crack fields
Directory of Open Access Journals (Sweden)
Elias C. Aifantis
2014-01-01
Full Text Available A brief account is provided on crack-tip solutions that have recently been published in the literature by employing the so-called GRADELA model and its variants. The GRADELA model is a simple gradient elasticity theory involving one internal length in addition to the two Lame' constants, in an effort to eliminate elastic singularities and discontinuities and to interpret elastic size effects. The non-singular strains and non-singular (but sometimes singular or even hypersingular stresses derived this way under different boundary conditions differ from each other and their physical meaning in not clear. This is discussed which focus on the form and physical meaning of non-singular solutions for crack-tip stresses and strains that are possible to obtain within the GRADELA model and its extensions.
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.
New Isotropic and Anisotropic Sudden Singularities
Barrow, J D; Barrow, John D.; Tsagas, Christos G.
2004-01-01
We show the existence of an infinite family of finite-time singularities in isotropically expanding universes which obey the weak, strong, and dominant energy conditions. We show what new type of energy condition is needed to exclude them ab initio. We also determine the conditions under which finite-time future singularities can arise in a wide class of anisotropic cosmological models. New types of finite-time singularity are possible which are characterised by divergences in the time-rate of change of the anisotropic-pressure tensor. We investigate the conditions for the formation of finite-time singularities in a Bianchi type $VII_{0}$ universe with anisotropic pressures and construct specific examples of anisotropic sudden singularities in these universes.
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....
$f(R,T)$ and future singularities
Mirza, Behrouz
2014-01-01
We investigate equations of motion and future singularities of $f(R,T)$ gravity where $R$ is the Ricci scalar and $T$ is the trace of stress-energy tensor. Future singularities for two kinds of equation of state (barotropic perfect fluid and generalized form of equation of state) are studied. While no future singularity is found for the first case, some kind of singularity is found to be possible for the second. Using the method of fixed points and certain assumptions, a large number of singularities can be removed. Finally, the effect of the Noether symmetry on $f(R,T)$ is studied and the consistent form of $f(R,T)$ function is found using the symmetry and the conserved charge.
On some singularities of the correlation functions that determine neutrino opacities
Sawyer, R F
1999-01-01
Certain perturbation graphs in the calculation of the effects of the medium on neutrino scattering in supernova matter have a nonintegrable singularity in a physical region. A number of papers have addressed the apparent pathology through an ansatz that invokes higher order (rescattering) effects. Taking the Gamow-Teller terms as an example, we display an expression for the spin-spin correlation function that determines the cross-sections. It is clear from the form that there are no pathologies in the order by order perturbation expansion. Explicit formulae are given for a simple case, leading to an answer that is very different from one given by other authors.
Verified Error Bounds for Isolated Singular Solutions of Polynomial Systems: Case of Breadth One
Li, Nan
2012-01-01
In this paper we describe how to improve the performance of the symbolic-numeric method in (Li and Zhi,2009, 2011) for computing the multiplicity structure and refining approximate isolated singular solutions in the breadth one case. By introducing a parameterized and deflated system with smoothing parameters, we generalize the algorithm in (Rump and Graillat, 2009) to compute verified error bounds such that a slightly perturbed polynomial system is guaranteed to have a breadth-one multiple root within the computed bounds.
A singular one-parameter family of solutions in cubic superstring field theory
Arroyo, E. Aldo
2016-05-01
Performing a gauge transformation of a simple identity-like solution of superstring field theory, we construct a one-parameter family of solutions, and by evaluating the energy associated to this family, we show that for most of the values of the parameter the solution represents the tachyon vacuum, except for two isolated singular points where the solution becomes the perturbative vacuum and the half brane solution.
Renormalization and resolution of singularities
Bergbauer, Christoph; Brunetti, Romeo; Kreimer, Dirk
2009-01-01
Since the seminal work of Epstein and Glaser it is well established that perturbative renormalization of ultraviolet divergences in position space amounts to extension of distributions onto diagonals. For a general Feynman graph the relevant diagonals form a nontrivial arrangement of linear subspaces. One may therefore ask if renormalization becomes simpler if one resolves this arrangement to a normal crossing divisor. In this paper we study the extension problem of distributions onto the won...
Perturbative Topological Field Theory
Dijkgraaf, Robbert
We give a review of the application of perturbative techniques to topological quantum field theories, in particular three-dimensional Chern-Simons-Witten theory and its various generalizations. To this end we give an introduction to graph homology and homotopy algebras and the work of Vassiliev and Kontsevich on perturbative knot invariants.
Perturbing supersymmetric black hole
Onozawa, H; Mishima, T; Ishihara, H; Onozawa, Hisashi; Okamura, Takashi; Mishima, Takashi; Ishihara, Hideki
1996-01-01
An investigation of the perturbations of the Reissner-Nordstr\\"{o}m black hole in the N=2 supergravity is presented. In the extreme case, the black hole responds to the perturbation of each field in the same manner. This is possibly because we can match the modes of the graviton, gravitino, and photon using supersymmetry transformations.
Odd-parity perturbations of the self-similar LTB spacetime
Energy Technology Data Exchange (ETDEWEB)
Duffy, Emily M; Nolan, Brien C, E-mail: emilymargaret.duffy27@mail.dcu.ie, E-mail: brien.nolan@dcu.ie [School of Mathematical Sciences, Dublin City University, Glasnevin, Dublin 9 (Ireland)
2011-05-21
We consider the behaviour of odd-parity perturbations of those self-similar LemaItre-Tolman-Bondi spacetimes which admit a naked singularity. We find that a perturbation which evolves from initially regular data remains finite on the Cauchy horizon. Finiteness is demonstrated by considering the behaviour of suitable energy norms of the perturbation (and pointwise values of these quantities) on natural spacelike hypersurfaces. This result holds for a general choice of initial data and initial data surface. Finally, we examine the perturbed Weyl scalars in order to provide a physical interpretation of our results. Taken on its own, this result does not support cosmic censorship; however, a full perturbation of this spacetime would include even-parity perturbations, so we cannot conclude that this spacetime is stable to all linear perturbations.
