One Critical Case in Singularly Perturbed Control Problems
Sobolev, Vladimir
2017-02-01
The aim of the paper is to describe the special critical case in the theory of singularly perturbed optimal control problems. We reduce the original singularly perturbed problem to a regularized one such that the existence of slow integral manifolds can be established by means of the standard theory. We illustrate our approach by an example of control problem.
The singular minimum entropy $H_\\infty$ control problem
Stoorvogel, A.A.
1990-01-01
In this paper we search for controllers which minimize an entropy function of the closed loop transfer matrix under the constraint of internal stability and under the constraint that the closed loop transfer matrix has $H_\\infty$ norm less than some a priori given bound $\\gamma$. We find an explicit
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.
Numerical method of singular problems on singular integrals
International Nuclear Information System (INIS)
Zhao Huaiguo; Mou Zongze
1992-02-01
As first part on the numerical research of singular problems, a numerical method is proposed for singular integrals. It is shown that the procedure is quite powerful for solving physics calculation with singularity such as the plasma dispersion function. Useful quadrature formulas for some class of the singular integrals are derived. In general, integrals with more complex singularities can be dealt by this method easily
On the singularities of solutions to singular perturbation problems
International Nuclear Information System (INIS)
Fruchard, A; Schaefke, R
2005-01-01
We consider a singularly perturbed complex first order ODE εu ' Φ(x, u, a, ε), x, u element of C, ε > 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
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.
A Singular Differential Equation Stemming from an Optimal Control Problem in Financial Economics
International Nuclear Information System (INIS)
Brunovský, Pavol; Černý, Aleš; Winkler, Michael
2013-01-01
We consider the ordinary differential equation x 2 u'' = axu'+bu-c(u'-1) 2 , x ∈ (0,x 0 ), with a∈R, b∈R , c>0 and the singular initial condition u(0)=0, which in financial economics describes optimal disposal of an asset in a market with liquidity effects. It is shown in the paper that if a+b 0 then there are infinitely many continuous solutions with indistinguishable asymptotics near 0. Moreover, it is proved that in the latter case there is precisely one solution u corresponding to the choice x 0 =∞ which is such that 0≤u(x)≤x for all x>0, and that this solution is strictly increasing and concave
A Singular Differential Equation Stemming from an Optimal Control Problem in Financial Economics
Energy Technology Data Exchange (ETDEWEB)
Brunovsky, Pavol, E-mail: brunovsky@fmph.uniba.sk [Comenius University Bratislava, Department of Applied Mathematics and Statistics (Slovakia); Cerny, Ales, E-mail: ales.cerny.1@city.ac.uk [City University London, Cass Business School (United Kingdom); Winkler, Michael, E-mail: michael.winkler@uni-due.de [Universitaet Paderborn, Institut fuer Mathematik (Germany)
2013-10-15
We consider the ordinary differential equation x{sup 2} u'' = axu'+bu-c(u'-1){sup 2}, x Element-Of (0,x{sub 0}), with a Element-Of R, b Element-Of R , c>0 and the singular initial condition u(0)=0, which in financial economics describes optimal disposal of an asset in a market with liquidity effects. It is shown in the paper that if a+b<0 then no continuous solutions exist, whereas if a+b>0 then there are infinitely many continuous solutions with indistinguishable asymptotics near 0. Moreover, it is proved that in the latter case there is precisely one solution u corresponding to the choice x{sub 0}={infinity} which is such that 0{<=}u(x){<=}x for all x>0, and that this solution is strictly increasing and concave.
The Finite-Horizon Singular H∞ Control Problem With Dynamic Measurement Feedback
Stoorvogel, A.A.; Trentelman, H.L.
1993-01-01
This paper is concerned with the finite-horizon version of the H∞ problem with measurement feedback. Given a finite-dimensional linear, time-varying system, together with a positive real number γ, we obtain necessary and sufficient conditions for the existence of a possibly time-varying dynamic
An adaptive singular ES-FEM for mechanics problems with singular field of arbitrary order
Nguyen-Xuan, H.; Liu, G. R.; Bordas, Stéphane; Natarajan, S.; Rabczuk, T.
2013-01-01
This paper presents a singular edge-based smoothed finite element method (sES-FEM) for mechanics problems with singular stress fields of arbitrary order. The sES-FEM uses a basic mesh of three-noded linear triangular (T3) elements and a special layer of five-noded singular triangular elements (sT5) connected to the singular-point of the stress field. The sT5 element has an additional node on each of the two edges connected to the singular-point. It allows us to represent simple and efficient ...
THE EXT RACORPOREAL FERTILIZATION TECHNOLOGIES AND THE SINGULARITY PROBLEMS
Directory of Open Access Journals (Sweden)
S. V. Denysenko
2013-05-01
Full Text Available The peculiarities of modern medicine development connected with the technological and informative singularity are analyzed. The risks of realization of extracorporeal fertilization are examined from positions of development of informative singularity. The warning problems of origin of singularity are discussed on t h e base of t h e newest technologies development.
An Exact Solution of the Binary Singular Problem
Directory of Open Access Journals (Sweden)
Baiqing Sun
2014-01-01
Full Text Available Singularity problem exists in various branches of applied mathematics. Such ordinary differential equations accompany singular coefficients. In this paper, by using the properties of reproducing kernel, the exact solution expressions of dual singular problem are given in the reproducing kernel space and studied, also for a class of singular problem. For the binary equation of singular points, I put it into the singular problem first, and then reuse some excellent properties which are applied to solve the method of solving differential equations for its exact solution expression of binary singular integral equation in reproducing kernel space, and then obtain its approximate solution through the evaluation of exact solutions. Numerical examples will show the effectiveness of this method.
A Connection between Singular Stochastic Control and Optimal Stopping
International Nuclear Information System (INIS)
Espen Benth, Fred; Reikvam, Kristin
2003-01-01
We show that the value function of a singular stochastic control problem is equal to the integral of the value function of an associated optimal stopping problem. The connection is proved for a general class of diffusions using the method of viscosity solutions
Solutions of dissimilar material singularity and contact problems
International Nuclear Information System (INIS)
Yang, Y.
2003-09-01
Due to the mismatch of the material properties of joined components, after a homogeneous temperature change or under a mechanical loading, very high stresses occur near the intersection of the interface and the outer surface, or near the intersection of two interfaces. For most material combinations and joint geometries, there exists even a stress singularity. These high stresses may cause fracture of the joint. The investigation of the stress situation near the singular point, therefore, is of great interest. Especially, the relationship between the singular stress exponent, the material data and joint geometry is important for choosing a suitable material combination and joint geometry. In this work, the singular stress field is described analytically in case of the joint having a real and a complex eigenvalue. Solutions of different singularity problems are given, which are two dissimilar materials joint with free edges; dissimilar materials joint with edge tractions; joint with interface corner; joint with a given displacement at one edge; cracks in dissimilar materials joint; contact problem in dissimilar materials and logarithmic stress singularity. For an arbitrary joint geometry and material combination, the stress singular exponent, the angular function and the regular stress term can be calculated analytically. The stress intensity factors for a finite joint can be determined applying numerical methods, e.g. the finite element method (FEM). The method to determine more than one stress intensity factor is presented. The characteristics of the eigenvalues and the stress intensity factors are shown for different joint conditions. (orig.)
On the collinear singularity problem of hot QCD
International Nuclear Information System (INIS)
Candelpergher, B.; Grandou, T.
2002-01-01
The collinear singularity problem of hot QCD is revisited within a perturbative resummation scheme (PR) of the leading thermal fluctuations. On the basis of actual calculations, new aspects are discovered concerning the origin of the singularity plaguing the soft real photon emission rate out of a quark-gluon plasma at thermal equilibrium, when the latter is calculated by means of the Resummation Program (RP)
Modified Differential Transform Method for Two Singular Boundary Values Problems
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Yinwei Lin
2014-01-01
Full Text Available This paper deals with the two singular boundary values problems of second order. Two singular points are both boundary values points of the differential equation. The numerical solutions are developed by modified differential transform method (DTM for expanded point. Linear and nonlinear models are solved by this method to get more reliable and efficient numerical results. It can also solve ordinary differential equations where the traditional one fails. Besides, we give the convergence of this new method.
Singular problems in shell theory. Computing and asymptotics
Energy Technology Data Exchange (ETDEWEB)
Sanchez-Palencia, Evariste [Institut Jean Le Rond d' Alembert, Paris (France); Millet, Olivier [La Rochelle Univ. (France). LEPTIAB; Bechet, Fabien [Metz Univ. (France). LPMM
2010-07-01
It is known that deformations of thin shells exhibit peculiarities such as propagation of singularities, edge and internal layers, piecewise quasi inextensional deformations, sensitive problems and others, leading in most cases to numerical locking phenomena under several forms, and very poor quality of computations for small relative thickness. Most of these phenomena have a local and often anisotropic character (elongated in some directions), so that efficient numerical schemes should take them in consideration. This book deals with various topics in this context: general geometric formalism, analysis of singularities, numerical computing of thin shell problems, estimates for finite element approximation (including non-uniform and anisotropic meshes), mathematical considerations on boundary value problems in connection with sensitive problems encountered for very thin shells; and others. Most of numerical computations presented here use an adaptive anisotropic mesh procedure which allows a good computation of the physical peculiarities on one hand, and the possibility to perform automatic computations (without a previous mathematical description of the singularities) on the other. The book is recommended for PhD students, postgraduates and researchers who want to improve their knowledge in shell theory and in particular in the areas addressed (analysis of singularities, numerical computing of thin and very thin shell problems, sensitive problems). The lecture of the book may not be continuous and the reader may refer directly to the chapters concerned. (orig.)
Adaptive Control of the Chaotic System via Singular System Approach
Directory of Open Access Journals (Sweden)
Yudong Li
2014-01-01
Full Text Available This paper deals with the control problem of the chaotic system subject to disturbance. The sliding mode surface is designed by singular system approach, and sufficient condition for convergence is given. Then, the adaptive sliding mode controller is designed to make the state arrive at the sliding mode surface in finite time. Finally, Lorenz system is considered as an example to show the effectiveness of the proposed method.
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.
Liu, Hongyu
2012-01-01
In this note, we present some interesting observations on the Schiffer's conjecture, interior transmission eigenvalue problem and their connections to singular and nonsingular invisibility cloaking problems of acoustic waves.
Nonlinear singular perturbation problems of arbitrary real orders
International Nuclear Information System (INIS)
Bijura, Angelina M.
2003-10-01
Higher order asymptotic solutions of singularly perturbed nonlinear fractional integral and derivatives of order 1/2 are investigated. It is particularly shown that whilst certain asymptotic expansions are applied successfully to linear equations and particular nonlinear problems, the standard formal asymptotic expansion is appropriate for the general class of nonlinear equations. This theory is then generalised to the general equation (of order β, 0 < β < 1). (author)
Complexity, Analysis and Control of Singular Biological Systems
Zhang, Qingling; Zhang, Xue
2012-01-01
Complexity, Analysis and Control of Singular Biological Systems follows the control of real-world biological systems at both ecological and phyisological levels concentrating on the application of now-extensively-investigated singular system theory. Much effort has recently been dedicated to the modelling and analysis of developing bioeconomic systems and the text establishes singular examples of these, showing how proper control can help to maintain sustainable economic development of biological resources. The book begins from the essentials of singular systems theory and bifurcations before tackling the use of various forms of control in singular biological systems using examples including predator-prey relationships and viral vaccination and quarantine control. Researchers and graduate students studying the control of complex biological systems are shown how a variety of methods can be brought to bear and practitioners working with the economics of biological systems and their control will also find the ...
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.
Singular perturbation techniques in the gravitational self-force problem
International Nuclear Information System (INIS)
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 show cannot determine a unique equation of motion. I formulate a refined condition that is sufficient to determine such an equation. However, I conclude that the method yields significantly weaker results than do alternative methods.
Synchronization and Control of Linearly Coupled Singular Systems
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Fang Qingxiang
2013-01-01
Full Text Available The synchronization and control problem of linearly coupled singular systems is investigated. The uncoupled dynamical behavior at each node is general and can be chaotic or, otherwise the coupling matrix is not assumed to be symmetrical. Some sufficient conditions for globally exponential synchronization are derived based on Lyapunov stability theory. These criteria, which are in terms of linear matrix inequality (LMI, indicate that the left and right eigenvectors corresponding to eigenvalue zero of the coupling matrix play key roles in the stability analysis of the synchronization manifold. The controllers are designed for state feedback control and pinning control, respectively. Finally, a numerical example is provided to illustrate the effectiveness of the proposed conditions.
Hybrid vehicle energy management: singular optimal control
Delprat, S.; Hofman, T.; Paganelli, S.
2017-01-01
Hybrid vehicle energymanagement is often studied in simulation as an optimal control problem. Under strict convexity assumptions, a solution can be developed using Pontryagin’s minimum principle. In practice, however, many engineers do not formally check these assumptions resulting in the possible
Singularity and steering logic for control moment gyros on flexible space structures
Hu, Quan; Guo, Chuandong; Zhang, Jun
2017-08-01
Control moment gyros (CMGs) are a widely used device for generating control torques for spacecraft attitude control without expending propellant. Because of its effectiveness and cleanness, it has been considered to be mounted on a space structure for active vibration suppression. The resultant system is the so-called gyroelastic body. Since CMGs could exert both torque and modal force to the structure, it can also be used to simultaneously achieve attitude maneuver and vibration reduction of a flexible spacecraft. In this paper, we consider the singularity problem in such application of CMGs. The dynamics of an unconstrained gyroelastic body is established, from which the output equations of the CMGs are extracted. Then, torque singular state and modal force singular state are defined and visualized to demonstrate the singularity. Numerical examples of several typical CMGs configurations on a gyroelastic body are given. Finally, a steering law allowing output error is designed and applied to the vibration suppression of a plate with distributed CMGs.
Exact Asymptotic Expansion of Singular Solutions for the (2+1-D Protter Problem
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Lubomir Dechevski
2012-01-01
Full Text Available We study three-dimensional boundary value problems for the nonhomogeneous wave equation, which are analogues of the Darboux problems in ℝ2. In contrast to the planar Darboux problem the three-dimensional version is not well posed, since its homogeneous adjoint problem has an infinite number of classical solutions. On the other hand, it is known that for smooth right-hand side functions there is a uniquely determined generalized solution that may have a strong power-type singularity at one boundary point. This singularity is isolated at the vertex of the characteristic light cone and does not propagate along the cone. The present paper describes asymptotic expansion of the generalized solutions in negative powers of the distance to this singular point. We derive necessary and sufficient conditions for existence of solutions with a fixed order of singularity and give a priori estimates for the singular solutions.
The eigenvalue problem for a singular quasilinear elliptic equation
Directory of Open Access Journals (Sweden)
Benjin Xuan
2004-02-01
Full Text Available We show that many results about the eigenvalues and eigenfunctions of a quasilinear elliptic equation in the non-singular case can be extended to the singular case. Among these results, we have the first eigenvalue is associated to a $C^{1,alpha}(Omega$ eigenfunction which is positive and unique (up to a multiplicative constant, that is, the first eigenvalue is simple. Moreover the first eigenvalue is isolated and is the unique positive eigenvalue associated to a non-negative eigenfunction. We also prove some variational properties of the second eigenvalue.
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
Directory of Open Access Journals (Sweden)
Winfried Auzinger
2006-01-01
Full Text Available We demonstrate that eigenvalue problems for ordinary differential equations can be recast in a formulation suitable for the solution by polynomial collocation. It is shown that the well-posedness of the two formulations is equivalent in the regular as well as in the singular case. Thus, a collocation code equipped with asymptotically correct error estimation and adaptive mesh selection can be successfully applied to compute the eigenvalues and eigenfunctions efficiently and with reliable control of the accuracy. Numerical examples illustrate this claim.
Topological regularizations of the triple collision singularity in the 3-vortex problem
International Nuclear Information System (INIS)
Hiraoka, Yasuaki
2008-01-01
The triple collision singularity in the 3-vortex problem is studied in this paper. Under the necessary condition k 1 -1 +k 2 -1 +k 3 -1 =0 for vorticities to have the triple collision, the main results are summarized as follows: (i) For k 1 = k 2 , the triple collision singularity is topologically regularizable. (ii) For 0 1 − k 2 | < ε with a sufficiently small ε, the triple collision singularity is not topologically regularizable. First of all, in order to prove these statements, all singularities in the 3-vortex problem are classified. Then, we introduce a dynamical system by blowing up the triple collision singularity with an appropriate time scaling. Roughly speaking, it corresponds to pasting an invariant manifold at the triple collision singularity on the original phase space. This technique is well known as McGehee's collision manifold (1974 Inventions Math. 27 191–227) in the N-body problem of celestial mechanics. Finally, by adopting the viewpoint of Easton (1971 J. Diff. Eqns 10 92–9), topological regularizations of the triple collision singularity are studied in detail
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Songlin Wo
2018-01-01
Full Text Available Singular systems arise in a great deal of domains of engineering and can be used to solve problems which are more difficult and more extensive than regular systems to solve. Therefore, in this paper, the definition of finite-time robust H∞ control for uncertain linear continuous-time singular systems is presented. The problem we address is to design a robust state feedback controller which can deal with the singular system with time-varying norm-bounded exogenous disturbance, such that the singular system is finite-time robust bounded (FTRB with disturbance attenuation γ. Sufficient conditions for the existence of solutions to this problem are obtained in terms of linear matrix equalities (LMIs. When these LMIs are feasible, the desired robust controller is given. A detailed solving method is proposed for the restricted linear matrix inequalities. Finally, examples are given to show the validity of the methodology.
The analysis of optimal singular controls for SEIR model of tuberculosis
Marpaung, Faridawaty; Rangkuti, Yulita M.; Sinaga, Marlina S.
2014-12-01
The optimally of singular control for SEIR model of Tuberculosis is analyzed. There are controls that correspond to time of the vaccination and treatment schedule. The optimally of singular control is obtained by differentiate a switching function of the model. The result shows that vaccination and treatment control are singular.
Kamenshchik, A. Yu.
2018-03-01
We investigate particular cosmological models, based either on tachyon fields or on perfect fluids, for which soft future singularities arise in a natural way. Our main result is the description of a smooth crossing of the soft singularity in models with an anti-Chaplygin gas or with a particular tachyon field in the presence of dust. Such a crossing is made possible by certain transformations of matter properties. We discuss and compare also different approaches to the problem of crossing of the Big Bang-Big Crunch singularities.
Maximal Cohen-Macaulay modules over non-isolated surface singularities and matrix problems
Burban, Igor
2017-01-01
In this article the authors develop a new method to deal with maximal Cohen-Macaulay modules over non-isolated surface singularities. In particular, they give a negative answer on an old question of Schreyer about surface singularities with only countably many indecomposable maximal Cohen-Macaulay modules. Next, the authors prove that the degenerate cusp singularities have tame Cohen-Macaulay representation type. The authors' approach is illustrated on the case of \\mathbb{k} x,y,z/(xyz) as well as several other rings. This study of maximal Cohen-Macaulay modules over non-isolated singularities leads to a new class of problems of linear algebra, which the authors call representations of decorated bunches of chains. They prove that these matrix problems have tame representation type and describe the underlying canonical forms.
On a non classical oblique derivative problem for parabolic singular integro-differential operators
International Nuclear Information System (INIS)
Nguyen Minh Chuong; Le Quang Trung
1989-10-01
In this paper an oblique derivative problem for parabolic singular integro-differential operators was studied. In this problem the direction of the derivative may be tangent to the boundary of the domain. By the large parameter method theorems of existence and uniqueness of solutions of the problem were obtained. (author). 10 refs
Simulating a singularity-free universe outside the problem boundary in poisson
International Nuclear Information System (INIS)
Halbach, K.; Schlueter, R.
1992-01-01
An exact analytical solution developed from the Dirichlet problem exterior to a circle is employed in the magnetostatics code POISSON to provide a boundary condition option which simulates a singularity-free universe external to the problem domain. Problems with domains of large unequal extents in perpendicular directions are treated by first conformally mapping the exterior of an ellipse onto the exterior of the unit circle. Problems exhibiting symmetry in one or two planes are modeled using a semi or quarter, respectively, in conjunction with the singularity-free rest-of-universe boundary condition
A numerical solution of a singular boundary value problem arising in boundary layer theory.
Hu, Jiancheng
2016-01-01
In this paper, a second-order nonlinear singular boundary value problem is presented, which is equivalent to the well-known Falkner-Skan equation. And the one-dimensional third-order boundary value problem on interval [Formula: see text] is equivalently transformed into a second-order boundary value problem on finite interval [Formula: see text]. The finite difference method is utilized to solve the singular boundary value problem, in which the amount of computational effort is significantly less than the other numerical methods. The numerical solutions obtained by the finite difference method are in agreement with those obtained by previous authors.
Nonlinear PI control of chaotic systems using singular perturbation theory
International Nuclear Information System (INIS)
Wang Jiang; Wang Jing; Li Huiyan
2005-01-01
In this paper, we develop the nonlinear PI controllers for a class of chaotic systems based on singular perturbation theory. The original system is decomposed into two reduced order systems, to which the nonlinear uncertain terms belongs. In order to alleviate the deterioration of these nonlinear uncertainties, the nonlinear PI controllers are applied to each subsystem and combined to construct the composite controller for the full order system. The effectiveness and feasibility of the proposed control scheme is demonstrated through numerical simulations on the chaotic Chua's circuit
Controllability of non-linear systems: generic singularities and their stability
International Nuclear Information System (INIS)
Davydov, Alexey A; Zakalyukin, Vladimir M
2012-01-01
This paper presents an overview of the state of the art in applications of singularity theory to the analysis of generic singularities of controllability of non-linear systems on manifolds. Bibliography: 40 titles.
NUMERICAL SOLUTION OF SINGULAR INVERSE NODAL PROBLEM BY USING CHEBYSHEV POLYNOMIALS
NEAMATY, ABDOLALI; YILMAZ, EMRAH; AKBARPOOR, SHAHRBANOO; DABBAGHIAN, ABDOLHADI
2017-01-01
In this study, we consider Sturm-Liouville problem in two cases: the first case having no singularity and the second case having a singularity at zero. Then, we calculate the eigenvalues and the nodal points and present the uniqueness theorem for the solution of the inverse problem by using a dense subset of the nodal points in two given cases. Also, we use Chebyshev polynomials of the first kind for calculating the approximate solution of the inverse nodal problem in these cases. Finally, we...
Controllability of switched singular mix-valued logical control networks with constraints
Deng, Lei; Gong, Mengmeng; Zhu, Peiyong
2018-03-01
The present paper investigates the controllability problem of switched singular mix-valued logical control networks (SSMLCNs) with constraints on states and controls. First, using the semi-tenser product (STP) of matrices, the SSMLCN is expressed in an algebraic form, based on which a necessary and sufficient condition is given for the uniqueness of solution of SSMLCNs. Second, a necessary and sufficient criteria is derived for the controllability of constrained SSMLCNs, by converting a constrained SSMLCN into a parallel constrained switched mix-valued logical control network. Third, an algorithm is presented to design a proper switching sequence and a control scheme which force a state to a reachable state. Finally, a numerical example is given to demonstrate the efficiency of the results obtained in this paper.
Propagation of Singularities and Some Inverse Problems in Wave Propagation
National Research Council Canada - National Science Library
Symes, William W
1989-01-01
... in various useful coefficient classes, separation of scales,...We explain the essential role of travel time in the study of these problems, and show how its function may be generalized to multidimensional (i.e. non-layered) problems.
B-spline solution of a singularly perturbed boundary value problem arising in biology
International Nuclear Information System (INIS)
Lin Bin; Li Kaitai; Cheng Zhengxing
2009-01-01
We use B-spline functions to develop a numerical method for solving a singularly perturbed boundary value problem associated with biology science. We use B-spline collocation method, which leads to a tridiagonal linear system. The accuracy of the proposed method is demonstrated by test problems. The numerical result is found in good agreement with exact solution.
Hybrid vehicle optimal control : Linear interpolation and singular control
Delprat, S.; Hofman, T.
2015-01-01
Hybrid vehicle energy management can be formulated as an optimal control problem. Considering that the fuel consumption is often computed using linear interpolation over lookup table data, a rigorous analysis of the necessary conditions provided by the Pontryagin Minimum Principle is conducted. For
Muskhelishvili, N I
2011-01-01
Singular integral equations play important roles in physics and theoretical mechanics, particularly in the areas of elasticity, aerodynamics, and unsteady aerofoil theory. They are highly effective in solving boundary problems occurring in the theory of functions of a complex variable, potential theory, the theory of elasticity, and the theory of fluid mechanics.This high-level treatment by a noted mathematician considers one-dimensional singular integral equations involving Cauchy principal values. Its coverage includes such topics as the Hölder condition, Hilbert and Riemann-Hilbert problem
Robust H∞ Control for Singular Time-Delay Systems via Parameterized Lyapunov Functional Approach
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Li-li Liu
2014-01-01
Full Text Available A new version of delay-dependent bounded real lemma for singular systems with state delay is established by parameterized Lyapunov-Krasovskii functional approach. In order to avoid generating nonconvex problem formulations in control design, a strategy that introduces slack matrices and decouples the system matrices from the Lyapunov-Krasovskii parameter matrices is used. Examples are provided to demonstrate that the results in this paper are less conservative than the existing corresponding ones in the literature.
Czech Academy of Sciences Publication Activity Database
Mukhigulashvili, Sulkhan
-, č. 35 (2015), s. 23-50 ISSN 1126-8042 Institutional support: RVO:67985840 Keywords : higher order functional differential equations * Dirichlet boundary value problem * strong singularity Subject RIV: BA - General Mathematics http://ijpam.uniud.it/online_issue/201535/03-Mukhigulashvili.pdf
Singular Initial Value Problem for Certain Classes of Systems of Ordinary Differential Equations
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Josef Diblík
2013-01-01
dimension of the set of initial data generating such solutions is estimated. An asymptotic behavior of solutions is determined as well and relevant asymptotic formulas are derived. The method of functions defined implicitly and the topological method (Ważewski's method are used in the proofs. The results generalize some previous ones on singular initial value problems for differential equations.
Directory of Open Access Journals (Sweden)
Xiaofeng Zhang
2017-12-01
Full Text Available In this paper, we consider the existence of positive solutions to a singular semipositone boundary value problem of nonlinear fractional differential equations. By applying the fixed point index theorem, some new results for the existence of positive solutions are obtained. In addition, an example is presented to demonstrate the application of our main results.
Three symmetric positive solutions of fourth-order singular nonlocal boundary value problems
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Fuyi Xu
2011-12-01
Full Text Available In this paper, we study the existence of three positive solutions of fourth-order singular nonlocal boundary value problems. We show that there exist triple symmetric positive solutions by using Leggett-Williams fixed-point theorem. The conclusions in this paper essentially extend and improve some known results.
Well-posedness of the second-order linear singular Dirichlet problem
Czech Academy of Sciences Publication Activity Database
Lomtatidze, Alexander; Opluštil, Z.
2015-01-01
Roč. 22, č. 3 (2015), s. 409-419 ISSN 1072-947X Institutional support: RVO:67985840 Keywords : singular Dirichlet problem * well-posedness Subject RIV: BA - General Mathematics Impact factor: 0.417, year: 2015 http://www.degruyter.com/view/j/gmj.2015.22.issue-3/gmj-2015-0023/gmj-2015-0023. xml
Czech Academy of Sciences Publication Activity Database
Mukhigulashvili, Sulkhan; Půža, B.
2015-01-01
Roč. 2015, January (2015), s. 17 ISSN 1687-2770 Institutional support: RVO:67985840 Keywords : higher order nonlinear functional-differential equations * two-point right-focal boundary value problem * strong singularity Subject RIV: BA - General Mathematics Impact factor: 0.642, year: 2015 http://link.springer.com/article/10.1186%2Fs13661-014-0277-1
Existence and non-existence of solutions for a singular problem with variable potentials
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Kamel Saoudi
2017-11-01
Full Text Available The purpose of this article is to prove some existence and nonexistence theorems for the inhomogeneous singular Dirichlet problem $$ - \\Delta_p u = \\frac{\\lambda k(x}{u^\\delta}\\pm h(x u^q. $$ For proving our results we use the sub and super solution method, and monotonicity arguments.
Periodic solutions of an indefinite singular equation arising from the Kepler problem on the sphere
Czech Academy of Sciences Publication Activity Database
Hakl, Robert; Zamora, M.
2018-01-01
Roč. 70, č. 1 (2018), s. 173-190 ISSN 0008-414X Institutional support: RVO:67985840 Keywords : indefinite singularity * periodic solution * Kepler problem on S^1 Subject RIV: BA - General Mathematics OBOR OECD: Applied mathematics Impact factor: 0.963, year: 2016 https://cms.math.ca/10.4153/CJM-2016-050-1
Wu, Sheng-Jhih; Chu, Moody T.
2017-08-01
An inverse eigenvalue problem usually entails two constraints, one conditioned upon the spectrum and the other on the structure. This paper investigates the problem where triple constraints of eigenvalues, singular values, and diagonal entries are imposed simultaneously. An approach combining an eclectic mix of skills from differential geometry, optimization theory, and analytic gradient flow is employed to prove the solvability of such a problem. The result generalizes the classical Mirsky, Sing-Thompson, and Weyl-Horn theorems concerning the respective majorization relationships between any two of the arrays of main diagonal entries, eigenvalues, and singular values. The existence theory fills a gap in the classical matrix theory. The problem might find applications in wireless communication and quantum information science. The technique employed can be implemented as a first-step numerical method for constructing the matrix. With slight modification, the approach might be used to explore similar types of inverse problems where the prescribed entries are at general locations.
International Nuclear Information System (INIS)
Wu, Sheng-Jhih; Chu, Moody T
2017-01-01
An inverse eigenvalue problem usually entails two constraints, one conditioned upon the spectrum and the other on the structure. This paper investigates the problem where triple constraints of eigenvalues, singular values, and diagonal entries are imposed simultaneously. An approach combining an eclectic mix of skills from differential geometry, optimization theory, and analytic gradient flow is employed to prove the solvability of such a problem. The result generalizes the classical Mirsky, Sing–Thompson, and Weyl-Horn theorems concerning the respective majorization relationships between any two of the arrays of main diagonal entries, eigenvalues, and singular values. The existence theory fills a gap in the classical matrix theory. The problem might find applications in wireless communication and quantum information science. The technique employed can be implemented as a first-step numerical method for constructing the matrix. With slight modification, the approach might be used to explore similar types of inverse problems where the prescribed entries are at general locations. (paper)
The Schroedinger equation as a singular perturbation problem
International Nuclear Information System (INIS)
Jager, E.M. de; Kuepper, T.
1978-01-01
Comparisons are made of the eigenvalues and the corresponding eigenfunctions of the eigenvalue problem connected with the one dimensional Schroedinger equation in Hilbert space. The difference of the eigenvalues is estimated by applying Weyl's monotonicity principle and the minimum maximum principle. The difference of the eigenfunctions is estimated in L 2 norm and in maximum norm obtained by using simple tools from operator theory in Hilbert spaces. An application concerning perturbations of the Planck ideal linear oscillator is given. (author)
Large-Scale Parallel Finite Element Analysis of the Stress Singular Problems
International Nuclear Information System (INIS)
Noriyuki Kushida; Hiroshi Okuda; Genki Yagawa
2002-01-01
In this paper, the convergence behavior of large-scale parallel finite element method for the stress singular problems was investigated. The convergence behavior of iterative solvers depends on the efficiency of the pre-conditioners. However, efficiency of pre-conditioners may be influenced by the domain decomposition that is necessary for parallel FEM. In this study the following results were obtained: Conjugate gradient method without preconditioning and the diagonal scaling preconditioned conjugate gradient method were not influenced by the domain decomposition as expected. symmetric successive over relaxation method preconditioned conjugate gradient method converged 6% faster as maximum if the stress singular area was contained in one sub-domain. (authors)
A singular initial value problem for some functional differential equations
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Ravi P. Agarwal
2004-01-01
Full Text Available For the initial value problem trx′(t=at+b1x(t+b2x(q1t+b3trx′(q2t+φ(t,x(t,x(q1t,x′(t,x′(q2t, x(0=0, where r>1, 0
International Nuclear Information System (INIS)
Kates, R.E.
1979-01-01
This thesis shows that a small body with possibly strong internal gravity moves through an empty region of a curved, and not necessarily asymptotically flat, external spacetime on an approximate geodesic. By approximate geodesic, the following is meant: Suppose the ratio epsilon = m/L 1 - where m is the body's mass and L is a curvature reference length of the external field - is a small parameter. Then the body's worldline deviates from a geodesic only by distances of at most THETA(epsilon) L over times of order L. The worldline is calculated directly from the Einstein field equation using a singular perturbation technique that has been generalized from the method of matched asymptotic expansions. The need for singular perturbation techniques has long been appreciated in fluid mechanics, where they are now standard procedure in problems in which the straightforward expansion in powers of a small parameter fails to give a correct qualitative picture. In part I of this thesis, singular perturbations on manifolds are formulated in a coordinate-free way suitable for treating problems in general relativity and other field theories. Most importantly for this thesis, the coordinate-free formulation of singular perturbations given in part I is essential for treatment of the problem of motion in part II
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. Copyright © 2014 ISA. Published by Elsevier Ltd. All rights reserved.
Belkina, T. A.; Konyukhova, N. B.; Kurochkin, S. V.
2016-01-01
Previous and new results are used to compare two mathematical insurance models with identical insurance company strategies in a financial market, namely, when the entire current surplus or its constant fraction is invested in risky assets (stocks), while the rest of the surplus is invested in a risk-free asset (bank account). Model I is the classical Cramér-Lundberg risk model with an exponential claim size distribution. Model II is a modification of the classical risk model (risk process with stochastic premiums) with exponential distributions of claim and premium sizes. For the survival probability of an insurance company over infinite time (as a function of its initial surplus), there arise singular problems for second-order linear integrodifferential equations (IDEs) defined on a semiinfinite interval and having nonintegrable singularities at zero: model I leads to a singular constrained initial value problem for an IDE with a Volterra integral operator, while II model leads to a more complicated nonlocal constrained problem for an IDE with a non-Volterra integral operator. A brief overview of previous results for these two problems depending on several positive parameters is given, and new results are presented. Additional results are concerned with the formulation, analysis, and numerical study of "degenerate" problems for both models, i.e., problems in which some of the IDE parameters vanish; moreover, passages to the limit with respect to the parameters through which we proceed from the original problems to the degenerate ones are singular for small and/or large argument values. Such problems are of mathematical and practical interest in themselves. Along with insurance models without investment, they describe the case of surplus completely invested in risk-free assets, as well as some noninsurance models of surplus dynamics, for example, charity-type models.
On the singular Sturm-Liouville problems that have the same spectrum
Energy Technology Data Exchange (ETDEWEB)
Gulsen, Tuba [Department of Mathematics, Firat University, 23119, Elazig (Turkey); Ulusoy, Ismail [Department of Mathematics, Adiyaman University, 02040,Adiyaman (Turkey)
2016-06-08
The problem of efficaciously constucting the potential q (x) and the numbers h and H was solved in [1]. Trubowitz [2] investigated the isospectrality problem which have the same spectrum with other same type of problems. Then Jodeit and Levitan [3] considered this problem with a different approach, based on transmutation operators and integral equation. In this work, we discussed this problem for singular Sturm-Liouville operator and obtained some important formulas for the number H, the potential q (x) and the norming constants α{sub n}.
Singular Solutions to a (3 + 1-D Protter-Morawetz Problem for Keldysh-Type Equations
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Nedyu Popivanov
2017-01-01
Full Text Available We study a boundary value problem for (3 + 1-D weakly hyperbolic equations of Keldysh type (problem PK. The Keldysh-type equations are known in some specific applications in plasma physics, optics, and analysis on projective spaces. Problem PK is not well-posed since it has infinite-dimensional cokernel. Actually, this problem is analogous to a similar one proposed by M. Protter in 1952, but for Tricomi-type equations which, in part, are closely connected with transonic fluid dynamics. We consider a properly defined, in a special function space, generalized solution to problem PK for which existence and uniqueness theorems hold. It is known that it may have a strong power-type singularity at one boundary point even for very smooth right-hand sides of the equation. In the present paper we study the asymptotic behavior of the generalized solutions of problem PK at the singular point. There are given orthogonality conditions on the right-hand side of the equation, which are necessary and sufficient for the existence of a generalized solution with fixed order of singularity.
Symplectic finite element scheme: application to a driven problem with a regular singularity
Energy Technology Data Exchange (ETDEWEB)
Pletzer, A. [Ecole Polytechnique Federale, Lausanne (Switzerland). Centre de Recherche en Physique des Plasma (CRPP)
1996-02-01
A new finite element (FE) scheme, based on the decomposition of a second order differential equation into a set of first order symplectic (Hamiltonian) equations, is presented and tested on one-dimensional, driven Sturm-Liouville problem. Error analysis shows improved cubic convergence in the energy norm for piecewise linear `tent` elements, as compared to quadratic convergence for the standard and hybrid FE methods. The convergence deteriorates in the presence of a regular singular point, but can be recovered by appropriate mesh node packing. Optimal mesh packing exponents are derived to ensure cubic (respectively quadratic) convergence with minimal numerical error. A further suppression of the numerical error by a factor proportional to the square of the leading exponent of the singular solution, is achieved for a model problem based on determining the nonideal magnetohydrodynamic stability of a fusion plasma. (author) 7 figs., 14 refs.
Symplectic finite element scheme: application to a driven problem with a regular singularity
International Nuclear Information System (INIS)
Pletzer, A.
1996-02-01
A new finite element (FE) scheme, based on the decomposition of a second order differential equation into a set of first order symplectic (Hamiltonian) equations, is presented and tested on one-dimensional, driven Sturm-Liouville problem. Error analysis shows improved cubic convergence in the energy norm for piecewise linear 'tent' elements, as compared to quadratic convergence for the standard and hybrid FE methods. The convergence deteriorates in the presence of a regular singular point, but can be recovered by appropriate mesh node packing. Optimal mesh packing exponents are derived to ensure cubic (respectively quadratic) convergence with minimal numerical error. A further suppression of the numerical error by a factor proportional to the square of the leading exponent of the singular solution, is achieved for a model problem based on determining the nonideal magnetohydrodynamic stability of a fusion plasma. (author) 7 figs., 14 refs
Solving Singular Two-Point Boundary Value Problems Using Continuous Genetic Algorithm
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Omar Abu Arqub
2012-01-01
Full Text Available In this paper, the continuous genetic algorithm is applied for the solution of singular two-point boundary value problems, where smooth solution curves are used throughout the evolution of the algorithm to obtain the required nodal values. The proposed technique might be considered as a variation of the finite difference method in the sense that each of the derivatives is replaced by an appropriate difference quotient approximation. This novel approach possesses main advantages; it can be applied without any limitation on the nature of the problem, the type of singularity, and the number of mesh points. Numerical examples are included to demonstrate the accuracy, applicability, and generality of the presented technique. The results reveal that the algorithm is very effective, straightforward, and simple.
Existence and Estimates of Positive Solutions for Some Singular Fractional Boundary Value Problems
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Habib Mâagli
2014-01-01
fractional boundary value problem:Dαu(x=−a(xuσ(x, x∈(0,1 with the conditions limx→0+x2−αu(x=0, u(1=0, where 1<α≤2, σ∈(−1,1, and a is a nonnegative continuous function on (0,1 that may be singular at x=0 or x=1. We also give the global behavior of such a solution.
International Nuclear Information System (INIS)
Khalfin, L.A.
1975-01-01
On the basis of the strong energy-momentum conservation law, the induced singularities of mass distributions of unstable particles connected with cascade decay are investigated. The possible solution of the CP-problem in the decay of Kaon neutral - Antikaon neutral mesons based on the mechanism of the induced singularities is proposed
Numerical static state feedback laws for closed-loop singular optimal control
Graaf, de S.C.; Stigter, J.D.; Straten, van G.
