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Sample records for singular linear system

  1. Synchronization and Control of Linearly Coupled Singular Systems

    Directory of Open Access Journals (Sweden)

    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.

  2. 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.

  3. Stability Analysis for Fractional-Order Linear Singular Delay Differential Systems

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    Hai Zhang

    2014-01-01

    Full Text Available We investigate the delay-independently asymptotic stability of fractional-order linear singular delay differential systems. Based on the algebraic approach, the sufficient conditions are presented to ensure the asymptotic stability for any delay parameter. By applying the stability criteria, one can avoid solving the roots of transcendental equations. An example is also provided to illustrate the effectiveness and applicability of the theoretical results.

  4. Finite-Time Stability Analysis of Discrete-Time Linear Singular Systems

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    Songlin Wo

    2014-01-01

    Full Text Available The finite-time stability (FTS problem of discrete-time linear singular systems (DTLSS is considered in this paper. A necessary and sufficient condition for FTS is obtained, which can be expressed in terms of matrix inequalities. Then, another form of the necessary and sufficient condition for FTS is also given by using matrix-null space technology. In order to solve the stability problem expediently, a sufficient condition for FTS is given via linear matrix inequality (LMI approach; this condition can be expressed in terms of LMIs. Finally, an illustrating example is also given to show the effectiveness of the proposed method.

  5. Finite-Time Robust H∞ Control for Uncertain Linear Continuous-Time Singular Systems with Exogenous Disturbances

    Directory of Open Access Journals (Sweden)

    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.

  6. Singular Linear Differential Equations in Two Variables

    NARCIS (Netherlands)

    Braaksma, B.L.J.; Put, M. van der

    2008-01-01

    The formal and analytic classification of integrable singular linear differential equations has been studied among others by R. Gerard and Y. Sibuya. We provide a simple proof of their main result, namely: For certain irregular systems in two variables there is no Stokes phenomenon, i.e. there is no

  7. On preconditioning techniques for dense linear systems arising from singular boundary integral equations

    Energy Technology Data Exchange (ETDEWEB)

    Chen, Ke [Univ. of Liverpool (United Kingdom)

    1996-12-31

    We study various preconditioning techniques for the iterative solution of boundary integral equations, and aim to provide a theory for a class of sparse preconditioners. Two related ideas are explored here: singularity separation and inverse approximation. Our preliminary conclusion is that singularity separation based preconditioners perform better than approximate inverse based while it is desirable to have both features.

  8. 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.

  9. Eigenstructure of of singular systems. Perturbation analysis of simple eigenvalues

    OpenAIRE

    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

  10. Coupled singular and non singular thermoelastic system and double lapalce decomposition methods

    OpenAIRE

    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

  11. Symmetries and singularities in Hamiltonian systems

    International Nuclear Information System (INIS)

    Miranda, Eva

    2009-01-01

    This paper contains several results concerning the role of symmetries and singularities in the mathematical formulation of many physical systems. We concentrate in systems which find their mathematical model on a symplectic or Poisson manifold and we present old and new results from a global perspective.

  12. Systems of evolution equations and the singular perturbation method

    International Nuclear Information System (INIS)

    Mika, J.

    Several fundamental theorems are presented important for the solution of linear evolution equations in the Banach space. The algorithm is deduced extending the solution of the system of singularly perturbed evolution equations into an asymptotic series with respect to a small positive parameter. The asymptotic convergence is shown of an approximate solution to the accurate solution. Singularly perturbed evolution equations of the resonance type were analysed. The special role is considered of the asymptotic equivalence of P1 equations obtained as the first order approximation if the spherical harmonics method is applied to the linear Boltzmann equation, and the diffusion equations of the linear transport theory where the small parameter approaches zero. (J.B.)

  13. 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

  14. On deformations of linear differential systems

    NARCIS (Netherlands)

    Gontsov, R.R.; Poberezhnyi, V.A.; Helminck, G.F.

    2011-01-01

    This article concerns deformations of meromorphic linear differential systems. Problems relating to their existence and classification are reviewed, and the global and local behaviour of solutions to deformation equations in a neighbourhood of their singular set is analysed. Certain classical

  15. Analysis and design of singular Markovian jump systems

    CERN Document Server

    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

  16. Load-Flow in Multiphase Distribution Networks: Existence, Uniqueness, Non-Singularity, and Linear Models

    Energy Technology Data Exchange (ETDEWEB)

    Bernstein, Andrey [National Renewable Energy Laboratory (NREL), Golden, CO (United States); Dall-Anese, Emiliano [National Renewable Energy Laboratory (NREL), Golden, CO (United States); Zhao, Changhong [National Renewable Energy Laboratory (NREL), Golden, CO (United States); Wang, Cong [Ecole Polytechnique Federale de Lausanne (EPFL); Le Boudec, Jean-Yves [Ecole Polytechnique Federale de Lausanne (EPFL)

    2018-04-06

    This paper considers unbalanced multiphase distribution systems with generic topology and different load models, and extends the Z-bus iterative load-flow algorithm based on a fixed-point interpretation of the AC load-flow equations. Explicit conditions for existence and uniqueness of load-flow solutions are presented. These conditions also guarantee convergence of the load-flow algorithm to the unique solution. The proposed methodology is applicable to generic systems featuring (i) wye connections; (ii) ungrounded delta connections; (iii) a combination of wye-connected and delta-connected sources/loads; and, (iv) a combination of line-to-line and line-to-grounded-neutral devices at the secondary of distribution transformers. Further, a sufficient condition for the non-singularity of the load-flow Jacobian is proposed. Finally, linear load-flow models are derived, and their approximation accuracy is analyzed. Theoretical results are corroborated through experiments on IEEE test feeders.

  17. Hybrid vehicle optimal control : Linear interpolation and singular control

    NARCIS (Netherlands)

    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

  18. 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.

  19. Complexity, Analysis and Control of Singular Biological Systems

    CERN Document Server

    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 ...

  20. On the multisummability of WKB solutions of certain singularly perturbed linear ordinary differential equations

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    Yoshitsugu Takei

    2015-01-01

    Full Text Available Using two concrete examples, we discuss the multisummability of WKB solutions of singularly perturbed linear ordinary differential equations. Integral representations of solutions and a criterion for the multisummability based on the Cauchy-Heine transform play an important role in the proof.

  1. 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.

  2. An investigation of singular Lagrangians as field systems

    International Nuclear Information System (INIS)

    Rabei, E.M.

    1995-07-01

    The link between the treatment of singular Lagrangians as field systems and the general approach is studied. It is shown that singular Lagrangians as field systems are always in exact agreement with the general approach. Two examples and the singular Lagrangian with zero rank Hessian matrix are studied. The equations of motion in the field systems are equivalent to the equations which contain acceleration, and the constraints are equivalent to the equations which do not contain acceleration in the general approach treatment. (author). 10 refs

  3. INTERVAL STATE ESTIMATION FOR SINGULAR DIFFERENTIAL EQUATION SYSTEMS WITH DELAYS

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    T. A. Kharkovskaia

    2016-07-01

    Full Text Available The paper deals with linear differential equation systems with algebraic restrictions (singular systems and a method of interval observer design for this kind of systems. The systems contain constant time delay, measurement noise and disturbances. Interval observer synthesis is based on monotone and cooperative systems technique, linear matrix inequations, Lyapunov function theory and interval arithmetic. The set of conditions that gives the possibility for interval observer synthesis is proposed. Results of synthesized observer operation are shown on the example of dynamical interindustry balance model. The advantages of proposed method are that it is adapted to observer design for uncertain systems, if the intervals of admissible values for uncertain parameters are given. The designed observer is capable to provide asymptotically definite limits on the estimation accuracy, since the interval of admissible values for the object state is defined at every instant. The obtained result provides an opportunity to develop the interval estimation theory for complex systems that contain parametric uncertainty, varying delay and nonlinear elements. Interval observers increasingly find applications in economics, electrical engineering, mechanical systems with constraints and optimal flow control.

  4. Adaptive Control of the Chaotic System via Singular System Approach

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    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.

  5. A singular value decomposition linear programming (SVDLP) optimization technique for circular cone based robotic radiotherapy

    Science.gov (United States)

    Liang, Bin; Li, Yongbao; Wei, Ran; Guo, Bin; Xu, Xuang; Liu, Bo; Li, Jiafeng; Wu, Qiuwen; Zhou, Fugen

    2018-01-01

    With robot-controlled linac positioning, robotic radiotherapy systems such as CyberKnife significantly increase freedom of radiation beam placement, but also impose more challenges on treatment plan optimization. The resampling mechanism in the vendor-supplied treatment planning system (MultiPlan) cannot fully explore the increased beam direction search space. Besides, a sparse treatment plan (using fewer beams) is desired to improve treatment efficiency. This study proposes a singular value decomposition linear programming (SVDLP) optimization technique for circular collimator based robotic radiotherapy. The SVDLP approach initializes the input beams by simulating the process of covering the entire target volume with equivalent beam tapers. The requirements on dosimetry distribution are modeled as hard and soft constraints, and the sparsity of the treatment plan is achieved by compressive sensing. The proposed linear programming (LP) model optimizes beam weights by minimizing the deviation of soft constraints subject to hard constraints, with a constraint on the l 1 norm of the beam weight. A singular value decomposition (SVD) based acceleration technique was developed for the LP model. Based on the degeneracy of the influence matrix, the model is first compressed into lower dimension for optimization, and then back-projected to reconstruct the beam weight. After beam weight optimization, the number of beams is reduced by removing the beams with low weight, and optimizing the weights of the remaining beams using the same model. This beam reduction technique is further validated by a mixed integer programming (MIP) model. The SVDLP approach was tested on a lung case. The results demonstrate that the SVD acceleration technique speeds up the optimization by a factor of 4.8. Furthermore, the beam reduction achieves a similar plan quality to the globally optimal plan obtained by the MIP model, but is one to two orders of magnitude faster. Furthermore, the SVDLP

  6. A singular value decomposition linear programming (SVDLP) optimization technique for circular cone based robotic radiotherapy.

    Science.gov (United States)

    Liang, Bin; Li, Yongbao; Wei, Ran; Guo, Bin; Xu, Xuang; Liu, Bo; Li, Jiafeng; Wu, Qiuwen; Zhou, Fugen

    2018-01-05

    With robot-controlled linac positioning, robotic radiotherapy systems such as CyberKnife significantly increase freedom of radiation beam placement, but also impose more challenges on treatment plan optimization. The resampling mechanism in the vendor-supplied treatment planning system (MultiPlan) cannot fully explore the increased beam direction search space. Besides, a sparse treatment plan (using fewer beams) is desired to improve treatment efficiency. This study proposes a singular value decomposition linear programming (SVDLP) optimization technique for circular collimator based robotic radiotherapy. The SVDLP approach initializes the input beams by simulating the process of covering the entire target volume with equivalent beam tapers. The requirements on dosimetry distribution are modeled as hard and soft constraints, and the sparsity of the treatment plan is achieved by compressive sensing. The proposed linear programming (LP) model optimizes beam weights by minimizing the deviation of soft constraints subject to hard constraints, with a constraint on the l 1 norm of the beam weight. A singular value decomposition (SVD) based acceleration technique was developed for the LP model. Based on the degeneracy of the influence matrix, the model is first compressed into lower dimension for optimization, and then back-projected to reconstruct the beam weight. After beam weight optimization, the number of beams is reduced by removing the beams with low weight, and optimizing the weights of the remaining beams using the same model. This beam reduction technique is further validated by a mixed integer programming (MIP) model. The SVDLP approach was tested on a lung case. The results demonstrate that the SVD acceleration technique speeds up the optimization by a factor of 4.8. Furthermore, the beam reduction achieves a similar plan quality to the globally optimal plan obtained by the MIP model, but is one to two orders of magnitude faster. Furthermore, the SVDLP

  7. The initial value problem for linearized gravitational perturbations of the Schwarzschild naked singularity

    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

  8. Linear integral equations and soliton systems

    International Nuclear Information System (INIS)

    Quispel, G.R.W.

    1983-01-01

    A study is presented of classical integrable dynamical systems in one temporal and one spatial dimension. The direct linearizations are given of several nonlinear partial differential equations, for example the Korteweg-de Vries equation, the modified Korteweg-de Vries equation, the sine-Gordon equation, the nonlinear Schroedinger equation, and the equation of motion for the isotropic Heisenberg spin chain; the author also discusses several relations between these equations. The Baecklund transformations of these partial differential equations are treated on the basis of a singular transformation of the measure (or equivalently of the plane-wave factor) occurring in the corresponding linear integral equations, and the Baecklund transformations are used to derive the direct linearization of a chain of so-called modified partial differential equations. Finally it is shown that the singular linear integral equations lead in a natural way to the direct linearizations of various nonlinear difference-difference equations. (Auth.)

  9. Singular perturbations introduction to system order reduction methods with applications

    CERN Document Server

    Shchepakina, Elena; Mortell, Michael P

    2014-01-01

    These lecture notes provide a fresh approach to investigating singularly perturbed systems using asymptotic and geometrical techniques. It gives many examples and step-by-step techniques, which will help beginners move to a more advanced level. Singularly perturbed systems appear naturally in the modelling of many processes that are characterized by slow and fast motions simultaneously, for example, in fluid dynamics and nonlinear mechanics. This book’s approach consists in separating out the slow motions of the system under investigation. The result is a reduced differential system of lesser order. However, it inherits the essential elements of the qualitative behaviour of the original system. Singular Perturbations differs from other literature on the subject due to its methods and wide range of applications. It is a valuable reference for specialists in the areas of applied mathematics, engineering, physics, biology, as well as advanced undergraduates for the earlier parts of the book, and graduate stude...

  10. 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.

  11. Non linear system become linear system

    Directory of Open Access Journals (Sweden)

    Petre Bucur

    2007-01-01

    Full Text Available The present paper refers to the theory and the practice of the systems regarding non-linear systems and their applications. We aimed the integration of these systems to elaborate their response as well as to highlight some outstanding features.

  12. Body frames and frame singularities for three-atom systems

    International Nuclear Information System (INIS)

    Littlejohn, R.G.; Mitchell, K.A.; Aquilanti, V.; Cavalli, S.

    1998-01-01

    The subject of body frames and their singularities for three-particle systems is important not only for large-amplitude rovibrational coupling in molecular spectroscopy, but also for reactive scattering calculations. This paper presents a geometrical analysis of the meaning of body frame conventions and their singularities in three-particle systems. Special attention is devoted to the principal axis frame, a certain version of the Eckart frame, and the topological inevitability of frame singularities. The emphasis is on a geometrical picture, which is intended as a preliminary study for the more difficult case of four-particle systems, where one must work in higher-dimensional spaces. The analysis makes extensive use of kinematic rotations. copyright 1998 The American Physical Society

  13. PWR control system design using advanced linear and non-linear methodologies

    International Nuclear Information System (INIS)

    Rabindran, N.; Whitmarsh-Everiss, M.J.

    2004-01-01

    Consideration is here given to the methodology deployed for non-linear heuristic analysis in the time domain supported by multi-variable linear control system design methods for the purposes of operational dynamics and control system analysis. This methodology is illustrated by the application of structural singular value μ analysis to Pressurised Water Reactor control system design. (author)

  14. 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...

  15. A class of singular Ro-matrices and extensions to semidefinite linear complementarity problems

    Directory of Open Access Journals (Sweden)

    Sivakumar K.C.

    2013-01-01

    Full Text Available For ARnxn and qRn, the linear complementarity problem LCP(A, q is to determine if there is xRn 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.

  16. A solid criterion based on strict LMI without invoking equality constraint for stabilization of continuous singular systems.

    Science.gov (United States)

    Zhang, Xuefeng; Chen, YangQuan

    2017-11-01

    The paper considers the stabilization issue of linear continuous singular systems by dealing with strict linear matrix inequalities (LMIs) without invoking equality constraint and proposes a complete and effective solved LMIs formulation. The criterion is necessary and sufficient condition and can be directly solved the feasible solutions with LMI toolbox and is much more tractable and reliable in numerical simulation than existing results, which involve positive semi-definite LMIs with equality constraints. The most important property of the criterion proposed in the paper is that it can overcome the drawbacks of the invalidity caused by the singularity of Ω=PE T +SQ for stabilization of singular systems. Two counterexamples are presented to avoid the disadvantages of the existing condition of stabilization of continuous singular systems. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

  17. Computational singular perturbation analysis of stochastic chemical systems with stiffness

    Science.gov (United States)

    Wang, Lijin; Han, Xiaoying; Cao, Yanzhao; Najm, Habib N.

    2017-04-01

    Computational singular perturbation (CSP) is a useful method for analysis, reduction, and time integration of stiff ordinary differential equation systems. It has found dominant utility, in particular, in chemical reaction systems with a large range of time scales at continuum and deterministic level. On the other hand, CSP is not directly applicable to chemical reaction systems at micro or meso-scale, where stochasticity plays an non-negligible role and thus has to be taken into account. In this work we develop a novel stochastic computational singular perturbation (SCSP) analysis and time integration framework, and associated algorithm, that can be used to not only construct accurately and efficiently the numerical solutions to stiff stochastic chemical reaction systems, but also analyze the dynamics of the reduced stochastic reaction systems. The algorithm is illustrated by an application to a benchmark stochastic differential equation model, and numerical experiments are carried out to demonstrate the effectiveness of the construction.

  18. Refined Fuchs inequalities for systems of linear differential equations

    International Nuclear Information System (INIS)

    Gontsov, R R

    2004-01-01

    We refine the Fuchs inequalities obtained by Corel for systems of linear meromorphic differential equations given on the Riemann sphere. Fuchs inequalities enable one to estimate the sum of exponents of the system over all its singular points. We refine these well-known inequalities by considering the Jordan structure of the leading coefficient of the Laurent series for the matrix of the right-hand side of the system in the neighbourhood of a singular point

  19. 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.

  20. Relaxation periodic solutions of one singular perturbed system with delay

    Science.gov (United States)

    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.

  1. Generalized Cross-Gramian for Linear Systems

    DEFF Research Database (Denmark)

    Shaker, Hamid Reza

    2012-01-01

    The cross-gramian is a well-known matrix with embedded controllability and observability information. The cross-gramian is related to the Hankel operator and the Hankel singular values of a linear square system and it has several interesting properties. These properties make the cross...... square symmetric systems, the ordinary cross-gramian does not exist. To cope with this problem, a new generalized cross-gramian is introduced in this paper. In contrast to the ordinary cross-gramian, the generalized cross-gramian can be easily obtained for general linear systems and therefore can be used...

  2. Robust Guaranteed Cost Observer Design for Singular Markovian Jump Time-Delay Systems with Generally Incomplete Transition Probability

    Directory of Open Access Journals (Sweden)

    Yanbo Li

    2014-01-01

    Full Text Available This paper is devoted to the investigation of the design of robust guaranteed cost observer for a class of linear singular Markovian jump time-delay systems with generally incomplete transition probability. In this singular model, each transition rate can be completely unknown or only its estimate value is known. Based on stability theory of stochastic differential equations and linear matrix inequality (LMI technique, we design an observer to ensure that, for all uncertainties, the resulting augmented system is regular, impulse free, and robust stochastically stable with the proposed guaranteed cost performance. Finally, a convex optimization problem with LMI constraints is formulated to design the suboptimal guaranteed cost filters for linear singular Markovian jump time-delay systems with generally incomplete transition probability.

  3. Linear system theory

    Science.gov (United States)

    Callier, Frank M.; Desoer, Charles A.

    1991-01-01

    The aim of this book is to provide a systematic and rigorous access to the main topics of linear state-space system theory in both the continuous-time case and the discrete-time case; and the I/O description of linear systems. The main thrusts of the work are the analysis of system descriptions and derivations of their properties, LQ-optimal control, state feedback and state estimation, and MIMO unity-feedback systems.

  4. 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

  5. Fuzzy Stochastic Optimal Guaranteed Cost Control of Bio-Economic Singular Markovian Jump Systems.

    Science.gov (United States)

    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.

  6. Bright, dark and singular optical solitons in a cascaded system

    International Nuclear Information System (INIS)

    Zhou, Qin; Zhu, Qiuping; Yu, Hua; Liu, Yaxian; Wei, Chun; Yao, Ping; Bhrawy, Ali H; Biswas, Anjan

    2015-01-01

    This work studies nonlinear dynamics of optical solitons in a cascaded system with Kerr law nonlinearity and spatio-temporal dispersion. The mathematical model that describes the propagation of optical solitons through a cascaded system is given by the vector-coupled nonlinear Schrödinger equation. It is investigated analytically using three integration algorithms. The Jacobian elliptic equation expansion method, Bernoulli equation expansion approach and Riccati equation expansion scheme are the integration tools of this model that are recruited to extract singular, bright and dark solitons. The restrictions that need to hold for the existence of these solitons are derived. (paper)

  7. Singular perturbation methods for nonlinear dynamic systems with time delays

    International Nuclear Information System (INIS)

    Hu, H.Y.; Wang, Z.H.

    2009-01-01

    This review article surveys the recent advances in the dynamics and control of time-delay systems, with emphasis on the singular perturbation methods, such as the method of multiple scales, the method of averaging, and two newly developed methods, the energy analysis and the pseudo-oscillator analysis. Some examples are given to demonstrate the advantages of the methods. The comparisons with other methods show that these methods lead to easier computations and higher accurate prediction on the local dynamics of time-delay systems near a Hopf bifurcation.

  8. SENR /NRPy + : Numerical relativity in singular curvilinear coordinate systems

    Science.gov (United States)

    Ruchlin, Ian; Etienne, Zachariah B.; Baumgarte, Thomas W.

    2018-03-01

    We report on a new open-source, user-friendly numerical relativity code package called SENR /NRPy + . Our code extends previous implementations of the BSSN reference-metric formulation to a much broader class of curvilinear coordinate systems, making it ideally suited to modeling physical configurations with approximate or exact symmetries. In the context of modeling black hole dynamics, it is orders of magnitude more efficient than other widely used open-source numerical relativity codes. NRPy + provides a Python-based interface in which equations are written in natural tensorial form and output at arbitrary finite difference order as highly efficient C code, putting complex tensorial equations at the scientist's fingertips without the need for an expensive software license. SENR provides the algorithmic framework that combines the C codes generated by NRPy + into a functioning numerical relativity code. We validate against two other established, state-of-the-art codes, and achieve excellent agreement. For the first time—in the context of moving puncture black hole evolutions—we demonstrate nearly exponential convergence of constraint violation and gravitational waveform errors to zero as the order of spatial finite difference derivatives is increased, while fixing the numerical grids at moderate resolution in a singular coordinate system. Such behavior outside the horizons is remarkable, as numerical errors do not converge to zero near punctures, and all points along the polar axis are coordinate singularities. The formulation addresses such coordinate singularities via cell-centered grids and a simple change of basis that analytically regularizes tensor components with respect to the coordinates. Future plans include extending this formulation to allow dynamical coordinate grids and bispherical-like distribution of points to efficiently capture orbiting compact binary dynamics.

  9. Branch-cut singularities in thermodynamics of Fermi liquid systems.

    Science.gov (United States)

    Shekhter, Arkady; Finkel'stein, Alexander M

    2006-10-24

    The recently measured spin susceptibility of the two-dimensional electron gas exhibits a strong dependence on temperature, which is incompatible with the standard Fermi liquid phenomenology. In this article, we show that the observed temperature behavior is inherent to ballistic two-dimensional electrons. Besides the single-particle and collective excitations, the thermodynamics of Fermi liquid systems includes effects of the branch-cut singularities originating from the edges of the continuum of pairs of quasiparticles. As a result of the rescattering induced by interactions, the branch-cut singularities generate nonanalyticities in the thermodynamic potential that reveal themselves in anomalous temperature dependences. Calculation of the spin susceptibility in such a situation requires a nonperturbative treatment of the interactions. As in high-energy physics, a mixture of the collective excitations and pairs of quasiparticles can effectively be described by a pole in the complex momentum plane. This analysis provides a natural explanation for the observed temperature dependence of the spin susceptibility, both in sign and in magnitude.

  10. Singular perturbation analysis of relaxation oscillations in reactor systems

    International Nuclear Information System (INIS)

    Ward, M.E.; Lee, J.C.

    1987-01-01

    A singular perturbation method for the analysis of large power oscillations in nuclear reactors is applied to obtain phase-plane solutions of the Ergen-Weinberg model. The system equations, recast in an appropriate form, directly give a first approximation to the closed trajectory in which the system behaviour is idealized as relaxation oscillations. Further approximations in the phase plane are determined using separate perturbation series on individual parts of the oscillation, with variations in the assignment of dependent and independent variables to consistently obtain convergent series. The accuracy of each order of the phase-plane solution increases with the magnitude of the power pulse in the actual physical situation. For realistic reactor conditions, both the trajectory and period of oscillation are well predicted using the first two terms of each perturbation series

  11. 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

  12. 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

  13. Linearization of the Lorenz system

    International Nuclear Information System (INIS)

    Li, Chunbiao; Sprott, Julien Clinton; Thio, Wesley

    2015-01-01

    A partial and complete piecewise linearized version of the Lorenz system is proposed. The linearized versions have an independent total amplitude control parameter. Additional further linearization leads naturally to a piecewise linear version of the diffusionless Lorenz system. A chaotic circuit with a single amplitude controller is then implemented using a new switch element, producing a chaotic oscillation that agrees with the numerical calculation for the piecewise linear diffusionless Lorenz system. - Highlights: • A partial and complete piecewise linearized version of the Lorenz system are addressed. • The linearized versions have an independent total amplitude control parameter. • A piecewise linear version of the diffusionless Lorenz system is derived by further linearization. • A corresponding chaotic circuit without any multiplier is implemented for the chaotic oscillation

  14. Linearization of the Lorenz system

    Energy Technology Data Exchange (ETDEWEB)

    Li, Chunbiao, E-mail: goontry@126.com [School of Electronic & Information Engineering, Nanjing University of Information Science & Technology, Nanjing 210044 (China); Engineering Technology Research and Development Center of Jiangsu Circulation Modernization Sensor Network, Jiangsu Institute of Commerce, Nanjing 211168 (China); Sprott, Julien Clinton [Department of Physics, University of Wisconsin–Madison, Madison, WI 53706 (United States); Thio, Wesley [Department of Electrical and Computer Engineering, The Ohio State University, Columbus, OH 43210 (United States)

    2015-05-08

    A partial and complete piecewise linearized version of the Lorenz system is proposed. The linearized versions have an independent total amplitude control parameter. Additional further linearization leads naturally to a piecewise linear version of the diffusionless Lorenz system. A chaotic circuit with a single amplitude controller is then implemented using a new switch element, producing a chaotic oscillation that agrees with the numerical calculation for the piecewise linear diffusionless Lorenz system. - Highlights: • A partial and complete piecewise linearized version of the Lorenz system are addressed. • The linearized versions have an independent total amplitude control parameter. • A piecewise linear version of the diffusionless Lorenz system is derived by further linearization. • A corresponding chaotic circuit without any multiplier is implemented for the chaotic oscillation.

  15. On the C(R) stability of uncertain singularly perturbed systems

    International Nuclear Information System (INIS)

    Sun, Y.-J.

    2009-01-01

    In this paper, a simple criterion for the C(R) stability of uncertain singularly perturbed systems is proposed. Such a criterion can be easily checked by some algebraic inequality. The upper bound of the singular perturbation parameter ε is also given by estimating the unique positive zero of specific function. Finally, a numerical example is provided to illustrate the main result

  16. The use of singular value gradients and optimization techniques to design robust controllers for multiloop systems

    Science.gov (United States)

    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.

  17. Chaos synchronization of a unified chaotic system via partial linearization

    International Nuclear Information System (INIS)

    Yu Yongguang; Li Hanxiong; Duan Jian

    2009-01-01

    A partial linearization method is proposed for realizing the chaos synchronization of an unified chaotic system. Through synchronizing partial state of the chaotic systems can result in the synchronization of their entire states, and the resulting controller is singularity free. The results can be easily extended to the synchronization of other similar chaotic systems. Simulation results are conducted to show the effectiveness of the method.

  18. Dynamical systems and linear algebra

    OpenAIRE

    Colonius, Fritz (Prof.)

    2007-01-01

    Dynamical systems and linear algebra / F. Colonius, W. Kliemann. - In: Handbook of linear algebra / ed. by Leslie Hogben. - Boca Raton : Chapman & Hall/CRC, 2007. - S. 56,1-56,22. - (Discrete mathematics and its applications)

  19. Harmonic analysis of electric locomotive and traction power system based on wavelet singular entropy

    Science.gov (United States)

    Dun, Xiaohong

    2018-05-01

    With the rapid development of high-speed railway and heavy-haul transport, the locomotive and traction power system has become the main harmonic source of China's power grid. In response to this phenomenon, the system's power quality issues need timely monitoring, assessment and governance. Wavelet singular entropy is an organic combination of wavelet transform, singular value decomposition and information entropy theory, which combines the unique advantages of the three in signal processing: the time-frequency local characteristics of wavelet transform, singular value decomposition explores the basic modal characteristics of data, and information entropy quantifies the feature data. Based on the theory of singular value decomposition, the wavelet coefficient matrix after wavelet transform is decomposed into a series of singular values that can reflect the basic characteristics of the original coefficient matrix. Then the statistical properties of information entropy are used to analyze the uncertainty of the singular value set, so as to give a definite measurement of the complexity of the original signal. It can be said that wavelet entropy has a good application prospect in fault detection, classification and protection. The mat lab simulation shows that the use of wavelet singular entropy on the locomotive and traction power system harmonic analysis is effective.

  20. Singularity-Free Neural Control for the Exponential Trajectory Tracking in Multiple-Input Uncertain Systems with Unknown Deadzone Nonlinearities

    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.

  1. On a class of strongly degenerate and singular linear elliptic equation

    International Nuclear Information System (INIS)

    Duong Minh Duc, D.M.; Le Dung.

    1992-11-01

    We consider a class of strongly degenerate linear elliptic equation. The boundedness and the Holder regularity of the weak solutions in the weighted Sobolev-Hardy spaces will be studied. (author). 9 refs

  2. 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.

  3. Spectral singularities, biorthonormal systems and a two-parameter family of complex point interactions

    International Nuclear Information System (INIS)

    Mostafazadeh, Ali; Mehri-Dehnavi, Hossein

    2009-01-01

    A curious feature of complex scattering potentials v(x) is the appearance of spectral singularities. We offer a quantitative description of spectral singularities that identifies them with an obstruction to the existence of a complete biorthonormal system consisting of the eigenfunctions of the Hamiltonian operator and its adjoint. We establish the equivalence of this description with the mathematicians' definition of spectral singularities for the potential v(x) = z - δ(x + a) + z + δ(x - a), where z ± and a are respectively complex and real parameters and δ(x) is the Dirac delta function. We offer a through analysis of the spectral properties of this potential and determine the regions in the space of the coupling constants z ± where it admits bound states and spectral singularities. In particular, we find an explicit bound on the size of certain regions in which the Hamiltonian is quasi-Hermitian and examine the consequences of imposing PT-symmetry

  4. Feedback systems for linear colliders

    CERN Document Server

    Hendrickson, L; Himel, Thomas M; Minty, Michiko G; Phinney, N; Raimondi, Pantaleo; Raubenheimer, T O; Shoaee, H; Tenenbaum, P G

    1999-01-01

    Feedback systems are essential for stable operation of a linear collider, providing a cost-effective method for relaxing tight tolerances. In the Stanford Linear Collider (SLC), feedback controls beam parameters such as trajectory, energy, and intensity throughout the accelerator. A novel dithering optimization system which adjusts final focus parameters to maximize luminosity contributed to achieving record performance in the 1997-98 run. Performance limitations of the steering feedback have been investigated, and improvements have been made. For the Next Linear Collider (NLC), extensive feedback systems are planned as an intregal part of the design. Feedback requiremetns for JLC (the Japanese Linear Collider) are essentially identical to NLC; some of the TESLA requirements are similar but there are significant differences. For NLC, algorithms which incorporate improvements upon the SLC implementation are being prototyped. Specialized systems for the damping rings, rf and interaction point will operate at hi...

  5. δ- and δ'-shock wave types of singular solutions of systems of conservation laws and transport and concentration processes

    International Nuclear Information System (INIS)

    Shelkovich, V M

    2008-01-01

    This is a survey of some results and problems connected with the theory of generalized solutions of quasi-linear conservation law systems which can admit delta-shaped singularities. They are the so-called δ-shock wave type solutions and the recently introduced δ (n) -shock wave type solutions, n=1,2,..., which cannot be included in the classical Lax-Glimm theory. The case of δ- and δ'-shock waves is analyzed in detail. A specific analytical technique is developed to deal with such solutions. In order to define them, some special integral identities are introduced which extend the concept of weak solution, and the Rankine-Hugoniot conditions are derived. Solutions of Cauchy problems are constructed for some typical systems of conservation laws. Also investigated are multidimensional systems of conservation laws (in particular, zero-pressure gas dynamics systems) which admit δ-shock wave type solutions. A geometric aspect of such solutions is considered: they are connected with transport and concentration processes, and the balance laws of transport of 'volume' and 'area' to δ- and δ'-shock fronts are derived for them. For a 'zero-pressure gas dynamics' system these laws are the mass and momentum transport laws. An algebraic aspect of these solutions is also considered: flux-functions are constructed for them which, being non-linear, are nevertheless uniquely defined Schwartz distributions. Thus, a singular solution of the Cauchy problem generates algebraic relations between its components (distributions).

  6. The method of normal forms for singularly perturbed systems of Fredholm integro-differential equations with rapidly varying kernels

    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.

  7. On the use of blowup to study regularizations of singularities of piecewise smooth dynamical systems in R^3

    DEFF Research Database (Denmark)

    Kristiansen, Kristian Uldall; Hogan, S. J.

    2015-01-01

    In this paper we use the blowup method of Dumortier and Roussarie, in the formulation due to Krupa and Szmolyan, to study the regularization of singularities of piecewise smooth dynamical systems in R3. Using the regularization method of Sotomayor and Teixeira, we first demonstrate the power of our...... approach by considering the case of a fold line. We quickly extend a main result of Reves and Seara in a simple manner. Then, for the two-fold singularity, we show that the regularized system only fully retains the features of the singular canards in the piecewise smooth system in the cases when...... the sliding region does not include a full sector of singular canards. In particular, we show that every locally unique primary singular canard persists the regularizing perturbation. For the case of a sector of primary singular canards, we show that the regularized system contains a canard, provided...

  8. Feedback Systems for Linear Colliders

    International Nuclear Information System (INIS)

    1999-01-01

    Feedback systems are essential for stable operation of a linear collider, providing a cost-effective method for relaxing tight tolerances. In the Stanford Linear Collider (SLC), feedback controls beam parameters such as trajectory, energy, and intensity throughout the accelerator. A novel dithering optimization system which adjusts final focus parameters to maximize luminosity contributed to achieving record performance in the 1997-98 run. Performance limitations of the steering feedback have been investigated, and improvements have been made. For the Next Linear Collider (NLC), extensive feedback systems are planned as an integral part of the design. Feedback requirements for JLC (the Japanese Linear Collider) are essentially identical to NLC; some of the TESLA requirements are similar but there are significant differences. For NLC, algorithms which incorporate improvements upon the SLC implementation are being prototyped. Specialized systems for the damping rings, rf and interaction point will operate at high bandwidth and fast response. To correct for the motion of individual bunches within a train, both feedforward and feedback systems are planned. SLC experience has shown that feedback systems are an invaluable operational tool for decoupling systems, allowing precision tuning, and providing pulse-to-pulse diagnostics. Feedback systems for the NLC will incorporate the key SLC features and the benefits of advancing technologies

  9. Window observers for linear systems

    Directory of Open Access Journals (Sweden)

    Utkin Vadim

    2000-01-01

    Full Text Available Given a linear system x ˙ = A x + B u with output y = C x and a window function ω ( t , i.e., ∀ t , ω ( t ∈ {0,1 }, and assuming that the window function is Lebesgue measurable, we refer to the following observer, x ˆ = A x + B u + ω ( t L C ( x − x ˆ as a window observer. The stability issue is treated in this paper. It is proven that for linear time-invariant systems, the window observer can be stabilized by an appropriate design under a very mild condition on the window functions, albeit for linear time-varying system, some regularity of the window functions is required to achieve observer designs with the asymptotic stability. The corresponding design methods are developed. An example is included to illustrate the possible applications

  10. Linear analysis of rotationally invariant, radially variant tomographic imaging systems

    International Nuclear Information System (INIS)

    Huesmann, R.H.

    1990-01-01

    This paper describes a method to analyze the linear imaging characteristics of rotationally invariant, radially variant tomographic imaging systems using singular value decomposition (SVD). When the projection measurements from such a system are assumed to be samples from independent and identically distributed multi-normal random variables, the best estimate of the emission intensity is given by the unweighted least squares estimator. The noise amplification of this estimator is inversely proportional to the singular values of the normal matrix used to model projection and backprojection. After choosing an acceptable noise amplification, the new method can determine the number of parameters and hence the number of pixels that should be estimated from data acquired from an existing system with a fixed number of angles and projection bins. Conversely, for the design of a new system, the number of angles and projection bins necessary for a given number of pixels and noise amplification can be determined. In general, computing the SVD of the projection normal matrix has cubic computational complexity. However, the projection normal matrix for this class of rotationally invariant, radially variant systems has a block circulant form. A fast parallel algorithm to compute the SVD of this block circulant matrix makes the singular value analysis practical by asymptotically reducing the computation complexity of the method by a multiplicative factor equal to the number of angles squared

  11. Systems of Inhomogeneous Linear Equations

    Science.gov (United States)

    Scherer, Philipp O. J.

    Many problems in physics and especially computational physics involve systems of linear equations which arise e.g. from linearization of a general nonlinear problem or from discretization of differential equations. If the dimension of the system is not too large standard methods like Gaussian elimination or QR decomposition are sufficient. Systems with a tridiagonal matrix are important for cubic spline interpolation and numerical second derivatives. They can be solved very efficiently with a specialized Gaussian elimination method. Practical applications often involve very large dimensions and require iterative methods. Convergence of Jacobi and Gauss-Seidel methods is slow and can be improved by relaxation or over-relaxation. An alternative for large systems is the method of conjugate gradients.

  12. Singular elliptic systems involving concave terms and critical Caffarelli-Kohn-Nirenberg exponents

    Directory of Open Access Journals (Sweden)

    Mohammed E. O. El Mokhtar

    2012-03-01

    Full Text Available In this article, we establish the existence of at least four solutions to a singular system with a concave term, a critical Caffarelli-Kohn-Nirenberg exponent, and sign-changing weight functions. Our main tools are the Nehari manifold and the mountain pass theorem.

  13. Exact solution of a key equation in a finite stellar atmosphere by the method of Laplace transform and linear singular operators

    International Nuclear Information System (INIS)

    Das, R.N.

    1980-01-01

    The key equation which commonly appears for radiative transfer in a finite stellar atmosphere having ground reflection according to Lambert's law is considered in this paper. The exact solution of this equation is obtained for surface quantities in terms of the X-Y equations of Chandrasekhar by the method of Laplace transform and linear singular operators. This exact method is widely applicable for obtaining the solution for surface quantities in a finite atmosphere. (orig.)

  14. Linear collider systems and costs

    International Nuclear Information System (INIS)

    Loew, G.A.

