Generalized perturbation theory (GPT) methods. A heuristic approach
International Nuclear Information System (INIS)
Gandini, A.
1987-01-01
Wigner first proposed a perturbation theory as early as 1945 to study fundamental quantities such as the reactivity worths of different materials. The first formulation, CPT, for conventional perturbation theory is based on universal quantum mechanics concepts. Since that early conception, significant contributions have been made to CPT, in particular, Soodak, who rendered a heuristic interpretation of the adjoint function, (referred to as the GPT method for generalized perturbation theory). The author illustrates the GPT methodology in a variety of linear and nonlinear domains encountered in nuclear reactor analysis. The author begins with the familiar linear neutron field and then generalizes the methodology to other linear and nonlinear fields, using heuristic arguments. The author believes that the inherent simplicity and elegance of the heuristic derivation, although intended here for reactor physics problems might be usefully adopted in collateral fields and includes such examples
Generalized perturbation theory based on the method of cyclic characteristics
Energy Technology Data Exchange (ETDEWEB)
Assawaroongruengchot, M.; Marleau, G. [Institut de Genie Nucleaire, Departement de Genie Physique, Ecole Polytechnique de Montreal, 2900 Boul. Edouard-Montpetit, Montreal, Que. H3T 1J4 (Canada)
2006-07-01
A GPT algorithm for estimation of eigenvalues and reaction-rate ratios is developed for the neutron transport problems in 2D fuel assemblies with isotropic scattering. In our study the GPT formulation is based on the integral transport equations. The mathematical relationship between the generalized flux importance and generalized source importance functions is applied to transform the generalized flux importance transport equations into the integro-differential forms. The resulting adjoint and generalized adjoint transport equations are then solved using the method of cyclic characteristics (MOCC). Because of the presence of negative adjoint sources, a biasing/decontamination scheme is applied to make the generalized adjoint functions positive in such a way that it can be used for the multigroup re-balance technique. To demonstrate the efficiency of the algorithms, perturbative calculations are performed on a 17 x 17 PWR lattice. (authors)
Generalized perturbation theory based on the method of cyclic characteristics
International Nuclear Information System (INIS)
Assawaroongruengchot, M.; Marleau, G.
2006-01-01
A GPT algorithm for estimation of eigenvalues and reaction-rate ratios is developed for the neutron transport problems in 2D fuel assemblies with isotropic scattering. In our study the GPT formulation is based on the integral transport equations. The mathematical relationship between the generalized flux importance and generalized source importance functions is applied to transform the generalized flux importance transport equations into the integro-differential forms. The resulting adjoint and generalized adjoint transport equations are then solved using the method of cyclic characteristics (MOCC). Because of the presence of negative adjoint sources, a biasing/decontamination scheme is applied to make the generalized adjoint functions positive in such a way that it can be used for the multigroup re-balance technique. To demonstrate the efficiency of the algorithms, perturbative calculations are performed on a 17 x 17 PWR lattice. (authors)
Estimation of CANDU reactor zone controller level by generalized perturbation method
International Nuclear Information System (INIS)
Kim, Do Heon; Kim, Jong Kyung; Choi, Hang Bok; Roh, Gyu Hong; Yang, Won Sik
1998-01-01
The zone controller level change due to refueling operation has been studied using a generalized perturbation method. The generalized perturbation method provides sensitivity of zone power to individual refueling operation and incremental change of zone controller level. By constructing a system equation for each zone power, the zone controller level change was obtained. The details and a proposed model for future work are described
Atomic and magnetic configurational energetics by the generalized perturbation method
DEFF Research Database (Denmark)
Ruban, Andrei V.; Shallcross, Sam; Simak, S.I.
2004-01-01
in the framework of the Korringa-Kohn-Rostoker method within the atomic sphere and coherent potential approximations. This is demonstrated with calculations of ordering energies, short-range order parameters, and transition temperatures in the CuZn, CuAu, CuPd, and PtCo systems. Furthermore, we show that the GPM...