2005-01-01
Singular and non-singular control trajectories of agricultural and (bio) chemical processes may need to be recalculated from time to time for use in closed-loop optimal control, because of unforeseen changes in state values and noise. This is time consuming. As an alternative, in this paper,
Cengizci, Süleyman; Atay, Mehmet Tarık; Eryılmaz, Aytekin
2016-01-01
This paper is concerned with two-point boundary value problems for singularly perturbed nonlinear ordinary differential equations. The case when the solution only has one boundary layer is examined. An efficient method so called Successive Complementary Expansion Method (SCEM) is used to obtain uniformly valid approximations to this kind of solutions. Four test problems are considered to check the efficiency and accuracy of the proposed method. The numerical results are found in good agreement with exact and existing solutions in literature. The results confirm that SCEM has a superiority over other existing methods in terms of easy-applicability and effectiveness.
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Svatoslav Stanêk
2008-03-01
Full Text Available The paper presents an existence principle for solving a large class of nonlocal regular discrete boundary value problems with the ÃÂ†-Laplacian. Applications of the existence principle to singular discrete problems are given.
Energy Technology Data Exchange (ETDEWEB)
Dotti, Gustavo; Gleiser, Reinaldo J [Facultad de Matematica, AstronomIa y Fisica (FaMAF), Universidad Nacional de Cordoba, Ciudad Universitaria, 5000 Cordoba (Argentina)
2009-11-07
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 deriv{sup 2}PSI{sub z} /partial derivt{sup 2} +HPSI{sub z} =0, where H= -partial deriv{sup 2} /partial derivx{sup 2} + V(x) is the Zerilli 'Hamiltonian' and x is the tortoise radial coordinate. From its definition, for smooth metric perturbations the field PSI{sub z} is singular at r{sub s} = -6M/(l - 1)(l +2), with l being the mode harmonic number. The equation PSI{sub z} obeys is also singular, since V has a second-order pole at r{sub s}. This is irrelevant to the black hole exterior stability problem, where r > 2M > 0, and r{sub s} < 0, but it introduces a non-trivial problem in the naked singular case where M < 0, then r{sub s} > 0, and the singularity appears in the relevant range of r (0 < r < infinity). We solve this problem by developing a new approach to the evolution of the even mode, based on a new gauge invariant function, PSI-circumflex, that is a regular function of the metric perturbation for any value of M. The relation of PSI-circumflex to PSI{sub z} is provided by an intertwiner operator. The spatial pieces of the (1 + 1) wave equations that PSI-circumflex and PSI{sub z} obey are related as a supersymmetric pair of quantum Hamiltonians H and H-circumflex. For M < 0,H-circumflex has a regular potential and a unique self-adjoint extension in a domain D defined by a physically motivated boundary condition at r = 0. This allows us to address the issue of evolution of gravitational perturbations in this non-globally hyperbolic background. This formulation is used to complete the proof of the linear instability of the Schwarzschild naked singularity, by showing that a previously found unstable mode belongs to a complete basis of H-circumflex in D, and thus is excitable by generic initial data. This is further illustrated by numerically solving the linearized equations for
Newsom, J. R.; Mukhopadhyay, V.
1983-01-01
A method for designing robust feedback controllers for multiloop systems is presented. Robustness is characterized in terms of the minimum singular value of the system return difference matrix at the plant input. Analytical gradients of the singular values with respect to design variables in the controller are derived. A cumulative measure of the singular values and their gradients with respect to the design variables is used with a numerical optimization technique to increase the system's robustness. Both unconstrained and constrained optimization techniques are evaluated. Numerical results are presented for a two output drone flight control system.
Creation-field cosmology: A possible solution to singularity, horizon, and flatness problems
International Nuclear Information System (INIS)
Narlikar, J.V.; Padmanabhan, T.
1985-01-01
A solution of Einstein's equations which admits radiation and a negative-energy massless scalar creation field as a source is presented. It is shown that the cosmological model based on this solution satisfies all the observational tests and thus is a viable alternative to the standard big-bang model. The present model is free from singularity and particle horizon and provides a natural explanation for the flatness problem. We argue that these features make the creation-field cosmological model theoretically superior to the big-bang model
One-dimensional singular problems involving the p-Laplacian and nonlinearities indefinite in sign
Kaufmann, Uriel; Medri, Iván
2015-01-01
Let $\\Omega$ be a bounded open interval, let $p>1$ and $\\gamma>0$, and let $m:\\Omega\\rightarrow\\mathbb{R}$ be a function that may change sign in $\\Omega $. In this article we study the existence and nonexistence of positive solutions for one-dimensional singular problems of the form $-(\\left\\vert u^{\\prime}\\right\\vert ^{p-2}u^{\\prime})^{\\prime}=m\\left( x\\right) u^{-\\gamma}$ in $\\Omega$, $u=0$ on $\\partial\\Omega$. As a consequence we also derive existence results for other related nonlinearities.
Mukhopadhyay, V.; Newsom, J. R.
1982-01-01
A stability margin evaluation method in terms of simultaneous gain and phase changes in all loops of a multiloop system is presented. A universal gain-phase margin evaluation diagram is constructed by generalizing an existing method using matrix singular value properties. Using this diagram and computing the minimum singular value of the system return difference matrix over the operating frequency range, regions of guaranteed stability margins can be obtained. Singular values are computed for a wing flutter suppression and a drone lateral attitude control problem. The numerical results indicate that this method predicts quite conservative stability margins. In the second example if the eigenvalue magnitude is used instead of the singular value, as a measure of nearness to singularity, more realistic stability margins are obtained. However, this relaxed measure generally cannot guarantee global stability.
Lebre, Amarino; Santos, António
2003-01-01
These proceedings comprise a large part of the papers presented at the International Conference Factorization, Singular Operators and related problems, which was held from January 28 to February 1, 2002, at the University of th Madeira, Funchal, Portugal, to mark Professor Georgii Litvinchuk's 70 birth day. Experts in a variety of fields came to this conference to pay tribute to the great achievements of Professor Georgii Litvinchuk in the development of vari ous areas of operator theory. The main themes of the conference were focussed around the theory of singular type operators and factorization problems, but other topics such as potential theory and fractional calculus, to name but a couple, were also presented. The goal of the conference was to bring together mathematicians from var ious fields within operator theory and function theory in order to highlight recent advances in problems many of which were originally studied by Profes sor Litvinchuk and his scientific school. A second aim was to sti...
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John A. DeRuntz Jr.
2005-01-01
Full Text Available The numerical solution of underwater shock fluid – structure interaction problems using boundary element/finite element techniques became tractable through the development of the family of Doubly Asymptotic Approximations (DAA. Practical implementation of the method has relied on the so-called augmentation of the DAA equations. The fluid and structural systems are respectively coupled by the structural acceleration vector in the surface normal direction on the right hand side of the DAA equations, and the total pressure applied to the structural equations on its right hand side. By formally solving for the acceleration vector from the structural system and substituting it into its place in the DAA equations, the augmentation introduces a term involving the inverse of the structural mass matrix. However there exist at least two important classes of problems in which the structural mass matrix is singular. This paper develops a method to carry out the augmentation for such problems using a generalized inverse technique.
Sayevand, K.; Pichaghchi, K.
2018-04-01
In this paper, we were concerned with the description of the singularly perturbed boundary value problems in the scope of fractional calculus. We should mention that, one of the main methods used to solve these problems in classical calculus is the so-called matched asymptotic expansion method. However we shall note that, this was not achievable via the existing classical definitions of fractional derivative, because they do not obey the chain rule which one of the key elements of the matched asymptotic expansion method. In order to accommodate this method to fractional derivative, we employ a relatively new derivative so-called the local fractional derivative. Using the properties of local fractional derivative, we extend the matched asymptotic expansion method to the scope of fractional calculus and introduce a reliable new algorithm to develop approximate solutions of the singularly perturbed boundary value problems of fractional order. In the new method, the original problem is partitioned into inner and outer solution equations. The reduced equation is solved with suitable boundary conditions which provide the terminal boundary conditions for the boundary layer correction. The inner solution problem is next solved as a solvable boundary value problem. The width of the boundary layer is approximated using appropriate resemblance function. Some theoretical results are established and proved. Some illustrating examples are solved and the results are compared with those of matched asymptotic expansion method and homotopy analysis method to demonstrate the accuracy and efficiency of the method. It can be observed that, the proposed method approximates the exact solution very well not only in the boundary layer, but also away from the layer.
Central configurations of the collinear three-body problem and singular surfaces in the mass space
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Xie, Zhifu, E-mail: zxie@vsu.edu [Department of Mathematics and Computer Science, Virginia State University, Petersburg, VA 23806 (United States)
2011-09-12
This Letter is to provide a new approach to study the phenomena of degeneracy of the number of the collinear central configurations under geometric equivalence. A direct and simple explicit parametric expression of the singular surface H{sub 3} is constructed in the mass space (m{sub 1},m{sub 2},m{sub 3}) element of (R{sup +}){sup 3}. The construction of H{sub 3} is from an inverse respective, that is, by specifying positions for the bodies and then determining the masses that are possible to yield a central configuration. It reveals the relationship between the phenomena of degeneracy and the inverse problem of central configurations. We prove that the number of central configurations is decreased to 3!/2-1=2, m{sub 1}, m{sub 2}, and m{sub 3} are mutually distinct if m element of H{sub 3}. Moreover, we know not only the number of central configurations but also what the nonequivalent central configurations are. -- Highlights: → Provide a new method to study the degeneracy of number of CC. → Results advanced the understanding of number of central configurations. → Singular mass surface H{sub 3} is given by a direct and simple parametric expression. → The proof only requires some basic knowledge of linear algebra. → The method can be applied to some other collinear n-body problem.
A class of singular Ro-matrices and extensions to semidefinite linear complementarity problems
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Sivakumar K.C.
2013-01-01
Full Text Available For ARnxn and qRn, the linear complementarity problem LCP(A, q is to determine if there is xRn such that x ≥ 0; y = Ax + q ≥ 0 and xT y = 0. Such an x is called a solution of LCP(A,q. A is called an Ro-matrix if LCP(A,0 has zero as the only solution. In this article, the class of R0-matrices is extended to include typically singular matrices, by requiring in addition that the solution x above belongs to a subspace of Rn. This idea is then extended to semidefinite linear complementarity problems, where a characterization is presented for the multplicative transformation.
International Nuclear Information System (INIS)
Costa, O. L. V.; Dufour, F.
2011-01-01
This paper deals with the expected discounted continuous control of piecewise deterministic Markov processes (PDMP’s) using a singular perturbation approach for dealing with rapidly oscillating parameters. The state space of the PDMP is written as the product of a finite set and a subset of the Euclidean space ℝ n . The discrete part of the state, called the regime, characterizes the mode of operation of the physical system under consideration, and is supposed to have a fast (associated to a small parameter ε>0) and a slow behavior. By using a similar approach as developed in Yin and Zhang (Continuous-Time Markov Chains and Applications: A Singular Perturbation Approach, Applications of Mathematics, vol. 37, Springer, New York, 1998, Chaps. 1 and 3) the idea in this paper is to reduce the number of regimes by considering an averaged model in which the regimes within the same class are aggregated through the quasi-stationary distribution so that the different states in this class are replaced by a single one. The main goal is to show that the value function of the control problem for the system driven by the perturbed Markov chain converges to the value function of this limit control problem as ε goes to zero. This convergence is obtained by, roughly speaking, showing that the infimum and supremum limits of the value functions satisfy two optimality inequalities as ε goes to zero. This enables us to show the result by invoking a uniqueness argument, without needing any kind of Lipschitz continuity condition.
Czech Academy of Sciences Publication Activity Database
Rontó, András; Samoilenko, A. M.
2007-01-01
Roč. 41, - (2007), s. 115-136 ISSN 1512-0015 R&D Projects: GA ČR(CZ) GA201/06/0254 Institutional research plan: CEZ:AV0Z10190503 Keywords : two-point problem * functional differential equation * singular boundary problem Subject RIV: BA - General Mathematics
Singular formalism and admissible control of spacecraft with rotating flexible solar array
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Lu Dongning
2014-02-01
Full Text Available This paper is concerned with the attitude control of a three-axis-stabilized spacecraft which consists of a central rigid body and a flexible sun-tracking solar array driven by a solar array drive assembly. Based on the linearization of the dynamics of the spacecraft and the modal identities about the flexible and rigid coupling matrices, the spacecraft attitude dynamics is reduced to a formally singular system with periodically varying parameters, which is quite different from a spacecraft with fixed appendages. In the framework of the singular control theory, the regularity and impulse-freeness of the singular system is analyzed and then admissible attitude controllers are designed by Lyapunov’s method. To improve the robustness against system uncertainties, an H∞ optimal control is designed by optimizing the H∞ norm of the system transfer function matrix. Comparative numerical experiments are performed to verify the theoretical results.
Singular Perturbations and Time Scales in Modeling and Control of Dynamic Systems,
1980-11-01
rTrp) (43) results in the initial value singularly perturbed matrix differential equations * providing there exist fta ’) and rT(p) uniquely...ReA(Af)ɘ then A1 is D-stable. Let us conditions may be more difficult. Our problem is assume that the network has n, inductors and nc to fmd
New Designs of Reduced-Order Observer-Based Controllers for Singularly Perturbed Linear Systems
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Heonjong Yoo
2017-01-01
Full Text Available The slow and fast reduced-order observers and reduced-order observer-based controllers are designed by using the two-stage feedback design technique for slow and fast subsystems. The new designs produce an arbitrary order of accuracy, while the previously known designs produce the accuracy of O(ϵ only where ϵ is a small singular perturbation parameter. Several cases of reduced-order observer designs are considered depending on the measured state space variables: only all slow variables are measured, only all fast variables are measured, and some combinations of the slow and fast variables are measured. Since the two-stage methods have been used to overcome the numerical ill-conditioning problem for Cases (III–(V, they have similar procedures. The numerical ill-conditioning problem is avoided so that independent feedback controllers can be applied to each subsystem. The design allows complete time-scale separation for both the reduced-order observer and controller through the complete and exact decomposition into slow and fast time scales. This method reduces both offline and online computations.
A locally convergent Jacobi iteration for the tensor singular value problem
Shekhawat, Hanumant Singh; Weiland, Siep
2018-01-01
Multi-linear functionals or tensors are useful in study and analysis multi-dimensional signal and system. Tensor approximation, which has various applications in signal processing and system theory, can be achieved by generalizing the notion of singular values and singular vectors of matrices to
Czech Academy of Sciences Publication Activity Database
Escudero, C.; Hakl, Robert; Peral, I.; Torres, P.J.
2014-01-01
Roč. 37, č. 6 (2014), s. 793-807 ISSN 0170-4214 Institutional support: RVO:67985840 Keywords : singular boundary value problem * epitaxial growth * radial solution Subject RIV: BA - General Mathematics Impact factor: 0.918, year: 2014 http://onlinelibrary.wiley.com/doi/10.1002/mma.2836/full
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V. Rukavishnikov
2014-01-01
Full Text Available The existence and uniqueness of the Rv-generalized solution for the first boundary value problem and a second order elliptic equation with coordinated and uncoordinated degeneracy of input data and with strong singularity solution on all boundary of a two-dimensional domain are established.
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Aang Nuryaman
2012-11-01
Full Text Available The governing equations describing the methane oxidation process in reverse flow reactor are given by a set of convective-diffusion equations with a nonlinear reaction term, where temperature and methane conversion are dependent variables. In this study, the process is assumed to be one-dimensional pseudo homogeneous model and takes place with a certain reaction rate in which the whole process of reactor is still workable. Thus, the reaction rate can proceed at a fixed temperature. Under this condition, we restrict ourselves to solve the equations for the conversion only. From the available data, it turns out that the ratio of the diffusion term to the reaction term is small. Hence, this ratio is considered as small parameter in our model and this leads to a singular perturbation problem. In the vicinity of small parameter in front of higher order term, the numerical difficulties will be found. Here, we present an analytical solution by means of matched asymptotic expansions. Result shows that, up to and including the first order of approximation, the solution is in agreement with the exact and numerical solutions of the boundary value problem.
Numerical solution of singularity-perturbed two-point boundary-value problems
International Nuclear Information System (INIS)
Masenge, R.W.P.
1993-07-01
Physical processes which involve transportation of slowly diffusing substances in a fast-flowing medium are mathematically modelled by so-called singularly-perturbed second order convection diffusion differential equations in which the convective first order terms dominate over the diffusive second order terms. In general, analytical solutions of such equations are characterized by having sharp solution fronts in some sections of the interior and/or the boundary of the domain of solution. The presence of these (usually very narrow) layer regions in the solution domain makes the task of globally approximating such solutions by standard numerical techniques very difficult. In this expository paper we use a simple one-dimensional prototype problem as a vehicle for analysing the nature of the numerical approximation difficulties involved. In the sequel we present, without detailed derivation, two practical numerical schemes which succeed in varying degrees in numerically resolving the layer of the solution to the prototype problem. (author). 3 refs, 1 fig., 1 tab
Directory of Open Access Journals (Sweden)
Gai Gongqi
2011-01-01
Full Text Available Abstract This article studies the boundary value problems for the third-order nonlinear singular difference equations Δ 3 u ( i - 2 + λ a ( i f ( i , u ( i = 0 , i ∈ [ 2 , T + 2 ] , satisfying five kinds of different boundary value conditions. This article shows the existence of positive solutions for positone and semi-positone type. The nonlinear term may be singular. Two examples are also given to illustrate the main results. The arguments are based upon fixed point theorems in a cone. MSC [2008]: 34B15; 39A10.
Belkina, T. A.; Konyukhova, N. B.; Kurochkin, S. V.
2012-10-01
A singular boundary value problem for a second-order linear integrodifferential equation with Volterra and non-Volterra integral operators is formulated and analyzed. The equation is defined on ℝ+, has a weak singularity at zero and a strong singularity at infinity, and depends on several positive parameters. Under natural constraints on the coefficients of the equation, existence and uniqueness theorems for this problem with given limit boundary conditions at singular points are proved, asymptotic representations of the solution are given, and an algorithm for its numerical determination is described. Numerical computations are performed and their interpretation is given. The problem arises in the study of the survival probability of an insurance company over infinite time (as a function of its initial surplus) in a dynamic insurance model that is a modification of the classical Cramer-Lundberg model with a stochastic process rate of premium under a certain investment strategy in the financial market. A comparative analysis of the results with those produced by the model with deterministic premiums is given.
Singular-perturbation--strong-coupling field theory and the moments problem
International Nuclear Information System (INIS)
Handy, C.R.
1981-01-01
Motivated by recent work of Bender, Cooper, Guralnik, Mjolsness, Rose, and Sharp, a new technique is presented for solving field equations in terms of singular-perturbation--strong-coupling expansions. Two traditional mathematical tools are combined into one effective procedure. Firstly, high-temperature lattice expansions are obtained for the corresponding power moments of the field solution. The approximate continuum-limit power moments are subsequently obtained through the application of Pade techniques. Secondly, in order to reconstruct the corresponding approximate global field solution, one must use function-moments reconstruction techniques. The latter involves reconsidering the traditional ''moments problem'' of interest to pure and applied mathematicians. The above marriage between lattice methods and moments reconstruction procedures for functions yields good results for the phi 4 field-theory kink, and the sine-Gordon kink solutions. It is argued that the power moments are the most efficient dynamical variables for the generation of strong-coupling expansions. Indeed, a momentum-space formulation is being advocated in which the long-range behavior of the space-dependent fields are determined by the small-momentum, infrared, domain
Local sensitivity analysis for inverse problems solved by singular value decomposition
Hill, M.C.; Nolan, B.T.
2010-01-01
Local sensitivity analysis provides computationally frugal ways to evaluate models commonly used for resource management, risk assessment, and so on. This includes diagnosing inverse model convergence problems caused by parameter insensitivity and(or) parameter interdependence (correlation), understanding what aspects of the model and data contribute to measures of uncertainty, and identifying new data likely to reduce model uncertainty. Here, we consider sensitivity statistics relevant to models in which the process model parameters are transformed using singular value decomposition (SVD) to create SVD parameters for model calibration. The statistics considered include the PEST identifiability statistic, and combined use of the process-model parameter statistics composite scaled sensitivities and parameter correlation coefficients (CSS and PCC). The statistics are complimentary in that the identifiability statistic integrates the effects of parameter sensitivity and interdependence, while CSS and PCC provide individual measures of sensitivity and interdependence. PCC quantifies correlations between pairs or larger sets of parameters; when a set of parameters is intercorrelated, the absolute value of PCC is close to 1.00 for all pairs in the set. The number of singular vectors to include in the calculation of the identifiability statistic is somewhat subjective and influences the statistic. To demonstrate the statistics, we use the USDA’s Root Zone Water Quality Model to simulate nitrogen fate and transport in the unsaturated zone of the Merced River Basin, CA. There are 16 log-transformed process-model parameters, including water content at field capacity (WFC) and bulk density (BD) for each of five soil layers. Calibration data consisted of 1,670 observations comprising soil moisture, soil water tension, aqueous nitrate and bromide concentrations, soil nitrate concentration, and organic matter content. All 16 of the SVD parameters could be estimated by
International Nuclear Information System (INIS)
Velichenko, V.V.
1994-01-01
The problem of catastrophe control is discussed. Catastrophe control aims to withdraw responsible engineering constructions out of the catastrophe. The mathematical framework of catastrophes control systems is constructed. It determines the principles of systems filling by the concrete physical contents and, simultaneously, permits to employ modern control methods for the synthesis of optimal withdrawal strategy for protected objects
Telescopic Hybrid Fast Solver for 3D Elliptic Problems with Point Singularities
Paszyńska, Anna; Jopek, Konrad; Banaś, Krzysztof; Paszyński, Maciej; Gurgul, Piotr; Lenerth, Andrew; Nguyen, Donald; Pingali, Keshav; Dalcind, Lisandro; Calo, Victor M.
2015-01-01
This paper describes a telescopic solver for two dimensional h adaptive grids with point singularities. The input for the telescopic solver is an h refined two dimensional computational mesh with rectangular finite elements. The candidates for point singularities are first localized over the mesh by using a greedy algorithm. Having the candidates for point singularities, we execute either a direct solver, that performs multiple refinements towards selected point singularities and executes a parallel direct solver algorithm which has logarithmic cost with respect to refinement level. The direct solvers executed over each candidate for point singularity return local Schur complement matrices that can be merged together and submitted to iterative solver. In this paper we utilize a parallel multi-thread GALOIS solver as a direct solver. We use Incomplete LU Preconditioned Conjugated Gradients (ILUPCG) as an iterative solver. We also show that elimination of point singularities from the refined mesh reduces significantly the number of iterations to be performed by the ILUPCG iterative solver.
Telescopic Hybrid Fast Solver for 3D Elliptic Problems with Point Singularities
Paszyńska, Anna
2015-06-01
This paper describes a telescopic solver for two dimensional h adaptive grids with point singularities. The input for the telescopic solver is an h refined two dimensional computational mesh with rectangular finite elements. The candidates for point singularities are first localized over the mesh by using a greedy algorithm. Having the candidates for point singularities, we execute either a direct solver, that performs multiple refinements towards selected point singularities and executes a parallel direct solver algorithm which has logarithmic cost with respect to refinement level. The direct solvers executed over each candidate for point singularity return local Schur complement matrices that can be merged together and submitted to iterative solver. In this paper we utilize a parallel multi-thread GALOIS solver as a direct solver. We use Incomplete LU Preconditioned Conjugated Gradients (ILUPCG) as an iterative solver. We also show that elimination of point singularities from the refined mesh reduces significantly the number of iterations to be performed by the ILUPCG iterative solver.
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. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.
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Zhang Xuemei
2009-01-01
Full Text Available By constructing available upper and lower solutions and combining the Schauder's fixed point theorem with maximum principle, this paper establishes sufficient and necessary conditions to guarantee the existence of as well as positive solutions for a class of singular boundary value problems on time scales. The results significantly extend and improve many known results for both the continuous case and more general time scales. We illustrate our results by one example.
International Nuclear Information System (INIS)
Chettab, M.; Lubuma, M.S.
1990-08-01
The behaviour of the weak solution of the Stokes problem on a polygon is considered with emphasis on the maximal regularity of the solution and on global formulae for the coefficients of singularities. This regularity leads to a slow convergent mixed finite element method of fractional order less than one while the use of the above formulae provides better approximations for the solution and for the coefficients. (author). 32 refs
Directory of Open Access Journals (Sweden)
Jufang Wang
2013-01-01
Full Text Available We establish the existence of triple positive solutions of an m-point boundary value problem for the nonlinear singular second-order differential equations of mixed type with a p-Laplacian operator by Leggett-William fixed point theorem. At last, we give an example to demonstrate the use of the main result of this paper. The conclusions in this paper essentially extend and improve the known results.
Dinesh Kumar, S.; Nageshwar Rao, R.; Pramod Chakravarthy, P.
2017-11-01
In this paper, we consider a boundary value problem for a singularly perturbed delay differential equation of reaction-diffusion type. We construct an exponentially fitted numerical method using Numerov finite difference scheme, which resolves not only the boundary layers but also the interior layers arising from the delay term. An extensive amount of computational work has been carried out to demonstrate the applicability of the proposed method.
Vibration control of an elastic strip by a singular force
Indian Academy of Sciences (India)
strip are changed by applying a lateral concentrated force to the plate. ... Predicting resonance frequency of plates is an important technological and scientific ... Ritz methods in a number of studies pertaining to control of flutter in aerospace ..... Bingham B, Atalla M J, Hagood N W 2001 Comparison of structural-acoustic ...
Butuzov, V. F.
2017-06-01
We construct and justify asymptotic expansions of solutions of a singularly perturbed elliptic problem with Dirichlet boundary conditions in the case when the corresponding degenerate equation has a triple root. In contrast to the case of a simple root, the expansion is with respect to fractional (non-integral) powers of the small parameter, the boundary-layer variables have another scaling, and the boundary layer has three zones. This gives rise to essential modifications in the algorithm for constructing the boundary functions. Solutions of the elliptic problem are stationary solutions of the corresponding parabolic problem. We prove that such a stationary solution is asymptotically stable and find its global domain of attraction.
Impulsive Controller Design for Complex Nonlinear Singular Networked Systems with Packet Dropouts
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Xian-Lin Zhao
2013-01-01
Full Text Available Globally exponential stability of Complex (with coupling Nonlinear Singular Impulsive Networked Control Systems (CNSINCS with packet dropouts and time-delay is investigated. Firstly, the mathematic model of CNSINCS is established. Then, by employing the method of Lyapunov functional, exponential stability criteria are obtained and the impulsive controller design method is given. Finally, some simulation results are provided to demonstrate the effectiveness of the proposed method.
Optimal control of dissipative nonlinear dynamical systems with triggers of coupled singularities
International Nuclear Information System (INIS)
Hedrih, K
2008-01-01
This paper analyses the controllability of motion of nonconservative nonlinear dynamical systems in which triggers of coupled singularities exist or appear. It is shown that the phase plane method is useful for the analysis of nonlinear dynamics of nonconservative systems with one degree of freedom of control strategies and also shows the way it can be used for controlling the relative motion in rheonomic systems having equivalent scleronomic conservative or nonconservative system For the system with one generalized coordinate described by nonlinear differential equation of nonlinear dynamics with trigger of coupled singularities, the functions of system potential energy and conservative force must satisfy some conditions defined by a Theorem on the existence of a trigger of coupled singularities and the separatrix in the form of 'an open a spiral form' of number eight. Task of the defined dynamical nonconservative system optimal control is: by using controlling force acting to the system, transfer initial state of the nonlinear dynamics of the system into the final state of the nonlinear dynamics in the minimal time for that optimal control task
Optimal control of dissipative nonlinear dynamical systems with triggers of coupled singularities
Stevanović Hedrih, K.
2008-02-01
This paper analyses the controllability of motion of nonconservative nonlinear dynamical systems in which triggers of coupled singularities exist or appear. It is shown that the phase plane method is useful for the analysis of nonlinear dynamics of nonconservative systems with one degree of freedom of control strategies and also shows the way it can be used for controlling the relative motion in rheonomic systems having equivalent scleronomic conservative or nonconservative system For the system with one generalized coordinate described by nonlinear differential equation of nonlinear dynamics with trigger of coupled singularities, the functions of system potential energy and conservative force must satisfy some conditions defined by a Theorem on the existence of a trigger of coupled singularities and the separatrix in the form of "an open a spiral form" of number eight. Task of the defined dynamical nonconservative system optimal control is: by using controlling force acting to the system, transfer initial state of the nonlinear dynamics of the system into the final state of the nonlinear dynamics in the minimal time for that optimal control task
Sensitivity analysis of automatic flight control systems using singular value concepts
Herrera-Vaillard, A.; Paduano, J.; Downing, D.
1985-01-01
A sensitivity analysis is presented that can be used to judge the impact of vehicle dynamic model variations on the relative stability of multivariable continuous closed-loop control systems. The sensitivity analysis uses and extends the singular-value concept by developing expressions for the gradients of the singular value with respect to variations in the vehicle dynamic model and the controller design. Combined with a priori estimates of the accuracy of the model, the gradients are used to identify the elements in the vehicle dynamic model and controller that could severely impact the system's relative stability. The technique is demonstrated for a yaw/roll damper stability augmentation designed for a business jet.
HEALTH CARE INFORMATIZATION: PROBLEMS, SOLVED AND UNSOLVED. QUESTION OF EFFICIENCY AND SINGULARITY
Directory of Open Access Journals (Sweden)
О. P. Mintser
2013-11-01
Full Text Available The considered questions of transformation of basic presentation are in relation to health care informatization. One idea is postulated. Although from the moment of researches beginning in this direction passed more then 50 years, complete clarity in determination to the best strategy of informatization is not defined. New risks are marked. It's related with the origin of technological and informative singularity.
A Jacobi-Davidson type method for the generalized singular value problem
Hochstenbach, M.E.
2009-01-01
We discuss a new method for the iterative computation of some of the generalized singular values and vectors of a large sparse matrix. Our starting point is the augmented matrix formulation of the GSVD. The subspace expansion is performed by (approximately) solving a Jacobi–Davidson type correction
Fuzzy Stochastic Optimal Guaranteed Cost Control of Bio-Economic Singular Markovian Jump Systems.
Li, Li; Zhang, Qingling; Zhu, Baoyan
2015-11-01
This paper establishes a bio-economic singular Markovian jump model by considering the price of the commodity as a Markov chain. The controller is designed for this system such that its biomass achieves the specified range with the least cost in a finite-time. Firstly, this system is described by Takagi-Sugeno fuzzy model. Secondly, a new design method of fuzzy state-feedback controllers is presented to ensure not only the regularity, nonimpulse, and stochastic singular finite-time boundedness of this kind of systems, but also an upper bound achieved for the cost function in the form of strict linear matrix inequalities. Finally, two examples including a practical example of eel seedling breeding are given to illustrate the merit and usability of the approach proposed in this paper.
Vatankhah, Saeed; Renaut, Rosemary A.; Ardestani, Vahid E.
2018-04-01
We present a fast algorithm for the total variation regularization of the 3-D gravity inverse problem. Through imposition of the total variation regularization, subsurface structures presenting with sharp discontinuities are preserved better than when using a conventional minimum-structure inversion. The associated problem formulation for the regularization is nonlinear but can be solved using an iteratively reweighted least-squares algorithm. For small-scale problems the regularized least-squares problem at each iteration can be solved using the generalized singular value decomposition. This is not feasible for large-scale, or even moderate-scale, problems. Instead we introduce the use of a randomized generalized singular value decomposition in order to reduce the dimensions of the problem and provide an effective and efficient solution technique. For further efficiency an alternating direction algorithm is used to implement the total variation weighting operator within the iteratively reweighted least-squares algorithm. Presented results for synthetic examples demonstrate that the novel randomized decomposition provides good accuracy for reduced computational and memory demands as compared to use of classical approaches.
International Nuclear Information System (INIS)
Kanki, Takashi; Uyama, Tadao; Tokuda, Shinji.
1995-07-01
In the numerical method to compute the matching data which are necessary for resistive MHD stability analyses, it is required to solve the eigenvalue problem and the associated singular equation. An iterative method is developed to solve the eigenvalue problem and the singular equation. In this method, the eigenvalue problem is replaced with an equivalent nonlinear equation and a singular equation is derived from Newton's method for the nonlinear equation. The multi-grid method (MGM), a high speed iterative method, can be applied to this method. The convergence of the eigenvalue and the eigenvector, and the CPU time in this method are investigated for a model equation. It is confirmed from the numerical results that this method is effective for solving the eigenvalue problem and the singular equation with numerical stability and high accuracy. It is shown by improving the MGM that the CPU time for this method is 50 times shorter than that of the direct method. (author)
Multiobjective suspension control problem
Jager, de A.G.
1995-01-01
The paper describes a (controller) design problem in the field of suspension systems for transport vehicles. A ten degrees-of-freedom model for a tractor-semitrailer vehicle is presented, using parameters derived from a real vehicle, which should be used for design and verification purposes. Road
Directory of Open Access Journals (Sweden)
Qiying Wei
2009-01-01
Full Text Available By using the well-known Schauder fixed point theorem and upper and lower solution method, we present some existence criteria for positive solution of an -point singular -Laplacian dynamic equation on time scales with the sign changing nonlinearity. These results are new even for the corresponding differential (=ℝ and difference equations (=ℤ, as well as in general time scales setting. As an application, an example is given to illustrate the results.
Topological effects in QCD and the problem of short-distance singularities
International Nuclear Information System (INIS)
Luescher, Martin
2004-01-01
The topological susceptibility and the higher moments of the topological charge distribution in QCD are expressed through certain n-point functions of the scalar and pseudo-scalar quark densities at vanishing momenta, which are free of short-distance singularities. Since the normalization of the correlation functions is determined by the non-singlet chiral Ward identities, these formulae provide an unambiguous regularization-independent definition of the moments and thus of the charge distribution
Directory of Open Access Journals (Sweden)
Meiqiang Feng
2009-01-01
Full Text Available By constructing available upper and lower solutions and combining the Schauder's fixed point theorem with maximum principle, this paper establishes sufficient and necessary conditions to guarantee the existence of Cld[0,1]𝕋 as well as CldΔ[0,1]𝕋 positive solutions for a class of singular boundary value problems on time scales. The results significantly extend and improve many known results for both the continuous case and more general time scales. We illustrate our results by one example.
International Nuclear Information System (INIS)
Celerier, Marie-Noeelle; Szekeres, Peter
2002-01-01
Extending the study of spherically symmetric metrics satisfying the dominant energy condition and exhibiting singularities of power-law type initiated by Szekeres and Iyer, we identify two classes of peculiar interest: focusing timelike singularity solutions with the stress-energy tensor of a radiative perfect fluid (equation of state: p=(1/3)ρ) and a set of null singularity classes verifying identical properties. We consider two important applications of these results: to cosmology, as regards the possibility of solving the horizon problem with no need to resort to any inflationary scenario, and to the strong cosmic censorship hypothesis to which we propose a class of physically consistent counterexamples
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Nicola Ponara
2012-11-01
Full Text Available Regularized Heaviside and Dirac delta function are used in several fields of computational physics and mechanics. Hence the issue of the quadrature of integrals of discontinuous and singular functions arises. In order to avoid ad-hoc quadrature procedures, regularization of the discontinuous and the singular fields is often carried out. In particular, weight functions of the signed distance with respect to the discontinuity interface are exploited. Tornberg and Engquist (Journal of Scientific Computing, 2003, 19: 527–552 proved that the use of compact support weight function is not suitable because it leads to errors that do not vanish for decreasing mesh size. They proposed the adoption of non-compact support weight functions. In the present contribution, the relationship between the Fourier transform of the weight functions and the accuracy of the regularization procedure is exploited. The proposed regularized approach was implemented in the eXtended Finite Element Method. As a three-dimensional example, we study a slender solid characterized by an inclined interface across which the displacement is discontinuous. The accuracy is evaluated for varying position of the discontinuity interfaces with respect to the underlying mesh. A procedure for the choice of the regularization parameters is proposed.
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George N. Galanis
2005-10-01
Full Text Available In this paper we prove the existence of positive solutions for the three-point singular boundary-value problem$$ -[phi _{p}(u']'=q(tf(t,u(t,quad 0
A singular perturbation approach to non-Markovian escape rate problems
International Nuclear Information System (INIS)
Dygas, M.M.; Matkowsky, B.J.; Schuss, Z.
1986-01-01
The authors employ singular perturbation methods to examine the generalized Langevin equation which describes the dynamics of a Brownian particle in an arbitrary potential force field, acted on by a fluctuating force describing collisions between the Brownian particle and lighter particles comprising a thermal bath. In contrast to models in which the collisions occur instantaneously, and the dynamics are modeled by a Langevin stochastic equation, they consider the situation in which the collisions do not occur instantaneously, so that the process is no longer a Markov process and the generalized Langevin equation must be employed. They compute expressions for the mean exit time of the Brownian particle from the potential well in which it is confined
On the W-hair of string black holes and the singularity problem
Ellis, John R.; Nanopoulos, Dimitri V.
1992-01-01
We argue that the infinitely many gauge symmetries of string theory provide an infinite set of conserved (gauge) quantum numbers (W-hair) which characterise black hole states and maintain quantum coherence, even during exotic processes like black hole evaporation/decay. We study ways of measuring the W-hair of spherically-symmetric four-dimensional objects with event horizons, treated as effectively two-dimensional string black holes. Measurements can be done either through the s-wave scattering of light particles off the string black-hole background, or through interference experiments of Aharonov-Bohm type. We also speculate on the role of the extended W-symmetries possessed by the topological field theories that describe the region of space-time around a singularity.
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.
Keum, Jung-Hoon; Ra, Sung-Woong
2009-12-01
Nonlinear sliding surface design in variable structure systems for spacecraft attitude control problems is studied. A robustness analysis is performed for regular form of system, and calculation of actuator bandwidth is presented by reviewing sliding surface dynamics. To achieve non-singular attitude description and minimal parameterization, spacecraft attitude control problems are considered based on modified Rodrigues parameters (MRP). It is shown that the derived controller ensures the sliding motion in pre-determined region irrespective of unmodeled effects and disturbances.
Directory of Open Access Journals (Sweden)
Suheel Abdullah Malik
2014-01-01
Full Text Available We present a hybrid heuristic computing method for the numerical solution of nonlinear singular boundary value problems arising in physiology. The approximate solution is deduced as a linear combination of some log sigmoid basis functions. A fitness function representing the sum of the mean square error of the given nonlinear ordinary differential equation (ODE and its boundary conditions is formulated. The optimization of the unknown adjustable parameters contained in the fitness function is performed by the hybrid heuristic computation algorithm based on genetic algorithm (GA, interior point algorithm (IPA, and active set algorithm (ASA. The efficiency and the viability of the proposed method are confirmed by solving three examples from physiology. The obtained approximate solutions are found in excellent agreement with the exact solutions as well as some conventional numerical solutions.
Non-linear singular problems in p-adic analysis: associative algebras of p-adic distributions
International Nuclear Information System (INIS)
Albeverio, S; Khrennikov, A Yu; Shelkovich, V M
2005-01-01
We propose an algebraic theory which can be used for solving both linear and non-linear singular problems of p-adic analysis related to p-adic distributions (generalized functions). We construct the p-adic Colombeau-Egorov algebra of generalized functions, in which Vladimirov's pseudo-differential operator plays the role of differentiation. This algebra is closed under Fourier transformation and associative convolution. Pointvalues of generalized functions are defined, and it turns out that any generalized function is uniquely determined by its pointvalues. We also construct an associative algebra of asymptotic distributions, which is generated by the linear span of the set of associated homogeneous p-adic distributions. This algebra is embedded in the Colombeau-Egorov algebra as a subalgebra. In addition, a new technique for constructing weak asymptotics is developed
Energy Technology Data Exchange (ETDEWEB)
Smirnov, A. G., E-mail: smirnov@lpi.ru [I. E. Tamm Theory Department, P. N. Lebedev Physical Institute, Leninsky Prospect 53, Moscow 119991 (Russian Federation)
2015-12-15
We develop a general technique for finding self-adjoint extensions of a symmetric operator that respects a given set of its symmetries. Problems of this type naturally arise when considering two- and three-dimensional Schrödinger operators with singular potentials. The approach is based on constructing a unitary transformation diagonalizing the symmetries and reducing the initial operator to the direct integral of a suitable family of partial operators. We prove that symmetry preserving self-adjoint extensions of the initial operator are in a one-to-one correspondence with measurable families of self-adjoint extensions of partial operators obtained by reduction. The general scheme is applied to the three-dimensional Aharonov-Bohm Hamiltonian describing the electron in the magnetic field of an infinitely thin solenoid. We construct all self-adjoint extensions of this Hamiltonian, invariant under translations along the solenoid and rotations around it, and explicitly find their eigenfunction expansions.