    1993-05-01

    The purpose of this paper is to examine some of the systems and sub-systems involved in so-called ''conventional'' e + e - linear colliders and to study how their design affects the overall cost of these machines. There are presently a total of at least six 500 GeV c. of m. linear collider projects under study in the world. Aside from TESLA (superconducting linac at 1.3 GHz) and CLIC (two-beam accelerator with main linac at 30GHz), the other four proposed e + e - linear colliders can be considered ''conventional'' in that their main linacs use the proven technique of driving room temperature accelerator sections with pulsed klystrons and modulators. The centrally distinguishing feature between these projects is their main linac rf frequency: 3 GHz for the DESY machine, 11.424 GHz for the SLAC and JLC machines, and 14 GHz for the VLEPP machine. The other systems, namely the electron and positron sources, preaccelerators, compressors, damping rings and final foci, are fairly similar from project to project. Probably more than 80% of the cost of these linear colliders will be incurred in the two main linacs facing each other and it is therefore in their design and construction that major savings or extra costs may be found

  15. Some singularity in rotor’s systems with limited excitation

    International Nuclear Information System (INIS)

    Jivkov, Venelin

    2016-01-01

    The aim of the present paper is to study virtual steady-state vibrations in the neighbourhood of resonance conditions of a rotor with six degrees of freedom in linear homogeneous elasto-viscous field. Unstable frequencies zones are determined by “limited” power of an electric motor with linear characteristic and only one time-constant. Bogoliubov–Mitropolsky’s asymptotical method is applied in the neighbourhood of single basic resonance by small difference between natural and driving frequencies. The influence of the motor’s time-constant is analyzed on the value of unstable frequency’s zones by quasi steady-state increasing/decreasing frequencies (jump phenomenon). By special condition increasing of the driving frequency in growing rate could be seen right after resonance due to transfer from “small” angular coordinates to main rotation. Experimental result is applied

  16. Singularity and stability in a periodic system of particle accelerators

    Science.gov (United States)

    Cai, Yunhai

    2018-05-01

    We study the single-particle dynamics in a general and parametrized alternating-gradient cell with zero chromaticity using the Lie algebra method. To our surprise, the first-order perturbation of the sextupoles largely determines the dynamics away from the major resonances. The dynamic aperture can be estimated from the topology and geometry of the phase space. In the linearly normalized phase space, it is scaled according to A ¯ ∝ϕ √{L } , where ϕ is the bending angle and L the length of the cell. For the 2 degrees of freedom with equal betatron tunes, the analytical perturbation theory leads us to the invariant or quasi-invariant tori, which play an important role in determining the stable volume in the four-dimensional phase space.

  17. 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

  18. Optimal control of dissipative nonlinear dynamical systems with triggers of coupled singularities

    Science.gov (United States)

    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

  19. A theoretical analysis of the feasibility of a singularity-induced micro-electroporation system.

    Directory of Open Access Journals (Sweden)

    Gregory D Troszak

    Full Text Available Electroporation, the permeabilization of the cell membrane lipid bilayer due to a pulsed electric field, has important implications in the biotechnology, medicine, and food industries. Traditional macro and micro-electroporation devices have facing electrodes, and require significant potential differences to induce electroporation. The goal of this theoretical study is to investigate the feasibility of singularity-induced micro-electroporation; an electroporation configuration aimed at minimizing the potential differences required to induce electroporation by separating adjacent electrodes with a nanometer-scale insulator. In particular, this study aims to understand the effect of (1 insulator thickness and (2 electrode kinetics on electric field distributions in the singularity-induced micro-electroporation configuration. A non-dimensional primary current distribution model of the micro-electroporation channel shows that while increasing insulator thickness results in smaller electric field magnitudes, electroporation can still be performed with insulators thick enough to be made with microfabrication techniques. Furthermore, a secondary current distribution model of the singularity-induced micro-electroporation configuration with inert platinum electrodes and water electrolyte indicates that electrode kinetics do not inhibit charge transfer to the extent that prohibitively large potential differences are required to perform electroporation. These results indicate that singularity-induced micro-electroporation could be used to develop an electroporation system that consumes minimal power, making it suitable for remote applications such as the sterilization of water and other liquids.

  20. Spectral singularities, biorthonormal systems and a two-parameter family of complex point interactions

    Energy Technology Data Exchange (ETDEWEB)

    Mostafazadeh, Ali [Department of Mathematics, Koc University, Rumelifeneri Yolu, 34450 Sariyer, Istanbul (Turkey); Mehri-Dehnavi, Hossein [Department of Physics, Institute for Advanced Studies in Basic Sciences, Zanjan 45195-1159 (Iran, Islamic Republic of)], E-mail: amostafazadeh@ku.edu.tr, E-mail: mehrideh@iasbs.ac.ir

    2009-03-27

    A curious feature of complex scattering potentials v(x) is the appearance of spectral singularities. We offer a quantitative description of spectral singularities that identifies them with an obstruction to the existence of a complete biorthonormal system consisting of the eigenfunctions of the Hamiltonian operator and its adjoint. We establish the equivalence of this description with the mathematicians' definition of spectral singularities for the potential v(x) = z{sub -}{delta}(x + a) + z{sub +}{delta}(x - a), where z{sub {+-}} and a are respectively complex and real parameters and {delta}(x) is the Dirac delta function. We offer a through analysis of the spectral properties of this potential and determine the regions in the space of the coupling constants z{sub {+-}} where it admits bound states and spectral singularities. In particular, we find an explicit bound on the size of certain regions in which the Hamiltonian is quasi-Hermitian and examine the consequences of imposing PT-symmetry.

  1. Unique solvability of some two-point boundary value problems for linear functional differential equations with singularities

    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

  2. Reduced-order model based active disturbance rejection control of hydraulic servo system with singular value perturbation theory.

    Science.gov (United States)

    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.

  3. Robust H∞ Control for Singular Time-Delay Systems via Parameterized Lyapunov Functional Approach

    Directory of Open Access Journals (Sweden)

    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.

  4. Dynamical singularities of glassy systems in a quantum quench.

    Science.gov (United States)

    Obuchi, Tomoyuki; Takahashi, Kazutaka

    2012-11-01

    We present a prototype of behavior of glassy systems driven by quantum dynamics in a quenching protocol by analyzing the random energy model in a transverse field. We calculate several types of dynamical quantum amplitude and find a freezing transition at some critical time. The behavior is understood by the partition-function zeros in the complex temperature plane. We discuss the properties of the freezing phase as a dynamical chaotic phase, which are contrasted to those of the spin-glass phase in the static system.

  5. Higher-order glass-transition singularities in systems with short-ranged attractive potentials

    International Nuclear Information System (INIS)

    Goetze, W; Sperl, M

    2003-01-01

    Within the mode-coupling theory for the evolution of structural relaxation, the A 4 -glass-transition singularities are identified for systems of particles interacting with a hard-sphere repulsion complemented by different short-ranged potentials: Baxter's singular potential regularized by a large-wavevector cut-off, a model for the Asakura-Oosawa depletion attraction, a triangular potential, a Yukawa attraction, and a square-well potential. The regular potentials yield critical packing fractions, critical Debye-Waller factors, and critical amplitudes very close to each other. The elastic moduli and the particle localization lengths for corresponding states of the Yukawa system and the square-well system may differ by up to 20 and 10%, respectively

  6. Semilinear hyperbolic systems and equations with singular initial data

    International Nuclear Information System (INIS)

    Gramchev, T.

    1991-07-01

    We study the weak limits of solutions u ε (t, ·) for ε→0 to semilinear strictly hyperbolic systems and wave equations with initial data u ε (0, ·) approximating a distribution κ, 0 ε (t, ·) for ε→0 exists. 13 refs

  7. Focal points and principal solutions of linear Hamiltonian systems revisited

    Science.gov (United States)

    Šepitka, Peter; Šimon Hilscher, Roman

    2018-05-01

    In this paper we present a novel view on the principal (and antiprincipal) solutions of linear Hamiltonian systems, as well as on the focal points of their conjoined bases. We present a new and unified theory of principal (and antiprincipal) solutions at a finite point and at infinity, and apply it to obtain new representation of the multiplicities of right and left proper focal points of conjoined bases. We show that these multiplicities can be characterized by the abnormality of the system in a neighborhood of the given point and by the rank of the associated T-matrix from the theory of principal (and antiprincipal) solutions. We also derive some additional important results concerning the representation of T-matrices and associated normalized conjoined bases. The results in this paper are new even for completely controllable linear Hamiltonian systems. We also discuss other potential applications of our main results, in particular in the singular Sturmian theory.

  8. Linear operator inequalities for strongly stable weakly regular linear systems

    NARCIS (Netherlands)

    Curtain, RF

    2001-01-01

    We consider the question of the existence of solutions to certain linear operator inequalities (Lur'e equations) for strongly stable, weakly regular linear systems with generating operators A, B, C, 0. These operator inequalities are related to the spectral factorization of an associated Popov

  9. Sensitivity analysis of automatic flight control systems using singular value concepts

    Science.gov (United States)

    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.

  10. Impulsive Controller Design for Complex Nonlinear Singular Networked Systems with Packet Dropouts

    Directory of Open Access Journals (Sweden)

    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.

  11. Global quantal canonical symmetry properties for a system with a singular Lagrangian

    International Nuclear Information System (INIS)

    Li Ziping

    1996-01-01

    Starting from the quantization formalism of the phase-space path integral for a system with a singular Lagrangian, the generalized canonical Ward identities and conserved charged at quantum level are deduced under the global transformation in extended phase space. In general, the quantal conserved charges are different from classical ones. We give a preliminary application to Yang-Mills theory, the new quantal conserved charges are found

  12. A robust computational technique for a system of singularly perturbed reaction–diffusion equations

    Directory of Open Access Journals (Sweden)

    Kumar Vinod

    2014-06-01

    Full Text Available In this paper, a singularly perturbed system of reaction–diffusion Boundary Value Problems (BVPs is examined. To solve such a type of problems, a Modified Initial Value Technique (MIVT is proposed on an appropriate piecewise uniform Shishkin mesh. The MIVT is shown to be of second order convergent (up to a logarithmic factor. Numerical results are presented which are in agreement with the theoretical results.

  13. Automatic classification of singular elements for the electrostatic analysis of microelectromechanical systems

    Science.gov (United States)

    Su, Y.; Ong, E. T.; Lee, K. H.

    2002-05-01

    The past decade has seen an accelerated growth of technology in the field of microelectromechanical systems (MEMS). The development of MEMS products has generated the need for efficient analytical and simulation methods for minimizing the requirement for actual prototyping. The boundary element method is widely used in the electrostatic analysis for MEMS devices. However, singular elements are needed to accurately capture the behavior at singular regions, such as sharp corners and edges, where standard elements fail to give an accurate result. The manual classification of boundary elements based on their singularity conditions is an immensely laborious task, especially when the boundary element model is large. This process can be automated by querying the geometric model of the MEMS device for convex edges based on geometric information of the model. The associated nodes of the boundary elements on these edges can then be retrieved. The whole process is implemented in the MSC/PATRAN platform using the Patran Command Language (the source code is available as supplementary data in the electronic version of this journal issue).

  14. Analytical singular-value decomposition of three-dimensional, proximity-based SPECT systems

    Energy Technology Data Exchange (ETDEWEB)

    Barrett, Harrison H. [Arizona Univ., Tucson, AZ (United States). College of Optical Sciences; Arizona Univ., Tucson, AZ (United States). Center for Gamma-Ray Imaging; Holen, Roel van [Ghent Univ. (Belgium). Medical Image and Signal Processing (MEDISIP); Arizona Univ., Tucson, AZ (United States). Center for Gamma-Ray Imaging

    2011-07-01

    An operator formalism is introduced for the description of SPECT imaging systems that use solid-angle effects rather than pinholes or collimators, as in recent work by Mitchell and Cherry. The object is treated as a 3D function, without discretization, and the data are 2D functions on the detectors. An analytic singular-value decomposition of the resulting integral operator is performed and used to compute the measurement and null components of the objects. The results of the theory are confirmed with a Landweber algorithm that does not require a system matrix. (orig.)

  15. Use Residual Correction Method and Monotone Iterative Technique to Calculate the Upper and Lower Approximate Solutions of Singularly Perturbed Non-linear Boundary Value Problems

    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.

  16. Algorithms for large scale singular value analysis of spatially variant tomography systems

    International Nuclear Information System (INIS)

    Cao-Huu, Tuan; Brownell, G.; Lachiver, G.

    1996-01-01

    The problem of determining the eigenvalues of large matrices occurs often in the design and analysis of modem tomography systems. As there is an interest in solving systems containing an ever-increasing number of variables, current research effort is being made to create more robust solvers which do not depend on some special feature of the matrix for convergence (e.g. block circulant), and to improve the speed of already known and understood solvers so that solving even larger systems in a reasonable time becomes viable. Our standard techniques for singular value analysis are based on sparse matrix factorization and are not applicable when the input matrices are large because the algorithms cause too much fill. Fill refers to the increase of non-zero elements in the LU decomposition of the original matrix A (the system matrix). So we have developed iterative solutions that are based on sparse direct methods. Data motion and preconditioning techniques are critical for performance. This conference paper describes our algorithmic approaches for large scale singular value analysis of spatially variant imaging systems, and in particular of PCR2, a cylindrical three-dimensional PET imager 2 built at the Massachusetts General Hospital (MGH) in Boston. We recommend the desirable features and challenges for the next generation of parallel machines for optimal performance of our solver

  17. Dynamic linearization system for a radiation gauge

    International Nuclear Information System (INIS)

    Panarello, J.A.

    1977-01-01

    The linearization system and process converts a high resolution non-linear analog input signal, representative of the thickness of an object, into a high resolution linear analog output signal suitable for use in driving a variety of output devices. The system requires only a small amount of memory for storing pre-calculated non-linear correction coefficients. The system channels the input signal to separate circuit paths so that it may be used directly to; locate an appropriate correction coefficient; develop a correction term after an appropriate correction coefficient is located; and develop a linearized signal having the same high resolution inherent in the input signal. The system processes the linearized signal to compensate for the possible errors introduced by radiation source noise. The processed linearized signal is the high resolution linear analog output signal which accurately represents the thickness of the object being gauged

  18. Linear quadratic optimization for positive LTI system

    Science.gov (United States)

    Muhafzan, Yenti, Syafrida Wirma; Zulakmal

    2017-05-01

    Nowaday the linear quadratic optimization subject to positive linear time invariant (LTI) system constitute an interesting study considering it can become a mathematical model of variety of real problem whose variables have to nonnegative and trajectories generated by these variables must be nonnegative. In this paper we propose a method to generate an optimal control of linear quadratic optimization subject to positive linear time invariant (LTI) system. A sufficient condition that guarantee the existence of such optimal control is discussed.

  19. Robust stability analysis of large power systems using the structured singular value theory

    Energy Technology Data Exchange (ETDEWEB)

    Castellanos, R.; Sarmiento, H. [Instituto de Investigaciones Electricas, Cuernavaca, Morelos (Mexico); Messina, A.R. [Cinvestav, Graduate Program in Electrical Engineering, Guadalajara, Jalisco (Mexico)

    2005-07-01

    This paper examines the application of structured singular value (SSV) theory to analyse robust stability of complex power systems with respect to a set of structured uncertainties. Based on SSV theory and the frequency sweep method, techniques for robust analysis of large-scale power systems are developed. The main interest is focused on determining robust stability for varying operating conditions and uncertainties in the structure of the power system. The applicability of the proposed techniques is verified through simulation studies on a large-scale power system. In particular, results for the system are considered for a wide range of uncertainties of operating conditions. Specifically, the developed technique is used to estimate the effect of variations in the parameters of a major system inter-tie on the nominal stability of a critical inter-area mode. (Author)

  20. 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)

  1. Fermi-edge singularity in one-dimensional electron systems with long-range Coulomb interactions

    International Nuclear Information System (INIS)

    Otani, H.; Ogawa, T.

    1996-01-01

    Effects of long-range Coulomb interactions on the Fermi-edge singularity in optical spectra are investigated theoretically for one-dimensional spin-1/2 fermion systems with the use of the Tomonaga-Luttinger bosonization technique. Low-energy excitation spectrum near the Fermi level shows that dispersion of the charge-density fluctuation remains gapless but is nonlinear when the electron-electron (e-e) Coulomb interaction is of the x -1 type (i.e., an infinite force range). Temporal behavior of the current-current correlation function is calculated analytically for arbitrary force ranges, λ e and λ h , of the e-e and the electron-hole (e-h) Coulomb interactions. (i) When both the e-e and the e-h interactions have large but finite force ranges (λ e h max[λ e ,λ h ]/v F . Corresponding optical spectrum near the Fermi edge (within an energy range of ℎv F /max[λ e ,λ h ]) exhibits the power-law divergence or the power-law convergence, which is an ordinary Fermi-edge singularity. (ii) When either the e-e or the e-h interaction is of the x -1 type (i.e., λ e →∞ and/or λ h →∞), an exponent of the correlation function is dependent on time to lead the faster decay than that of any power laws. Then the optical spectra show no power law dependence and always converge (become zero) at the Fermi edge, which is in striking contrast to the ordinary power-law singularity

  2. Coloured phase singularities

    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)

  3. Initial time singularities and admissible initial states for a system of coupled scalar fields

    Energy Technology Data Exchange (ETDEWEB)

    Baacke, Juergen [Technische Univ. Dortmund (Germany). Fakultaet Physik; Kevlishvili, Nina [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); GAS, Tbilisi (Georgia). Andronikashvili Inst. of Physics

    2009-10-15

    We discuss the problem of initial states for a system of coupled scalar fields out of equilibrium in the one-loop approximation. The fields consist of classical background fields, taken constant in space, and quantum fluctuations. If the initial state is the adiabatic vacuum, i.e., the ground state of a Fock space of particle excitations that diagonalize the mass matrix, the energy-momentum tensor is infinite at t=0, its most singular part behaves as 1/t. When the system is coupled to gravity this presents a problem that we solve by a Bogoliubov transformation of the naive initial state. As a side result we also discuss the canonical formalism and the adiabatic particle number for such a system. Most of the formalism is presented for Minkowksi space. Embedding the system and its dynamics into a flat FRW universe is straightforward and we briefly address the essential modifications. (orig.)

  4. Initial time singularities and admissible initial states for a system of coupled scalar fields

    International Nuclear Information System (INIS)

    Baacke, Juergen; Kevlishvili, Nina; GAS, Tbilisi

    2009-10-01

    We discuss the problem of initial states for a system of coupled scalar fields out of equilibrium in the one-loop approximation. The fields consist of classical background fields, taken constant in space, and quantum fluctuations. If the initial state is the adiabatic vacuum, i.e., the ground state of a Fock space of particle excitations that diagonalize the mass matrix, the energy-momentum tensor is infinite at t=0, its most singular part behaves as 1/t. When the system is coupled to gravity this presents a problem that we solve by a Bogoliubov transformation of the naive initial state. As a side result we also discuss the canonical formalism and the adiabatic particle number for such a system. Most of the formalism is presented for Minkowksi space. Embedding the system and its dynamics into a flat FRW universe is straightforward and we briefly address the essential modifications. (orig.)

  5. On pole structure assignment in linear systems

    Czech Academy of Sciences Publication Activity Database

    Loiseau, J.-J.; Zagalak, Petr

    2009-01-01

    Roč. 82, č. 7 (2009), s. 1179-1192 ISSN 0020-7179 R&D Projects: GA ČR(CZ) GA102/07/1596 Institutional research plan: CEZ:AV0Z10750506 Keywords : linear systems * linear state feedback * pole structure assignment Subject RIV: BC - Control Systems Theory Impact factor: 1.124, year: 2009 http://library.utia.cas.cz/separaty/2009/AS/zagalak-on pole structure assignment in linear systems.pdf

  6. Homoclinic Solutions for a Class of Second Order Nonautonomous Singular Hamiltonian Systems

    Directory of Open Access Journals (Sweden)

    Ziheng Zhang

    2014-01-01

    Full Text Available We are concerned with the existence of homoclinic solutions for the following second order nonautonomous singular Hamiltonian systems u¨+atWuu=0, (HS where -∞singularity at 0≠ξ∈ℝN, and Wuu is the gradient of W at u. The novelty of this paper is that, for the case that N≥3 and (HS is nonautonomous (neither periodic nor almost periodic, we show that (HS possesses at least one nontrivial homoclinic solution. Our main hypotheses are the strong force condition of Gordon and the uniqueness of a global maximum of W. Different from the cases that (HS is autonomous at≡1 or (HS is periodic or almost periodic, as far as we know, this is the first result concerning the case that (HS is nonautonomous and N≥3. Besides the usual conditions on W, we need the assumption that a′t<0 for all t∈ℝ to guarantee the existence of homoclinic solution. Recent results in the literature are generalized and significantly improved.

  7. Patterns and singular features of extreme fluctuational paths of a periodically driven system

    International Nuclear Information System (INIS)

    Chen, Zhen; Liu, Xianbin

    2016-01-01

    Large fluctuations of an overdamped periodically driven oscillating system are investigated theoretically and numerically in the limit of weak noise. Optimal paths fluctuating to certain point are given by statistical analysis using the concept of prehistory probability distribution. The validity of statistical results is verified by solutions of boundary value problem. Optimal paths are found to change topologically when terminating points lie at opposite side of a switching line. Patterns of extreme paths are plotted through a proper parameterization of Lagrangian manifold having complicated structures. Several extreme paths to the same point are obtained by multiple solutions of boundary value solutions. Actions along various extreme paths are calculated and associated analysis is performed in relation to the singular features of the patterns. - Highlights: • Both extreme and optimal paths are obtained by various methods. • Boundary value problems are solved to ensure the validity of statistical results. • Topological structure of Lagrangian manifold is considered. • Singularities of the pattern of extreme paths are studied.

  8. Examples of integrable and non-integrable systems on singular symplectic manifolds

    Science.gov (United States)

    Delshams, Amadeu; Kiesenhofer, Anna; Miranda, Eva

    2017-05-01

    We present a collection of examples borrowed from celestial mechanics and projective dynamics. In these examples symplectic structures with singularities arise naturally from regularization transformations, Appell's transformation or classical changes like McGehee coordinates, which end up blowing up the symplectic structure or lowering its rank at certain points. The resulting geometrical structures that model these examples are no longer symplectic but symplectic with singularities which are mainly of two types: bm-symplectic and m-folded symplectic structures. These examples comprise the three body problem as non-integrable exponent and some integrable reincarnations such as the two fixed-center problem. Given that the geometrical and dynamical properties of bm-symplectic manifolds and folded symplectic manifolds are well-understood [10-12,9,15,13,14,24,20,22,25,28], we envisage that this new point of view in this collection of examples can shed some light on classical long-standing problems concerning the study of dynamical properties of these systems seen from the Poisson viewpoint.

  9. Displacement measurement system for linear array detector

    International Nuclear Information System (INIS)

    Zhang Pengchong; Chen Ziyu; Shen Ji

    2011-01-01

    It presents a set of linear displacement measurement system based on encoder. The system includes displacement encoders, optical lens and read out circuit. Displacement read out unit includes linear CCD and its drive circuit, two amplifier circuits, second order Butterworth low-pass filter and the binarization circuit. The coding way is introduced, and various parts of the experimental signal waveforms are given, and finally a linear experimental test results are given. The experimental results are satisfactory. (authors)

  10. Numerical solution of large sparse linear systems

    International Nuclear Information System (INIS)

    Meurant, Gerard; Golub, Gene.

    1982-02-01

    This note is based on one of the lectures given at the 1980 CEA-EDF-INRIA Numerical Analysis Summer School whose aim is the study of large sparse linear systems. The main topics are solving least squares problems by orthogonal transformation, fast Poisson solvers and solution of sparse linear system by iterative methods with a special emphasis on preconditioned conjuguate gradient method [fr

  11. Balanced truncation for linear switched systems

    DEFF Research Database (Denmark)

    Petreczky, Mihaly; Wisniewski, Rafal; Leth, John-Josef

    2013-01-01

    In this paper, we present a theoretical analysis of the model reduction algorithm for linear switched systems from Shaker and Wisniewski (2011, 2009) and . This algorithm is a reminiscence of the balanced truncation method for linear parameter varying systems (Wood et al., 1996) [3]. Specifically...

  12. A locally convergent Jacobi iteration for the tensor singular value problem

    NARCIS (Netherlands)

    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

  13. Observability of linear systems with saturated outputs

    NARCIS (Netherlands)

    Koplon, R.; Sontag, E.D.; Hautus, M.L.J.

    1994-01-01

    We present necessary and sufficient conditions for observability of the class of output-saturated systems. These are linear systems whose output passes through a saturation function before it can be measured.

  14. Non-isothermal Smoluchowski-Poisson equation as a singular limit of the Navier-Stokes-Fourier-Poisson system

    Czech Academy of Sciences Publication Activity Database

    Feireisl, Eduard; Laurençot, P.

    2007-01-01

    Roč. 88, - (2007), s. 325-349 ISSN 0021-7824 R&D Projects: GA ČR GA201/05/0164 Institutional research plan: CEZ:AV0Z10190503 Keywords : Navier-Stokes-Fourier- Poisson system * Smoluchowski- Poisson system * singular limit Subject RIV: BA - General Mathematics Impact factor: 1.118, year: 2007

  15. Quantum solitonic wave-packet of a meso-scopic system in singularity free gravity

    Science.gov (United States)

    Buoninfante, Luca; Lambiase, Gaetano; Mazumdar, Anupam

    2018-06-01

    In this paper we will discuss how to localise a quantum wave-packet due to self-gravitating meso-scopic object by taking into account gravitational self-interaction in the Schrödinger equation beyond General Relativity. In particular, we will study soliton-like solutions in infinite derivative ghost free theories of gravity, which resolves the gravitational 1 / r singularity in the potential. We will show a unique feature that the quantum spread of such a gravitational system is larger than that of the Newtonian gravity, therefore enabling us a window of opportunity to test classical and quantum properties of such theories of gravity in the near future at a table-top experiment.

  16. Isolators Including Main Spring Linear Guide Systems

    Science.gov (United States)

    Goold, Ryan (Inventor); Buchele, Paul (Inventor); Hindle, Timothy (Inventor); Ruebsamen, Dale Thomas (Inventor)

    2017-01-01

    Embodiments of isolators, such as three parameter isolators, including a main spring linear guide system are provided. In one embodiment, the isolator includes first and second opposing end portions, a main spring mechanically coupled between the first and second end portions, and a linear guide system extending from the first end portion, across the main spring, and toward the second end portion. The linear guide system expands and contracts in conjunction with deflection of the main spring along the working axis, while restricting displacement and rotation of the main spring along first and second axes orthogonal to the working axis.

  17. Singular value decomposition for photon-processing nuclear imaging systems and applications for reconstruction and computing null functions

    Science.gov (United States)

    Jha, Abhinav K.; Barrett, Harrison H.; Frey, Eric C.; Clarkson, Eric; Caucci, Luca; Kupinski, Matthew A.

    2015-09-01

    Recent advances in technology are enabling a new class of nuclear imaging systems consisting of detectors that use real-time maximum-likelihood (ML) methods to estimate the interaction position, deposited energy, and other attributes of each photon-interaction event and store these attributes in a list format. This class of systems, which we refer to as photon-processing (PP) nuclear imaging systems, can be described by a fundamentally different mathematical imaging operator that allows processing of the continuous-valued photon attributes on a per-photon basis. Unlike conventional photon-counting (PC) systems that bin the data into images, PP systems do not have any binning-related information loss. Mathematically, while PC systems have an infinite-dimensional null space due to dimensionality considerations, PP systems do not necessarily suffer from this issue. Therefore, PP systems have the potential to provide improved performance in comparison to PC systems. To study these advantages, we propose a framework to perform the singular-value decomposition (SVD) of the PP imaging operator. We use this framework to perform the SVD of operators that describe a general two-dimensional (2D) planar linear shift-invariant (LSIV) PP system and a hypothetical continuously rotating 2D single-photon emission computed tomography (SPECT) PP system. We then discuss two applications of the SVD framework. The first application is to decompose the object being imaged by the PP imaging system into measurement and null components. We compare these components to the measurement and null components obtained with PC systems. In the process, we also present a procedure to compute the null functions for a PC system. The second application is designing analytical reconstruction algorithms for PP systems. The proposed analytical approach exploits the fact that PP systems acquire data in a continuous domain to estimate a continuous object function. The approach is parallelizable and

  18. Singular value decomposition for photon-processing nuclear imaging systems and applications for reconstruction and computing null functions.

    Science.gov (United States)

    Jha, Abhinav K; Barrett, Harrison H; Frey, Eric C; Clarkson, Eric; Caucci, Luca; Kupinski, Matthew A

    2015-09-21

    Recent advances in technology are enabling a new class of nuclear imaging systems consisting of detectors that use real-time maximum-likelihood (ML) methods to estimate the interaction position, deposited energy, and other attributes of each photon-interaction event and store these attributes in a list format. This class of systems, which we refer to as photon-processing (PP) nuclear imaging systems, can be described by a fundamentally different mathematical imaging operator that allows processing of the continuous-valued photon attributes on a per-photon basis. Unlike conventional photon-counting (PC) systems that bin the data into images, PP systems do not have any binning-related information loss. Mathematically, while PC systems have an infinite-dimensional null space due to dimensionality considerations, PP systems do not necessarily suffer from this issue. Therefore, PP systems have the potential to provide improved performance in comparison to PC systems. To study these advantages, we propose a framework to perform the singular-value decomposition (SVD) of the PP imaging operator. We use this framework to perform the SVD of operators that describe a general two-dimensional (2D) planar linear shift-invariant (LSIV) PP system and a hypothetical continuously rotating 2D single-photon emission computed tomography (SPECT) PP system. We then discuss two applications of the SVD framework. The first application is to decompose the object being imaged by the PP imaging system into measurement and null components. We compare these components to the measurement and null components obtained with PC systems. In the process, we also present a procedure to compute the null functions for a PC system. The second application is designing analytical reconstruction algorithms for PP systems. The proposed analytical approach exploits the fact that PP systems acquire data in a continuous domain to estimate a continuous object function. The approach is parallelizable and

  19. Linear systems a measurement based approach

    CERN Document Server

    Bhattacharyya, S P; Mohsenizadeh, D N

    2014-01-01

    This brief presents recent results obtained on the analysis, synthesis and design of systems described by linear equations. It is well known that linear equations arise in most branches of science and engineering as well as social, biological and economic systems. The novelty of this approach is that no models of the system are assumed to be available, nor are they required. Instead, a few measurements made on the system can be processed strategically to directly extract design values that meet specifications without constructing a model of the system, implicitly or explicitly. These new concepts are illustrated by applying them to linear DC and AC circuits, mechanical, civil and hydraulic systems, signal flow block diagrams and control systems. These applications are preliminary and suggest many open problems. The results presented in this brief are the latest effort in this direction and the authors hope these will lead to attractive alternatives to model-based design of engineering and other systems.

  20. Robust Stability Analysis of the Space Launch System Control Design: A Singular Value Approach

    Science.gov (United States)

    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.

  1. The Oberbeck-Boussinesq approximation as a singular limit of the full Navier-Stokes-Fourier system

    Czech Academy of Sciences Publication Activity Database

    Feireisl, Eduard; Novotný, A.

    2009-01-01

    Roč. 11, č. 2 (2009), s. 274-302 ISSN 1422-6928 R&D Projects: GA ČR GA201/05/0164 Institutional research plan: CEZ:AV0Z10190503 Keywords : singular limit * Navier-Stokes-Fourier system * Oberbeck -Boussinesq approximation Subject RIV: BA - General Mathematics Impact factor: 1.214, year: 2009

  2. Final focus systems for linear colliders

    International Nuclear Information System (INIS)

    Erickson, R.A.

    1987-11-01

    The final focus system of a linear collider must perform two primary functions, it must focus the two opposing beams so that their transverse dimensions at the interaction point are small enough to yield acceptable luminosity, and it must steer the beams together to maintain collisions. In addition, the final focus system must transport the outgoing beams to a location where they can be recycled or safely dumped. Elementary optical considerations for linear collider final focus systems are discussed, followed by chromatic aberrations. The design of the final focus system of the SLAC Linear Collider (SLC) is described. Tuning and diagnostics and steering to collision are discussed. Most of the examples illustrating the concepts covered are drawn from the SLC, but the principles and conclusions are said to be generally applicable to other linear collider designs as well. 26 refs., 17 figs

  3. Superconducting linear accelerator system for NSC

    Indian Academy of Sciences (India)

    59, No. 5. — journal of. November 2002 physics pp. 849–858. Superconducting linear accelerator system for NSC ... cryogenics facility, RF electronics development, facilities for fabricating niobium resonators indige- ... Prototype resonator was.

  4. Fast Solvers for Dense Linear Systems

    Energy Technology Data Exchange (ETDEWEB)

    Kauers, Manuel [Research Institute for Symbolic Computation (RISC), Altenbergerstrasse 69, A4040 Linz (Austria)

    2008-10-15

    It appears that large scale calculations in particle physics often require to solve systems of linear equations with rational number coefficients exactly. If classical Gaussian elimination is applied to a dense system, the time needed to solve such a system grows exponentially in the size of the system. In this tutorial paper, we present a standard technique from computer algebra that avoids this exponential growth: homomorphic images. Using this technique, big dense linear systems can be solved in a much more reasonable time than using Gaussian elimination over the rationals.

  5. Algorithms in Singular

    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].

  6. Signals and transforms in linear systems analysis

    CERN Document Server

    Wasylkiwskyj, Wasyl

    2013-01-01

    Signals and Transforms in Linear Systems Analysis covers the subject of signals and transforms, particularly in the context of linear systems theory. Chapter 2 provides the theoretical background for the remainder of the text. Chapter 3 treats Fourier series and integrals. Particular attention is paid to convergence properties at step discontinuities. This includes the Gibbs phenomenon and its amelioration via the Fejer summation techniques. Special topics include modulation and analytic signal representation, Fourier transforms and analytic function theory, time-frequency analysis and frequency dispersion. Fundamentals of linear system theory for LTI analogue systems, with a brief account of time-varying systems, are covered in Chapter 4 . Discrete systems are covered in Chapters 6 and 7.  The Laplace transform treatment in Chapter 5 relies heavily on analytic function theory as does Chapter 8 on Z -transforms. The necessary background on complex variables is provided in Appendix A. This book is intended to...

  7. STABILITY OF LINEAR SYSTEMS WITH MARKOVIAN JUMPS

    Directory of Open Access Journals (Sweden)

    Jorge Enrique Mayta Guillermo

    2016-12-01

    Full Text Available In this work we will analyze the stability of linear systems governed by a Markov chain, this family is known in the specialized literature as linear systems with Markov jumps or by its acronyms in English MJLS as it is denoted in [1]. Linear systems governed by a Markov chain are dynamic systems with abrupt changes. We give some denitions of stability for the MJLS system, where these types of stability are equivalent as long as the state space of the Markov chain is nite. Finally we present a theorem that characterizes the stochastic stability by means of an equation of the Lyapunov type. The result is a generalization of a theorem in classical theory.

  8. Correlated Levy Noise in Linear Dynamical Systems

    International Nuclear Information System (INIS)

    Srokowski, T.

    2011-01-01

    Linear dynamical systems, driven by a non-white noise which has the Levy distribution, are analysed. Noise is modelled by a specific stochastic process which is defined by the Langevin equation with a linear force and the Levy distributed symmetric white noise. Correlation properties of the process are discussed. The Fokker-Planck equation driven by that noise is solved. Distributions have the Levy shape and their width, for a given time, is smaller than for processes in the white noise limit. Applicability of the adiabatic approximation in the case of the linear force is discussed. (author)

  9. Introduction to linear systems of differential equations

    CERN Document Server

    Adrianova, L Ya

    1995-01-01

    The theory of linear systems of differential equations is one of the cornerstones of the whole theory of differential equations. At its root is the concept of the Lyapunov characteristic exponent. In this book, Adrianova presents introductory material and further detailed discussions of Lyapunov exponents. She also discusses the structure of the space of solutions of linear systems. Classes of linear systems examined are from the narrowest to widest: 1)�autonomous, 2)�periodic, 3)�reducible to autonomous, 4)�nearly reducible to autonomous, 5)�regular. In addition, Adrianova considers the following: stability of linear systems and the influence of perturbations of the coefficients on the stability the criteria of uniform stability and of uniform asymptotic stability in terms of properties of the solutions several estimates of the growth rate of solutions of a linear system in terms of its coefficients How perturbations of the coefficients change all the elements of the spectrum of the system is defin...

  10. Final Focus Systems in Linear Colliders

    International Nuclear Information System (INIS)

    Raubenheimer, Tor

    1998-01-01

    In colliding beam facilities, the ''final focus system'' must demagnify the beams to attain the very small spot sizes required at the interaction points. The first final focus system with local chromatic correction was developed for the Stanford Linear Collider where very large demagnifications were desired. This same conceptual design has been adopted by all the future linear collider designs as well as the SuperConducting Supercollider, the Stanford and KEK B-Factories, and the proposed Muon Collider. In this paper, the over-all layout, physics constraints, and optimization techniques relevant to the design of final focus systems for high-energy electron-positron linear colliders are reviewed. Finally, advanced concepts to avoid some of the limitations of these systems are discussed

  11. Linear dynamic coupling in geared rotor systems

    Science.gov (United States)

    David, J. W.; Mitchell, L. D.

    1986-01-01

    The effects of high frequency oscillations caused by the gear mesh, on components of a geared system that can be modeled as rigid discs are analyzed using linear dynamic coupling terms. The coupled, nonlinear equations of motion for a disc attached to a rotating shaft are presented. The results of a trial problem analysis show that the inclusion of the linear dynamic coupling terms can produce significant changes in the predicted response of geared rotor systems, and that the produced sideband responses are greater than the unbalanced response. The method is useful in designing gear drives for heavy-lift helicopters, industrial speed reducers, naval propulsion systems, and heavy off-road equipment.

  12. On output regulation for linear systems

    NARCIS (Netherlands)

    Saberi, Ali; Stoorvogel, Antonie Arij; Sannuti, Peddapullaiah

    For both continuous- and discrete-time systems, we revisit the output regulation problem for linear systems. We generalize the problem formulation in order • to expand the class of reference or disturbance signals, • to utilize the derivative or feedforward information of reference signals whenever

  13. Linear response theory for quantum open systems

    OpenAIRE

    Wei, J. H.; Yan, YiJing

    2011-01-01

    Basing on the theory of Feynman's influence functional and its hierarchical equations of motion, we develop a linear response theory for quantum open systems. Our theory provides an effective way to calculate dynamical observables of a quantum open system at its steady-state, which can be applied to various fields of non-equilibrium condensed matter physics.

  14. When to call a linear system nonnegative

    NARCIS (Netherlands)

    Nieuwenhuis, J.W.

    1998-01-01

    In this paper we will consider discrete time invariant linear systems that allow for an input-state-output representation with a finite dimensional state space, and that have a finite number of inputs and outputs. The basic issue in this paper is when to call these systems nonnegative. An important

  15. Tikhonov theorem for linear hyperbolic systems

    OpenAIRE

    Tang , Ying; Prieur , Christophe; Girard , Antoine

    2015-01-01

    International audience; A class of linear systems of conservation laws with a small perturbation parameter is introduced. By setting the perturbation parameter to zero, two subsystems, the reduced system standing for the slow dynamics and the boundary-layer system representing the fast dynamics, are computed. It is first proved that the exponential stability of the full system implies the stability of both subsystems. Secondly, a counter example is given to indicate that the converse is not t...