Frame independent cosmological perturbations
Energy Technology Data Exchange (ETDEWEB)
Prokopec, Tomislav; Weenink, Jan, E-mail: t.prokopec@uu.nl, E-mail: j.g.weenink@uu.nl [Institute for Theoretical Physics and Spinoza Institute, Utrecht University, Leuvenlaan 4, 3585 CE Utrecht (Netherlands)
2013-09-01
We compute the third order gauge invariant action for scalar-graviton interactions in the Jordan frame. We demonstrate that the gauge invariant action for scalar and tensor perturbations on one physical hypersurface only differs from that on another physical hypersurface via terms proportional to the equation of motion and boundary terms, such that the evolution of non-Gaussianity may be called unique. Moreover, we demonstrate that the gauge invariant curvature perturbation and graviton on uniform field hypersurfaces in the Jordan frame are equal to their counterparts in the Einstein frame. These frame independent perturbations are therefore particularly useful in relating results in different frames at the perturbative level. On the other hand, the field perturbation and graviton on uniform curvature hypersurfaces in the Jordan and Einstein frame are non-linearly related, as are their corresponding actions and n-point functions.
Definition and classification of singularities in GR: classical and quantum
Konkowski, D A
2004-01-01
We will briefly review the definition and classification of classical and quantum singularities in general relativity. Examples of classically singular spacetimes that do not have quantum singularities will be given. We will present results on quantum singularities in quasiregular spacetimes. We will also show that a strong repulsive "potential" near the classical singularity can turn a classically singular spacetime into a quantum mechanically nonsingular spacetime.
Fluctuations in a Cosmology with a Space-Like Singularity and their Gauge Theory Dual Description
Brandenberger, Robert H; Das, Sumit R; Ferreira, Elisa G M; Morrison, Ian A; Wang, Yi
2016-01-01
We consider a time-dependent deformation of anti-de-Sitter (AdS) space-time which contains a cosmological "singularity" - a space-like region of high curvature. Making use of the AdS/CFT correspondence we can map the bulk dynamics onto the boundary. The boundary theory has a time dependent coupling constant which becomes small at times when the bulk space-time is highly curved. We investigate the propagation of small fluctuations of a test scalar field from early times before the bulk singularity to late times after the singularity. Under the assumption that the AdS/CFT correspondence extends to deformed AdS space-times, we can map the bulk evolution of the scalar field onto the evolution of the boundary gauge field. The time evolution of linearized fluctuations is well defined in the boundary theory as long as the coupling remains finite, so that we can extend the boundary perturbations to late times after the singularity. Assuming that the spacetime in the future of the singularity has a weakly coupled regi...
Sidi, A.; Israeli, M.
1986-01-01
High accuracy numerical quadrature methods for integrals of singular periodic functions are proposed. These methods are based on the appropriate Euler-Maclaurin expansions of trapezoidal rule approximations and their extrapolations. They are used to obtain accurate quadrature methods for the solution of singular and weakly singular Fredholm integral equations. Such periodic equations are used in the solution of planar elliptic boundary value problems, elasticity, potential theory, conformal mapping, boundary element methods, free surface flows, etc. The use of the quadrature methods is demonstrated with numerical examples.
Yin, J. L.; Xing, Q. Q.; Tian, L. X.
2015-03-01
The behavior of non-smooth solitary waves switching to chaos is studied. Firstly, we present some singular homoclinic orbits of an unperturbed system. These singular homoclinic orbits correspond to non-smooth solutions. Secondly, we find that the peculiar solitary waves are more likely to be chaos by using the Melnikov theory. Finally, chaos thresholds under different amplitudes and frequencies of a periodic perturbation are given. One interesting finding is that there exists a peculiar perturbation frequency, which has significant effect on the system. The system is not well-controlled under this frequency. However, the system can be well controlled, when the frequency of the perturbation surpasses the peculiar perturbation frequency with fixed parameters of the unperturbed system.
Second order singular pertubative theory for gravitational lenses
Alard, C
2016-01-01
The extension of the singular perturbative approach to the second order is presented in this paper. The general expansion to the second order is derived. The second order expansion is considered as a small correction to the first order expansion. Using this approach it is demonstrated that the second order expansion is reducible to a first order expansion via a re-definition of the first order pertubative fields. Even if in practice the second order correction is small the reducibility of the second order expansion to the first order expansion indicates a degeneracy problem. In general this degeneracy is hard to break. A useful and simple second order approximation is the thin source approximation which offers a direct estimation of the correction. The practical application of the corrections derived in this paper are illustrated by using an elliptical NFW lens model. The second order pertubative expansion provides a noticeable improvement, even for the simplest case of thin source approximation. To conclude ...
Singularity of Farhi-Gutmann Analog Quantum Search
Institute of Scientific and Technical Information of China (English)
LUO Shun-Long; ZHANG Zheng-Min
2004-01-01
We show that the Farhi-Gutmann analog quantum search is a singular algorithm in the following sense:when the original driving Hamiltonian is perturbed slightly such that it is made of projections to the starting state and to the target state with different energies, the maximum fidelity (transition probability) between the searching state and thetarget state is strictly less than 1 over the entire evolution period, and the first time to achieve this maximum fidelity is of order √n/√1+cN, whose behavior depends crucially on whether c = 0 or not (here N is the total number of items, and the original Farhi-Gutmann case corresponds to c = 0). Moreover, when c ≠ 0 and N tends to infinity, the maximum fidelity tends to zero, and the first time to achieve the maximum fidelity tends to a positive constant! The condition for guaranteeing the algorithm's efficiency is determined explicitly.
The structure of the classical cosmological singularity
Tipler, Frank J.
The existence of an all-encompassing initial classical cosmological singularity is established: it is shown that if: (1) global hyperbolicity, (2) the timelike convergence condition, and (3) all past-directed nonspacelike geodesics start to reconverge within a compact region in the causal past of the present-day earth, then all timelike curves in the past have a finite proper time length less than a universal constant L. It is argued that an analogue of this predicted cosmological singularity should exist even when quantum effects are taken into account. In particular, in a closed Friedmann radiation-filled universe quantized via the ADM method, the R = 0 singularity still exists and influences wave packet evolution at all times. Furthermore, quantum effects can in most cases eliminate curvature singularities only by introducing singularities in the universal action; most classical closed universes have finite action if and only if they begin and end in curvature singularities. Finally, the two basic ways of studying the structure of cosmological singularities are reviewed: completion methods (e.g., the c-boundary construction), and approach methods (e.g., analyzing metric behavior in a synchronous coordinate system).
Denkiewicz, Tomasz
2015-01-01
The question of the origin of the recent acceleration of the Universes expansion is still pending. What is making the situation even worst, it is impossible to distinguish the vast majority of the proposed models of the dynamical dark energy and modified gravity from the $\\Lambda CDM$ in view of recent geometrical and dynamical, observational data. On the other hand on scales much smaller than the present Hubble scale, there are differences in the growth of the matter perturbations for different modes of the perturbations in the $\\Lambda CDM$. In the view of the new planned observations that will give insight into the perturbations of the dark sector this issue is being worth of further investigation. We analyze the evolution of the dark matter perturbations in the dynamical dark energy models with the singularities, such as the sudden future singularity and the finite scale factor singularity. We employ the Newtonian gauge formulation for derivation of the perturbation equations for the growth function. We a...