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 li......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...
Shao, S.; Gao, Z.
2017-10-01
Stability of active disturbance rejection control (ADRC) is analysed in the presence of unknown, nonlinear, and time-varying dynamics. In the framework of singular perturbations, the closed-loop error dynamics are semi-decoupled into a relatively slow subsystem (the feedback loop) and a relatively fast subsystem (the extended state observer), respectively. It is shown, analytically and geometrically, that there exists a unique exponential stable solution if the size of the initial observer error is sufficiently small, i.e. in the same order of the inverse of the observer bandwidth. The process of developing the uniformly asymptotic solution of the system reveals the condition on the stability of the ADRC and the relationship between the rate of change in the total disturbance and the size of the estimation error. The differentiability of the total disturbance is the only assumption made.
The critical slab problem for pure-triplet anisotropic scattering by singular eigenfunction method
Energy Technology Data Exchange (ETDEWEB)
Tuereci, R.G. [Kirikkale Univ. (Turkey). Kirikkale Vocational School; Tuereci, D. [Ministery of Education, Ankara (Turkey). General Directorate of Secondary Education
2017-12-15
The infinite medium Green function can be written by using the jump condition, found Case's eigenfunctions. Thus, any reactor theory problem which is inplane geometry such the criticality problem as can be investigated by using the proper boundary conditions and suggested flux definitions. By using the criticality equation the critical thicknesses can be calculated as numerically. The selected numerical results can be tabulated.
Nonlinear singular elliptic equations
International Nuclear Information System (INIS)
Dong Minh Duc.
1988-09-01
We improve the Poincare inequality, the Sobolev imbedding theorem and the Trudinger imbedding theorem and prove a Mountain pass theorem. Applying these results we study a nonlinear singular mixed boundary problem. (author). 22 refs
Singular Cauchy Initial Value Problem for Certain Classes of Integro-Differential Equations
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Šmarda Zdeněk
2010-01-01
Full Text Available The existence and uniqueness of solutions and asymptotic estimate of solution formulas are studied for the following initial value problem: , , , where is a constant and . An approach which combines topological method of T. Ważewski and Schauder's fixed point theorem is used.
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Shihuang Hong
2009-01-01
Full Text Available We present sufficient conditions for the existence of at least twin or triple positive solutions of a nonlinear four-point singular boundary value problem with a p-Laplacian dynamic equation on a time scale. Our results are obtained via some new multiple fixed point theorems.
DeRuntz Jr., John A.
2005-01-01
The numerical solution of underwater shock fluid – structure interaction problems using boundary element/finite element techniques became tractable through the development of the family of Doubly Asymptotic Approximations (DAA). Practical implementation of the method has relied on the so-called augmentation of the DAA equations. The fluid and structural systems are respectively coupled by the structural acceleration vector in the surface normal direction on the right hand side of the DAA equa...
Robust Stability Analysis of the Space Launch System Control Design: A Singular Value Approach
Pei, Jing; Newsome, Jerry R.
2015-01-01
Classical stability analysis consists of breaking the feedback loops one at a time and determining separately how much gain or phase variations would destabilize the stable nominal feedback system. For typical launch vehicle control design, classical control techniques are generally employed. In addition to stability margins, frequency domain Monte Carlo methods are used to evaluate the robustness of the design. However, such techniques were developed for Single-Input-Single-Output (SISO) systems and do not take into consideration the off-diagonal terms in the transfer function matrix of Multi-Input-Multi-Output (MIMO) systems. Robust stability analysis techniques such as H(sub infinity) and mu are applicable to MIMO systems but have not been adopted as standard practices within the launch vehicle controls community. This paper took advantage of a simple singular-value-based MIMO stability margin evaluation method based on work done by Mukhopadhyay and Newsom and applied it to the SLS high-fidelity dynamics model. The method computes a simultaneous multi-loop gain and phase margin that could be related back to classical margins. The results presented in this paper suggest that for the SLS system, traditional SISO stability margins are similar to the MIMO margins. This additional level of verification provides confidence in the robustness of the control design.
Computation at a coordinate singularity
Prusa, Joseph M.
2018-05-01
Coordinate singularities are sometimes encountered in computational problems. An important example involves global atmospheric models used for climate and weather prediction. Classical spherical coordinates can be used to parameterize the manifold - that is, generate a grid for the computational spherical shell domain. This particular parameterization offers significant benefits such as orthogonality and exact representation of curvature and connection (Christoffel) coefficients. But it also exhibits two polar singularities and at or near these points typical continuity/integral constraints on dependent fields and their derivatives are generally inadequate and lead to poor model performance and erroneous results. Other parameterizations have been developed that eliminate polar singularities, but problems of weaker singularities and enhanced grid noise compared to spherical coordinates (away from the poles) persist. In this study reparameterization invariance of geometric objects (scalars, vectors and the forms generated by their covariant derivatives) is utilized to generate asymptotic forms for dependent fields of interest valid in the neighborhood of a pole. The central concept is that such objects cannot be altered by the metric structure of a parameterization. The new boundary conditions enforce symmetries that are required for transformations of geometric objects. They are implemented in an implicit polar filter of a structured grid, nonhydrostatic global atmospheric model that is simulating idealized Held-Suarez flows. A series of test simulations using different configurations of the asymptotic boundary conditions are made, along with control simulations that use the default model numerics with no absorber, at three different grid sizes. Typically the test simulations are ∼ 20% faster in wall clock time than the control-resulting from a decrease in noise at the poles in all cases. In the control simulations adverse numerical effects from the polar
Singular Cauchy Initial Value Problem for Certain Classes of Integro-Differential Equations
Directory of Open Access Journals (Sweden)
Zdeněk Šmarda
2010-01-01
Full Text Available The existence and uniqueness of solutions and asymptotic estimate of solution formulas are studied for the following initial value problem: g(ty′(t=ay(t[1+f(t,y(t,∫0+tK(t,s,y(t,y(sds], y(0+=0, t∈(0,t0], where a>0 is a constant and t0>0. An approach which combines topological method of T. Ważewski and Schauder's fixed point theorem is used.
Jia, Zhongxiao; Yang, Yanfei
2018-05-01
In this paper, we propose new randomization based algorithms for large scale linear discrete ill-posed problems with general-form regularization: subject to , where L is a regularization matrix. Our algorithms are inspired by the modified truncated singular value decomposition (MTSVD) method, which suits only for small to medium scale problems, and randomized SVD (RSVD) algorithms that generate good low rank approximations to A. We use rank-k truncated randomized SVD (TRSVD) approximations to A by truncating the rank- RSVD approximations to A, where q is an oversampling parameter. The resulting algorithms are called modified TRSVD (MTRSVD) methods. At every step, we use the LSQR algorithm to solve the resulting inner least squares problem, which is proved to become better conditioned as k increases so that LSQR converges faster. We present sharp bounds for the approximation accuracy of the RSVDs and TRSVDs for severely, moderately and mildly ill-posed problems, and substantially improve a known basic bound for TRSVD approximations. We prove how to choose the stopping tolerance for LSQR in order to guarantee that the computed and exact best regularized solutions have the same accuracy. Numerical experiments illustrate that the best regularized solutions by MTRSVD are as accurate as the ones by the truncated generalized singular value decomposition (TGSVD) algorithm, and at least as accurate as those by some existing truncated randomized generalized singular value decomposition (TRGSVD) algorithms. This work was supported in part by the National Science Foundation of China (Nos. 11771249 and 11371219).
Bowel Control Problems (Fecal Incontinence)
... Causes Diagnosis Treatment Eating, Diet, & Nutrition Clinical Trials Hemorrhoids Definition & Facts Symptoms & Causes Diagnosis Treatment Eating, Diet, & ... Control Problems in Women (Urinary Incontinence) Constipation Diarrhea Hemorrhoids Related Diagnostic Tests Colonoscopy Flexible Sigmoidoscopy Lower GI ...
Control Problems of Hydrodynamic Type
National Research Council Canada - National Science Library
Krishnaprasad, P. S; Manikonda, Vikram
1998-01-01
It has been known for some time that the classical work of Kirchhoff, Love, and Birkhoff on rigid bodies in incompressible, irrotational flows provides effective models for treating control problems...
Ballard, Patrick
2016-12-01
The steady sliding frictional contact problem between a moving rigid indentor of arbitrary shape and an isotropic homogeneous elastic half-space in plane strain is extensively analysed. The case where the friction coefficient is a step function (with respect to the space variable), that is, where there are jumps in the friction coefficient, is considered. The problem is put under the form of a variational inequality which is proved to always have a solution which, in addition, is unique in some cases. The solutions exhibit different kinds of universal singularities that are explicitly given. In particular, it is shown that the nature of the universal stress singularity at a jump of the friction coefficient is different depending on the sign of the jump.
Directory of Open Access Journals (Sweden)
J. Humberto Pérez-Cruz
2014-01-01
Full Text Available The trajectory tracking for a class of uncertain nonlinear systems in which the number of possible states is equal to the number of inputs and each input is preceded by an unknown symmetric deadzone is considered. The unknown dynamics is identified by means of a continuous time recurrent neural network in which the control singularity is conveniently avoided by guaranteeing the invertibility of the coupling matrix. Given this neural network-based mathematical model of the uncertain system, a singularity-free feedback linearization control law is developed in order to compel the system state to follow a reference trajectory. By means of Lyapunov-like analysis, the exponential convergence of the tracking error to a bounded zone can be proven. Likewise, the boundedness of all closed-loop signals can be guaranteed.
Czech Academy of Sciences Publication Activity Database
Hakl, Robert; Zamora, M.
2013-01-01
Roč. 20, č. 3 (2013), s. 469-491 ISSN 1072-947X Institutional support: RVO:67985840 Keywords : second-order singular equation * Dirichlet problem * solvability Subject RIV: BA - General Mathematics Impact factor: 0.340, year: 2013 http://www.degruyter.com/view/j/gmj.2013.20.issue-3/gmj-2013-0030/gmj-2013-0030. xml ?format=INT
Directory of Open Access Journals (Sweden)
Farid Chighoub
2014-01-01
the stochastic calculus of jump diffusions and some properties of singular controls. Then, we give, under smoothness conditions, a useful verification theorem and we show that the solution of the adjoint equation coincides with the spatial gradient of the value function, evaluated along the optimal trajectory of the state equation. Finally, using these theoretical results, we solve explicitly an example, on optimal harvesting strategy, for a geometric Brownian motion with jumps.
Kinematic rate control of simulated robot hand at or near wrist singularity
Barker, K.; Houck, J. A.; Carzoo, S. W.
1985-01-01
A robot hand should obey movement commands from an operator on a computer program as closely as possible. However, when two of the three rotational axes of the robot wrist are colinear, the wrist loses a degree of freedom, and the usual resolved rate equations (used to move the hand in response to an operator's inputs) are indeterminant. Furthermore, rate limiting occurs in close vicinity to this singularity. An analysis shows that rate limiting occurs not only in the vicinity of this singularity but also substantially away from it, even when the operator commands rotational rates of the robot hand that are only a small percentage of the operational joint rate limits. Therefore, joint angle rates are scaled when they exceed operational limits in a real time simulation of a robot arm. Simulation results show that a small dead band avoids the wrist singularity in the resolved rate equations but can introduce a high frequency oscillation close to the singularity. However, when a coordinated wrist movement is used in conjunction with the resolved rate equations, the high frequency oscillation disappears.
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].
Barker, L. K.; Houck, J. A.; Carzoo, S. W.
1984-01-01
An operator commands a robot hand to move in a certain direction relative to its own axis system by specifying a velocity in that direction. This velocity command is then resolved into individual joint rotational velocities in the robot arm to effect the motion. However, the usual resolved-rate equations become singular when the robot arm is straightened. To overcome this elbow joint singularity, equations were developed which allow continued translational control of the robot hand even though the robot arm is (or is nearly) fully extended. A feature of the equations near full arm extension is that an operator simply extends and retracts the robot arm to reverse the direction of the elbow bend (difficult maneuver for the usual resolved-rate equations). Results show successful movement of a graphically simulated robot arm.
International Nuclear Information System (INIS)
Amirkhanov, I.V.; Zhidkov, E.P.; Konnova, S.V.
2000-01-01
For the case of spherical-symmetrical potential we have considered the convergence of the solution of singular-perturbated Schroedinger equation of the 4th order to the solution of the corresponding standard nonrelativistic Schroedinger equation by numerical and analytical methods. The questions of existence of the solutions are explored. Numerical results are given. (author)
Analysis of singularity in redundant manipulators
International Nuclear Information System (INIS)
Watanabe, Koichi
2000-03-01
In the analysis of arm positions and configurations of redundant manipulators, the singularity avoidance problems are important themes. This report presents singularity avoidance computations of a 7 DOF manipulator by using a computer code based on human-arm models. The behavior of the arm escaping from the singular point can be identified satisfactorily through the use of 3-D plotting tools. (author)
Directory of Open Access Journals (Sweden)
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.
Meng, Xin-You; Wu, Yu-Qian
In this paper, a delayed differential algebraic phytoplankton-zooplankton-fish model with taxation and nonlinear fish harvesting is proposed. In the absence of time delay, the existence of singularity induced bifurcation is discussed by regarding economic interest as bifurcation parameter. A state feedback controller is designed to eliminate singularity induced bifurcation. Based on Liu’s criterion, Hopf bifurcation occurs at the interior equilibrium when taxation is taken as bifurcation parameter and is more than its corresponding critical value. In the presence of time delay, by analyzing the associated characteristic transcendental equation, the interior equilibrium loses local stability when time delay crosses its critical value. What’s more, the direction of Hopf bifurcation and stability of the bifurcating periodic solutions are investigated based on normal form theory and center manifold theorem, and nonlinear state feedback controller is designed to eliminate Hopf bifurcation. Furthermore, Pontryagin’s maximum principle has been used to obtain optimal tax policy to maximize the benefit as well as the conservation of the ecosystem. Finally, some numerical simulations are given to demonstrate our theoretical analysis.
Energy Technology Data Exchange (ETDEWEB)
Nagata, Keitaro [KEK Theory Center, High Energy Accelerator Research Organization,1-1 Oho, Tsukuba 305-0801 (Japan); Nishimura, Jun [KEK Theory Center, High Energy Accelerator Research Organization,1-1 Oho, Tsukuba 305-0801 (Japan); Department of Particle and Nuclear Physics, School of High Energy Accelerator Science,Graduate University for Advanced Studies (SOKENDAI), 1-1 Oho, Tsukuba 305-0801 (Japan); Shimasaki, Shinji [KEK Theory Center, High Energy Accelerator Research Organization,1-1 Oho, Tsukuba 305-0801 (Japan); Research and Education Center for Natural Sciences, Keio University,Hiyoshi 4-1-1, Yokohama, Kanagawa 223-8521 (Japan)
2016-07-14
Recently, the complex Langevin method has been applied successfully to finite density QCD either in the deconfinement phase or in the heavy dense limit with the aid of a new technique called the gauge cooling. In the confinement phase with light quarks, however, convergence to wrong limits occurs due to the singularity in the drift term caused by small eigenvalues of the Dirac operator including the mass term. We propose that this singular-drift problem should also be overcome by the gauge cooling with different criteria for choosing the complexified gauge transformation. The idea is tested in chiral Random Matrix Theory for finite density QCD, where exact results are reproduced at zero temperature with light quarks. It is shown that the gauge cooling indeed changes drastically the eigenvalue distribution of the Dirac operator measured during the Langevin process. Despite its non-holomorphic nature, this eigenvalue distribution has a universal diverging behavior at the origin in the chiral limit due to a generalized Banks-Casher relation as we confirm explicitly.
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
Singular perturbation of simple eigenvalues
International Nuclear Information System (INIS)
Greenlee, W.M.
1976-01-01
Two operator theoretic theorems which generalize those of asymptotic regular perturbation theory and which apply to singular perturbation problems are proved. Application of these theorems to concrete problems is involved, but the perturbation expansions for eigenvalues and eigenvectors are developed in terms of solutions of linear operator equations. The method of correctors, as well as traditional boundary layer techniques, can be used to apply these theorems. The current formulation should be applicable to highly singular ''hard core'' potential perturbations of the radial equation of quantum mechanics. The theorems are applied to a comparatively simple model problem whose analysis is basic to that of the quantum mechanical problem
Loop quantum cosmology and singularities.
Struyve, Ward
2017-08-15
Loop quantum gravity is believed to eliminate singularities such as the big bang and big crunch singularity. This belief is based on studies of so-called loop quantum cosmology which concerns symmetry-reduced models of quantum gravity. In this paper, the problem of singularities is analysed in the context of the Bohmian formulation of loop quantum cosmology. In this formulation there is an actual metric in addition to the wave function, which evolves stochastically (rather than deterministically as the case of the particle evolution in non-relativistic Bohmian mechanics). Thus a singularity occurs whenever this actual metric is singular. It is shown that in the loop quantum cosmology for a homogeneous and isotropic Friedmann-Lemaître-Robertson-Walker space-time with arbitrary constant spatial curvature and cosmological constant, coupled to a massless homogeneous scalar field, a big bang or big crunch singularity is never obtained. This should be contrasted with the fact that in the Bohmian formulation of the Wheeler-DeWitt theory singularities may exist.
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.
Naked singularities are not singular in distorted gravity
Garattini, Remo; Majumder, Barun
2014-07-01
We compute the Zero Point Energy (ZPE) induced by a naked singularity with the help of a reformulation of the Wheele-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.
Naked singularities are not singular in distorted gravity
International Nuclear Information System (INIS)
Garattini, Remo; Majumder, Barun
2014-01-01
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
Deformations of surface singularities
Szilárd, ágnes
2013-01-01
The present publication contains a special collection of research and review articles on deformations of surface singularities, that put together serve as an introductory survey of results and methods of the theory, as well as open problems, important examples and connections to other areas of mathematics. The aim is to collect material that will help mathematicians already working or wishing to work in this area to deepen their insight and eliminate the technical barriers in this learning process. This also is supported by review articles providing some global picture and an abundance of examples. Additionally, we introduce some material which emphasizes the newly found relationship with the theory of Stein fillings and symplectic geometry. This links two main theories of mathematics: low dimensional topology and algebraic geometry. The theory of normal surface singularities is a distinguished part of analytic or algebraic geometry with several important results, its own technical machinery, and several op...
Multifractal signal reconstruction based on singularity power spectrum
International Nuclear Information System (INIS)
Xiong, Gang; Yu, Wenxian; Xia, Wenxiang; Zhang, Shuning
2016-01-01
Highlights: • We propose a novel multifractal reconstruction method based on singularity power spectrum analysis (MFR-SPS). • The proposed MFR-SPS method has better power characteristic than the algorithm in Fraclab. • Further, the SPS-ISE algorithm performs better than the SPS-MFS algorithm. • Based on the proposed MFR-SPS method, we can restructure singularity white fractal noise (SWFN) and linear singularity modulation (LSM) multifractal signal, in equivalent sense, similar with the linear frequency modulation(LFM) signal and WGN in the Fourier domain. - Abstract: Fractal reconstruction (FR) and multifractal reconstruction (MFR) can be considered as the inverse problem of singularity spectrum analysis, and it is challenging to reconstruct fractal signal in accord with multifractal spectrum (MFS). Due to the multiple solutions of fractal reconstruction, the traditional methods of FR/MFR, such as FBM based method, wavelet based method, random wavelet series, fail to reconstruct fractal signal deterministically, and besides, those methods neglect the power spectral distribution in the singular domain. In this paper, we propose a novel MFR method based singularity power spectrum (SPS). Supposing the consistent uniform covering of multifractal measurement, we control the traditional power law of each scale of wavelet coefficients based on the instantaneous singularity exponents (ISE) or MFS, simultaneously control the singularity power law based on the SPS, and deduce the principle and algorithm of MFR based on SPS. Reconstruction simulation and error analysis of estimated ISE, MFS and SPS show the effectiveness and the improvement of the proposed methods compared to those obtained by the Fraclab package.
Viswanathan, Sasi Prabhakaran
Design, dynamics, control and implementation of a novel spacecraft attitude control actuator called the "Adaptive Singularity-free Control Moment Gyroscope" (ASCMG) is presented in this dissertation. In order to construct a comprehensive attitude dynamics model of a spacecraft with internal actuators, the dynamics of a spacecraft with an ASCMG, is obtained in the framework of geometric mechanics using the principles of variational mechanics. The resulting dynamics is general and complete model, as it relaxes the simplifying assumptions made in prior literature on Control Moment Gyroscopes (CMGs) and it also addresses the adaptive parameters in the dynamics formulation. The simplifying assumptions include perfect axisymmetry of the rotor and gimbal structures, perfect alignment of the centers of mass of the gimbal and the rotor etc. These set of simplifying assumptions imposed on the design and dynamics of CMGs leads to adverse effects on their performance and results in high manufacturing cost. The dynamics so obtained shows the complex nonlinear coupling between the internal degrees of freedom associated with an ASCMG and the spacecraft bus's attitude motion. By default, the general ASCMG cluster can function as a Variable Speed Control Moment Gyroscope, and reduced to function in CMG mode by spinning the rotor at constant speed, and it is shown that even when operated in CMG mode, the cluster can be free from kinematic singularities. This dynamics model is then extended to include the effects of multiple ASCMGs placed in the spacecraft bus, and sufficient conditions for non-singular ASCMG cluster configurations are obtained to operate the cluster both in VSCMG and CMG modes. The general dynamics model of the ASCMG is then reduced to that of conventional VSCMGs and CMGs by imposing the standard set of simplifying assumptions used in prior literature. The adverse effects of the simplifying assumptions that lead to the complexities in conventional CMG design, and
Slow Integral Manifolds and Control Problems in Critical and Twice Critical Cases
International Nuclear Information System (INIS)
Sobolev, Vladimir
2016-01-01
We consider singularly perturbed differential systems in cases where the standard theory to establish a slow integral manifold existence does not work. The theory has traditionally dealt only with perturbation problems near normally hyperbolic manifold of singularities and this manifold is supposed to isolated. Applying transformations we reduce the original singularly perturbed problem to a regularized one such that the existence of slow integral manifolds can be established by means of the standard theory. We illustrate our approach by several examples. (paper)
Bladder Control Problems in Women
... the parts of the brain that control thought, memory, and language injury multiple sclerosis—a disease that ... into the urine. Patches on the dipstick change color when blood or protein is present in urine. ...
Discrete Control Processes, Dynamic Games and Multicriterion Control Problems
Directory of Open Access Journals (Sweden)
Dumitru Lozovanu
2002-07-01
Full Text Available The discrete control processes with state evaluation in time of dynamical system is considered. A general model of control problems with integral-time cost criterion by a trajectory is studied and a general scheme for solving such classes of problems is proposed. In addition the game-theoretical and multicriterion models for control problems are formulated and studied.
Perturbation analysis of linear control problems
International Nuclear Information System (INIS)
Petkov, Petko; Konstantinov, Mihail
2017-01-01
The paper presents a brief overview of the technique of splitting operators, proposed by the authors and intended for perturbation analysis of control problems involving unitary and orthogonal matrices. Combined with the technique of Lyapunov majorants and the implementation of the Banach and Schauder fixed point principles, it allows to obtain rigorous non-local perturbation bounds for a set of sensitivity analysis problems. Among them are the reduction of linear systems into orthogonal canonical forms, the feedback synthesis problem and pole assignment problem in particular, as well as other important problems in control theory and linear algebra. Key words: perturbation analysis, canonical forms, feedback synthesis
Stochastic Linear Quadratic Optimal Control Problems
International Nuclear Information System (INIS)
Chen, S.; Yong, J.
2001-01-01
This paper is concerned with the stochastic linear quadratic optimal control problem (LQ problem, for short) for which the coefficients are allowed to be random and the cost functional is allowed to have a negative weight on the square of the control variable. Some intrinsic relations among the LQ problem, the stochastic maximum principle, and the (linear) forward-backward stochastic differential equations are established. Some results involving Riccati equation are discussed as well
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...
Generic phase transitions and profit singularities in Arnol'd's model
International Nuclear Information System (INIS)
Davydov, Aleksei A; Matos, Helena Mena
2007-01-01
For a smooth one-parameter family of pairs of control systems and profit densities on a circle, the generic transitions between optimal rotations and stationary strategies are studied in the problem of maximization of the time-averaged profit on the infinite horizon. It is shown that there are only two types of such transitions, the corresponding singularities of the average profit as a function of the family parameter are found, and it is proved that these singularities are stable under small perturbations of a generic family. The classification of singularities of the maximum average profit is completed for generic families. Bibliography: 16 titles.
Singularities in four-body final-state amplitudes
International Nuclear Information System (INIS)
Adhikari, S.K.
1978-01-01
Like three-body amplitudes, four-body amplitudes have subenergy threshold singularities over and above total-energy singularities. In the four-body problem we encounter a new type of subenergy singularity besides the usual two- and three-body subenergy threshold singularities. This singularity will be referred to as ''independent-pair threshold singularity'' and involves pair-subenergy threshold singularities in each of the two independent pair subenergies in four-body final states. We also study the particularly interesting case of resonant two- and three-body interactions in the four-body isobar model and the rapid (singular) dependence of the isobar amplitudes they generate in the four-body phase space. All these singularities are analyzed in the multiple-scattering formalism and it is shown that they arise from the ''next-to-last'' rescattering and hence may be represented correctly by an approximate amplitude which has that rescattering
Singular and degenerate cauchy problems
Carroll, R.W
1976-01-01
In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation;methods for low-rank mat
Naked singularity, firewall, and Hawking radiation.
Zhang, Hongsheng
2017-06-21
Spacetime singularity has always been of interest since the proof of the Penrose-Hawking singularity theorem. Naked singularity naturally emerges from reasonable initial conditions in the collapsing process. A recent interesting approach in black hole information problem implies that we need a firewall to break the surplus entanglements among the Hawking photons. Classically, the firewall becomes a naked singularity. We find some vacuum analytical solutions in R n -gravity of the firewall-type and use these solutions as concrete models to study the naked singularities. By using standard quantum theory, we investigate the Hawking radiation emitted from the black holes with naked singularities. Here we show that the singularity itself does not destroy information. A unitary quantum theory works well around a firewall-type singularity. We discuss the validity of our result in general relativity. Further our result demonstrates that the temperature of the Hawking radiation still can be expressed in the form of the surface gravity divided by 2π. This indicates that a naked singularity may not compromise the Hakwing evaporation process.
Quadcopter Aggressive Maneuvers along Singular Configurations: An Energy-Quaternion Based Approach
Directory of Open Access Journals (Sweden)
Ayman A. El-Badawy
2016-01-01
Full Text Available Automatic aggressive maneuvers with quadcopters are regarded as a highly challenging control problem. The aim is to tackle the singularities that exist in a vertical looping maneuver. Modeling singularities are resolved by writing the equations-of-motion of the quadcopter in quaternion form. Physical singularities due to underactuation are resolved by using an energy-based control. Energy-based control is utilized to overcome the uncontrollability of the quadcopter at physical singular configurations, for instance, when commanding the quadcopter to gain altitude while pitched at 90∘. Three looping strategies (circular, clothoidal, and newly developed constant thrust are implemented on a nonlinear model of the quadcopter. The three looping strategies are discussed along with their advantages and limitations.
Solved problems in dynamical systems and control
Tenreiro-Machado, J; Valério, Duarte; Galhano, Alexandra M
2016-01-01
This book presents a collection of exercises on dynamical systems, modelling and control. Each topic covered includes a summary of the theoretical background, problems with solutions, and further exercises.
A numerical method for solving singular De`s
Energy Technology Data Exchange (ETDEWEB)
Mahaver, W.T.
1996-12-31
A numerical method is developed for solving singular differential equations using steepest descent based on weighted Sobolev gradients. The method is demonstrated on a variety of first and second order problems, including linear constrained, unconstrained, and partially constrained first order problems, a nonlinear first order problem with irregular singularity, and two second order variational problems.
Minimal Time Problem with Impulsive Controls
Energy Technology Data Exchange (ETDEWEB)
Kunisch, Karl, E-mail: karl.kunisch@uni-graz.at [University of Graz, Institute for Mathematics and Scientific Computing (Austria); Rao, Zhiping, E-mail: zhiping.rao@ricam.oeaw.ac.at [Austrian Academy of Sciences, Radon Institute of Computational and Applied Mathematics (Austria)
2017-02-15
Time optimal control problems for systems with impulsive controls are investigated. Sufficient conditions for the existence of time optimal controls are given. A dynamical programming principle is derived and Lipschitz continuity of an appropriately defined value functional is established. The value functional satisfies a Hamilton–Jacobi–Bellman equation in the viscosity sense. A numerical example for a rider-swing system is presented and it is shown that the reachable set is enlargered by allowing for impulsive controls, when compared to nonimpulsive controls.
Hybrid Predictive Control for Dynamic Transport Problems
Núñez, Alfredo A; Cortés, Cristián E
2013-01-01
Hybrid Predictive Control for Dynamic Transport Problems develops methods for the design of predictive control strategies for nonlinear-dynamic hybrid discrete-/continuous-variable systems. The methodology is designed for real-time applications, particularly the study of dynamic transport systems. Operational and service policies are considered, as well as cost reduction. The control structure is based on a sound definition of the key variables and their evolution. A flexible objective function able to capture the predictive behaviour of the system variables is described. Coupled with efficient algorithms, mainly drawn from the area of computational intelligence, this is shown to optimize performance indices for real-time applications. The framework of the proposed predictive control methodology is generic and, being able to solve nonlinear mixed-integer optimization problems dynamically, is readily extendable to other industrial processes. The main topics of this book are: ●hybrid predictive control (HPC) ...
Remarks on Risk-Sensitive Control Problems
International Nuclear Information System (INIS)
Menaldi, Jose-Luis; Robin, Maurice
2005-01-01
The main purpose of this paper is to investigate the asymptotic behavior of the discounted risk-sensitive control problem for periodic diffusion processes when the discount factor α goes to zero. If u α (θ,x) denotes the optimal cost function, θ being the risk factor, then it is shown that lim { α to 0}α u α (θ,x)=ξ(θ) where ξ(θ) is the average on ]0,θ[ of the optimal cost of the (usual) infinite horizon risk-sensitive control problem
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.
Prevalence of Multiply Controlled Problem Behavior
Beavers, Gracie A.; Iwata, Brian A.
2011-01-01
We examined articles in the "Journal of Applied Behavior Analysis" in which results of functional analyses indicated that problem behavior was maintained by multiple sources of reinforcement. Data for 88 (16.9%) of 521 subjects reported in 168 studies met the criteria for multiple control. Data for 11 subjects (2.1%) involved a single response…
Existence of weak solutions to a nonlinear reaction-diffusion system with singular sources
Directory of Open Access Journals (Sweden)
Ida de Bonis
2017-09-01
Full Text Available We discuss the existence of a class of weak solutions to a nonlinear parabolic system of reaction-diffusion type endowed with singular production terms by reaction. The singularity is due to a potential occurrence of quenching localized to the domain boundary. The kind of quenching we have in mind is due to a twofold contribution: (i the choice of boundary conditions, modeling in our case the contact with an infinite reservoir filled with ready-to-react chemicals and (ii the use of a particular nonlinear, non-Lipschitz structure of the reaction kinetics. Our working techniques use fine energy estimates for approximating non-singular problems and uniform control on the set where singularities are localizing.
Discrete variable representation for singular Hamiltonians
DEFF Research Database (Denmark)
Schneider, B. I.; Nygaard, Nicolai
2004-01-01
We discuss the application of the discrete variable representation (DVR) to Schrodinger problems which involve singular Hamiltonians. Unlike recent authors who invoke transformations to rid the eigenvalue equation of singularities at the cost of added complexity, we show that an approach based...... solely on an orthogonal polynomial basis is adequate, provided the Gauss-Lobatto or Gauss-Radau quadrature rule is used. This ensures that the mesh contains the singular points and by simply discarding the DVR functions corresponding to those points, all matrix elements become well behaved. the boundary...
Problems in event based engine control
DEFF Research Database (Denmark)
Hendricks, Elbert; Jensen, Michael; Chevalier, Alain Marie Roger
1994-01-01
Physically a four cycle spark ignition engine operates on the basis of four engine processes or events: intake, compression, ignition (or expansion) and exhaust. These events each occupy approximately 180° of crank angle. In conventional engine controllers, it is an accepted practice to sample...... the engine variables synchronously with these events (or submultiples of them). Such engine controllers are often called event-based systems. Unfortunately the main system noise (or disturbance) is also synchronous with the engine events: the engine pumping fluctuations. Since many electronic engine...... problems on accurate air/fuel ratio control of a spark ignition (SI) engine....
Quantum evolution across singularities
International Nuclear Information System (INIS)
Craps, Ben; Evnin, Oleg
2008-01-01
Attempts to consider evolution across space-time singularities often lead to quantum systems with time-dependent Hamiltonians developing an isolated singularity as a function of time. Examples include matrix theory in certain singular time-dependent backgounds and free quantum fields on the two-dimensional compactified Milne universe. Due to the presence of the singularities in the time dependence, the conventional quantum-mechanical evolution is not well-defined for such systems. We propose a natural way, mathematically analogous to renormalization in conventional quantum field theory, to construct unitary quantum evolution across the singularity. We carry out this procedure explicitly for free fields on the compactified Milne universe and compare our results with the matching conditions considered in earlier work (which were based on the covering Minkowski space)
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...
Singularities in Free Surface Flows
Thete, Sumeet Suresh
Free surface flows where the shape of the interface separating two or more phases or liquids are unknown apriori, are commonplace in industrial applications and nature. Distribution of drop sizes, coalescence rate of drops, and the behavior of thin liquid films are crucial to understanding and enhancing industrial practices such as ink-jet printing, spraying, separations of chemicals, and coating flows. When a contiguous mass of liquid such as a drop, filament or a film undergoes breakup to give rise to multiple masses, the topological transition is accompanied with a finite-time singularity . Such singularity also arises when two or more masses of liquid merge into each other or coalesce. Thus the dynamics close to singularity determines the fate of about-to-form drops or films and applications they are involved in, and therefore needs to be analyzed precisely. The primary goal of this thesis is to resolve and analyze the dynamics close to singularity when free surface flows experience a topological transition, using a combination of theory, experiments, and numerical simulations. The first problem under consideration focuses on the dynamics following flow shut-off in bottle filling applications that are relevant to pharmaceutical and consumer products industry, using numerical techniques based on Galerkin Finite Element Methods (GFEM). The second problem addresses the dual flow behavior of aqueous foams that are observed in oil and gas fields and estimates the relevant parameters that describe such flows through a series of experiments. The third problem aims at understanding the drop formation of Newtonian and Carreau fluids, computationally using GFEM. The drops are formed as a result of imposed flow rates or expanding bubbles similar to those of piezo actuated and thermal ink-jet nozzles. The focus of fourth problem is on the evolution of thinning threads of Newtonian fluids and suspensions towards singularity, using computations based on GFEM and experimental
Problems of substance abuse: exploitation and control.
Ray, L
1985-01-01
The notion of substance abuse is highly problematic. There is considerable disagreement amongst 'experts' as to the relative hazards and addictive properties of both legally and illegally available substances. There are also widely divergent sub-cultural attitudes to the harmfulness or benefit of drug use. One can assume no social consensus as to the nature of the contemporary 'drug problem', nor about the most appropriate means of dealing with it. There is, however, considerable evidence that criminalization of drug use, and harsh penalties against users and suppliers, are ineffective and counter-productive. Other models of control need to be considered, and in particular the merits and de-merits of the medicalization of drug abuse require examination. However, this is only one aspect of the problem. On the other side are the national and international corporations and syndicates, both legitimate and criminal, that earn vast profits from trade in toxic substances. Tobacco is legally available in every country in the world, and the industry is rarely subject to strict control. Thus the issue of substance abuse and control should be seen in a global context, in which account is taken of both legitimate and underworld operations. In attempts to control international trade in toxic substances, the limited success and the problems of already existing legal controls should be acknowledged. Local awareness and regulation of trade in substances is essential, but not sufficient. Amongst other avenues to be explored is the possibility of diverting presently illicitly grown narcotics into indigenous pharmaceutical industries in the Third World. Some problems with this strategy are noted.(ABSTRACT TRUNCATED AT 250 WORDS)
Control problems in very large accelerators
International Nuclear Information System (INIS)
Crowley-Milling, M.C.
1985-06-01
There is no fundamental difference of kind in the control requirements between a small and a large accelerator since they are built of the same types of components, which individually have similar control inputs and outputs. The main difference is one of scale; the large machine has many more components of each type, and the distances involved are much greater. Both of these factors must be taken into account in determining the optimum way of carrying out the control functions. Small machines should use standard equipment and software for control as much as possible, as special developments for small quantities cannot normally be justified if all costs are taken into account. On the other hand, the very great number of devices needed for a large machine means that, if special developments can result in simplification, they may make possible an appreciable reduction in the control equipment costs. It is the purpose of this report to look at the special control problems of large accelerators, which the author shall arbitarily define as those with a length of circumference in excess of 10 km, and point out where special developments, or the adoption of developments from outside the accelerator control field, can be of assistance in minimizing the cost of the control system. Most of the first part of this report was presented as a paper to the 1985 Particle Accelerator Conference. It has now been extended to include a discussion on the special case of the controls for the SSC
Existence of localizing solutions in plasticity via the geometric singular perturbation theory
Lee, Min-Gi; Tzavaras, Athanasios
2017-01-01
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
Properties of kinematic singularities
Energy Technology Data Exchange (ETDEWEB)
Coley, A A [Department of Mathematics and Statistics, Dalhousie University, Halifax, Nova Scotia B3H 3J5 (Canada); Hervik, S [Department of Mathematics and Natural Sciences, University of Stavanger, N-4036 Stavanger (Norway); Lim, W C [Albert-Einstein-Institut, Am Muehlenberg 1, D-14476 Potsdam (Germany); MacCallum, M A H, E-mail: aac@mathstat.dal.c, E-mail: sigbjorn.hervik@uis.n, E-mail: wclim@aei.mpg.d, E-mail: m.a.h.maccallum@qmul.ac.u [School of Mathematical Sciences, Queen Mary University of London, E1 4NS (United Kingdom)
2009-11-07
The locally rotationally symmetric tilted perfect fluid Bianchi type V cosmological model provides examples of future geodesically complete spacetimes that admit a 'kinematic singularity' at which the fluid congruence is inextendible but all frame components of the Weyl and Ricci tensors remain bounded. We show that for any positive integer n there are examples of Bianchi type V spacetimes admitting a kinematic singularity such that the covariant derivatives of the Weyl and Ricci tensors up to the nth order also stay bounded. We briefly discuss singularities in classical spacetimes.
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}.
International Nuclear Information System (INIS)
Berry, M.V.
2002-01-01
For illumination with white light, the spectra near a typical isolated phase singularity (nodal point of the component wavelengths) can be described by a universal function of position, up to linear distortion and a weak dependence on the spectrum of the source. The appearance of the singularity when viewed by a human observer is predicted by transforming the spectrum to trichromatic variables and chromaticity coordinates, and then rendering the colours, scaled to constant luminosity, on a computer monitor. The pattern far from the singularity is a white that depends on the source temperature, and the centre of the pattern is flanked by intensely coloured 'eyes', one orange and one blue, separated by red, and one of the eyes is surrounded by a bright white circle. Only a small range of possible colours appears near the singularity; in particular, there is no green. (author)
Ling, Eric
The big bang theory is a model of the universe which makes the striking prediction that the universe began a finite amount of time in the past at the so called "Big Bang singularity." We explore the physical and mathematical justification of this surprising result. After laying down the framework of the universe as a spacetime manifold, we combine physical observations with global symmetrical assumptions to deduce the FRW cosmological models which predict a big bang singularity. Next we prove a couple theorems due to Stephen Hawking which show that the big bang singularity exists even if one removes the global symmetrical assumptions. Lastly, we investigate the conditions one needs to impose on a spacetime if one wishes to avoid a singularity. The ideas and concepts used here to study spacetimes are similar to those used to study Riemannian manifolds, therefore we compare and contrast the two geometries throughout.