  16. Existence of infinitely many solutions for degenerate and singular elliptic systems with indefinite concave nonlinearities

    Directory of Open Access Journals (Sweden)

    Nguyen Thanh Chung

    2011-02-01

    Full Text Available In this article, we consider degenerate and singular elliptic systems of the form $$displaylines{ - hbox{div}(h_1(xabla u = b_1(x|u|^{r-2}u + F_u(x,u,v quad hbox{in } Omega,cr - hbox{div}(h_2(xabla v = b_2(x|v|^{r-2}v + F_v(x,u,v quad hbox{in } Omega, }$$ where $Omega$ is a bounded domain in $mathbb{R}^N$, $N geq 2$, with smooth boundary $partialOmega$; $h_i: Omega o [0, infty$, $h_i in L^1_{loc}(Omega$, and are allowed to have ``essential'' zeroes; $1 < r < 2$; the weight functions $b_i: Omega o mathbb{R}$, may be sign-changing; and $(F_u,F_v = abla F$. Using variational techniques, a variant of the Caffarelli - Kohn - Nirenberg inequality, and a variational principle by Clark [9], we prove the rxistence of infinitely many solutions in a weighted Sobolev space.

  17. Singular value decomposition analysis of a photoacoustic imaging system and 3D imaging at 0.7 FPS.

    Science.gov (United States)

    Roumeliotis, Michael B; Stodilka, Robert Z; Anastasio, Mark A; Ng, Eldon; Carson, Jeffrey J L

    2011-07-04

    Photoacoustic imaging is a non-ionizing imaging modality that provides contrast consistent with optical imaging techniques while the resolution and penetration depth is similar to ultrasound techniques. In a previous publication [Opt. Express 18, 11406 (2010)], a technique was introduced to experimentally acquire the imaging operator for a photoacoustic imaging system. While this was an important foundation for future work, we have recently improved the experimental procedure allowing for a more densely populated imaging operator to be acquired. Subsets of the imaging operator were produced by varying the transducer count as well as the measurement space temporal sampling rate. Examination of the matrix rank and the effect of contributing object space singular vectors to image reconstruction were performed. For a PAI system collecting only limited data projections, matrix rank increased linearly with transducer count and measurement space temporal sampling rate. Image reconstruction using a regularized pseudoinverse of the imaging operator was performed on photoacoustic signals from a point source, line source, and an array of point sources derived from the imaging operator. As expected, image quality increased for each object with increasing transducer count and measurement space temporal sampling rate. Using the same approach, but on experimentally sampled photoacoustic signals from a moving point-like source, acquisition, data transfer, reconstruction and image display took 1.4 s using one laser pulse per 3D frame. With relatively simple hardware improvements to data transfer and computation speed, our current imaging results imply that acquisition and display of 3D photoacoustic images at laser repetition rates of 10Hz is easily achieved.

  18. ITMETH, Iterative Routines for Linear System

    International Nuclear Information System (INIS)

    Greenbaum, A.

    1989-01-01

    1 - Description of program or function: ITMETH is a collection of iterative routines for solving large, sparse linear systems. 2 - Method of solution: ITMETH solves general linear systems of the form AX=B using a variety of methods: Jacobi iteration; Gauss-Seidel iteration; incomplete LU decomposition or matrix splitting with iterative refinement; diagonal scaling, matrix splitting, or incomplete LU decomposition with the conjugate gradient method for the problem AA'Y=B, X=A'Y; bi-conjugate gradient method with diagonal scaling, matrix splitting, or incomplete LU decomposition; and ortho-min method with diagonal scaling, matrix splitting, or incomplete LU decomposition. ITMETH also solves symmetric positive definite linear systems AX=B using the conjugate gradient method with diagonal scaling or matrix splitting, or the incomplete Cholesky conjugate gradient method

  19. Singular vectors, predictability and ensemble forecasting for weather and climate

    International Nuclear Information System (INIS)

    Palmer, T N; Zanna, Laure

    2013-01-01

    The local instabilities of a nonlinear dynamical system can be characterized by the leading singular vectors of its linearized operator. The leading singular vectors are perturbations with the greatest linear growth and are therefore key in assessing the system’s predictability. In this paper, the analysis of singular vectors for the predictability of weather and climate and ensemble forecasting is discussed. An overview of the role of singular vectors in informing about the error growth rate in numerical models of the atmosphere is given. This is followed by their use in the initialization of ensemble weather forecasts. Singular vectors for the ocean and coupled ocean–atmosphere system in order to understand the predictability of climate phenomena such as ENSO and meridional overturning circulation are reviewed and their potential use to initialize seasonal and decadal forecasts is considered. As stochastic parameterizations are being implemented, some speculations are made about the future of singular vectors for the predictability of weather and climate for theoretical applications and at the operational level. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Lyapunov analysis: from dynamical systems theory to applications’. (review)

  20. Application of matrix singular value properties for evaluating gain and phase margins of multiloop systems. [stability margins for wing flutter suppression and drone lateral attitude control

    Science.gov (United States)

    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.

  1. Conduction cooling systems for linear accelerator cavities

    Science.gov (United States)

    Kephart, Robert

    2017-05-02

    A conduction cooling system for linear accelerator cavities. The system conducts heat from the cavities to a refrigeration unit using at least one cavity cooler interconnected with a cooling connector. The cavity cooler and cooling connector are both made from solid material having a very high thermal conductivity of approximately 1.times.10.sup.4 W m.sup.-1 K.sup.-1 at temperatures of approximately 4 degrees K. This allows for very simple and effective conduction of waste heat from the linear accelerator cavities to the cavity cooler, along the cooling connector, and thence to the refrigeration unit.

  2. Rf system specifications for a linear accelerator

    International Nuclear Information System (INIS)

    Young, A.; Eaton, L.E.

    1992-01-01

    A linear accelerator contains many systems; however, the most complex and costly is the RF system. The goal of an RF system is usually simply stated as maintaining the phase and amplitude of the RF signal within a given tolerance to accelerate the charged particle beam. An RF system that drives a linear accelerator needs a complete system specification, which should contain specifications for all the subsystems (i.e., high-power RF, low-level RF, RF generation/distribution, and automation control). This paper defines a format for the specifications of these subsystems and discusses each RF subsystem independently to provide a comprehensive understanding of the function of each subsystem. This paper concludes with an example of a specification spreadsheet allowing one to input the specifications of a subsystem. Thus, some fundamental parameters (i.e., the cost and size) of the RF system can be determined

  3. Chaos as an intermittently forced linear system.

    Science.gov (United States)

    Brunton, Steven L; Brunton, Bingni W; Proctor, Joshua L; Kaiser, Eurika; Kutz, J Nathan

    2017-05-30

    Understanding the interplay of order and disorder in chaos is a central challenge in modern quantitative science. Approximate linear representations of nonlinear dynamics have long been sought, driving considerable interest in Koopman theory. We present a universal, data-driven decomposition of chaos as an intermittently forced linear system. This work combines delay embedding and Koopman theory to decompose chaotic dynamics into a linear model in the leading delay coordinates with forcing by low-energy delay coordinates; this is called the Hankel alternative view of Koopman (HAVOK) analysis. This analysis is applied to the Lorenz system and real-world examples including Earth's magnetic field reversal and measles outbreaks. In each case, forcing statistics are non-Gaussian, with long tails corresponding to rare intermittent forcing that precedes switching and bursting phenomena. The forcing activity demarcates coherent phase space regions where the dynamics are approximately linear from those that are strongly nonlinear.The huge amount of data generated in fields like neuroscience or finance calls for effective strategies that mine data to reveal underlying dynamics. Here Brunton et al.develop a data-driven technique to analyze chaotic systems and predict their dynamics in terms of a forced linear model.

  4. Final focus systems for linear colliders

    International Nuclear Information System (INIS)

    Helm, R.; Irwin, J.

    1992-08-01

    Final focus systems for linear colliders present many exacting challenges in beam optics, component design, and beam quality. Efforts to resolve these problems as they relate to a new generation of linear colliders are under way at several laboratories around the world. We will outline criteria for final focus systems and discuss the current state of understanding and resolution of the outstanding problems. We will discuss tolerances on alignment, field quality and stability for optical elements, and the implications for beam parameters such as emittance, energy spread, bunch length, and stability in position and energy. Beam-based correction procedures, which in principle can alleviate many of the tolerances, will be described. Preliminary results from the Final Focus Test Beam (FFTB) under construction at SLAC will be given. Finally, we mention conclusions from operating experience at the Stanford Linear Collider (SLC)

  5. Final focus systems for linear colliders

    International Nuclear Information System (INIS)

    Helm, R.; Irwing, J.

    1992-01-01

    Final focus systems for linear colliders present many exacting challenges in beam optics, component design, and beam quality. Efforts to resolve these problems as they relate to a new generation of linear colliders are under way at several laboratories around the world. We outline criteria for final focus systems and discuss the current state of understanding and resolution of the outstanding problems. We discuss tolerances on alignment, field quality and stability for optical elements, and the implications for beam parameters such as emittance, energy spread , bunch length, and stability in position and energy. Beam-based correction procedures, which in principle can alleviate many of the tolerances, are described. Preliminary results from the Final Focus Test Beam (FFTB) under construction at SLAC are given. Finally, we mention conclusions from operating experience at the Stanford Linear Collider (SLC). (Author) 16 refs., 4 tabs., 6 figs

  6. Dual-range linearized transimpedance amplifier system

    Science.gov (United States)

    Wessendorf, Kurt O.

    2010-11-02

    A transimpedance amplifier system is disclosed which simultaneously generates a low-gain output signal and a high-gain output signal from an input current signal using a single transimpedance amplifier having two different feedback loops with different amplification factors to generate two different output voltage signals. One of the feedback loops includes a resistor, and the other feedback loop includes another resistor in series with one or more diodes. The transimpedance amplifier system includes a signal linearizer to linearize one or both of the low- and high-gain output signals by scaling and adding the two output voltage signals from the transimpedance amplifier. The signal linearizer can be formed either as an analog device using one or two summing amplifiers, or alternately can be formed as a digital device using two analog-to-digital converters and a digital signal processor (e.g. a microprocessor or a computer).

  7. H∞ Filtering for Discrete Markov Jump Singular Systems with Mode-Dependent Time Delay Based on T-S Fuzzy Model

    Directory of Open Access Journals (Sweden)

    Cheng Gong

    2014-01-01

    Full Text Available This paper investigates the H∞ filtering problem of discrete singular Markov jump systems (SMJSs with mode-dependent time delay based on T-S fuzzy model. First, by Lyapunov-Krasovskii functional approach, a delay-dependent sufficient condition on H∞-disturbance attenuation is presented, in which both stability and prescribed H∞ performance are required to be achieved for the filtering-error systems. Then, based on the condition, the delay-dependent H∞ filter design scheme for SMJSs with mode-dependent time delay based on T-S fuzzy model is developed in term of linear matrix inequality (LMI. Finally, an example is given to illustrate the effectiveness of the result.

  8. An Explicit Formulation of Singularity-Free Dynamic Equations of Mechanical Systems in Lagrangian Form---Part Two: Multibody Systems

    Directory of Open Access Journals (Sweden)

    Pål Johan From

    2012-04-01

    Full Text Available This paper presents the explicit dynamic equations of multibody mechanical systems. This is the second paper on this topic. In the first paper the dynamics of a single rigid body from the Boltzmann--Hamel equations were derived. In this paper these results are extended to also include multibody systems. We show that when quasi-velocities are used, the part of the dynamic equations that appear from the partial derivatives of the system kinematics are identical to the single rigid body case, but in addition we get terms that come from the partial derivatives of the inertia matrix, which are not present in the single rigid body case. We present for the first time the complete and correct derivation of multibody systems based on the Boltzmann--Hamel formulation of the dynamics in Lagrangian form where local position and velocity variables are used in the derivation to obtain the singularity-free dynamic equations. The final equations are written in global variables for both position and velocity. The main motivation of these papers is to allow practitioners not familiar with differential geometry to implement the dynamic equations of rigid bodies without the presence of singularities. Presenting the explicit dynamic equations also allows for more insight into the dynamic structure of the system. Another motivation is to correct some errors commonly found in the literature. Unfortunately, the formulation of the Boltzmann-Hamel equations used here are presented incorrectly. This has been corrected by the authors, but we present here, for the first time, the detailed mathematical details on how to arrive at the correct equations. We also show through examples that using the equations presented here, the dynamics of a single rigid body is reduced to the standard equations on a Lagrangian form, for example Euler's equations for rotational motion and Euler--Lagrange equations for free motion.

  9. Consys Linear Control System Design Software Package

    International Nuclear Information System (INIS)

    Diamantidis, Z.

    1987-01-01

    This package is created in order to help engineers, researchers, students and all who work on linear control systems. The software includes all time and frequency domain analysises, spectral analysises and networks, active filters and regulators design aids. The programmes are written on Hewlett Packard computer in Basic 4.0

  10. Disturbance Decoupling of Switched Linear Systems

    NARCIS (Netherlands)

    Yurtseven, E.; Heemels, W.P.M.H.; Camlibel, M.K.

    2010-01-01

    In this paper we consider disturbance decoupling problems for switched linear systems. We will provide necessary and sufficient conditions for three different versions of disturbance decoupling, which differ based on which signals are considered to be the disturbance. In the first version the

  11. Uzawa method for fuzzy linear system

    OpenAIRE

    Ke Wang

    2013-01-01

    An Uzawa method is presented for solving fuzzy linear systems whose coefficient matrix is crisp and the right-hand side column is arbitrary fuzzy number vector. The explicit iterative scheme is given. The convergence is analyzed with convergence theorems and the optimal parameter is obtained. Numerical examples are given to illustrate the procedure and show the effectiveness and efficiency of the method.

  12. The theory of singular perturbations

    CERN Document Server

    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

  13. Collimation systems in the next linear collider

    International Nuclear Information System (INIS)

    Merminga, N.; Irwin, J.; Helm, R.; Ruth, R.D.

    1991-02-01

    Experience indicates that beam collimation will be an essential element of the next generation e + E - linear colliders. A proposal for using nonlinear lenses to drive beam tails to large amplitudes was presented in a previous paper. Here we study the optimization of such systems including effects of wakefields and optical aberrations. Protection and design of the scrapers in these systems are discussed. 9 refs., 7 figs

  14. Standard diffusive systems are well-posed linear systems

    NARCIS (Netherlands)

    Matignon, Denis; Zwart, Heiko J.

    2004-01-01

    The class of well-posed linear systems as introduced by Salamon has become a well-understood class of systems, see e.g. the work of Weiss and the book of Staffans. Many partial partial differential equations with boundary control and point observation can be formulated as a well-posed linear system.

  15. Spectral Analysis of a Quantum System with a Double Line Singular Interaction

    Czech Academy of Sciences Publication Activity Database

    Kondej, S.; Krejčiřík, David

    2013-01-01

    Roč. 49, č. 4 (2013), s. 831-859 ISSN 0034-5318 R&D Projects: GA ČR GAP203/11/0701 Institutional support: RVO:61389005 Keywords : Schrödinger operator * singular perturbation * spectral analysis * Hardy inequality * resonance Subject RIV: BE - Theoretical Physics Impact factor: 0.614, year: 2013

  16. Singular Initial Value Problem for Certain Classes of Systems of Ordinary Differential Equations

    Directory of Open Access Journals (Sweden)

    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.

  17. Existence of Positive Solutions to a Singular Semipositone Boundary Value Problem of Nonlinear Fractional Differential Systems

    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.

  18. Singular Perturbations and Time Scales in Modeling and Control of Dynamic Systems,

    Science.gov (United States)

    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

  19. Parameter identifiability of linear dynamical systems

    Science.gov (United States)

    Glover, K.; Willems, J. C.

    1974-01-01

    It is assumed that the system matrices of a stationary linear dynamical system were parametrized by a set of unknown parameters. The question considered here is, when can such a set of unknown parameters be identified from the observed data? Conditions for the local identifiability of a parametrization are derived in three situations: (1) when input/output observations are made, (2) when there exists an unknown feedback matrix in the system and (3) when the system is assumed to be driven by white noise and only output observations are made. Also a sufficient condition for global identifiability is derived.

  20. Stability problems for linear hyperbolic systems

    International Nuclear Information System (INIS)

    Eckhoff, K.S.

    1975-05-01

    The stability properties for the trivial solution of a general linear hyperbolic system of partial differential equations of the first order are studied. It is shown that results may be obtained by studying the stability properties of certain systems of ordinary differential equations which can be constructed from the hyperbolic system (the so-called transport equations). In some cases the associated stability problem for the transport equations can in fact be shown to be equivalent to the stability problem for the hyperbolic system, but in general the transport equations will only give the necessary conditions for stability. (Auth.)

  1. Multidimensional singular integrals and integral equations

    CERN Document Server

    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

  2. Identification of general linear mechanical systems

    Science.gov (United States)

    Sirlin, S. W.; Longman, R. W.; Juang, J. N.

    1983-01-01

    Previous work in identification theory has been concerned with the general first order time derivative form. Linear mechanical systems, a large and important class, naturally have a second order form. This paper utilizes this additional structural information for the purpose of identification. A realization is obtained from input-output data, and then knowledge of the system input, output, and inertia matrices is used to determine a set of linear equations whereby we identify the remaining unknown system matrices. Necessary and sufficient conditions on the number, type and placement of sensors and actuators are given which guarantee identificability, and less stringent conditions are given which guarantee generic identifiability. Both a priori identifiability and a posteriori identifiability are considered, i.e., identifiability being insured prior to obtaining data, and identifiability being assured with a given data set.

  3. Linear systems optimal and robust control

    CERN Document Server

    Sinha, Alok

    2007-01-01

    Introduction Overview Contents of the Book State Space Description of a Linear System Transfer Function of a Single Input/Single Output (SISO) System State Space Realizations of a SISO System SISO Transfer Function from a State Space Realization Solution of State Space Equations Observability and Controllability of a SISO System Some Important Similarity Transformations Simultaneous Controllability and Observability Multiinput/Multioutput (MIMO) Systems State Space Realizations of a Transfer Function Matrix Controllability and Observability of a MIMO System Matrix-Fraction Description (MFD) MFD of a Transfer Function Matrix for the Minimal Order of a State Space Realization Controller Form Realization from a Right MFD Poles and Zeros of a MIMO Transfer Function Matrix Stability Analysis State Feedback Control and Optimization State Variable Feedback for a Single Input System Computation of State Feedback Gain Matrix for a Multiinput System State Feedback Gain Matrix for a Multi...

  4. 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)

  5. Lectures on algebraic system theory: Linear systems over rings

    Science.gov (United States)

    Kamen, E. W.

    1978-01-01

    The presentation centers on four classes of systems that can be treated as linear systems over a ring. These are: (1) discrete-time systems over a ring of scalars such as the integers; (2) continuous-time systems containing time delays; (3) large-scale discrete-time systems; and (4) time-varying discrete-time systems.

  6. Analytical Solutions for Systems of Singular Partial Differential-Algebraic Equations

    Directory of Open Access Journals (Sweden)

    U. Filobello-Nino

    2015-01-01

    Full Text Available This paper proposes power series method (PSM in order to find solutions for singular partial differential-algebraic equations (SPDAEs. We will solve three examples to show that PSM method can be used to search for analytical solutions of SPDAEs. What is more, we will see that, in some cases, Padé posttreatment, besides enlarging the domain of convergence, may be employed in order to get the exact solution from the truncated series solutions of PSM.

  7. The generic unfolding of a codimension-two connection to a two-fold singularity of planar Filippov systems

    Science.gov (United States)

    Novaes, Douglas D.; Teixeira, Marco A.; Zeli, Iris O.

    2018-05-01

    Generic bifurcation theory was classically well developed for smooth differential systems, establishing results for k-parameter families of planar vector fields. In the present study we focus on a qualitative analysis of 2-parameter families, , of planar Filippov systems assuming that Z 0,0 presents a codimension-two minimal set. Such object, named elementary simple two-fold cycle, is characterized by a regular trajectory connecting a visible two-fold singularity to itself, for which the second derivative of the first return map is nonvanishing. We analyzed the codimension-two scenario through the exhibition of its bifurcation diagram.

  8. Linear systems and multiplicity of ideals

    International Nuclear Information System (INIS)

    Le Dung Trang

    2008-06-01

    Using a geometric interpretation of the multiplicity, we give a geometric way to calculate the multiplicity. We consider the particular case of a non-singular complex surface and give an example with a geometric proof of a result. Most of this note is written in the language of complex analytic spaces, but the results can be stated and proved in the case of schemes of finite type over an infinite field with equi-characteristic local rings

  9. An injection system for a linear accelerator

    International Nuclear Information System (INIS)

    Santos, A.C.R.

    1978-03-01

    An injection system for the Linear Accelerator is developed using the parameters of machines at the Centro Brasileiro de Pesquisas Fisicas and the Instituto Militar de Engenharia. The proposed system consists basically of a prebuncher and a chopper. The pre-buncher is used to improve the energy resolution and also to increase the accelerator target current. The chopper is used to remove from the beam the electrons that have no possibility of attaining the desired energy and that are usually lost in the walls and the cavity tube, thus producing undesirable background. Theoretical development of the chopper is performed in order to obtain its dimensions for future construction. The complete design the pre-buncher and its feed supply system and the experimental verication of its performance are also presented. It is intended to give the necessary information for the design and construction of the complete injection system proposed. (Author) [pt

  10. Operator approach to linear control systems

    CERN Document Server

    Cheremensky, A

    1996-01-01

    Within the framework of the optimization problem for linear control systems with quadratic performance index (LQP), the operator approach allows the construction of a systems theory including a number of particular infinite-dimensional optimization problems with hardly visible concreteness. This approach yields interesting interpretations of these problems and more effective feedback design methods. This book is unique in its emphasis on developing methods for solving a sufficiently general LQP. Although this is complex material, the theory developed here is built on transparent and relatively simple principles, and readers with less experience in the field of operator theory will find enough material to give them a good overview of the current state of LQP theory and its applications. Audience: Graduate students and researchers in the fields of mathematical systems theory, operator theory, cybernetics, and control systems.

  11. Iterative solution of large linear systems

    CERN Document Server

    Young, David Matheson

    1971-01-01

    This self-contained treatment offers a systematic development of the theory of iterative methods. Its focal point resides in an analysis of the convergence properties of the successive overrelaxation (SOR) method, as applied to a linear system with a consistently ordered matrix. The text explores the convergence properties of the SOR method and related techniques in terms of the spectral radii of the associated matrices as well as in terms of certain matrix norms. Contents include a review of matrix theory and general properties of iterative methods; SOR method and stationary modified SOR meth

  12. a Continuous-Time Positive Linear System

    Directory of Open Access Journals (Sweden)

    Kyungsup Kim

    2013-01-01

    Full Text Available This paper discusses a computational method to construct positive realizations with sparse matrices for continuous-time positive linear systems with multiple complex poles. To construct a positive realization of a continuous-time system, we use a Markov sequence similar to the impulse response sequence that is used in the discrete-time case. The existence of the proposed positive realization can be analyzed with the concept of a polyhedral convex cone. We provide a constructive algorithm to compute positive realizations with sparse matrices of some positive systems under certain conditions. A sufficient condition for the existence of a positive realization, under which the proposed constructive algorithm works well, is analyzed.

  13. Linear and non-linear energy barriers in systems of interacting single-domain ferromagnetic particles

    International Nuclear Information System (INIS)

    Petrila, Iulian; Bodale, Ilie; Rotarescu, Cristian; Stancu, Alexandru

    2011-01-01

    A comparative analysis between linear and non-linear energy barriers used for modeling statistical thermally-excited ferromagnetic systems is presented. The linear energy barrier is obtained by new symmetry considerations about the anisotropy energy and the link with the non-linear energy barrier is also presented. For a relevant analysis we compare the effects of linear and non-linear energy barriers implemented in two different models: Preisach-Neel and Ising-Metropolis. The differences between energy barriers which are reflected in different coercive field dependence of the temperature are also presented. -- Highlights: → The linear energy barrier is obtained from symmetry considerations. → The linear and non-linear energy barriers are calibrated and implemented in Preisach-Neel and Ising-Metropolis models. → The temperature and time effects of the linear and non-linear energy barriers are analyzed.

  14. New approach to solve symmetric fully fuzzy linear systems

    Indian Academy of Sciences (India)

    concepts of fuzzy set theory and then define a fully fuzzy linear system of equations. .... To represent the above problem as fully fuzzy linear system, we represent x .... Fully fuzzy linear systems can be solved by Linear programming approach, ...

  15. Point force singularities outside a drop covered with an incompressible surfactant: Image systems and their applications

    Science.gov (United States)

    Shaik, Vaseem A.; Ardekani, Arezoo M.

    2017-11-01

    In this work we derive the image flow fields for point force singularities placed outside a stationary drop covered with an insoluble, nondiffusing, and incompressible surfactant. We assume the interface to be Newtonian and use the Boussinesq-Scriven constitutive law for the interfacial stress tensor. We use this analytical solution to investigate two different problems. First, we derive the mobility matrix for two drops of arbitrary sizes covered with an incompressible surfactant. In the second example, we calculate the velocity of a swimming microorganism (modeled as a Stokes dipole) outside a drop covered with an incompressible surfactant.

  16. Investigation of relation between singular points and number of limit cycles for a rotor-AMBs system

    International Nuclear Information System (INIS)

    Li, J.; Tian, Y.; Zhang, W.

    2009-01-01

    The relation between singular points and the number of limit cycles is investigated for a rotor-active magnetic bearings system with time-varying stiffness and single-degree-of-freedom. The averaged equation of the system is a perturbed polynomial Hamiltonian system of degree 5. The dynamic characteristics of the unperturbed system are first analyzed for a certain parameter group. The number of limit cycles and their configurations of the perturbed system under eight different parametric groups are obtained and the influence of eight control conditions on the number of limit cycles is studied. The results obtained here will play an important leading role in the study of the properties of nonlinear dynamics and control of the rotor-active magnetic bearings system with time-varying stiffness.

  17. SLAP, Large Sparse Linear System Solution Package

    International Nuclear Information System (INIS)

    Greenbaum, A.

    1987-01-01

    1 - Description of program or function: SLAP is a set of routines for solving large sparse systems of linear equations. One need not store the entire matrix - only the nonzero elements and their row and column numbers. Any nonzero structure is acceptable, so the linear system solver need not be modified when the structure of the matrix changes. Auxiliary storage space is acquired and released within the routines themselves by use of the LRLTRAN POINTER statement. 2 - Method of solution: SLAP contains one direct solver, a band matrix factorization and solution routine, BAND, and several interactive solvers. The iterative routines are as follows: JACOBI, Jacobi iteration; GS, Gauss-Seidel Iteration; ILUIR, incomplete LU decomposition with iterative refinement; DSCG and ICCG, diagonal scaling and incomplete Cholesky decomposition with conjugate gradient iteration (for symmetric positive definite matrices only); DSCGN and ILUGGN, diagonal scaling and incomplete LU decomposition with conjugate gradient interaction on the normal equations; DSBCG and ILUBCG, diagonal scaling and incomplete LU decomposition with bi-conjugate gradient iteration; and DSOMN and ILUOMN, diagonal scaling and incomplete LU decomposition with ORTHOMIN iteration

  18. ROBUST MPC FOR STABLE LINEAR SYSTEMS

    Directory of Open Access Journals (Sweden)

    M.A. Rodrigues

    2002-03-01

    Full Text Available In this paper, a new model predictive controller (MPC, which is robust for a class of model uncertainties, is developed. Systems with stable dynamics and time-invariant model uncertainty are treated. The development herein proposed is focused on real industrial systems where the controller is part of an on-line optimization scheme and works in the output-tracking mode. In addition, the system has a time-varying number of degrees of freedom since some of the manipulated inputs may become constrained. Moreover, the number of controlled outputs may also vary during system operation. Consequently, the actual system may show operating conditions with a number of controlled outputs larger than the number of available manipulated inputs. The proposed controller uses a state-space model, which is aimed at the representation of the output-predicted trajectory. Based on this model, a cost function is proposed whereby the output error is integrated along an infinite prediction horizon. It is considered the case of multiple operating points, where the controller stabilizes a set of models corresponding to different operating conditions for the system. It is shown that closed-loop stability is guaranteed by the feasibility of a linear matrix optimization problem.

  19. Optimal Control of Switching Linear Systems

    Directory of Open Access Journals (Sweden)

    Ali Benmerzouga

    2004-06-01

    Full Text Available A solution to the control of switching linear systems with input constraints was given in Benmerzouga (1997 for both the conventional enumeration approach and the new approach. The solution given there turned out to be not unique. The main objective in this work is to determine the optimal control sequences {Ui(k ,  i = 1,..., M ;  k = 0, 1, ...,  N -1} which transfer the system from a given initial state  X0  to a specific target state  XT  (or to be as close as possible by using the same discrete time solution obtained in Benmerzouga (1997 and minimizing a running cost-to-go function. By using the dynamic programming technique, the optimal solution is found for both approaches given in Benmerzouga (1997. The computational complexity of the modified algorithm is also given.

  20. Well logging system with linearity control

    International Nuclear Information System (INIS)

    Jones, J.M.

    1973-01-01

    Apparatus is described for controlling the gain of a nuclear well logging system comprising: (1) means for measuring the energy spectrum of gamma rays produced by earth formation materials surrounding a well borehole; (2) means for measuring the number of counts of a gamma rays having an energy falling within each of at least two predetermined energy band portions of the gamma ray energy spectrum; (3) means for generating a signal proportional to the ratio of the gamma ray counts and for comparing the ratio signal with at least one constant ratio calibration signal; (4) means for generating an error signal representative of the difference of the ratio signal and the constant ratio calibration signal; and (5) means for using the error signal to control the linearity of the well logging system. (author)

  1. Linear concentration system; Sistema de concentracion lineal

    Energy Technology Data Exchange (ETDEWEB)

    Gonzalez Lugo, J.I; Leon Rovira, N; Aguayo Tellez, H [Instituto Tecnologico y de Estudios Superiores de Monterrey, Monterrey, Nuevo Leon (Mexico)]. E-mails: a00812662@itesm.mx; noel.leon@itesm.mx; haguayo@itesm.mx

    2013-03-15

    Solar linear concentration technologies to generate high temperatures are limited to the ranges of 200 to 500 degrees Celsius. While its performance has been tested through prototypes and pilot plants around the world, there are still areas of opportunity that can be exploited to obtain a linear concentration that achieves temperatures above this range in order to have a better use of the available solar energy. Because of this: It is possible to develop a linear concentration system that can track the sun with minimal movement of the absorber-receiver while maintaining temperatures above 850 degrees Celsius sufficient for industrial processes that require that temperature. The methodology consists of a series of stages (conceptual design, simulation, evaluation, development concept, results and validation) through which concepts are generated that allow design and evaluation of solar concentrator configurations with the help of simulation software. We have designed a linear parabolic concentrating system which comprises a set of mirrors segments with different focal lengths that works within the range of 600 degrees Celsius; however, it is advancing in the development of a double concentration to reach 850 degrees Celsius. [Spanish] Las tecnologias de concentracion lineal solar para generar altas temperaturas se ven limitadas a los rangos de 200 a 500 grados centigrados. Si bien su funcionamiento ha sido probado a traves de prototipos y plantas piloto alrededor del mundo, aun existen areas de oportunidad que pueden ser aprovechadas para obtener un sistema de concentracion lineal que permita alcanzar temperaturas mayores a este rango para asi tener un mejor aprovechamiento de la energia solar disponible. Debido a esto: Es posible desarrollar un sistema de concentracion lineal capaz de seguir la trayectoria del Sol con minimo movimiento del absorbedor-recibidor al mismo tiempo que mantiene temperaturas superiores a los 850 grados centigrados suficientes para

  2. An adaptive singular ES-FEM for mechanics problems with singular field of arbitrary order

    OpenAIRE

    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 ...

  3. Integrated Urban System and Energy Consumption Model: Public and Singular Buildings

    Directory of Open Access Journals (Sweden)

    Rocco Papa

    2014-05-01

    Full Text Available The present paper illustrates the results of the first steps of a study on one aspect investigated as the preliminary step of the definition of the analysis - comprehension model of the relation between: city, buildings, and user behavior, for the reduction of energy consumption within the research project “Smart Energy Master” for the energetic governance of the territory (PON_MIUR n. pos. 04a2_00120 CUP Ricerca: E61H12000130005, at the Department of Civil, Building and Environmental Engineering - University of Naples Federico II, principal investigator prof. Carmela Gargiulo.Specifically the literary review aimed at determining if, and in what measure, the presence of public and singular buildings is present in the energy consumption estimate models,  proposed by the scientific community, for the city or neighborhood scale.The difficulties in defining the weight of these singular buildings on the total energy consumption and the impossibility to define mean values that are significant for all subsets and different types as well as for each one, have forced model makers to either ignore them completely or chose a portion of this specific stock to include.

  4. Linear Actuator System for the NASA Docking System

    Science.gov (United States)

    Dick, Brandon N.; Oesch, Christopher; Rupp, Timothy W.

    2017-01-01

    The Linear Actuator System (LAS) is a major sub-system within the NASA Docking System (NDS). The NDS Block 1 will be used on the Boeing Crew Space Transportation (CST-100) system to achieve docking with the International Space Station. Critical functions in the Soft Capture aspect of docking are performed by the LAS. This paper describes the general function of the LAS, the system's key requirements and technical challenges, and the development and qualification approach for the system.

  5. A Blind Adaptive Color Image Watermarking Scheme Based on Principal Component Analysis, Singular Value Decomposition and Human Visual System

    Directory of Open Access Journals (Sweden)

    M. Imran

    2017-09-01

    Full Text Available A blind adaptive color image watermarking scheme based on principal component analysis, singular value decomposition, and human visual system is proposed. The use of principal component analysis to decorrelate the three color channels of host image, improves the perceptual quality of watermarked image. Whereas, human visual system and fuzzy inference system helped to improve both imperceptibility and robustness by selecting adaptive scaling factor, so that, areas more prone to noise can be added with more information as compared to less prone areas. To achieve security, location of watermark embedding is kept secret and used as key at the time of watermark extraction, whereas, for capacity both singular values and vectors are involved in watermark embedding process. As a result, four contradictory requirements; imperceptibility, robustness, security and capacity are achieved as suggested by results. Both subjective and objective methods are acquired to examine the performance of proposed schemes. For subjective analysis the watermarked images and watermarks extracted from attacked watermarked images are shown. For objective analysis of proposed scheme in terms of imperceptibility, peak signal to noise ratio, structural similarity index, visual information fidelity and normalized color difference are used. Whereas, for objective analysis in terms of robustness, normalized correlation, bit error rate, normalized hamming distance and global authentication rate are used. Security is checked by using different keys to extract the watermark. The proposed schemes are compared with state-of-the-art watermarking techniques and found better performance as suggested by results.

  6. Relative null controllability of linear systems with multiple delays in ...

    African Journals Online (AJOL)

    varying multiple delays in state and control are developed. If the uncontrolled system is uniformly asymptotically stable, and if the linear system is controllable, then the linear system is null controllable. Journal of the Nigerian Association of ...

  7. Linear optical response of finite systems using multishift linear system solvers

    Energy Technology Data Exchange (ETDEWEB)

    Hübener, Hannes; Giustino, Feliciano [Department of Materials, University of Oxford, Oxford OX1 3PH (United Kingdom)

    2014-07-28

    We discuss the application of multishift linear system solvers to linear-response time-dependent density functional theory. Using this technique the complete frequency-dependent electronic density response of finite systems to an external perturbation can be calculated at the cost of a single solution of a linear system via conjugate gradients. We show that multishift time-dependent density functional theory yields excitation energies and oscillator strengths in perfect agreement with the standard diagonalization of the response matrix (Casida's method), while being computationally advantageous. We present test calculations for benzene, porphin, and chlorophyll molecules. We argue that multishift solvers may find broad applicability in the context of excited-state calculations within density-functional theory and beyond.

  8. Control system analysis for the perturbed linear accelerator rf system

    CERN Document Server

    Sung Il Kwon

    2002-01-01

    This paper addresses the modeling problem of the linear accelerator RF system in SNS. Klystrons are modeled as linear parameter varying systems. The effect of the high voltage power supply ripple on the klystron output voltage and the output phase is modeled as an additive disturbance. The cavity is modeled as a linear system and the beam current is modeled as the exogenous disturbance. The output uncertainty of the low level RF system which results from the uncertainties in the RF components and cabling is modeled as multiplicative uncertainty. Also, the feedback loop uncertainty and digital signal processing signal conditioning subsystem uncertainties are lumped together and are modeled as multiplicative uncertainty. Finally, the time delays in the loop are modeled as a lumped time delay. For the perturbed open loop system, the closed loop system performance, and stability are analyzed with the PI feedback controller.

  9. CONTROL SYSTEM ANALYSIS FOR THE PERTURBED LINEAR ACCELERATOR RF SYSTEM

    International Nuclear Information System (INIS)

    SUNG-IL KWON; AMY H. REGAN

    2002-01-01

    This paper addresses the modeling problem of the linear accelerator RF system in SNS. Klystrons are modeled as linear parameter varying systems. The effect of the high voltage power supply ripple on the klystron output voltage and the output phase is modeled as an additive disturbance. The cavity is modeled as a linear system and the beam current is modeled as the exogenous disturbance. The output uncertainty of the low level RF system which results from the uncertainties in the RF components and cabling is modeled as multiplicative uncertainty. Also, the feedback loop uncertainty and digital signal processing signal conditioning subsystem uncertainties are lumped together and are modeled as multiplicative uncertainty. Finally, the time delays in the loop are modeled as a lumped time delay. For the perturbed open loop system, the closed loop system performance, and stability are analyzed with the PI feedback controller

  10. Linear-array systems for aerospace NDE

    International Nuclear Information System (INIS)

    Smith, Robert A.; Willsher, Stephen J.; Bending, Jamie M.

    1999-01-01

    Rapid large-area inspection of composite structures for impact damage and multi-layered aluminum skins for corrosion has been a recognized priority for several years in both military and civil aerospace applications. Approaches to this requirement have followed two clearly different routes: the development of novel large-area inspection systems, and the enhancement of current ultrasonic or eddy-current methods to reduce inspection times. Ultrasonic inspection is possible with standard flaw detection equipment but the addition of a linear ultrasonic array could reduce inspection times considerably. In order to investigate their potential, 9-element and 17-element linear ultrasonic arrays for composites, and 64-element arrays for aluminum skins, have been developed to DERA specifications for use with the ANDSCAN area scanning system. A 5 m 2 composite wing surface has been scanned with a scan resolution of approximately 3 mm in 6 hours. With subsequent software and hardware improvements all four composite wing surfaces (top/bottom, left/right) of a military fighter aircraft can potentially be inspected in less than a day. Array technology has been very widely used in the medical ultrasound field although rarely above 10 MHz, whereas lap-joint inspection requires a pulse center-frequency of 12 to 20 MHz in order to resolve the separate interfaces in the lap joint. A 128 mm-long multi-element array of 5 mmx2 mm ultrasonic elements for use with the ANDSCAN scanning software was produced to a DERA specification by an NDT manufacturer with experience in the medical imaging field. This paper analyses the performance of the transducers that have been produced and evaluates their use in scanning systems of different configurations

  11. Model Predictive Control for Linear Complementarity and Extended Linear Complementarity Systems

    Directory of Open Access Journals (Sweden)

    Bambang Riyanto

    2005-11-01

    Full Text Available In this paper, we propose model predictive control method for linear complementarity and extended linear complementarity systems by formulating optimization along prediction horizon as mixed integer quadratic program. Such systems contain interaction between continuous dynamics and discrete event systems, and therefore, can be categorized as hybrid systems. As linear complementarity and extended linear complementarity systems finds applications in different research areas, such as impact mechanical systems, traffic control and process control, this work will contribute to the development of control design method for those areas as well, as shown by three given examples.