Approximate solution of generalized Ginzburg-Landau-Higgs system via homotopy perturbation method
Energy Technology Data Exchange (ETDEWEB)
Lu Juhong [School of Physics and Electromechanical Engineering, Shaoguan Univ., Guangdong (China); Dept. of Information Engineering, Coll. of Lishui Professional Tech., Zhejiang (China); Zheng Chunlong [School of Physics and Electromechanical Engineering, Shaoguan Univ., Guangdong (China); Shanghai Inst. of Applied Mathematics and Mechanics, Shanghai Univ., SH (China)
2010-04-15
Using the homotopy perturbation method, a class of nonlinear generalized Ginzburg-Landau-Higgs systems (GGLH) is considered. Firstly, by introducing a homotopic transformation, the nonlinear problem is changed into a system of linear equations. Secondly, by selecting a suitable initial approximation, the approximate solution with arbitrary degree accuracy to the generalized Ginzburg-Landau-Higgs system is derived. Finally, another type of homotopic transformation to the generalized Ginzburg-Landau-Higgs system reported in previous literature is briefly discussed. (orig.)
Generalized chiral perturbation theory
International Nuclear Information System (INIS)
Knecht, M.; Stern, J.
1994-01-01
The Generalized Chiral Perturbation Theory enlarges the framework of the standard χPT (Chiral Perturbation Theory), relaxing certain assumptions which do not necessarily follow from QCD or from experiment, and which are crucial for the usual formulation of the low energy expansion. In this way, experimental tests of the foundations of the standard χPT become possible. Emphasis is put on physical aspects rather than on formal developments of GχPT. (author). 31 refs
Nayfeh, Ali H
2008-01-01
1. Introduction 1 2. Straightforward Expansions and Sources of Nonuniformity 23 3. The Method of Strained Coordinates 56 4. The Methods of Matched and Composite Asymptotic Expansions 110 5. Variation of Parameters and Methods of Averaging 159 6. The Method of Multiple Scales 228 7. Asymptotic Solutions of Linear Equations 308 References and Author Index 387 Subject Index 417
Optimization of Candu fuel management with gradient methods using generalized perturbation theory
International Nuclear Information System (INIS)
Chambon, R.; Varin, E.; Rozon, D.
2005-01-01
CANDU fuel management problems are solved using time-average representation of the core. Optimization problems based on this representation have been defined in the early nineties. The mathematical programming using the generalized perturbation theory (GPT) that was developed has been implemented in the reactor code DONJON. The use of the augmented Lagrangian (AL) method is presented and evaluated in this paper. This approach is mandatory for new constraint problems. Combined with the classical Lemke method, it proves to be very efficient to reach optimal solution in a very limited number of iterations. (authors)
Generalized perturbation series
International Nuclear Information System (INIS)
Baird, L.C.; Stinchcomb, G.
1973-01-01
An approximate solution of the Green's function equation may be used to generate an exact solution of the Schroedinger equation. This is accomplished through an iterative procedure. The procedure is equivalent to a perturbation expansion if the approximate Green's function is exact with respect to some reference potential
Introduction to perturbation methods
Holmes, M
1995-01-01
This book is an introductory graduate text dealing with many of the perturbation methods currently used by applied mathematicians, scientists, and engineers. The author has based his book on a graduate course he has taught several times over the last ten years to students in applied mathematics, engineering sciences, and physics. The only prerequisite for the course is a background in differential equations. Each chapter begins with an introductory development involving ordinary differential equations. The book covers traditional topics, such as boundary layers and multiple scales. However, it also contains material arising from current research interest. This includes homogenization, slender body theory, symbolic computing, and discrete equations. One of the more important features of this book is contained in the exercises. Many are derived from problems of up- to-date research and are from a wide range of application areas.
Papasotiriou, P. J.; Geroyannis, V. S.
We implement Hartle's perturbation method to the computation of relativistic rigidly rotating neutron star models. The program has been written in SCILAB (© INRIA ENPC), a matrix-oriented high-level programming language. The numerical method is described in very detail and is applied to many models in slow or fast rotation. We show that, although the method is perturbative, it gives accurate results for all practical purposes and it should prove an efficient tool for computing rapidly rotating pulsars.
Perturbation methods for power and reactivity reconstruction
International Nuclear Information System (INIS)
Palmiotti, G.; Salvatores, M.; Estiot, J.C.; Broccoli, U.; Bruna, G.; Gomit, J.M.
1987-01-01
This paper deals with recent developments and applications in perturbation methods. Two types of methods are used. The first one is an explicit method, which allows the explicit reconstruction of a perturbed flux using a linear combination of a library of functions. In our application, these functions are the harmonics (i.e. the high order eigenfunctions of the system). The second type is based on the Generalized Perturbation Theory GPT and needs the calculation of an importance function for each integral parameter of interest. Recent developments of a particularly useful high order formulation allows to obtain satisfactory results also for very large perturbations
International Nuclear Information System (INIS)
Murray, J.J.