Directory of Open Access Journals (Sweden)
Gabriel Martínez-Niconoff
2012-01-01
Full Text Available With the purpose to compare the physical features of the electromagnetic field, we describe the synthesis of optical singularities propagating in the free space and on a metal surface. In both cases the electromagnetic field has a slit-shaped curve as a boundary condition, and the singularities correspond to a shock wave that is a consequence of the curvature of the slit curve. As prototypes, we generate singularities that correspond to fold and cusped regions. We show that singularities in free space may generate bifurcation effects while plasmon fields do not generate these kinds of effects. Experimental results for free-space propagation are presented and for surface plasmon fields, computer simulations are shown.
International Nuclear Information System (INIS)
Goswami, Rituparno; Joshi, Pankaj S.; Vaz, Cenalo; Witten, Louis
2004-01-01
We construct a class of spherically symmetric collapse models in which a naked singularity may develop as the end state of collapse. The matter distribution considered has negative radial and tangential pressures, but the weak energy condition is obeyed throughout. The singularity forms at the center of the collapsing cloud and continues to be visible for a finite time. The duration of visibility depends on the nature of energy distribution. Hence the causal structure of the resulting singularity depends on the nature of the mass function chosen for the cloud. We present a general model in which the naked singularity formed is timelike, neither pointlike nor null. Our work represents a step toward clarifying the necessary conditions for the validity of the Cosmic Censorship Conjecture
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.
Directory of Open Access Journals (Sweden)
Fuyi Xu
2010-04-01
\\end{array}\\right.$$ where $1\\leq k\\leq s\\leq m-2, a_i, b_i\\in(0,+\\infty$ with $0<\\sum_{i=1}^{k}b_{i}-\\sum_{i=k+1}^{s}b_{i}<1, 0<\\sum_{i=1}^{m-2}a_{i}<1, 0<\\xi_1<\\xi_2<\\cdots<\\xi_{m-2}<\\rho(T$, $f\\in C( [0,+\\infty,[0,+\\infty$, $a(t$ may be singular at $t=0$. We show that there exist two positive solutions by using two different fixed point theorems respectively. As an application, some examples are included to illustrate the main results. In particular, our criteria extend and improve some known results.
Amirjanyan, A. A.; Sahakyan, A. V.
2017-08-01
A singular integral equation with a Cauchy kernel and a logarithmic singularity on its righthand side is considered on a finite interval. An algorithm is proposed for the numerical solution of this equation. The contact elasticity problem of a П-shaped rigid punch indented into a half-plane is solved in the case of a uniform hydrostatic pressure occurring under the punch, which leads to a logarithmic singularity at an endpoint of the integration interval. The numerical solution of this problem shows the efficiency of the proposed approach and suggests that the singularity has to be taken into account in solving the equation.
A hybrid iterative scheme for optimal control problems governed by ...
African Journals Online (AJOL)
MRT
KEY WORDS: Optimal control problem; Fredholm integral equation; ... control problems governed by Fredholm integral and integro-differential equations is given in (Brunner and Yan, ..... The exact optimal trajectory and control functions are. 2.
Directory of Open Access Journals (Sweden)
Khaled Loukhaoukha
2013-01-01
Full Text Available We present a new optimal watermarking scheme based on discrete wavelet transform (DWT and singular value decomposition (SVD using multiobjective ant colony optimization (MOACO. A binary watermark is decomposed using a singular value decomposition. Then, the singular values are embedded in a detailed subband of host image. The trade-off between watermark transparency and robustness is controlled by multiple scaling factors (MSFs instead of a single scaling factor (SSF. Determining the optimal values of the multiple scaling factors (MSFs is a difficult problem. However, a multiobjective ant colony optimization is used to determine these values. Experimental results show much improved performances of the proposed scheme in terms of transparency and robustness compared to other watermarking schemes. Furthermore, it does not suffer from the problem of high probability of false positive detection of the watermarks.
Spatio-temporal problems of locomotion control
International Nuclear Information System (INIS)
Smolyaninov, Vladimir V
2000-01-01
The problem of the spatio-temporal construction of legged movements involves structural freedoms due to the multi-link structure of the extremities, kinematic freedoms of the stepping cycle, and interextremity coordination freedoms, whose purposive organization is established by means of appropriate synergies, i.e. additional functional links the brain's control system forms. The main focus of attention in this work is on the kinematic and coordination synergies of the legged movements of humans and animals. The comparative historical analysis of experimental data and modelling metaphors concentrates on obtaining a unified description, whereas the ultimate mathematical metaphor reduces to space-time geometry, with base step synergies as its invariants. Thus, the concept of a synergetic organization for biomechanical movement freedoms is transformed to the geochronometry concept, actually a modification of Minkowskian geometry. To determine the spectrum of possible geochronometries, the consequences of a generalized 'postulate of a constant speed of light' are studied and different models of wave chronometers compared. (reviews of topical problems)
Singularities in FLRW spacetimes
het Lam, Huibert; Prokopec, Tomislav
2017-12-01
We point out that past-incompleteness of geodesics in FLRW spacetimes does not necessarily imply that these spacetimes start from a singularity. Namely, if a test particle that follows such a trajectory has a non-vanishing velocity, its energy was super-Planckian at some time in the past if it kept following that geodesic. That indicates a breakdown of the particle's description, which is why we should not consider those trajectories for the definition of an initial singularity. When one only considers test particles that do not have this breakdown of their trajectory, it turns out that the only singular FLRW spacetimes are the ones that have a scale parameter that vanishes at some initial time.
Propagation of singularities for linearised hybrid data impedance tomography
DEFF Research Database (Denmark)
Bal, Guillaume; Hoffmann, Kristoffer; Knudsen, Kim
2017-01-01
For a general formulation of linearised hybrid inverse problems in impedance tomography, the qualitative properties of the solutions are analysed. Using an appropriate scalar pseudo-differential formulation, the problems are shown to permit propagating singularities under certain non-elliptic con......For a general formulation of linearised hybrid inverse problems in impedance tomography, the qualitative properties of the solutions are analysed. Using an appropriate scalar pseudo-differential formulation, the problems are shown to permit propagating singularities under certain non...
Analysis and design of singular Markovian jump systems
Wang, Guoliang; Yan, Xinggang
2014-01-01
This monograph is an up-to-date presentation of the analysis and design of singular Markovian jump systems (SMJSs) in which the transition rate matrix of the underlying systems is generally uncertain, partially unknown and designed. The problems addressed include stability, stabilization, H∞ control and filtering, observer design, and adaptive control. applications of Markov process are investigated by using Lyapunov theory, linear matrix inequalities (LMIs), S-procedure and the stochastic Barbalat's Lemma, among other techniques.Features of the book include:·???????? study of the stability pr
Eigenstructure of of singular systems. Perturbation analysis of simple eigenvalues
García Planas, María Isabel; Tarragona Romero, Sonia
2014-01-01
The problem to study small perturbations of simple eigenvalues with a change of parameters is of general interest in applied mathematics. After to introduce a systematic way to know if an eigenvalue of a singular system is simple or not, the aim of this work is to study the behavior of a simple eigenvalue of singular linear system family
Infinite derivative gravity : non-singular cosmology & blackhole solutions
Mazumdar, Anupam
2017-01-01
Both Einstein's theory of General Relativity and Newton's theory of gravity possess a short dis- tance and small time scale catastrophe. The blackhole singularity and cosmological Big Bang singularity problems highlight that current theories of gravity are incomplete description at early times and
Pseudospherical surfaces with singularities
DEFF Research Database (Denmark)
Brander, David
2017-01-01
We study a generalization of constant Gauss curvature −1 surfaces in Euclidean 3-space, based on Lorentzian harmonic maps, that we call pseudospherical frontals. We analyse the singularities of these surfaces, dividing them into those of characteristic and non-characteristic type. We give methods...
Supersymmetry in singular spaces
Bergshoeff, Eric
2002-01-01
We discuss supersymmetry in spaces with a boundary, i.e. singular spaces. In particular, we discuss the situation in ten and five dimensions. In both these cases we review the construction of supersymmetric domain wall actions situated at the boundary. These domain walls act as sources inducing a
Singularities in FLRW Spacetimes
Lam, Huibert het; Prokopec, Tom
2017-01-01
We point out that past-incompleteness of geodesics in FLRW spacetimes does not necessarily imply that these spacetimes start from a singularity. Namely, if a test particle that follows such a trajectory has a non-vanishing velocity, its energy was super-Planckian at some time in the past if it kept
Charged singularities: repulsive effects
Energy Technology Data Exchange (ETDEWEB)
De Felice, F; Nobili, L [Padua Univ. (Italy). Ist. di Fisica; Calvani, M [Padua Univ. (Italy). Ist. di Astronomia
1980-07-01
The repulsive phenomena which a particle experiences in the vicinity of a naked singularity are investigated in the Kerr-Newman space-time. The aim is to extend the knowledge of this fact to charged solutions and to have a direct indication of how, in these situations, the gravitational and electrostatic interactions are competing.
Papapetrou's naked singularity is a strong curvature singularity
International Nuclear Information System (INIS)
Hollier, G.P.
1986-01-01
Following Papapetrou [1985, a random walk in General Relativity ed. J. Krishna-Rao (New Delhi: Wiley Eastern)], a spacetime with a naked singularity is analysed. This singularity is shown to be a strong curvature singularity and thus a counterexample to a censorship conjecture. (author)
Nuclear power proliferation. Problems of international control
Energy Technology Data Exchange (ETDEWEB)
Johnson, B [International Inst. for Environment and Development, London (UK)
1977-09-01
The nuclear industry is experiencing a multiple crisis in which economic, technical and ethical aspects are blended inextricably. Nuclear hardware costs have everywhere soared far beyond inflation in the last five years, largely as a result of delays in programme completion arising from problems of reactor and fuel cycle. Meanwhile, partly as a result of this cost escalation, there is widespread and growing doubt as to whether capital will be available to finance the electricity generating levels projected by the industry and by governments for the 1990s. The nuclear industry is now in trouble at every stage of the fuel cycle. The industry's difficulties have also revealed a lack of overall - but particularly nuclear - energy strategy at either national or international levels, and a lack of will to create regulations and institutional machinery at either of these levels which might reassure both concerned publics and the energy industries themselves. This paper appraises some of the present limitations of international institutions in achieving control and management of nuclear power.
Nuclear power proliferation: problems of international control
Energy Technology Data Exchange (ETDEWEB)
Johnson, B
1977-09-01
Some of the present limitations of international institutions in achieving control and management of nuclear power are reviewed and appraised. The nuclear industry is experiencing a multiple crisis in which economic, technical, and ethical aspects are blended. Nuclear hardware costs have increased faster than inflation in the last five years, largely as a result of delays in program completion arising from reactor and fuel-cycle safety problems. Meanwhile, there is a widespread and growing doubt, partly as a result of this cost escalation, as to whether capital will be available to finance the electricity-generating levels projected by the industry and by governments for the 1990s. The nuclear industry is now in trouble at every stage of the fuel cycle. The industry's difficulties have also revealed a lack of overall--but particularly nuclear--energy strategy at either national or international levels, and a lack of will to create regulations and institutional machinery at either of these levels that could reassure the concerned public and the energy industries.
Singular potentials in quantum mechanics
International Nuclear Information System (INIS)
Aguilera-Navarro, V.C.; Koo, E. Ley
1995-10-01
This paper is a review of some mathematical methods as recently developed and applied to deal with singular potentials in Quantum Mechanics. Regular and singular perturbative methods as well as variational treatments are considered. (author). 25 refs
'Footballs', conical singularities, and the Liouville equation
International Nuclear Information System (INIS)
Redi, Michele
2005-01-01
We generalize the football shaped extra dimensions scenario to an arbitrary number of branes. The problem is related to the solution of the Liouville equation with singularities, and explicit solutions are presented for the case of three branes. The tensions of the branes do not need to be tuned with each other but only satisfy mild global constraints
Singular interactions supported by embedded curves
International Nuclear Information System (INIS)
Kaynak, Burak Tevfik; Turgut, O Teoman
2012-01-01
In this work, singular interactions supported by embedded curves on Riemannian manifolds are discussed from a more direct and physical perspective, via the heat kernel approach. We show that the renormalized problem is well defined, the ground state is finite and the corresponding wavefunction is positive. The renormalization group invariance of the model is also discussed. (paper)
Singularities: the Brieskorn anniversary volume
National Research Council Canada - National Science Library
Brieskorn, Egbert; Arnolʹd, V. I; Greuel, G.-M; Steenbrink, J. H. M
1998-01-01
...... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Main theorem ... 3 Ideals of ideal-unimodal plane curve singularities. . . . . . . . . . . . . . . . References ... Gert-Martin Greuel and Gerhard Pfister...
String theory and cosmological singularities
Indian Academy of Sciences (India)
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.
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.
Are naked singularities really visible
Energy Technology Data Exchange (ETDEWEB)
Calvani, M [Padua Univ. (Italy). Ist. di Astronomia; De Felice, F [Alberta Univ., Edmonton (Canada); Nobili, L [Padua Univ. (Italy). Ist. di Fisica
1978-12-09
The question whether a Kerr naked singularity is actually visible from infinity is investigated; it is shown that in fact any signal which could be emitted from the singularity is infinitely red-shifted. This implies that naked singularities would be indistinguishable from a black hole.
Holographic complexity and spacetime singularities
International Nuclear Information System (INIS)
Barbón, José L.F.; Rabinovici, Eliezer
2016-01-01
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.
The Propulsive-Only Flight Control Problem
Blezad, Daniel J.
1996-01-01
Attitude control of aircraft using only the throttles is investigated. The long time constants of both the engines and of the aircraft dynamics, together with the coupling between longitudinal and lateral aircraft modes make piloted flight with failed control surfaces hazardous, especially when attempting to land. This research documents the results of in-flight operation using simulated failed flight controls and ground simulations of piloted propulsive-only control to touchdown. Augmentation control laws to assist the pilot are described using both optimal control and classical feedback methods. Piloted simulation using augmentation shows that simple and effective augmented control can be achieved in a wide variety of failed configurations.
Belinski, Vladimir
2018-01-01
Written for researchers focusing on general relativity, supergravity, and cosmology, this is a self-contained exposition of the structure of the cosmological singularity in generic solutions of the Einstein equations, and an up-to-date mathematical derivation of the theory underlying the Belinski–Khalatnikov–Lifshitz (BKL) conjecture on this field. Part I provides a comprehensive review of the theory underlying the BKL conjecture. The generic asymptotic behavior near the cosmological singularity of the gravitational field, and fields describing other kinds of matter, is explained in detail. Part II focuses on the billiard reformulation of the BKL behavior. Taking a general approach, this section does not assume any simplifying symmetry conditions and applies to theories involving a range of matter fields and space-time dimensions, including supergravities. Overall, this book will equip theoretical and mathematical physicists with the theoretical fundamentals of the Big Bang, Big Crunch, Black Hole singula...
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....
International Nuclear Information System (INIS)
Habis, M.; Robichon, F.; Demonet, J.F.
1996-01-01
Of late ten years, neurologists are studying the brain of the dyslectics. The cerebral imagery (NMR imaging, positron computed tomography) has allowed to confirm the anatomical particularities discovered by some of them: asymmetry default of cerebral hemispheres, size abnormally large of the white substance mass which connect the two hemispheres. The functional imagery, when visualizing this singular brain at work, allows to understand why it labors to reading. (O.M.)
Applications of functional analysis to optimal control problems
International Nuclear Information System (INIS)
Mizukami, K.
1976-01-01
Some basic concepts in functional analysis, a general norm, the Hoelder inequality, functionals and the Hahn-Banach theorem are described; a mathematical formulation of two optimal control problems is introduced by the method of functional analysis. The problem of time-optimal control systems with both norm constraints on control inputs and on state variables at discrete intermediate times is formulated as an L-problem in the theory of moments. The simplex method is used for solving a non-linear minimizing problem inherent in the functional analysis solution to this problem. Numerical results are presented for a train operation. The second problem is that of optimal control of discrete linear systems with quadratic cost functionals. The problem is concerned with the case of unconstrained control and fixed endpoints. This problem is formulated in terms of norms of functionals on suitable Banach spaces. (author)
Light-like big bang singularities in string and matrix theories
International Nuclear Information System (INIS)
Craps, Ben; Evnin, Oleg
2011-01-01
Important open questions in cosmology require a better understanding of the big bang singularity. In string and matrix theories, light-like analogues of cosmological singularities (singular plane wave backgrounds) turn out to be particularly tractable. We give a status report on the current understanding of such light-like big bang models, presenting both solved and open problems.
SIAM symposium on control problems in industry
Energy Technology Data Exchange (ETDEWEB)
NONE
1994-12-31
This symposium focused on industrial control applications that have benefited from recent mathematical and technological developments. The themes featured included: applications of control techniques in aerospace industry, automotive industry, environmental sciences, manufacturing processes, and petroleum industry; optimal shape design in aerospace applications; optimal design of micro-optics; robust control and H-infinity methods.
Take control of font problems in Leopard
Zardetto, Sharon
2009-01-01
Are you suffering from mysterious font problems using Microsoft Office, the Adobe Creative Suite, or other programs in Mac OS X Leopard? Help is at hand, with troubleshooting steps and real-world advice that help you solve problems fast. If you've experienced seemingly inexplicable trouble with characters displaying incorrectly, being unable to type a particular character, fonts missing from Font menus, Font Book crashing, or Character Palette misbehaving, turn to font expert Sharon Zardetto for help. Read this ebook to find the answers to questions such as: Where do fonts belong on my hard
Singularity theory and equivariant symplectic maps
Bridges, Thomas J
1993-01-01
The monograph is a study of the local bifurcations of multiparameter symplectic maps of arbitrary dimension in the neighborhood of a fixed point.The problem is reduced to a study of critical points of an equivariant gradient bifurcation problem, using the correspondence between orbits ofa symplectic map and critical points of an action functional. New results onsingularity theory for equivariant gradient bifurcation problems are obtained and then used to classify singularities of bifurcating period-q points. Of particular interest is that a general framework for analyzing group-theoretic aspects and singularities of symplectic maps (particularly period-q points) is presented. Topics include: bifurcations when the symplectic map has spatial symmetry and a theory for the collision of multipliers near rational points with and without spatial symmetry. The monograph also includes 11 self-contained appendices each with a basic result on symplectic maps. The monograph will appeal to researchers and graduate student...
Inverse and Control Problems in Electromagnetics
1994-10-14
subject of multicriteria optimization has been most thoroughly developed in the literature of mathematical economics and is most often associated there...8217, Lecture Notes in Economics and Marhemcrical Systems. Vol. 152. Springer. Berlin. 1978. 6. Kirsch. A. and Wilde. P., "Tie optimization of directivity and...indentation D, The geometry of the problem is shown in Fig. 1. The domain the upper half wace , and a such that (E. H) and (E’, HI) of interest is that
Metric dimensional reduction at singularities with implications to Quantum Gravity
International Nuclear Information System (INIS)
Stoica, Ovidiu Cristinel
2014-01-01
A series of old and recent theoretical observations suggests that the quantization of gravity would be feasible, and some problems of Quantum Field Theory would go away if, somehow, the spacetime would undergo a dimensional reduction at high energy scales. But an identification of the deep mechanism causing this dimensional reduction would still be desirable. The main contribution of this article is to show that dimensional reduction effects are due to General Relativity at singularities, and do not need to be postulated ad-hoc. Recent advances in understanding the geometry of singularities do not require modification of General Relativity, being just non-singular extensions of its mathematics to the limit cases. They turn out to work fine for some known types of cosmological singularities (black holes and FLRW Big-Bang), allowing a choice of the fundamental geometric invariants and physical quantities which remain regular. The resulting equations are equivalent to the standard ones outside the singularities. One consequence of this mathematical approach to the singularities in General Relativity is a special, (geo)metric type of dimensional reduction: at singularities, the metric tensor becomes degenerate in certain spacetime directions, and some properties of the fields become independent of those directions. Effectively, it is like one or more dimensions of spacetime just vanish at singularities. This suggests that it is worth exploring the possibility that the geometry of singularities leads naturally to the spontaneous dimensional reduction needed by Quantum Gravity. - Highlights: • The singularities we introduce are described by finite geometric/physical objects. • Our singularities are accompanied by dimensional reduction effects. • They affect the metric, the measure, the topology, the gravitational DOF (Weyl = 0). • Effects proposed in other approaches to Quantum Gravity are obtained naturally. • The geometric dimensional reduction obtained
CSIR Research Space (South Africa)
Roux, FS
2013-09-01
Full Text Available Roux Presented at the International Conference on Correlation Optics 2013 Chernivtsi, Ukraine 18-20 September 2013 CSIR National Laser Centre, Pretoria, South Africa – p. 1/24 Contents ⊲ Defining Stochastic Singular Optics (SSO) ⊲ Tools of Stochastic... of vortices: topological charge ±1 (higher order are unstable). Positive and negative vortex densities np(x, y, z) and nn(x, y, z) ⊲ Vortex density: V = np + nn ⊲ Topological charge density: T = np − nn – p. 4/24 Subfields of SSO ⊲ Homogeneous, normally...
Cosmological models without singularities
International Nuclear Information System (INIS)
Petry, W.
1981-01-01
A previously studied theory of gravitation in flat space-time is applied to homogeneous and isotropic cosmological models. There exist two different classes of models without singularities: (i) ever-expanding models, (ii) oscillating models. The first class contains models with hot big bang. For these models there exist at the beginning of the universe-in contrast to Einstein's theory-very high but finite densities of matter and radiation with a big bang of very short duration. After short time these models pass into the homogeneous and isotropic models of Einstein's theory with spatial curvature equal to zero and cosmological constant ALPHA >= O. (author)
PACS quality control and automatic problem notifier
Honeyman-Buck, Janice C.; Jones, Douglas; Frost, Meryll M.; Staab, Edward V.
1997-05-01
One side effect of installing a clinical PACS Is that users become dependent upon the technology and in some cases it can be very difficult to revert back to a film based system if components fail. The nature of system failures range from slow deterioration of function as seen in the loss of monitor luminance through sudden catastrophic loss of the entire PACS networks. This paper describes the quality control procedures in place at the University of Florida and the automatic notification system that alerts PACS personnel when a failure has happened or is anticipated. The goal is to recover from a failure with a minimum of downtime and no data loss. Routine quality control is practiced on all aspects of PACS, from acquisition, through network routing, through display, and including archiving. Whenever possible, the system components perform self and between platform checks for active processes, file system status, errors in log files, and system uptime. When an error is detected or a exception occurs, an automatic page is sent to a pager with a diagnostic code. Documentation on each code, trouble shooting procedures, and repairs are kept on an intranet server accessible only to people involved in maintaining the PACS. In addition to the automatic paging system for error conditions, acquisition is assured by an automatic fax report sent on a daily basis to all technologists acquiring PACS images to be used as a cross check that all studies are archived prior to being removed from the acquisition systems. Daily quality control is preformed to assure that studies can be moved from each acquisition and contrast adjustment. The results of selected quality control reports will be presented. The intranet documentation server will be described with the automatic pager system. Monitor quality control reports will be described and the cost of quality control will be quantified. As PACS is accepted as a clinical tool, the same standards of quality control must be established
Controllability Problem of Fractional Neutral Systems: A Survey
Directory of Open Access Journals (Sweden)
Artur Babiarz
2017-01-01
Full Text Available The following article presents recent results of controllability problem of dynamical systems in infinite-dimensional space. Generally speaking, we describe selected controllability problems of fractional order systems, including approximate controllability of fractional impulsive partial neutral integrodifferential inclusions with infinite delay in Hilbert spaces, controllability of nonlinear neutral fractional impulsive differential inclusions in Banach space, controllability for a class of fractional neutral integrodifferential equations with unbounded delay, controllability of neutral fractional functional equations with impulses and infinite delay, and controllability for a class of fractional order neutral evolution control systems.
Plane waves with weak singularities
International Nuclear Information System (INIS)
David, Justin R.
2003-03-01
We study a class of time dependent solutions of the vacuum Einstein equations which are plane waves with weak null singularities. This singularity is weak in the sense that though the tidal forces diverge at the singularity, the rate of divergence is such that the distortion suffered by a freely falling observer remains finite. Among such weak singular plane waves there is a sub-class which does not exhibit large back reaction in the presence of test scalar probes. String propagation in these backgrounds is smooth and there is a natural way to continue the metric beyond the singularity. This continued metric admits string propagation without the string becoming infinitely excited. We construct a one parameter family of smooth metrics which are at a finite distance in the space of metrics from the extended metric and a well defined operator in the string sigma model which resolves the singularity. (author)
3rd Singularity Theory Meeting of Northeast region & the Brazil-Mexico 2nd Meeting on Singularities
Neto, Aurélio; Mond, David; Saia, Marcelo; Snoussi, Jawad; BMMS 2/NBMS 3; ENSINO; Singularities and foliations geometry, topology and applications
2018-01-01
This proceedings book brings selected works from two conferences, the 2nd Brazil-Mexico Meeting on Singularity and the 3rd Northeastern Brazilian Meeting on Singularities, that were hold in Salvador, in July 2015. All contributions were carefully peer-reviewed and revised, and cover topics like Equisingularity, Topology and Geometry of Singularities, Topological Classification of Singularities of Mappings, and more. They were written by mathematicians from several countries, including Brazil, Spain, Mexico, Japan and the USA, on relevant topics on Theory of Singularity, such as studies on deformations, Milnor fibration, foliations, Catastrophe theory, and myriad applications. Open problems are also introduced, making this volume a must-read both for graduate students and active researchers in this field.
Optimal control problem for the extended Fisher–Kolmogorov equation
Indian Academy of Sciences (India)
In this paper, the optimal control problem for the extended Fisher–Kolmogorov equation is studied. The optimal control under boundary condition is given, the existence of optimal solution to the equation is proved and the optimality system is established.
Dissipative differential systems and the state space H∞ control problem
Trentelman, H.L.; Willems, J.C.
2000-01-01
The purpose of this paper is to apply our very recent results on the synthesis of dissipative linear differential systems to the 'classical' state space H∞ control problem. We first review our general problem set-up, where the problem of rendering a given plant dissipative by general
A General Theory of Markovian Time Inconsistent Stochastic Control Problems
DEFF Research Database (Denmark)
Björk, Tomas; Murgochi, Agatha
We develop a theory for stochastic control problems which, in various ways, are time inconsistent in the sense that they do not admit a Bellman optimality principle. We attach these problems by viewing them within a game theoretic framework, and we look for Nash subgame perfect equilibrium points...... examples of time inconsistency in the literature are easily seen to be special cases of the present theory. We also prove that for every time inconsistent problem, there exists an associated time consistent problem such that the optimal control and the optimal value function for the consistent problem...
Feed Forward Neural Network and Optimal Control Problem with Control and State Constraints
Kmet', Tibor; Kmet'ová, Mária
2009-09-01
A feed forward neural network based optimal control synthesis is presented for solving optimal control problems with control and state constraints. The paper extends adaptive critic neural network architecture proposed by [5] to the optimal control problems with control and state constraints. The optimal control problem is transcribed into a nonlinear programming problem which is implemented with adaptive critic neural network. The proposed simulation method is illustrated by the optimal control problem of nitrogen transformation cycle model. Results show that adaptive critic based systematic approach holds promise for obtaining the optimal control with control and state constraints.
Keulen, van T.A.C.; Gillot, J.; Jager, de A.G.; Steinbuch, M.
2014-01-01
This paper presents a numerical solution for scalar state constrained optimal control problems. The algorithm rewrites the constrained optimal control problem as a sequence of unconstrained optimal control problems which can be solved recursively as a two point boundary value problem. The solution
On a Highly Nonlinear Self-Obstacle Optimal Control Problem
Energy Technology Data Exchange (ETDEWEB)
Di Donato, Daniela, E-mail: daniela.didonato@unitn.it [University of Trento, Department of Mathematics (Italy); Mugnai, Dimitri, E-mail: dimitri.mugnai@unipg.it [Università di Perugia, Dipartimento di Matematica e Informatica (Italy)
2015-10-15
We consider a non-quadratic optimal control problem associated to a nonlinear elliptic variational inequality, where the obstacle is the control itself. We show that, fixed a desired profile, there exists an optimal solution which is not far from it. Detailed characterizations of the optimal solution are given, also in terms of approximating problems.
Residues and duality for singularity categories of isolated Gorenstein singularities
Murfet, Daniel
2009-01-01
We study Serre duality in the singularity category of an isolated Gorenstein singularity and find an explicit formula for the duality pairing in terms of generalised fractions and residues. For hypersurfaces we recover the residue formula of the string theorists Kapustin and Li. These results are obtained from an explicit construction of complete injective resolutions of maximal Cohen-Macaulay modules.
Material control: Problems in assessing effectiveness
International Nuclear Information System (INIS)
Sanborn, J.
1989-01-01
This paper discusses the evaluation of material accounting and control systems at facilities processing large quantities of strategic nuclear materials. The subject is timely because of the content of new orders and procedures adopted by the U.S. Department of Energy (DOE), in particular the performance requirements in DOE order 5633.3. This order requires the contractor to demonstrate specified levels of detection probability by the safeguards system for actions involving the attempted removal of specified target quantities of material from a facility. The paper reviews some of the difficulties involved in developing methods for determining adequacy with respect to this and similar requirements
Control and Alcohol-Problem Recognition among College Students
Simons, Raluca M.; Hahn, Austin M.; Simons, Jeffrey S.; Gaster, Sam
2015-01-01
Objective: This study examined negative control (ie, perceived lack of control over life outcomes) and need for control as predictors of alcohol-problem recognition, evaluations (good/bad), and expectancies (likely/unlikely) among college students. The study also explored the interaction between the need for control and alcohol consumption in…
Singularity, initial conditions and quantum tunneling in modern cosmology
International Nuclear Information System (INIS)
Khalatnikov, I M; Kamenshchik, A Yu
1998-01-01
The key problems of modern cosmology, such as the cosmological singularity, initial conditions, and the quantum tunneling hypothesis, are discussed. The relationship between the latest cosmological trends and L D Landau's old ideas is analyzed. Particular attention is given to the oscillatory approach to singularity; quantum tunneling processes determining wave function of the Universe in the presence of a compex scalar field; and the role of quantum corrections in these processes. The classical dynamics of closed models with a real scalar field is investigated from the standpoint of chaotic, fractal, and singularity-avoiding properties. (special issue)
Self-reported impulsivity and inhibitory control in problem gamblers.
Lorains, Felicity K; Stout, Julie C; Bradshaw, John L; Dowling, Nicki A; Enticott, Peter G
2014-01-01
Impulsivity is considered a core feature of problem gambling; however, self-reported impulsivity and inhibitory control may reflect disparate constructs. We examined self-reported impulsivity and inhibitory control in 39 treatment-seeking problem gamblers and 41 matched controls using a range of self-report questionnaires and laboratory inhibitory control tasks. We also investigated differences between treatment-seeking problem gamblers who prefer strategic (e.g., sports betting) and nonstrategic (e.g., electronic gaming machines) gambling activities. Treatment-seeking problem gamblers demonstrated elevated self-reported impulsivity, more go errors on the Stop Signal Task, and a lower gap score on the Random Number Generation task than matched controls. However, overall we did not find strong evidence that treatment-seeking problem gamblers are more impulsive on laboratory inhibitory control measures. Furthermore, strategic and nonstrategic problem gamblers did not differ from their respective controls on either self-reported impulsivity questionnaires or laboratory inhibitory control measures. Contrary to expectations, our results suggest that inhibitory dyscontrol may not be a key component for some treatment-seeking problem gamblers.
International Nuclear Information System (INIS)
Littlejohn, R.G.
1982-01-01
The Hamiltonian structures discovered by Morrison and Greene for various fluid equations were obtained by guessing a Hamiltonian and a suitable Poisson bracket formula, expressed in terms of noncanonical (but physical) coordinates. In general, such a procedure for obtaining a Hamiltonian system does not produce a Hamiltonian phase space in the usual sense (a symplectic manifold), but rather a family of symplectic manifolds. To state the matter in terms of a system with a finite number of degrees of freedom, the family of symplectic manifolds is parametrized by a set of Casimir functions, which are characterized by having vanishing Poisson brackets with all other functions. The number of independent Casimir functions is the corank of the Poisson tensor J/sup ij/, the components of which are the Poisson brackets of the coordinates among themselves. Thus, these Casimir functions exist only when the Poisson tensor is singular
Turnpike theory of continuous-time linear optimal control problems
Zaslavski, Alexander J
2015-01-01
Individual turnpike results are of great interest due to their numerous applications in engineering and in economic theory; in this book the study is focused on new results of turnpike phenomenon in linear optimal control problems. The book is intended for engineers as well as for mathematicians interested in the calculus of variations, optimal control, and in applied functional analysis. Two large classes of problems are studied in more depth. The first class studied in Chapter 2 consists of linear control problems with periodic nonsmooth convex integrands. Chapters 3-5 consist of linear control problems with autonomous nonconvex and nonsmooth integrands. Chapter 6 discusses a turnpike property for dynamic zero-sum games with linear constraints. Chapter 7 examines genericity results. In Chapter 8, the description of structure of variational problems with extended-valued integrands is obtained. Chapter 9 ends the exposition with a study of turnpike phenomenon for dynamic games with extended value integran...
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...
Transcendental smallness in singularly perturbed equations of volterra type
International Nuclear Information System (INIS)
Bijura, Angelina M.
2003-11-01
The application of different limit processes to a physical problem is an important tool in layer type techniques. Hence the study of initial layer correction functions is of central importance for understanding layer-type problems. It is shown that for singularly perturbed problems of Volterra type, the concept of transcendental smallness is an asymptotic one. Transcendentally small terms may be numerically important. (author)
On some control problems of dynamic of reactor
Baskakov, A. V.; Volkov, N. P.
2017-12-01
The paper analyzes controllability of the transient processes in some problems of nuclear reactor dynamics. In this case, the mathematical model of nuclear reactor dynamics is described by a system of integro-differential equations consisting of the non-stationary anisotropic multi-velocity kinetic equation of neutron transport and the balance equation of delayed neutrons. The paper defines the formulation of the linear problem on control of transient processes in nuclear reactors with application of spatially distributed actions on internal neutron sources, and the formulation of the nonlinear problems on control of transient processes with application of spatially distributed actions on the neutron absorption coefficient and the neutron scattering indicatrix. The required control actions depend on the spatial and velocity coordinates. The theorems on existence and uniqueness of these control actions are proved in the paper. To do this, the control problems mentioned above are reduced to equivalent systems of integral equations. Existence and uniqueness of the solution for this system of integral equations is proved by the method of successive approximations, which makes it possible to construct an iterative scheme for numerical analyses of transient processes in a given nuclear reactor with application of the developed mathematical model. Sufficient conditions for controllability of transient processes are also obtained. In conclusion, a connection is made between the control problems and the observation problems, which, by to the given information, allow us to reconstruct either the function of internal neutron sources, or the neutron absorption coefficient, or the neutron scattering indicatrix....
Optimal Control Problems for Nonlinear Variational Evolution Inequalities
Directory of Open Access Journals (Sweden)
Eun-Young Ju
2013-01-01
Full Text Available We deal with optimal control problems governed by semilinear parabolic type equations and in particular described by variational inequalities. We will also characterize the optimal controls by giving necessary conditions for optimality by proving the Gâteaux differentiability of solution mapping on control variables.
Higher-Order Generalized Invexity in Control Problems
Directory of Open Access Journals (Sweden)
S. K. Padhan
2011-01-01
Full Text Available We introduce a higher-order duality (Mangasarian type and Mond-Weir type for the control problem. Under the higher-order generalized invexity assumptions on the functions that compose the primal problems, higher-order duality results (weak duality, strong duality, and converse duality are derived for these pair of problems. Also, we establish few examples in support of our investigation.
Higher-order techniques for some problems of nonlinear control
Directory of Open Access Journals (Sweden)
Sarychev Andrey V.
2002-01-01
Full Text Available A natural first step when dealing with a nonlinear problem is an application of some version of linearization principle. This includes the well known linearization principles for controllability, observability and stability and also first-order optimality conditions such as Lagrange multipliers rule or Pontryagin's maximum principle. In many interesting and important problems of nonlinear control the linearization principle fails to provide a solution. In the present paper we provide some examples of how higher-order methods of differential geometric control theory can be used for the study nonlinear control systems in such cases. The presentation includes: nonlinear systems with impulsive and distribution-like inputs; second-order optimality conditions for bang–bang extremals of optimal control problems; methods of high-order averaging for studying stability and stabilization of time-variant control systems.
Schoenfeld's problem solving theory in a student controlled learning environment
Harskamp, E.; Suhre, C.
2007-01-01
This paper evaluates the effectiveness of a student controlled computer program for high school mathematics based on instruction principles derived from Schoenfeld's theory of problem solving. The computer program allows students to choose problems and to make use of hints during different episodes
Analysis of convergence for control problems governed by evolution ...
African Journals Online (AJOL)
The convergence of a scheme to minimize a class of a system of continuous optimal control problems characterized by a system of evolution equations and a system of linear inequality and equality constraints with multiplier imbedding is considered. The result is applied to some problems and the scheme is found to exhibit ...
Bladder Control Problems: Medications for Treating Urinary Incontinence
... control problems, including how they work to treat urinary incontinence and possible side effects. By Mayo Clinic Staff ... a look at medications commonly prescribed to treat urinary incontinence and their possible side effects. Keep in mind ...
Singularities in the general theory of relativity
International Nuclear Information System (INIS)
Treder, H.J.
1980-01-01
'Regular solutions of Einstein's equations' mean very different things. In the case of the empty-space equations, Rsub(ik) = o, such solutions must be metrics gsub(ik)(xsup(l)) without additionaly singular 'field sources' (Einstein's 'Particle problem'). However the 'phenomenological matter' is defined by the Einstein equations Rsub(ik) - 1/2gsub(ik)R = -kappaTsub(ik) itselves. Therefore if 10 regular functions gsub(ik)(xsup(l)) are given (which the inequalities of Lorentz-signature fulfil) then these gsub(ik) define 10 functions Tsub(ik)(xsup(l)) without singularities. But, the matter-tensor Tsub(ik) must fulfil the two inequalities T >= o, T 0 0 >= 1/2 T only and therefore the Einstein-equations with 'phenomenological matter' mean the two inequalities R >= o, R 0 0 <= o which are incompatible with a permanently regular metric with Lorentz-signature, generally. (author)
Singularity resolution in quantum gravity
International Nuclear Information System (INIS)
Husain, Viqar; Winkler, Oliver
2004-01-01
We examine the singularity resolution issue in quantum gravity by studying a new quantization of standard Friedmann-Robertson-Walker geometrodynamics. The quantization procedure is inspired by the loop quantum gravity program, and is based on an alternative to the Schroedinger representation normally used in metric variable quantum cosmology. We show that in this representation for quantum geometrodynamics there exists a densely defined inverse scale factor operator, and that the Hamiltonian constraint acts as a difference operator on the basis states. We find that the cosmological singularity is avoided in the quantum dynamics. We discuss these results with a view to identifying the criteria that constitute 'singularity resolution' in quantum gravity
Van Hove singularities revisited
International Nuclear Information System (INIS)
Dzyaloshinskii, I.