  12. Thermodynamics of (1-alkanol + linear monoether) systems

    International Nuclear Information System (INIS)

    Gonzalez, Juan Antonio; Mozo, Ismael; Garcia de la Fuente, Isaias; Cobos, Jose Carlos; Riesco, Nicolas

    2008-01-01

    Densities, ρ, and speeds of sound, u, of systems formed by 1-heptanol, or 1-octanol, or 1-decanol and dibutylether have been measured at a temperature of (293.15, 298.15, and 303.15) K and atmospheric pressure using a vibrating tube densimeter and sound analyser Anton Paar model DSA-5000. The ρ and u values were used to calculate excess molar volumes, V E , and deviations from the ideal behaviour of the thermal expansion coefficient, Δα p and of the isentropic compressibilities, Δκ S . The available database on molar excess enthalpies, H E , and V E for (1-alkanol + linear monoether) systems was used to investigate interactional and structural effects in such mixtures. The enthalpy of the OH...O bonds is lower for methanol solutions, and for the remainder systems, it is practically independent of the mixture compounds. The V E variation with the chain length of the 1-alkanol points out the existence of structural effects for systems including longer 1-alkanols. The ERAS model is applied to the studied mixtures. ERAS represents quite accurately H E and V E data using parameters which consistently depend on the molecular structure

  13. Identification problems in linear transformation system

    International Nuclear Information System (INIS)

    Delforge, Jacques.

    1975-01-01

    An attempt was made to solve the theoretical and numerical difficulties involved in the identification problem relative to the linear part of P. Delattre's theory of transformation systems. The theoretical difficulties are due to the very important problem of the uniqueness of the solution, which must be demonstrated in order to justify the value of the solution found. Simple criteria have been found when measurements are possible on all the equivalence classes, but the problem remains imperfectly solved when certain evolution curves are unknown. The numerical difficulties are of two kinds: a slow convergence of iterative methods and a strong repercussion of numerical and experimental errors on the solution. In the former case a fast convergence was obtained by transformation of the parametric space, while in the latter it was possible, from sensitivity functions, to estimate the errors, to define and measure the conditioning of the identification problem then to minimize this conditioning as a function of the experimental conditions [fr

  14. Singularity Structure Analysis of the Higher-Dimensional Time-Gated Manakov System: Periodic Excitations and Elastic Scattering

    International Nuclear Information System (INIS)

    Kuetche, Victor Kamgang; Bouetou, Thomas Bouetou; Kofane, Timoleon Crepin

    2010-12-01

    We investigate the singularity structure analysis of the higher-dimensional time-gated Manakov system referring to the (2+1)-dimensional coupled nonlinear Schroedinger (CNLS) equations, and we show that these equations are Painleve-integrable. By means of the Weiss et al.'s methodology, we show the arbitrariness of the expansion coefficients and the consistency of the truncation corresponding to a special Baecklund transformation (BT) of these CNLS equations. In the wake of such transformation, following the Hirota's formalism, we derive a one-soliton solution. Besides, by using the Zakharov-Shabat (ZS) scheme which provides a general Lax-representation of an evolution system, we show that the (2+1)-dimensional CNLS system under interests is completely integrable. Furthermore, using the arbitrariness of the above coefficients, we unearth and investigate a typical spectrum of periodic coherent structures while depicting elastic interactions amongst such patterns. (author)

  15. System theory as applied differential geometry. [linear system

    Science.gov (United States)

    Hermann, R.

    1979-01-01

    The invariants of input-output systems under the action of the feedback group was examined. The approach used the theory of Lie groups and concepts of modern differential geometry, and illustrated how the latter provides a basis for the discussion of the analytic structure of systems. Finite dimensional linear systems in a single independent variable are considered. Lessons of more general situations (e.g., distributed parameter and multidimensional systems) which are increasingly encountered as technology advances are presented.

  16. Normal form of linear systems depending on parameters

    International Nuclear Information System (INIS)

    Nguyen Huynh Phan.

    1995-12-01

    In this paper we resolve completely the problem to find normal forms of linear systems depending on parameters for the feedback action that we have studied for the special case of controllable linear systems. (author). 24 refs

  17. 随机奇异系统分布式最优融合降阶卡尔曼滤波器%Distributed Reduced-order Optimal Fusion Kalman Filters for Stochastic Singular Systems

    Institute of Scientific and Technical Information of China (English)

    孙书利; 马静

    2006-01-01

    Based on the optimal fusion algorithm weighted by matrices in the linear minimum variance (LMV) sense, a distributed full-order optimal fusion Kalman filter (DFFKF) is given for discrete-time stochastic singular systems with multiple sensors, which involves the inverse of a highdimension matrix to compute matrix weights. To reduce the computational burden, a distributed reduced-order fusion Kalman filter (DRFKF) is presented, which involves in parallel the inverses of two relatively low-dimension matrices to compute matrix weights. A simulation example shows the effectiveness.

  18. Method of mechanical quadratures for solving singular integral equations of various types

    Science.gov (United States)

    Sahakyan, A. V.; Amirjanyan, H. A.

    2018-04-01

    The method of mechanical quadratures is proposed as a common approach intended for solving the integral equations defined on finite intervals and containing Cauchy-type singular integrals. This method can be used to solve singular integral equations of the first and second kind, equations with generalized kernel, weakly singular equations, and integro-differential equations. The quadrature rules for several different integrals represented through the same coefficients are presented. This allows one to reduce the integral equations containing integrals of different types to a system of linear algebraic equations.

  19. 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

  20. LQG/LTR [linear quadratic Gaussian with loop transfer recovery] robust control system design for a low-pressure feedwater heater train

    International Nuclear Information System (INIS)

    Murphy, G.V.; Bailey, J.M.

    1990-01-01

    This paper uses the linear quadratic Gaussian with loop transfer recovery (LQG/LTR) control system design method to obtain a level control system for a low-pressure feedwater heater train. The control system performance and stability robustness are evaluated for a given set of system design specifications. The tools for analysis are the return ratio, return difference, and inverse return difference singular-valve plots for a loop break at the plant output. 3 refs., 7 figs., 2 tabs

  1. Superconducting linear accelerator system for NSC

    Indian Academy of Sciences (India)

    This paper reports the construction of a superconducting linear accelerator as a booster to the 15 UD Pelletron accelerator at Nuclear Science Centre, New Delhi. The LINAC will use superconducting niobium quarter wave resonators as the accelerating element. Construction of the linear accelerator has progressed ...

  2. Symmetric linear systems - An application of algebraic systems theory

    Science.gov (United States)

    Hazewinkel, M.; Martin, C.

    1983-01-01

    Dynamical systems which contain several identical subsystems occur in a variety of applications ranging from command and control systems and discretization of partial differential equations, to the stability augmentation of pairs of helicopters lifting a large mass. Linear models for such systems display certain obvious symmetries. In this paper, we discuss how these symmetries can be incorporated into a mathematical model that utilizes the modern theory of algebraic systems. Such systems are inherently related to the representation theory of algebras over fields. We will show that any control scheme which respects the dynamical structure either implicitly or explicitly uses the underlying algebra.

  3. A study on switched linear system identification using game ...

    African Journals Online (AJOL)

    A study on switched linear system identification using game-theoretic strategies and neural computing. ... This study deals with application of game-theoretic strategies and neural computing to switched linear ... AJOL African Journals Online.

  4. Reduction of Linear Functional Systems using Fuhrmann's Equivalence

    Directory of Open Access Journals (Sweden)

    Mohamed S. Boudellioua

    2016-11-01

    Full Text Available Functional systems arise in the treatment of systems of partial differential equations, delay-differential equations, multidimensional equations, etc. The problem of reducing a linear functional system to a system containing fewer equations and unknowns was first studied by Serre. Finding an equivalent presentation of a linear functional system containing fewer equations and fewer unknowns can generally simplify both the study of the structural properties of the linear functional system and of different numerical analysis issues, and it can sometimes help in solving the linear functional system. In this paper, Fuhrmann's equivalence is used to present a constructive result on the reduction of under-determined linear functional systems to a single equation involving a single unknown. This equivalence transformation has been studied by a number of authors and has been shown to play an important role in the theory of linear functional systems.

  5. Classification of subsurface objects using singular values derived from signal frames

    Science.gov (United States)

    Chambers, David H; Paglieroni, David W

    2014-05-06

    The classification system represents a detected object with a feature vector derived from the return signals acquired by an array of N transceivers operating in multistatic mode. The classification system generates the feature vector by transforming the real-valued return signals into complex-valued spectra, using, for example, a Fast Fourier Transform. The classification system then generates a feature vector of singular values for each user-designated spectral sub-band by applying a singular value decomposition (SVD) to the N.times.N square complex-valued matrix formed from sub-band samples associated with all possible transmitter-receiver pairs. The resulting feature vector of singular values may be transformed into a feature vector of singular value likelihoods and then subjected to a multi-category linear or neural network classifier for object classification.

  6. High density linear systems for fusion power

    International Nuclear Information System (INIS)

    Ellis, W.R.; Krakowski, R.A.

    1975-01-01

    The physics and technological limitations and uncertainties associated with the linear theta pinch are discussed in terms of a generalized energy balance, which has as its basis the ratio (Q/sub E/) of total electrical energy generated to net electrical energy consumed. Included in this total is the virtual energy of bred fissile fuel, if a hybrid blanket is used, as well as the actual of real energy deposited in the blanket by the fusion neutron. The advantages and disadvantages of the pulsed operation demanded by the linear theta pinch are also discussed

  7. Quantum dynamical effects as a singular perturbation for observables in open quasi-classical nonlinear mesoscopic systems

    International Nuclear Information System (INIS)

    Berman, G.P.; Borgonovi, F.; Dalvit, D.A.R.

    2009-01-01

    We review our results on a mathematical dynamical theory for observables for open many-body quantum nonlinear bosonic systems for a very general class of Hamiltonians. We show that non-quadratic (nonlinear) terms in a Hamiltonian provide a singular 'quantum' perturbation for observables in some 'mesoscopic' region of parameters. In particular, quantum effects result in secular terms in the dynamical evolution, that grow in time. We argue that even for open quantum nonlinear systems in the deep quasi-classical region, these quantum effects can survive after decoherence and relaxation processes take place. We demonstrate that these quantum effects in open quantum systems can be observed, for example, in the frequency Fourier spectrum of the dynamical observables, or in the corresponding spectral density of noise. Estimates are presented for Bose-Einstein condensates, low temperature mechanical resonators, and nonlinear optical systems prepared in large amplitude coherent states. In particular, we show that for Bose-Einstein condensate systems the characteristic time of deviation of quantum dynamics for observables from the corresponding classical dynamics coincides with the characteristic time-scale of the well-known quantum nonlinear effect of phase diffusion.

  8. Analysis of Linear Hybrid Systems in CLP

    DEFF Research Database (Denmark)

    Banda, Gourinath; Gallagher, John Patrick

    2009-01-01

    In this paper we present a procedure for representing the semantics of linear hybrid automata (LHAs) as constraint logic programs (CLP); flexible and accurate analysis and verification of LHAs can then be performed using generic CLP analysis and transformation tools. LHAs provide an expressive...

  9. Linear System of Equations, Matrix Inversion, and Linear Programming Using MS Excel

    Science.gov (United States)

    El-Gebeily, M.; Yushau, B.

    2008-01-01

    In this note, we demonstrate with illustrations two different ways that MS Excel can be used to solve Linear Systems of Equation, Linear Programming Problems, and Matrix Inversion Problems. The advantage of using MS Excel is its availability and transparency (the user is responsible for most of the details of how a problem is solved). Further, we…

  10. Dynamics of a linear system coupled to a chain of light nonlinear oscillators analyzed through a continuous approximation

    Science.gov (United States)

    Charlemagne, S.; Ture Savadkoohi, A.; Lamarque, C.-H.

    2018-07-01

    The continuous approximation is used in this work to describe the dynamics of a nonlinear chain of light oscillators coupled to a linear main system. A general methodology is applied to an example where the chain has local nonlinear restoring forces. The slow invariant manifold is detected at fast time scale. At slow time scale, equilibrium and singular points are sought around this manifold in order to predict periodic regimes and strongly modulated responses of the system. Analytical predictions are in good accordance with numerical results and represent a potent tool for designing nonlinear chains for passive control purposes.

  11. Study on sampling of continuous linear system based on generalized Fourier transform

    Science.gov (United States)

    Li, Huiguang

    2003-09-01

    In the research of signal and system, the signal's spectrum and the system's frequency characteristic can be discussed through Fourier Transform (FT) and Laplace Transform (LT). However, some singular signals such as impulse function and signum signal don't satisfy Riemann integration and Lebesgue integration. They are called generalized functions in Maths. This paper will introduce a new definition -- Generalized Fourier Transform (GFT) and will discuss generalized function, Fourier Transform and Laplace Transform under a unified frame. When the continuous linear system is sampled, this paper will propose a new method to judge whether the spectrum will overlap after generalized Fourier transform (GFT). Causal and non-causal systems are studied, and sampling method to maintain system's dynamic performance is presented. The results can be used on ordinary sampling and non-Nyquist sampling. The results also have practical meaning on research of "discretization of continuous linear system" and "non-Nyquist sampling of signal and system." Particularly, condition for ensuring controllability and observability of MIMO continuous systems in references 13 and 14 is just an applicable example of this paper.

  12. A SYSTEMIC VISION OF BIOLOGY: OVERCOMING LINEARITY

    Directory of Open Access Journals (Sweden)

    M. Mayer

    2005-07-01

    were used to build  a hipermedia  material.  This  technology  permit  overcomes a linear  communication, improving the  comprehension  of the network perspective.   The teachers  speeches revealed  their  conceptual  con- structions along the  course,  showed the development of the  competences  in identify  interconnection points  in the flow and chemical cycling of energy, compatible  with a systemic view of life.

  13. Solving Fully Fuzzy Linear System of Equations in General Form

    Directory of Open Access Journals (Sweden)

    A. Yousefzadeh

    2012-06-01

    Full Text Available In this work, we propose an approach for computing the positive solution of a fully fuzzy linear system where the coefficient matrix is a fuzzy $nimes n$ matrix. To do this, we use arithmetic operations on fuzzy numbers that introduced by Kaffman in and convert the fully fuzzy linear system into two $nimes n$ and $2nimes 2n$ crisp linear systems. If the solutions of these linear systems don't satisfy in positive fuzzy solution condition, we introduce the constrained least squares problem to obtain optimal fuzzy vector solution by applying the ranking function in given fully fuzzy linear system. Using our proposed method, the fully fuzzy linear system of equations always has a solution. Finally, we illustrate the efficiency of proposed method by solving some numerical examples.

  14. Biclustering via Sparse Singular Value Decomposition

    KAUST Repository

    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.

  15. Dynamics of unsymmetric piecewise-linear/non-linear systems using finite elements in time

    Science.gov (United States)

    Wang, Yu

    1995-08-01

    The dynamic response and stability of a single-degree-of-freedom system with unsymmetric piecewise-linear/non-linear stiffness are analyzed using the finite element method in the time domain. Based on a Hamilton's weak principle, this method provides a simple and efficient approach for predicting all possible fundamental and sub-periodic responses. The stability of the steady state response is determined by using Floquet's theory without any special effort for calculating transition matrices. This method is applied to a number of examples, demonstrating its effectiveness even for a strongly non-linear problem involving both clearance and continuous stiffness non-linearities. Close agreement is found between available published findings and the predictions of the finite element in time approach, which appears to be an efficient and reliable alternative technique for non-linear dynamic response and stability analysis of periodic systems.

  16. Reliability modelling and simulation of switched linear system ...

    African Journals Online (AJOL)

    Reliability modelling and simulation of switched linear system control using temporal databases. ... design of fault-tolerant real-time switching systems control and modelling embedded micro-schedulers for complex systems maintenance.

  17. Solving block linear systems with low-rank off-diagonal blocks is easily parallelizable

    Energy Technology Data Exchange (ETDEWEB)

    Menkov, V. [Indiana Univ., Bloomington, IN (United States)

    1996-12-31

    An easily and efficiently parallelizable direct method is given for solving a block linear system Bx = y, where B = D + Q is the sum of a non-singular block diagonal matrix D and a matrix Q with low-rank blocks. This implicitly defines a new preconditioning method with an operation count close to the cost of calculating a matrix-vector product Qw for some w, plus at most twice the cost of calculating Qw for some w. When implemented on a parallel machine the processor utilization can be as good as that of those operations. Order estimates are given for the general case, and an implementation is compared to block SSOR preconditioning.

  18. 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.

  19. Dynamic analysis and electronic circuit implementation of a novel 3D autonomous system without linear terms

    Science.gov (United States)

    Kengne, J.; Jafari, S.; Njitacke, Z. T.; Yousefi Azar Khanian, M.; Cheukem, A.

    2017-11-01

    Mathematical models (ODEs) describing the dynamics of almost all continuous time chaotic nonlinear systems (e.g. Lorenz, Rossler, Chua, or Chen system) involve at least a nonlinear term in addition to linear terms. In this contribution, a novel (and singular) 3D autonomous chaotic system without linear terms is introduced. This system has an especial feature of having two twin strange attractors: one ordinary and one symmetric strange attractor when the time is reversed. The complex behavior of the model is investigated in terms of equilibria and stability, bifurcation diagrams, Lyapunov exponent plots, time series and Poincaré sections. Some interesting phenomena are found including for instance, period-doubling bifurcation, antimonotonicity (i.e. the concurrent creation and annihilation of periodic orbits) and chaos while monitoring the system parameters. Compared to the (unique) case previously reported by Xu and Wang (2014) [31], the system considered in this work displays a more 'elegant' mathematical expression and experiences richer dynamical behaviors. A suitable electronic circuit (i.e. the analog simulator) is designed and used for the investigations. Pspice based simulation results show a very good agreement with the theoretical analysis.

  20. Singularity Theory and its Applications

    CERN Document Server

    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.

  1. Energy balance in a system with quasispherical linear compression

    International Nuclear Information System (INIS)

    Es'kov, A.G.; Kozlov, N.P.; Kurtmullaev, R.K.; Semenov, V.N.; Khvesyuk, V.I.; Yaminskii, A.V.

    1983-01-01

    This letter reports the resists of some experimental studies and a numerical simulation of the Tor-linear fusion system, 1 in which a heavy plasma shell with a closed magnetic structure is compressed in a quasispherical manner. The parameters of the Tor-Linear, at the Kurchatov Institute of Atomic Energy in Moscow are as follows: The energy stored in the system which accelerates the linear is E = 0.5 MJ; the linear mass is m = 0.2 kg; the working volume of the linear module is 1.5 x 10 -3 m 3 ; the linear velocity is approx.10 3 m/s; the guiding field in the toriod in the linear is 1--10 x 10 21 m -3 ; and the intial volume of the plasma in the linear chamber is 2.5 x 10 -4 m 3 . In this series of experiments, new solutions were developed for all the systems of the plasma--linear complex of the Tor-Linear: to produce a plasma toroid, to transport it, and to trap it in the linear cavity

  2. A Proposed Method for Solving Fuzzy System of Linear Equations

    Directory of Open Access Journals (Sweden)

    Reza Kargar

    2014-01-01

    Full Text Available This paper proposes a new method for solving fuzzy system of linear equations with crisp coefficients matrix and fuzzy or interval right hand side. Some conditions for the existence of a fuzzy or interval solution of m×n linear system are derived and also a practical algorithm is introduced in detail. The method is based on linear programming problem. Finally the applicability of the proposed method is illustrated by some numerical examples.

  3. Indirect synthesis of multi-degree of freedom transient systems. [linear programming for a kinematically linear system

    Science.gov (United States)

    Pilkey, W. D.; Chen, Y. H.

    1974-01-01

    An indirect synthesis method is used in the efficient optimal design of multi-degree of freedom, multi-design element, nonlinear, transient systems. A limiting performance analysis which requires linear programming for a kinematically linear system is presented. The system is selected using system identification methods such that the designed system responds as closely as possible to the limiting performance. The efficiency is a result of the method avoiding the repetitive systems analyses accompanying other numerical optimization methods.

  4. A Methodology for Multiple Rule System Integration and Resolution Within a Singular Knowledge Base

    Science.gov (United States)

    Kautzmann, Frank N., III

    1988-01-01

    Expert Systems which support knowledge representation by qualitative modeling techniques experience problems, when called upon to support integrated views embodying description and explanation, especially when other factors such as multiple causality, competing rule model resolution, and multiple uses of knowledge representation are included. A series of prototypes are being developed to demonstrate the feasibility of automating the process of systems engineering, design and configuration, and diagnosis and fault management. A study involves not only a generic knowledge representation; it must also support multiple views at varying levels of description and interaction between physical elements, systems, and subsystems. Moreover, it will involve models of description and explanation for each level. This multiple model feature requires the development of control methods between rule systems and heuristics on a meta-level for each expert system involved in an integrated and larger class of expert system. The broadest possible category of interacting expert systems is described along with a general methodology for the knowledge representation and control of mutually exclusive rule systems.

  5. LINPACK, Subroutine Library for Linear Equation System Solution and Matrix Calculation

    International Nuclear Information System (INIS)

    Dongarra, J.J.

    1979-01-01

    1 - Description of problem or function: LINPACK is a collection of FORTRAN subroutines which analyze and solve various classes of systems of simultaneous linear algebraic equations. The collection deals with general, banded, symmetric indefinite, symmetric positive definite, triangular, and tridiagonal square matrices, as well as with least squares problems and the QR and singular value decompositions of rectangular matrices. A subroutine-naming convention is employed in which each subroutine name consists of five letters which represent a coded specification (TXXYY) of the computation done by that subroutine. The first letter, T, indicates the matrix data type. Standard FORTRAN allows the use of three such types: S REAL, D DOUBLE PRECISION, and C COMPLEX. In addition, some FORTRAN systems allow a double-precision complex type: Z COMPLEX*16. The second and third letters of the subroutine name, XX, indicate the form of the matrix or its decomposition: GE: General, GB: General band, PO: Positive definite, PP: Positive definite packed, PB: Positive definite band, SI: Symmetric indefinite, SP: Symmetric indefinite packed, HI: Hermitian indefinite, HP: Hermitian indefinite packed, TR: Triangular, GT: General tridiagonal, PT: Positive definite tridiagonal, CH: Cholesky decomposition, QR: Orthogonal-triangular decomposition, SV: Singular value decomposition. The final two letters, YY, indicate the computation done by the particular subroutine: FA: Factor, CO: Factor and estimate condition, SL: Solve, DI: Determinant and/or inverse and/or inertia, DC: Decompose, UD: Update, DD: Down-date, EX Exchange. The following chart shows all the LINPACK subroutines. The initial 'S' in the names may be replaced by D, C or Z and the initial 'C' in the complex-only names may be replaced by a Z. SGE: FA, CO, SL, DI; SGB: FA, CO, SL, DI; SPO: FA, CO, SL, DI; SPP: FA, CO, SL, DI; SPB: FA, CO, SL, DI; SSI: FA, CO, SL, DI; SSP: FA, CO, SL, DI; CHI: FA, CO, SL, DI; CHP: FA, CO, SL, DI; STR

  6. Minimal solution of general dual fuzzy linear systems

    International Nuclear Information System (INIS)

    Abbasbandy, S.; Otadi, M.; Mosleh, M.

    2008-01-01

    Fuzzy linear systems of equations, play a major role in several applications in various area such as engineering, physics and economics. In this paper, we investigate the existence of a minimal solution of general dual fuzzy linear equation systems. Two necessary and sufficient conditions for the minimal solution existence are given. Also, some examples in engineering and economic are considered

  7. Partial Linearization of Mechanical Systems with Application to Observer Design

    NARCIS (Netherlands)

    Sarras, Ioannis; Venkatraman, Aneesh; Ortega, Romeo; Schaft, Arjan van der

    2008-01-01

    We consider general mechanical systems and establish a necessary and sufficient condition for the existence of a suitable change in the generalized momentum coordinates such that the new dynamics become linear in the transformed momenta. The class of systems which can be (partially) linearized by

  8. Simultaneous Balancing and Model Reduction of Switched Linear Systems

    NARCIS (Netherlands)

    Monshizadeh, Nima; Trentelman, Hendrikus; Camlibel, M.K.

    2011-01-01

    In this paper, first, balanced truncation of linear systems is revisited. Then, simultaneous balancing of multiple linear systems is investigated. Necessary and sufficient conditions are introduced to identify the case where simultaneous balancing is possible. The validity of these conditions is not

  9. Linear System Control Using Stochastic Learning Automata

    Science.gov (United States)

    Ziyad, Nigel; Cox, E. Lucien; Chouikha, Mohamed F.

    1998-01-01

    This paper explains the use of a Stochastic Learning Automata (SLA) to control switching between three systems to produce the desired output response. The SLA learns the optimal choice of the damping ratio for each system to achieve a desired result. We show that the SLA can learn these states for the control of an unknown system with the proper choice of the error criteria. The results of using a single automaton are compared to using multiple automata.

  10. Useful tools for non-linear systems: Several non-linear integral inequalities

    Czech Academy of Sciences Publication Activity Database

    Agahi, H.; Mohammadpour, A.; Mesiar, Radko; Vaezpour, M. S.

    2013-01-01

    Roč. 49, č. 1 (2013), s. 73-80 ISSN 0950-7051 R&D Projects: GA ČR GAP402/11/0378 Institutional support: RVO:67985556 Keywords : Monotone measure * Comonotone functions * Integral inequalities * Universal integral Subject RIV: BA - General Mathematics Impact factor: 3.058, year: 2013 http://library.utia.cas.cz/separaty/2013/E/mesiar-useful tools for non-linear systems several non-linear integral inequalities.pdf

  11. The elimination of singularities in pair correlation functions of a multicomponent liquid system

    International Nuclear Information System (INIS)

    Vasil'jev, O.M.; Chalij, O.V.

    2004-01-01

    In this paper we propose a method that allows to find nonsingular expressions for pair correlation functions of a multicomponent liquid system. The nature of the method deals with using integral and differential Ornstein-Zernike equations for finding asymptotic expressions for pair correlation functions and their subsequent precision. The obtained results are analyzed taking into account their possible applicability for studying the correlative behaviour of multicomponent liquid systems

  12. Decentralized linear quadratic power system stabilizers for multi ...

    Indian Academy of Sciences (India)

    Introduction. Modern excitation systems considerably enhance the overall transient stability of power systems ..... to the local bus rather than the angle δ measured with respect to the remote bus. ... With this in view, the linear and nonlinear per-.

  13. Lyapunov, singular and bred vectors in a multi-scale system: an empirical exploration of vectors related to instabilities

    International Nuclear Information System (INIS)

    Norwood, Adrienne; Kalnay, Eugenia; Ide, Kayo; Yang, Shu-Chih; Wolfe, Christopher

    2013-01-01

    We compute and compare the three types of vectors frequently used to explore the instability properties of dynamical models, namely Lyapunov vectors (LVs), singular vectors (SVs) and bred vectors (BVs) in two systems, using the Wolfe–Samelson (2007 Tellus A 59 355–66) algorithm to compute all of the Lyapunov vectors. The first system is the Lorenz (1963 J. Atmos. Sci. 20 130–41) three-variable model. Although the leading Lyapunov vector, LV1, grows fastest globally, the second Lyapunov vector, LV2, which has zero growth globally, often grows faster than LV1 locally. Whenever this happens, BVs grow closer to LV2, suggesting that in larger atmospheric or oceanic models where several instabilities can grow in different areas of the world, BVs will grow toward the fastest growing local unstable mode. A comparison of their growth rates at different times shows that all three types of dynamical vectors have the ability to predict regime changes and the duration of the new regime based on their growth rates in the last orbit of the old regime, as shown for BVs by Evans et al (2004 Bull. Am. Meteorol. Soc. 520–4). LV1 and BVs have similar predictive skill, LV2 has a tendency to produce false alarms, and even LV3 shows that maximum decay is also associated with regime change. Initial and final SVs grow much faster and are the most accurate predictors of regime change, although the characteristics of the initial SVs are strongly dependent on the length of the optimization window. The second system is the toy ‘ocean-atmosphere’ model developed by Peña and Kalnay (2004 Nonlinear Process. Geophys. 11 319–27) coupling three Lorenz (1963 J. Atmos. Sci. 20 130–41) systems with different time scales, in order to test the effects of fast and slow modes of growth on the dynamical vectors. A fast ‘extratropical atmosphere’ is weakly coupled to a fast ‘tropical atmosphere’ which is, in turn, strongly coupled to a slow ‘ocean’ system, the latter coupling

  14. A new active absorption system and its performance to linear and non-linear waves

    DEFF Research Database (Denmark)

    Andersen, Thomas Lykke; Clavero, M.; Frigaard, Peter Bak

    2016-01-01

    Highlights •An active absorption system for wavemakers has been developed. •The theory for flush mounted gauges has been extended to cover also small gaps. •The new system has been validated in a wave flume with wavemakers in both ends. •A generation and absorption procedure for highly non-linear...

  15. Singular perturbation solutions of steady-state Poisson-Nernst-Planck systems.

    Science.gov (United States)

    Wang, Xiang-Sheng; He, Dongdong; Wylie, Jonathan J; Huang, Huaxiong

    2014-02-01

    We study the Poisson-Nernst-Planck (PNP) system with an arbitrary number of ion species with arbitrary valences in the absence of fixed charges. Assuming point charges and that the Debye length is small relative to the domain size, we derive an asymptotic formula for the steady-state solution by matching outer and boundary layer solutions. The case of two ionic species has been extensively studied, the uniqueness of the solution has been proved, and an explicit expression for the solution has been obtained. However, the case of three or more ions has received significantly less attention. Previous work has indicated that the solution may be nonunique and that even obtaining numerical solutions is a difficult task since one must solve complicated systems of nonlinear equations. By adopting a methodology that preserves the symmetries of the PNP system, we show that determining the outer solution effectively reduces to solving a single scalar transcendental equation. Due to the simple form of the transcendental equation, it can be solved numerically in a straightforward manner. Our methodology thus provides a standard procedure for solving the PNP system and we illustrate this by solving some practical examples. Despite the fact that for three ions, previous studies have indicated that multiple solutions may exist, we show that all except for one of these solutions are unphysical and thereby prove the existence and uniqueness for the three-ion case.

  16. Uncertainty modelling and structured singular value computation applied to an electro-mechanical system

    NARCIS (Netherlands)

    Steinbuch, M.; Terlouw, J.C.; Bosgra, O.H.; Smit, S.G.

    1992-01-01

    The investigation of closed-loop systems subject to model perturbations is an important issue to assure stability robustness of a control design. A large variety of model perturbations can be described by norm-bounded uncertainty models. A general approach for modelling structured complex and

  17. On Optimal Feedback Control for Stationary Linear Systems

    International Nuclear Information System (INIS)

    Russell, David L.

    2010-01-01

    We study linear-quadratic optimal control problems for finite dimensional stationary linear systems AX+BU=Z with output Y=CX+DU from the viewpoint of linear feedback solution. We interpret solutions in relation to system robustness with respect to disturbances Z and relate them to nonlinear matrix equations of Riccati type and eigenvalue-eigenvector problems for the corresponding Hamiltonian system. Examples are included along with an indication of extensions to continuous, i.e., infinite dimensional, systems, primarily of elliptic type.

  18. Virtual Estimator for Piecewise Linear Systems Based on Observability Analysis

    Science.gov (United States)

    Morales-Morales, Cornelio; Adam-Medina, Manuel; Cervantes, Ilse; Vela-Valdés and, Luis G.; García Beltrán, Carlos Daniel

    2013-01-01

    This article proposes a virtual sensor for piecewise linear systems based on observability analysis that is in function of a commutation law related with the system's outpu. This virtual sensor is also known as a state estimator. Besides, it presents a detector of active mode when the commutation sequences of each linear subsystem are arbitrary and unknown. For the previous, this article proposes a set of virtual estimators that discern the commutation paths of the system and allow estimating their output. In this work a methodology in order to test the observability for piecewise linear systems with discrete time is proposed. An academic example is presented to show the obtained results. PMID:23447007

  19. Singular Poisson tensors

    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

  20. Mathematical models of incompressible fluids as singular limits of complete fluid systems

    Czech Academy of Sciences Publication Activity Database

    Feireisl, Eduard

    2010-01-01

    Roč. 78, č. 2 (2010), s. 523-560 ISSN 1424-9286 R&D Projects: GA ČR GA201/08/0315 Institutional research plan: CEZ:AV0Z10190503 Keywords : scale analysis * Navier-Stokes-Fourier system * incompressible limit Subject RIV: BA - General Mathematics Impact factor: 0.933, year: 2010 http://link.springer.com/article/10.1007%2Fs00032-010-0128-1

  1. Canonical symmetry in a system with singular Lagrangian and ward identities

    International Nuclear Information System (INIS)

    Li Ziping

    1994-01-01

    An algorithm to construct the generator of gauge transformation for a constrained Hamiltonian system is given. The relationships among the coefficients connecting with first-class constraints in the generator is cleared. Based on the phase space generating function, the corresponding Ward identities in canonical formalism is deduced. The preliminary applications of above results to a model in field theory which is functionally equivalent to the mixed Chern-Simons Lagrangian is discussed in detail

  2. Singular stochastic differential equations

    CERN Document Server

    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.

  3. Constructing Current Singularity in a 3D Line-tied Plasma

    Science.gov (United States)

    Zhou, Yao; Huang, Yi-Min; Qin, Hong; Bhattacharjee, A.

    2018-01-01

    We revisit Parker’s conjecture of current singularity formation in 3D line-tied plasmas using a recently developed numerical method, variational integration for ideal magnetohydrodynamics in Lagrangian labeling. With the frozen-in equation built-in, the method is free of artificial reconnection, and hence it is arguably an optimal tool for studying current singularity formation. Using this method, the formation of current singularity has previously been confirmed in the Hahm–Kulsrud–Taylor problem in 2D. In this paper, we extend this problem to 3D line-tied geometry. The linear solution, which is singular in 2D, is found to be smooth for arbitrary system length. However, with finite amplitude, the linear solution can become pathological when the system is sufficiently long. The nonlinear solutions turn out to be smooth for short systems. Nonetheless, the scaling of peak current density versus system length suggests that the nonlinear solution may become singular at finite length. With the results in hand, we can neither confirm nor rule out this possibility conclusively, since we cannot obtain solutions with system length near the extrapolated critical value.

  4. Gradient remediability in linear distributed parabolic systems ...

    African Journals Online (AJOL)

    The aim of this paper is the introduction of a new concept that concerned the analysis of a large class of distributed parabolic systems. It is the general concept of gradient remediability. More precisely, we study with respect to the gradient observation, the existence of an input operator (gradient efficient actuators) ensuring ...

  5. Linearization of Nonautonomous Impulsive System with Nonuniform Exponential Dichotomy

    Directory of Open Access Journals (Sweden)

    Yongfei Gao

    2014-01-01

    Full Text Available This paper gives a version of Hartman-Grobman theorem for the impulsive differential equations. We assume that the linear impulsive system has a nonuniform exponential dichotomy. Under some suitable conditions, we proved that the nonlinear impulsive system is topologically conjugated to its linear system. Indeed, we do construct the topologically equivalent function (the transformation. Moreover, the method to prove the topological conjugacy is quite different from those in previous works (e.g., see Barreira and Valls, 2006.

  6. On the discretization of linear fractional representations of LPV systems

    NARCIS (Netherlands)

    Toth, R.; Lovera, M.; Heuberger, P.S.C.; Corno, M.; Hof, Van den P.M.J.

    2012-01-01

    Commonly, controllers for linear parameter-varying (LPV) systems are designed in continuous time using a linear fractional representation (LFR) of the plant. However, the resulting controllers are implemented on digital hardware. Furthermore, discrete-time LPV synthesis approaches require a

  7. Automatic frequency control system for driving a linear accelerator

    International Nuclear Information System (INIS)

    Helgesson, A.L.

    1976-01-01

    An automatic frequency control system is described for maintaining the drive frequency applied to a linear accelerator to produce maximum particle output from the accelerator. The particle output amplitude is measured and the frequency of the radio frequency source powering the linear accelerator is adjusted to maximize particle output amplitude

  8. Application of Nearly Linear Solvers to Electric Power System Computation

    Science.gov (United States)

    Grant, Lisa L.

    To meet the future needs of the electric power system, improvements need to be made in the areas of power system algorithms, simulation, and modeling, specifically to achieve a time frame that is useful to industry. If power system time-domain simulations could run in real-time, then system operators would have situational awareness to implement online control and avoid cascading failures, significantly improving power system reliability. Several power system applications rely on the solution of a very large linear system. As the demands on power systems continue to grow, there is a greater computational complexity involved in solving these large linear systems within reasonable time. This project expands on the current work in fast linear solvers, developed for solving symmetric and diagonally dominant linear systems, in order to produce power system specific methods that can be solved in nearly-linear run times. The work explores a new theoretical method that is based on ideas in graph theory and combinatorics. The technique builds a chain of progressively smaller approximate systems with preconditioners based on the system's low stretch spanning tree. The method is compared to traditional linear solvers and shown to reduce the time and iterations required for an accurate solution, especially as the system size increases. A simulation validation is performed, comparing the solution capabilities of the chain method to LU factorization, which is the standard linear solver for power flow. The chain method was successfully demonstrated to produce accurate solutions for power flow simulation on a number of IEEE test cases, and a discussion on how to further improve the method's speed and accuracy is included.

  9. 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.

  10. Feedback linearizing control of a MIMO power system

    Science.gov (United States)

    Ilyes, Laszlo

    Prior research has demonstrated that either the mechanical or electrical subsystem of a synchronous electric generator may be controlled using single-input single-output (SISO) nonlinear feedback linearization. This research suggests a new approach which applies nonlinear feedback linearization to a multi-input multi-output (MIMO) model of the synchronous electric generator connected to an infinite bus load model. In this way, the electrical and mechanical subsystems may be linearized and simultaneously decoupled through the introduction of a pair of auxiliary inputs. This allows well known, linear, SISO control methods to be effectively applied to the resulting systems. The derivation of the feedback linearizing control law is presented in detail, including a discussion on the use of symbolic math processing as a development tool. The linearizing and decoupling properties of the control law are validated through simulation. And finally, the robustness of the control law is demonstrated.

  11. Singular and interactive effects of blowdown, salvage logging, and wildfire in sub-boreal pine systems

    Science.gov (United States)

    D'Amato, A.W.; Fraver, S.; Palik, B.J.; Bradford, J.B.; Patty, L.