Potential singularity mechanism for the Euler equations
Brenner, Michael P.; Hormoz, Sahand; Pumir, Alain
2016-12-01
Singular solutions to the Euler equations could provide essential insight into the formation of very small scales in highly turbulent flows. Previous attempts to find singular flow structures have proven inconclusive. We reconsider the problem of interacting vortex tubes, for which it has long been observed that the flattening of the vortices inhibits sustained self-amplification of velocity gradients. Here we consider an iterative mechanism, based on the transformation of vortex filaments into sheets and their subsequent instability back into filaments. Elementary fluid mechanical arguments are provided to support the formation of a singular structure via this iterated mechanism, which we analyze based on a simplified model of filament interactions.
Isotropic cosmological singularities other matter models
Tod, K P
2003-01-01
Isotropic cosmological singularities are singularities which can be removed by rescaling the metric. In some cases already studied (gr-qc/9903008, gr-qc/9903009, gr-qc/9903018) existence and uniqueness of cosmological models with data at the singularity has been established. These were cosmologies with, as source, either perfect fluids with linear equations of state or massless, collisionless particles. In this article we consider how to extend these results to a variety of other matter models. These are scalar fields, massive collisionless matter, the Yang-Mills plasma of Choquet-Bruhat, or matter satisfying the Einstein-Boltzmann equation.
Non-singular circulant graphs and digraphs
Lal, A K
2011-01-01
We give necessary and sufficient conditions for a few classes of circulant graphs/digraphs to be singular. We also give two generalizations of the above graphs/digraphs, namely $(r,s,t)$-digraphs for non-negative integers $r,s$ and $t$, and the digraph $C_n^{i,j,k,l}$ with certain restrictions. A necessary and sufficient condition for the digraphs $C_n^{i,j,k,l}$ to be singular is obtained. Some necessary conditions are given under which the $(r,s,t)$-digraphs are singular.
Quantum dress for a naked singularity
Directory of Open Access Journals (Sweden)
Marc Casals
2016-09-01
Full Text Available We investigate semiclassical backreaction on a conical naked singularity space–time with a negative cosmological constant in (2+1-dimensions. In particular, we calculate the renormalized quantum stress–energy tensor for a conformally coupled scalar field on such naked singularity space–time. We then obtain the backreacted metric via the semiclassical Einstein equations. We show that, in the regime where the semiclassical approximation can be trusted, backreaction dresses the naked singularity with an event horizon, thus enforcing (weak cosmic censorship.
Singular Value Decomposition for Unitary Symmetric Matrix
Institute of Scientific and Technical Information of China (English)
ZOUHongxing; WANGDianjun; DAIQionghai; LIYanda
2003-01-01
A special architecture called unitary sym-metric matrix which embodies orthogonal, Givens, House-holder, permutation, and row (or column) symmetric ma-trices as its special cases, is proposed, and a precise corre-spondence of singular values and singular vectors between the unitary symmetric matrix and its mother matrix is de-rived. As an illustration of potential, it is shown that, for a class of unitary symmetric matrices, the singular value decomposition (SVD) using the mother matrix rather than the unitary symmetric matrix per se can save dramatically the CPU time and memory without loss of any numerical precision.
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.
Rong, Shu-Jun; Liu, Qiu-Yu
2012-04-01
The puma model on the basis of the Lorentz and CPT violation may bring an economical interpretation to the conventional neutrinos oscillation and part of the anomalous oscillations. We study the effect of the perturbation to the puma model. In the case of the first-order perturbation which keeps the (23) interchange symmetry, the mixing matrix element Ue3 is always zero. The nonzero mixing matrix element Ue3 is obtained in the second-order perturbation that breaks the (23) interchange symmetry.
ON THE SINGULAR VARIATIONAL PROBLEMS
Institute of Scientific and Technical Information of China (English)
谭经刚; 杨健夫
2004-01-01
The authors deal with the singular variational problem S(a,b,λ0):=infu∈E,u(≡／)0 ∫RN(||X|-a(△)u|m+∫|x|-(a+1)m|u|m)dx/(∫RN||X|-bU|P dx)m/p as well as (S)=(S)(a,b,λ1,λ2):=u,ν,E∈,u(u,ν)(≡／)(1,1) ∫RN J(u,ν)dx/(∫RN|x|-bp|u|α|ν|βdx)m/p, whereJ(u, v) = ||x|- au|m + λ1|x|- (a+1)m|u|m + ||x|- av|m + λ2|x|- (a+1)m|v|m,N ≥ m+ 1 ＞ 2, 0 ≤ a ＜ N-m/m, a ≤ b ＜ a+ 1 and p = p(a,b) = α+β =Nm/N-m+m(b-a), α, β≥ 1, E = D1,mα(RN). The aim of this paper is to show the existence of minimizer for S(a, b, A0) and S(a, b, λ1, λ2).
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...
Perturbations of planar algebras
Das, Paramita; Gupta, Ved Prakash
2010-01-01
We introduce the concept of {\\em weight} of a planar algebra $P$ and construct a new planar algebra referred as the {\\em perturbation of $P$} by the weight. We establish a one-to-one correspondence between pivotal structures on 2-categories and perturbations of planar algebras by weights. To each bifinite bimodule over $II_1$-factors, we associate a {\\em bimodule planar algebra} bimodule corresponds naturally with sphericality of the bimodule planar algebra. As a consequence of this, we reproduce an extension of Jones' theorem (of associating 'subfactor planar algebras' to extremal subfactors). Conversely, given a bimodule planar algebra, we construct a bifinite bimodule whose associated bimodule planar algebra is the one which we start with using perturbations and Jones-Walker-Shlyakhtenko-Kodiyalam-Sunder method of reconstructing an extremal subfactor from a subfactor planar algebra. We show that the perturbation class of a bimodule planar algebra contains a unique spherical unimodular bimodule planar algeb...
Introduction to perturbation techniques
Nayfeh, Ali H
2011-01-01
Similarities, differences, advantages and limitations of perturbation techniques are pointed out concisely. The techniques are described by means of examples that consist mainly of algebraic and ordinary differential equations. Each chapter contains a number of exercises.