1987-07-01
Beginning with the work of Hirsch and Scalapino the importance of ln 2 -Van Hove singularity in T c -enhancement in La 2 CuO 4 -based compounds was realized, which is nicely reviewed by Rice. However, the theoretical treatment carried out before is incomplete. Two things were apparently not paid due attention to: interplay of particle-particle and particle-hole channels and Umklapp processes. In what follows a two-dimensional weak coupling model of LaCuO 4 will be solved exactly in the ln 2 -approximation. The result in the Hubbard limit (one bare charge) is that the system is unstable at any sign of interaction. Symmetry breaking moreover is pretty peculiar. Of course, there are separate singlet superconducting pairings in the pp-channel (attraction) and SDW (repulsion) and CDW (attraction) in the ph-channel. It is natural that Umklapps produce an SDW + CDW mixture at either sign of the interaction. What is unusual is that both the pp-ph interplay and the Umklapps give rise to a monster-coherent SS + SDW + CDW mixture, again at either sign of the bare charge. In the general model where all 4 charges involved are substantially different, the system might remain metallic. A more realistic approach which takes into account dopping in La-M-Cu-O and interlayer interaction provides at least a qualitative understanding of the experimental picture. 10 refs, 5 figs
An optimal control approach to manpower planning problem
Directory of Open Access Journals (Sweden)
H. W. J. Lee
2001-01-01
Full Text Available A manpower planning problem is studied in this paper. The model includes scheduling different types of workers over different tasks, employing and terminating different types of workers, and assigning different types of workers to various trainning programmes. The aim is to find an optimal way to do all these while keeping the time-varying demand for minimum number of workers working on each different tasks satisfied. The problem is posed as an optimal discrete-valued control problem in discrete time. A novel numerical scheme is proposed to solve the problem, and an illustrative example is provided.
CHILES, Singularity Strength of Linear Elastic Bodies by Finite Elements Method
International Nuclear Information System (INIS)
Benzley, S.E.; Beisinger, Z.E.
1981-01-01
1 - Description of problem or function: CHILES is a finite element computer program that calculates the strength of singularities in linear elastic bodies. Plane stress, plane strain, and axisymmetric conditions are treated. Crack tip singularity problems are solved by this version of the code, but any type of integrable singularity may be properly modeled by modifying selected subroutines in the program. 2 - Method of solution: A generalized, quadrilateral finite element that includes a singular point at a corner node is incorporated in the code. The displacement formulation is used and inter-element compatibility is maintained so that monotone convergence is preserved. 3 - Restrictions on the complexity of the problem: CHILES allows three singular points to be modeled in the body being analyzed and each singular point may have coupled Mode I and II deformations. 1000 nodal points may be used
Cirant, Marco; Gomes, Diogo A.; Pimentel, Edgard A.; Sá nchez-Morgado, Hé ctor
2016-01-01
Here, we prove the existence of smooth solutions for mean-field games with a singular mean-field coupling; that is, a coupling in the Hamilton-Jacobi equation of the form $g(m)=-m^{-\\alpha}$. We consider stationary and time-dependent settings. The function $g$ is monotone, but it is not bounded from below. With the exception of the logarithmic coupling, this is the first time that MFGs whose coupling is not bounded from below is examined in the literature. This coupling arises in models where agents have a strong preference for low-density regions. Paradoxically, this causes the agents to spread and prevents the creation of solutions with a very-low density. To prove the existence of solutions, we consider an approximate problem for which the existence of smooth solutions is known. Then, we prove new a priori bounds for the solutions that show that $\\frac 1 m$ is bounded. Finally, using a limiting argument, we obtain the existence of solutions. The proof in the stationary case relies on a blow-up argument and in the time-dependent case on new bounds for $m^{-1}$.
Cirant, Marco
2016-11-22
Here, we prove the existence of smooth solutions for mean-field games with a singular mean-field coupling; that is, a coupling in the Hamilton-Jacobi equation of the form $g(m)=-m^{-\\\\alpha}$. We consider stationary and time-dependent settings. The function $g$ is monotone, but it is not bounded from below. With the exception of the logarithmic coupling, this is the first time that MFGs whose coupling is not bounded from below is examined in the literature. This coupling arises in models where agents have a strong preference for low-density regions. Paradoxically, this causes the agents to spread and prevents the creation of solutions with a very-low density. To prove the existence of solutions, we consider an approximate problem for which the existence of smooth solutions is known. Then, we prove new a priori bounds for the solutions that show that $\\\\frac 1 m$ is bounded. Finally, using a limiting argument, we obtain the existence of solutions. The proof in the stationary case relies on a blow-up argument and in the time-dependent case on new bounds for $m^{-1}$.
Singularity: Raychaudhuri equation once again
Indian Academy of Sciences (India)
Cosmology; Raychaudhuri equation; Universe; quantum gravity; loop quan- tum gravity ... than the observation verifying the prediction of theory. This gave .... which was now expanding, would have had a singular beginning in a hot Big Bang.
Do job demands and job control affect problem-solving?
Bergman, Peter N; Ahlberg, Gunnel; Johansson, Gun; Stoetzer, Ulrich; Aborg, Carl; Hallsten, Lennart; Lundberg, Ingvar
2012-01-01
The Job Demand Control model presents combinations of working conditions that may facilitate learning, the active learning hypothesis, or have detrimental effects on health, the strain hypothesis. To test the active learning hypothesis, this study analysed the effects of job demands and job control on general problem-solving strategies. A population-based sample of 4,636 individuals (55% women, 45% men) with the same job characteristics measured at two times with a three year time lag was used. Main effects of demands, skill discretion, task authority and control, and the combined effects of demands and control were analysed in logistic regressions, on four outcomes representing general problem-solving strategies. Those reporting high on skill discretion, task authority and control, as well as those reporting high demand/high control and low demand/high control job characteristics were more likely to state using problem solving strategies. Results suggest that working conditions including high levels of control may affect how individuals cope with problems and that workplace characteristics may affect behaviour in the non-work domain.
ON THE OPTIMAL CONTROL OF A PROBLEM OF ENVIRONMENTAL POLLUTION
Directory of Open Access Journals (Sweden)
José Dávalos Chuquipoma
2016-06-01
Full Text Available This article is studied the optimal control of distributed parameter systems applied to an environmental pollution problem. The model consists of a differential equation partial parabolic modeling of a pollutant transport in a fluid. The model is considered the speed with which the pollutant spreads in the environment and degradation that suffers the contaminant by the presence of a factor biological inhibitor, which breaks the contaminant at a rate that is not dependent on space and time. Using the method of Lagrange multipliers is possible to prove the existence solving the problem of control and obtaining optimality conditions for optimal control.
Problems of Mathematical Finance by Stochastic Control Methods
Stettner, Łukasz
The purpose of this paper is to present main ideas of mathematics of finance using the stochastic control methods. There is an interplay between stochastic control and mathematics of finance. On the one hand stochastic control is a powerful tool to study financial problems. On the other hand financial applications have stimulated development in several research subareas of stochastic control in the last two decades. We start with pricing of financial derivatives and modeling of asset prices, studying the conditions for the absence of arbitrage. Then we consider pricing of defaultable contingent claims. Investments in bonds lead us to the term structure modeling problems. Special attention is devoted to historical static portfolio analysis called Markowitz theory. We also briefly sketch dynamic portfolio problems using viscosity solutions to Hamilton-Jacobi-Bellman equation, martingale-convex analysis method or stochastic maximum principle together with backward stochastic differential equation. Finally, long time portfolio analysis for both risk neutral and risk sensitive functionals is introduced.
Directory of Open Access Journals (Sweden)
Weifeng Wang
2014-01-01
Full Text Available We study an optimal control problem governed by a semilinear parabolic equation, whose control variable is contained only in the boundary condition. An existence theorem for the optimal control is obtained.
Directory of Open Access Journals (Sweden)
Xiang Chen
2015-01-01
Full Text Available Singularity is an inherent characteristic of parallel robots and is also a typical mathematical problem in engineering application. In general, to identify singularity configuration, the singular solution in mathematics should be derived. This work introduces an alternative approach to the singularity identification of lower-mobility parallel robots considering the motion/force transmissibility and constrainability. The theory of screws is used as the mathematic tool to define the transmission and constraint indices of parallel robots. The singularity is hereby classified into four types concerning both input and output members of a parallel robot, that is, input transmission singularity, output transmission singularity, input constraint singularity, and output constraint singularity. Furthermore, we take several typical parallel robots as examples to illustrate the process of singularity analysis. Particularly, the input and output constraint singularities which are firstly proposed in this work are depicted in detail. The results demonstrate that the method can not only identify all possible singular configurations, but also explain their physical meanings. Therefore, the proposed approach is proved to be comprehensible and effective in solving singularity problems in parallel mechanisms.
Constraint theory, singular lagrangians and multitemporal dynamics
International Nuclear Information System (INIS)
Lusanna, L.
1988-01-01
Singular Lagrangians and constraint theory permeate theoretical physics, as shown by the relevance of gauge theories, string models and general relativity. Their study used finite---dimensional models as a guide to develop the theory, but their main use was in classical field theory, due to the necessity of understanding their quantization. The covariant quantization of singular Lagrangians led to the BRST approach and to the theory of the effective action. On the other hand their phase---space formulation, culminated with the BFV approach for first class, second class and reducible constraints. It, in turn, gave new insights in the theory of singular Lagrangians and constraints and in their cohomological aspects. However the Hamiltonian approach to field theory is highly nontrivial, is open to criticism due to its problems with locality, geometry and manifest covariance and its canonical quantization has still to be developed, because there is no proof of the renormalizability of the Schroedinger representation of field theory. This paper discusses how, notwithstanding these developments, there is still a big amount of ambiguity at every level of the theory
Local and nonlocal space-time singularities
International Nuclear Information System (INIS)
Konstantinov, M.Yu.
1985-01-01
The necessity to subdivide the singularities into two classes: local and nonlocal, each of them to be defined independently, is proved. Both classes of the singularities are defined, and the relation between the definitions introduced and the standard definition of singularities, based on space-time, incompleteness, is established. The relation between definitions introduced and theorems on the singularity existence is also established
Singularly perturbed Burger-Huxley equation: Analytical solution ...
African Journals Online (AJOL)
The work presented considers the initial boundary value problem for nonlinear singularly perturbed time dependent Burger- Huxley equation. The equation contains two terms with nonlinearities, the cubic term and the advection term. Generally, the severe difficulties of two types encounter in solving this problem. The first ...
Infinite-horizon optimal control problems in economics
Energy Technology Data Exchange (ETDEWEB)
Aseev, Sergei M; Besov, Konstantin O; Kryazhimskii, Arkadii V
2012-04-30
This paper extends optimal control theory to a class of infinite-horizon problems that arise in studying models of optimal dynamic allocation of economic resources. In a typical problem of this sort the initial state is fixed, no constraints are imposed on the behaviour of the admissible trajectories at large times, and the objective functional is given by a discounted improper integral. We develop the method of finite-horizon approximations in a broad context and use it to derive complete versions of the Pontryagin maximum principle for such problems. We provide sufficient conditions for the normality of infinite-horizon optimal control problems and for the validity of the 'standard' limit transversality conditions with time going to infinity. As a meaningful example, we consider a new two-sector model of optimal economic growth subject to a random jump in prices. Bibliography: 53 titles.
Infinite-horizon optimal control problems in economics
International Nuclear Information System (INIS)
Aseev, Sergei M; Besov, Konstantin O; Kryazhimskii, Arkadii V
2012-01-01
This paper extends optimal control theory to a class of infinite-horizon problems that arise in studying models of optimal dynamic allocation of economic resources. In a typical problem of this sort the initial state is fixed, no constraints are imposed on the behaviour of the admissible trajectories at large times, and the objective functional is given by a discounted improper integral. We develop the method of finite-horizon approximations in a broad context and use it to derive complete versions of the Pontryagin maximum principle for such problems. We provide sufficient conditions for the normality of infinite-horizon optimal control problems and for the validity of the 'standard' limit transversality conditions with time going to infinity. As a meaningful example, we consider a new two-sector model of optimal economic growth subject to a random jump in prices. Bibliography: 53 titles.
Dissipative Control Systems and Disturbance Attenuation for Nonlinear H∞ Problems
International Nuclear Information System (INIS)
Frankowska, H.; Quincampoix, M.
1999-01-01
We characterize functions satisfying a dissipative inequality associated with a control problem. Such a characterization is provided in terms of an epicontingent solution, or a viscosity supersolution to a partial differential equation called Isaacs' equation. Links between supersolutions and epicontingent solutions to Isaacs' equation are studied. Finally, we derive (possibly discontinuous) disturbance attenuation feedback of the H ∞ problem from contingent formulation of Isaacs' equation
Behavioral Problems in Iranian Epileptic Children; A Case Control Study
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Maryam Aludari
2017-12-01
Full Text Available Background Epilepsy is among the most common neurological disorders in childhood, prevalence of which is increasing. Unpredictable and chronic nature of the disease affects physical, social and mental functions of the children and their family. This study was aimed to compare behavioral problems in epileptic children group versus healthy control group. Materials and Methods This study is a case-control one conducted from January 2013 to June 2016 in Tehran, Iran. The epileptic children in age of 7-10 years old that were diagnosed by neurologist referred to the researcher for further process. Their parents were provided with Child Behavior Checklist (CBCL to be completed. For matching by age and gender, the healthy group was sampled after the epilepsy group. Multivariate Analysis of Variance was used for statistical analysis. Results In this study 94 children with epilepsy and 83 healthy children in age of 7-10 years old were studied. The results indicated that there were significantly higher behavioral problems in the children with epilepsy than in control group in nine categories of seclusiveness, physical complaints, anxiety and depression, social problems, thought problems, attention problems, delinquent behaviors, aggressive behaviors, and other problems. Comparison of two generalized and partial epilepsy groups indicated that there was a significant difference only in attention problems (p = 0.024. Conclusion The present study indicates that the children with epilepsy have more behavioral problems as compared to control group. Therefore, educational and psychological interventions are necessary for supporting desirable psychosocial growth and development of such children.
Controlled neural network application in track-match problem
International Nuclear Information System (INIS)
Baginyan, S.A.; Ososkov, G.A.
1993-01-01
Track-match problem of high energy physics (HEP) data handling is formulated in terms of incidence matrices. The corresponding Hopfield neural network is developed to solve this type of constraint satisfaction problems (CSP). A special concept of the controlled neural network is proposed as a basis of an algorithm for the effective CSP solution. Results of comparable calculations show the very high performance of this algorithm against conventional search procedures. 8 refs.; 1 fig.; 1 tab
Infinite Horizon Discrete Time Control Problems for Bounded Processes
Directory of Open Access Journals (Sweden)
2009-03-01
Full Text Available We establish Pontryagin Maximum Principles in the strong form for infinite horizon optimal control problems for bounded processes, for systems governed by difference equations. Results due to Ioffe and Tihomirov are among the tools used to prove our theorems. We write necessary conditions with weakened hypotheses of concavity and without invertibility, and we provide new results on the adjoint variable. We show links between bounded problems and nonbounded ones. We also give sufficient conditions of optimality.
Geometric singular perturbation analysis of systems with friction
DEFF Research Database (Denmark)
Bossolini, Elena
This thesis is concerned with the application of geometric singular perturbation theory to mechanical systems with friction. The mathematical background on geometric singular perturbation theory, on the blow-up method, on non-smooth dynamical systems and on regularization is presented. Thereafter......, two mechanical problems with two diﬀerent formulations of the friction force are introduced and analysed. The ﬁrst mechanical problem is a one-dimensional spring-block model describing earthquake faulting. The dynamics of earthquakes is naturally a multiple timescale problem: the timescale...... scales. The action of friction is generally explained as the loss and restoration of linkages between the surface asperities at the molecular scale. However, the consequences of friction are noticeable at much larger scales, like hundreds of kilometers. By using geometric singular perturbation theory...
The problem of the driverless vehicle specified path stability control
Buznikov, S. E.; Endachev, D. V.; Elkin, D. S.; Strukov, V. O.
2018-02-01
Currently the effort of many leading foreign companies is focused on creation of driverless transport for transportation of cargo and passengers. Among many practical problems arising while creating driverless vehicles, the problem of the specified path stability control occupies a central place. The purpose of this paper is formalization of the problem in question in terms of the quadratic functional of the control quality, the comparative analysis of the possible solutions and justification of the choice of the optimum technical solution. As square value of the integral of the deviation from the specified path is proposed as the quadratic functional of the control quality. For generation of the set of software and hardware solution variants the Zwicky “morphological box” method is used within the hardware and software environments. The heading control algorithms use the wheel steering angle data and the deviation from the lane centerline (specified path) calculated based on the navigation data and the data from the video system. Where the video system does not detect the road marking, the control is carried out based on the wheel navigation system data and where recognizable road marking exits - based on to the video system data. The analysis of the test results allows making the conclusion that the application of the combined navigation system algorithms that provide quasi-optimum solution of the problem while meeting the strict functional limits for the technical and economic indicators of the driverless vehicle control system under development is effective.
Galerkin approximations of nonlinear optimal control problems in Hilbert spaces
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Mickael D. Chekroun
2017-07-01
Full Text Available Nonlinear optimal control problems in Hilbert spaces are considered for which we derive approximation theorems for Galerkin approximations. Approximation theorems are available in the literature. The originality of our approach relies on the identification of a set of natural assumptions that allows us to deal with a broad class of nonlinear evolution equations and cost functionals for which we derive convergence of the value functions associated with the optimal control problem of the Galerkin approximations. This convergence result holds for a broad class of nonlinear control strategies as well. In particular, we show that the framework applies to the optimal control of semilinear heat equations posed on a general compact manifold without boundary. The framework is then shown to apply to geoengineering and mitigation of greenhouse gas emissions formulated here in terms of optimal control of energy balance climate models posed on the sphere $\\mathbb{S}^2$.
Optimal Control Problems for Partial Differential Equations on Reticulated Domains
Kogut, Peter I
2011-01-01
In the development of optimal control, the complexity of the systems to which it is applied has increased significantly, becoming an issue in scientific computing. In order to carry out model-reduction on these systems, the authors of this work have developed a method based on asymptotic analysis. Moving from abstract explanations to examples and applications with a focus on structural network problems, they aim at combining techniques of homogenization and approximation. Optimal Control Problems for Partial Differential Equations on Reticulated Domains is an excellent reference tool for gradu
Propagation of singularities for linearised hybrid data impedance tomography
Bal, Guillaume; Hoffmann, Kristoffer; Knudsen, Kim
2018-02-01
For a general formulation of linearised hybrid inverse problems in impedance tomography, the qualitative properties of the solutions are analysed. Using an appropriate scalar pseudo-differential formulation, the problems are shown to permit propagating singularities under certain non-elliptic conditions, and the associated directions of propagation are precisely identified relative to the directions in which ellipticity is lost. The same result is found in the setting for the corresponding normal formulation of the scalar pseudo-differential equations. A numerical reconstruction procedure based of the least squares finite element method is derived, and a series of numerical experiments visualise exactly how the loss of ellipticity manifests itself as propagating singularities.
Problems of quality assurance and quality control in diagnostic radiology
International Nuclear Information System (INIS)
Angerstein, W.
1986-01-01
Topical problems of quality assurance and quality control in diagnostic radiology are discussed and possible solutions are shown. Complex units are differentiated with reference to physicians, technicians, organization of labour, methods of examination and indication. Quality control of radiologic imaging systems should involve three stages: (1) simple tests carried out by radiologic technicians, (2) measurements by service technicians, (3) testing of products by the manufacturer and independent governmental or health service test agencies. (author)
The heat treatment of steel. A mathematical control problem
Energy Technology Data Exchange (ETDEWEB)
Hoemberg, Dietmar; Kern, Daniela
2009-07-21
The goal of this paper is to show how the heat treatment of steel can be modelled in terms of a mathematical optimal control problem. The approach is applied to laser surface hardening and the cooling of a steel slab including mechanical effects. Finally, it is shown how the results can be utilized in industrial practice by a coupling with machine-based control. (orig.)
Integrals of Motion for Discrete-Time Optimal Control Problems
Torres, Delfim F. M.
2003-01-01
We obtain a discrete time analog of E. Noether's theorem in Optimal Control, asserting that integrals of motion associated to the discrete time Pontryagin Maximum Principle can be computed from the quasi-invariance properties of the discrete time Lagrangian and discrete time control system. As corollaries, results for first-order and higher-order discrete problems of the calculus of variations are obtained.
On global error estimation and control for initial value problems
J. Lang (Jens); J.G. Verwer (Jan)
2007-01-01
textabstractThis paper addresses global error estimation and control for initial value problems for ordinary differential equations. The focus lies on a comparison between a novel approach based onthe adjoint method combined with a small sample statistical initialization and the classical approach
On global error estimation and control for initial value problems
Lang, J.; Verwer, J.G.
2007-01-01
Abstract. This paper addresses global error estimation and control for initial value problems for ordinary differential equations. The focus lies on a comparison between a novel approach based on the adjoint method combined with a small sample statistical initialization and the classical approach
Delayed Stochastic Linear-Quadratic Control Problem and Related Applications
Directory of Open Access Journals (Sweden)
Li Chen
2012-01-01
stochastic differential equations (FBSDEs with Itô’s stochastic delay equations as forward equations and anticipated backward stochastic differential equations as backward equations. Especially, we present the optimal feedback regulator for the time delay system via a new type of Riccati equations and also apply to a population optimal control problem.
Is the cosmological singularity compulsory
International Nuclear Information System (INIS)
Bekenstein, J.D.; Meisels, A.
1980-01-01
The cosmological singularity is inherent in all conventional general relativistic cosmological models. There can be no question that it is an unphysical feature; yet there does not seem to be any convervative way of eliminating it. Here we present singularity-free isotropic cosmological models which are indistinguishable from general relativistic ones at late times. They are based on the general theory of variable rest masses that we developed recently. Outside cosmology this theory simulates general relativity well. Thus it provides a framework incorporating those features which have made geneal relativity so sucessful while providing a way out of singularity dilemma. The cosmological models can be made to incorporate Dirac's large numbers hypothesis. G(now)/G(0)approx.10 -38
A 1 + 5-dimensional gravitational-wave solution. Curvature singularity and spacetime singularity
Energy Technology Data Exchange (ETDEWEB)
Chen, Yu-Zhu [Tianjin University, Department of Physics, Tianjin (China); Li, Wen-Du [Tianjin University, Department of Physics, Tianjin (China); Nankai University, Theoretical Physics Division, Chern Institute of Mathematics, Tianjin (China); Dai, Wu-Sheng [Nankai University, Theoretical Physics Division, Chern Institute of Mathematics, Tianjin (China); Nankai University and Tianjin University, LiuHui Center for Applied Mathematics, Tianjin (China)
2017-12-15
We solve a 1 + 5-dimensional cylindrical gravitational-wave solution of the Einstein equation, in which there are two curvature singularities. Then we show that one of the curvature singularities can be removed by an extension of the spacetime. The result exemplifies that the curvature singularity is not always a spacetime singularity; in other words, the curvature singularity cannot serve as a criterion for spacetime singularities. (orig.)
The Similar Structures and Control Problems of Complex Systems
Institute of Scientific and Technical Information of China (English)
无
2002-01-01
In this paper, the naturally evolving complex systems, such as biotic and social ones, are considered. Focusing on their structures, a feature is noteworthy, i.e., the similarity in structures. The relations between the functions and behaviors of these systems and their similar structures will be studied. Owing to the management of social systems and the course of evolution of biotic systems may be regarded as control processes, the researches will be within the scope of control problems. Moreover, since it is difficult to model for biotic and social systems, it will start with the control problems of complex systems, possessing similar structures, in engineering.The obtained results show that for either linear or nonlinear systems and for a lot of control problemssimilar structures lead to a series of simplifications. In general, the original system may be decomposed into reduced amount of subsystems with lower dimensions and simpler structures. By virtue of such subsystems, the control problems of original system can be solved more simply.At last, it turns round to observe the biotic and social systems and some analyses are given.
Within Your Control? When Problem Solving May Be Most Helpful.
Sarfan, Laurel D; Gooch, Peter; Clerkin, Elise M
2017-08-01
Emotion regulation strategies have been conceptualized as adaptive or maladaptive, but recent evidence suggests emotion regulation outcomes may be context-dependent. The present study tested whether the adaptiveness of a putatively adaptive emotion regulation strategy-problem solving-varied across contexts of high and low controllability. The present study also tested rumination, suggested to be one of the most putatively maladaptive strategies, which was expected to be associated with negative outcomes regardless of context. Participants completed an in vivo speech task, in which they were randomly assigned to a controllable ( n = 65) or an uncontrollable ( n = 63) condition. Using moderation analyses, we tested whether controllability interacted with emotion regulation use to predict negative affect, avoidance, and perception of performance. Partially consistent with hypotheses, problem solving was associated with certain positive outcomes (i.e., reduced behavioral avoidance) in the controllable (vs. uncontrollable) condition. Consistent with predictions, rumination was associated with negative outcomes (i.e., desired avoidance, negative affect, negative perception of performance) in both conditions. Overall, findings partially support contextual models of emotion regulation, insofar as the data suggest that the effects of problem solving may be more adaptive in controllable contexts for certain outcomes, whereas rumination may be maladaptive regardless of context.
Singularities in geodesic surface congruence
International Nuclear Information System (INIS)
Cho, Yong Seung; Hong, Soon-Tae
2008-01-01
In the stringy cosmology, we investigate singularities in geodesic surface congruences for the timelike and null strings to yield the Raychaudhuri type equations possessing correction terms associated with the novel features owing to the strings. Assuming the stringy strong energy condition, we have a Hawking-Penrose type inequality equation. If the initial expansion is negative so that the congruence is converging, we show that the expansion must pass through the singularity within a proper time. We observe that the stringy strong energy conditions of both the timelike and null string congruences produce the same inequality equation.
Singularity Theory and its Applications
Stewart, Ian; Mond, David; Montaldi, James
1991-01-01
A workshop on Singularities, Bifuraction and Dynamics was held at Warwick in July 1989, as part of a year-long symposium on Singularity Theory and its applications. The proceedings fall into two halves: Volume I mainly on connections with algebraic geometry and volume II on connections with dynamical systems theory, bifurcation theory and applications in the sciences. The papers are original research, stimulated by the symposium and workshop: All have been refereed and none will appear elsewhere. The main topic of volume II is new methods for the study of bifurcations in nonlinear dynamical systems, and applications of these.
Ambient cosmology and spacetime singularities
International Nuclear Information System (INIS)
Antoniadis, Ignatios; Cotsakis, Spiros
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.)
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.
Singular moduli and Arakelov intersection
International Nuclear Information System (INIS)
Weng Lin.
1994-05-01
The value of the modular function j(τ) at imaginary quadratic arguments τ in the upper half plane is usually called singular moduli. In this paper, we use Arakelov intersection to give the prime factorizations of a certain combination of singular moduli, coming from the Hecke correspondence. Such a result may be considered as the degenerate one of Gross and Zagier on Heegner points and derivatives of L-series in their paper [GZ1], and is parallel to the result in [GZ2]. (author). 2 refs
Multiresolution strategies for the numerical solution of optimal control problems
Jain, Sachin
There exist many numerical techniques for solving optimal control problems but less work has been done in the field of making these algorithms run faster and more robustly. The main motivation of this work is to solve optimal control problems accurately in a fast and efficient way. Optimal control problems are often characterized by discontinuities or switchings in the control variables. One way of accurately capturing the irregularities in the solution is to use a high resolution (dense) uniform grid. This requires a large amount of computational resources both in terms of CPU time and memory. Hence, in order to accurately capture any irregularities in the solution using a few computational resources, one can refine the mesh locally in the region close to an irregularity instead of refining the mesh uniformly over the whole domain. Therefore, a novel multiresolution scheme for data compression has been designed which is shown to outperform similar data compression schemes. Specifically, we have shown that the proposed approach results in fewer grid points in the grid compared to a common multiresolution data compression scheme. The validity of the proposed mesh refinement algorithm has been verified by solving several challenging initial-boundary value problems for evolution equations in 1D. The examples have demonstrated the stability and robustness of the proposed algorithm. The algorithm adapted dynamically to any existing or emerging irregularities in the solution by automatically allocating more grid points to the region where the solution exhibited sharp features and fewer points to the region where the solution was smooth. Thereby, the computational time and memory usage has been reduced significantly, while maintaining an accuracy equivalent to the one obtained using a fine uniform mesh. Next, a direct multiresolution-based approach for solving trajectory optimization problems is developed. The original optimal control problem is transcribed into a
Scaling the robustness of the solutions for quantum controllable problems
International Nuclear Information System (INIS)
Kallush, S.; Kosloff, R.
2011-01-01
The major task in quantum control theory is to find an external field that transforms the system from one state to another or executes a predetermined unitary transformation. We investigate the difficulty of computing the control field as the size of the Hilbert space is increased. In the models studied the controls form a small closed subalgebra of operators. Complete controllability is obtained by the commutators of the controls with the stationary Hamiltonian. We investigate the scaling of the computation effort required to converge a solution for the quantum control task with respect to the size of the Hilbert space. The models studied include the double-well Bose Hubbard model with the SU(2) control subalgebra and the Morse oscillator with the Heisenberg-Weil algebra. We find that for initial and target states that are classified as generalized coherent states (GCSs) of the control subalgebra the control field is easily found independent of the size of the Hilbert space. For such problems, a control field generated for a small system can serve as a pilot for finding the field for larger systems. Attempting to employ pilot fields that generate superpositions of GCSs or cat states failed. No relation was found between control solutions of different Hilbert space sizes. In addition the task of finding such a field scales unfavorably with Hilbert space sizes. We demonstrate the use of symmetry to obtain quantum transitions between states without phase information. Implications to quantum computing are discussed.
Relaxation with high-speed plasma flows and singularity analysis in MHD equilibrium
International Nuclear Information System (INIS)
Shiraishi, Junya; Ohsaki, Shuichi; Yoshida, Zensho
2004-01-01
Relaxation model that leads to plasma confinement with rigid-rotation is presented. This model applies to Jupiter's magnetosphere. It is shown that the invariance of canonical angular momentum of electron fluid, which is realized by axisymmetry through self-organization process, yields plasma confinement. including poloidal flows in equilibrium equation makes the problem rather complicated. Singularity due to the poloidal flow is focused on. It is shown that the singular equation for equilibrium has the same structure as the equation for linear Alfven wave. Since the singular solution for equilibrium equation is physically inadequate, the singularity may be removed by another physical effect. The Hall-effect is taken into account as a singular perturbation that removes the singularity of equilibrium equation for ideal magnetohydrodynamics. (author)
A Parameter Robust Method for Singularly Perturbed Delay Differential Equations
Directory of Open Access Journals (Sweden)
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.
THE RIS K OF EDUCATIONAL SINGULARITY RISE: TENDENCIES AND THE FEASIBLE CONSEQUENCES
Directory of Open Access Journals (Sweden)
Yu. V. Voronenko
2013-05-01
Full Text Available There are considered the peculiarities of transition of the system of education from industrial to postindustrial model (informational society. Expert conclusions about the risks of technological and informative singularity are analysed. The prevention problems of technological and informative singularity on the base of newest technologies development, in particular post-graduate medical education are discussed.
Removability of singularity for nonlinear elliptic equations with p(x-growth
Directory of Open Access Journals (Sweden)
Yongqiang Fu
2013-09-01
Full Text Available Using Moser's iteration method, we investigate the problem of removable isolated singularities for elliptic equations with p(x-type nonstandard growth. We give a sufficient condition for removability of singularity for the equations in the framework of variable exponent Sobolev spaces.
Travelling wave solutions for a singularly perturbed Burgers–KdV ...
Indian Academy of Sciences (India)
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 ...
String theory and cosmological singularities
Indian Academy of Sciences (India)
recent times, string theory is providing new perspectives of such singularities which .... holes appear as stacks of a large number of D-branes wrapped in internal .... results into a well-known measure factor which makes the wave function into a.
Charged singularities: the causality violation
Energy Technology Data Exchange (ETDEWEB)
De Felice, F; Nobili, L [Padua Univ. (Italy). Ist. di Fisica; Calvani, M [Padua Univ. (Italy). Ist. di Astronomia
1980-12-01
A search is made for examples of particle trajectories which, approaching a naked singularity from infinity, make up for lost time before going back to infinity. In the Kerr-Newman metric a whole family of such trajectories is found showing that the causality violation is indeed a non-avoidable pathology.
Interval matrices: Regularity generates singularity
Czech Academy of Sciences Publication Activity Database
Rohn, Jiří; Shary, S.P.
2018-01-01
Roč. 540, 1 March (2018), s. 149-159 ISSN 0024-3795 Institutional support: RVO:67985807 Keywords : interval matrix * regularity * singularity * P-matrix * absolute value equation * diagonally singilarizable matrix Subject RIV: BA - General Mathematics Impact factor: 0.973, year: 2016
On psichological problem of NPP operation and control
International Nuclear Information System (INIS)
Mashin, V.A.
1994-01-01
The role of psichological factor as a reserve for increasing NPP safety connected with human factor is discussed. It is emphasized that the process of NPP personnel professional training should not be restricted by formation of a certain set of knowledge, skills and experience. It is necessary to initiate ability for constant self-developing. Control for assurance of effective interaction of the whole NPP personnel is an important problem
A fractional optimal control problem for maximizing advertising efficiency
Igor Bykadorov; Andrea Ellero; Stefania Funari; Elena Moretti
2007-01-01
We propose an optimal control problem to model the dynamics of the communication activity of a firm with the aim of maximizing its efficiency. We assume that the advertising effort undertaken by the firm contributes to increase the firm's goodwill and that the goodwill affects the firm's sales. The aim is to find the advertising policies in order to maximize the firm's efficiency index which is computed as the ratio between "outputs" and "inputs" properly weighted; the outputs are represented...
The Accountable Animal: Naturalising the management control problem
Eskenazi, Philip
2015-01-01
markdownabstract__Abstract__ In this dissertation we investigate two themes around the topic of social relations in management control structures. We use developments in neuroscience and eye-tracking to supplement the traditional psychological and economic perspective on management accounting. First, process accountability changes processes of judgement and problem solving. Some mental processes are more difficult to access introspectively than others, and this opacity makes it troublesome to...
Uniqueness for the inverse backscattering problem for angularly controlled potentials
International Nuclear Information System (INIS)
Rakesh; Uhlmann, Gunther
2014-01-01
We consider the problem of recovering a smooth, compactly supported potential on R 3 from its backscattering data. We show that if two such potentials have the same backscattering data and the difference of the two potentials has controlled angular derivatives, then the two potentials are identical. In particular, if two potentials differ by a finite linear combination of spherical harmonics with radial coefficients and have the same backscattering data then the two potentials are identical. (paper)
Remarks on gauge variables and singular Lagrangians
International Nuclear Information System (INIS)
Chela-Flores, J.; Janica-de-la-Torre, R.; Kalnay, A.J.; Rodriguez-Gomez, J.; Rodriguez-Nunez, J.; Tascon, R.
1977-01-01
The relevance is discussed of gauge theory, based on a singular Lagrangian density, to the foundations of field theory. The idea that gauge transformations could change the physics of systems where the Lagrangian is singular is examined. (author)
Singular multiparameter dynamic equations with distributional ...
African Journals Online (AJOL)
Singular multiparameter dynamic equations with distributional potentials on time scales. ... In this paper, we consider both singular single and several multiparameter ... multiple function which is of one sign and nonzero on the given time scale.
A novel singular pattern in the sine-Gordon equation
International Nuclear Information System (INIS)
Huang, Debin
2003-01-01
By the scatter problem and the Backlund transformation of the sine-Gordon equation, we find a novel solution with the singularity of jumping phenomenon, which displays pattern structure similar respectively to soliton, kink, anti-kink and double pole solution with the different choice of the purely imaginary spectrum of the sine-Gordon equation
New singularities in nonrelativistic coupled channel scattering. II. Fourth order
International Nuclear Information System (INIS)
Khuri, N.N.; Tsun Wu, T.
1997-01-01
We consider a two-channel nonrelativistic potential scattering problem, and study perturbation theory in fourth order for the forward amplitude. The main result is that the new singularity demonstrated in second order in the preceding paper I also occurs at the same point in fourth order. Its strength is again that of a pole. copyright 1997 The American Physical Society
Kalman Filtering for Delayed Singular Systems with Multiplicative Noise
Institute of Scientific and Technical Information of China (English)
Xiao Lu; Linglong Wang; Haixia Wang; Xianghua Wang
2016-01-01
Kalman filtering problem for singular systems is dealt with, where the measurements consist of instantaneous measurements and delayed ones, and the plant includes multiplicative noise. By utilizing standard singular value decomposition, the restricted equivalent delayed system is presented, and the Kalman filters for the restricted equivalent system are given by using the well-known re-organization of innovation analysis lemma. The optimal Kalman filter for the original system is given based on the above Kalman filter by recursive Riccati equations, and a numerical example is presented to show the validity and efficiency of the proposed approach, where the comparison between the filter and predictor is also given.
Special relativity with a discrete spectrum of singular velocities
International Nuclear Information System (INIS)
Gonzales Gascon, F.
1977-01-01
The introduction of real transformation formulae containing a whole discrete spectrum of singularities is suggested. Some phenomenological hypotheses are introduced and the group property is substituted by weaker conditions. The first singular speed (c 1 =c) is invariant with respect to the measures of it from subluminal frames, but the remaining speeds are not invariant. The proposed transformations do not form a closed set (for the superluminal speeds) and, therefore, the problem of having (within this framework) a principle of relativity valid for any velocity remains open
Identity and singularity: Metastability and morphogenesis in light of Deleuze
Directory of Open Access Journals (Sweden)
Barison Marcello
2015-01-01
Full Text Available The question of life is inextricably connected with the problem of identification and with the fact that each identification process includes the acquisition of a form. Nevertheless, it appears that at the biological level, that is, for what concerns a morphogenetic description of the status of the living being, the term singularity comes into play right there where you would expect to get into the notion of identity. According to Christian De Duve, the organic form has no identity, but it expresses - and is an expression of - a singularity. Given these observations, this is the object of the paper: to explain in a clear and consistent way how these terms - namely identity and singularity - differ and whether it is possible to ground their distinction in a coherent theoretical manner.
International Nuclear Information System (INIS)
Garon, Ariane
2014-01-01
Since the foundations of quantum physics have been laid, our knowledge of it never ceased to grow and this field of science naturally split into diverse specialized branches. The first part of this thesis focuses on a problem which concerns all branches of quantum physics, which is the visualization of quantum systems. The non-intuitive aspect of quantum physics justifies a shared desire to visualize quantum systems. In the present work, we develop a method to visualize any operators in these systems, including in particular state operators (density matrices), Hamiltonians and propagators. The method, referred to as DROPS (Discrete Representation of spin OPeratorS), is based on a generalization of Wigner representations, presented in this document. The resulting visualization of an operator A is called its DROPS representation or visualization. We demonstrate its intuitive character by illustrating a series of concepts in nuclear magnetic resonance (NMR) spectroscopy for systems consisting of two spin-1/2 particles. The second part of this thesis is concerned with a problem of optimal control which finds applications in the fields of NMR spectroscopy, medical imagery and quantum computing, to cite a few. The problem of creating a propagator in the shortest amount of time is considered, and the results are extended to solve the closely related problem of creating rotations in the smallest amount of time. The approach used here differs from the previous results on the subject by solving the problem using the Pontryagin's maximum principle and by its detailed consideration of singular controls and trajectories.
PID controller tuning using metaheuristic optimization algorithms for benchmark problems
Gholap, Vishal; Naik Dessai, Chaitali; Bagyaveereswaran, V.
2017-11-01
This paper contributes to find the optimal PID controller parameters using particle swarm optimization (PSO), Genetic Algorithm (GA) and Simulated Annealing (SA) algorithm. The algorithms were developed through simulation of chemical process and electrical system and the PID controller is tuned. Here, two different fitness functions such as Integral Time Absolute Error and Time domain Specifications were chosen and applied on PSO, GA and SA while tuning the controller. The proposed Algorithms are implemented on two benchmark problems of coupled tank system and DC motor. Finally, comparative study has been done with different algorithms based on best cost, number of iterations and different objective functions. The closed loop process response for each set of tuned parameters is plotted for each system with each fitness function.
Teamwork and problem solving in the control room
International Nuclear Information System (INIS)
Nygard, F.I.; Dedon, J.M.; Fuld, R.B.