    2011-01-01

    The role of disturbance in structuring vegetation is widely recognized; however, we are only beginning to understand the effects of multiple interacting disturbances on ecosystem recovery and development. Of particular interest is the impact of post-disturbance management interventions, particularly in light of the global controversy surrounding the effects of salvage logging on forest ecosystem recovery. Studies of salvage logging impacts have focused on the effects of post-disturbance salvage logging within the context of a single natural disturbance event. There have been no formal evaluations of how these effects may differ when followed in short sequence by a second, high severity natural disturbance. To evaluate the impact of this management practice within the context of multiple disturbances, we examined the structural and woody plant community responses of sub-boreal Pinus banksiana systems to a rapid sequence of disturbances. Specifically, we compared responses to Blowdown (B), Fire (F), Blowdown-Fire, and Blowdown-Salvage-Fire (BSF) and compared these to undisturbed control (C) stands. Comparisons between BF and BSF indicated that the primary effect of salvage logging was a decrease in the abundance of structural legacies, such as downed woody debris and snags. Both of these compound disturbance sequences (BF and BSF), resulted in similar woody plant communities, largely dominated by Populus tremuloides; however, there was greater homogeneity in community composition in salvage logged areas. Areas experiencing solely fire (F stands) were dominated by P. banksiana regeneration, and blowdown areas (B stands) were largely characterized by regeneration from shade tolerant conifer species. Our results suggest that salvage logging impacts on woody plant communities are diminished when followed by a second high severity disturbance; however, impacts on structural legacies persist. Provisions for the retention of snags, downed logs, and surviving trees as part

  12. 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.

  13. State control of discrete-time linear systems to be bound in state variables by equality constraints

    International Nuclear Information System (INIS)

    Filasová, Anna; Krokavec, Dušan; Serbák, Vladimír

    2014-01-01

    The paper is concerned with the problem of designing the discrete-time equivalent PI controller to control the discrete-time linear systems in such a way that the closed-loop state variables satisfy the prescribed equality constraints. Since the problem is generally singular, using standard form of the Lyapunov function and a symmetric positive definite slack matrix, the design conditions are proposed in the form of the enhanced Lyapunov inequality. The results, offering the conditions of the control existence and the optimal performance with respect to the prescribed equality constraints for square discrete-time linear systems, are illustrated with the numerical example to note effectiveness and applicability of the considered approach

  14. Portable, x-band, linear accelerator systems

    International Nuclear Information System (INIS)

    Schonberg, R.G.; Deruyter, H.; Fowkes, W.R.; Johnson, W.A.; Miller, R.H.; Potter, J.M.; Weaver, J.N.

    1985-01-01

    Three light-weight, x-band, electron accelerators have been developed to provide a series of highly portable sources of x-rays and neutrons for nondestructive testing. The 1.5 MeV x-ray unit has a 200 kW magnetron for an RF source and an air-cooled, traveling wave accelerating structure to minimize its weight. The 4 and 6 MeV units share the same drive system which contains a 1.2 MW magnetron. The 4 MeV unit uses a traveling-wave guide to produce x-rays and the 6MeV unit uses a standing-wave guide to produce x-rays or neutrons. The choice of 9.3 GHz was dictated by the availability of a high power coaxial magnetron and by the obvious dimensional and weight advantages of a higher frequency over the more common S-band frequencies around 3 GHz

  15. Structure Learning in Stochastic Non-linear Dynamical Systems

    Science.gov (United States)

    Morris, R. D.; Smelyanskiy, V. N.; Luchinsky, D. G.

    2005-12-01

    A great many systems can be modeled in the non-linear dynamical systems framework, as x˙ = f(x) + ξ(t), where f(x) is the potential function for the system, and ξ(t) is the driving noise. Modeling the potential using a set of basis functions, we derive the posterior for the basis coefficients. A more challenging problem is to determine the set of basis functions that are required to model a particular system. We show that using the Bayesian Information Criteria (BIC) to rank models, and the beam search technique, that we can accurately determine the structure of simple non-linear dynamical system models, and the structure of the coupling between non-linear dynamical systems where the individual systems are known. This last case has important ecological applications, for example in predator-prey systems, where the very structure of the coupling between predator-prey pairs can have great ecological significance.

  16. СREATION OF CORRELATION FUNCTIONS OF LINEAR CONTINUOUS SYSTEMS BASED ON THEIR FUNDAMENTAL MATRICES

    Directory of Open Access Journals (Sweden)

    N. A. Vunder

    2015-11-01

    Full Text Available The paper presents a method of creating correlation matrices and functions of the state vectors and outputs of the linear continuous systems functioning under the conditions of stochastic stationary, in a broad sense, effects. Fundamental matrices form the basis of the method. We have shown that for the linear continuous systems with single dimensional input and single dimensional output the correlation output function of such system can be found as the free movement of this system generated by its initial state. This state is constructed from the variance matrix of the state vector and the transposed output matrix. We have elucidated that when a continuous system belongs to a class of multi-dimensional input – multi-dimensional output systems, the following options are available for solving the problem of creation of the correlation function of a linear system. The first option is to partition the system into separate channels. Then the approach developed for systems with onedimensional input and one-dimensional output is applied to each of the separate channels. The second option is used to preserve the vector nature of the stochastic external influence. It consists in partition of output vector to scalar components by separating output matrix into separate rows with subsequent formation of the correlation function according to the scheme for single dimensional input and single dimensional output type systems. The third option is based on the scalarization of matrix correlation output function by applying the singular value decomposition to it. That gives the possibility to form scalar majorant and minorant of correlation output functions. We have established that a key component of a computational procedure of creating the correlation function of continuous linear system is a variance matrix of the system state vector. In the case of functioning under an exogenous stochastic effect like "white noise" the variance matrix is calculated by

  17. Portable, x-band, linear accelerator systems

    International Nuclear Information System (INIS)

    Schonberg, R.G.; Deruyter, H.; Fowkes, W.R.; Johnson, W.A.; Miller, R.H.; Potter, J.M.; Weaver, J.N.

    1985-01-01

    Three light-weight, x-band, electron accelerators have been developed to provide a series of highly portable sources of x-rays and neutrons for non-destructive testing. The 1.5 MeV x-ray unit has a 200 kW magnetron for an RF source and an air-cooled, traveling wave accelerating structure to minimize its weight. The 4 and 6 MeV units share the same drive system which contains a 1.2 MW magnetron. The 4 MeV unit uses a traveling-wave guide to produce x-rays and the 6MeV unit uses a standing-wave guide to produce x-rays or neutrons. The choice of 9.3 GHz was dictated by the availability of a high power coaxial magnetron and by the obvious dimensional and weight advantages of a higher frequency over the more common S-band frequencies around 3 GHz

  18. Linear quadratic Gaussian balancing for discrete-time infinite-dimensional linear systems

    NARCIS (Netherlands)

    Opmeer, MR; Curtain, RF

    2004-01-01

    In this paper, we study the existence of linear quadratic Gaussian (LQG)-balanced realizations for discrete-time infinite-dimensional systems. LQG-balanced realizations are those for which the smallest nonnegative self-adjoint solutions of the control and filter Riccati equations are equal. We show

  19. Sparse Linear Solver for Power System Analysis Using FPGA

    National Research Council Canada - National Science Library

    Johnson, J. R; Nagvajara, P; Nwankpa, C

    2005-01-01

    .... Numerical solution to load flow equations are typically computed using Newton-Raphson iteration, and the most time consuming component of the computation is the solution of a sparse linear system...

  20. Perfect commuting-operator strategies for linear system games

    Science.gov (United States)

    Cleve, Richard; Liu, Li; Slofstra, William

    2017-01-01

    Linear system games are a generalization of Mermin's magic square game introduced by Cleve and Mittal. They show that perfect strategies for linear system games in the tensor-product model of entanglement correspond to finite-dimensional operator solutions of a certain set of non-commutative equations. We investigate linear system games in the commuting-operator model of entanglement, where Alice and Bob's measurement operators act on a joint Hilbert space, and Alice's operators must commute with Bob's operators. We show that perfect strategies in this model correspond to possibly infinite-dimensional operator solutions of the non-commutative equations. The proof is based around a finitely presented group associated with the linear system which arises from the non-commutative equations.

  1. Introduction to singularities

    CERN Document Server

    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...

  2. A conceptual design of Final Focus Systems for linear colliders

    International Nuclear Information System (INIS)

    Brown, K.L.

    1987-06-01

    Linear colliders are a relatively recent development in the evolution of particle accelerators. This report discusses some of the approaches that have been considered for the design of Final Focus Systems to demagnify the beam exiting from a linac to the small size suitable for collisions at the interaction point. The system receiving the most attention is the one adopted for the SLAC Linear Collider. However, the theory and optical techniques discussed should be applicable to the design efforts for future machines

  3. ON THE STABILIZATION OF THE LINEAR HYBRID SYSTEM STRUCTURE

    Directory of Open Access Journals (Sweden)

    Kirillov

    2014-11-01

    Full Text Available The linear control hybrid system, consisting of a fi- nite set of subsystems (modes having different dimensions, is considered. The moments of reset time are determined by some complementary function – evolutionary time. This function satisfies the special complementary ordinary differential equation. The mode stabilization problem is solved for some class of piecewise linear controls. The method of stabilization relies on the set of invariant planes, the existence of which is due to the special form of the hybrid system.

  4. Iterative algorithms for large sparse linear systems on parallel computers

    Science.gov (United States)

    Adams, L. M.

    1982-01-01

    Algorithms for assembling in parallel the sparse system of linear equations that result from finite difference or finite element discretizations of elliptic partial differential equations, such as those that arise in structural engineering are developed. Parallel linear stationary iterative algorithms and parallel preconditioned conjugate gradient algorithms are developed for solving these systems. In addition, a model for comparing parallel algorithms on array architectures is developed and results of this model for the algorithms are given.

  5. Simultaneous Balancing and Model Reduction of Switched Linear Systems

    OpenAIRE

    Monshizadeh, Nima; Trentelman, Hendrikus; Camlibel, M.K.

    2011-01-01

    In this paper, first, balanced truncation of linear systems is revisited. Then, simultaneous balancing of multiple linear systems is investigated. Necessary and sufficient conditions are introduced to identify the case where simultaneous balancing is possible. The validity of these conditions is not limited to a certain type of balancing, and they are applicable for different types of balancing corresponding to different equations, like Lyapunov or Riccati equations. The results obtained are ...

  6. 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.

  7. Solar photovoltaic water pumping system using a new linear actuator

    OpenAIRE

    Andrada Gascón, Pedro; Castro, Javier

    2007-01-01

    In this paper a photovoltaic solar pumping system using a new linear actuator is presented. This linear actuator is a double-sided flat two-phase variable-reluctance linear stepper motor that moves a piston-type water pump with the help of a rope, a pulley and a counterweight. The entire actuator pump ensemble is controlled by a simple electronic unit that manages the electric power generated by a photovoltaic array. The proposed system is suitable for rural communities in developing...

  8. The effect of a curvature-dependent surface tension on the singularities at the tips of a straight interface crack

    KAUST Repository

    Zemlyanova, A. Y.

    2013-03-08

    A problem of an interface crack between two semi-planes made out of different materials under an action of an in-plane loading of general tensile-shear type is treated in a semi-analytical manner with the help of Dirichlet-to-Neumann mappings. The boundaries of the crack and the interface between semi-planes are subjected to a curvature-dependent surface tension. The resulting system of six singular integro-differential equations is reduced to the system of three Fredholm equations. It is shown that the introduction of the curvature-dependent surface tension eliminates both classical integrable power singularity of the order 1/2 and an oscillating singularity present in a classical linear elasticity solutions. The numerical results are obtained by solving the original system of singular integro-differential equations by approximating unknown functions with Taylor polynomials. © 2013 The Author.

  9. The H-N method for solving linear transport equation: theory and application

    International Nuclear Information System (INIS)

    Kaskas, A.; Gulecyuz, M.C.; Tezcan, C.

    2002-01-01

    The system of singular integral equation which is obtained from the integro-differential form of the linear transport equation as a result of Placzec lemma is solved. Application are given using the exit distributions and the infinite medium Green's function. The same theoretical results are also obtained with the use of the singular eigenfunction of the method of elementary solutions

  10. Phase and amplitude detection system for the Stanford Linear Accelerator

    International Nuclear Information System (INIS)

    Fox, J.D.; Schwarz, H.D.

    1983-01-01

    A computer controlled phase and amplitude detection system to measure and stabilize the rf power sources in the Stanford Linear Accelerator is described. This system measures the instantaneous phase and amplitude of a 1 microsecond 2856 MHz rf pulse and will be used for phase feedback control and for amplitude and phase jitter detection. This paper discusses the measurement system performance requirements for the operation of the Stanford Linear Collider, and the design and implementation of the phase and amplitude detection system. The fundamental software algorithms used in the measurement are described, as is the performance of the prototype phase and amplitude detector system

  11. Synchronization of linearly coupled unified chaotic systems based on linear balanced feedback scheme with constraints

    International Nuclear Information System (INIS)

    Chen, H.-H.; Chen, C.-S.; Lee, C.-I

    2009-01-01

    This paper investigates the synchronization of unidirectional and bidirectional coupled unified chaotic systems. A balanced coupling coefficient control method is presented for global asymptotic synchronization using the Lyapunov stability theorem and a minimum scheme with no constraints/constraints. By using the result of the above analysis, the balanced coupling coefficients are then designed to achieve the chaos synchronization of linearly coupled unified chaotic systems. The feasibility and effectiveness of the proposed chaos synchronization scheme are verified via numerical simulations.

  12. Solution of generalized shifted linear systems with complex symmetric matrices

    International Nuclear Information System (INIS)

    Sogabe, Tomohiro; Hoshi, Takeo; Zhang, Shao-Liang; Fujiwara, Takeo

    2012-01-01

    We develop the shifted COCG method [R. Takayama, T. Hoshi, T. Sogabe, S.-L. Zhang, T. Fujiwara, Linear algebraic calculation of Green’s function for large-scale electronic structure theory, Phys. Rev. B 73 (165108) (2006) 1–9] and the shifted WQMR method [T. Sogabe, T. Hoshi, S.-L. Zhang, T. Fujiwara, On a weighted quasi-residual minimization strategy of the QMR method for solving complex symmetric shifted linear systems, Electron. Trans. Numer. Anal. 31 (2008) 126–140] for solving generalized shifted linear systems with complex symmetric matrices that arise from the electronic structure theory. The complex symmetric Lanczos process with a suitable bilinear form plays an important role in the development of the methods. The numerical examples indicate that the methods are highly attractive when the inner linear systems can efficiently be solved.

  13. Economic MPC for a linear stochastic system of energy units

    DEFF Research Database (Denmark)

    Jørgensen, John Bagterp; Sokoler, Leo Emil; Standardi, Laura

    2016-01-01

    This paper summarizes comprehensively the work in four recent PhD theses from the Technical University of Denmark related to Economic MPC of future power systems. Future power systems will consist of a large number of decentralized power producers and a large number of controllable power consumers...... in addition to stochastic power producers such as wind turbines and solar power plants. Control of such large scale systems requires new control algorithms. In this paper, we formulate the control of such a system as an Economic Model Predictive Control (MPC) problem. When the power producers and controllable...... power consumers have linear dynamics, the Economic MPC may be expressed as a linear program. We provide linear models for a number of energy units in an energy system, formulate an Economic MPC for coordination of such a system. We indicate how advances in computational MPC makes the solutions...

  14. Singular formalism and admissible control of spacecraft with rotating flexible solar array

    Directory of Open Access Journals (Sweden)

    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.

  15. Stability analysis of switched linear systems defined by graphs

    NARCIS (Netherlands)

    Athanasopoulos, N.; Lazar, M.

    2014-01-01

    We present necessary and sufficient conditions for global exponential stability for switched discrete-time linear systems, under arbitrary switching, which is constrained within a set of admissible transitions. The class of systems studied includes the family of systems under arbitrary switching,

  16. Euclidean null controllability of linear systems with delays in state ...

    African Journals Online (AJOL)

    Sufficient conditions are developed for the Euclidean controllability of linear systems with delay in state and in control. Namely, if the uncontrolled system is uniformly asymptotically stable and the control equation proper, then the control system is Euclidean null controllable. Journal of the Nigerian Association of ...

  17. Incremental Closed-loop Identification of Linear Parameter Varying Systems

    DEFF Research Database (Denmark)

    Bendtsen, Jan Dimon; Trangbæk, Klaus

    2011-01-01

    , closed-loop system identification is more difficult than open-loop identification. In this paper we prove that the so-called Hansen Scheme, a technique known from linear time-invariant systems theory for transforming closed-loop system identification problems into open-loop-like problems, can be extended...

  18. Stability and response bounds of non-conservative linear systems

    DEFF Research Database (Denmark)

    Pommer, Christian

    2003-01-01

    For a linear system of second order differential equations the stability is studied by Lyapunov's direct method. The Lyapunov matrix equation is solved and a sufficient condition for stability is expressed by the system matrices. For a system which satisfies the condition for stability the Lyapunov...

  19. Linear Optimization of Frequency Spectrum Assignments Across System

    Science.gov (United States)

    2016-03-01

    selection tools, frequency allocation, transmission optimization, electromagnetic maneuver warfare, electronic protection, assignment model 15. NUMBER ...Characteristics Modeled ...............................................................29 Table 10.   Antenna Systems Modeled , Number of Systems and...surveillance EW early warning GAMS general algebraic modeling system GHz gigahertz IDE integrated development environment ILP integer linear program

  20. Observer-dependent sign inversions of polarization singularities.

    Science.gov (United States)

    Freund, Isaac

    2014-10-15

    We describe observer-dependent sign inversions of the topological charges of vector field polarization singularities: C points (points of circular polarization), L points (points of linear polarization), and two virtually unknown singularities we call γ(C) and α(L) points. In all cases, the sign of the charge seen by an observer can change as she changes the direction from which she views the singularity. Analytic formulas are given for all C and all L point sign inversions.

  1. Quantum propagation across cosmological singularities

    Science.gov (United States)

    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.

  2. Stability analysis of switched linear systems defined by graphs

    OpenAIRE

    Athanasopoulos, Nikolaos; Lazar, Mircea

    2015-01-01

    We present necessary and sufficient conditions for global exponential stability for switched discrete-time linear systems, under arbitrary switching, which is constrained within a set of admissible transitions. The class of systems studied includes the family of systems under arbitrary switching, periodic systems, and systems with minimum and maximum dwell time specifications. To reach the result, we describe the set of rules that define the admissible transitions with a weighted directed gra...

  3. Modeling and analysis of linear hyperbolic systems of balance laws

    CERN Document Server

    Bartecki, Krzysztof

    2016-01-01

    This monograph focuses on the mathematical modeling of distributed parameter systems in which mass/energy transport or wave propagation phenomena occur and which are described by partial differential equations of hyperbolic type. The case of linear (or linearized) 2 x 2 hyperbolic systems of balance laws is considered, i.e., systems described by two coupled linear partial differential equations with two variables representing physical quantities, depending on both time and one-dimensional spatial variable. Based on practical examples of a double-pipe heat exchanger and a transportation pipeline, two typical configurations of boundary input signals are analyzed: collocated, wherein both signals affect the system at the same spatial point, and anti-collocated, in which the input signals are applied to the two different end points of the system. The results of this book emerge from the practical experience of the author gained during his studies conducted in the experimental installation of a heat exchange cente...

  4. A convex optimization approach for solving large scale linear systems

    Directory of Open Access Journals (Sweden)

    Debora Cores

    2017-01-01

    Full Text Available The well-known Conjugate Gradient (CG method minimizes a strictly convex quadratic function for solving large-scale linear system of equations when the coefficient matrix is symmetric and positive definite. In this work we present and analyze a non-quadratic convex function for solving any large-scale linear system of equations regardless of the characteristics of the coefficient matrix. For finding the global minimizers, of this new convex function, any low-cost iterative optimization technique could be applied. In particular, we propose to use the low-cost globally convergent Spectral Projected Gradient (SPG method, which allow us to extend this optimization approach for solving consistent square and rectangular linear system, as well as linear feasibility problem, with and without convex constraints and with and without preconditioning strategies. Our numerical results indicate that the new scheme outperforms state-of-the-art iterative techniques for solving linear systems when the symmetric part of the coefficient matrix is indefinite, and also for solving linear feasibility problems.

  5. 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.

  6. A comparison between linear and toroidal Extrap systems

    International Nuclear Information System (INIS)

    Lehnert, B.

    1988-09-01

    The Extrap scheme consists of a Z-pinch immersed in an octupole field generated by currents in a set of external conductors. A comparison between linear and toroidal Extrap geometry is made in this paper. As compared to toroidal systems, linear geometry has the advantages of relative simplicity and of a current drive by means of electrodes. Linear devices are convenient for basic studies of Extrap, at moderately high pinch currents and plasma temperatures. Within the parameter ranges of experiments at high pinch currents and plasma temperatures, linear systems have on the other hand some substantial disadvantages, on account of the plasma interaction with the end regions. This results in a limitation of the energy confinement time, and leads in the case of an ohmically heated plasma to excessively high plasma densities and small pinch radii which also complicate the introduction of the external conductors. (author)

  7. Linear local stability of electrostatic drift modes in helical systems

    International Nuclear Information System (INIS)

    Yamagishi, O.; Nakajima, N.; Sugama, H.; Nakamura, Y.

    2003-01-01

    We investigate the stability of the drift wave in helical systems. For this purpose, we solve the linear local gyrokinetic-Poisson equation, in the electrostatic regime. As a model of helical plasmas, Large helical Device (LHD) is considered. The equation we apply is rather exact in the framework of linear gyrokinetic theory, where only the approximation is the ballooning representation. In this paper, we consider only collisionless cases. All the frequency regime can be naturally reated without any assumptions, and in such cases, ion temperature gradient modes (ITG), trapped electron modes (TEM), and electron temperature gradient modes (ETG) are expected to become unstable linearly independently. (orig.)

  8. H 2 guaranteed cost control of discrete linear systems

    Directory of Open Access Journals (Sweden)

    Colmenares W.

    2000-01-01

    Full Text Available This paper presents necessary and sufficient conditions for the existence of a quadratically stabilizing output feedback controller which also assures H 2 guaranteed cost performance on a discrete linear uncertain system where the uncertainty is of the norm bounded type. The conditions are presented as a collection of linear matrix inequalities.The solution, however requires a search over a scalar parameter space.

  9. Structured Control of Affine Linear Parameter Varying Systems

    DEFF Research Database (Denmark)

    Adegas, Fabiano Daher; Stoustrup, Jakob

    2011-01-01

    This paper presents a new procedure to design structured controllers for discrete-time affine linear parametervarying systems (A LPV). The class of control structures includes decentralized of any order, fixed order output feedback, simultaneous plant-control design, among others. A parametervarying...... non-convex condition for an upper bound on the induced L2-norm performance is solved by an iterative linear matrix inequalities (LMI) optimization algorithm. Numerical examples demostrate the effectiveness of the proposed approach....

  10. On the stability of non-linear systems

    International Nuclear Information System (INIS)

    Guelman, M.

    1968-09-01

    A study is made of the absolute stability of nonlinear systems, using Liapounov's second method and taking into account the results obtained from V.M. Popov's work. The results already established are first presented, in particular concerning the frequency domain criterions for absolute stability of automatic control systems containing one single non linearity. The results have been extended to show the existence of a limiting parabola. New use is then made of the methods studied for deriving absolute stability criterions for a system containing a different type of non linearity. Finally, the results obtained are considered from the point of view of Aizerman's conjecture. (author) [fr

  11. Applications of equivalent linearization approaches to nonlinear piping systems

    International Nuclear Information System (INIS)

    Park, Y.; Hofmayer, C.; Chokshi, N.

    1997-01-01

    The piping systems in nuclear power plants, even with conventional snubber supports, are highly complex nonlinear structures under severe earthquake loadings mainly due to various mechanical gaps in support structures. Some type of nonlinear analysis is necessary to accurately predict the piping responses under earthquake loadings. The application of equivalent linearization approaches (ELA) to seismic analyses of nonlinear piping systems is presented. Two types of ELA's are studied; i.e., one based on the response spectrum method and the other based on the linear random vibration theory. The test results of main steam and feedwater piping systems supported by snubbers and energy absorbers are used to evaluate the numerical accuracy and limitations

  12. State space and input-output linear systems

    CERN Document Server

    Delchamps, David F

    1988-01-01

    It is difficult for me to forget the mild sense of betrayal I felt some ten years ago when I discovered, with considerable dismay, that my two favorite books on linear system theory - Desoer's Notes for a Second Course on Linear Systems and Brockett's Finite Dimensional Linear Systems - were both out of print. Since that time, of course, linear system theory has undergone a transformation of the sort which always attends the maturation of a theory whose range of applicability is expanding in a fashion governed by technological developments and by the rate at which such advances become a part of engineering practice. The growth of the field has inspired the publication of some excellent books; the encyclopedic treatises by Kailath and Chen, in particular, come immediately to mind. Nonetheless, I was inspired to write this book primarily by my practical needs as a teacher and researcher in the field. For the past five years, I have taught a one semester first year gradu­ ate level linear system theory course i...

  13. Unification of three linear models for the transient visual system

    NARCIS (Netherlands)

    Brinker, den A.C.

    1989-01-01

    Three different linear filters are considered as a model describing the experimentally determined triphasic impulse responses of discs. These impulse responses arc associated with the transient visual system. Each model reveals a different feature of the system. Unification of the models is

  14. Punctuated equilibrium in a non-linear system of action

    NARCIS (Netherlands)

    J.S. Timmermans (Jos)

    2008-01-01

    textabstractColeman's equilibrium model of social development, the Linear System of Action, is extended to cover the dynamics of societal transitions. The model implemented has the characteristics of a dissipative system. A variation and selection algorithm favoring the retention of relatively

  15. Lag synchronization of chaotic systems with time-delayed linear

    Indian Academy of Sciences (India)

    In this paper, the lag synchronization of chaotic systems with time-delayed linear terms via impulsive control is investigated. Based on the stability theory of impulsive delayed differential equations, some sufficient conditions are obtained guaranteeing the synchronized behaviours between two delayed chaotic systems.

  16. INPUT-OUTPUT STRUCTURE OF LINEAR-DIFFERENTIAL ALGEBRAIC SYSTEMS

    NARCIS (Netherlands)

    KUIJPER, M; SCHUMACHER, JM

    Systems of linear differential and algebraic equations occur in various ways, for instance, as a result of automated modeling procedures and in problems involving algebraic constraints, such as zero dynamics and exact model matching. Differential/algebraic systems may represent an input-output

  17. Frequency Interval Cross Gramians for Linear and Bilinear Systems

    DEFF Research Database (Denmark)

    Jazlan, Ahmad; Sreeram, Victor; Shaker, Hamid Reza

    2017-01-01

    In many control engineering problems, it is desired to analyze the systems at particular frequency intervals of interest. This paper focuses on the development of frequency interval cross gramians for both linear and bilinear systems. New generalized Sylvester equations for calculating the freque...

  18. Switching control of linear systems for generating chaos

    International Nuclear Information System (INIS)

    Liu Xinzhi; Teo, Kok-Lay; Zhang Hongtao; Chen Guanrong

    2006-01-01

    In this paper, a new switching method is developed, which can be applied to generating different types of chaos or chaos-like dynamics from two or more linear systems. A numerical simulation is given to illustrate the generated chaotic dynamic behavior of the systems with some variable parameters. Finally, a circuit is built to realize various chaotic dynamical behaviors

  19. New approach to solve symmetric fully fuzzy linear systems

    Indian Academy of Sciences (India)

    In this paper, we present a method to solve fully fuzzy linear systems with symmetric coefficient matrix. The symmetric coefficient matrix is decomposed into two systems of equations by using Cholesky method and then a solution can be obtained. Numerical examples are given to illustrate our method.

  20. Criteria for stability of linear dynamical systems with multiple delays ...

    African Journals Online (AJOL)

    In this study we considered a linear Dynamical system with multiple delays and find suitable conditions on the systems parameters such that for a given initial function, we can define a mapping in a carefully chosen complete metric space on which the mapping has a unique fixed point. An asymptotic stability theory for the ...

  1. A data-acquisition system for high speed linear CCD

    International Nuclear Information System (INIS)

    Liu Zhiyan; Chen Xiangcai; Jiang Xiaoshan; Zhang Hongyu; Liang Zhongwang; Xiang Haisheng; Hu Jun

    2010-01-01

    A data-acquisition system for high speed linear CCD (Charge Coupled device) is mainly introduced. The optical fiber transmission technology is used. The data is sent to PC through USB or PCI interface. The construction of the system, the design of the PCI interface hardware, software design and the design of the control program running on host computer are also introduced. (authors)

  2. Partial Synchronization Manifolds for Linearly Time-Delay Coupled Systems

    OpenAIRE

    Steur, Erik; van Leeuwen, Cees; Michiels, Wim

    2014-01-01

    Sometimes a network of dynamical systems shows a form of incomplete synchronization characterized by synchronization of some but not all of its systems. This type of incomplete synchronization is called partial synchronization. Partial synchronization is associated with the existence of partial synchronization manifolds, which are linear invariant subspaces of C, the state space of the network of systems. We focus on partial synchronization manifolds in networks of system...

  3. 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

  4. The Big Bang Singularity

    Science.gov (United States)

    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.

  5. Surface Plasmon Singularities

    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.

  6. Timelike naked singularity

    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

  7. The linear sizes tolerances and fits system modernization

    Science.gov (United States)

    Glukhov, V. I.; Grinevich, V. A.; Shalay, V. V.

    2018-04-01

    The study is carried out on the urgent topic for technical products quality providing in the tolerancing process of the component parts. The aim of the paper is to develop alternatives for improving the system linear sizes tolerances and dimensional fits in the international standard ISO 286-1. The tasks of the work are, firstly, to classify as linear sizes the elements additionally linear coordinating sizes that determine the detail elements location and, secondly, to justify the basic deviation of the tolerance interval for the element's linear size. The geometrical modeling method of real details elements, the analytical and experimental methods are used in the research. It is shown that the linear coordinates are the dimensional basis of the elements linear sizes. To standardize the accuracy of linear coordinating sizes in all accuracy classes, it is sufficient to select in the standardized tolerance system only one tolerance interval with symmetrical deviations: Js for internal dimensional elements (holes) and js for external elements (shafts). The main deviation of this coordinating tolerance is the average zero deviation, which coincides with the nominal value of the coordinating size. Other intervals of the tolerance system are remained for normalizing the accuracy of the elements linear sizes with a fundamental change in the basic deviation of all tolerance intervals is the maximum deviation corresponding to the limit of the element material: EI is the lower tolerance for the of the internal elements (holes) sizes and es is the upper tolerance deviation for the outer elements (shafts) sizes. It is the sizes of the material maximum that are involved in the of the dimensional elements mating of the shafts and holes and determine the fits type.

  8. On reliability of singular-value decomposition in attractor reconstruction

    International Nuclear Information System (INIS)

    Palus, M.; Dvorak, I.

    1990-12-01

    Applicability of singular-value decomposition for reconstructing the strange attractor from one-dimensional chaotic time series, proposed by Broomhead and King, is extensively tested and discussed. Previously published doubts about its reliability are confirmed: singular-value decomposition, by nature a linear method, is only of a limited power when nonlinear structures are studied. (author). 29 refs, 9 figs

  9. 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.

  10. Damped oscillations of linear systems a mathematical introduction

    CERN Document Server

    Veselić, Krešimir

    2011-01-01

    The theory of linear damped oscillations was originally developed more than hundred years ago and is still of vital research interest to engineers, mathematicians and physicists alike. This theory plays a central role in explaining the stability of mechanical structures in civil engineering, but it also has applications in other fields such as electrical network systems and quantum mechanics. This volume gives an introduction to linear finite dimensional damped systems as they are viewed by an applied mathematician. After a short overview of the physical principles leading to the linear system model, a largely self-contained mathematical theory for this model is presented. This includes the geometry of the underlying indefinite metric space, spectral theory of J-symmetric matrices and the associated quadratic eigenvalue problem. Particular attention is paid to the sensitivity issues which influence numerical computations. Finally, several recent research developments are included, e.g. Lyapunov stability and ...

  11. Ultra-high Frequency Linear Fiber Optic Systems

    CERN Document Server

    Lau, Kam

    2011-01-01

    This book provides an in-depth treatment of both linear fiber-optic systems and their key enabling devices. It presents a concise but rigorous treatment of the theory and practice of analog (linear) fiber-optics links and systems that constitute the foundation of Hybrid Fiber Coax infrastructure in present-day CATV distribution and cable modem Internet access. Emerging applications in remote fiber-optic feed for free-space millimeter wave enterprise campus networks are also described. Issues such as dispersion and interferometric noise are treated quantitatively, and means for mitigating them are explained. This broad but concise text will thus be invaluable not only to students of fiber-optics communication but also to practicing engineers. To the second edition of this book important new aspects of linear fiber-optic transmission technologies are added, such as high level system architectural issues, algorithms for deriving the optimal frequency assignment, directly modulated or externally modulated laser t...

  12. 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

  13. 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

  14. System identication of a linearized hysteretic system using covariance driven stochastic subspace identication

    DEFF Research Database (Denmark)

    Bajric, Anela

    A single mass Bouc-Wen oscillator with linear static restoring force contribution is approximated by an equivalent linear system. The aim of the linearized model is to emulate the correct force-displacement response of the Bouc-Wenmodel with characteristic hysteretic behaviour. The linearized mod...

  15. Linearly and nonlinearly bidirectionally coupled synchronization of hyperchaotic systems

    International Nuclear Information System (INIS)

    Zhou Jin; Lu Junan; Wu Xiaoqun

    2007-01-01

    To date, there have been many results about unidirectionally coupled synchronization of chaotic systems. However, much less work is reported on bidirectionally-coupled synchronization. In this paper, we investigate the synchronization of two bidirectionally coupled Chen hyperchaotic systems, which are coupled linearly and nonlinearly respectively. Firstly, linearly coupled synchronization of two hyperchaotic Chen systems is investigated, and a theorem on how to choose the coupling coefficients are developed to guarantee the global asymptotical synchronization of two coupled hyperchaotic systems. Analysis shows that the choice of the coupling coefficients relies on the bound of the chaotic system. Secondly, the nonlinearly coupled synchronization is studied; a sufficient condition for the locally asymptotical synchronization is derived, which is independent of the bound of the hyperchaotic system. Finally, numerical simulations are included to verify the effectiveness and feasibility of the developed theorems

  16. Linear dynamical quantum systems analysis, synthesis, and control

    CERN Document Server

    Nurdin, Hendra I

    2017-01-01

    This monograph provides an in-depth treatment of the class of linear-dynamical quantum systems. The monograph presents a detailed account of the mathematical modeling of these systems using linear algebra and quantum stochastic calculus as the main tools for a treatment that emphasizes a system-theoretic point of view and the control-theoretic formulations of quantum versions of familiar problems from the classical (non-quantum) setting, including estimation and filtering, realization theory, and feedback control. Both measurement-based feedback control (i.e., feedback control by a classical system involving a continuous-time measurement process) and coherent feedback control (i.e., feedback control by another quantum system without the intervention of any measurements in the feedback loop) are treated. Researchers and graduates studying systems and control theory, quantum probability and stochastics or stochastic control whether from backgrounds in mechanical or electrical engineering or applied mathematics ...

  17. Nonautonomous linear system of the terrestrial carbon cycle

    Science.gov (United States)

    Luo, Y.

    2012-12-01

    Carbon cycle has been studied by uses of observation through various networks, field and laboratory experiments, and simulation models. Much less has been done on theoretical thinking and analysis to understand fundament properties of carbon cycle and then guide observatory, experimental, and modeling research. This presentation is to explore what would be the theoretical properties of terrestrial carbon cycle and how those properties can be used to make observatory, experimental, and modeling research more effective. Thousands of published data sets from litter decomposition and soil incubation studies almost all indicate that decay processes of litter and soil organic carbon can be well described by first order differential equations with one or more pools. Carbon pool dynamics in plants and soil after disturbances (e.g., wildfire, clear-cut of forests, and plows of soil for cropping) and during natural recovery or ecosystem restoration also exhibit characteristics of first-order linear systems. Thus, numerous lines of empirical evidence indicate that the terrestrial carbon cycle can be adequately described as a nonautonomous linear system. The linearity reflects the nature of the carbon cycle that carbon, once fixed by photosynthesis, is linearly transferred among pools within an ecosystem. The linear carbon transfer, however, is modified by nonlinear functions of external forcing variables. In addition, photosynthetic carbon influx is also nonlinearly influenced by external variables. This nonautonomous linear system can be mathematically expressed by a first-order linear ordinary matrix equation. We have recently used this theoretical property of terrestrial carbon cycle to develop a semi-analytic solution of spinup. The new methods have been applied to five global land models, including NCAR's CLM and CABLE models and can computationally accelerate spinup by two orders of magnitude. We also use this theoretical property to develop an analytic framework to

  18. The graphics software of the Saclay linear accelerator control system

    International Nuclear Information System (INIS)

    Gournay, J.F.

    1987-06-01

    The Control system of the Saclay Linear Accelerator is based upon modern technology hardware. In the graphic software, pictures are created in exactly the same manner for all the graphic devices supported by the system. The informations used to draw a picture are stored in an array called a graphic segment. Three output primitives are used to add graphic material in a segment. Three coordinate systems are defined

  19. Stability analysis of linear switching systems with time delays

    International Nuclear Information System (INIS)

    Li Ping; Zhong Shouming; Cui Jinzhong

    2009-01-01

    The issue of stability analysis of linear switching system with discrete and distributed time delays is studied in this paper. An appropriate switching rule is applied to guarantee the stability of the whole switching system. Our results use a Riccati-type Lyapunov functional under a condition on the time delay. So, switching systems with mixed delays are developed. A numerical example is given to illustrate the effectiveness of our results.

  20. SNR Estimation in Linear Systems with Gaussian Matrices

    KAUST Repository

    Suliman, Mohamed Abdalla Elhag; Alrashdi, Ayed; Ballal, Tarig; Al-Naffouri, Tareq Y.

    2017-01-01

    This letter proposes a highly accurate algorithm to estimate the signal-to-noise ratio (SNR) for a linear system from a single realization of the received signal. We assume that the linear system has a Gaussian matrix with one sided left correlation. The unknown entries of the signal and the noise are assumed to be independent and identically distributed with zero mean and can be drawn from any distribution. We use the ridge regression function of this linear model in company with tools and techniques adapted from random matrix theory to achieve, in closed form, accurate estimation of the SNR without prior statistical knowledge on the signal or the noise. Simulation results show that the proposed method is very accurate.

  1. SNR Estimation in Linear Systems with Gaussian Matrices

    KAUST Repository

    Suliman, Mohamed Abdalla Elhag

    2017-09-27

    This letter proposes a highly accurate algorithm to estimate the signal-to-noise ratio (SNR) for a linear system from a single realization of the received signal. We assume that the linear system has a Gaussian matrix with one sided left correlation. The unknown entries of the signal and the noise are assumed to be independent and identically distributed with zero mean and can be drawn from any distribution. We use the ridge regression function of this linear model in company with tools and techniques adapted from random matrix theory to achieve, in closed form, accurate estimation of the SNR without prior statistical knowledge on the signal or the noise. Simulation results show that the proposed method is very accurate.