Self-similar singular solution of doubly singular parabolic equation with gradient absorption term
Directory of Open Access Journals (Sweden)
2006-01-01
Full Text Available We deal with the self-similar singular solution of doubly singular parabolic equation with a gradient absorption term u t = div ( | ∇ u m | p − 2 ∇ u m − | ∇ u | q for 1$"> p > 1 , 1$"> m ( p − 1 > 1 and 1$"> q > 1 in ℝ n × ( 0 , ∞ . By shooting and phase plane methods, we prove that when {1+n}/({1+mn}q+{mn}/({mn+1}$"> p > 1 + n / ( 1 + m n q + m n / ( m n + 1 there exists self-similar singular solution, while p ≤ n + 1 / ( 1 + m n q + m n / ( m n + 1 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.
Curvature singularities and abstract boundary singularity theorems for space-time
Ashley, M J S L; Ashley, Michael J. S. L.; Scott, Susan M.
2003-01-01
The abstract boundary construction of Scott and Szekeres is a general and flexible way to define singularities in General Relativity. The abstract boundary construction also proves of great utility when applied to questions about more general boundary features of space-time. Within this construction an essential singularity is a non-regular boundary point which is accessible by a curve of interest (e.g. a geodesic) within finite (affine) parameter distance and is not removable. Ashley and Scott proved the first theorem linking abstract boundary essential singularities with the notion of causal geodesic incompleteness for strongly causal, maximally extended space-times. The relationship between this result and the classical singularity theorems of Penrose and Hawking has enabled us to obtain abstract boundary singularity theorems. This paper describes essential singularity results for maximally extended space-times and presents our recent efforts to establish a relationship between the strong curvature singula...
D-brane gauge theories from toric singularities of the form $C^3/\\Gamma$ and $C^4/\\Gamma$
Sarkar, Tapobrata
2000-01-01
We discuss examples of D-branes probing toric singularities, and the computation of their world-volume gauge theories from the geometric data of the singularities. We consider several such examples of D-branes on partial resolutions of the orbifolds ${\\bf C^3/Z_2\\times Z_2}$,${\\bf C^3/Z_2\\times Z_3}$ and ${\\bf C^4/Z_2\\times Z_2 \\times Z_2}$.
Perturbations around black holes
Wang, B
2005-01-01
Perturbations around black holes have been an intriguing topic in the last few decades. They are particularly important today, since they relate to the gravitational wave observations which may provide the unique fingerprint of black holes' existence. Besides the astrophysical interest, theoretically perturbations around black holes can be used as testing grounds to examine the proposed AdS/CFT and dS/CFT correspondence.
Perturbations and quantum relaxation
Kandhadai, Adithya
2016-01-01
We investigate whether small perturbations can cause relaxation to quantum equilibrium over very long timescales. We consider in particular a two-dimensional harmonic oscillator, which can serve as a model of a field mode on expanding space. We assume an initial wave function with small perturbations to the ground state. We present evidence that the trajectories are highly confined so as to preclude relaxation to equilibrium even over very long timescales. Cosmological implications are briefly discussed.
Interaction Dynamics of Singular Wave Fronts
Holm, Darryl D
2013-01-01
Some of the most impressive singular wave fronts seen in Nature are the transbasin oceanic internal waves, which may be observed from the Space Shuttle as they propagate and interact with each other, for example, in the South China Sea. The characteristic feature of these strongly nonlinear wavefronts is that they reconnect when two of them collide transversely. We derive the EPDiff equation, and use it to model this phenomenon as elastic collisions between singular wave fronts (solitons) whose momentum is distributed along curves moving in the plane. Numerical methods for EPDiff based on compatible differencing algorithms (CDAs) are used for simulating these collisions among curves. The numerical results show the same nonlinear behavior of wavefront reconnections as that observed for internal waves in the South China Sea. We generalize the singular solutions of EPDiff for other applications, in computational anatomy and in imaging science, where the singular wavefronts are evolving image outlines, whose mome...
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.
Dark matter annihilation near a naked singularity
Patil, Mandar
2011-01-01
We investigate here the dark matter annihilation near a Kerr naked singularity. We show that when dark matter particles collide and annihilate in vicinity of the singularity, the escape fraction to infinity of particles produced is much larger, at least 10^2 - 10^3 times the corresponding black hole values. As high energy collisions are generically possible near a naked singularity, this provides an excellent environment for efficient conversion of dark matter into ordinary standard model particles. If the center of galaxy harbored such a naked singularity, it follows that the observed emergent flux of particles with energy comparable to mass of the dark matter particles is much larger compared to the blackhole case, thus providing an intriguing observational test on the nature of the galactic center
Resonance Van Hove Singularities in Wave Kinetics
Shi, Yi-Kang
2015-01-01
Wave kinetic theory has been developed to describe the statistical dynamics of weakly nonlinear, dispersive waves. However, we show that systems which are generally dispersive can have resonant sets of wave modes with identical group velocities, leading to a local breakdown of dispersivity. This shows up as a geometric singularity of the resonant manifold and possibly as an infinite phase measure in the collision integral. Such singularities occur widely for classical wave systems, including acoustical waves, Rossby waves, helical waves in rotating fluids, light waves in nonlinear optics and also in quantum transport, e.g. kinetics of electron-hole excitations (matter waves) in graphene. These singularities are the exact analogue of the critical points found by Van Hove in 1953 for phonon dispersion relations in crystals. The importance of these singularities in wave kinetics depends on the dimension of phase space $D=(N-2)d$ ($d$ physical space dimension, $N$ the number of waves in resonance) and the degree ...
NEW RESULTS ON ESTIMATES FOR SINGULAR VALUES
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
New results are provided to estimate matrix singular values in terms of partial absolute deleted row sums and column sums. Illustrative examples are presented to show comparisons with results in literature.
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.
A reinterpretation of the Taub singularity
Jensen, Bjorn; Kučera, Jaromír
1994-01-01
We reinterpret the well known Taub-singularity in terms of a cylinder symmetric geometry. It is shown that a cylindrical analog to the Einstein-Rosen bridge as well as a cosmic string will be present in the geometry.
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.
Tidal Forces in Naked Singularity Backgrounds
Goel, Akash; Roy, Pratim; Sarkar, Tapobrata
2015-01-01
The end stage of a gravitational collapse process can generically result in a black hole or a naked singularity. Here we undertake a comparative analysis of the nature of tidal forces in these backgrounds. The effect of such forces is generically exemplified by the Roche limit, which predicts the distance within which a celestial object disintegrates due to the tidal effects of a second more massive object. In this paper, using Fermi normal coordinates, we numerically compute the Roche limit for a class of non-rotating naked singularity backgrounds, and compare them with known results for Schwarzschild black holes. Our analysis indicates that there might be substantially large deviations in the magnitudes of tidal forces in naked singularity backgrounds, compared to the black hole cases. If observationally established, these can prove to be an effective indicator of the nature of the singularity at a galactic centre.