1989-01-01
The importance of teamwork and communications in the control room of a nuclear power plant has been the subject of significant attention during the 10 yr since the Three Mile Island accident. The ability to conduct effective problem solving, especially under unexpected conditions, requires that the control room crew be well trained in techniques that produce synergism and avoid ambiguous or conflicting interactions. This paper describes the foundations of a training program developed and conducted by Combustion Engineering to produce a winning team in the control room. The complete licensed operations staffs of three utilities, Florida Power ampersand Light, Louisiana Power ampersand Light, and Omaha Public Power District, have completed this program. Thus, the results of the experience of ∼150 licensed operators is reported
Mayer control problem with probabilistic uncertainty on initial positions
Marigonda, Antonio; Quincampoix, Marc
2018-03-01
In this paper we introduce and study an optimal control problem in the Mayer's form in the space of probability measures on Rn endowed with the Wasserstein distance. Our aim is to study optimality conditions when the knowledge of the initial state and velocity is subject to some uncertainty, which are modeled by a probability measure on Rd and by a vector-valued measure on Rd, respectively. We provide a characterization of the value function of such a problem as unique solution of an Hamilton-Jacobi-Bellman equation in the space of measures in a suitable viscosity sense. Some applications to a pursuit-evasion game with uncertainty in the state space is also discussed, proving the existence of a value for the game.
Günüşen, Neslihan Partlak; Serçekuş, Pınar; Edeer, Aylin Durmaz
2014-06-01
The purpose of this study is to compare the locus of control and problem-solving skills of nursing students studying with the problem-based learning method with those of nursing students studying with the traditional method. This is a descriptive and comparative study. For data collection, the Problem-Solving Skills Inventory and the Locus of Control Scale were used. The study sample included 680 nursing students. It was determined that the problem-based learning method was more effective in the development of problem-solving skills and internal locus of control than was the traditional method. © 2014 NANDA International.
Energy conditions and spacetime singularities
International Nuclear Information System (INIS)
Tipler, F.J.
1978-01-01
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
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
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.
Fundamental solutions of singular SPDEs
International Nuclear Information System (INIS)
Selesi, Dora
2011-01-01
Highlights: → Fundamental solutions of linear SPDEs are constructed. → Wick-convolution product is introduced for the first time. → Fourier transformation maps Wick-convolution into Wick product. → Solutions of linear SPDEs are expressed via Wick-convolution with fundamental solutions. → Stochastic Helmholtz equation is solved. - Abstract: This paper deals with some models of mathematical physics, where random fluctuations are modeled by white noise or other singular Gaussian generalized processes. White noise, as the distributional derivative od Brownian motion, which is the most important case of a Levy process, is defined in the framework of Hida distribution spaces. The Fourier transformation in the framework of singular generalized stochastic processes is introduced and its applications to solving stochastic differential equations involving Wick products and singularities such as the Dirac delta distribution are presented. Explicit solutions are obtained in form of a chaos expansion in the Kondratiev white noise space, while the coefficients of the expansion are tempered distributions. Stochastic differential equations of the form P(ω, D) ◊ u(x, ω) = A(x, ω) are considered, where A is a singular generalized stochastic process and P(ω, D) is a partial differential operator with random coefficients. We introduce the Wick-convolution operator * which enables us to express the solution as u = s*A ◊ I ◊(-1) , where s denotes the fundamental solution and I is the unit random variable. In particular, the stochastic Helmholtz equation is solved, which in physical interpretation describes waves propagating with a random speed from randomly appearing point sources.
Why the Singularity Cannot Happen
Modis, Theodore
2012-01-01
The concept of a Singularity as described in Ray Kurzweil's book cannot happen for a number of reasons. One reason is that all natural growth processes that follow exponential patterns eventually reveal themselves to be following S-curves thus excluding runaway situations. The remaining growth potential from Kurzweil's ''knee'', which could be approximated as the moment when an S-curve pattern begins deviating from the corresponding exponential, is a factor of only one order of magnitude grea...
Black holes, singularities and predictability
International Nuclear Information System (INIS)
Wald, R.M.
1984-01-01
The paper favours the view that singularities may play a central role in quantum gravity. The author reviews the arguments leading to the conclusion, that in the process of black hole formation and evaporation, an initial pure state evolves to a final density matrix, thus signaling a breakdown in ordinary quantum dynamical evolution. Some related issues dealing with predictability in the dynamical evolution, are also discussed. (U.K.)
On singularities of lattice varieties
Mukherjee, Himadri
2013-01-01
Toric varieties associated with distributive lattices arise as a fibre of a flat degeneration of a Schubert variety in a minuscule. The singular locus of these varieties has been studied by various authors. In this article we prove that the number of diamonds incident on a lattice point $\\a$ in a product of chain lattices is more than or equal to the codimension of the lattice. Using this we also show that the lattice varieties associated with product of chain lattices is smooth.
Using Model Checking for Analyzing Distributed Power Control Problems
DEFF Research Database (Denmark)
Brihaye, Thomas; Jungers, Marc; Lasaulce, Samson
2010-01-01
Model checking (MC) is a formal verification technique which has been known and still knows a resounding success in the computer science community. Realizing that the distributed power control ( PC) problem can be modeled by a timed game between a given transmitter and its environment, the authors...... objectives a transmitter-receiver pair would like to reach. The network is modeled by a game where transmitters are considered as timed automata interacting with each other. The objectives are then translated into timed alternating-time temporal logic formulae and MC is exploited to know whether the desired...
Magnetic sensorless control experiment without drift problem on HT-7
International Nuclear Information System (INIS)
Nakamura, K.; Luo, J.R.; Wang, H.Z.; Ji, Z.S.; Wang, H.; Wang, F.; Qi, N.; Sato, K.N.; Hanada, K.; Sakamoto, M.; Idei, H.; Hasegawa, M.; Iyomasa, A.; Kawasaki, S.; Nakashima, H.; Higashijima, A.
2006-01-01
Magnetic sensorless control experiments of the plasma horizontal position have been carried out in the superconducting tokamak HT-7. Previously the horizontal position was calculated from the vertical field coil current and voltage without using signals of magnetic sensors like magnetic coils and flux loops placed near the plasma. The calculations are made focusing on the ripple frequency component of the power supply with thyristor and directly from them without time integration. There is no drift problem of integrator of magnetic sensors. Two kinds of experiments were carried out, to keep the position constant and swing the position in a triangular waveform
Quantum propagation across cosmological singularities
Gielen, Steffen; Turok, Neil
2017-05-01
The initial singularity is the most troubling feature of the standard cosmology, which quantum effects are hoped to resolve. In this paper, we study quantum cosmology with conformal (Weyl) invariant matter. We show that it is natural to extend the scale factor to negative values, allowing a large, collapsing universe to evolve across a quantum "bounce" into an expanding universe like ours. We compute the Feynman propagator for Friedmann-Robertson-Walker backgrounds exactly, identifying curious pathologies in the case of curved (open or closed) universes. We then include anisotropies, fixing the operator ordering of the quantum Hamiltonian by imposing covariance under field redefinitions and again finding exact solutions. We show how complex classical solutions allow one to circumvent the singularity while maintaining the validity of the semiclassical approximation. The simplest isotropic universes sit on a critical boundary, beyond which there is qualitatively different behavior, with potential for instability. Additional scalars improve the theory's stability. Finally, we study the semiclassical propagation of inhomogeneous perturbations about the flat, isotropic case, at linear and nonlinear order, showing that, at least at this level, there is no particle production across the bounce. These results form the basis for a promising new approach to quantum cosmology and the resolution of the big bang singularity.
Problems and achievements of cotton (Gossypium Hirsutum L. weeds control
Directory of Open Access Journals (Sweden)
T. Barakova
2017-09-01
Full Text Available Abstract. Weed control in the cultivation of cotton is critical to the yield and quality of production. The influence of economically important weeds was studied. Chemical control is the most effective method of weed control in cotton but much of the information on it relates to primary weed infestation. Problems with primary weed infestation in cotton have been solved to a significant extent. The question of secondary weed infestation with annual and perennial graminaceous weeds during the period of cotton vegetation is also determined largely by the use of antigraminaceous herbicides. The data related to herbicides to effectively control secondary germinated broadleaf weeds in conventional technology for cotton growing are quite scarce, even globally. We are still seeking effective herbicides for control of these weeds in cotton crops. Studies on their influence on the sowing characteristics of cotton seed and the quality of cotton fiber are still insufficient. In the scientific literature there is not enough information on these questions. The combinations of herbicides, as well as their tank mixtures with fertilizers or plant growth regulators are more efficient than autonomous application. Often during their combined application higher synergistic effect on yield is produced. There is information about cotton cultivars resistant to glyphosate. These cultivars are GMO and they are banned within the European Union, including Bulgaria.
Experience with control valve cavitation problems and their solutions
International Nuclear Information System (INIS)
Ozol, J.
1988-01-01
Pressure reduction in control valves can induce cavitation, which has three effects on the control valve. Firstly, it modifies or changes the hydraulic performance of the control valve. Since control valves are designed for noncavitating conditions, the result is usually reduced stability of the control valve or, in extreme cavitating conditions known as supercavitation, the valve may limit the flow rate and thus be undersized. Secondly, cavitation can cause material damage to valve parts, trim, or valve body, or erodes downstream piping; consequently, the valve or piping leaks. Thirdly, cavitation causes noise and vibration, which may cause major damage or destruction to equipment such as valve positioners, actuators, pipe supports and sometimes to other downstream valves. The purpose of this paper is twofold: (1) It describes the I.S.A. valve sizing equations and how they relate to cavitation. (2) It describes experiences with these three problems, and discusses corrective actions and practical approaches to their solution. This paper discusses thirteen cavitation experiences
THE CONTROL VARIATIONAL METHOD FOR ELASTIC CONTACT PROBLEMS
Directory of Open Access Journals (Sweden)
Mircea Sofonea
2010-07-01
Full Text Available We consider a multivalued equation of the form Ay + F(y = fin a real Hilbert space, where A is a linear operator and F represents the (Clarke subdifferential of some function. We prove existence and uniqueness results of the solution by using the control variational method. The main idea in this method is to minimize the energy functional associated to the nonlinear equation by arguments of optimal control theory. Then we consider a general mathematical model describing the contact between a linearly elastic body and an obstacle which leads to a variational formulation as above, for the displacement field. We apply the abstract existence and uniqueness results to prove the unique weak solvability of the corresponding contact problem. Finally, we present examples of contact and friction laws for which our results work.
Problems is applying new internal dose coefficients to radiation control
Energy Technology Data Exchange (ETDEWEB)
Sato, Yuichi [Oarai Laboratory, Chiyoda Technol Corporation, Ibaraki (Japan)
1998-06-01
The author discussed problems concerning the conceivable influence in the radiation control and those newly developing when the new internal dose coefficients are applied in the law in the future. For the conceivable influence, the occupational and public exposure was discussed: In the former, the effective dose equivalent limit (at present, 50 mSv/y) was thought to be reduced and in the latter, the limit to be obscure although it might be more greatly influenced by the new coefficients. For newly developing problems, since the new biological model which is more realistic was introduced for calculation of the internal dose and made the calculation more complicated, use of computer is requisite. The effective dose of the internal exposure in the individual monitoring should be conveniently calculated as done at present even after application of the new coefficients. For calculation of the effective dose of the internal exposure, there are such problems as correction of the inhaled particle size and of the individual personal parameter. A model calculation of residual rate in the chest where the respiratory tract alone participated was presented as an example but for the whole body, more complicated functions were pointed out necessary. The concept was concluded to be incorporated in the law in a convenient and easy manner and a software for calculation of internal dose using the new coefficients was wanted. (K.H.)
Directory of Open Access Journals (Sweden)
A. S. Koval
2010-01-01
Full Text Available The paper considers problems concerning electromechanical interaction in elevators with an adjustable asynchronous electric drive equipped with the vector control systems under direct torque control and direct torque control with pulse-width modulator. A mathematical description of electromechanical elevator system with due account of nonlinearity of the worm gear is given in the paper. The paper presents a simplified circuit design of a control system with a fuzzy speed controller. It has been established that the factor of electromechanical interaction in electromechanical system with the adjustable asynchronous electric drive and an fuzzy speed controller is within the range which corresponds to existence of the essential electromechanical interaction.
A technical overview of air pollution problems and its control
International Nuclear Information System (INIS)
Rusheed, A.
1997-01-01
Air pollution is a well known phenomenon experienced in every day life. The air we breathe consist of gases and aerosol particles on which pollutants such as toxic elements and bacteria reside. These microscopic particles are transported to long distances from the source of origin the direction and magnitude of which depends upon the prevailing meteorological conditions. In order to assess the impact of air pollution, systematic studies are carried out which consist of: 1) sampling of air, 2) measurement of pollutants, 3) identification of pollutant source and 4) adoption of control methods. Each of these topics are fairly exhaustive and their understanding requires accurate scientific approach. An overview of these topic has been presented in this talk. Air samples are best collected by filtering air through suitable medium and analyses are carried out by diverse analytical techniques. Source identifications is a very important step which is done either by emission modeling or receptor modeling techniques. A general survey of these techniques, especially receptor modeling is presented in this talk. The control of air pollution is carried out by using carried devices and the processes especially developed for this purpose. Air pollution has given rise to a number of global problems such as depletion of stratospheric ozone, acid rain and greenhouse effect, which are being tackled on international scale. These problems have been discussed very briefly and a summary of international efforts has been presented. (author)
Optimal Control Approaches to the Aggregate Production Planning Problem
Directory of Open Access Journals (Sweden)
Yasser A. Davizón
2015-12-01
Full Text Available In the area of production planning and control, the aggregate production planning (APP problem represents a great challenge for decision makers in production-inventory systems. Tradeoff between inventory-capacity is known as the APP problem. To address it, static and dynamic models have been proposed, which in general have several shortcomings. It is the premise of this paper that the main drawback of these proposals is, that they do not take into account the dynamic nature of the APP. For this reason, we propose the use of an Optimal Control (OC formulation via the approach of energy-based and Hamiltonian-present value. The main contribution of this paper is the mathematical model which integrates a second order dynamical system coupled with a first order system, incorporating production rate, inventory level, and capacity as well with the associated cost by work force in the same formulation. Also, a novel result in relation with the Hamiltonian-present value in the OC formulation is that it reduces the inventory level compared with the pure energy based approach for APP. A set of simulations are provided which verifies the theoretical contribution of this work.
Quantum gravity removes classical singularities and shortens the life of black holes
International Nuclear Information System (INIS)
Frolov, V.P.; Vilkovisky, G.A.
1979-07-01
The problem of the gravitational collapse is considered in the framework of the quantum gravity effective action. It is shown that quantum gravity removes classical singularity and possibly shortens the lifetime of the black hole. (author)
Energy Technology Data Exchange (ETDEWEB)
Bobodzhanov, A A; Safonov, V F [National Research University " Moscow Power Engineering Institute" , Moscow (Russian Federation)
2013-07-31
The paper deals with extending the Lomov regularization method to classes of singularly perturbed Fredholm-type integro-differential systems, which have not so far been studied. In these the limiting operator is discretely noninvertible. Such systems are commonly known as problems with unstable spectrum. Separating out the essential singularities in the solutions to these problems presents great difficulties. The principal one is to give an adequate description of the singularities induced by 'instability points' of the spectrum. A methodology for separating singularities by using normal forms is developed. It is applied to the above type of systems and is substantiated in these systems. Bibliography: 10 titles.
Human factors implications of unmanned aircraft accidents : flight-control problems
2006-04-01
This research focuses on three types of flight control problems associated with unmanned aircraft systems. The : three flight control problems are: 1) external pilot difficulties with inconsistent mapping of the controls to the : movement of the airc...
Lecture notes on mean curvature flow, barriers and singular perturbations
Bellettini, Giovanni
2013-01-01
The aim of the book is to study some aspects of geometric evolutions, such as mean curvature flow and anisotropic mean curvature flow of hypersurfaces. We analyze the origin of such flows and their geometric and variational nature. Some of the most important aspects of mean curvature flow are described, such as the comparison principle and its use in the definition of suitable weak solutions. The anisotropic evolutions, which can be considered as a generalization of mean curvature flow, are studied from the view point of Finsler geometry. Concerning singular perturbations, we discuss the convergence of the Allen–Cahn (or Ginsburg–Landau) type equations to (possibly anisotropic) mean curvature flow before the onset of singularities in the limit problem. We study such kinds of asymptotic problems also in the static case, showing convergence to prescribed curvature-type problems.
On important precursor of singular optics (tutorial)
Polyanskii, Peter V.; Felde, Christina V.; Bogatyryova, Halina V.; Konovchuk, Alexey V.
2018-01-01
The rise of singular optics is usually associated with the seminal paper by J. F. Nye and M. V. Berry [Proc. R. Soc. Lond. A, 336, 165-189 (1974)]. Intense development of this area of modern photonics has started since the early eighties of the XX century due to invention of the interfrence technique for detection and diagnostics of phase singularities, such as optical vortices in complex speckle-structured light fields. The next powerful incentive for formation of singular optics into separate area of the science on light was connectected with discovering of very practical technique for creation of singular optical beams of various kinds on the base of computer-generated holograms. In the eghties and ninetieth of the XX century, singular optics evolved, almost entirely, under the approximation of complete coherency of light field. Only at the threshold of the XXI century, it has been comprehended that the singular-optics approaches can be fruitfully expanded onto partially spatially coherent, partially polarized and polychromatic light fields supporting singularities of new kinds, that has been resulted in establishing of correlation singular optics. Here we show that correlation singular optics has much deeper roots, ascending to "pre-singular" and even pre-laser epoch and associated with the concept of partial coherence and polarization. It is remarcable that correlation singular optics in its present interpretation has forestalled the standard coherent singular optics. This paper is timed to the sixtieth anniversary of the most profound precursor of modern correlation singular optics [J. Opt. Soc. Am., 47, 895-902 (1957)].
Formation and morphological transformation of polarization singularities: hunting the monstar
International Nuclear Information System (INIS)
Kumar, Vijay; Philip, Geo M; Viswanathan, Nirmal K
2013-01-01
The theoretical formalism and experimental measurements to form and transform between the three morphologies of the polarization singular patterns—star, lemon and monstar—are presented here. The monstar is statistically rare in isotropic random fields but its controllable realization is achieved by tuning the field anisotropy in three-beam interference. (paper)
Anomalous singularities in the complex Kohn variational principle of quantum scattering theory
International Nuclear Information System (INIS)
Lucchese, R.R.
1989-01-01
Variational principles for symmetric complex scattering matrices (e.g., the S matrix or the T matrix) based on the Kohn variational principle have been thought to be free from anomalous singularities. We demonstrate that singularities do exist for these variational principles by considering single and multichannel model problems based on exponential interaction potentials. The singularities are found by considering simultaneous variations in two nonlinear parameters in the variational calculation (e.g., the energy and the cutoff function for the irregular continuum functions). The singularities are found when the cutoff function for the irregular continuum functions extends over a range of the radial coordinate where the square-integrable basis set does not have sufficient flexibility. Effects of these singularities generally should not appear in applications of the complex Kohn method where a fixed variational basis set is considered and only the energy is varied
Using Model Checking for Analyzing Distributed Power Control Problems
Directory of Open Access Journals (Sweden)
Thomas Brihaye
2010-01-01
Full Text Available Model checking (MC is a formal verification technique which has been known and still knows a resounding success in the computer science community. Realizing that the distributed power control (PC problem can be modeled by a timed game between a given transmitter and its environment, the authors wanted to know whether this approach can be applied to distributed PC. It turns out that it can be applied successfully and allows one to analyze realistic scenarios including the case of discrete transmit powers and games with incomplete information. The proposed methodology is as follows. We state some objectives a transmitter-receiver pair would like to reach. The network is modeled by a game where transmitters are considered as timed automata interacting with each other. The objectives are then translated into timed alternating-time temporal logic formulae and MC is exploited to know whether the desired properties are verified and determine a winning strategy.
Diversity Controlling Genetic Algorithm for Order Acceptance and Scheduling Problem
Directory of Open Access Journals (Sweden)
Cheng Chen
2014-01-01
Full Text Available Selection and scheduling are an important topic in production systems. To tackle the order acceptance and scheduling problem on a single machine with release dates, tardiness penalty, and sequence-dependent setup times, in this paper a diversity controlling genetic algorithm (DCGA is proposed, in which a diversified population is maintained during the whole search process through survival selection considering both the fitness and the diversity of individuals. To measure the similarity between individuals, a modified Hamming distance without considering the unaccepted orders in the chromosome is adopted. The proposed DCGA was validated on 1500 benchmark instances with up to 100 orders. Compared with the state-of-the-art algorithms, the experimental results show that DCGA improves the solution quality obtained significantly, in terms of the deviation from upper bound.
Symmetry generators in singular theories
International Nuclear Information System (INIS)
Lavrov, P.M.; Tyutin, I.V.
1989-01-01
It is proved that in the singular nondegenerate theories any symmetry of the lagrangian under non-point transformations of lagrangian variables with the open (in the general case) algebra in the hamiltonian approach generates corresponding transformations of canonical variables the generator of which is the Noether charge with respect to the Dirac brackets. On the surface of all constraints these transformations leave the hamiltonian invariant and the algebra of the Noether charges is closed. As a consequence it is shown that the nilpotent BRST charge operator always exists in gauge theories of the general form (if possible anomalies are not taken into account)
Topological resolution of gauge theory singularities
Saracco, Fabio; Tomasiello, Alessandro; Torroba, Gonzalo
2013-08-01
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.
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.
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.
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.
The dominant balance at cosmological singularities
International Nuclear Information System (INIS)
Cotsakis, Spiros; Barrow, John D
2007-01-01
We define the notion of a finite-time singularity of a vector field and then discuss a technique suitable for the asymptotic analysis of vector fields and their integral curves in the neighborhood of such a singularity. Having in mind the application of this method to cosmology, we also provide an analysis of the time singularities of an isotropic universe filled with a perfect fluid in general relativity
Exact solutions and singularities in string theory
International Nuclear Information System (INIS)
Horowitz, G.T.; Tseytlin, A.A.
1994-01-01
We construct two new classes of exact solutions to string theory which are not of the standard plane wave of gauged WZW type. Many of these solutions have curvature singularities. The first class includes the fundamental string solution, for which the string coupling vanishes near the singularity. This suggests that the singularity may not be removed by quantum corrections. The second class consists of hybrids of plane wave and gauged WZW solutions. We discuss a four-dimensional example in detail
Dressing up a Kerr naked singularity
Energy Technology Data Exchange (ETDEWEB)
Calvani, M [Padua Univ. (Italy). Ist. di Astronomia; Nobili, L [Padua Univ. (Italy). Ist. di Fisica
1979-06-11
The evolution of a naked singularity surrounded by an accreting disk of matter is studied; two kinds of disks are considered: the standard thin-disk model and the thick barytropic model, for several initial conditions. It is shown that any Kerr naked singularity slows down in a finite time to a maximal Kerr black hole. The final mass, the luminosity and the time of evolution of the singularity are evaluated.
Density control problems in large stellarators with neoclassical transport
International Nuclear Information System (INIS)
Maassberg, H.; Beidler, C.D.; Simmet, E.E.
1999-01-01
With respect to the particle flux, the off-diagonal term in the neoclassical transport matrix becomes crucial in the stellarator long-mean-free-path regime. Central heating with peaked temperature profiles can make an active density profile control by central particle refuelling mandatory. The neoclassical particle confinement can significantly exceed the energy confinement at the outer radii. As a consequence, the required central refuelling may be larger than the neoclassical particle fluxes at outer radii leading to the loss of the global density control. Radiative losses as well as additional 'anomalous' electron heat diffusivities further exacerbate this problem. In addition to the analytical formulation of the neoclassical link of particle and energy fluxes, simplified model simulations as well as time-dependent ASTRA code simulations are described. In particular, the 'low-' and 'high-mirror' W7-X configurations are compared. For the W7-X 'high-mirror' configuration especially, the appearance of the neoclassical particle transport barrier is predicted at higher densities. (author)
Spacetime averaging of exotic singularity universes
International Nuclear Information System (INIS)
Dabrowski, Mariusz P.
2011-01-01
Taking a spacetime average as a measure of the strength of singularities we show that big-rips (type I) are stronger than big-bangs. The former have infinite spacetime averages while the latter have them equal to zero. The sudden future singularities (type II) and w-singularities (type V) have finite spacetime averages. The finite scale factor (type III) singularities for some values of the parameters may have an infinite average and in that sense they may be considered stronger than big-bangs.
On local invariants of singular symplectic forms
Domitrz, Wojciech
2017-04-01
We find a complete set of local invariants of singular symplectic forms with the structurally stable Martinet hypersurface on a 2 n-dimensional manifold. In the C-analytic category this set consists of the Martinet hypersurface Σ2, the restriction of the singular symplectic form ω to TΣ2 and the kernel of ω n - 1 at the point p ∈Σ2. In the R-analytic and smooth categories this set contains one more invariant: the canonical orientation of Σ2. We find the conditions to determine the kernel of ω n - 1 at p by the other invariants. In dimension 4 we find sufficient conditions to determine the equivalence class of a singular symplectic form-germ with the structurally smooth Martinet hypersurface by the Martinet hypersurface and the restriction of the singular symplectic form to it. We also study the singular symplectic forms with singular Martinet hypersurfaces. We prove that the equivalence class of such singular symplectic form-germ is determined by the Martinet hypersurface, the canonical orientation of its regular part and the restriction of the singular symplectic form to its regular part if the Martinet hypersurface is a quasi-homogeneous hypersurface with an isolated singularity.
Coupled singular and non singular thermoelastic system and double lapalce decomposition methods
Hassan Gadain; Hassan Gadain
2016-01-01
In this paper, the double Laplace decomposition methods are applied to solve the non singular and singular one dimensional thermo-elasticity coupled system and. The technique is described and illustrated with some examples
Singular Value Decomposition and Ligand Binding Analysis
Directory of Open Access Journals (Sweden)
André Luiz Galo
2013-01-01
Full Text Available Singular values decomposition (SVD is one of the most important computations in linear algebra because of its vast application for data analysis. It is particularly useful for resolving problems involving least-squares minimization, the determination of matrix rank, and the solution of certain problems involving Euclidean norms. Such problems arise in the spectral analysis of ligand binding to macromolecule. Here, we present a spectral data analysis method using SVD (SVD analysis and nonlinear fitting to determine the binding characteristics of intercalating drugs to DNA. This methodology reduces noise and identifies distinct spectral species similar to traditional principal component analysis as well as fitting nonlinear binding parameters. We applied SVD analysis to investigate the interaction of actinomycin D and daunomycin with native DNA. This methodology does not require prior knowledge of ligand molar extinction coefficients (free and bound, which potentially limits binding analysis. Data are acquired simply by reconstructing the experimental data and by adjusting the product of deconvoluted matrices and the matrix of model coefficients determined by the Scatchard and McGee and von Hippel equation.
Directory of Open Access Journals (Sweden)
Alexander N. Kvitko
2017-01-01
Full Text Available An algorithm for constructing a control function that transfers a wide class of stationary nonlinear systems of ordinary differential equations from an initial state to a final state under certain control restrictions is proposed. The algorithm is designed to be convenient for numerical implementation. A constructive criterion of the desired transfer possibility is presented. The problem of an interorbital flight is considered as a test example and it is simulated numerically with the presented method.
Debbarma, Sanjoy; Saikia, Lalit Chandra; Sinha, Nidul
2014-03-01
Present work focused on automatic generation control (AGC) of a three unequal area thermal systems considering reheat turbines and appropriate generation rate constraints (GRC). A fractional order (FO) controller named as I(λ)D(µ) controller based on crone approximation is proposed for the first time as an appropriate technique to solve the multi-area AGC problem in power systems. A recently developed metaheuristic algorithm known as firefly algorithm (FA) is used for the simultaneous optimization of the gains and other parameters such as order of integrator (λ) and differentiator (μ) of I(λ)D(µ) controller and governor speed regulation parameters (R). The dynamic responses corresponding to optimized I(λ)D(µ) controller gains, λ, μ, and R are compared with that of classical integer order (IO) controllers such as I, PI and PID controllers. Simulation results show that the proposed I(λ)D(µ) controller provides more improved dynamic responses and outperforms the IO based classical controllers. Further, sensitivity analysis confirms the robustness of the so optimized I(λ)D(µ) controller to wide changes in system loading conditions and size and position of SLP. Proposed controller is also found to have performed well as compared to IO based controllers when SLP takes place simultaneously in any two areas or all the areas. Robustness of the proposed I(λ)D(µ) controller is also tested against system parameter variations. © 2013 ISA. Published by Elsevier Ltd. All rights reserved.
Papapetrou's naked singularity is a strong curvature singularity
Energy Technology Data Exchange (ETDEWEB)
Hollier, G.P.
1986-11-01
Following Papapetrou (1985, a random walk in General Relativity ed. J. Krishna-Rao (New Delhi: Wiley Eastern)), a spacetime with a naked singularity is analysed. This singularity is shown to be a strong curvature singularity and thus a counterexample to a censorship conjecture.
Relaxation periodic solutions of one singular perturbed system with delay
Kashchenko, A. A.
2017-12-01
In this paper, we consider a singularly perturbed system of two differential equations with delay, simulating two coupled oscillators with a nonlinear compactly supported feedback. We reduce studying nonlocal dynamics of initial system to studying dynamics of special finite-dimensional mappings: rough stable (unstable) cycles of these mappings correspond to exponentially orbitally stable (unstable) relaxation solutions of initial problem. We show that dynamics of initial model depends on coupling coefficient crucially. Multistability is proved.
The Semantics of Plurals: A Defense of Singularism
Florio, Salvatore
2010-01-01
In this dissertation, I defend "semantic singularism", which is the view that syntactically plural terms, such as "they" or "Russell and Whitehead", are semantically singular. A semantically singular term is a term that denotes a single entity. Semantic singularism is to be distinguished from "syntactic singularism", according to which…
Distributed Systems for Problems in Robust Control and Visual Tracking
National Research Council Canada - National Science Library
Tannenbaum, Allen
2000-01-01
.... A key application is in controlled active vision, including visual tracking, the control of autonomous vehicles, motion planning, and the utilization of visual information in guidance and control...
Botrytis cinerea Control and the Problem of Fungicide Resistance
Directory of Open Access Journals (Sweden)
Brankica Tanović
2011-01-01
Full Text Available Botrytis cinerea, the causal agent of grey mould, greatly affects fruit, grapevine, vegetable and ornamental crops production. It is a common causal agent of diseases in plants grown in protected areas, as well as fruit decay during storage and transport. The fungusinvades almost all parts of the plant in all developmental stages, and the symptoms are usually described as grey mould, grey mildew, brown rot and seedling blight. The paper reviews the current knowledge on control possibilities of this necrotrophic pathogen. Theattention is particularly paid to the mode of action of novel fungicides and to the problem of resistance. It is pointed out that by limiting the number of treatments in the growing season, avoiding the use of only one fungicide with a high risk for resistance development,appropriate application rate and timing, using mixtures of pesticides with different modes of action, as well as by alternative use of pesticides from different resistance groups, a longterm preservation of pesticide efficacy is provided.
Discrete Time McKean–Vlasov Control Problem: A Dynamic Programming Approach
Energy Technology Data Exchange (ETDEWEB)
Pham, Huyên, E-mail: pham@math.univ-paris-diderot.fr; Wei, Xiaoli, E-mail: tyswxl@gmail.com [Laboratoire de Probabilités et Modèles Aléatoires, CNRS, UMR 7599, Université Paris Diderot (France)
2016-12-15
We consider the stochastic optimal control problem of nonlinear mean-field systems in discrete time. We reformulate the problem into a deterministic control problem with marginal distribution as controlled state variable, and prove that dynamic programming principle holds in its general form. We apply our method for solving explicitly the mean-variance portfolio selection and the multivariate linear-quadratic McKean–Vlasov control problem.
Discrete Time McKean–Vlasov Control Problem: A Dynamic Programming Approach
International Nuclear Information System (INIS)
Pham, Huyên; Wei, Xiaoli
2016-01-01
We consider the stochastic optimal control problem of nonlinear mean-field systems in discrete time. We reformulate the problem into a deterministic control problem with marginal distribution as controlled state variable, and prove that dynamic programming principle holds in its general form. We apply our method for solving explicitly the mean-variance portfolio selection and the multivariate linear-quadratic McKean–Vlasov control problem.
Quantum gravity removes classical singularities and shortens the life of black holes
International Nuclear Information System (INIS)
Frolov, V.P.; Vilkovisky, G.A.
1982-01-01
One of the fundamental problems in classical General Relativity is what is to be done with singularities which inevitably arise in the theoretical description of the massive body (or total Universe) collapse. Although the singularities arising as a result of the gravitational collapse are believed to be hidden under event horizons and thus are not visible to an external observer, their very existence means the crisis of the classical gravitational physics. It is generally believed that the proper account of quantum effects may cure this disease. The aim of the present work is to show that it really happens, and quantum gravity does remove classical singularities. (Auth.)
Stable singularities in string theory
International Nuclear Information System (INIS)
Aspinwall, P.S.; Morrison, D.R.; Gross, M.
1996-01-01
We study a topological obstruction of a very stringy nature concerned with deforming the target space of an N=2 non-linear σ-model. This target space has a singularity which may be smoothed away according to the conventional rules of geometry, but when one studies the associated conformal field theory one sees that such a deformation is not possible without a discontinuous change in some of the correlation functions. This obstruction appears to come from torsion in the homology of the target space (which is seen by deforming the theory by an irrelevant operator). We discuss the link between this phenomenon and orbifolds with discrete torsion as studied by Vafa and Witten. (orig.). With 3 figs
Directory of Open Access Journals (Sweden)
Elvio Alccinelli
2001-07-01
Full Text Available En este artículo pretendemos mostrar que le conjunto de las economías singulares, si bien pequeño desde el punto de vista de la topología y/o desde el punto de vista de la teoría de la medida, tiene importantes efectos en el desarrollo de los regímenes económicos. Es el responsable de los cambios abruptos en los estados de equilibrio y de la multiplicidad de tales estados. Permite además establecer a partir de los tipos de singularidades posibles, una partición del conjunto de economías según tenga lugar uno u otro tipo de singularidad cuya presencia o no, caracteriza el comportamiento posible de la economía en cuestión.
Quantum transitions through cosmological singularities
Energy Technology Data Exchange (ETDEWEB)
Bramberger, Sebastian F.; Lehners, Jean-Luc [Max Planck Institute for Gravitational Physics (Albert Einstein Institute), 14476 Potsdam-Golm (Germany); Hertog, Thomas; Vreys, Yannick, E-mail: sebastian.bramberger@aei.mpg.de, E-mail: thomas.hertog@kuleuven.be, E-mail: jlehners@aei.mpg.de, E-mail: yannick.vreys@kuleuven.be [Institute for Theoretical Physics, KU Leuven, 3001 Leuven (Belgium)
2017-07-01
In a quantum theory of cosmology spacetime behaves classically only in limited patches of the configuration space on which the wave function of the universe is defined. Quantum transitions can connect classical evolution in different patches. Working in the saddle point approximation and in minisuperspace we compute quantum transitions connecting inflationary histories across a de Sitter like throat or a singularity. This supplies probabilities for how an inflating universe, when evolved backwards, transitions and branches into an ensemble of histories on the opposite side of a quantum bounce. Generalising our analysis to scalar potentials with negative regions we identify saddle points describing a quantum transition between a classically contracting, crunching ekpyrotic phase and an inflationary universe.
Coulomb branches with complex singularities
Argyres, Philip C.; Martone, Mario
2018-06-01
We construct 4d superconformal field theories (SCFTs) whose Coulomb branches have singular complex structures. This implies, in particular, that their Coulomb branch coordinate rings are not freely generated. Our construction also gives examples of distinct SCFTs which have identical moduli space (Coulomb, Higgs, and mixed branch) geometries. These SCFTs thus provide an interesting arena in which to test the relationship between moduli space geometries and conformal field theory data. We construct these SCFTs by gauging certain discrete global symmetries of N = 4 superYang-Mills (sYM) theories. In the simplest cases, these discrete symmetries are outer automorphisms of the sYM gauge group, and so these theories have lagrangian descriptions as N = 4 sYM theories with disconnected gauge groups.
Quantum transitions through cosmological singularities
International Nuclear Information System (INIS)
Bramberger, Sebastian F.; Lehners, Jean-Luc; Hertog, Thomas; Vreys, Yannick
2017-01-01
In a quantum theory of cosmology spacetime behaves classically only in limited patches of the configuration space on which the wave function of the universe is defined. Quantum transitions can connect classical evolution in different patches. Working in the saddle point approximation and in minisuperspace we compute quantum transitions connecting inflationary histories across a de Sitter like throat or a singularity. This supplies probabilities for how an inflating universe, when evolved backwards, transitions and branches into an ensemble of histories on the opposite side of a quantum bounce. Generalising our analysis to scalar potentials with negative regions we identify saddle points describing a quantum transition between a classically contracting, crunching ekpyrotic phase and an inflationary universe.
International Nuclear Information System (INIS)
Luo, Yamei; Lü, Baida
2010-01-01
The dynamic behavior of spectral Stokes singularities of partially coherent radially polarized beams focused by a high numerical aperture (NA) objective is studied by using the vectorial Debye diffraction theory and complex spectral Stokes fields. It is shown that there exist s 12 , s 23 , and s 31 singularities, as well as P (completely polarized) and U (unpolarized) singularities. The motion, pair creation and annihilation, and changes in the degree of polarization of s 12 , s 23 , and s 31 singularities, and the handedness reversal of s 12 singularities (C-points) may appear by varying a controlling parameter, such as the truncation parameter, NA, or spatial correlation length. The creation and annihilation occur for a pair of s 12 singularities with opposite topological charge but the same handedness, and for a pair of oppositely charged s 23 or s 31 singularities. The critical value of the truncation parameter, at which the pair annihilation takes place, increases as the semi-angle of the aperture lens (or, equivalently, NA) or spatial correlation length increases. The collision of an s 12 singularity with an L-line (s 3 = 0 contour) leads to a V-point, which is located at the intersection of contours of s 12 = 0 and s 23 = 0 (or s 31 = 0) and is unstable
Building Reproducible Science with Singularity Containers
CERN. Geneva
2018-01-01
Michael Bauer first began working with containers at GSI national lab in Darmstadt, Germany, in 2017 while taking a semester off of school at the University of Michigan. Michael met Greg Kurtzer, project lead of Singularity, during his time at GSI and he began contributing heavily to the Singularity project. At the start of summer 2017, Greg hired Michael to work at the ...
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 dela...
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.
Singularities in the nonisotropic Boltzmann equation
International Nuclear Information System (INIS)
Garibotti, C.R.; Martiarena, M.L.; Zanette, D.
1987-09-01
We consider solutions of the nonlinear Boltzmann equation (NLBE) with anisotropic singular initial conditions, which give a simplified model for the penetration of a monochromatic beam on a rarified target. The NLBE is transformed into an integral equation which is solved iteratively and the evolution of the initial singularities is discussed. (author). 5 refs
Cold atoms in singular potentials
International Nuclear Information System (INIS)
Denschlag, J. P.
1998-09-01
We studied both theoretically and experimentally the interaction between cold Li atoms from a magnetic-optical trap (MOT) and a charged or current-carrying wire. With this system, we were able to realize 1/r 2 and 1/r potentials in two dimensions and to observe the motion of cold atoms in both potentials. For an atom in an attractive 1/r 2 potential, there exist no stable trajectories, instead there is a characteristic class of trajectories for which atoms fall into the singularity. We were able to observe this falling of atoms into the center of the potential. Moreover, by probing the singular 1/r 2 potential with atomic clouds of varying size and temperature we extracted scaling properties of the atom-wire interaction. For very cold atoms, and very thin wires the motion of the atoms must be treated quantum mechanically. Here we predict that the absorption cross section for the 1/r 2 potential should exhibit quantum steps. These quantum steps are a manifestation of the quantum mechanical decomposition of plane waves into partial waves. For the second part of this work, we realized a two dimensional 1/r potential for cold atoms. If the potential is attractive, the atoms can be bound and follow Kepler-like orbits around the wire. The motion in the third dimension along the wire is free. We were able to exploit this property and constructed a novel cold atom guide, the 'Kepler guide'. We also demonstrated another type of atom guide (the 'side guide'), by combining the magnetic field of the wire with a homogeneous offset magnetic field. In this case, the atoms are held in a potential 'tube' on the side of the wire. The versatility, simplicity, and scaling properties of this guide make it an interesting technique. (author)
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...