  2. Experimental quantum computing to solve systems of linear equations.

    Science.gov (United States)

    Cai, X-D; Weedbrook, C; Su, Z-E; Chen, M-C; Gu, Mile; Zhu, M-J; Li, Li; Liu, Nai-Le; Lu, Chao-Yang; Pan, Jian-Wei

    2013-06-07

    Solving linear systems of equations is ubiquitous in all areas of science and engineering. With rapidly growing data sets, such a task can be intractable for classical computers, as the best known classical algorithms require a time proportional to the number of variables N. A recently proposed quantum algorithm shows that quantum computers could solve linear systems in a time scale of order log(N), giving an exponential speedup over classical computers. Here we realize the simplest instance of this algorithm, solving 2×2 linear equations for various input vectors on a quantum computer. We use four quantum bits and four controlled logic gates to implement every subroutine required, demonstrating the working principle of this algorithm.

  3. Singular system analysis of the Local Power Range Monitor (LPRM) readings of a Boiling Water Reactor (BWR) in an unstable event

    International Nuclear Information System (INIS)

    Ginestar Peiro, D.; Verdu, G.; Miro, R.

    2006-01-01

    Singular system analysis is a successful technique to separate oscillating components from a given signal. A methodology is proposed to apply this technique to the signals obtained from the LPRMs of a boiling water reactor core and extract the contributions of the in-phase oscillation and the out-of-phase oscillations from the LPRM readings during an unstable event. This methodology has been validated with synthetic signals and simulations of in-phase and out-of-phase oscillations of the Leibstadt reactor. Finally, one case of Ringhals I Stability Benchmark has been analysed. (author)

  4. Periodic solutions of asymptotically linear Hamiltonian systems without twist conditions

    Energy Technology Data Exchange (ETDEWEB)

    Cheng Rong [Coll. of Mathematics and Physics, Nanjing Univ. of Information Science and Tech., Nanjing (China); Dept. of Mathematics, Southeast Univ., Nanjing (China); Zhang Dongfeng [Dept. of Mathematics, Southeast Univ., Nanjing (China)

    2010-05-15

    In dynamical system theory, especially in many fields of applications from mechanics, Hamiltonian systems play an important role, since many related equations in mechanics can be written in an Hamiltonian form. In this paper, we study the existence of periodic solutions for a class of Hamiltonian systems. By applying the Galerkin approximation method together with a result of critical point theory, we establish the existence of periodic solutions of asymptotically linear Hamiltonian systems without twist conditions. Twist conditions play crucial roles in the study of periodic solutions for asymptotically linear Hamiltonian systems. The lack of twist conditions brings some difficulty to the study. To the authors' knowledge, very little is known about the case, where twist conditions do not hold. (orig.)

  5. Theoretical analysis of balanced truncation for linear switched systems

    DEFF Research Database (Denmark)

    Petreczky, Mihaly; Wisniewski, Rafal; Leth, John-Josef

    2012-01-01

    In this paper we present theoretical analysis of model reduction of linear switched systems based on balanced truncation, presented in [1,2]. More precisely, (1) we provide a bound on the estimation error using L2 gain, (2) we provide a system theoretic interpretation of grammians and their singu......In this paper we present theoretical analysis of model reduction of linear switched systems based on balanced truncation, presented in [1,2]. More precisely, (1) we provide a bound on the estimation error using L2 gain, (2) we provide a system theoretic interpretation of grammians...... for showing this independence is realization theory of linear switched systems. [1] H. R. Shaker and R. Wisniewski, "Generalized gramian framework for model/controller order reduction of switched systems", International Journal of Systems Science, Vol. 42, Issue 8, 2011, 1277-1291. [2] H. R. Shaker and R....... Wisniewski, "Switched Systems Reduction Framework Based on Convex Combination of Generalized Gramians", Journal of Control Science and Engineering, 2009....

  6. Linear-constraint wavefront control for exoplanet coronagraphic imaging systems

    Science.gov (United States)

    Sun, He; Eldorado Riggs, A. J.; Kasdin, N. Jeremy; Vanderbei, Robert J.; Groff, Tyler Dean

    2017-01-01

    A coronagraph is a leading technology for achieving high-contrast imaging of exoplanets in a space telescope. It uses a system of several masks to modify the diffraction and achieve extremely high contrast in the image plane around target stars. However, coronagraphic imaging systems are very sensitive to optical aberrations, so wavefront correction using deformable mirrors (DMs) is necessary to avoid contrast degradation in the image plane. Electric field conjugation (EFC) and Stroke minimization (SM) are two primary high-contrast wavefront controllers explored in the past decade. EFC minimizes the average contrast in the search areas while regularizing the strength of the control inputs. Stroke minimization calculates the minimum DM commands under the constraint that a target average contrast is achieved. Recently in the High Contrast Imaging Lab at Princeton University (HCIL), a new linear-constraint wavefront controller based on stroke minimization was developed and demonstrated using numerical simulation. Instead of only constraining the average contrast over the entire search area, the new controller constrains the electric field of each single pixel using linear programming, which could led to significant increases in speed of the wavefront correction and also create more uniform dark holes. As a follow-up of this work, another linear-constraint controller modified from EFC is demonstrated theoretically and numerically and the lab verification of the linear-constraint controllers is reported. Based on the simulation and lab results, the pros and cons of linear-constraint controllers are carefully compared with EFC and stroke minimization.

  7. Seismic analysis of equipment system with non-linearities such as gap and friction using equivalent linearization method

    International Nuclear Information System (INIS)

    Murakami, H.; Hirai, T.; Nakata, M.; Kobori, T.; Mizukoshi, K.; Takenaka, Y.; Miyagawa, N.

    1989-01-01

    Many of the equipment systems of nuclear power plants contain a number of non-linearities, such as gap and friction, due to their mechanical functions. It is desirable to take such non-linearities into account appropriately for the evaluation of the aseismic soundness. However, in usual design works, linear analysis method with rough assumptions is applied from engineering point of view. An equivalent linearization method is considered to be one of the effective analytical techniques to evaluate non-linear responses, provided that errors to a certain extent are tolerated, because it has greater simplicity in analysis and economization in computing time than non-linear analysis. The objective of this paper is to investigate the applicability of the equivalent linearization method to evaluate the maximum earthquake response of equipment systems such as the CANDU Fuelling Machine which has multiple non- linearities

  8. Design techniques for large scale linear measurement systems

    International Nuclear Information System (INIS)

    Candy, J.V.

    1979-03-01

    Techniques to design measurement schemes for systems modeled by large scale linear time invariant systems, i.e., physical systems modeled by a large number (> 5) of ordinary differential equations, are described. The techniques are based on transforming the physical system model to a coordinate system facilitating the design and then transforming back to the original coordinates. An example of a three-stage, four-species, extraction column used in the reprocessing of spent nuclear fuel elements is presented. The basic ideas are briefly discussed in the case of noisy measurements. An example using a plutonium nitrate storage vessel (reprocessing) with measurement uncertainty is also presented

  9. Decentralized linear quadratic power system stabilizers for multi ...

    Indian Academy of Sciences (India)

    Linear quadratic stabilizers are well-known for their superior control capabilities when compared to the conventional lead–lag power system stabilizers. However, they have not seen much of practical importance as the state variables are generally not measurable; especially the generator rotor angle measurement is not ...

  10. Force analysis of linear induction motor for magnetic levitation system

    NARCIS (Netherlands)

    Kuijpers, A.A.; Nemlioglu, C.; Sahin, F.; Verdel, A.J.D.; Compter, J.C.; Lomonova, E.

    2010-01-01

    This paper presents the analyses of thrust and normal forces of linear induction motor (LIM) segments which are implemented in a rotating ring system. To obtain magnetic levitation in a cost effective and sustainable way, decoupled control of thrust and normal forces is required. This study includes

  11. Input design for linear dynamic systems using maxmin criteria

    DEFF Research Database (Denmark)

    Sadegh, Payman; Hansen, Lars H.; Madsen, Henrik

    1998-01-01

    This paper considers the problem of input design for maximizing the smallest eigenvalue of the information matrix for linear dynamic systems. The optimization of the smallest eigenvalue is of interest in parameter estimation and parameter change detection problems. We describe a simple cutting...

  12. Generating Nice Linear Systems for Matrix Gaussian Elimination

    Science.gov (United States)

    Homewood, L. James

    2004-01-01

    In this article an augmented matrix that represents a system of linear equations is called nice if a sequence of elementary row operations that reduces the matrix to row-echelon form, through matrix Gaussian elimination, does so by restricting all entries to integers in every step. Many instructors wish to use the example of matrix Gaussian…

  13. Daylighting System Based on Novel Design of Linear Fresnel lens

    Directory of Open Access Journals (Sweden)

    Thanh Tuan Pham

    2017-10-01

    Full Text Available In this paper, we present a design and optical simulation of a daylighting system using a novel design of linear Fresnel lens, which is constructed based on the conservation of optical path length and edge ray theorem. The linear Fresnel lens can achieve a high uniformity by using a new idea of design in which each groove of the lens distributes sunlight uniformly over the receiver so that the whole lens also uniformly distributes sunlight over the receiver. In this daylighting system, the novel design of linear Fresnel lens significantly improves the uniformity of collector and distributor. Therefore, it can help to improve the performance of the daylighting system. The structure of the linear Fresnel lenses is designed by using Matlab. Then, the structure of lenses is appreciated by ray tracing in LightToolsTM to find out the optimum lens shape. In addition, the simulation is performed by using LightToolsTM to estimate the efficiency of the daylighting system. The results show that the designed collector can achieve the efficiency of ~80% with the tolerance of ~0.60 and the concentration ratio of 340 times, while the designed distributor can reach a high uniformity of >90%.

  14. Robust self-triggered MPC for constrained linear systems

    NARCIS (Netherlands)

    Brunner, F.D.; Heemels, W.P.M.H.; Allgöwer, F.

    2014-01-01

    In this paper we propose a robust self-triggered model predictive control algorithm for linear systems with additive bounded disturbances and hard constraints on the inputs and state. In self-triggered control, at every sampling instant the time until the next sampling instant is computed online

  15. Stability Analysis for Multi-Parameter Linear Periodic Systems

    DEFF Research Database (Denmark)

    Seyranian, A.P.; Solem, Frederik; Pedersen, Pauli

    1999-01-01

    This paper is devoted to stability analysis of general linear periodic systems depending on real parameters. The Floquet method and perturbation technique are the basis of the development. We start out with the first and higher-order derivatives of the Floquet matrix with respect to problem...

  16. Relative controllability and null controllability of linear delay systems ...

    African Journals Online (AJOL)

    Necessary and sufficient conditions are established for the relative, absolute controllability and null controllability of the generalized linear delay system and its discrete prototype. The paper presents illuminating examples on previous controllability results by Manitius and Olbrot [7] and carries over the results of Onwuatu [8] ...

  17. Time-optimal feedback control for linear systems

    International Nuclear Information System (INIS)

    Mirica, S.

    1976-01-01

    The paper deals with the results of qualitative investigations of the time-optimal feedback control for linear systems with constant coefficients. In the first section, after some definitions and notations, two examples are given and it is shown that even the time-optimal control problem for linear systems with constant coefficients which looked like ''completely solved'' requires a further qualitative investigation of the stability to ''permanent perturbations'' of optimal feedback control. In the second section some basic results of the linear time-optimal control problem are reviewed. The third section deals with the definition of Boltyanskii's ''regular synthesis'' and its connection to Filippov's theory of right-hand side discontinuous differential equations. In the fourth section a theorem is proved concerning the stability to perturbations of time-optimal feedback control for linear systems with scalar control. In the last two sections it is proved that, if the matrix which defines the system has only real eigenvalues or is three-dimensional, the time-optimal feedback control defines a regular synthesis and therefore is stable to perturbations. (author)

  18. Linear and non-linear systems identification for adaptive control in mechanical applications vibration suppression

    Science.gov (United States)

    Cazzulani, Gabriele; Resta, Ferruccio; Ripamonti, Francesco

    2012-04-01

    During the last years, more and more mechanical applications saw the introduction of active control strategies. In particular, the need of improving the performances and/or the system health is very often associated to vibration suppression. This goal can be achieved considering both passive and active solutions. In this sense, many active control strategies have been developed, such as the Independent Modal Space Control (IMSC) or the resonant controllers (PPF, IRC, . . .). In all these cases, in order to tune and optimize the control strategy, the knowledge of the system dynamic behaviour is very important and it can be achieved both considering a numerical model of the system or through an experimental identification process. Anyway, dealing with non-linear or time-varying systems, a tool able to online identify the system parameters becomes a key-point for the control logic synthesis. The aim of the present work is the definition of a real-time technique, based on ARMAX models, that estimates the system parameters starting from the measurements of piezoelectric sensors. These parameters are returned to the control logic, that automatically adapts itself to the system dynamics. The problem is numerically investigated considering a carbon-fiber plate model forced through a piezoelectric patch.

  19. Observability of linear control systems on Lie groups

    International Nuclear Information System (INIS)

    Ayala, V.; Hacibekiroglu, A.K.

    1995-01-01

    In this paper, we study the observability problem for a linear control system Σ on a Lie group G. The drift vector field of Σ is an infinitesimal automorphism of G and the control vectors are elements in the Lie algebra of G. We establish algebraic conditions to characterize locally and globally observability for Σ. As in the linear case on R n , these conditions are independent of the control vector. We give an algorithm on the co-tangent bundle of G to calculate the equivalence class of the neutral element. (author). 6 refs

  20. Monitoring and control system of the Saclay electron linear accelerator

    International Nuclear Information System (INIS)

    Lafontaine, Antoine

    1974-01-01

    A description is given of the automatic monitoring and control system of the 60MeV electron linear accelerator of the Centre d'Etudes Nucleaires de Saclay. The paper is mostly concerned with the programmation of the system. However, in a real time device, there is a very close association between computer and electronics, the latter are therefore described in details and make up most of the paper. [fr

  1. A new timing system for the Stanford Linear Collider

    International Nuclear Information System (INIS)

    Paffrath, L.; Bernstein, D.; Kang, H.; Koontz, R.; Leger, G.; Pierce, W.; Ross, M.; Wilmunder, A.

    1985-01-01

    In order to be able to meet the goals of the Stanford Linear Collider, a much more precise timing system had to be implemented. This paper describes the specification and design of this system, and the results obtained from its use on 1/3 of the SLAC linac. The functions of various elements are described, and a programmable delay unit (PDU) is described in detail

  2. Hyperchaotic encryption based on multi-scroll piecewise linear Systems

    Czech Academy of Sciences Publication Activity Database

    García-Martínez, M.; Ontanon-García, L.J.; Campos-Cantón, E.; Čelikovský, Sergej

    2015-01-01

    Roč. 270, č. 1 (2015), s. 413-424 ISSN 0096-3003 R&D Projects: GA ČR GA13-20433S Institutional support: RVO:67985556 Keywords : Hyperchaotic encryption * Piecewise linear systems * Stream cipher * Pseudo-random bit generator * Chaos theory * Multi-scrollattractors Subject RIV: BC - Control Systems Theory Impact factor: 1.345, year: 2015 http://library.utia.cas.cz/separaty/2015/TR/celikovsky-0446895.pdf

  3. Global Linear Representations of Nonlinear Systems and the Adjoint Map

    OpenAIRE

    Banks, S.P.

    1988-01-01

    In this paper we shall study the global linearization of nonlinear systems on a manifold by two methods. The first consists of an expansion of the vector field in the space of square integrable vector fields. In the second method we use the adjoint representation of the Lie algebra vector fields to obtain an infinite-dimensional matrix representation of the system. A connection between the two approaches will be developed.

  4. Comments on new iterative methods for solving linear systems

    Directory of Open Access Journals (Sweden)

    Wang Ke

    2017-06-01

    Full Text Available Some new iterative methods were presented by Du, Zheng and Wang for solving linear systems in [3], where it is shown that the new methods, comparing to the classical Jacobi or Gauss-Seidel method, can be applied to more systems and have faster convergence. This note shows that their methods are suitable for more matrices than positive matrices which the authors suggested through further analysis and numerical examples.

  5. A representation theorem for linear discrete-space systems

    Directory of Open Access Journals (Sweden)

    Sandberg Irwin W.

    1998-01-01

    Full Text Available The cornerstone of the theory of discrete-time single-input single-output linear systems is the idea that every such system has an input–output map H that can be represented by a convolution or the familiar generalization of a convolution. This thinking involves an oversight which is corrected in this note by adding an additional term to the representation.

  6. A Sparse Approximate Inverse Preconditioner for Nonsymmetric Linear Systems

    Czech Academy of Sciences Publication Activity Database

    Benzi, M.; Tůma, Miroslav

    1998-01-01

    Roč. 19, č. 3 (1998), s. 968-994 ISSN 1064-8275 R&D Projects: GA ČR GA201/93/0067; GA AV ČR IAA230401 Keywords : large sparse systems * interative methods * preconditioning * approximate inverse * sparse linear systems * sparse matrices * incomplete factorizations * conjugate gradient -type methods Subject RIV: BA - General Mathematics Impact factor: 1.378, year: 1998

  7. Design and performance of the Stanford Linear Collider Control System

    International Nuclear Information System (INIS)

    Melen, R.E.

    1984-10-01

    The success of the Stanford Linear Collider (SLC) will be dependent upon the implementation of a very large advanced computer-based instrumentation and control system. This paper describes the architectural design of this system as well as a critique of its performance. This critique is based on experience obtained from its use in the control and monitoring of 1/3 of the SLAC linac and in support of an expensive experimental machine physics experimental program. 11 references, 3 figures

  8. 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.

  9. Universal Linear Precoding for NBI-Proof Widely Linear Equalization in MC Systems

    Directory of Open Access Journals (Sweden)

    Donatella Darsena

    2007-09-01

    Full Text Available In multicarrier (MC systems, transmitter redundancy, which is introduced by means of finite-impulse response (FIR linear precoders, allows for perfect or zero-forcing (ZF equalization of FIR channels (in the absence of noise. Recently, it has been shown that the noncircular or improper nature of some symbol constellations offers an intrinsic source of redundancy, which can be exploited to design efficient FIR widely-linear (WL receiving structures for MC systems operating in the presence of narrowband interference (NBI. With regard to both cyclic-prefixed and zero-padded transmission techniques, it is shown in this paper that, with appropriately designed precoders, it is possible to synthesize in both cases WL-ZF universal equalizers, which guarantee perfect symbol recovery for any FIR channel. Furthermore, it is theoretically shown that the intrinsic redundancy of the improper symbol sequence also enables WL-ZF equalization, based on the minimum mean output-energy criterion, with improved NBI suppression capabilities. Finally, results of numerical simulations are presented, which assess the merits of the proposed precoding designs and validate the theoretical analysis carried out.

  10. Singularities in FLRW spacetimes

    Science.gov (United States)

    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.

  11. Self-Tuning Control of Linear Systems Followed by Deadzones

    Directory of Open Access Journals (Sweden)

    K. Kazlauskas

    2014-02-01

    Full Text Available The aim of the present paper is to increase the efficiency of self-tuning generalized minimum variance (GMV control of linear time-invariant (LTI systems followed by deadzone nonlinearities. An approach, based on reordering of observations to be processed for the reconstruction of an unknown internal signal that acts between LTI system and a static nonlinear block of the closed-loop Wiener system, has been developed. The results of GMV self-tuning control of the second order LTI system with an ordinary deadzone are given.

  12. Algorithmic Approach to Abstracting Linear Systems by Timed Automata

    DEFF Research Database (Denmark)

    Sloth, Christoffer; Wisniewski, Rafael

    2011-01-01

    This paper proposes an LMI-based algorithm for abstracting dynamical systems by timed automata, which enables automatic formal verification of linear systems. The proposed abstraction is based on partitioning the state space of the system using positive invariant sets, generated by Lyapunov...... functions. This partitioning ensures that the vector field of the dynamical system is transversal to all facets of the cells, which induces some desirable properties of the abstraction. The algorithm is based on identifying intersections of level sets of quadratic Lyapunov functions, and determining...

  13. Fundamentals of linear systems for physical scientists and engineers

    CERN Document Server

    Puri, N N

    2009-01-01

    Thanks to the advent of inexpensive computing, it is possible to analyze, compute, and develop results that were unthinkable in the '60s. Control systems, telecommunications, robotics, speech, vision, and digital signal processing are but a few examples of computing applications. While there are many excellent resources available that focus on one or two topics, few books cover most of the mathematical techniques required for a broader range of applications. Fundamentals of Linear Systems for Physical Scientists and Engineers is such a resource. The book draws from diverse areas of engineering and the physical sciences to cover the fundamentals of linear systems. Assuming no prior knowledge of complex mathematics on the part of the reader, the author uses his nearly 50 years of teaching experience to address all of the necessary mathematical techniques. Original proofs, hundreds of examples, and proven theorems illustrate and clarify the material. An extensive table provides Lyapunov functions for differentia...

  14. Computer Based Dose Control System on Linear Accelerator

    International Nuclear Information System (INIS)

    Taxwim; Djoko-SP; Widi-Setiawan; Agus-Budi Wiyatna

    2000-01-01

    The accelerator technology has been used for radio therapy. DokterKaryadi Hospital in Semarang use electron or X-ray linear accelerator (Linac)for cancer therapy. One of the control parameter of linear accelerator isdose rate. It is particle current or amount of photon rate to the target. Thecontrol of dose rate in linac have been done by adjusting repetition rate ofanode pulse train of electron source. Presently the control is stillproportional control. To enhance the quality of the control result (minimalstationer error, velocity and stability), the dose control system has beendesigned by using the PID (Proportional Integral Differential) controlalgorithm and the derivation of transfer function of control object.Implementation of PID algorithm control system is done by giving an input ofdose error (the different between output dose and dose rate set point). Theoutput of control system is used for correction of repetition rate set pointfrom pulse train of electron source anode. (author)

  15. Linear and nonlinear dynamic systems in financial time series prediction

    Directory of Open Access Journals (Sweden)

    Salim Lahmiri

    2012-10-01

    Full Text Available Autoregressive moving average (ARMA process and dynamic neural networks namely the nonlinear autoregressive moving average with exogenous inputs (NARX are compared by evaluating their ability to predict financial time series; for instance the S&P500 returns. Two classes of ARMA are considered. The first one is the standard ARMA model which is a linear static system. The second one uses Kalman filter (KF to estimate and predict ARMA coefficients. This model is a linear dynamic system. The forecasting ability of each system is evaluated by means of mean absolute error (MAE and mean absolute deviation (MAD statistics. Simulation results indicate that the ARMA-KF system performs better than the standard ARMA alone. Thus, introducing dynamics into the ARMA process improves the forecasting accuracy. In addition, the ARMA-KF outperformed the NARX. This result may suggest that the linear component found in the S&P500 return series is more dominant than the nonlinear part. In sum, we conclude that introducing dynamics into the ARMA process provides an effective system for S&P500 time series prediction.

  16. A parallel solver for huge dense linear systems

    Science.gov (United States)

    Badia, J. M.; Movilla, J. L.; Climente, J. I.; Castillo, M.; Marqués, M.; Mayo, R.; Quintana-Ortí, E. S.; Planelles, J.

    2011-11-01

    HDSS (Huge Dense Linear System Solver) is a Fortran Application Programming Interface (API) to facilitate the parallel solution of very large dense systems to scientists and engineers. The API makes use of parallelism to yield an efficient solution of the systems on a wide range of parallel platforms, from clusters of processors to massively parallel multiprocessors. It exploits out-of-core strategies to leverage the secondary memory in order to solve huge linear systems O(100.000). The API is based on the parallel linear algebra library PLAPACK, and on its Out-Of-Core (OOC) extension POOCLAPACK. Both PLAPACK and POOCLAPACK use the Message Passing Interface (MPI) as the communication layer and BLAS to perform the local matrix operations. The API provides a friendly interface to the users, hiding almost all the technical aspects related to the parallel execution of the code and the use of the secondary memory to solve the systems. In particular, the API can automatically select the best way to store and solve the systems, depending of the dimension of the system, the number of processes and the main memory of the platform. Experimental results on several parallel platforms report high performance, reaching more than 1 TFLOP with 64 cores to solve a system with more than 200 000 equations and more than 10 000 right-hand side vectors. New version program summaryProgram title: Huge Dense System Solver (HDSS) Catalogue identifier: AEHU_v1_1 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEHU_v1_1.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 87 062 No. of bytes in distributed program, including test data, etc.: 1 069 110 Distribution format: tar.gz Programming language: Fortran90, C Computer: Parallel architectures: multiprocessors, computer clusters Operating system

  17. Galerkin projection methods for solving multiple related linear systems

    Energy Technology Data Exchange (ETDEWEB)

    Chan, T.F.; Ng, M.; Wan, W.L.

    1996-12-31

    We consider using Galerkin projection methods for solving multiple related linear systems A{sup (i)}x{sup (i)} = b{sup (i)} for 1 {le} i {le} s, where A{sup (i)} and b{sup (i)} are different in general. We start with the special case where A{sup (i)} = A and A is symmetric positive definite. The method generates a Krylov subspace from a set of direction vectors obtained by solving one of the systems, called the seed system, by the CG method and then projects the residuals of other systems orthogonally onto the generated Krylov subspace to get the approximate solutions. The whole process is repeated with another unsolved system as a seed until all the systems are solved. We observe in practice a super-convergence behaviour of the CG process of the seed system when compared with the usual CG process. We also observe that only a small number of restarts is required to solve all the systems if the right-hand sides are close to each other. These two features together make the method particularly effective. In this talk, we give theoretical proof to justify these observations. Furthermore, we combine the advantages of this method and the block CG method and propose a block extension of this single seed method. The above procedure can actually be modified for solving multiple linear systems A{sup (i)}x{sup (i)} = b{sup (i)}, where A{sup (i)} are now different. We can also extend the previous analytical results to this more general case. Applications of this method to multiple related linear systems arising from image restoration and recursive least squares computations are considered as examples.

  18. An extended GS method for dense linear systems

    Science.gov (United States)

    Niki, Hiroshi; Kohno, Toshiyuki; Abe, Kuniyoshi

    2009-09-01

    Davey and Rosindale [K. Davey, I. Rosindale, An iterative solution scheme for systems of boundary element equations, Internat. J. Numer. Methods Engrg. 37 (1994) 1399-1411] derived the GSOR method, which uses an upper triangular matrix [Omega] in order to solve dense linear systems. By applying functional analysis, the authors presented an expression for the optimum [Omega]. Moreover, Davey and Bounds [K. Davey, S. Bounds, A generalized SOR method for dense linear systems of boundary element equations, SIAM J. Comput. 19 (1998) 953-967] also introduced further interesting results. In this note, we employ a matrix analysis approach to investigate these schemes, and derive theorems that compare these schemes with existing preconditioners for dense linear systems. We show that the convergence rate of the Gauss-Seidel method with preconditioner PG is superior to that of the GSOR method. Moreover, we define some splittings associated with the iterative schemes. Some numerical examples are reported to confirm the theoretical analysis. We show that the EGS method with preconditioner produces an extremely small spectral radius in comparison with the other schemes considered.

  19. Essential uncontrollability of discrete linear, time-invariant, dynamical systems

    Science.gov (United States)

    Cliff, E. M.

    1975-01-01

    The concept of a 'best approximating m-dimensional subspace' for a given set of vectors in n-dimensional whole space is introduced. Such a subspace is easily described in terms of the eigenvectors of an associated Gram matrix. This technique is used to approximate an achievable set for a discrete linear time-invariant dynamical system. This approximation characterizes the part of the state space that may be reached using modest levels of control. If the achievable set can be closely approximated by a proper subspace of the whole space then the system is 'essentially uncontrollable'. The notion finds application in studies of failure-tolerant systems, and in decoupling.

  20. The new control system of the Saclay linear accelerator

    International Nuclear Information System (INIS)

    Gournay, J.F.; Gourcy, G.; Garreau, F.; Giraud, A.; Rouault, J.

    1985-05-01

    A new control system for the Safety Linear Accelerator is now being designed. The computer control architecture is based on 3 dedicated VME crates with MC68000 micro-processors: one crate with a disk-based operating system will run the high level application programs and the data base management facilities, another one will manage the man-machine communications and the third one will interface the system to the linac equipments. Communications between the VME microcomputers will be done through 16 bit parallel links. The software is modular and organized in specific layers, the data base is fully distributed. About 90% of the code is written in Fortran

  1. Kalman filtering for time-delayed linear systems

    Institute of Scientific and Technical Information of China (English)

    LU Xiao; WANG Wei

    2006-01-01

    This paper is to study the linear minimum variance estimation for discrete- time systems. A simple approach to the problem is presented by developing re-organized innovation analysis for the systems with instantaneous and double time-delayed measurements. It is shown that the derived estimator involves solving three different standard Kalman filtering with the same dimension as the original system. The obtained results form the basis for solving some complicated problems such as H∞ fixed-lag smoothing, preview control, H∞ filtering and control with time delays.

  2. Fundamental Matrix for a Class of Point Delay Linear Systems

    International Nuclear Information System (INIS)

    Sen, M. de la; Alastruey, C. F.

    1998-01-01

    It is difficult to establish explicit analytic forms for fundamental matrices of delayed linear systems. In this paper, an explicit form of exponential type is given for such a matrix in the case of punctual delays. The existence of real and complex fundamental matrices, for the case of real parameterizations of the differential system, is studied and discussed. Some additional commutativity properties involving the matrices parameters and the fundamental matrices as well as explicit expressions for the solution of the delayed differential system are also given. (Author)

  3. Control of Non-linear Marine Cooling System

    DEFF Research Database (Denmark)

    Hansen, Michael; Stoustrup, Jakob; Bendtsen, Jan Dimon

    2011-01-01

    We consider the problem of designing control laws for a marine cooling system used for cooling the main engine and auxiliary components aboard several classes of container vessels. We focus on achieving simple set point control for the system and do not consider compensation of the non-linearitie......-linearities, closed circuit flow dynamics or transport delays that are present in the system. Control laws are therefore designed using classical control theory and the performance of the design is illustrated through two simulation examples....

  4. Coherent versus Measurement Feedback: Linear Systems Theory for Quantum Information

    Directory of Open Access Journals (Sweden)

    Naoki Yamamoto

    2014-11-01

    Full Text Available To control a quantum system via feedback, we generally have two options in choosing a control scheme. One is the coherent feedback, which feeds the output field of the system, through a fully quantum device, back to manipulate the system without involving any measurement process. The other one is measurement-based feedback, which measures the output field and performs a real-time manipulation on the system based on the measurement results. Both schemes have advantages and disadvantages, depending on the system and the control goal; hence, their comparison in several situations is important. This paper considers a general open linear quantum system with the following specific control goals: backaction evasion, generation of a quantum nondemolished variable, and generation of a decoherence-free subsystem, all of which have important roles in quantum information science. Some no-go theorems are proven, clarifying that those goals cannot be achieved by any measurement-based feedback control. On the other hand, it is shown that, for each control goal there exists a coherent feedback controller accomplishing the task. The key idea to obtain all the results is system theoretic characterizations of the above three notions in terms of controllability and observability properties or transfer functions of linear systems, which are consistent with their standard definitions.

  5. Relative Error Model Reduction via Time-Weighted Balanced Stochastic Singular Perturbation

    DEFF Research Database (Denmark)

    Tahavori, Maryamsadat; Shaker, Hamid Reza

    2012-01-01

    A new mixed method for relative error model reduction of linear time invariant (LTI) systems is proposed in this paper. This order reduction technique is mainly based upon time-weighted balanced stochastic model reduction method and singular perturbation model reduction technique. Compared...... by using the concept and properties of the reciprocal systems. The results are further illustrated by two practical numerical examples: a model of CD player and a model of the atmospheric storm track....

  6. Optimal linear precoding for indoor visible light communication system

    KAUST Repository

    Sifaou, Houssem

    2017-07-31

    Visible light communication (VLC) is an emerging technique that uses light-emitting diodes (LED) to combine communication and illumination. It is considered as a promising scheme for indoor wireless communication that can be deployed at reduced costs while offering high data rate performance. In this paper, we focus on the design of the downlink of a multi-user VLC system. Inherent to multi-user systems is the interference caused by the broadcast nature of the medium. Linear precoding based schemes are among the most popular solutions that have recently been proposed to mitigate inter-user interference. This paper focuses on the design of the optimal linear precoding scheme that solves the max-min signal-to-interference-plus-noise ratio (SINR) problem. The performance of the proposed precoding scheme is studied under different working conditions and compared with the classical zero-forcing precoding. Simulations have been provided to illustrate the high gain of the proposed scheme.

  7. Solution of the fully fuzzy linear systems using iterative techniques

    International Nuclear Information System (INIS)

    Dehghan, Mehdi; Hashemi, Behnam; Ghatee, Mehdi

    2007-01-01

    This paper mainly intends to discuss the iterative solution of fully fuzzy linear systems which we call FFLS. We employ Dubois and Prade's approximate arithmetic operators on LR fuzzy numbers for finding a positive fuzzy vector x-tilde which satisfies A-tildex-tilde=b, where A-tilde and b-tilde are a fuzzy matrix and a fuzzy vector, respectively. Please note that the positivity assumption is not so restrictive in applied problems. We transform FFLS and propose iterative techniques such as Richardson, Jacobi, Jacobi overrelaxation (JOR), Gauss-Seidel, successive overrelaxation (SOR), accelerated overrelaxation (AOR), symmetric and unsymmetric SOR (SSOR and USSOR) and extrapolated modified Aitken (EMA) for solving FFLS. In addition, the methods of Newton, quasi-Newton and conjugate gradient are proposed from nonlinear programming for solving a fully fuzzy linear system. Various numerical examples are also given to show the efficiency of the proposed schemes

  8. Solution methods for large systems of linear equations in BACCHUS

    International Nuclear Information System (INIS)

    Homann, C.; Dorr, B.

    1993-05-01

    The computer programme BACCHUS is used to describe steady state and transient thermal-hydraulic behaviour of a coolant in a fuel element with intact geometry in a fast breeder reactor. In such computer programmes generally large systems of linear equations with sparse matrices of coefficients, resulting from discretization of coolant conservation equations, must be solved thousands of times giving rise to large demands of main storage and CPU time. Direct and iterative solution methods of the systems of linear equations, available in BACCHUS, are described, giving theoretical details and experience with their use in the programme. Besides use of a method of lines, a Runge-Kutta-method, for solution of the partial differential equation is outlined. (orig.) [de

  9. Nonautonomous linear Hamiltonian systems oscillation, spectral theory and control

    CERN Document Server

    Johnson, Russell; Novo, Sylvia; Núñez, Carmen; Fabbri, Roberta

    2016-01-01

    This monograph contains an in-depth analysis of the dynamics given by a linear Hamiltonian system of general dimension with nonautonomous bounded and uniformly continuous coefficients, without other initial assumptions on time-recurrence. Particular attention is given to the oscillation properties of the solutions as well as to a spectral theory appropriate for such systems. The book contains extensions of results which are well known when the coefficients are autonomous or periodic, as well as in the nonautonomous two-dimensional case. However, a substantial part of the theory presented here is new even in those much simpler situations. The authors make systematic use of basic facts concerning Lagrange planes and symplectic matrices, and apply some fundamental methods of topological dynamics and ergodic theory. Among the tools used in the analysis, which include Lyapunov exponents, Weyl matrices, exponential dichotomy, and weak disconjugacy, a fundamental role is played by the rotation number for linear Hami...

  10. Optimal approximation of linear systems by artificial immune response

    Institute of Scientific and Technical Information of China (English)

    2006-01-01

    This paper puts forward a novel artificial immune response algorithm for optimal approximation of linear systems. A quaternion model of artificial immune response is proposed for engineering computing. The model abstracts four elements, namely, antigen, antibody, reaction rules among antibodies, and driving algorithm describing how the rules are applied to antibodies, to simulate the process of immune response. Some reaction rules including clonal selection rules, immunological memory rules and immune regulation rules are introduced. Using the theorem of Markov chain, it is proofed that the new model is convergent. The experimental study on the optimal approximation of a stable linear system and an unstable one show that the approximate models searched by the new model have better performance indices than those obtained by some existing algorithms including the differential evolution algorithm and the multi-agent genetic algorithm.

  11. Large linear magnetoresistivity in strongly inhomogeneous planar and layered systems

    International Nuclear Information System (INIS)

    Bulgadaev, S.A.; Kusmartsev, F.V.

    2005-01-01

    Explicit expressions for magnetoresistance R of planar and layered strongly inhomogeneous two-phase systems are obtained, using exact dual transformation, connecting effective conductivities of in-plane isotropic two-phase systems with and without magnetic field. These expressions allow to describe the magnetoresistance of various inhomogeneous media at arbitrary concentrations x and magnetic fields H. All expressions show large linear magnetoresistance effect with different dependencies on the phase concentrations. The corresponding plots of the x- and H-dependencies of R(x,H) are represented for various values, respectively, of magnetic field and concentrations at some values of inhomogeneity parameter. The obtained results show a remarkable similarity with the existing experimental data on linear magnetoresistance in silver chalcogenides Ag 2+δ Se. A possible physical explanation of this similarity is proposed. It is shown that the random, stripe type, structures of inhomogeneities are the most suitable for a fabrication of magnetic sensors and a storage of information at room temperatures

  12. 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...

  13. Supersymmetry in singular spaces

    NARCIS (Netherlands)

    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

  14. Singularities in FLRW Spacetimes

    NARCIS (Netherlands)

    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

  15. 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.

  16. Maximization of energy in the output of a linear system

    International Nuclear Information System (INIS)

    Dudley, D.G.

    1976-01-01

    A time-limited signal which, when passed through a linear system, maximizes the total output energy is considered. Previous work has shown that the solution is given by the eigenfunction associated with the maximum eigenvalue in a Hilbert-Schmidt integral equation. Analytical results are available for the case where the transfer function is a low-pass filter. This work is extended by obtaining a numerical solution to the integral equation which allows results for reasonably general transfer functions

  17. Linear Quantum Systems: Non-Classical States and Robust Stability

    Science.gov (United States)

    2016-06-29

    modulation and entanglement in a compound gradient echo memory, Physical Review A 93(2) 023809 2016. We present a theoretical model for a Kerr...Carvalho, M. Hedges and M R James, Analysis of the operation of gradient echo memories using a quantum input-output model, New Journal of Physics , 15...new structured uncertainty methods that ensure robust stability of quantum systems based on nominal linear models, and (v) physical realizability

  18. Dynamic logic architecture based on piecewise-linear systems

    International Nuclear Information System (INIS)

    Peng Haipeng; Liu Fei; Li Lixiang; Yang Yixian; Wang Xue

    2010-01-01

    This Letter explores piecewise-linear systems to construct dynamic logic architecture. The proposed schemes can discriminate the two input signals and obtain 16 kinds of logic operations by different combinations of parameters and conditions for determining the output. Each logic cell performs more flexibly, that makes it possible to achieve complex logic operations more simply and construct computing architecture with less logic cells. We also analyze the various performances of our schemes under different conditions and the characteristics of these schemes.

  19. CHEBYSHEV ACCELERATION TECHNIQUE FOR SOLVING FUZZY LINEAR SYSTEM

    Directory of Open Access Journals (Sweden)

    S.H. Nasseri

    2011-07-01

    Full Text Available In this paper, Chebyshev acceleration technique is used to solve the fuzzy linear system (FLS. This method is discussed in details and followed by summary of some other acceleration techniques. Moreover, we show that in some situations that the methods such as Jacobi, Gauss-Sidel, SOR and conjugate gradient is divergent, our proposed method is applicable and the acquired results are illustrated by some numerical examples.