1976-07-01
It may be expected that solenoid magnets will be used in many storage ring experiments. Typically an insert would consist of a main solenoid at the interaction point with a symmetrical pair of compensating solenoids located somewhere between the main solenoid and the ends of the interaction region. The magnetic fields of such an insert may significantly affect storage ring performance. We suggest here a simple, systematic method for evaluation of the effects, which together with adequate design supervision and field measurements will help to prevent any serious operational problems that might result if significant perturbations went unnoticed. 5 refs
Energy Technology Data Exchange (ETDEWEB)
Mai, Sebastian; Marquetand, Philipp; González, Leticia [Institute of Theoretical Chemistry, University of Vienna, Währinger Str. 17, 1090 Vienna (Austria); Müller, Thomas, E-mail: th.mueller@fz-juelich.de [Institute for Advanced Simulation, Jülich Supercomputing Centre, Forschungszentrum Jülich, 52425 Jülich (Germany); Plasser, Felix [Interdisciplinary Center for Scientific Computing, University of Heidelberg, Im Neuenheimer Feld 368, 69120 Heidelberg (Germany); Lischka, Hans [Institute of Theoretical Chemistry, University of Vienna, Währinger Str. 17, 1090 Vienna (Austria); Department of Chemistry and Biochemistry, Texas Tech University, Lubbock, Texas 79409-1061 (United States)
2014-08-21
An efficient perturbational treatment of spin-orbit coupling within the framework of high-level multi-reference techniques has been implemented in the most recent version of the COLUMBUS quantum chemistry package, extending the existing fully variational two-component (2c) multi-reference configuration interaction singles and doubles (MRCISD) method. The proposed scheme follows related implementations of quasi-degenerate perturbation theory (QDPT) model space techniques. Our model space is built either from uncontracted, large-scale scalar relativistic MRCISD wavefunctions or based on the scalar-relativistic solutions of the linear-response-theory-based multi-configurational averaged quadratic coupled cluster method (LRT-MRAQCC). The latter approach allows for a consistent, approximatively size-consistent and size-extensive treatment of spin-orbit coupling. The approach is described in detail and compared to a number of related techniques. The inherent accuracy of the QDPT approach is validated by comparing cuts of the potential energy surfaces of acrolein and its S, Se, and Te analoga with the corresponding data obtained from matching fully variational spin-orbit MRCISD calculations. The conceptual availability of approximate analytic gradients with respect to geometrical displacements is an attractive feature of the 2c-QDPT-MRCISD and 2c-QDPT-LRT-MRAQCC methods for structure optimization and ab inito molecular dynamics simulations.
International Nuclear Information System (INIS)
Mai, Sebastian; Marquetand, Philipp; González, Leticia; Müller, Thomas; Plasser, Felix; Lischka, Hans
2014-01-01
An efficient perturbational treatment of spin-orbit coupling within the framework of high-level multi-reference techniques has been implemented in the most recent version of the COLUMBUS quantum chemistry package, extending the existing fully variational two-component (2c) multi-reference configuration interaction singles and doubles (MRCISD) method. The proposed scheme follows related implementations of quasi-degenerate perturbation theory (QDPT) model space techniques. Our model space is built either from uncontracted, large-scale scalar relativistic MRCISD wavefunctions or based on the scalar-relativistic solutions of the linear-response-theory-based multi-configurational averaged quadratic coupled cluster method (LRT-MRAQCC). The latter approach allows for a consistent, approximatively size-consistent and size-extensive treatment of spin-orbit coupling. The approach is described in detail and compared to a number of related techniques. The inherent accuracy of the QDPT approach is validated by comparing cuts of the potential energy surfaces of acrolein and its S, Se, and Te analoga with the corresponding data obtained from matching fully variational spin-orbit MRCISD calculations. The conceptual availability of approximate analytic gradients with respect to geometrical displacements is an attractive feature of the 2c-QDPT-MRCISD and 2c-QDPT-LRT-MRAQCC methods for structure optimization and ab inito molecular dynamics simulations
A generalized perturbation program for CANDU reactor
Energy Technology Data Exchange (ETDEWEB)
Kim, Do Heon; Kim, Jong Kyung [Hanyang University, Seoul (Korea, Republic of); Choi, Hang Bok; Roh, Gyu Hong [Korea Atomic Energy Research Institute, Taejon (Korea, Republic of); Yang, Won Sik [Chosun University, Kwangju (Korea, Republic of)
1999-12-31
A generalized perturbation program has been developed for the purpose of estimating zonal power variation of a CANDU reactor upon refueling operation. The forward and adjoint calculation modules of RFSP code were used to construct the generalized perturbation program. The numerical algorithm for the generalized adjoint flux calculation was verified by comparing the zone power estimates upon refueling with those of forward calculation. It was, however, noticed that the truncation error from the iteration process of the generalized adjoint flux is not negligible. 2 refs., 1 figs., 1 tab. (Author)