Constraints on Singular Evolution from Gravitational Baryogenesis
Oikonomou, V K
2015-01-01
We investigate how the gravitational baryogenesis mechanism can potentially constrain the form of a Type IV singularity. Specifically, we study two different models with interesting phenomenology, that realize two distinct Type IV singularities, one occurring at the end of inflation and one during the radiation domination era or during the matter domination era. As we demonstrate, the Type IV singularities occurring at the matter domination era or during the radiation domination era, are constrained by the gravitational baryogenesis, in such a way so that these do not render the baryon to entropy ratio singular. Both the cosmological models we study cannot be realized in the context of ordinary Einstein-Hilbert gravity, and hence our work can only be realized in the context of $F(R)$ gravity and more generally in the context of modified gravity only.
SINGULAR INTEGRAL EQUATIONS ALONG AN OPEN ARC WITH SOLUTIONS HAVING SINGULARITIES OF HIGHER ORDER
Institute of Scientific and Technical Information of China (English)
Zhong Shouguo
2005-01-01
In this paper, the difficulties on calculation in solving singular integral equations are overcome when the restriction of curve of integration to be a closed contour is cancelled. When the curve is an open arc and the solutions for singular integral equations possess singularities of higher order, the solution and the solvable condition for characteristic equations as well as the generalized Noether theorem for complete equations are given.
Institute of Scientific and Technical Information of China (English)
RONG Shu-Jun; LIU Qiu-Yu
2012-01-01
The puma model on the basis of the Lorentz and CPT violation may bring an economical interpretation to the conventional neutrinos oscillation and part of the anomalous oscillations.We study the effect of the perturbation to the puma model.In the case of the first-order perturbation which keeps the (23) interchange symmetry,the mixing matrix element Ue3 is always zero.The nonzero mixing matrix element Ue3 is obtained in the second-order perturbation that breaks the (23) interchange symmetry.%The puma model on the basis of the Lorentz and CPT violation may bring an economical interpretation to the conventional neutrinos oscillation and part of the anomalous oscillations. We study the effect of the perturbation to the puma model. In the case of the first-order perturbation which keeps the (23) interchange symmetry, the mixing matrix element Ue3 is always zero. The nonzero mixing matrix element Ue3 is obtained in the second-order perturbation that breaks the (23) interchange symmetry.
Singularities in universes with negative cosmological constant
Energy Technology Data Exchange (ETDEWEB)
Tipler, F.J.
1976-10-01
It is well known that many universes with negative cosmological constant contain singularities. We shall generalize this result by proving that all closed universes with negative cosmological constant are both future and past timelike geodesically incomplete if the strong energy condition holds. No global causality conditions or restrictions on the initial data are used in the proof. Furthermore, we shall show that all open universes with a Cauchy surface and a negative cosmological constant are singular if the strong energy condition holds. (AIP)
Noncommutative Black Holes and the Singularity Problem
Energy Technology Data Exchange (ETDEWEB)
Bastos, C; Bertolami, O [Instituto de Plasmas e Fusao Nuclear, Instituto Superior Tecnico, Avenida Rovisco Pais 1, 1049-001 Lisboa (Portugal); Dias, N C; Prata, J N, E-mail: cbastos@fisica.ist.utl.pt, E-mail: orfeu.bertolami@fc.up.pt, E-mail: ncdias@mail.telepac.pt, E-mail: joao.prata@mail.telepac.pt [Departamento de Matematica, Universidade Lusofona de Humanidades e Tecnologias, Avenida Campo Grande, 376, 1749-024 Lisboa (Portugal)
2011-09-22
A phase-space noncommutativity in the context of a Kantowski-Sachs cosmological model is considered to study the interior of a Schwarzschild black hole. Due to the divergence of the probability of finding the black hole at the singularity from a canonical noncommutativity, one considers a non-canonical noncommutativity. It is shown that this more involved type of noncommutativity removes the problem of the singularity in a Schwarzschild black hole.
Perturbing Misiurewicz Parameters in the Exponential Family
Dobbs, Neil
2015-04-01
In one-dimensional real and complex dynamics, a map whose post-singular (or post-critical) set is bounded and uniformly repelling is often called a Misiurewicz map. In results hitherto, perturbing a Misiurewicz map is likely to give a non-hyperbolic map, as per Jakobson's Theorem for unimodal interval maps. This is despite genericity of hyperbolic parameters (at least in the interval setting). We show the contrary holds in the complex exponential family Misiurewicz maps are Lebesgue density points for hyperbolic parameters. As a by-product, we also show that Lyapunov exponents almost never exist for exponential Misiurewicz maps. The lower Lyapunov exponent is -∞ almost everywhere. The upper Lyapunov exponent is non-negative and depends on the choice of metric.
Toroidal Energy Principle (TEP) and perturbed equilibrium code STB
Zakharov, Leonid; Hu, Di
2016-10-01
The MHD energy principle TEP is presented in terms of perturbations of the vector potential, rather than plasma displacement. This form makes TEP capable to discribe both the ideal plasmas stability and the perturbed equilibria. The functional is expressed in two terms. The first one represents the energy of magnetic field and is calculated using working equilibrium coordinate system. The second term, containing plasma displacement is expressed in the compact form using Hamada coordinates. This representation uses the same combinations of metric coefficients as in the equilibrium calculations. The STB code implements the TEP for both ideal MHD and perturbed equilibria. In the first case, it uses the matching conditions of the ideal MHD. In the second case, the 2-D equilibrium islands are introduced in order to resolve the singularity and match the solutions across the resonant surfaces Partially by (a) US DoE Contract No. DE-AC02-09-CH11466, (b) General Fusion Inc.
Optimal RG-Improvement of Perturbative Calculations in QCD
Elias, V
2003-01-01
Using renormalization-group methods, differential equations can be obtained for the all-orders summation of leading and subsequent non-leading logarithmic corrections to QCD perturbative series for a number of processes and correlation functions. For a QCD perturbative series known to four orders, such as the e+ e- annihilation cross-section, explicit solutions to these equations are obtained for the summation to all orders in alpha_s of the leading set and the subsequent two non-leading sets of logarithms. Such summations are shown for a number of processes to lead to a substantial reduction in sensitivity to the renormalization scale parameter. Surprisingly, such summations are also shown to lower the infrared singularity within the perturbative expression for the e+ e- annihilation cross-section to coincide with the Landau pole of the naive one-loop running QCD couplant.