  20. CHEBYSHEV ACCELERATION TECHNIQUE FOR SOLVING FUZZY LINEAR SYSTEM

    Directory of Open Access Journals (Sweden)

    S.H. Nasseri

    2009-10-01

    Full Text Available In this paper, Chebyshev acceleration technique is used to solve the fuzzy linear system (FLS. This method is discussed in details and followed by summary of some other acceleration techniques. Moreover, we show that in some situations that the methods such as Jacobi, Gauss-Sidel, SOR and conjugate gradient is divergent, our proposed method is applicable and the acquired results are illustrated by some numerical examples.

  1. Efficient Preconditioning of Sequences of Nonsymmetric Linear Systems

    Czech Academy of Sciences Publication Activity Database

    Duintjer Tebbens, Jurjen; Tůma, Miroslav

    2007-01-01

    Roč. 29, č. 5 (2007), s. 1918-1941 ISSN 1064-8275 R&D Projects: GA AV ČR 1ET400300415; GA AV ČR KJB100300703 Institutional research plan: CEZ:AV0Z10300504 Keywords : preconditioned iterative methods * sparse matrices * sequences of linear algebraic systems * incomplete factorizations * factorization updates * Gauss–Jordan transformations * minimum spanning tree Subject RIV: BA - General Mathematics Impact factor: 1.784, year: 2007

  2. AZTEC: A parallel iterative package for the solving linear systems

    Energy Technology Data Exchange (ETDEWEB)

    Hutchinson, S.A.; Shadid, J.N.; Tuminaro, R.S. [Sandia National Labs., Albuquerque, NM (United States)

    1996-12-31

    We describe a parallel linear system package, AZTEC. The package incorporates a number of parallel iterative methods (e.g. GMRES, biCGSTAB, CGS, TFQMR) and preconditioners (e.g. Jacobi, Gauss-Seidel, polynomial, domain decomposition with LU or ILU within subdomains). Additionally, AZTEC allows for the reuse of previous preconditioning factorizations within Newton schemes for nonlinear methods. Currently, a number of different users are using this package to solve a variety of PDE applications.

  3. 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)

  4. Feedback Linearization Controller for a Wind Energy Power System

    Directory of Open Access Journals (Sweden)

    Muthana Alrifai

    2016-09-01

    Full Text Available This paper deals with the control of a doubly-fed induction generator (DFIG-based variable speed wind turbine power system. A system of eight ordinary differential equations is used to model the wind energy conversion system. The generator has a wound rotor type with back-to-back three-phase power converter bridges between its rotor and the grid; it is modeled using the direct-quadrature rotating reference frame with aligned stator flux. An input-state feedback linearization controller is proposed for the wind energy power system. The controller guarantees that the states of the system track the desired states. Simulation results are presented to validate the proposed control scheme. Moreover, further simulation results are shown to investigate the robustness of the proposed control scheme to changes in some of the parameters of the system.

  5. Stochastic Reformulations of Linear Systems: Algorithms and Convergence Theory

    KAUST Repository

    Richtarik, Peter; Taká č, Martin

    2017-01-01

    We develop a family of reformulations of an arbitrary consistent linear system into a stochastic problem. The reformulations are governed by two user-defined parameters: a positive definite matrix defining a norm, and an arbitrary discrete or continuous distribution over random matrices. Our reformulation has several equivalent interpretations, allowing for researchers from various communities to leverage their domain specific insights. In particular, our reformulation can be equivalently seen as a stochastic optimization problem, stochastic linear system, stochastic fixed point problem and a probabilistic intersection problem. We prove sufficient, and necessary and sufficient conditions for the reformulation to be exact. Further, we propose and analyze three stochastic algorithms for solving the reformulated problem---basic, parallel and accelerated methods---with global linear convergence rates. The rates can be interpreted as condition numbers of a matrix which depends on the system matrix and on the reformulation parameters. This gives rise to a new phenomenon which we call stochastic preconditioning, and which refers to the problem of finding parameters (matrix and distribution) leading to a sufficiently small condition number. Our basic method can be equivalently interpreted as stochastic gradient descent, stochastic Newton method, stochastic proximal point method, stochastic fixed point method, and stochastic projection method, with fixed stepsize (relaxation parameter), applied to the reformulations.

  6. Linear circuits, systems and signal processing: theory and application

    International Nuclear Information System (INIS)

    Byrnes, C.I.; Saeks, R.E.; Martin, C.F.

    1988-01-01

    In part because of its universal role as a first approximation of more complicated behaviour and in part because of the depth and breadth of its principle paradigms, the study of linear systems continues to play a central role in control theory and its applications. Enhancing more traditional applications to aerospace and electronics, application areas such as econometrics, finance, and speech and signal processing have contributed to a renaissance in areas such as realization theory and classical automatic feedback control. Thus, the last few years have witnessed a remarkable research effort expended in understanding both new algorithms and new paradigms for modeling and realization of linear processes and in the analysis and design of robust control strategies. The papers in this volume reflect these trends in both the theory and applications of linear systems and were selected from the invited and contributed papers presented at the 8th International Symposium on the Mathematical Theory of Networks and Systems held in Phoenix on June 15-19, 1987

  7. Stochastic Reformulations of Linear Systems: Algorithms and Convergence Theory

    KAUST Repository

    Richtarik, Peter

    2017-06-04

    We develop a family of reformulations of an arbitrary consistent linear system into a stochastic problem. The reformulations are governed by two user-defined parameters: a positive definite matrix defining a norm, and an arbitrary discrete or continuous distribution over random matrices. Our reformulation has several equivalent interpretations, allowing for researchers from various communities to leverage their domain specific insights. In particular, our reformulation can be equivalently seen as a stochastic optimization problem, stochastic linear system, stochastic fixed point problem and a probabilistic intersection problem. We prove sufficient, and necessary and sufficient conditions for the reformulation to be exact. Further, we propose and analyze three stochastic algorithms for solving the reformulated problem---basic, parallel and accelerated methods---with global linear convergence rates. The rates can be interpreted as condition numbers of a matrix which depends on the system matrix and on the reformulation parameters. This gives rise to a new phenomenon which we call stochastic preconditioning, and which refers to the problem of finding parameters (matrix and distribution) leading to a sufficiently small condition number. Our basic method can be equivalently interpreted as stochastic gradient descent, stochastic Newton method, stochastic proximal point method, stochastic fixed point method, and stochastic projection method, with fixed stepsize (relaxation parameter), applied to the reformulations.

  8. Identification of Nonlinear Dynamic Systems Possessing Some Non-linearities

    Directory of Open Access Journals (Sweden)

    Y. N. Pavlov

    2015-01-01

    Full Text Available The subject of this work is the problem of identification of nonlinear dynamic systems based on the experimental data obtained by applying test signals to the system. The goal is to determinate coefficients of differential equations of systems by experimental frequency hodographs and separate similar, but different, in essence, forces: dissipative forces with the square of the first derivative in the motion equations and dissipative force from the action of dry friction. There was a proposal to use the harmonic linearization method to approximate each of the nonlinearity of "quadratic friction" and "dry friction" by linear friction with the appropriate harmonic linearization coefficient.Assume that a frequency transfer function of the identified system has a known form. Assume as well that there are disturbances while obtaining frequency characteristics of the realworld system. As a result, the points of experimentally obtained hodograph move randomly. Searching for solution of the identification problem was in the hodograph class, specified by the system model, which has the form of the frequency transfer function the same as the form of the frequency transfer function of the system identified. Minimizing a proximity criterion (measure of the experimentally obtained system hodograph and the system hodograph model for all the experimental points described and previously published by one of the authors allowed searching for the unknown coefficients of the frequenc ransfer function of the system model. The paper shows the possibility to identify a nonlinear dynamic system with multiple nonlinearities, obtained on the experimental samples of the frequency system hodograph. The proposed algorithm allows to select the nonlinearity of the type "quadratic friction" and "dry friction", i.e. also in the case where the nonlinearity is dependent on the same dynamic parameter, in particular, on the derivative of the system output value. For the dynamic

  9. 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

  10. 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...

  11. Linear filtering of systems with memory and application to finance

    Directory of Open Access Journals (Sweden)

    2006-01-01

    Full Text Available We study the linear filtering problem for systems driven by continuous Gaussian processes V ( 1 and V ( 2 with memory described by two parameters. The processes V ( j have the virtue that they possess stationary increments and simple semimartingale representations simultaneously. They allow for straightforward parameter estimations. After giving the semimartingale representations of V ( j by innovation theory, we derive Kalman-Bucy-type filtering equations for the systems. We apply the result to the optimal portfolio problem for an investor with partial observations. We illustrate the tractability of the filtering algorithm by numerical implementations.

  12. 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

  13. Parametric Linear Hybrid Automata for Complex Environmental Systems Modeling

    Directory of Open Access Journals (Sweden)

    Samar Hayat Khan Tareen

    2015-07-01

    Full Text Available Environmental systems, whether they be weather patterns or predator-prey relationships, are dependent on a number of different variables, each directly or indirectly affecting the system at large. Since not all of these factors are known, these systems take on non-linear dynamics, making it difficult to accurately predict meaningful behavioral trends far into the future. However, such dynamics do not warrant complete ignorance of different efforts to understand and model close approximations of these systems. Towards this end, we have applied a logical modeling approach to model and analyze the behavioral trends and systematic trajectories that these systems exhibit without delving into their quantification. This approach, formalized by René Thomas for discrete logical modeling of Biological Regulatory Networks (BRNs and further extended in our previous studies as parametric biological linear hybrid automata (Bio-LHA, has been previously employed for the analyses of different molecular regulatory interactions occurring across various cells and microbial species. As relationships between different interacting components of a system can be simplified as positive or negative influences, we can employ the Bio-LHA framework to represent different components of the environmental system as positive or negative feedbacks. In the present study, we highlight the benefits of hybrid (discrete/continuous modeling which lead to refinements among the fore-casted behaviors in order to find out which ones are actually possible. We have taken two case studies: an interaction of three microbial species in a freshwater pond, and a more complex atmospheric system, to show the applications of the Bio-LHA methodology for the timed hybrid modeling of environmental systems. Results show that the approach using the Bio-LHA is a viable method for behavioral modeling of complex environmental systems by finding timing constraints while keeping the complexity of the model

  14. 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.

  15. 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.

  16. 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.

  17. 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.

  18. Development of a linear induction motor based artificial muscle system.

    Science.gov (United States)

    Gruber, A; Arguello, E; Silva, R

    2013-01-01

    We present the design of a linear induction motor based on electromagnetic interactions. The engine is capable of producing a linear movement from electricity. The design consists of stators arranged in parallel, which produce a magnetic field sufficient to displace a plunger along its axial axis. Furthermore, the winding has a shell and cap of ferromagnetic material that amplifies the magnetic field. This produces a force along the length of the motor that is similar to that of skeletal muscle. In principle, the objective is to use the engine in the development of an artificial muscle system for prosthetic applications, but it could have multiple applications, not only in the medical field, but in other industries.

  19. Demultiplexing of photonic temporal modes by a linear system

    Science.gov (United States)

    Xu, Shuang; Shen, H. Z.; Yi, X. X.

    2018-03-01

    Temporally and spatially overlapping but field-orthogonal photonic temporal modes (TMs) that intrinsically span a high-dimensional Hilbert space are recently suggested as a promising means of encoding information on photons. Presently, the realization of photonic TM technology, particularly to retrieve the information it carries, i.e., demultiplexing of photonic TMs, is mostly dependent on nonlinear medium and frequency conversion. Meanwhile, its miniaturization, simplification, and optimization remain the focus of research. In this paper, we propose a scheme of TM demultiplexing using linear systems consisting of resonators with linear couplings. Specifically, we examine a unidirectional array of identical resonators with short environment correlations. For both situations with and without tunable couplers, propagation formulas are derived to demonstrate photonic TM demultiplexing capabilities. The proposed scheme, being entirely feasible with current technologies, might find potential applications in quantum information processing.

  20. Linear and Non-Linear Dielectric Response of Periodic Systems from Quantum Monte Carlo

    Science.gov (United States)

    Umari, Paolo

    2006-03-01

    We present a novel approach that allows to calculate the dielectric response of periodic systems in the quantum Monte Carlo formalism. We employ a many-body generalization for the electric enthalpy functional, where the coupling with the field is expressed via the Berry-phase formulation for the macroscopic polarization. A self-consistent local Hamiltonian then determines the ground-state wavefunction, allowing for accurate diffusion quantum Monte Carlo calculations where the polarization's fixed point is estimated from the average on an iterative sequence. The polarization is sampled through forward-walking. This approach has been validated for the case of the polarizability of an isolated hydrogen atom, and then applied to a periodic system. We then calculate the linear susceptibility and second-order hyper-susceptibility of molecular-hydrogen chains whith different bond-length alternations, and assess the quality of nodal surfaces derived from density-functional theory or from Hartree-Fock. The results found are in excellent agreement with the best estimates obtained from the extrapolation of quantum-chemistry calculations.P. Umari, A.J. Williamson, G. Galli, and N. MarzariPhys. Rev. Lett. 95, 207602 (2005).

  1. Linearization Technologies for Broadband Radio-Over-Fiber Transmission Systems

    Directory of Open Access Journals (Sweden)

    Xiupu Zhang

    2014-11-01

    Full Text Available Linearization technologies that can be used for linearizing RoF transmission are reviewed. Three main linearization methods, i.e. electrical analog linearization, optical linearization, and electrical digital linearization are presented and compared. Analog linearization can be achieved using analog predistortion circuits, and can be used for suppression of odd order nonlinear distortion components, such as third and fifth order. Optical linearization includes mixed-polarization, dual-wavelength, optical channelization and the others, implemented in optical domain, to suppress both even and odd order nonlinear distortion components, such as second and third order. Digital predistortion has been a widely used linearization method for RF power amplifiers. However, digital linearization that requires analog to digital converter is severely limited to hundreds of MHz bandwidth. Instead, analog and optical linearization provide broadband linearization with up to tens of GHz. Therefore, for broadband radio over fiber transmission that can be used for future broadband cloud radio access networks, analog and optical linearization are more appropriate than digital linearization. Generally speaking, both analog and optical linearization are able to improve spur-free dynamic range greater than 10 dB over tens of GHz. In order for current digital linearization to be used for broadband radio over fiber transmission, the reduced linearization complexity and increased linearization bandwidth are required. Moreover, some digital linearization methods in which the complexity can be reduced, such as Hammerstein type, may be more promising and require further investigation.

  2. Control of Linear Parameter Varying Systems with Applications

    CERN Document Server

    Mohammadpour, Javad

    2012-01-01

    Control of Linear Parameter Varying Systems with Applications compiles state-of-the-art contributions on novel analytical and computational methods to address system modeling and identification, complexity reduction, performance analysis and control design for time-varying and nonlinear systems in the LPV framework. The book has an interdisciplinary character by emphasizing techniques that can be commonly applied in various engineering fields. It also includes a rich collection of illustrative applications in diverse domains to substantiate the effectiveness of the design methodologies and provide pointers to open research directions. The book is divided into three parts. The first part collects chapters of a more tutorial character on the background of LPV systems modeling and control. The second part gathers chapters devoted to the theoretical advancement of LPV analysis and synthesis methods to cope with the design constraints such as uncertainties and time delay. The third part of the volume showcases con...

  3. The new control system of the Saclay linear accelerator

    International Nuclear Information System (INIS)

    Gournay, J.F.

    1985-10-01

    A new control system for the Saclay Linear Accelerator designed during the two past years is now in operation. The computer control architecture is based on 3 dedicated VME crates: one crate with a disk-based operating system runs the high level application programs and the database management facilities, another one manages the man-machine communications and the third one interfaces the system to the linac equipments. At the present time, communications between the VME micro-computers are done through 16 bit parallel links. The software is modular and organized in specific layers, the database is fully distributed. About 90% of the code is written in Fortran. The present status of the system is discussed and the hardware and software developments are described

  4. Core reset system design for linear induction accelerator

    International Nuclear Information System (INIS)

    Durga Praveen Kumar, D.; Mitra, S.; Sharma, Archana; Nagesh, K.V.; Chakravarthy, D.P.

    2006-01-01

    A repetitive pulsed power system based Linear Induction Accelerator (LIA-200) is being developed at BARC to get an electron beam of 200keV, 5kA, 50ns, 10-100 Hz. Amorphous core is the heart of these accelerators. It serves various functions in different subsystems viz. pulse power modulator, pulse transformer, magnetic switches and induction cavities. One of the factors that make the magnetic components compact is utilization of the total flux swing available in the core. In the present system, magnetic switches, pulse transformers, and induction cavity are designed to avail the full flux swing available in the core. For achieving this objective, flux density in the core has to be kept at the reverse saturation, before the main pulse is applied. The electrical circuit which makes it possible is called the core reset system. In this paper the details of core reset system designed for LIA-200 are described. (author)

  5. Managing focal fields of vector beams with multiple polarization singularities.

    Science.gov (United States)

    Han, Lei; Liu, Sheng; Li, Peng; Zhang, Yi; Cheng, Huachao; Gan, Xuetao; Zhao, Jianlin

    2016-11-10

    We explore the tight focusing behavior of vector beams with multiple polarization singularities, and analyze the influences of the number, position, and topological charge of the singularities on the focal fields. It is found that the ellipticity of the local polarization states at the focal plane could be determined by the spatial distribution of the polarization singularities of the vector beam. When the spatial location and topological charge of singularities have even-fold rotation symmetry, the transverse fields at the focal plane are locally linearly polarized. Otherwise, the polarization state becomes a locally hybrid one. By appropriately arranging the distribution of the polarization singularities in the vector beam, the polarization distributions of the focal fields could be altered while the intensity maintains unchanged.

  6. Fold points and singularity induced bifurcation in inviscid transonic flow

    International Nuclear Information System (INIS)

    Marszalek, Wieslaw

    2012-01-01

    Transonic inviscid flow equation of elliptic–hyperbolic type when written in terms of the velocity components and similarity variable results in a second order nonlinear ODE having several features typical of differential–algebraic equations rather than ODEs. These features include the fold singularities (e.g. folded nodes and saddles, forward and backward impasse points), singularity induced bifurcation behavior and singularity crossing phenomenon. We investigate the above properties and conclude that the quasilinear DAEs of transonic flow have interesting properties that do not occur in other known quasilinear DAEs, for example, in MHD. Several numerical examples are included. -- Highlights: ► A novel analysis of inviscid transonic flow and its similarity solutions. ► Singularity induced bifurcation, singular points of transonic flow. ► Projection method, index of transonic flow DAEs, linearization via matrix pencil.

  7. The cosmological singularity

    CERN Document Server

    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...

  8. Deformations of surface singularities

    CERN Document Server

    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...

  9. Multiscale singularity trees

    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....

  10. Dyslexia singular brain

    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.)

  11. Practical application of equivalent linearization approaches to nonlinear piping systems

    International Nuclear Information System (INIS)

    Park, Y.J.; Hofmayer, C.H.

    1995-01-01

    The use of mechanical energy absorbers as an alternative to conventional hydraulic and mechanical snubbers for piping supports has attracted a wide interest among researchers and practitioners in the nuclear industry. The basic design concept of energy absorbers (EA) is to dissipate the vibration energy of piping systems through nonlinear hysteretic actions of EA exclamation point s under design seismic loads. Therefore, some type of nonlinear analysis needs to be performed in the seismic design of piping systems with EA supports. The equivalent linearization approach (ELA) can be a practical analysis tool for this purpose, particularly when the response approach (RSA) is also incorporated in the analysis formulations. In this paper, the following ELA/RSA methods are presented and compared to each other regarding their practice and numerical accuracy: Response approach using the square root of sum of squares (SRSS) approximation (denoted RS in this paper). Classical ELA based on modal combinations and linear random vibration theory (denoted CELA in this paper). Stochastic ELA based on direct solution of response covariance matrix (denoted SELA in this paper). New algorithms to convert response spectra to the equivalent power spectral density (PSD) functions are presented for both the above CELA and SELA methods. The numerical accuracy of the three EL are studied through a parametric error analysis. Finally, the practicality of the presented analysis is demonstrated in two application examples for piping systems with EA supports

  12. A RECIPE FOR LINEAR COLLIDER FINAL FOCUS SYSTEM DESIGN

    International Nuclear Information System (INIS)

    Seryi, Andrei

    2003-01-01

    The design of Final Focus systems for linear colliders is challenging because of the large demagnifications needed to produce nanometer-sized beams at the interaction point. Simple first- and second-order matrix matching have proven insufficient for this task, and minimization of third- and higher-order aberrations is essential. An appropriate strategy is required for the latter to be successful. A recipe for Final Focus design, and a set of computational tools used to implement this approach, are described herein. An example of the use of this procedure is given

  13. Periodic orbits from Δ-modulation of stable linear systems

    OpenAIRE

    Xia, X.; Zinober, A.

    2004-01-01

    The �-modulated control of a single input, discrete time, linear stable system is investigated. The modulation direction is given by cTx where c �Rn/{0} is a given, otherwise arbitrary, vector. We obtain necessary and sufficient conditions for the existence of periodic points of a finite order. Some concrete results about the existence of a certain order of periodic points are also derived. We also study the relationship between certain polyhedra and the periodicity of the �-modulated orb...

  14. Probing LINEAR Collider Final Focus Systems in SuperKEKB

    CERN Document Server

    Thrane, Paul Conrad Vaagen

    2017-01-01

    A challenge for future linear collider final focus systems is the large chromaticity produced by the final quadrupoles. SuperKEKB will be correcting high levels of chromaticity using the traditional scheme which has been also proposed for the CLIC FFS. We present early simulation results indicating that lowering β*у in the SuperKEKB Low Energy Ring might be possible given on-axis injection and low bunch current, opening the possibility of testing chromaticity correction beyond FFTB level, similar to ILC and approaching that of CLIC. CLIC – Note – 1077

  15. Optimal Robust Fault Detection for Linear Discrete Time Systems

    Directory of Open Access Journals (Sweden)

    Nike Liu

    2008-01-01

    Full Text Available This paper considers robust fault-detection problems for linear discrete time systems. It is shown that the optimal robust detection filters for several well-recognized robust fault-detection problems, such as ℋ−/ℋ∞, ℋ2/ℋ∞, and ℋ∞/ℋ∞ problems, are the same and can be obtained by solving a standard algebraic Riccati equation. Optimal filters are also derived for many other optimization criteria and it is shown that some well-studied and seeming-sensible optimization criteria for fault-detection filter design could lead to (optimal but useless fault-detection filters.

  16. A novel linear switched reluctance motor for railway transportation systems

    International Nuclear Information System (INIS)

    Daldaban, Ferhat; Ustkoyuncu, Nurettin

    2010-01-01

    This paper presents the design and realization of a new linear switched reluctance motor (LSRM) structure, especially suitable for high-speed railway systems. The new model has a double active stator configuration and provides high force for many applications with low cost. The characteristics of the LSRM are obtained by using finite element analysis (FEA) and analytical calculations. The results of the FEA and analytical calculations are presented, and compared with experimental results. In addition, a classical double-sided LSRM (DSLSRM) is modeled with the same specifications of the new motor structure and the results are compared.

  17. Novel Approach to Linear Accelerator Superconducting Magnet System

    International Nuclear Information System (INIS)

    Kashikhin, Vladimir

    2011-01-01

    Superconducting Linear Accelerators include a superconducting magnet system for particle beam transportation that provides the beam focusing and steering. This system consists of a large number of quadrupole magnets and dipole correctors mounted inside or between cryomodules with SCRF cavities. Each magnet has current leads and powered from its own power supply. The paper proposes a novel approach to magnet powering based on using superconducting persistent current switches. A group of magnets is powered from the same power supply through the common, for the group of cryomodules, electrical bus and pair of current leads. Superconducting switches direct the current to the chosen magnet and close the circuit providing the magnet operation in a persistent current mode. Two persistent current switches were fabricated and tested. In the paper also presented the results of magnetic field simulations, decay time constants analysis, and a way of improving quadrupole magnetic center stability. Such approach substantially reduces the magnet system cost and increases the reliability.

  18. Considering system non-linearity in transmission pricing

    International Nuclear Information System (INIS)

    Oloomi-Buygi, M.; Salehizadeh, M. Reza

    2008-01-01

    In this paper a new approach for transmission pricing is presented. The contribution of a contract on power flow of a transmission line is used as extent-of-use criterion for transmission pricing. In order to determine the contribution of each contract on power flow of each transmission line, first the contribution of each contract on each voltage angle is determined, which is called voltage angle decomposition. To this end, DC power flow is used to compute a primary solution for voltage angle decomposition. To consider the impacts of system non-linearity on voltage angle decomposition, a method is presented to determine the share of different terms of sine argument in sine value. Then the primary solution is corrected in different iterations of decoupled Newton-Raphson power flow using the presented sharing method. The presented approach is applied to a 4-bus test system and IEEE 30-bus test system and the results are analyzed. (author)

  19. Data acquisition system for linear PSD based neutron diffractometer

    International Nuclear Information System (INIS)

    Pande, S.S.; Borkar, S.P.; Behere, Anita; Ghodgaonkar, M.D.

    2001-01-01

    Single or multi-PSD configurations are used in different neutron diffractometer setups. A data acquisition system is developed to serve the gross requirements of all the diffractometer setups. It is also customized to specific requirements of different setups. The hardware is developed as a Transputer based add-on card. Most of the hardware functionality is handled in the Transputer program thus improving throughput of the system. The card can handle 16 RDCs, a few motor controls and on/off controls. The software comprises of a front-end Windows98 application, a Transputer program and a device driver. The data acquisition system performs data acquisition, analysis, display and storage. Analysis includes converting raw data of linear PSD to equiangular format, merging and clubbing the data to make a continuous equiangular spectrum. Calibration of individual PSD is a crucial activity in correctly merging the data coming from PSDs. (author)

  20. Applied linear algebra

    CERN Document Server

    Olver, Peter J

    2018-01-01

    This textbook develops the essential tools of linear algebra, with the goal of imparting technique alongside contextual understanding. Applications go hand-in-hand with theory, each reinforcing and explaining the other. This approach encourages students to develop not only the technical proficiency needed to go on to further study, but an appreciation for when, why, and how the tools of linear algebra can be used across modern applied mathematics. Providing an extensive treatment of essential topics such as Gaussian elimination, inner products and norms, and eigenvalues and singular values, this text can be used for an in-depth first course, or an application-driven second course in linear algebra. In this second edition, applications have been updated and expanded to include numerical methods, dynamical systems, data analysis, and signal processing, while the pedagogical flow of the core material has been improved. Throughout, the text emphasizes the conceptual connections between each application and the un...

  1. Final focus system tuning studies towards Compact Linear Collider feasibility

    Science.gov (United States)

    Marin, E.; Latina, A.; Tomás, R.; Schulte, D.

    2018-01-01

    In this paper we present the latest results regarding the tuning study of the baseline design of the final focus system of the Compact Linear Collider (CLIC-FFS). CLIC aims to provide collisions to the experiments at a luminosity above 1034 c m-2 s-1 . In order to deliver such luminosity in a single pass machine, the vertical beam size at the interaction point (IP) is reduced to about 1 nm, which imposes unprecedented tuning difficulties to the system. In previous studies, 90% of the machines reached 90% of the nominal luminosity at the expense of 18 000 luminosity measurements, when considering beam position monitor errors and transverse misalignments of magnets for a single beam case. In the present study, additional static imperfections as, roll misalignments, strength v2.epss are included. Moreover both e- and e+ beamlines are properly simulated. A new tuning procedure based on linear and nonlinear knobs is implemented to effectively cure the most relevant beam size aberrations at the IP. The obtained results for single and double beam studies under solely static imperfections are presented.

  2. Efficient Feedforward Linearization Technique Using Genetic Algorithms for OFDM Systems

    Directory of Open Access Journals (Sweden)

    García Paloma

    2010-01-01

    Full Text Available Feedforward is a linearization method that simultaneously offers wide bandwidth and good intermodulation distortion suppression; so it is a good choice for Orthogonal Frequency Division Multiplexing (OFDM systems. Feedforward structure consists of two loops, being necessary an accurate adjustment between them along the time, and when temperature, environmental, or operating changes are produced. Amplitude and phase imbalances of the circuit elements in both loops produce mismatched effects that lead to degrade its performance. A method is proposed to compensate these mismatches, introducing two complex coefficients calculated by means of a genetic algorithm. A full study is carried out to choose the optimal parameters of the genetic algorithm applied to wideband systems based on OFDM technologies, which are very sensitive to nonlinear distortions. The method functionality has been verified by means of simulation.

  3. On modulated complex non-linear dynamical systems

    International Nuclear Information System (INIS)

    Mahmoud, G.M.; Mohamed, A.A.; Rauh, A.

    1999-01-01

    This paper is concerned with the development of an approximate analytical method to investigate periodic solutions and their stability in the case of modulated non-linear dynamical systems whose equation of motion is describe. Such differential equations appear, for example, in problems of colliding particle beams in high-energy accelerators or one-mass systems with two or more degrees of freedom, e.g. rotors. The significance of periodic solutions lies on the fact that all non-periodic responses, if convergent, would approach to periodic solutions at the steady-state conditions. The example shows a good agreement between numerical and analytical results for small values of ε. The effect of the periodic modulation on the stability of the 2π-periodic solutions is discussed

  4. Thermodynamic Optimality criteria for biological systems in linear irreversible thermodynamics

    International Nuclear Information System (INIS)

    Chimal, J C; Sánchez, N; Ramírez, PR

    2017-01-01

    In this paper the methodology of the so-called Linear Irreversible Thermodynamics (LIT) is applied; although traditionally used locally to study general systems in non-equilibrium states in which it is consider both internal and external contributions to the entropy increments in order to analyze the efficiency of two coupled processes with generalized fluxes J 1 , J 2 and their corresponding forces X 1 , X 2 . We extend the former analysis to takes into account two different operating regimes namely: Omega Function and Efficient Power criterion, respectively. Results show analogies in the optimal performance between and we can say that there exist a criteria of optimization which can be used specially for biological systems where a good design of the biological parameters made by nature at maximum efficient power conditions lead to more efficient engines than those at the maximum power conditions or ecological conditions. (paper)

  5. Linear system identification via backward-time observer models

    Science.gov (United States)

    Juang, Jer-Nan; Phan, Minh

    1993-01-01

    This paper presents an algorithm to identify a state-space model of a linear system using a backward-time approach. The procedure consists of three basic steps. First, the Markov parameters of a backward-time observer are computed from experimental input-output data. Second, the backward-time observer Markov parameters are decomposed to obtain the backward-time system Markov parameters (backward-time pulse response samples) from which a backward-time state-space model is realized using the Eigensystem Realization Algorithm. Third, the obtained backward-time state space model is converted to the usual forward-time representation. Stochastic properties of this approach will be discussed. Experimental results are given to illustrate when and to what extent this concept works.

  6. Ultra-high Frequency Linear Fiber Optic Systems

    CERN Document Server

    Lau, Kam Y

    2009-01-01

    Designed for a one-semester course on fiber-optics systems and communication links, this book provides a concise but rigorous treatment of the theory and practice of analog (linear) fiber-optics links and systems that constitute the foundation of Hybrid Fiber Coax infrastructure in present-day CATV distribution and cable modem Internet access. Emerging applications in remote fiber-optic feed for free-space millimeter wave enterprise campus networks are also described. Issues such as dispersion and interferometric noise are treated quantitatively, and means for mitigating them are explained. This broad but concise text will thus be invaluable not only to students of fiber-optics communication but also to practicing engineers.

  7. On the singular perturbations for fractional differential equation.

    Science.gov (United States)

    Atangana, Abdon

    2014-01-01

    The goal of this paper is to examine the possible extension of the singular perturbation differential equation to the concept of fractional order derivative. To achieve this, we presented a review of the concept of fractional calculus. We make use of the Laplace transform operator to derive exact solution of singular perturbation fractional linear differential equations. We make use of the methodology of three analytical methods to present exact and approximate solution of the singular perturbation fractional, nonlinear, nonhomogeneous differential equation. These methods are including the regular perturbation method, the new development of the variational iteration method, and the homotopy decomposition method.

  8. On the Singular Perturbations for Fractional Differential Equation

    Directory of Open Access Journals (Sweden)

    Abdon Atangana

    2014-01-01

    Full Text Available The goal of this paper is to examine the possible extension of the singular perturbation differential equation to the concept of fractional order derivative. To achieve this, we presented a review of the concept of fractional calculus. We make use of the Laplace transform operator to derive exact solution of singular perturbation fractional linear differential equations. We make use of the methodology of three analytical methods to present exact and approximate solution of the singular perturbation fractional, nonlinear, nonhomogeneous differential equation. These methods are including the regular perturbation method, the new development of the variational iteration method, and the homotopy decomposition method.

  9. Linear theory for filtering nonlinear multiscale systems with model error.

    Science.gov (United States)

    Berry, Tyrus; Harlim, John

    2014-07-08

    In this paper, we study filtering of multiscale dynamical systems with model error arising from limitations in resolving the smaller scale processes. In particular, the analysis assumes the availability of continuous-time noisy observations of all components of the slow variables. Mathematically, this paper presents new results on higher order asymptotic expansion of the first two moments of a conditional measure. In particular, we are interested in the application of filtering multiscale problems in which the conditional distribution is defined over the slow variables, given noisy observation of the slow variables alone. From the mathematical analysis, we learn that for a continuous time linear model with Gaussian noise, there exists a unique choice of parameters in a linear reduced model for the slow variables which gives the optimal filtering when only the slow variables are observed. Moreover, these parameters simultaneously give the optimal equilibrium statistical estimates of the underlying system, and as a consequence they can be estimated offline from the equilibrium statistics of the true signal. By examining a nonlinear test model, we show that the linear theory extends in this non-Gaussian, nonlinear configuration as long as we know the optimal stochastic parametrization and the correct observation model. However, when the stochastic parametrization model is inappropriate, parameters chosen for good filter performance may give poor equilibrium statistical estimates and vice versa; this finding is based on analytical and numerical results on our nonlinear test model and the two-layer Lorenz-96 model. Finally, even when the correct stochastic ansatz is given, it is imperative to estimate the parameters simultaneously and to account for the nonlinear feedback of the stochastic parameters into the reduced filter estimates. In numerical experiments on the two-layer Lorenz-96 model, we find that the parameters estimated online , as part of a filtering

  10. Modified Differential Transform Method for Two Singular Boundary Values Problems

    Directory of Open Access Journals (Sweden)

    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.

  11. Linear homotopy solution of nonlinear systems of equations in geodesy

    Science.gov (United States)

    Paláncz, Béla; Awange, Joseph L.; Zaletnyik, Piroska; Lewis, Robert H.

    2010-01-01

    A fundamental task in geodesy is solving systems of equations. Many geodetic problems are represented as systems of multivariate polynomials. A common problem in solving such systems is improper initial starting values for iterative methods, leading to convergence to solutions with no physical meaning, or to convergence that requires global methods. Though symbolic methods such as Groebner bases or resultants have been shown to be very efficient, i.e., providing solutions for determined systems such as 3-point problem of 3D affine transformation, the symbolic algebra can be very time consuming, even with special Computer Algebra Systems (CAS). This study proposes the Linear Homotopy method that can be implemented easily in high-level computer languages like C++ and Fortran that are faster than CAS by at least two orders of magnitude. Using Mathematica, the power of Homotopy is demonstrated in solving three nonlinear geodetic problems: resection, GPS positioning, and affine transformation. The method enlarging the domain of convergence is found to be efficient, less sensitive to rounding of numbers, and has lower complexity compared to other local methods like Newton-Raphson.

  12. 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.

  13. 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.)

  14. 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.

  15. The theory of a general quantum system interacting with a linear dissipative system

    International Nuclear Information System (INIS)

    Feynman, R.P.; Vernon, F.L.

    2000-01-01

    A formalism has been developed, using Feynman's space-time formulation of nonrelativistic quantum mechanics whereby the behavior of a system of interest, which is coupled to other external quantum systems, may be calculated in terms of its own variables only. It is shown that the effect of the external systems in such a formalism can always be included in a general class of functionals (influence functionals) of the coordinates of the system only. The properties of influence functionals for general systems are examined. Then, specific forms of influence functionals representing the effect of definite and random classical forces, linear dissipative systems at finite temperatures, and combinations of these are analyzed in detail. The linear system analysis is first done for perfectly linear systems composed of combinations of harmonic oscillators, loss being introduced by continuous distributions of oscillators. Then approximately linear systems and restrictions necessary for the linear behavior are considered. Influence functionals for all linear systems are shown to have the same form in terms of their classical response functions. In addition, a fluctuation-dissipation theorem is derived relating temperature and dissipation of the linear system to a fluctuating classical potential acting on the system of interest which reduces to the Nyquist-Johnson relation for noise in the case of electric circuits. Sample calculations of transition probabilities for the spontaneous emission of an atom in free space and in a cavity are made. Finally, a theorem is proved showing that within the requirements of linearity all sources of noise or quantum fluctuation introduced by maser-type amplification devices are accounted for by a classical calculation of the characteristics of the maser

  16. Stochastic singular optics

    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...

  17. 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)

  18. Radii of Solvability and Unsolvability of Linear Systems

    Czech Academy of Sciences Publication Activity Database

    Hladík, M.; Rohn, Jiří

    2016-01-01

    Roč. 503, 15 August (2016), s. 120-134 ISSN 0024-3795 Institutional support: RVO:67985807 Keywords : interval matrix * linear equations * linear inequalities * matrix norm Subject RIV: BA - General Mathematics Impact factor: 0.973, year: 2016

  19. Numerical Study of Concentration Characteristics of Linear Fresnel Reflector System

    International Nuclear Information System (INIS)

    Lee, Hyun Jin; Kim, Jong Kyu; Lee, Sang Nam

    2015-01-01

    In this study, we numerically investigated the concentration characteristics of a linear Fresnel reflector system that can drive a solar thermal absorption refrigeration system to be installed in Saudi Arabia. Using an optical modeling program based on the Monte Carlo ray-tracing method, we simulated the concentrated solar flux, concentration efficiency, and concentrated solar energy on four representative days of the year - the vernal equinox, summer solstice, autumnal equinox, and winter solstice. Except the winter solstice, the concentrations were approximately steady from 9 AM to 15 PM, and the concentration efficiencies exceed 70%. Moreover, the maximum solar flux around the solar receiver center changes only within the range of 13.0 - 14.6 kW/m 2 . When we investigated the effects of the receiver installation height, reflector width, and reflector gap, the optimal receiver installation height was found to be 5 m. A smaller reflector width had a greater concentration efficiency. However, the design of the reflector width should be based on the capacity of the refrigeration system because it dominantly affects the concentrated solar energy. The present study was an essential prerequisite for thermal analyses of the solar receiver. Thus, an optical-thermal integration study in the future will assist with the performance prediction and design of the entire system

  20. Numerical Study of Concentration Characteristics of Linear Fresnel Reflector System

    Energy Technology Data Exchange (ETDEWEB)

    Lee, Hyun Jin [Kookmin Univ., Seoul (Korea, Republic of); Kim, Jong Kyu; Lee, Sang Nam [Korea Institute of Energy Research, Daejeon (Korea, Republic of)

    2015-12-15

    In this study, we numerically investigated the concentration characteristics of a linear Fresnel reflector system that can drive a solar thermal absorption refrigeration system to be installed in Saudi Arabia. Using an optical modeling program based on the Monte Carlo ray-tracing method, we simulated the concentrated solar flux, concentration efficiency, and concentrated solar energy on four representative days of the year - the vernal equinox, summer solstice, autumnal equinox, and winter solstice. Except the winter solstice, the concentrations were approximately steady from 9 AM to 15 PM, and the concentration efficiencies exceed 70%. Moreover, the maximum solar flux around the solar receiver center changes only within the range of 13.0 - 14.6 kW/m{sup 2}. When we investigated the effects of the receiver installation height, reflector width, and reflector gap, the optimal receiver installation height was found to be 5 m. A smaller reflector width had a greater concentration efficiency. However, the design of the reflector width should be based on the capacity of the refrigeration system because it dominantly affects the concentrated solar energy. The present study was an essential prerequisite for thermal analyses of the solar receiver. Thus, an optical-thermal integration study in the future will assist with the performance prediction and design of the entire system.