A generalized perturbation program for CANDU reactor
Energy Technology Data Exchange (ETDEWEB)
Kim, Do Heon; Kim, Jong Kyung [Hanyang University, Seoul (Korea, Republic of); Choi, Hang Bok; Roh, Gyu Hong [Korea Atomic Energy Research Institute, Taejon (Korea, Republic of); Yang, Won Sik [Chosun University, Kwangju (Korea, Republic of)
1998-12-31
A generalized perturbation program has been developed for the purpose of estimating zonal power variation of a CANDU reactor upon refueling operation. The forward and adjoint calculation modules of RFSP code were used to construct the generalized perturbation program. The numerical algorithm for the generalized adjoint flux calculation was verified by comparing the zone power estimates upon refueling with those of forward calculation. It was, however, noticed that the truncation error from the iteration process of the generalized adjoint flux is not negligible. 2 refs., 1 figs., 1 tab. (Author)
Advances in heuristically based generalized perturbation theory
International Nuclear Information System (INIS)
Gandini, A.
1994-01-01
A distinctive feature of heuristically based generalized perturbation theory methodology consists in the systematic use of importance conservation concepts. As well known, this use leads to fundamental reciprocity relationship. Instead, the alternative variational and differential one approaches make a consistent use of the properties and adjoint functions. The equivalence between the importance and the adjoint functions have been demonstrated in important cases. There are some instances, however, in which the commonly known operator governing the adjoint function are not adequate. In this paper ways proposed to generalize this rules, as adopted with the heuristic generalized perturbation theory methodology, are illustrated. When applied to the neutron/nuclide field characterizing the core evolution in a power reactor system, in which also an intensive control variable (ρ) is defined, these rules leas to an orthogonality relationship connected to this same control variable. A set of ρ-mode eigenfunctions may be correspondingly defined and an extended concept of reactivity (generalizing that commonly associated with the multiplication factor) proposed as more directly indicative of the controllability of a critical reactor system. (author). 25 refs
Implementation of static generalized perturbation theory for LWR design applications
International Nuclear Information System (INIS)
Byron, R.F.; White, J.R.
1987-01-01
A generalized perturbation theory (GPT) formulation is developed for application to light water reactor (LWR) design. The extensions made to standard generalized perturbation theory are the treatment of thermal-hydraulic and fission product poisoning feedbacks, and criticality reset. This formulation has been implemented into a standard LWR design code. The method is verified by comparing direct calculations with GPT calculations. Data are presented showing that feedback effects need to be considered when using GPT for LWR problems. Some specific potential applications of this theory to the field of LWR design are discussed
Generalized perturbation theory in DRAGON: application to CANDU cell calculations
International Nuclear Information System (INIS)
Courau, T.; Marleau, G.
2001-01-01
Generalized perturbation theory (GPT) in neutron transport is a means to evaluate eigenvalue and reaction rate variations due to small changes in the reactor properties (macroscopic cross sections). These variations can be decomposed in two terms: a direct term corresponding to the changes in the cross section themselves and an indirect term that takes into account the perturbations in the neutron flux. As we will show, taking into account the indirect term using a GPT method is generally straight forward since this term is the scalar product of the unperturbed generalized adjoint with the product of the variation of the transport operator and the unperturbed flux. In the case where the collision probability (CP) method is used to solve the transport equation, evaluating the perturbed transport operator involves calculating the variations in the CP matrix for each change in the reactor properties. Because most of the computational effort is dedicated to the CP matrix calculation the gains expected form the GPT method would therefore be annihilated. Here we will present a technique to approximate the variations in the CP matrices thereby replacing the variations in the transport operator with source term variations. We will show that this approximation yields errors fully compatible with the standard generalized perturbation theory errors. Results for 2D CANDU cell calculations will be presented. (author)
Modified method of perturbed stationary states. I
International Nuclear Information System (INIS)
Green, T.A.