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.
One dimensional systems with singular perturbations
International Nuclear Information System (INIS)
Alvarez, J J; Gadella, M; Nieto, L M; Glasser, L M; Lara, L P
2011-01-01
This paper discusses some one dimensional quantum models with singular perturbations. Eventually, a mass discontinuity is added at the points that support the singular perturbations. The simplest model includes an attractive singular potential with a mass jump both located at the origin. We study the form of the only bound state. Another model exhibits a hard core at the origin plus one or more repulsive deltas with mass jumps at the points supporting these deltas. We study the location and the multiplicity of these resonances for the case of one or two deltas and settle the basis for a generalization. Finally, we consider the harmonic oscillator and the infinite square well plus a singular potential at the origin. We see how the energy of bound states is affected by the singular perturbation.
Noncrossing timelike singularities of irrotational dust collapse
International Nuclear Information System (INIS)
Liang, E.P.T.
1979-01-01
Known naked singularities in spherical dust collapse are either due to shell-crossing or localized to the central world line. They will probably be destroyed by pressure gradients or blue-shift instabilities. To violate the cosmic censorship hypothesis in a more convincing and general context, collapse solutions with naked singularities that are at least nonshell-crossing and nonlocalized need to be constructed. Some results concerning the probable structure of a class of nonshellcrossing and nonlocalized timelike singularities are reviewed. The cylindrical dust model is considered but this model is not asymptotically flat. To make these noncrossing singularities viable counter examples to the cosmic censorship hypothesis, the occurrence of such singularities in asymptotically flat collapse needs to be demonstrated. (UK)
Singularity fitting in hydrodynamical calculations II
International Nuclear Information System (INIS)
Richtmyer, R.D.; Lazarus, R.B.
1975-09-01
This is the second report in a series on the development of techniques for the proper handling of singularities in fluid-dynamical calculations; the first was called Progress Report on the Shock-Fitting Project. This report contains six main results: derivation of a free-surface condition, which relates the acceleration of the surface with the gradient of the square of the sound speed just behind it; an accurate method for the early and middle stages of the development of a rarefaction wave, two orders of magnitude more accurate than a simple direct method used for comparison; the similarity theory of the collapsing free surface, where it is shown that there is a two-parameter family of self-similar solutions for γ = 3.9; the similarity theory for the outgoing shock, which takes into account the entropy increase; a ''zooming'' method for the study of the asymptotic behavior of solutions of the full initial boundary-value problem; comparison of two methods for determining the similarity parameter delta by zooming, which shows that the second method is preferred. Future reports in the series will contain discussions of the self-similar solutions for this problem, and for that of the collapsing shock, in more detail and for the full range (1, infinity) of γ; the values of certain integrals related to neutronic and thermonuclear rates near collapse; and methods for fitting shocks, contact discontinuities, interfaces, and free surfaces in two-dimensional flows
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...
Sediment problems in reservoirs. Control of sediment deposits
Energy Technology Data Exchange (ETDEWEB)
Jacobsen, Tom
1997-12-31
When a reservoir is formed on a river, sediment will deposit in the reservoir. Such processes are unfortunate, for instance, for the implementation of hydroelectric energy. This thesis studies the problem of reservoir sedimentation and discusses methods of removing the sediments. Various aspects of reservoir sedimentation are discussed. Anthropogenic impacts seem to greatly affect the erosion processes. Temporal distribution is uneven, mainly because of the very large flood events. A world map showing the Reservoir Capacity: Annual Sediment Inflow ratio for reservoirs with volume equal to 10% of annual inflow has been prepared. The map shows that sedimentation is severe in the western parts of North and South America, eastern, southern and northern Africa, parts of Australia and most of Asia. The development of medium-sized reservoirs is difficult, as they are too large for conventional flushing technique and too small to store the sediment that accumulates during their economic lifetime. A computer model, SSIIM, was used with good results in a case study of two flood drawdown trials in Lake Roxburg, New Zealand. Two techniques have been developed that permits controlled suction of sediment and water into a pipe: the Slotted Pipe Sediment Sluicer (SPSS) and the Saxophone Sediment Sluicer (SSS). The techniques exploit the inflow pattern in through a slot in a pipe. An equation describing this inflow pattern was derived and verified experimentally. The SPSS is fixed near the reservoir bed, and sediment that deposits on top of it is removed in the sluicing process. The SSS sluices sediment from the surface of the sediment deposits. Some technical and economic conditions affecting the economics of sediment removal from reservoirs have been identified and studied. 79 refs., 112 figs., 14 tabs.
Le probleme du controle de la liquidité en France. (The problem of controlling liquidity in France
Directory of Open Access Journals (Sweden)
H. FOURNIER
2014-07-01
Full Text Available The idea of liquidity in France finds expression in more or less the same way as in the other western countries. It is normal practice to distinguish between the “liquidity of the economy” on the one hand, and the “liquidity of the banking system” on the other. The former corresponds to the money supply, while the latter comprises the banks’ holdings of notes and coin and their balances on sight accounts with the Bank of France, together with the total amount of the items which they can put into the Bank of France. The methods of influencing liquidity are also similar to those employed in other countries. However, to make them easier to understand, the present article first recalls certain special features of France’s monetary institutions, namely the banks, the specialised institutions and the Treasury. The author then examines the duel problems of controlling the liquidity of the economy and bank liquidity.JEL: E51, E52, E58, G21
To the problem of electron temperature control in plasma
International Nuclear Information System (INIS)
Galechyan, G.A.; Anna, P.R.
1995-01-01
One of the main problems in low temperature plasma is control plasma parameters at fixed values of current and gas pressure in the discharge. It is known that an increase in the intensity of sound wave directed along the positive column to values in excess of a definite threshold leads to essential rise of the temperature of electrons. However, no less important is the reduction of electron temperature in the discharge down to the value less than that in plasma in the absence external influence. It is known that to reduce the electron temperature in the plasma of CO 2 laser, easily ionizable admixture are usually introduced in the discharge area with the view of increasing the overpopulation. In the present work we shall show that the value of electron temperature can be reduced by varying of sound wave intensity at its lower values. The experiment was performed on an experimental setup consisted of the tube with length 52 cm and diameter 9.8 cm, two electrodes placed at the distance of 27 cm from each other. An electrodynamical radiator of sound wave was fastened to one of tube ends. Fastened to the flange at the opposite end was a microphone for the control of sound wave parameters. The studies were performed in range of pressures from 40 to 180 Torr and discharge currents from 40 to 110 mA. The intensity of sound wave was varied from 74 to 92 dB. The measurement made at the first resonance frequency f = 150 Hz of sound in the discharge tube, at which a quarter of wave length keep within the length of the tube. The measurement of longitudinal electric field voltage in plasma of positive column was conducted with the help of two probes according to the compensation method. Besides, the measurement of gas temperature in the discharge were taken. Two thermocouple sensors were arranged at the distance of 8 cm from the anode, one of them being installed on the discharge tube axis, the second-fixed the tube wall
To the problem of electron temperature control in plasma
Energy Technology Data Exchange (ETDEWEB)
Galechyan, G.A. [Institute of Applied Problem of Physics, Yerevan (Armenia); Anna, P.R. [Raritan Valley Community College, Somerville, NJ (United States)
1995-12-31
One of the main problems in low temperature plasma is control plasma parameters at fixed values of current and gas pressure in the discharge. It is known that an increase in the intensity of sound wave directed along the positive column to values in excess of a definite threshold leads to essential rise of the temperature of electrons. However, no less important is the reduction of electron temperature in the discharge down to the value less than that in plasma in the absence external influence. It is known that to reduce the electron temperature in the plasma of CO{sub 2} laser, easily ionizable admixture are usually introduced in the discharge area with the view of increasing the overpopulation. In the present work we shall show that the value of electron temperature can be reduced by varying of sound wave intensity at its lower values. The experiment was performed on an experimental setup consisted of the tube with length 52 cm and diameter 9.8 cm, two electrodes placed at the distance of 27 cm from each other. An electrodynamical radiator of sound wave was fastened to one of tube ends. Fastened to the flange at the opposite end was a microphone for the control of sound wave parameters. The studies were performed in range of pressures from 40 to 180 Torr and discharge currents from 40 to 110 mA. The intensity of sound wave was varied from 74 to 92 dB. The measurement made at the first resonance frequency f = 150 Hz of sound in the discharge tube, at which a quarter of wave length keep within the length of the tube. The measurement of longitudinal electric field voltage in plasma of positive column was conducted with the help of two probes according to the compensation method. Besides, the measurement of gas temperature in the discharge were taken. Two thermocouple sensors were arranged at the distance of 8 cm from the anode, one of them being installed on the discharge tube axis, the second-fixed the tube wall.
DEFF Research Database (Denmark)
Wang, W.; Duan, Z.H.; Hanson, Steen Grüner
2006-01-01
By controlling the irradiance of an extended quasimonochromatic, spatially incoherent source, an optical field is generated that exhibits spatial coherence with phase singularities, called coherence vortices. A simple optical geometry for direct visualization of coherence vortices is proposed, an...
Minimal solution for inconsistent singular fuzzy matrix equations
Directory of Open Access Journals (Sweden)
M. Nikuie
2013-10-01
Full Text Available The fuzzy matrix equations $Ailde{X}=ilde{Y}$ is called a singular fuzzy matrix equations while the coefficients matrix of its equivalent crisp matrix equations be a singular matrix. The singular fuzzy matrix equations are divided into two parts: consistent singular matrix equations and inconsistent fuzzy matrix equations. In this paper, the inconsistent singular fuzzy matrix equations is studied and the effect of generalized inverses in finding minimal solution of an inconsistent singular fuzzy matrix equations are investigated.
Czech Academy of Sciences Publication Activity Database
Axelsson, Owe; Farouq, S.; Neytcheva, M.
2017-01-01
Roč. 310, January 2017 (2017), s. 5-18 ISSN 0377-0427 R&D Projects: GA MŠk ED1.1.00/02.0070 Institutional support: RVO:68145535 Keywords : optimal control * time-harmonic Stokes problem * preconditioning Subject RIV: BA - General Mathematics OBOR OECD: Applied mathematics Impact factor: 1.357, year: 2016 http://www. science direct.com/ science /article/pii/S0377042716302631?via%3Dihub
Czech Academy of Sciences Publication Activity Database
Axelsson, Owe; Farouq, S.; Neytcheva, M.
2017-01-01
Roč. 310, January 2017 (2017), s. 5-18 ISSN 0377-0427 R&D Projects: GA MŠk ED1.1.00/02.0070 Institutional support: RVO:68145535 Keywords : optimal control * time-harmonic Stokes problem * preconditioning Subject RIV: BA - General Mathematics OBOR OECD: Applied mathematics Impact factor: 1.357, year: 2016 http://www.sciencedirect.com/science/article/pii/S0377042716302631?via%3Dihub
Cosmological singularities in electrovacuum spacetimes with two-parameter spacelike isometry groups
International Nuclear Information System (INIS)
Mansfield, P.A.
1989-01-01
The big bang singularities occurring in an infinite-dimensional class of solutions to the source-free Einstein-Maxwell equations are presented. These solutions are essentially Gowdy three-torus universes (not necessarily polarized) with electromagnetic radiation added. The problem is reformulated in terms of complex potentials analogous to those used by Ernst in the study of stationary axisymmetric metrics. It is shown that in these new variables the problem admits a harmonic map formulation. Its general solution is written as a perturbation series, where the background solutions being perturbed are a special class of real analytic functions obtained by evolving analytic data specified right at the singularity. The perturbation problem is solved to all orders, and terms which dominate as the singularity is approached are identified at each order. It is possible to sum the dominant terms, and thereby obtain explicit expressions representing the asymptotic structure of the singularities. This representation of asymptotic structure is developed into a simple geometric model. Specializing to the case of no electromagnetic fields, the model is then used to determine asymptotic metric and curvature properties in Gowdy spacetimes. The Gowdy metrics are Kasner-like near their singularity, which is generically a curvature singularity. Curvature-nonsingular solutions can be constructed, and extended into the past beyond a Cauchy horizon. However, such solutions are unstable, a fact which is consistent with Strong Cosmic Censorship
An optimal control problem by controlling heat source of the surface of tissue
Dhar, 1Rikhiya; Dhar, Ranajit; Dhar, Piyanka
2013-01-01
A distributed optimal control problem for a system described by bio-heat equation for a homogeneous plane tissue is analytically investigated such that a desired temperature of the tissue at a particular point of location of tumour in hyperthermia can be attained at the end of a total time of operation of the process due to induced microwave on the surface of the tissue which is taken as control. Here the temperature of the tissue along the length of the tissue at different times of operation...
Kalman Filtering for Delayed Singular Systems with Multiplicative Noise
Institute of Scientific and Technical Information of China (English)
Xiao Lu; Linglong Wang; Haixia Wang; Xianghua Wang
2016-01-01
Kalman filtering problem for singular systems is dealt with,where the measurements consist of instantaneous measurements and delayed ones,and the plant includes multiplicative noise.By utilizing standard singular value decomposition,the restricted equivalent delayed system is presented,and the Kalman filters for the restricted equivalent system are given by using the well-known re-organization of innovation analysis lemma.The optimal Kalman filter for the original system is given based on the above Kalman filter by recursive Riccati equations,and a numerical example is presented to show the validity and efficiency of the proposed approach,where the comparison between the filter and predictor is also given.
Naked singularity in the global structure of critical collapse spacetimes
International Nuclear Information System (INIS)
Frolov, Andrei V.; Pen, U.-L.
2003-01-01
We examine the global structure of scalar field critical collapse spacetimes using a characteristic double-null code. It can integrate past the horizon without any coordinate problems, due to the careful choice of constraint equations used in the evolution. The limiting sequence of sub- and supercritical spacetimes presents an apparent paradox in the expected Penrose diagrams, which we address in this paper. We argue that the limiting spacetime converges pointwise to a unique limit for all r>0, but not uniformly. The r=0 line is different in the two limits. We interpret that the two different Penrose diagrams differ by a discontinuous gauge transformation. We conclude that the limiting spacetime possesses a singular event, with a future removable naked singularity
Quantum cosmology and late-time singularities
International Nuclear Information System (INIS)
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 behavior 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 of such modification on the nature and the existence of soft singularities. We review also quantum cosmology of models, where the initial quantum state of the universe is presented by the density matrix (mixed state). Finally, we discuss the exotic singularities arising in the braneworld cosmological models. (topical review)
Directory of Open Access Journals (Sweden)
Maria eHuber
2015-07-01
Full Text Available The aims of the present multi-center study were to investigate the extent of mental health problems in adolescents with a hearing loss and cochlear implants (CIs in comparison to normal hearing (NH peers and to investigate possible relations between the extent of mental health problems of young CI users and hearing variables, such as age at implantation, or functional gain of CI. The survey included 140 adolescents with CI (mean age = 14.7, SD = 1.5 years and 140 NH adolescents (mean age = 14.8, SD = 1.4 years, their parents and teachers. Participants were matched by age, gender and social background. Within the CI group, 35 adolescents were identified as risk cases due to possible and manifest additional handicaps, and 11 adolescents were non-classifiable. Mental health problems were assessed with the Strengths and Difficulties Questionnaire (SDQ in the versions Self, Parent, and Teacher. The CI group showed significantly more Peer Problems than the NH group. When the CI group was split into a risk-group (35 risk cases and 11 non-classifiable persons and a non-risk group (n = 94, increased peer problems were perceived in both CI subgroups by adolescents themselves. However, no further differences between the CI non-risk group and the NH group were observed in any rater. The CI-risk group showed significantly more hyperactivity compared to the NH group and more hyperactivity and conduct problems compared to the CI non-risk group. Cluster analyses confirmed that there were significantly more adolescents with high problems in the CI-risk group compared to the CI non-risk group and the NH group. Adolescents with CI, who were able to understand speech in noise had significantly less difficulties compared to constricted CI users. Parents, teachers, and clinicians should be aware that CI users with additionally special needs may have mental health problems. However, peer problems were also experienced by CI adolescents without additional handicaps
An inverse optimal control problem in the electrical discharge ...
Indian Academy of Sciences (India)
Marin Gostimirovic
2018-05-10
May 10, 2018 ... Keywords. EDM process; discharge energy; heat source parameters; inverse problem; optimization. 1. Introduction .... ation, thermal modeling of the EDM process would become ..... simulation of die-sinking EDM. CIRP Ann.
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.
Exact Controllability and Perturbation Analysis for Elastic Beams
International Nuclear Information System (INIS)
Moreles, Miguel Angel
2004-01-01
The Rayleigh beam is a perturbation of the Bernoulli-Euler beam. We establish convergence of the solution of the Exact Controllability Problem for the Rayleigh beam to the corresponding solution of the Bernoulli-Euler beam. Convergence is related to a Singular Perturbation Problem. The main tool in solving this perturbation problem is a weak version of a lower bound for hyperbolic polynomials
Control of systems with I/O delay via reduction to a one-block problem
Meinsma, Gjerrit; Mirkin, Leonid; Zhong, Qing-Chang
2002-01-01
In this paper, the standard (four-block) H/sup /spl infin// control problem for systems with a single delay in the feedback loop is studied. A simple procedure of the reduction of the problem to an equivalent one-block problem having particularly simple structure is proposed. The one-block problem
Directory of Open Access Journals (Sweden)
M. E. Haji Abadi
2013-09-01
Full Text Available In this paper, the continuous optimal control theory is used to model and solve the maximum entropy problem for a continuous random variable. The maximum entropy principle provides a method to obtain least-biased probability density function (Pdf estimation. In this paper, to find a closed form solution for the maximum entropy problem with any number of moment constraints, the entropy is considered as a functional measure and the moment constraints are considered as the state equations. Therefore, the Pdf estimation problem can be reformulated as the optimal control problem. Finally, the proposed method is applied to estimate the Pdf of the hourly electricity prices of New England and Ontario electricity markets. Obtained results show the efficiency of the proposed method.
Initial singularity and pure geometric field theories
Wanas, M. I.; Kamal, Mona M.; Dabash, Tahia F.
2018-01-01
In the present article we use a modified version of the geodesic equation, together with a modified version of the Raychaudhuri equation, to study initial singularities. These modified equations are used to account for the effect of the spin-torsion interaction on the existence of initial singularities in cosmological models. Such models are the results of solutions of the field equations of a class of field theories termed pure geometric. The geometric structure used in this study is an absolute parallelism structure satisfying the cosmological principle. It is shown that the existence of initial singularities is subject to some mathematical (geometric) conditions. The scheme suggested for this study can be easily generalized.
Transmutation of singularities in optical instruments
Energy Technology Data Exchange (ETDEWEB)
Tyc, Tomas [Institute of Theoretical Physics and Astrophysics, Masaryk University, Kotlarska 2, 61137 Brno (Czech Republic); Leonhardt, Ulf [School of Physics and Astronomy, University of St Andrews, North Haugh, St Andrews KY16 9SS (United Kingdom)], E-mail: tomtyc@physics.muni.cz
2008-11-15
We propose a method for eliminating a class of singularities in optical media where the refractive index goes to zero or infinity at one or more isolated points. Employing transformation optics, we find a refractive index distribution equivalent to the original one that is nonsingular but shows a slight anisotropy. In this way, the original singularity is 'transmuted' into another, weaker type of singularity where the permittivity and permeability tensors are discontinuous at one point. The method is likely to find applications in designing and improving optical devices by making them easier to implement or to operate in a broad band of the spectrum.
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 boundary perturbations of distributed systems
DEFF Research Database (Denmark)
Pedersen, Michael
1990-01-01
Some problems arising in real-life control applications are addressed--namely, problems concerning non-smooth control inputs on the boundary of the spatial domain. The classical variational approach is extended, and sufficient conditions are given for the solutions to continuous functions of time...
Optimal control problem for the extended Fisher–Kolmogorov equation
Indian Academy of Sciences (India)
by methods of optimal control, such as chemical engineering and vehicle ... ern optimal control theories and applied models are not only represented by .... Obviously, equation (2.5) is an ordinary differential equation and according to ODE.
Comments on `A discrete optimal control problem for descriptor systems'
DEFF Research Database (Denmark)
Ravn, Hans
1990-01-01
In the above-mentioned work (see ibid., vol.34, p.177-81 (1989)), necessary and sufficient optimality conditions are derived for a discrete-time optimal problem, as well as other specific cases of implicit and explicit dynamic systems. The commenter corrects a mistake and demonstrates that there ......In the above-mentioned work (see ibid., vol.34, p.177-81 (1989)), necessary and sufficient optimality conditions are derived for a discrete-time optimal problem, as well as other specific cases of implicit and explicit dynamic systems. The commenter corrects a mistake and demonstrates...
Energy conditions of non-singular black hole spacetimes in conformal gravity
Energy Technology Data Exchange (ETDEWEB)
Toshmatov, Bobir [Silesian University in Opava, Faculty of Philosophy and Science, Institute of Physics, Opava (Czech Republic); Ulugh Beg Astronomical Institute, Tashkent (Uzbekistan); Bambi, Cosimo [Fudan University, Department of Physics, Center for Field Theory and Particle Physics, Shanghai (China); Eberhard-Karls Universitaet Tuebingen, Theoretical Astrophysics, Tuebingen (Germany); Ahmedov, Bobomurat [Ulugh Beg Astronomical Institute, Tashkent (Uzbekistan); National University of Uzbekistan, Tashkent (Uzbekistan); Abdujabbarov, Ahmadjon [Ulugh Beg Astronomical Institute, Tashkent (Uzbekistan); National University of Uzbekistan, Tashkent (Uzbekistan); Tashkent University of Information Technologies, Tashkent (Uzbekistan); Stuchlik, Zdenek [Silesian University in Opava, Faculty of Philosophy and Science, Institute of Physics, Opava (Czech Republic)
2017-08-15
Conformal gravity can elegantly solve the problem of spacetime singularities present in Einstein's gravity. For every physical spacetime, there is an infinite family of conformally equivalent singularity-free metrics. In the unbroken phase, every non-singular metric is equivalent and can be used to infer the physical properties of the spacetime. In the broken phase, a Higgs-like mechanism should select a certain vacuum, which thus becomes the physical one. However, in the absence of the complete theoretical framework we do not know how to select the right vacuum. In this paper, we study the energy conditions of non-singular black hole spacetimes obtained in conformal gravity assuming they are solutions of Einstein's gravity with an effective energy-momentum tensor. We check whether such conditions can be helpful to select the vacuum of the broken phase. (orig.)
Energy conditions of non-singular black hole spacetimes in conformal gravity
International Nuclear Information System (INIS)
Toshmatov, Bobir; Bambi, Cosimo; Ahmedov, Bobomurat; Abdujabbarov, Ahmadjon; Stuchlik, Zdenek
2017-01-01
Conformal gravity can elegantly solve the problem of spacetime singularities present in Einstein's gravity. For every physical spacetime, there is an infinite family of conformally equivalent singularity-free metrics. In the unbroken phase, every non-singular metric is equivalent and can be used to infer the physical properties of the spacetime. In the broken phase, a Higgs-like mechanism should select a certain vacuum, which thus becomes the physical one. However, in the absence of the complete theoretical framework we do not know how to select the right vacuum. In this paper, we study the energy conditions of non-singular black hole spacetimes obtained in conformal gravity assuming they are solutions of Einstein's gravity with an effective energy-momentum tensor. We check whether such conditions can be helpful to select the vacuum of the broken phase. (orig.)
Irregular singularities in Liouville theory and Argyres-Douglas type gauge theories, I
Energy Technology Data Exchange (ETDEWEB)
Gaiotto, D. [Institute for Advanced Study (IAS), Princeton, NJ (United States); Teschner, J. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)
2012-03-15
Motivated by problems arising in the study of N=2 supersymmetric gauge theories we introduce and study irregular singularities in two-dimensional conformal field theory, here Liouville theory. Irregular singularities are associated to representations of the Virasoro algebra in which a subset of the annihilation part of the algebra act diagonally. In this paper we define natural bases for the space of conformal blocks in the presence of irregular singularities, describe how to calculate their series expansions, and how such conformal blocks can be constructed by some delicate limiting procedure from ordinary conformal blocks. This leads us to a proposal for the structure functions appearing in the decomposition of physical correlation functions with irregular singularities into conformal blocks. Taken together, we get a precise prediction for the partition functions of some Argyres-Douglas type theories on S{sup 4}. (orig.)
Transformations between Jordan and Einstein frames: Bounces, antigravity, and crossing singularities
Kamenshchik, Alexander Yu.; Pozdeeva, Ekaterina O.; Vernov, Sergey Yu.; Tronconi, Alessandro; Venturi, Giovanni
2016-09-01
We study the relation between the Jordan-Einstein frame transition and the possible description of the crossing of singularities in flat Friedmann universes, using the fact that the regular evolution in one frame can correspond to crossing singularities in the other frame. We show that some interesting effects arise in simple models such as one with a massless scalar field or another wherein the potential is constant in the Einstein frame. The dynamics in these models and in their conformally coupled counterparts are described in detail, and a method for the continuation of such cosmological evolutions beyond the singularity is developed. We compare our approach with some other, recently developed, approaches to the problem of the crossing of singularities.
Irregular singularities in Liouville theory and Argyres-Douglas type gauge theories, I
International Nuclear Information System (INIS)
Gaiotto, D.; Teschner, J.
2012-03-01
Motivated by problems arising in the study of N=2 supersymmetric gauge theories we introduce and study irregular singularities in two-dimensional conformal field theory, here Liouville theory. Irregular singularities are associated to representations of the Virasoro algebra in which a subset of the annihilation part of the algebra act diagonally. In this paper we define natural bases for the space of conformal blocks in the presence of irregular singularities, describe how to calculate their series expansions, and how such conformal blocks can be constructed by some delicate limiting procedure from ordinary conformal blocks. This leads us to a proposal for the structure functions appearing in the decomposition of physical correlation functions with irregular singularities into conformal blocks. Taken together, we get a precise prediction for the partition functions of some Argyres-Douglas type theories on S 4 . (orig.)
Short time propagation of a singular wave function: Some surprising results
Marchewka, A.; Granot, E.; Schuss, Z.
2007-08-01
The Schrödinger evolution of an initially singular wave function was investigated. First it was shown that a wide range of physical problems can be described by initially singular wave function. Then it was demonstrated that outside the support of the initial wave function the time evolution is governed to leading order by the values of the wave function and its derivatives at the singular points. Short-time universality appears where it depends only on a single parameter—the value at the singular point (not even on its derivatives). It was also demonstrated that the short-time evolution in the presence of an absorptive potential is different than in the presence of a nonabsorptive one. Therefore, this dynamics can be harnessed to the determination whether a potential is absorptive or not simply by measuring only the transmitted particles density.
Common Occupational Health Problems In Disease Control In Nigeria
African Journals Online (AJOL)
This article reviews some common occupational health problems among health workers due to exposure to hazardous or pathogenic biological, chemical and physical agents in the line of duty. Highlighted biological agents are pathogenic viruses, bacteria etc; chemical agents are laboratory reagents, mercury and ...
Are marketing students in control in problem-based learning?
Geitz, Gerry; Joosten-ten Brinke, Desirée; Kirschner, Paul A.
2018-01-01
This study investigated to what extent self-efficacy, learning behavior, and performance outcomes relate to each other and how they can be positively influenced by students asking for and seeking feedback within a problem-based learning (PBL) environment in order to meet today’s requirements of
Singularities in cosmologies with interacting fluids
International Nuclear Information System (INIS)
Cotsakis, Spiros; Kittou, Georgia
2012-01-01
We study the dynamics near finite-time singularities of flat isotropic universes filled with two interacting but otherwise arbitrary perfect fluids. The overall dynamical picture reveals a variety of asymptotic solutions valid locally around the spacetime singularity. We find the attractor of all solutions with standard decay, and for ‘phantom’ matter asymptotically at early times. We give a number of special asymptotic solutions describing universes collapsing to zero size and others ending at a big rip singularity. We also find a very complicated singularity corresponding to a logarithmic branch point that resembles a cyclic universe, and give an asymptotic local series representation of the general solution in the neighborhood of infinity.
Singularities: the state of the art
International Nuclear Information System (INIS)
Clarke, C.J.S.; Schmidt, B.G.
1977-01-01
A brief, but precise and unified account is given of the results that have been rigorously established at the time of writing concerning the existence and nature of singularities in classical relativity. (author)
Technological Singularity: What Do We Really Know?
Directory of Open Access Journals (Sweden)
Alexey Potapov
2018-04-01
Full Text Available The concept of the technological singularity is frequently reified. Futurist forecasts inferred from this imprecise reification are then criticized, and the reified ideas are incorporated in the core concept. In this paper, I try to disentangle the facts related to the technological singularity from more speculative beliefs about the possibility of creating artificial general intelligence. I use the theory of metasystem transitions and the concept of universal evolution to analyze some misconceptions about the technological singularity. While it may be neither purely technological, nor truly singular, we can predict that the next transition will take place, and that the emerged metasystem will demonstrate exponential growth in complexity with a doubling time of less than half a year, exceeding the complexity of the existing cybernetic systems in few decades.
Algunas aclaraciones acerca del conocimiento del singular.
Directory of Open Access Journals (Sweden)
Carlos Llano Cifuentes
2013-11-01
Full Text Available Llano tries to explain the main purpose of El Conocimiento del Singular, showing how the individuals about which the book is concerned are basically human individuals: people as decision makers.
Topological Signals of Singularities in Ricci Flow
Directory of Open Access Journals (Sweden)
Paul M. Alsing
2017-08-01
Full Text Available We implement methods from computational homology to obtain a topological signal of singularity formation in a selection of geometries evolved numerically by Ricci flow. Our approach, based on persistent homology, produces precise, quantitative measures describing the behavior of an entire collection of data across a discrete sample of times. We analyze the topological signals of geometric criticality obtained numerically from the application of persistent homology to models manifesting singularities under Ricci flow. The results we obtain for these numerical models suggest that the topological signals distinguish global singularity formation (collapse to a round point from local singularity formation (neckpinch. Finally, we discuss the interpretation and implication of these results and future applications.
Asymptotic safety, singularities, and gravitational collapse
International Nuclear Information System (INIS)
Casadio, Roberto; Hsu, Stephen D.H.; Mirza, Behrouz
2011-01-01
Asymptotic safety (an ultraviolet fixed point with finite-dimensional critical surface) offers the possibility that a predictive theory of quantum gravity can be obtained from the quantization of classical general relativity. However, it is unclear what becomes of the singularities of classical general relativity, which, it is hoped, might be resolved by quantum effects. We study dust collapse with a running gravitational coupling and find that a future singularity can be avoided if the coupling becomes exactly zero at some finite energy scale. The singularity can also be avoided (pushed off to infinite proper time) if the coupling approaches zero sufficiently rapidly at high energies. However, the evolution deduced from perturbation theory still implies a singularity at finite proper time.
Self-teaching neural network learns difficult reactor control problem
International Nuclear Information System (INIS)
Jouse, W.C.
1989-01-01
A self-teaching neural network used as an adaptive controller quickly learns to control an unstable reactor configuration. The network models the behavior of a human operator. It is trained by allowing it to operate the reactivity control impulsively. It is punished whenever either the power or fuel temperature stray outside technical limits. Using a simple paradigm, the network constructs an internal representation of the punishment and of the reactor system. The reactor is constrained to small power orbits
On Borel singularities in quantum field theory
International Nuclear Information System (INIS)
Chadha, S.; Olesen, P.
1977-10-01
The authors consider the effective one-loop Lagrangian in a constant electric field. It is shown that perturbation theory behaves as n factorial giving rise to singularities in the Borel plane. Comparing with the known exact result it is shown how to integrate these singularities. It is suggested that renormalons in QED and QCD should be integrated in a similar way. A speculation is made on a possible interpretation of this integration. (Auth.)
Singularity theorems from weakened energy conditions
International Nuclear Information System (INIS)
Fewster, Christopher J; Galloway, Gregory J
2011-01-01
We establish analogues of the Hawking and Penrose singularity theorems based on (a) averaged energy conditions with exponential damping; (b) conditions on local stress-energy averages inspired by the quantum energy inequalities satisfied by a number of quantum field theories. As particular applications, we establish singularity theorems for the Einstein equations coupled to a classical scalar field, which violates the strong energy condition, and the nonminimally coupled scalar field, which also violates the null energy condition.
International Nuclear Information System (INIS)
Xunjing, L.
1981-12-01
The vector-valued measure defined by the well-posed linear boundary value problems is discussed. The maximum principle of the optimal control problem with non-convex constraint is proved by using the vector-valued measure. Especially, the necessary conditions of the optimal control of elliptic systems is derived without the convexity of the control domain and the cost function. (author)
Numerical Methods for Solution of the Extended Linear Quadratic Control Problem
DEFF Research Database (Denmark)
Jørgensen, John Bagterp; Frison, Gianluca; Gade-Nielsen, Nicolai Fog
2012-01-01
In this paper we present the extended linear quadratic control problem, its efficient solution, and a discussion of how it arises in the numerical solution of nonlinear model predictive control problems. The extended linear quadratic control problem is the optimal control problem corresponding...... to the Karush-Kuhn-Tucker system that constitute the majority of computational work in constrained nonlinear and linear model predictive control problems solved by efficient MPC-tailored interior-point and active-set algorithms. We state various methods of solving the extended linear quadratic control problem...... and discuss instances in which it arises. The methods discussed in the paper have been implemented in efficient C code for both CPUs and GPUs for a number of test examples....
Enclothed Cognition and Controlled Attention during Insight Problem-Solving
Van Stockum, Charles A., Jr.; DeCaro, Marci S.
2014-01-01
Individual differences in working memory capacity (WMC) increase the ability and tendency to devote greater attentional control to a task--improving performance on a wide range of skills. In addition, recent research on enclothed cognition demonstrates that the situational influence of wearing a white lab coat increases controlled attention, due…
Chaos controlling problems for circuit systems with Josephson junction
International Nuclear Information System (INIS)
Gou, X-F; Wang, X; Xie, J-L
2008-01-01
The complex dynamical characters of the Josephson junction circuit system are studied and the tunnel effect is considered. The dynamical equation of the system is established. The route from periodic motion to chaos is illustrated using bifurcation diagram. An adscititious coupling controller is constructed to control the chaos
Behavior Self-Control and the Contract Problem.
Worthington, Everett L.
1979-01-01
Describes study to determine the success of university students' behavioral self-control projects. Results indicate that the teaching of self-control principles is easily integrated into personal adjustment classes and can have lasting effects on students' coping skills. (KC)
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.)
Observational constraints on cosmological future singularities
International Nuclear Information System (INIS)
Beltran Jimenez, Jose; Lazkoz, Ruth; Saez-Gomez, Diego; Salzano, Vincenzo
2016-01-01
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.)
Removal of apparent singularity in grid computations
International Nuclear Information System (INIS)
Jakubovics, J.P.
1993-01-01
A self-consistency test for magnetic domain wall models was suggested by Aharoni. The test consists of evaluating the ratio S = var-epsilon wall /var-epsilon wall , where var-epsilon wall is the wall energy, and var-epsilon wall is the integral of a certain function of the direction cosines of the magnetization, α, β, γ over the volume occupied by the domain wall. If the computed configuration is a good approximation to one corresponding to an energy minimum, the ratio is close to 1. The integrand of var-epsilon wall contains terms that are inversely proportional to γ. Since γ passes through zero at the centre of the domain wall, these terms have a singularity at these points. The integral is finite and its evaluation does not usually present any problems when the direction cosines are known in terms of continuous functions. In many cases, significantly better results for magnetization configurations of domain walls can be obtained by computations using finite element methods. The direction cosines are then only known at a set of discrete points, and integration over the domain wall is replaced by summation over these points. Evaluation of var-epsilon wall becomes inaccurate if the terms in the summation are taken to be the values of the integrand at the grid points, because of the large contribution of points close to where γ changes sign. The self-consistency test has recently been generalised to a larger number of cases. The purpose of this paper is to suggest a method of improving the accuracy of the evaluation of integrals in such cases. Since the self-consistency test has so far only been applied to two-dimensional magnetization configurations, the problem and its solution will be presented for that specific case. Generalisation to three or more dimensions is straight forward
Singular Hopf bifurcation in a differential equation with large state-dependent delay.
Kozyreff, G; Erneux, T
2014-02-08
We study the onset of sustained oscillations in a classical state-dependent delay (SDD) differential equation inspired by control theory. Owing to the large delays considered, the Hopf bifurcation is singular and the oscillations rapidly acquire a sawtooth profile past the instability threshold. Using asymptotic techniques, we explicitly capture the gradual change from nearly sinusoidal to sawtooth oscillations. The dependence of the delay on the solution can be either linear or nonlinear, with at least quadratic dependence. In the former case, an asymptotic connection is made with the Rayleigh oscillator. In the latter, van der Pol's equation is derived for the small-amplitude oscillations. SDD differential equations are currently the subject of intense research in order to establish or amend general theorems valid for constant-delay differential equation, but explicit analytical construction of solutions are rare. This paper illustrates the use of singular perturbation techniques and the unusual way in which solvability conditions can arise for SDD problems with large delays.
A Benchmark Environment Motivated by Industrial Control Problems
Hein, Daniel; Depeweg, Stefan; Tokic, Michel; Udluft, Steffen; Hentschel, Alexander; Runkler, Thomas A.; Sterzing, Volkmar
2017-01-01
In the research area of reinforcement learning (RL), frequently novel and promising methods are developed and introduced to the RL community. However, although many researchers are keen to apply their methods on real-world problems, implementing such methods in real industry environments often is a frustrating and tedious process. Generally, academic research groups have only limited access to real industrial data and applications. For this reason, new methods are usually developed, evaluated...
The effect of high and low assertiveness on locus of control and health problems.
Williams, J M; Stout, J K
1985-03-01
The effect of high and low assertiveness on locus of control and health problems was examined with 78 direct-service workers in mental health and mental retardation settings in northeastern Pennsylvania. The direct-service workers completed the Rathus (1973) Assertiveness Schedule, the Rotter (1966) Internal-External Locus of Control Scale, and a health-problems inventory. Highly assertive individuals were found to be more internally controlled and to experience fewer health problems than were individuals low in assertiveness.
Naked singularities and cosmic censorship: comment on the current situation
International Nuclear Information System (INIS)
Seifert, H.J.
1979-01-01
The current discussion is mainly concerned with how, or indeed, whether space-times possessing naked singularities can be ruled out as being too unrealistic or not being singular at all. The present position is summarized, with references, under the following headings: the Hawking-Penrose existence theorems, hydrodynamical singularities and the strength of naked singularities. (UK)
On the problem of quantum control in infinite dimensions
Mendes, R. Vilela; Man'ko, Vladimir I.
2010-01-01
In the framework of bilinear control of the Schr\\"odinger equation with bounded control operators, it has been proved that the reachable set has a dense complemement in ${\\cal S}\\cap {\\cal H}^{2}$. Hence, in this setting, exact quantum control in infinite dimensions is not possible. On the other hand it is known that there is a simple choice of operators which, when applied to an arbitrary state, generate dense orbits in Hilbert space. Compatibility of these two results is established in this...