  1. Periodic inventory system in cafeteria using linear programming

    Science.gov (United States)

    Usop, Mohd Fais; Ishak, Ruzana; Hamdan, Ahmad Ridhuan

    2017-11-01

    Inventory management is an important factor in running a business. It plays a big role of managing the stock in cafeteria. If the inventories are failed to be managed wisely, it will affect the profit of the cafeteria. Therefore, the purpose of this study is to find the solution of the inventory management in cafeteria. Most of the cafeteria in Malaysia did not manage their stock well. Therefore, this study is to propose a database system of inventory management and to develop the inventory model in cafeteria management. In this study, new database system to improve the management of the stock in a weekly basis will be provided using Linear Programming Model to get the optimal range of the inventory needed for selected categories. Data that were collected by using the Periodic Inventory System at the end of the week within three months period being analyzed by using the Food Stock-take Database. The inventory model was developed from the collected data according to the category of the inventory in the cafeteria. Results showed the effectiveness of using the Periodic Inventory System and will be very helpful to the cafeteria management in organizing the inventory. Moreover, the findings in this study can reduce the cost of operation and increased the profit.

  2. Supersymmetric quantum mechanics under point singularities

    International Nuclear Information System (INIS)

    Uchino, Takashi; Tsutsui, Izumi

    2003-01-01

    We provide a systematic study on the possibility of supersymmetry (SUSY) for one-dimensional quantum mechanical systems consisting of a pair of lines R or intervals [-l, l] each having a point singularity. We consider the most general singularities and walls (boundaries) at x = ±l admitted quantum mechanically, using a U(2) family of parameters to specify one singularity and similarly a U(1) family of parameters to specify one wall. With these parameter freedoms, we find that for a certain subfamily the line systems acquire an N = 1 SUSY which can be enhanced to N = 4 if the parameters are further tuned, and that these SUSY are generically broken except for a special case. The interval systems, on the other hand, can accommodate N = 2 or N = 4 SUSY, broken or unbroken, and exhibit a rich variety of (degenerate) spectra. Our SUSY systems include the familiar SUSY systems with the Dirac δ(x)-potential, and hence are extensions of the known SUSY quantum mechanics to those with general point singularities and walls. The self-adjointness of the supercharge in relation to the self-adjointness of the Hamiltonian is also discussed

  3. 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)

  4. Singularities of elastic scattering amplitude by long-range potentials

    International Nuclear Information System (INIS)

    Kvitsinsky, A.A.; Komarov, I.V.; Merkuriev, S.P.

    1982-01-01

    The angular peculiarities and the zero energy singularities of the elastic scattering amplitude by a long-range potential are described. The singularities of the elastic (2 → 2) scattering amplitude for a system of three Coulomb particles are considered [ru

  5. Singularly perturbed volterra integro-differential equations | Bijura ...

    African Journals Online (AJOL)

    Several investigations have been made on singularly perturbed integral equations. This paper aims at presenting an algorithm for the construction of asymptotic solutions and then provide a proof asymptotic correctness to singularly perturbed systems of Volterra integro-differential equations. Mathematics Subject

  6. Incomplete factorization technique for positive definite linear systems

    International Nuclear Information System (INIS)

    Manteuffel, T.A.

    1980-01-01

    This paper describes a technique for solving the large sparse symmetric linear systems that arise from the application of finite element methods. The technique combines an incomplete factorization method called the shifted incomplete Cholesky factorization with the method of generalized conjugate gradients. The shifted incomplete Cholesky factorization produces a splitting of the matrix A that is dependent upon a parameter α. It is shown that if A is positive definite, then there is some α for which this splitting is possible and that this splitting is at least as good as the Jacobi splitting. The method is shown to be more efficient on a set of test problems than either direct methods or explicit iteration schemes

  7. Stability and complexity of small random linear systems

    Science.gov (United States)

    Hastings, Harold

    2010-03-01

    We explore the stability of the small random linear systems, typically involving 10-20 variables, motivated by dynamics of the world trade network and the US and Canadian power grid. This report was prepared as an account of work sponsored by an agency of the US Government. Neither the US Government nor any agency thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the US Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the US Government or any agency thereof.

  8. IMPROVING THE PERFORMANCE OF THE LINEAR SYSTEMS SOLVERS USING CUDA

    Directory of Open Access Journals (Sweden)

    BOGDAN OANCEA

    2012-05-01

    Full Text Available Parallel computing can offer an enormous advantage regarding the performance for very large applications in almost any field: scientific computing, computer vision, databases, data mining, and economics. GPUs are high performance many-core processors that can obtain very high FLOP rates. Since the first idea of using GPU for general purpose computing, things have evolved and now there are several approaches to GPU programming: CUDA from NVIDIA and Stream from AMD. CUDA is now a popular programming model for general purpose computations on GPU for C/C++ programmers. A great number of applications were ported to CUDA programming model and they obtain speedups of orders of magnitude comparing to optimized CPU implementations. In this paper we present an implementation of a library for solving linear systems using the CCUDA framework. We present the results of performance tests and show that using GPU one can obtain speedups of about of approximately 80 times comparing with a CPU implementation.

  9. Compressive System Identification in the Linear Time-Invariant framework

    KAUST Repository

    Toth, Roland

    2011-12-01

    Selection of an efficient model parametrization (model order, delay, etc.) has crucial importance in parametric system identification. It navigates a trade-off between representation capabilities of the model (structural bias) and effects of over-parametrization (variance increase of the estimates). There exists many approaches to this widely studied problem in terms of statistical regularization methods and information criteria. In this paper, an alternative ℓ 1 regularization scheme is proposed for estimation of sparse linear-regression models based on recent results in compressive sensing. It is shown that the proposed scheme provides consistent estimation of sparse models in terms of the so-called oracle property, it is computationally attractive for large-scale over-parameterized models and it is applicable in case of small data sets, i.e., underdetermined estimation problems. The performance of the approach w.r.t. other regularization schemes is demonstrated in an extensive Monte Carlo study. © 2011 IEEE.

  10. Existence of localizing solutions in plasticity via the geometric singular perturbation theory

    KAUST Repository

    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

  11. Sampled-data models for linear and nonlinear systems

    CERN Document Server

    Yuz, Juan I

    2014-01-01

    Sampled-data Models for Linear and Nonlinear Systems provides a fresh new look at a subject with which many researchers may think themselves familiar. Rather than emphasising the differences between sampled-data and continuous-time systems, the authors proceed from the premise that, with modern sampling rates being as high as they are, it is becoming more appropriate to emphasise connections and similarities. The text is driven by three motives: ·      the ubiquity of computers in modern control and signal-processing equipment means that sampling of systems that really evolve continuously is unavoidable; ·      although superficially straightforward, sampling can easily produce erroneous results when not treated properly; and ·      the need for a thorough understanding of many aspects of sampling among researchers and engineers dealing with applications to which they are central. The authors tackle many misconceptions which, although appearing reasonable at first sight, are in fact either p...

  12. Embarked electrical network robust control based on singular perturbation model.

    Science.gov (United States)

    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.

  13. Comparison of linear, mixed integer and non-linear programming methods in energy system dispatch modelling

    DEFF Research Database (Denmark)

    Ommen, Torben Schmidt; Markussen, Wiebke Brix; Elmegaard, Brian

    2014-01-01

    In the paper, three frequently used operation optimisation methods are examined with respect to their impact on operation management of the combined utility technologies for electric power and DH (district heating) of eastern Denmark. The investigation focusses on individual plant operation...... differences and differences between the solution found by each optimisation method. One of the investigated approaches utilises LP (linear programming) for optimisation, one uses LP with binary operation constraints, while the third approach uses NLP (non-linear programming). The LP model is used...... as a benchmark, as this type is frequently used, and has the lowest amount of constraints of the three. A comparison of the optimised operation of a number of units shows significant differences between the three methods. Compared to the reference, the use of binary integer variables, increases operation...

  14. Residues and duality for singularity categories of isolated Gorenstein singularities

    OpenAIRE

    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.

  15. 2-D linear motion system. Innovative technology summary report

    International Nuclear Information System (INIS)

    1998-11-01

    The US Department of Energy's (DOE's) nuclear facility decontamination and decommissioning (D and D) program requires buildings to be decontaminated, decommissioned, and surveyed for radiological contamination in an expeditious and cost-effective manner. Simultaneously, the health and safety of personnel involved in the D and D activities is of primary concern. D and D workers must perform duties high off the ground, requiring the use of manlifts or scaffolding, often, in radiologically or chemically contaminated areas or in areas with limited access. Survey and decontamination instruments that are used are sometimes heavy or awkward to use, particularly when the worker is operating from a manlift or scaffolding. Finding alternative methods of performing such work on manlifts or scaffolding is important. The 2-D Linear Motion System (2-D LMS), also known as the Wall Walker trademark, is designed to remotely position tools and instruments on walls for use in such activities as radiation surveys, decontamination, and painting. Traditional (baseline) methods for operating equipment for these tasks require workers to perform duties on elevated platforms, sometimes several meters above the ground surface and near potential sources of contamination. The Wall Walker 2-D LMS significantly improves health and safety conditions by facilitating remote operation of equipment. The Wall Walker 2-D LMS performed well in a demonstration of its precision, accuracy, maneuverability, payload capacity, and ease of use. Thus, this innovative technology is demonstrated to be a viable alternative to standard methods of performing work on large, high walls, especially those that have potential contamination concerns. The Wall Walker was used to perform a final release radiological survey on over 167 m 2 of walls. In this application, surveying using a traditional (baseline) method that employs an aerial lift for manual access was 64% of the total cost of the improved technology. However

  16. Normal forms of Hopf-zero singularity

    International Nuclear Information System (INIS)

    Gazor, Majid; Mokhtari, Fahimeh

    2015-01-01

    The Lie algebra generated by Hopf-zero classical normal forms is decomposed into two versal Lie subalgebras. Some dynamical properties for each subalgebra are described; one is the set of all volume-preserving conservative systems while the other is the maximal Lie algebra of nonconservative systems. This introduces a unique conservative–nonconservative decomposition for the normal form systems. There exists a Lie-subalgebra that is Lie-isomorphic to a large family of vector fields with Bogdanov–Takens singularity. This gives rise to a conclusion that the local dynamics of formal Hopf-zero singularities is well-understood by the study of Bogdanov–Takens singularities. Despite this, the normal form computations of Bogdanov–Takens and Hopf-zero singularities are independent. Thus, by assuming a quadratic nonzero condition, complete results on the simplest Hopf-zero normal forms are obtained in terms of the conservative–nonconservative decomposition. Some practical formulas are derived and the results implemented using Maple. The method has been applied on the Rössler and Kuramoto–Sivashinsky equations to demonstrate the applicability of our results. (paper)

  17. Normal forms of Hopf-zero singularity

    Science.gov (United States)

    Gazor, Majid; Mokhtari, Fahimeh

    2015-01-01

    The Lie algebra generated by Hopf-zero classical normal forms is decomposed into two versal Lie subalgebras. Some dynamical properties for each subalgebra are described; one is the set of all volume-preserving conservative systems while the other is the maximal Lie algebra of nonconservative systems. This introduces a unique conservative-nonconservative decomposition for the normal form systems. There exists a Lie-subalgebra that is Lie-isomorphic to a large family of vector fields with Bogdanov-Takens singularity. This gives rise to a conclusion that the local dynamics of formal Hopf-zero singularities is well-understood by the study of Bogdanov-Takens singularities. Despite this, the normal form computations of Bogdanov-Takens and Hopf-zero singularities are independent. Thus, by assuming a quadratic nonzero condition, complete results on the simplest Hopf-zero normal forms are obtained in terms of the conservative-nonconservative decomposition. Some practical formulas are derived and the results implemented using Maple. The method has been applied on the Rössler and Kuramoto-Sivashinsky equations to demonstrate the applicability of our results.

  18. Low-Rank Linear Dynamical Systems for Motor Imagery EEG.

    Science.gov (United States)

    Zhang, Wenchang; Sun, Fuchun; Tan, Chuanqi; Liu, Shaobo

    2016-01-01

    The common spatial pattern (CSP) and other spatiospectral feature extraction methods have become the most effective and successful approaches to solve the problem of motor imagery electroencephalography (MI-EEG) pattern recognition from multichannel neural activity in recent years. However, these methods need a lot of preprocessing and postprocessing such as filtering, demean, and spatiospectral feature fusion, which influence the classification accuracy easily. In this paper, we utilize linear dynamical systems (LDSs) for EEG signals feature extraction and classification. LDSs model has lots of advantages such as simultaneous spatial and temporal feature matrix generation, free of preprocessing or postprocessing, and low cost. Furthermore, a low-rank matrix decomposition approach is introduced to get rid of noise and resting state component in order to improve the robustness of the system. Then, we propose a low-rank LDSs algorithm to decompose feature subspace of LDSs on finite Grassmannian and obtain a better performance. Extensive experiments are carried out on public dataset from "BCI Competition III Dataset IVa" and "BCI Competition IV Database 2a." The results show that our proposed three methods yield higher accuracies compared with prevailing approaches such as CSP and CSSP.

  19. A virtual linear accelerator for verification of treatment planning systems

    International Nuclear Information System (INIS)

    Wieslander, Elinore

    2000-01-01

    A virtual linear accelerator is implemented into a commercial pencil-beam-based treatment planning system (TPS) with the purpose of investigating the possibility of verifying the system using a Monte Carlo method. The characterization set for the TPS includes depth doses, profiles and output factors, which is generated by Monte Carlo simulations. The advantage of this method over conventional measurements is that variations in accelerator output are eliminated and more complicated geometries can be used to study the performance of a TPS. The difference between Monte Carlo simulated and TPS calculated profiles and depth doses in the characterization geometry is less than ±2% except for the build-up region. This is of the same order as previously reported results based on measurements. In an inhomogeneous, mediastinum-like case, the deviations between TPS and simulations are small in the unit-density regions. In low-density regions, the TPS overestimates the dose, and the overestimation increases with increasing energy from 3.5% for 6 MV to 9.5% for 18 MV. This result points out the widely known fact that the pencil beam concept does not handle changes in lateral electron transport, nor changes in scatter due to lateral inhomogeneities. It is concluded that verification of a pencil-beam-based TPS with a Monte Carlo based virtual accelerator is possible, which facilitates the verification procedure. (author)

  20. Stochastic linear hybrid systems: Modeling, estimation, and application

    Science.gov (United States)

    Seah, Chze Eng

    Hybrid systems are dynamical systems which have interacting continuous state and discrete state (or mode). Accurate modeling and state estimation of hybrid systems are important in many applications. We propose a hybrid system model, known as the Stochastic Linear Hybrid System (SLHS), to describe hybrid systems with stochastic linear system dynamics in each mode and stochastic continuous-state-dependent mode transitions. We then develop a hybrid estimation algorithm, called the State-Dependent-Transition Hybrid Estimation (SDTHE) algorithm, to estimate the continuous state and discrete state of the SLHS from noisy measurements. It is shown that the SDTHE algorithm is more accurate or more computationally efficient than existing hybrid estimation algorithms. Next, we develop a performance analysis algorithm to evaluate the performance of the SDTHE algorithm in a given operating scenario. We also investigate sufficient conditions for the stability of the SDTHE algorithm. The proposed SLHS model and SDTHE algorithm are illustrated to be useful in several applications. In Air Traffic Control (ATC), to facilitate implementations of new efficient operational concepts, accurate modeling and estimation of aircraft trajectories are needed. In ATC, an aircraft's trajectory can be divided into a number of flight modes. Furthermore, as the aircraft is required to follow a given flight plan or clearance, its flight mode transitions are dependent of its continuous state. However, the flight mode transitions are also stochastic due to navigation uncertainties or unknown pilot intents. Thus, we develop an aircraft dynamics model in ATC based on the SLHS. The SDTHE algorithm is then used in aircraft tracking applications to estimate the positions/velocities of aircraft and their flight modes accurately. Next, we develop an aircraft conformance monitoring algorithm to detect any deviations of aircraft trajectories in ATC that might compromise safety. In this application, the SLHS

  1. Popov–Belevitch–Hautus type tests for the controllability of linear complementarity systems

    NARCIS (Netherlands)

    Camlibel, M. Kanat

    2007-01-01

    It is well-known that checking certain controllability properties of very simple piecewise linear systems are undecidable problems. This paper deals with the controllability problem of a class of piecewise linear systems, known as linear complementarity systems. By exploiting the underlying

  2. EDITORIAL: The plurality of optical singularities

    Science.gov (United States)

    Berry, Michael; Dennis, Mark; Soskin, Marat

    2004-05-01

    electric (or magnetic) polarization ellipse is purely circular (C lines) or purely linear (L lines). The patterns of ellipse-fields are different for purely paraxial and fully three-dimensional fields. White-light diffraction generates richly coloured vortices—the colours of dark light. The description of these chromatic effects, and also those associated with polarization singularities, leads to new applications of coherence theory. For non-monochromatic light, it is natural to seek singularities of the full electromagnetic field, rather than of the electric or magnetic field separately. Such electromagnetic singularities are the Riemann-Silberstein vortices; these are relativistically covariant nodal lines of a complex scalar field constructed from the electromagnetic field. Optical fields have dynamical aspects, particularly those associated with angular momentum. Although angular momentum is not inevitably associated with optical singularities, in practice the two phenomena can occur together. Orbital angular momentum is associated with the spatial structure of light, and in beams with optical vortices it can be used to rotate particles in the field. Spin angular momentum is associated with the polarization structure of the light. There are tricky questions associated with the angular momentum of light in a refracting medium, echoing the Abraham-Minkowski controversy about linear momentum. In optically nonlinear materials (leading to second-harmonic generation, for example), new classes of phenomena can occur, such as, for example, dynamical interaction between vortex lines, whose stability needs to be considered. At a more fundamental level, it is important to investigate quantum effects associated with optical singularities, and a start has been made. The dark centre of an optical vortex can be regarded as a window onto the vacuum fluctuations of quantum optics, with the quantum core emerging as a distinct entity when the classical light is intense. And for light

  3. On bifurcations of a system of cubic differential equations with an integrating multiplier singular along a second-order curve

    Directory of Open Access Journals (Sweden)

    Aleksandr Alekseev

    2015-07-01

    Full Text Available We establish necessary and sufficient conditions for existence of an integrating multiplier of a special form for systems of two cubic differential equations of the first order. We further study bifurcations of such systems with the change of parameters of their integrating multipliers.

  4. On computation of Groebner bases for linear difference systems

    Energy Technology Data Exchange (ETDEWEB)

    Gerdt, Vladimir P. [Laboratory of Information Technologies, Joint Institute for Nuclear Research, 141980 Dubna (Russian Federation)]. E-mail: gerdt@jinr.ru

    2006-04-01

    In this paper, we present an algorithm for computing Groebner bases of linear ideals in a difference polynomial ring over a ground difference field. The input difference polynomials generating the ideal are also assumed to be linear. The algorithm is an adaptation to difference ideals of our polynomial algorithm based on Janet-like reductions.

  5. On computation of Groebner bases for linear difference systems

    International Nuclear Information System (INIS)

    Gerdt, Vladimir P.

    2006-01-01

    In this paper, we present an algorithm for computing Groebner bases of linear ideals in a difference polynomial ring over a ground difference field. The input difference polynomials generating the ideal are also assumed to be linear. The algorithm is an adaptation to difference ideals of our polynomial algorithm based on Janet-like reductions

  6. Stability and Linear Quadratic Differential Games of Discrete-Time Markovian Jump Linear Systems with State-Dependent Noise

    Directory of Open Access Journals (Sweden)

    Huiying Sun

    2014-01-01

    Full Text Available We mainly consider the stability of discrete-time Markovian jump linear systems with state-dependent noise as well as its linear quadratic (LQ differential games. A necessary and sufficient condition involved with the connection between stochastic Tn-stability of Markovian jump linear systems with state-dependent noise and Lyapunov equation is proposed. And using the theory of stochastic Tn-stability, we give the optimal strategies and the optimal cost values for infinite horizon LQ stochastic differential games. It is demonstrated that the solutions of infinite horizon LQ stochastic differential games are concerned with four coupled generalized algebraic Riccati equations (GAREs. Finally, an iterative algorithm is presented to solve the four coupled GAREs and a simulation example is given to illustrate the effectiveness of it.

  7. Evaluation of beach cleanup effects using linear system analysis.

    Science.gov (United States)

    Kataoka, Tomoya; Hinata, Hirofumi

    2015-02-15

    We established a method for evaluating beach cleanup effects (BCEs) based on a linear system analysis, and investigated factors determining BCEs. Here we focus on two BCEs: decreasing the total mass of toxic metals that could leach into a beach from marine plastics and preventing the fragmentation of marine plastics on the beach. Both BCEs depend strongly on the average residence time of marine plastics on the beach (τ(r)) and the period of temporal variability of the input flux of marine plastics (T). Cleanups on the beach where τ(r) is longer than T are more effective than those where τ(r) is shorter than T. In addition, both BCEs are the highest near the time when the remnants of plastics reach the local maximum (peak time). Therefore, it is crucial to understand the following three factors for effective cleanups: the average residence time, the plastic input period and the peak time. Copyright © 2014 Elsevier Ltd. All rights reserved.

  8. On differential operators generating iterative systems of linear ODEs of maximal symmetry algebra

    Science.gov (United States)

    Ndogmo, J. C.

    2017-06-01

    Although every iterative scalar linear ordinary differential equation is of maximal symmetry algebra, the situation is different and far more complex for systems of linear ordinary differential equations, and an iterative system of linear equations need not be of maximal symmetry algebra. We illustrate these facts by examples and derive families of vector differential operators whose iterations are all linear systems of equations of maximal symmetry algebra. Some consequences of these results are also discussed.

  9. Daily Average Wind Power Interval Forecasts Based on an Optimal Adaptive-Network-Based Fuzzy Inference System and Singular Spectrum Analysis

    Directory of Open Access Journals (Sweden)

    Zhongrong Zhang

    2016-01-01

    Full Text Available Wind energy has increasingly played a vital role in mitigating conventional resource shortages. Nevertheless, the stochastic nature of wind poses a great challenge when attempting to find an accurate forecasting model for wind power. Therefore, precise wind power forecasts are of primary importance to solve operational, planning and economic problems in the growing wind power scenario. Previous research has focused efforts on the deterministic forecast of wind power values, but less attention has been paid to providing information about wind energy. Based on an optimal Adaptive-Network-Based Fuzzy Inference System (ANFIS and Singular Spectrum Analysis (SSA, this paper develops a hybrid uncertainty forecasting model, IFASF (Interval Forecast-ANFIS-SSA-Firefly Alogorithm, to obtain the upper and lower bounds of daily average wind power, which is beneficial for the practical operation of both the grid company and independent power producers. To strengthen the practical ability of this developed model, this paper presents a comparison between IFASF and other benchmarks, which provides a general reference for this aspect for statistical or artificially intelligent interval forecast methods. The comparison results show that the developed model outperforms eight benchmarks and has a satisfactory forecasting effectiveness in three different wind farms with two time horizons.

  10. 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.

  11. 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)

  12. Linear algebra

    CERN Document Server

    Liesen, Jörg

    2015-01-01

    This self-contained textbook takes a matrix-oriented approach to linear algebra and presents a complete theory, including all details and proofs, culminating in the Jordan canonical form and its proof. Throughout the development, the applicability of the results is highlighted. Additionally, the book presents special topics from applied linear algebra including matrix functions, the singular value decomposition, the Kronecker product and linear matrix equations. The matrix-oriented approach to linear algebra leads to a better intuition and a deeper understanding of the abstract concepts, and therefore simplifies their use in real world applications. Some of these applications are presented in detailed examples. In several ‘MATLAB-Minutes’ students can comprehend the concepts and results using computational experiments. Necessary basics for the use of MATLAB are presented in a short introduction. Students can also actively work with the material and practice their mathematical skills in more than 300 exerc...

  13. Electron linear accelerator system for natural rubber vulcanization

    Science.gov (United States)

    Rimjaem, S.; Kongmon, E.; Rhodes, M. W.; Saisut, J.; Thongbai, C.

    2017-09-01

    Development of an electron accelerator system, beam diagnostic instruments, an irradiation apparatus and electron beam processing methodology for natural rubber vulcanization is underway at the Plasma and Beam Physics Research Facility, Chiang Mai University, Thailand. The project is carried out with the aims to improve the qualities of natural rubber products. The system consists of a DC thermionic electron gun, 5-cell standing-wave radio-frequency (RF) linear accelerator (linac) with side-coupling cavities and an electron beam irradiation apparatus. This system is used to produce electron beams with an adjustable energy between 0.5 and 4 MeV and a pulse current of 10-100 mA at a pulse repetition rate of 20-400 Hz. An average absorbed dose between 160 and 640 Gy is expected to be archived for 4 MeV electron beam when the accelerator is operated at 400 Hz. The research activities focus firstly on assembling of the accelerator system, study on accelerator properties and electron beam dynamic simulations. The resonant frequency of the RF linac in π/2 operating mode is 2996.82 MHz for the operating temperature of 35 °C. The beam dynamic simulations were conducted by using the code ASTRA. Simulation results suggest that electron beams with an average energy of 4.002 MeV can be obtained when the linac accelerating gradient is 41.7 MV/m. The rms transverse beam size and normalized rms transverse emittance at the linac exit are 0.91 mm and 10.48 π mm·mrad, respectively. This information can then be used as the input data for Monte Carlo simulations to estimate the electron beam penetration depth and dose distribution in the natural rubber latex. The study results from this research will be used to define optimal conditions for natural rubber vulcanization with different electron beam energies and doses. This is very useful for development of future practical industrial accelerator units.

  14. Direct linear driving systems; Les entrainements lineaires directs

    Energy Technology Data Exchange (ETDEWEB)

    Favre, E.; Brunner, C.; Piaget, D. [ETEL SA (France)

    1999-11-01

    The linear motor is one of the most important developments in electrical drive technology. However, it only, began to be adopted on a large scale at the beginning of the 1990's and will not be considered a mature technology until well into the next millennium. Actuators based on linear motor technology have a number of technical advantages including high speed, high positional accuracy and fine resolution. They also require fewer component parts. Some precautions are necessary when using linear motors. Care must be taken to avoid overheating and excessive vibration, and the magnetic components must be protected.

  15. 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.

  16. Naked singularities are not singular in distorted gravity

    Science.gov (United States)

    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.

  17. 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

  18. First-order systems of linear partial differential equations: normal forms, canonical systems, transform methods

    Directory of Open Access Journals (Sweden)

    Heinz Toparkus

    2014-04-01

    Full Text Available In this paper we consider first-order systems with constant coefficients for two real-valued functions of two real variables. This is both a problem in itself, as well as an alternative view of the classical linear partial differential equations of second order with constant coefficients. The classification of the systems is done using elementary methods of linear algebra. Each type presents its special canonical form in the associated characteristic coordinate system. Then you can formulate initial value problems in appropriate basic areas, and you can try to achieve a solution of these problems by means of transform methods.

  19. Badly approximable systems of linear forms in absolute value

    DEFF Research Database (Denmark)

    Hussain, M.; Kristensen, Simon

    In this paper we show that the set of mixed type badly approximable simultaneously small linear forms is of maximal dimension. As a consequence of this theorem we settle the conjecture stated in [9]....

  20. The graphics software of the Saclay Linear Accelerator control system

    International Nuclear Information System (INIS)

    Gournay, J.F.

    1988-01-01

    The graphics software used for the control of the Saclay Linear Accelerator is described. The specific requirements that such a software must have in this environment are outlined and some typical applications are presented. (orig.)

  1. Lag synchronization of chaotic systems with time-delayed linear ...

    Indian Academy of Sciences (India)

    delayed linear terms via impulsive control is investigated. Based on the stability theory of impulsive delayed differen- tial equations, some sufficient conditions are obtained guaranteeing the synchronized behaviours between two delayed chaotic ...

  2. Design, dynamics and control of an Adaptive Singularity-Free Control Moment Gyroscope actuator for microspacecraft Attitude Determination and Control System

    Science.gov (United States)

    Viswanathan, Sasi Prabhakaran

    how they lead to CMG singularities, are described. General ideas on control of the angular momentum of the spacecraft using changes in the momentum variables of a finite number of ASCMGs, are provided. Control schemes for agile and precise attitude maneuvers using ASCMG cluster in the absence of external torques and when the total angular momentum of the spacecraft is zero, is presented for both constant speed and variable speed modes. A Geometric Variational Integrator (GVI) that preserves the geometry of the state space and the conserved norm of the total angular momentum is constructed for numerical simulation and microcontroller implementation of the control scheme. The GVI is obtained by discretizing the Lagrangian of the rnultibody systems, in which the rigid body attitude is globally represented on the Lie group of rigid body rotations. Hardware and software architecture of a novel spacecraft Attitude Determination and Control System (ADCS) based on commercial smartphones and a bare minimum hardware prototype of an ASCMG using low cost COTS components is also described. A lightweight, dynamics model-free Variational Attitude Estimator (VAE) suitable for smartphone implementation is employed for attitude determination and the attitude control is performed by ASCMG actuators. The VAE scheme presented here is implemented and validated onboard an Unmanned Aerial Vehicle (UAV) platform and the real time performance is analyzed. On-board sensing, data acquisition, data uplink/downlink, state estimation and real-time feedback control objectives can be performed using this novel spacecraft ADCS. The mechatronics realization of the attitude determination through variational attitude estimation scheme and control implementation using ASCMG actuators are presented here. Experimental results of the attitude estimation (filtering) scheme using smartphone sensors as an Inertial Measurement Unit (IMU) on the Hardware In the Loop (HIL) simulator testbed are given. These

  3. Metrical theorems on systems of small inhomogeneous linear forms

    DEFF Research Database (Denmark)

    Hussain, Mumtaz; Kristensen, Simon

    In this paper we establish complete Khintchine-Groshev and Schmidt type theorems for inhomogeneous small linear forms in the so-called doubly metric case, in which the inhomogeneous parameter is not fixed.......In this paper we establish complete Khintchine-Groshev and Schmidt type theorems for inhomogeneous small linear forms in the so-called doubly metric case, in which the inhomogeneous parameter is not fixed....

  4. Metrical results on systems of small linear forms

    DEFF Research Database (Denmark)

    Hussain, M.; Kristensen, Simon

    In this paper the metric theory of Diophantine approximation associated with the small linear forms is investigated. Khintchine--Groshev theorems are established along with Hausdorff measure generalization without the monotonic assumption on the approximating function.......In this paper the metric theory of Diophantine approximation associated with the small linear forms is investigated. Khintchine--Groshev theorems are established along with Hausdorff measure generalization without the monotonic assumption on the approximating function....

  5. Robustness of Linear Systems towards Multi-Dissipative Pertubations

    DEFF Research Database (Denmark)

    Thygesen, Uffe Høgsbro; Poulsen, Niels Kjølstad

    1997-01-01

    We consider the question of robust stability of a linear time invariant plant subject to dynamic perturbations, which are dissipative in the sense of Willems with respect to several quadratic supply rates. For instance, parasitic dynamics are often both small gain and passive. We reduce several...... robustness analysis questions to linear matrix inequalities: robust stability, robust H2 performance and robust performance in presence of disturbances with finite signal-to-noise ratios...

  6. Singularities of n-fold integrals of the Ising class and the theory of elliptic curves

    International Nuclear Information System (INIS)

    Boukraa, S; Hassani, S; Maillard, J-M; Zenine, N

    2007-01-01

    We introduce some multiple integrals that are expected to have the same singularities as the singularities of the n-particle contributions χ (n) to the susceptibility of the square lattice Ising model. We find the Fuchsian linear differential equation satisfied by these multiple integrals for n = 1, 2, 3, 4 and only modulo some primes for n = 5 and 6, thus providing a large set of (possible) new singularities of χ (n) . We discuss the singularity structure for these multiple integrals by solving the Landau conditions. We find that the singularities of the associated ODEs identify (up to n = 6) with the leading pinch Landau singularities. The second remarkable obtained feature is that the singularities of the ODEs associated with the multiple integrals reduce to the singularities of the ODEs associated with a finite number of one-dimensional integrals. Among the singularities found, we underline the fact that the quadratic polynomial condition 1 + 3w + 4w 2 = 0, that occurs in the linear differential equation of χ (3) , actually corresponds to a remarkable property of selected elliptic curves, namely the occurrence of complex multiplication. The interpretation of complex multiplication for elliptic curves as complex fixed points of the selected generators of the renormalization group, namely isogenies of elliptic curves, is sketched. Most of the other singularities occurring in our multiple integrals are not related to complex multiplication situations, suggesting an interpretation in terms of (motivic) mathematical structures beyond the theory of elliptic curves

  7. Linear Matrix Inequalities for Analysis and Control of Linear Vector Second-Order Systems

    DEFF Research Database (Denmark)

    Adegas, Fabiano Daher; Stoustrup, Jakob

    2015-01-01

    the Lyapunov matrix and the system matrices by introducing matrix multipliers, which potentially reduce conservativeness in hard control problems. Multipliers facilitate the usage of parameter-dependent Lyapunov functions as certificates of stability of uncertain and time-varying vector second-order systems......SUMMARY Many dynamical systems are modeled as vector second-order differential equations. This paper presents analysis and synthesis conditions in terms of LMI with explicit dependence in the coefficient matrices of vector second-order systems. These conditions benefit from the separation between....... The conditions introduced in this work have the potential to increase the practice of analyzing and controlling systems directly in vector second-order form. Copyright © 2014 John Wiley & Sons, Ltd....

  8. Loop quantum cosmology and singularities.

    Science.gov (United States)

    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.

  9. A note on the time decay of solutions for the linearized Wigner-Poisson system

    KAUST Repository

    Gamba, Irene; Gualdani, Maria; Sparber, Christof

    2009-01-01

    We consider the one-dimensional Wigner-Poisson system of plasma physics, linearized around a (spatially homogeneous) Lorentzian distribution and prove that the solution of the corresponding linearized problem decays to zero in time. We also give

  10. New approach to solve fully fuzzy system of linear equations using ...

    Indian Academy of Sciences (India)

    Known example problems are solved to illustrate the efficacy and ... The concept of fuzzy set and fuzzy number were first introduced by Zadeh .... (iii) Fully fuzzy linear systems can be solved by linear programming approach, Gauss elim-.

  11. 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

  12. CFORM- LINEAR CONTROL SYSTEM DESIGN AND ANALYSIS: CLOSED FORM SOLUTION AND TRANSIENT RESPONSE OF THE LINEAR DIFFERENTIAL EQUATION

    Science.gov (United States)

    Jamison, J. W.

    1994-01-01

    CFORM was developed by the Kennedy Space Center Robotics Lab to assist in linear control system design and analysis using closed form and transient response mechanisms. The program computes the closed form solution and transient response of a linear (constant coefficient) differential equation. CFORM allows a choice of three input functions: the Unit Step (a unit change in displacement); the Ramp function (step velocity); and the Parabolic function (step acceleration). It is only accurate in cases where the differential equation has distinct roots, and does not handle the case for roots at the origin (s=0). Initial conditions must be zero. Differential equations may be input to CFORM in two forms - polynomial and product of factors. In some linear control analyses, it may be more appropriate to use a related program, Linear Control System Design and Analysis (KSC-11376), which uses root locus and frequency response methods. CFORM was written in VAX FORTRAN for a VAX 11/780 under VAX VMS 4.7. It has a central memory requirement of 30K. CFORM was developed in 1987.

  13. A singular value sensitivity approach to robust eigenstructure assignment

    DEFF Research Database (Denmark)

    Søgaard-Andersen, Per; Trostmann, Erik; Conrad, Finn

    1986-01-01

    A design technique for improving the feedback properties of multivariable state feedback systems designed using eigenstructure assignment is presented. Based on a singular value analysis of the feedback properties a design parameter adjustment procedure is outlined. This procedure allows...

  14. Evaluation of Linear and Non-Linear Control Schemes Applied to a Hydraulic Servo System

    DEFF Research Database (Denmark)

    Andersen, Torben Ole; Hansen, Michael Rygaard; Pedersen, Henrik Clemmensen

    2005-01-01

    Due to the innovation of low-cost electronics such as sensors, microcontrollers etc., the focus on highperformance motion control is increasing. This work focuses on position control of single-input single-output hydraulic servo-systems in general. A hydraulically actuated robotic manipulator...

  15. Practical Implementations of Advanced Process Control for Linear Systems

    DEFF Research Database (Denmark)

    Knudsen, Jørgen K . H.; Huusom, Jakob Kjøbsted; Jørgensen, John Bagterp

    2013-01-01

    This paper describes some practical problems encountered, when implementing Advanced Process Control, APC, schemes on linear processes. The implemented APC controllers discussed will be LQR, Riccati MPC and Condensed MPC controllers illustrated by simulation of the Four Tank Process and a lineari......This paper describes some practical problems encountered, when implementing Advanced Process Control, APC, schemes on linear processes. The implemented APC controllers discussed will be LQR, Riccati MPC and Condensed MPC controllers illustrated by simulation of the Four Tank Process...... on pilot plant equipment on the department of Chemical Engineering DTU Lyngby....

  16. 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.

  17. Smoothing identification of systems with small non-linearities

    Czech Academy of Sciences Publication Activity Database

    Kozánek, Jan; Piranda, J.

    2003-01-01

    Roč. 38, č. 1 (2003), s. 71-84 ISSN 0025-6455 R&D Projects: GA ČR GA101/00/1471 Institutional research plan: CEZ:AV0Z2076919 Keywords : identification * small non-linearities * smoothing methods Subject RIV: BI - Acoustics Impact factor: 0.237, year: 2003

  18. Estimation of Physical Parameters in Linear and Nonlinear Dynamic Systems

    DEFF Research Database (Denmark)

    Knudsen, Morten

    variance and confidence ellipsoid is demonstrated. The relation is based on a new theorem on maxima of an ellipsoid. The procedure for input signal design and physical parameter estimation is tested on a number of examples, linear as well as nonlinear and simulated as well as real processes, and it appears...

  19. Estimation of failure probabilities of linear dynamic systems by ...

    Indian Academy of Sciences (India)

    An iterative method for estimating the failure probability for certain time-variant reliability problems has been developed. In the paper, the focus is on the displacement response of a linear oscillator driven by white noise. Failure is then assumed to occur when the displacement response exceeds a critical threshold.

  20. Linear wave systems on n-D spatial domains

    NARCIS (Netherlands)

    Kurula, Mikael; Zwart, Heiko J.

    2015-01-01

    In this paper, we study the linear wave equation on an n-dimensional spatial domain.We show that there is a boundary triplet associated to the undamped wave equation. This enables us to characterise all boundary conditions for which the undamped wave equation possesses a unique solution