Dynamic Singularity Spectrum Distribution of Sea Clutter
Xiong, Gang; Yu, Wenxian; Zhang, Shuning
2015-12-01
The fractal and multifractal theory have provided new approaches for radar signal processing and target-detecting under the background of ocean. However, the related research mainly focuses on fractal dimension or multifractal spectrum (MFS) of sea clutter. In this paper, a new dynamic singularity analysis method of sea clutter using MFS distribution is developed, based on moving detrending analysis (DMA-MFSD). Theoretically, we introduce the time information by using cyclic auto-correlation of sea clutter. For transient correlation series, the instantaneous singularity spectrum based on multifractal detrending moving analysis (MF-DMA) algorithm is calculated, and the dynamic singularity spectrum distribution of sea clutter is acquired. In addition, we analyze the time-varying singularity exponent ranges and maximum position function in DMA-MFSD of sea clutter. For the real sea clutter data, we analyze the dynamic singularity spectrum distribution of real sea clutter in level III sea state, and conclude that the radar sea clutter has the non-stationary and time-varying scale characteristic and represents the time-varying singularity spectrum distribution based on the proposed DMA-MFSD method. The DMA-MFSD will also provide reference for nonlinear dynamics and multifractal signal processing.
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.)
Hitchin Equation, Irregular Singularity, and $N=2$ Asymptotical Free Theories
Nanopoulos, Dimitri
2010-01-01
In this paper, we study irregular singular solution to Hitchin's equation and use it to describe four dimensional $N=2$ asymptotically free gauge theories. For $SU(2)$ $A$ type quiver, two kinds of irregular singularities besides one regular singularity are needed for the solution of Hitchin's equation; We then classify irregular singularities needed for the general $SU(N)$ $A$ type quiver.
Minimal solution of singular LR fuzzy linear systems.
Nikuie, M; Ahmad, M Z
2014-01-01
In this paper, the singular LR fuzzy linear system is introduced. Such systems are divided into two parts: singular consistent LR fuzzy linear systems and singular inconsistent LR fuzzy linear systems. The capability of the generalized inverses such as Drazin inverse, pseudoinverse, and {1}-inverse in finding minimal solution of singular consistent LR fuzzy linear systems is investigated.
Design of switched controllers for discrete singular bilinear systems
Institute of Scientific and Technical Information of China (English)
Xiuhua ZHANG; Qingling ZHANG
2007-01-01
In this paper, switched controllers are designed for a class of nonlinear discrete singular systems and a class of discrete singular bilinear systems. An invariant principle is presented for such switched nonlinear singular systems.The invariant principle and the switched controllers are used to globally stabilize a class of singular bilinear systems that are not open-loop stable.
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.
Geometric perturbation theory and plasma physics
Energy Technology Data Exchange (ETDEWEB)
Omohundro, S.M.
1985-04-04
Modern differential geometric techniques are used to unify the physical asymptotics underlying mechanics, wave theory and statistical mechanics. The approach gives new insights into the structure of physical theories and is suited to the needs of modern large-scale computer simulation and symbol manipulation systems. A coordinate-free formulation of non-singular perturbation theory is given, from which a new Hamiltonian perturbation structure is derived and related to the unperturbed structure. The theory of perturbations in the presence of symmetry is developed, and the method of averaging is related to reduction by a circle group action. The pseudo-forces and magnetic Poisson bracket terms due to reduction are given a natural asymptotic interpretation. Similar terms due to changing reference frames are related to the method of variation of parameters, which is also given a Hamiltonian formulation. These methods are used to answer a question about nearly periodic systems. The answer leads to a new secular perturbation theory that contains no ad hoc elements. Eikonal wave theory is given a Hamiltonian formulation that generalizes Whitham's Lagrangian approach. The evolution of wave action density on ray phase space is given a Hamiltonian structure using a Lie-Poisson bracket. The relationship between dissipative and Hamiltonian systems is discussed. A new type of attractor is defined which attracts both forward and backward in time and is shown to occur in infinite-dimensional Hamiltonian systems with dissipative behavior. The theory of Smale horseshoes is applied to gyromotion in the neighborhood of a magnetic field reversal and the phenomenon of reinsertion in area-preserving horseshoes is introduced. The central limit theorem is proved by renormalization group techniques. A natural symplectic structure for thermodynamics is shown to arise asymptotically from the maximum entropy formalism.
Mu, Mu; Dijkstra, Henk A
2004-01-01
Within a simple model context, the sensitivity and stability of the thermohaline circulation to finite amplitude perturbations is studied. A new approach is used to tackle this nonlinear problem. The method is based on the computation of the so-called Conditional Nonlinear Optimal Perturbation (CNOP) which is a nonlinear generalization of the linear singular vector approach (LSV). It is shown that linearly stable thermohaline circulation states can become nonlinearly unstable and the properties of the perturbations with optimal nonlinear growth are determined. An asymmetric nonlinear response to perturbations exists with respect to the sign of finite amplitude freshwater perturbations, on both thermally dominated and salinity dominated thermohaline flows. This asymmetry is due to the nonlinear interaction of the perturbations through advective processes.
Gravitational self-force from radiation-gauge metric perturbations
Pound, Adam; Barack, Leor
2014-01-01
Calculations of the gravitational self-force (GSF) in curved spacetime require as input the metric perturbation in a sufficiently regular gauge. A basic challenge in the program to compute the GSF for orbits around a Kerr black hole is that the standard procedure for reconstructing the perturbation is formulated in a class of radiation gauges, in which the particle singularity is non-isotropic and extends away from the particle's location. Here we present two practical schemes for calculating the GSF using a radiation-gauge reconstructed metric as input. The schemes are based on a detailed analysis of the local structure of the particle singularity in the radiation gauges. We identify 3 types of radiation gauges: two containing a radial string-like singularity emanating from the particle, either in one direction ("half-string" gauges) or both directions ("full-string" gauges); and a third type containing no strings but with a jump discontinuity across a surface intersecting the particle. Based on a flat-space...
Landau singularity and the instability of vacuum state in QED
Azam, Mofazzal
2008-01-01
Quantum Eletrodynamics (QED) is considered as the most successful of all physical theories. It can predict numerical values of physical quantities to a spectacular degree of accuracy. However, from the very early days it has been known that, in QED, there are two important problems which are linked with the very foundation of the theory. In 1952, Dyson put forward strong argumnts to suggest that the perturbation seires in quantum electrodynamics can not be convergent. Just three years latter, in 1955, Landau argued that the effective running coupling constant in QED has a pole (Landau singularity) albeit at some very high energy scale. This paper addresses, in details, the question of stability of perturbative vacuum state of QED in the light of these two well known problems. Landau has been a cult-like figure for many of us who studied theoretical physics in the former Soviet Union. As an undergraduate student in the department of theoretical physics of People's Friendship University, Moscow, in 1970's, I gr...