Directory of Open Access Journals (Sweden)
José M. Sánchez Vázqez
2006-12-01
Full Text Available As part of the supply chain, manufacturing firms are increasingly placing greater emphasis on the management of their outsourced distribution channels (DCs. However, the role that interorganizational Management Control Systems (MCS can play in managing DC problems is still not clearly understood. Through an exploratory case study, we show how intra-organizational control problems persist in an inter-organizational context, rooted in informational asymmetries and conflicts of interest and aggravated by interdependencies. Likewise, the case study illustrates the way in which MCS assists the manufacturing firm to communicate to its representatives what the organization wants from them, motivating them and transferring capabilities. Thus, MCS can help to complement and re-orientate inter-firm agreements and constitutes a key tool for managing DCs in a flexible way.Como parte de la cadena de suministros, las empresas productoras están poniendo mayor énfasis en la gestión de sus canales de distribución externalizados (DCs. Sin embargo, aún no existe una clara comprensión sobre el papel que los Sistemas de Control de Gestión inter-organizativos (MCS pueden desarrollar en la gestión de los problemas de los DCs. A través de un estudio de caso, se muestra cómo los problemas de control intra-organizativos persisten en un contexto inter-organizativo, causados por las asimetrías informativas y el conflicto de intereses, y agravándose por las interdependencias. Asimismo, se expone cómo los MCS ayudan a la empresa productora a comunicar a sus distribuidores lo que la organización desea de ellos, motivándolos y capacitándolos. De esta forma, los MCS pueden ayudar a completar y redirigir acuerdos entre firmas y constituir una herramienta clave en la gestión flexible de los DCs.
DEFF Research Database (Denmark)
Hansen, Lars Jørgen; Olivarius, Niels de Fine; Beich, Anders
1999-01-01
intervention, problem drinking, randomized controlled trial, family practice, marketing of health services......intervention, problem drinking, randomized controlled trial, family practice, marketing of health services...
The Accountable Animal : Naturalising the management control problem
P.I. Eskenazi (Philip)
2015-01-01
markdownabstract__Abstract__ In this dissertation we investigate two themes around the topic of social relations in management control structures. We use developments in neuroscience and eye-tracking to supplement the traditional psychological and economic perspective on management
Uncertainty Quantification in Control Problems for Flocking Models
Directory of Open Access Journals (Sweden)
Giacomo Albi
2015-01-01
Full Text Available The optimal control of flocking models with random inputs is investigated from a numerical point of view. The effect of uncertainty in the interaction parameters is studied for a Cucker-Smale type model using a generalized polynomial chaos (gPC approach. Numerical evidence of threshold effects in the alignment dynamic due to the random parameters is given. The use of a selective model predictive control permits steering of the system towards the desired state even in unstable regimes.
Tomar, S.K.
2002-01-01
It is well known that elliptic problems when posed on non-smooth domains, develop singularities. We examine such problems within the framework of spectral element methods and resolve the singularities with exponential accuracy.
Safety problems in vehicles with adaptive cruise control system
Directory of Open Access Journals (Sweden)
Yadav Arun K.
2017-06-01
Full Text Available In today’s world automotive industries are still putting efforts towards more autonomous vehicles (AVs. The main concern of introducing the autonomous technology is safety of driver. According to a survey 90% of accidents happen due to mistake of driver. The adaptive cruise control system (ACC is a system which combines cruise control with a collision avoidance system. The ACC system is based on laser and radar technologies. This system is capable of controlling the velocity of vehicle automatically to match the velocity of car, bus or truck in front of vehicle. If the lead vehicle gets slow down or accelerate, than ACC system automatically matches that velocity. The proposed paper is focusing on more accurate methods of detecting the preceding vehicle by using a radar and lidar sensors by considering the vehicle side slip and by controlling the distance between two vehicles. By using this approach i.e. logic for calculation of former vehicle distance and controlling the throttle valve of ACC equipped vehicle, an improvement in driving stability was achieved. The own contribution results with fuel efficient driving and with more safer and reliable driving system, but still some improvements are going on to make it more safe and reliable.
Abdulhameed, M.; Vieru, D.; Roslan, R.
2017-10-01
This paper investigates the electro-magneto-hydrodynamic flow of the non-Newtonian behavior of biofluids, with heat transfer, through a cylindrical microchannel. The fluid is acted by an arbitrary time-dependent pressure gradient, an external electric field and an external magnetic field. The governing equations are considered as fractional partial differential equations based on the Caputo-Fabrizio time-fractional derivatives without singular kernel. The usefulness of fractional calculus to study fluid flows or heat and mass transfer phenomena was proven. Several experimental measurements led to conclusion that, in such problems, the models described by fractional differential equations are more suitable. The most common time-fractional derivative used in Continuum Mechanics is Caputo derivative. However, two disadvantages appear when this derivative is used. First, the definition kernel is a singular function and, secondly, the analytical expressions of the problem solutions are expressed by generalized functions (Mittag-Leffler, Lorenzo-Hartley, Robotnov, etc.) which, generally, are not adequate to numerical calculations. The new time-fractional derivative Caputo-Fabrizio, without singular kernel, is more suitable to solve various theoretical and practical problems which involve fractional differential equations. Using the Caputo-Fabrizio derivative, calculations are simpler and, the obtained solutions are expressed by elementary functions. Analytical solutions of the biofluid velocity and thermal transport are obtained by means of the Laplace and finite Hankel transforms. The influence of the fractional parameter, Eckert number and Joule heating parameter on the biofluid velocity and thermal transport are numerically analyzed and graphic presented. This fact can be an important in Biochip technology, thus making it possible to use this analysis technique extremely effective to control bioliquid samples of nanovolumes in microfluidic devices used for biological
Cosmologies with quasiregular singularities. II. Stability considerations
International Nuclear Information System (INIS)
Konkowski, D.A.; Helliwell, T.M.
1985-01-01
The stability properties of a class of spacetimes with quasiregular singularities is discussed. Quasiregular singularities are the end points of incomplete, inextendible geodesics at which the Riemann tensor and its derivatives remain at least bounded in all parallel-propagated orthonormal (PPON) frames; observers approaching such a singularity would find that their world lines come to an end in a finite proper time. The Taub-NUT (Newman-Unti-Tamburino)-type cosmologies investigated are R 1 x T 3 and R 3 x S 1 flat Kasner spacetimes, the two-parameter family of spatially homogeneous but anisotropic Bianchi type-IX Taub-NUT spacetimes, and an infinite-dimensional family of Einstein-Rosen-Gowdy spacetimes studied by Moncrief. The behavior of matter near the quasiregular singularity in each of these spacetimes is explored through an examination of the behavior of the stress-energy tensors and scalars for conformally coupled and minimally coupled, massive and massless scalar waves as observed in both coordinate and PPON frames. A conjecture is postulated concerning the stability of the nature of the singularity in these spacetimes. The conjecture for a Taub-NUT-type background spacetime is that if a test-field stress-energy tensor evaluated in a PPON frame mimics the behavior of the Riemann tensor components which indicate a particular type of singularity (quasiregular, nonscalar curvature, or scalar curvature), then a complete nonlinear backreaction calculation, in which the fields are allowed to influence the geometry, would show that this type of singularity actually occurs. Evidence supporting the conjecture is presented for spacetimes whose symmetries are unchanged when fields with the same symmetries are added
Identifying Initial Condition in Degenerate Parabolic Equation with Singular Potential
Directory of Open Access Journals (Sweden)
K. Atifi
2017-01-01
Full Text Available A hybrid algorithm and regularization method are proposed, for the first time, to solve the one-dimensional degenerate inverse heat conduction problem to estimate the initial temperature distribution from point measurements. The evolution of the heat is given by a degenerate parabolic equation with singular potential. This problem can be formulated in a least-squares framework, an iterative procedure which minimizes the difference between the given measurements and the value at sensor locations of a reconstructed field. The mathematical model leads to a nonconvex minimization problem. To solve it, we prove the existence of at least one solution of problem and we propose two approaches: the first is based on a Tikhonov regularization, while the second approach is based on a hybrid genetic algorithm (married genetic with descent method type gradient. Some numerical experiments are given.
Brief telephone interventions for problem gambling: a randomized controlled trial.
Abbott, Max; Hodgins, David C; Bellringer, Maria; Vandal, Alain C; Palmer Du Preez, Katie; Landon, Jason; Sullivan, Sean; Rodda, Simone; Feigin, Valery
2018-05-01
Problem gambling is a significant public health issue world-wide. There is substantial investment in publicly funded intervention services, but limited evaluation of effectiveness. This study investigated three brief telephone interventions to determine whether they were more effective than standard helpline treatment in helping people to reduce gambling. Randomized clinical trial. National gambling helpline in New Zealand. A total of 462 adults with problem gambling. INTERVENTIONS AND COMPARATOR: (1) Single motivational interview (MI), (2) single motivational interview plus cognitive-behavioural self-help workbook (MI + W) and (3) single motivational interview plus workbook plus four booster follow-up telephone interviews (MI + W + B). Comparator was helpline standard care [treatment as usual (TAU)]. Blinded follow-up was at 3, 6 and 12 months. Primary outcomes were days gambled, dollars lost per day and treatment goal success. There were no differences across treatment arms, although participants showed large reductions in gambling during the 12-month follow-up period [mean reduction of 5.5 days, confidence interval (CI) = 4.8, 6.2; NZ$38 lost ($32, $44; 80.6%), improved (77.2%, 84.0%)]. Subgroup analysis revealed improved days gambled and dollars lost for MI + W + B over MI or MI + W for a goal of reduction of gambling (versus quitting) and improvement in dollars lost by ethnicity, gambling severity and psychological distress (all P gambling severity than TAU or MI at 12 months and also better for those with higher psychological distress and lower self-efficacy to MI (all P gambling in New Zealand, brief telephone interventions are associated with changes in days gambling and dollars lost similar to more intensive interventions, suggesting that more treatment is not necessarily better than less. Some client subgroups, in particular those with greater problem severity and greater distress, achieve better outcomes when they receive more
Directory of Open Access Journals (Sweden)
Nikita Agarwal
2017-07-01
Full Text Available In this article, we study the approximate controllability and homegenization results of a semi-linear elliptic problem with Robin boundary condition in a periodically perforated domain. We prove the existence of minimal norm control using Lions constructive approach, which is based on Fenchel-Rockafeller duality theory, and by means of Zuazua's fixed point arguments. Then, as the homogenization parameter goes to zero, we link the limit of the optimal controls (the limit of fixed point of the controllability problems with the optimal control of the corresponding homogenized problem.
General problems of dynamics and control of vibratory gyroscopes
CSIR Research Space (South Africa)
Shatalov, MY
2008-05-01
Full Text Available A general model of operation of vibratory gyroscopes, which is applicable to a broad class of instruments, including cylindrical, disc and micro-machined gyros, is formulated on the basis of analysis of dynamics and control of a hemispherical...
van Woezik, Anne F. G.; Braakman-Jansen, Louise M. A.; Kulyk, Olga; Siemons, Liseth; van Gemert-Pijnen, Julia E. W. C.
2016-01-01
Background: Infection prevention and control can be seen as a wicked public health problem as there is no consensus regarding problem definition and solution, multiple stakeholders with different needs and values are involved, and there is no clear end-point of the problem-solving process.
van Woezik, Anne; Braakman-Jansen, Louise Marie Antoinette; Kulyk, Olga Anatoliyivna; Tjin-Kam-Jet-Siemons, Liseth; van Gemert-Pijnen, Julia E.W.C.
2016-01-01
Background Infection prevention and control can be seen as a wicked public health problem as there is no consensus regarding problem definition and solution, multiple stakeholders with different needs and values are involved, and there is no clear end-point of the problem-solving process.
Problems Of Resource Control In Nigeria And The Way Forward ...
African Journals Online (AJOL)
In recent times, the issues of Resources Control in Nigeria have generated a lot of controversies. In discussing these issues, this paper focuses primarily on Crude Oil and its allied products from an historic standpoint, the issues of Federalism, Inter-governmental Relations in Nigeria, Fiscal federalism and the distribution of ...
Luo, Jianhua; Mou, Zhiying; Qin, Binjie; Li, Wanqing; Ogunbona, Philip; Robini, Marc C; Zhu, Yuemin
2017-12-09
Reconstructing magnetic resonance images from undersampled k-space data is a challenging problem. This paper introduces a novel method of image reconstruction from undersampled k-space data based on the concept of singularizing operators and a novel singular k-space model. Exploring the sparsity of an image in the k-space, the singular k-space model (SKM) is proposed in terms of the k-space functions of a singularizing operator. The singularizing operator is constructed by combining basic difference operators. An algorithm is developed to reliably estimate the model parameters from undersampled k-space data. The estimated parameters are then used to recover the missing k-space data through the model, subsequently achieving high-quality reconstruction of the image using inverse Fourier transform. Experiments on physical phantom and real brain MR images have shown that the proposed SKM method constantly outperforms the popular total variation (TV) and the classical zero-filling (ZF) methods regardless of the undersampling rates, the noise levels, and the image structures. For the same objective quality of the reconstructed images, the proposed method requires much less k-space data than the TV method. The SKM method is an effective method for fast MRI reconstruction from the undersampled k-space data. Graphical abstract Two Real Images and their sparsified images by singularizing operator.
Novel Remarks on Point Mass Sources, Firewalls, Null Singularities and Gravitational Entropy
Perelman, Carlos Castro
2016-01-01
A continuous family of static spherically symmetric solutions of Einstein's vacuum field equations with a spatial singularity at the origin r = 0 is found. These solutions are parametrized by a real valued parameter λ (ranging from 0 to 1) and such that the radial horizon's location is displaced continuously towards the singularity ( r = 0 ) as λ increases. In the extreme limit λ = 1, the location of the singularity and horizon merges leading to a null singularity. In this extreme case, any infalling observer hits the null singularity at the very moment he/she crosses the horizon. This fact may have important consequences for the resolution of the fire wall problem and the complementarity controversy in black holes. An heuristic argument is provided how one might avoid the Hawking particle emission process in this extreme case when the singularity and horizon merges. The field equations due to a delta-function point-mass source at r = 0 are solved and the Euclidean gravitational action corresponding to those solutions is evaluated explicitly. It is found that the Euclidean action is precisely equal to the black hole entropy (in Planck area units). This result holds in any dimensions D ≥ 3.
Control room annunciation - problem assessment and selection of improvement priorities
International Nuclear Information System (INIS)
Hartley, P.; Yaraskavitch, E.; Davey, E.
1998-01-01
In 1997, Pickering B undertook a project to examine current annunciation practice and identify improvement opportunities and priorities. The objectives and scope of the study were to: document the deficiencies with control room annunciation and the subsequent operational and financial impacts to station operations, develop an operations-based definition of the requirements for annunciation to adequately support control room staff, propose annunciation improvements based on a comparison of the annunciation deficiencies identified and the operational needs to be met, assess the relative operational impact, and financial benefits and costs of the improvement initiatives proposed, and recommend annunciation improvement priorities that offer a mix of operational and financial return for improvement investment. This paper discusses the rationale for the project, outlines the approaches applied in achieving the assessment objectives, reviews the key assessment findings and describes the improvement initiatives recommended. (author)
Asymmetric forecasting and commitment policy in a robust control problem
Taro Ikeda
2013-01-01
This paper provides a piece of results regarding asymmetric forecasting and commitment monetary policy with a robust control algorithm. Previous studies provide no clarification of the connection between asymmetric preference and robust commitment policy. Three results emerge from general equilibrium modeling with asymmetric preference: (i) the condition for system stability implies an average inflation bias with respect to asymmetry (ii) the effect of asymmetry can be mitigated if policy mak...
Parallel Implementation of Riccati Recursion for Solving Linear-Quadratic Control Problems
DEFF Research Database (Denmark)
Frison, Gianluca; Jørgensen, John Bagterp
2013-01-01
In both Active-Set (AS) and Interior-Point (IP) algorithms for Model Predictive Control (MPC), sub-problems in the form of linear-quadratic (LQ) control problems need to be solved at each iteration. The solution of these sub-problems is usually the main computational effort. In this paper...... an alternative version of the Riccati recursion solver for LQ control problems is presented. The performance of both the classical and the alternative version is analyzed from a theoretical as well as a numerical point of view, and the alternative version is found to be approximately 50% faster than...
Efficient Implementation of the Riccati Recursion for Solving Linear-Quadratic Control Problems
DEFF Research Database (Denmark)
Frison, Gianluca; Jørgensen, John Bagterp
2013-01-01
In both Active-Set (AS) and Interior-Point (IP) algorithms for Model Predictive Control (MPC), sub-problems in the form of linear-quadratic (LQ) control problems need to be solved at each iteration. The solution of these sub-problems is typically the main computational effort at each iteration....... In this paper, we compare a number of solvers for an extended formulation of the LQ control problem: a Riccati recursion based solver can be considered the best choice for the general problem with dense matrices. Furthermore, we present a novel version of the Riccati solver, that makes use of the Cholesky...... factorization of the Pn matrices to reduce the number of flops. When combined with regularization and mixed precision, this algorithm can solve large instances of the LQ control problem up to 3 times faster than the classical Riccati solver....
Directory of Open Access Journals (Sweden)
Sie Long Kek
2015-01-01
Full Text Available A computational approach is proposed for solving the discrete time nonlinear stochastic optimal control problem. Our aim is to obtain the optimal output solution of the original optimal control problem through solving the simplified model-based optimal control problem iteratively. In our approach, the adjusted parameters are introduced into the model used such that the differences between the real system and the model used can be computed. Particularly, system optimization and parameter estimation are integrated interactively. On the other hand, the output is measured from the real plant and is fed back into the parameter estimation problem to establish a matching scheme. During the calculation procedure, the iterative solution is updated in order to approximate the true optimal solution of the original optimal control problem despite model-reality differences. For illustration, a wastewater treatment problem is studied and the results show the efficiency of the approach proposed.
Scheduling and control strategies for the departure problem in air traffic control
Bolender, Michael Alan
Two problems relating to the departure problem in air traffic control automation are examined. The first problem that is addressed is the scheduling of aircraft for departure. The departure operations at a major US hub airport are analyzed, and a discrete event simulation of the departure operations is constructed. Specifically, the case where there is a single departure runway is considered. The runway is fed by two queues of aircraft. Each queue, in turn, is fed by a single taxiway. Two salient areas regarding scheduling are addressed. The first is the construction of optimal departure sequences for the aircraft that are queued. Several greedy search algorithms are designed to minimize the total time to depart a set of queued aircraft. Each algorithm has a different set of heuristic rules to resolve situations within the search space whenever two branches of the search tree with equal edge costs are encountered. These algorithms are then compared and contrasted with a genetic search algorithm in order to assess the performance of the heuristics. This is done in the context of a static departure problem where the length of the departure queue is fixed. A greedy algorithm which deepens the search whenever two branches of the search tree with non-unique costs are encountered is shown to outperform the other heuristic algorithms. This search strategy is then implemented in the discrete event simulation. A baseline performance level is established, and a sensitivity analysis is performed by implementing changes in traffic mix, routing, and miles-in-trail restrictions for comparison. It is concluded that to minimize the average time spent in the queue for different traffic conditions, a queue assignment algorithm is needed to maintain an even balance of aircraft in the queues. A necessary consideration is to base queue assignment upon traffic management restrictions such as miles-in-trail constraints. The second problem addresses the technical challenges associated
Sleep and metabolic control: waking to a problem?
Trenell, Michael I; Marshall, Nathaniel S; Rogers, Naomi L
2007-01-01
1. The aim of the present review is to outline: (i) the association between sleep and metabolism; (ii) how sleep duration influences the development of disease; and (iii) how sex differences, ageing and obesity may potentially influence the relationship between sleep, metabolic control and subsequent disease. 2. Sleep is associated with a number of endocrine changes, including a change in insulin action in healthy young individuals. Sleep duration shows a prospective U-shaped relationship with all-cause mortality, cardiovascular disease and Type 2 diabetes. 3. Chronic sleep restriction is becoming more common. Experimental sleep restriction impedes daytime glucose control and increases appetite. 4. The sex hormones oestrogen and testosterone influence sleep duration and quality and may account for sex differences in the prevalence of sleep-related disorders. 5. Ageing is associated with a decreased sleep duration, decreased muscle mass and impaired insulin action. 6. Obesity impairs insulin action and is associated with the incidence and severity of obstructive sleep apnoea. 7. Sleep plays an integral role in metabolic control. Consequently, insufficient sleep may represent a modifiable risk factor for the development of Type 2 diabetes. The challenge ahead is to identify how sex differences, ageing and obesity could potentially influence the relationship between sleep and metabolism.
Robust, nonlinear, high angle-of-attack control design for a supermaneuverable vehicle
Adams, Richard J.
1993-01-01
High angle-of-attack flight control laws are developed for a supermaneuverable fighter aircraft. The methods of dynamic inversion and structured singular value synthesis are combined into an approach which addresses both the nonlinearity and robustness problems of flight at extreme operating conditions. The primary purpose of the dynamic inversion control elements is to linearize the vehicle response across the flight envelope. Structured singular value synthesis is used to design a dynamic controller which provides robust tracking to pilot commands. The resulting control system achieves desired flying qualities and guarantees a large margin of robustness to uncertainties for high angle-of-attack flight conditions. The results of linear simulation and structured singular value stability analysis are presented to demonstrate satisfaction of the design criteria. High fidelity nonlinear simulation results show that the combined dynamics inversion/structured singular value synthesis control law achieves a high level of performance in a realistic environment.
Conical flow near singular rays. [shock generation in ideal gas
Zahalak, G. I.; Myers, M. K.
1974-01-01
The steady flow of an ideal gas past a conical body is investigated by the method of matched asymptotic expansions, with particular emphasis on the flow near the singular ray occurring in linearized theory. The first-order problem governing the flow in this region is formulated, leading to the equation of Kuo, and an approximate solution is obtained in the case of compressive flow behind the main front. This solution is compared with the results of previous investigations with a view to assessing the applicability of the Lighthill-Whitham theories.
Pullback attractors for a singularly nonautonomous plate equation
Directory of Open Access Journals (Sweden)
Vera Lucia Carbone
2011-06-01
Full Text Available We consider the family of singularly nonautonomous plate equations with structural damping $$ u_{tt} + a(t,xu_t - Delta u_t + (-Delta^2 u + lambda u = f(u, $$ in a bounded domain $Omega subset mathbb{R}^n$, with Navier boundary conditions. When the nonlinearity f is dissipative we show that this problem is globally well posed in $H^2_0(Omega imes L^2(Omega$ and has a family of pullback attractors which is upper-semicontinuous under small perturbations of the damping a.
Optimal control problems with delay, the maximum principle and necessary conditions
Frankena, J.F.
1975-01-01
In this paper we consider a rather general optimal control problem involving ordinary differential equations with delayed arguments and a set of equality and inequality restrictions on state- and control variables. For this problem a maximum principle is given in pointwise form, using variational
Generalized teleparallel cosmology and initial singularity crossing
Energy Technology Data Exchange (ETDEWEB)
Awad, Adel; Nashed, Gamal, E-mail: Adel.Awad@bue.edu.eg, E-mail: gglnashed@sci.asu.edu.eg [Center for Theoretical Physics, the British University in Egypt, Suez Desert Road, Sherouk City 11837 (Egypt)
2017-02-01
We present a class of cosmological solutions for a generalized teleparallel gravity with f ( T )= T +α̃ (− T ) {sup n} , where α̃ is some parameter and n is an integer or half-integer. Choosing α̃ ∼ G {sup n} {sup −1}, where G is the gravitational constant, and working with an equation of state p = w ρ, one obtains a cosmological solution with multiple branches. The dynamics of the solution describes standard cosmology at late times, but the higher-torsion correction changes the nature of the initial singularity from big bang to a sudden singularity. The milder behavior of the sudden singularity enables us to extend timelike or lightlike curves, through joining two disconnected branches of solution at the singularity, leaving the singularity traversable. We show that this extension is consistent with the field equations through checking the known junction conditions for generalized teleparallel gravity. This suggests that these solutions describe a contracting phase a prior to the expanding phase of the universe.
A boundary control problem with a nonlinear reaction term
Directory of Open Access Journals (Sweden)
John R. Cannon
2009-04-01
Full Text Available The authors study the problem $u_t=u_{xx}-au$, $0
A Fast Condensing Method for Solution of Linear-Quadratic Control Problems
DEFF Research Database (Denmark)
Frison, Gianluca; Jørgensen, John Bagterp
2013-01-01
consider a condensing (or state elimination) method to solve an extended version of the LQ control problem, and we show how to exploit the structure of this problem to both factorize the dense Hessian matrix and solve the system. Furthermore, we present two efficient implementations. The first......In both Active-Set (AS) and Interior-Point (IP) algorithms for Model Predictive Control (MPC), sub-problems in the form of linear-quadratic (LQ) control problems need to be solved at each iteration. The solution of these sub-problems is usually the main computational effort. In this paper we...... implementation is formally identical to the Riccati recursion based solver and has a computational complexity that is linear in the control horizon length and cubic in the number of states. The second implementation has a computational complexity that is quadratic in the control horizon length as well...
Microbiological problems of radiation sterilization control of disposable medical products
International Nuclear Information System (INIS)
Horakova, V.
1975-01-01
Dose-response curves were determined for three strains of cocci and seven strains of aerobic spore-forming rods after irradiation by two different 60 Co sources and Van de Graaff electron accelerator. Besides the test strains Streptococcus faecium A 2 1, Bacillus sphericus Csub(I)A and Bacillus pumilus E601, some strains isolated from irradiated vaccines and animal diets, or found among common air-contaminating bacteria and pathogenic cocci were examined. The efficiency of the used radiation sources was compared. The control of the microbiological efficiency of radiation sterilization is discussed regarding routine practice. (author)
Singularities in Structural Optimization of the Ziegler Pendulum
Directory of Open Access Journals (Sweden)
O. N. Kirillov
2011-01-01
Full Text Available Structural optimization of non-conservative systems with respect to stability criteria is a research area with important applications in fluid-structure interactions, friction-induced instabilities, and civil engineering. In contrast to optimization of conservative systems where rigorously proven optimal solutions in buckling problems have been found, for nonconservative optimization problems only numerically optimized designs have been reported. The proof of optimality in non-conservative optimization problems is a mathematical challenge related to multiple eigenvalues, singularities in the stability domain, and non-convexity of the merit functional. We present here a study of optimal mass distribution in a classical Ziegler pendulum where local and global extrema can be found explicitly. In particular, for the undamped case, the two maxima of the critical flutter load correspond to a vanishing mass either in a joint or at the free end of the pendulum; in the minimum, the ratio of the masses is equal to the ratio of the stiffness coefficients. The role of the singularities on the stability boundary in the optimization is highlighted, and an extension to the damped case as well as to the case of higher degrees of freedom is discussed.
Phantom cosmology without Big Rip singularity
Energy Technology Data Exchange (ETDEWEB)
Astashenok, Artyom V. [Baltic Federal University of I. Kant, Department of Theoretical Physics, 236041, 14, Nevsky st., Kaliningrad (Russian Federation); Nojiri, Shin' ichi, E-mail: nojiri@phys.nagoya-u.ac.jp [Department of Physics, Nagoya University, Nagoya 464-8602 (Japan); Kobayashi-Maskawa Institute for the Origin of Particles and the Universe, Nagoya University, Nagoya 464-8602 (Japan); Odintsov, Sergei D. [Department of Physics, Nagoya University, Nagoya 464-8602 (Japan); Institucio Catalana de Recerca i Estudis Avancats - ICREA and Institut de Ciencies de l' Espai (IEEC-CSIC), Campus UAB, Facultat de Ciencies, Torre C5-Par-2a pl, E-08193 Bellaterra (Barcelona) (Spain); Tomsk State Pedagogical University, Tomsk (Russian Federation); Yurov, Artyom V. [Baltic Federal University of I. Kant, Department of Theoretical Physics, 236041, 14, Nevsky st., Kaliningrad (Russian Federation)
2012-03-23
We construct phantom energy models with the equation of state parameter w which is less than -1, w<-1, but finite-time future singularity does not occur. Such models can be divided into two classes: (i) energy density increases with time ('phantom energy' without 'Big Rip' singularity) and (ii) energy density tends to constant value with time ('cosmological constant' with asymptotically de Sitter evolution). The disintegration of bound structure is confirmed in Little Rip cosmology. Surprisingly, we find that such disintegration (on example of Sun-Earth system) may occur even in asymptotically de Sitter phantom universe consistent with observational data. We also demonstrate that non-singular phantom models admit wormhole solutions as well as possibility of Big Trip via wormholes.
Radioanatomy of the singular nerve canal
Energy Technology Data Exchange (ETDEWEB)
Muren, C. [Dept. of Diagnostic Radiology, Sabbatsbergs Hospital, Stockholm (Sweden); Wadin, K. [University Hospital, Uppsala (Sweden); Dimopoulos, P. [University Hospital, Uppsala (Sweden)
1991-08-01
The singular canal conveys vestibular nerve fibers from the ampulla of the posterior semicircular canal to the posteroinferior border of the internal auditory meatus. Radiographic identification of this anatomic structure helps to distinguish it from a fracture. It is also a landmark in certain surgical procedures. Computed tomography (CT) examinations of deep-frozen temporal bone specimens were compared with subsequently prepared plastic casts of these bones, showing good correlation between the anatomy and the images. The singular canal and its variable anatomy were studied in CT examinations of 107 patients. The singular canal could be identified, in both the axial and in the coronal planes. Its point of entry into the internal auditory meatus varied considerably. (orig.)
Enveloping branes and brane-world singularities
Energy Technology Data Exchange (ETDEWEB)
Antoniadis, Ignatios; Cotsakis, Spiros [CERN-Theory Division, Department of Physics, Geneva 23 (Switzerland); Klaoudatou, Ifigeneia [University of the Aegean, Research Group of Geometry, Dynamical Systems and Cosmology, Department of Information and Communication Systems Engineering, Samos (Greece)
2014-12-01
The existence of envelopes is studied for systems of differential equations in connection with the method of asymptotic splittings which allows one to determine the singularity structure of the solutions. The result is applied to brane-worlds consisting of a 3-brane in a five-dimensional bulk, in the presence of an analog of a bulk perfect fluid parameterizing a generic class of bulk matter. We find that all flat brane solutions suffer from a finite-distance singularity contrary to previous claims. We then study the possibility of avoiding finite-distance singularities by cutting the bulk and gluing regular solutions at the position of the brane. Further imposing physical conditions such as finite Planck mass on the brane and positive energy conditions on the bulk fluid, excludes, however, this possibility as well. (orig.)
Phantom cosmology without Big Rip singularity
International Nuclear Information System (INIS)
Astashenok, Artyom V.; Nojiri, Shin'ichi; Odintsov, Sergei D.; Yurov, Artyom V.
2012-01-01
We construct phantom energy models with the equation of state parameter w which is less than -1, w<-1, but finite-time future singularity does not occur. Such models can be divided into two classes: (i) energy density increases with time (“phantom energy” without “Big Rip” singularity) and (ii) energy density tends to constant value with time (“cosmological constant” with asymptotically de Sitter evolution). The disintegration of bound structure is confirmed in Little Rip cosmology. Surprisingly, we find that such disintegration (on example of Sun-Earth system) may occur even in asymptotically de Sitter phantom universe consistent with observational data. We also demonstrate that non-singular phantom models admit wormhole solutions as well as possibility of Big Trip via wormholes.
Global embeddings for branes at toric singularities
Balasubramanian, Vijay; Braun, Volker; García-Etxebarria, Iñaki
2012-01-01
We describe how local toric singularities, including the Toric Lego construction, can be embedded in compact Calabi-Yau manifolds. We study in detail the addition of D-branes, including non-compact flavor branes as typically used in semi-realistic model building. The global geometry provides constraints on allowable local models. As an illustration of our discussion we focus on D3 and D7-branes on (the partially resolved) (dP0)^3 singularity, its embedding in a specific Calabi-Yau manifold as a hypersurface in a toric variety, the related type IIB orientifold compactification, as well as the corresponding F-theory uplift. Our techniques generalize naturally to complete intersections, and to a large class of F-theory backgrounds with singularities.
Holographic subregion complexity for singular surfaces
Energy Technology Data Exchange (ETDEWEB)
Bakhshaei, Elaheh [Isfahan University of Technology, Department of Physics, Isfahan (Iran, Islamic Republic of); Mollabashi, Ali [Institute for Research in Fundamental Sciences (IPM), School of Physics, Tehran (Iran, Islamic Republic of); Shirzad, Ahmad [Isfahan University of Technology, Department of Physics, Isfahan (Iran, Islamic Republic of); Institute for Research in Fundamental Sciences (IPM), School of Particles and Accelerators, Tehran (Iran, Islamic Republic of)
2017-10-15
Recently holographic prescriptions were proposed to compute the quantum complexity of a given state in the boundary theory. A specific proposal known as 'holographic subregion complexity' is supposed to calculate the complexity of a reduced density matrix corresponding to a static subregion. We study different families of singular subregions in the dual field theory and find the divergence structure and universal terms of holographic subregion complexity for these singular surfaces. We find that there are new universal terms, logarithmic in the UV cut-off, due to the singularities of a family of surfaces including a kink in (2 + 1) dimensions and cones in even dimensional field theories. We also find examples of new divergent terms such as squared logarithm and negative powers times the logarithm of the UV cut-off parameter. (orig.)
Singularity hypotheses a scientific and philosophical assessment
Moor, James; Søraker, Johnny; Steinhart, Eric
2012-01-01
Singularity Hypotheses: A Scientific and Philosophical Assessment offers authoritative, jargon-free essays and critical commentaries on accelerating technological progress and the notion of technological singularity. It focuses on conjectures about the intelligence explosion, transhumanism, and whole brain emulation. Recent years have seen a plethora of forecasts about the profound, disruptive impact that is likely to result from further progress in these areas. Many commentators however doubt the scientific rigor of these forecasts, rejecting them as speculative and unfounded. We therefore invited prominent computer scientists, physicists, philosophers, biologists, economists and other thinkers to assess the singularity hypotheses. Their contributions go beyond speculation, providing deep insights into the main issues and a balanced picture of the debate.
Energy Technology Data Exchange (ETDEWEB)
Ringstroem, Hans [Max-Planck-Institut fuer Gravitationsphysik, Am Muehlenberg 1, D-14476 Golm (Germany)
2004-02-07
We consider Gowdy spacetimes under the assumption that the spatial hypersurfaces are diffeomorphic to the torus. The relevant equations are then wave map equations with the hyperbolic space as a target. In a paper by Grubisic and Moncrief, a formal expansion of solutions in the direction towards the singularity was proposed. Later, Kichenassamy and Rendall constructed a family of real analytic solutions with the maximum number of free functions and the desired asymptotics at the singularity. The condition of real analyticity was subsequently removed by Rendall. In a previous paper, we proved that one can put a condition on initial data that leads to asymptotic expansions. However, control of up to and including three derivatives in L{sup 2} was necessary, and the condition was rather technical. The main point of the present paper is to demonstrate the existence of certain monotone quantities and to illustrate how these can be used to weaken the assumptions to one derivative in the sup norm. Furthermore, we demonstrate that the false spikes do not appear in the disc model. Finally, we show that knowledge concerning the behaviour of the solution (as time tends to the singularity) for one fixed spatial point in some situations can be used to conclude that there are smooth expansions in the neighbourhood of that spatial point.
Burman, Erik; Hansbo, Peter; Larson, Mats G.
2018-03-01
Tikhonov regularization is one of the most commonly used methods for the regularization of ill-posed problems. In the setting of finite element solutions of elliptic partial differential control problems, Tikhonov regularization amounts to adding suitably weighted least squares terms of the control variable, or derivatives thereof, to the Lagrangian determining the optimality system. In this note we show that the stabilization methods for discretely ill-posed problems developed in the setting of convection-dominated convection-diffusion problems, can be highly suitable for stabilizing optimal control problems, and that Tikhonov regularization will lead to less accurate discrete solutions. We consider some inverse problems for Poisson’s equation as an illustration and derive new error estimates both for the reconstruction of the solution from the measured data and reconstruction of the source term from the measured data. These estimates include both the effect of the discretization error and error in the measurements.
Swamp Buffalo in South Kalimantan : Problem, Disease and Control
Directory of Open Access Journals (Sweden)
Lily Natalia
2006-12-01
Full Text Available In recent years, several studies have been carried out to evaluate and investigate the important diseases of swamp buffaloes (Bubalus carabanensis in Kalimantan . More attention has been focused on the case of acute infectious diseases and sudden death in the buffaloes . Fasciolosis black disease, acute enteritis, especially fatal enterotoxaemia haemorrhagic septicaemia . and trypanosomiasis (Surra, are some of the important diseases found in these animals . Black disease caused by toxigenic Clostridium novyi occurs in the presence of the organism in the liver and the degree of liver fluke Fasciola gigantica infestation . In regions where black disease is enzootic, Cl. novvi can be isolated from livers of normal healthy animals . In Hulu Sungai Utara district, South Kalimantan, the prevalence of fasciolosis caused by Fasciola gigantica in swamp buffalo was 77% in 1991 . A gross sudden change in diet due to seasonal changes could induce rumen and intestinal stasis, which provide a favourable environment for the rapid proliferation of commensal toxigenic Clostridium perfringens in the small intestine . Subsequent absorption of the toxin produced through the gut wall and its generalized dissemination culminated in a fatal enterotoxaemia . Haemorrhagic septicaemia (HS is an acute, fatal disease affecting swamp buffalo, and caused by Pasteurella multocida B : 2 . The swamp buffalo is particularly susceptible for HS, and the reported greatest losses of swamp buffalo in Kalimantan due to HS is recorded in 1980s. The clinical signs of Surra in swamp buffalo were also found in certain areas in Danau Panggang area . Hulu Sungai Utara district . Vaccination is the accepted method for controlling Black disease, enterotoxaemia and HS. Multi component vaccine, alum adjuvant containing at least 5 types of clostridial toxoids and P. multocida B2 bacterin have been used and provide good protection to the animals . Control and treatment of liver fluke infestation
Endpoint singularities in unintegrated parton distributions
Hautmann, F
2007-01-01
We examine the singular behavior from the endpoint region x -> 1 in parton distributions unintegrated in both longitudinal and transverse momenta. We identify and regularize the singularities by using the subtraction method, and compare this with the cut-off regularization method. The counterterms for the distributions with subtractive regularization are given in coordinate space by compact all-order expressions in terms of eikonal-line operators. We carry out an explicit calculation at one loop for the unintegrated quark distribution. We discuss the relation of the unintegrated parton distributions in subtractive regularization with the ordinary parton distributions.
Characteristic classes, singular embeddings, and intersection homology.
Cappell, S E; Shaneson, J L
1987-06-01
This note announces some results on the relationship between global invariants and local topological structure. The first section gives a local-global formula for Pontrjagin classes or L-classes. The second section describes a corresponding decomposition theorem on the level of complexes of sheaves. A final section mentions some related aspects of "singular knot theory" and the study of nonisolated singularities. Analogous equivariant analogues, with local-global formulas for Atiyah-Singer classes and their relations to G-signatures, will be presented in a future paper.
Cosmic censorship and the strengths of singularities
International Nuclear Information System (INIS)
Newman, R.P.
1986-01-01
This paper considers the principal definitions concerning limiting curvature strength on geodesics, and on non-spacelike geodesics in particular. They are formulated in terms of focussing conditions. Two definitions suggest themselves, and these are given in terms of a concept of a generalized Jacobi field. An historical survey is presented on some important developments concerning examples of naked singularities. The historical context is recalled in which these models, and cosmic censorship in general, have arisen. It is the author's opinion that one can expect to obtain theoretical limitations on the strengths of any naked singularities which do occur
Inverse problems of geophysics
International Nuclear Information System (INIS)
Yanovskaya, T.B.
2003-07-01
This report gives an overview and the mathematical formulation of geophysical inverse problems. General principles of statistical estimation are explained. The maximum likelihood and least square fit methods, the Backus-Gilbert method and general approaches for solving inverse problems are discussed. General formulations of linearized inverse problems, singular value decomposition and properties of pseudo-inverse solutions are given
Analysis of the problems, which have the users employing software packages in the production control
International Nuclear Information System (INIS)
Vortherms, B.; Moeller, C.
1977-08-01
The use of EDP is particularly effective in the dispositive area of enterprises. The realization of adequate systems, however, is involving considerable problems. This study is analyzing such problems of production control which have been obtained by investigations carried out in several enterprises. The problems of production control, the procedure in carrying out investigations and the prevalence of EDP in enterprises are demonstrated. The problems found out and their causes are then systematized and analyzed. The solution proposals derived are orientation aids for an optimum use of EDP. (orig.) [de