Institute of Scientific and Technical Information of China (English)
2008-01-01
This paper presents a novel disturbance function method to avoid turning point singularities for the semi-regular hexagons 6-SPS Gough-Stewart manipulator. Through analysis of the configuration bifurcation characteristics of the manipulator at the type-II singular points, it is found that the type-II singularities under signal input parameter belong to turning point bifurcation. The configuration patterns for the manipulator to pass through the turning points are divided into three types: persistent, non-persistent and path configuration. Utilizing the universal unfolding approach, the configuration bifurcation characteristics under the perturbation pa- rameters applied to the extendable legs are analyzed. The investigation reveals that all configuration branches converged in the same singular point in the unperturbed system will be separated in the disturbed system. Based on this discovery, a novel method for the parallel manipulator to pass through the singular points with the desired configuration is presented. Then the disturbance functions for the manipulator to pass through the turning points with the persistent configuration and the non-persistent configuration are constructed. The method presented in this paper can be applied to avoiding the singularities in such cases where the path and orientation of the manipulator are strictly programmed.
Clustering under Perturbation Resilience
Balcan, Maria Florina
2011-01-01
Recently, Bilu and Linial \\cite{BL} formalized an implicit assumption often made when choosing a clustering objective: that the optimum clustering to the objective should be preserved under small multiplicative perturbations to distances between points. They showed that for max-cut clustering it is possible to circumvent NP-hardness and obtain polynomial-time algorithms for instances resilient to large (factor $O(\\sqrt{n})$) perturbations, and subsequently Awasthi et al. \\cite{ABS10} considered center-based objectives, giving algorithms for instances resilient to O(1) factor perturbations. In this paper, we greatly advance this line of work. For the $k$-median objective, we present an algorithm that can optimally cluster instances resilient to $(1 + \\sqrt{2})$-factor perturbations, solving an open problem of Awasthi et al.\\cite{ABS10}. We additionally give algorithms for a more relaxed assumption in which we allow the optimal solution to change in a small $\\epsilon$ fraction of the points after perturbation. ...
Nonperturbative Quantum Physics from Low-Order Perturbation Theory.
Mera, Héctor; Pedersen, Thomas G; Nikolić, Branislav K
2015-10-02
The Stark effect in hydrogen and the cubic anharmonic oscillator furnish examples of quantum systems where the perturbation results in a certain ionization probability by tunneling processes. Accordingly, the perturbed ground-state energy is shifted and broadened, thus acquiring an imaginary part which is considered to be a paradigm of nonperturbative behavior. Here we demonstrate how the low order coefficients of a divergent perturbation series can be used to obtain excellent approximations to both real and imaginary parts of the perturbed ground state eigenenergy. The key is to use analytic continuation functions with a built-in singularity structure within the complex plane of the coupling constant, which is tailored by means of Bender-Wu dispersion relations. In the examples discussed the analytic continuation functions are Gauss hypergeometric functions, which take as input fourth order perturbation theory and return excellent approximations to the complex perturbed eigenvalue. These functions are Borel consistent and dramatically outperform widely used Padé and Borel-Padé approaches, even for rather large values of the coupling constant.
Renormalized Cosmological Perturbation Theory
Crocce, M
2006-01-01
We develop a new formalism to study nonlinear evolution in the growth of large-scale structure, by following the dynamics of gravitational clustering as it builds up in time. This approach is conveniently represented by Feynman diagrams constructed in terms of three objects: the initial conditions (e.g. perturbation spectrum), the vertex (describing non-linearities) and the propagator (describing linear evolution). We show that loop corrections to the linear power spectrum organize themselves into two classes of diagrams: one corresponding to mode-coupling effects, the other to a renormalization of the propagator. Resummation of the latter gives rise to a quantity that measures the memory of perturbations to initial conditions as a function of scale. As a result of this, we show that a well-defined (renormalized) perturbation theory follows, in the sense that each term in the remaining mode-coupling series dominates at some characteristic scale and is subdominant otherwise. This is unlike standard perturbatio...
Singular Integral Equations with Cosecant Kernel in Solutions with Singularities of High Order
Institute of Scientific and Technical Information of China (English)
HAN Hui-li; DU Jin-yuan
2005-01-01
We have discussed and solved the boundary value problem with period 2aπ and the singular integral equation with kernel csc t-t0/a in solution having singularities of high order, where the smooth contour of integration is in the strip 0＜Rez＜aπ.
Institute of Scientific and Technical Information of China (English)
Chen Hua; Zhang Zhixiong
2005-01-01
In this paper the authors consider the summability of formal solutions for some first order singular PDEs with irregular singularity. They prove that in this case the formal solutions will be divergent, but except a enumerable directions, the formal solutions are Borel summable.
Current Singularities at Quasi-separatrix Layers and Three-dimensional Magnetic Nulls
Craig, I. J. D.; Effenberger, Frederic
2014-11-01
The open problem of how singular current structures form in line-tied, three-dimensional magnetic fields is addressed. A Lagrangian magneto-frictional relaxation method is employed to model the field evolution toward the final near-singular state. Our starting point is an exact force-free solution of the governing magnetohydrodynamic equations that is sufficiently general to allow for topological features like magnetic nulls to be inside or outside the computational domain, depending on a simple set of parameters. Quasi-separatrix layers (QSLs) are present in these structures and, together with the magnetic nulls, they significantly influence the accumulation of current. It is shown that perturbations affecting the lateral boundaries of the configuration lead not only to collapse around the magnetic null but also to significant QSL currents. Our results show that once a magnetic null is present, the developing currents are always attracted to that specific location and show a much stronger scaling with resolution than the currents that form along the QSL. In particular, the null-point scalings can be consistent with models of "fast" reconnection. The QSL currents also appear to be unbounded but give rise to weaker singularities, independent of the perturbation amplitude.
Saini, Sahil; Singh, Parampreet
2016-12-01
Resolution of singularities in the Kantowski-Sachs model due to non-perturbative quantum gravity effects is investigated. Using the effective spacetime description for the improved dynamics version of loop quantum Kantowski-Sachs spacetimes, we show that even though expansion and shear scalars are universally bounded, there can exist events where curvature invariants can diverge. However, such events can occur only for very exotic equations of state when pressure or derivatives of energy density with respect to triads become infinite at a finite energy density. In all other cases curvature invariants are proved to remain finite for any evolution in finite proper time. We find the novel result that all strong singularities are resolved for arbitrary matter. Weak singularities pertaining to above potential curvature divergence events can exist. The effective spacetime is found to be geodesically complete for particle and null geodesics in finite time evolution. Our results add to a growing evidence for generic resolution of strong singularities using effective dynamics in loop quantum cosmology by generalizing earlier results on isotropic and Bianchi-I spacetimes.
Non-singular AdS-dS transitions in a landscape scenario
Gupt, Brajesh
2013-01-01
Understanding transitions between different vacua of a multiverse allowing eternal inflation is an open problem whose resolution is important to gain insights on the global structure of the spacetime as well as the problem of measure. In the classical theory, transitions from the anti-deSitter to deSitter vacua are forbidden due to the big crunch singularity. In this article, we consider toy landscape potentials: a double well and a triple well potential allowing anti-deSitter and de-Sitter vacua, in the effective dynamics of loop quantum cosmology for the $k=-1$ FRW model. We show that due to the non-perturbative quantum gravity effects as understood in loop quantum cosmology, non-singular anti-deSitter to de-Sitter transitions are possible. In the future evolution, an anti-deSitter bubble universe does not encounter a big crunch singularity but undergoes a big bounce occurring at a scale determined by the underlying quantum geometry. These non-singular transitions provide a mechanism through which a probe o...
Singular Value Decomposition of Pinhole SPECT Systems.
Palit, Robin; Kupinski, Matthew A; Barrett, Harrison H; Clarkson, Eric W; Aarsvold, John N; Volokh, Lana; Grobshtein, Yariv
2009-03-12
A single photon emission computed tomography (SPECT) imaging system can be modeled by a linear operator H that maps from object space to detector pixels in image space. The singular vectors and singular-value spectra of H provide useful tools for assessing system performance. The number of voxels used to discretize object space and the number of collection angles and pixels used to measure image space make the matrix dimensions H large. As a result, H must be stored sparsely which renders several conventional singular value decomposition (SVD) methods impractical. We used an iterative power methods SVD algorithm (Lanczos) designed to operate on very large sparsely stored matrices to calculate the singular vectors and singular-value spectra for two small animal pinhole SPECT imaging systems: FastSPECT II and M(3)R. The FastSPECT II system consisted of two rings of eight scintillation cameras each. The resulting dimensions of H were 68921 voxels by 97344 detector pixels. The M(3)R system is a four camera system that was reconfigured to measure image space using a single scintillation camera. The resulting dimensions of H were 50864 voxels by 6241 detector pixels. In this paper we present results of the SVD of each system and discuss calculation of the measurement and null space for each system.
Quantum cosmology and late-time singularities
Kamenshchik, A Yu
2013-01-01
The development of dark energy models has stimulated interest to cosmological singularities, which differ from the traditional Big Bang and Big Crunch singularities. We review a broad class of phenomena connected with soft cosmological singularities in classical and quantum cosmology. We discuss the classification of singularities from the geometrical point of view and from the point of view of the behaviour of finite size objects, crossing such singularities. We discuss in some detail quantum and classical cosmology of models based on perfect fluids (anti-Chaplygin gas and anti-Chaplygin gas plus dust), of models based on the Born-Infeld-type fields and of the model of a scalar field with a potential inversely proportional to the field itself. We dwell also on the phenomenon of the phantom divide line crossing in the scalar field models with cusped potentials. Then we discuss the Friedmann equations modified by quantum corrections to the effective action of the models under considerations and the influence o...
Linear Stability of Hill's Vortex to Axisymmetric Perturbations
Protas, Bartosz
2015-01-01
We consider the linear stability of Hill's vortex with respect to axisymmetric perturbations. Given that Hill's vortex is a solution of a free-boundary problem, this stability analysis is performed by applying methods of shape differentiation to the contour dynamics formulation of the problem in a 3D axisymmetric geometry. This approach allows us to systematically account for the effect of boundary deformations on the linearized evolution of the vortex under the constraint of constant circulation. The resulting singular integro-differential operator defined on the vortex boundary is discretized with a highly accurate spectral approach. This operator has two unstable and two stable eigenvalues complemented by a continuous spectrum of neutrally-stable eigenvalues. By considering a family of suitably regularized (smoothed) eigenvalue problems solved with a range of numerical resolutions we demonstrate that the corresponding eigenfunctions are in fact singular objects in the form of infinitely sharp peaks localiz...
Singular vector decomposition of the internal variability of the Canadian Regional Climate Model
Energy Technology Data Exchange (ETDEWEB)
Diaconescu, Emilia Paula; Laprise, Rene [University of Quebec at Montreal (UQAM), Department of Earth and Atmospheric Sciences, Canadian Network for Regional Climate Modelling and Diagnostics, P.O. Box 8888, Montreal, QC (Canada); Centre ESCER (Etude et Simulation du Climat a l' Echelle Regionale), Montreal, QC (Canada); Zadra, Ayrton [University of Quebec at Montreal (UQAM), Department of Earth and Atmospheric Sciences, Canadian Network for Regional Climate Modelling and Diagnostics, P.O. Box 8888, Montreal, QC (Canada); Environment Canada, Meteorological Research Division, Montreal, QC (Canada); Centre ESCER (Etude et Simulation du Climat a l' Echelle Regionale), Montreal, QC (Canada)
2012-03-15
Previous studies have shown that Regional Climate Models (RCM) internal variability (IV) fluctuates in time depending on synoptic events. This study focuses on the physical understanding of episodes with rapid growth of IV. An ensemble of 21 simulations, differing only in their initial conditions, was run over North America using version 5 of the Canadian RCM (CRCM). The IV is quantified in terms of energy of CRCM perturbations with respect to a reference simulation. The working hypothesis is that IV is arising through rapidly growing perturbations developed in dynamically unstable regions. If indeed IV is triggered by the growth of unstable perturbations, a large proportion of the CRCM perturbations must project onto the most unstable singular vectors (SVs). A set of ten SVs was computed to identify the orthogonal set of perturbations that provide the maximum growth with respect to the dry total-energy norm during the course of the CRCM ensemble of simulations. CRCM perturbations were then projected onto the subspace of SVs. The analysis of one episode of rapid growth of IV is presented in detail. It is shown that a large part of the IV growth is explained by initially small-amplitude unstable perturbations represented by the ten leading SVs, the SV subspace accounting for over 70% of the CRCM IV growth in 36 h. The projection on the leading SV at final time is greater than the projection on the remaining SVs and there is a high similarity between the CRCM perturbations and the leading SV after 24-36 h tangent-linear model integration. The vertical structure of perturbations revealed that the baroclinic conversion is the dominant process in IV growth for this particular episode. (orig.)