1978-10-01
The reaction coordinate approach of Mittleman is used to generalize the method of Perturbed Stationary States. A reaction coordinate is defined for each state in the scattering expansion in terms of parameters which depend on the internuclear separation. These are to be determined from a variational principle described by Demkov. The variational result agrees with that of Bates and McCarroll in the limit of separated atoms, but is generally different elsewhere. The theory is formulated for many-electron systems, and the construction of the scattering expansion is discussed for simple one-, two-, and three-electron systsm. The scattering expansion and the Lagrangian for the radial scattering functions are given in detail for a heteronuclear one-electron system. 2 figures
Fuel management optimization based on generalized perturbation theory
International Nuclear Information System (INIS)
White, J.R.; Chapman, D.M.; Biswas, D.
1986-01-01
A general methodology for optimization of assembly shuffling and burnable poison (BP) loadings for LWR reload design has been developed. The uniqueness of this approach lies in the coupling of Generalized Perturbation Theory (GPT) methods and standard Integer Programming (IP) techniques. An IP algorithm can simulate the discrete nature of the fuel shuffling and BP loading problems, and the use of GPT sensitivity data provides an efficient means for modeling the behavior of the important core performance parameters. The method is extremely flexible since the choice of objective function and the number and mix of constraints depend only on the ability of GPT to determine the appropriate sensitivity functions
Perturbations of spacetimes in general relativity
International Nuclear Information System (INIS)
Walker, M.
1977-01-01
In the case of gravitation, the differential equation of interest is Einstein's equation. Being a tensor equation, this is rather complicated. Moreover, gravitational theory throws up its own peculiar difficulty, the lack of a fixed background space on which to expand things. The plan of these lecture notes is therefore to discuss linear vs. nonlinear differential equations, perturbation theory for ordinary differential equations (ODE), partial differential equations (PDE), and finally, spacetimes. In this way, the basic ideas can be introduced without interference from non-essential complications. (orig.) [de
Perturbation method for fuel evolution and shuffling analysis
International Nuclear Information System (INIS)
Gandini, A.
1987-01-01
A perturbation methodology is described by which the behaviour of a reactor system during burnup can be analyzed making use of Generalized Perturbation Theory (GPT) codes already available in the linear domain. Typical quantities that can be studied with the proposed methodology are the amount of a specified material at the end of cycle, the fluence in a specified region, the residual reactivity at end of reactor life cycle. The potentiality of the method for fuel shuffling studies is also described. (author)
Application of generalized perturbation theory to flux disadvantage factor calculations
International Nuclear Information System (INIS)
Sallam, O.H.; Akimov, I.S.; Naguib, K.; Hamouda, I.
1979-01-01
The possibility of using the generalized perturbation theory to calculate the perturbation of the flux disadvantage factors of reactor cell, resulting from the variation of the cell parameters, is studied. For simplicity the one-group diffusion approximation is considered. All necessary equations are derived for variations both of the cell dimensions. Numerical results are presented in the paper
On-Shell Methods in Perturbative QCD
International Nuclear Information System (INIS)
Bern, Zvi; Dixon, Lance J.; Kosower, David A.
2007-01-01
We review on-shell methods for computing multi-parton scattering amplitudes in perturbative QCD, utilizing their unitarity and factorization properties. We focus on aspects which are useful for the construction of one-loop amplitudes needed for phenomenological studies at the Large Hadron Collider
Cosmological perturbations in a family of deformations of general relativity
International Nuclear Information System (INIS)
Krasnov, Kirill; Shtanov, Yuri
2010-01-01
We study linear cosmological perturbations in a previously introduced family of deformations of general relativity characterized by the absence of new degrees of freedom. The homogeneous and isotropic background in this class of theories is unmodified and is described by the usual Friedmann equations. The theory of cosmological perturbations is modified and the relevant deformation parameter has the dimension of length. Gravitational perturbations of the scalar type can be described by a certain relativistic potential related to the matter perturbations just as in general relativity. A system of differential equations describing the evolution of this potential and of the stress-energy density perturbations is obtained. We find that the evolution of scalar perturbations proceeds with a modified effective time-dependent speed of sound, which, contrary to the case of general relativity, does not vanish even at the matter-dominated stage. In a broad range of values of the length parameter controlling the deformation, a specific transition from the regime of modified gravity to the regime of general relativity in the evolution of scalar perturbations takes place during the radiation domination. In this case, the resulting power spectrum of perturbations in radiation and dark matter is suppressed on the comoving spatial scales that enter the Hubble radius before this transition. We estimate the bounds on the deformation parameter for which this suppression does not lead to observable consequences. Evolution of scalar perturbations at the inflationary stage is modified but very slightly and the primordial spectrum generated during inflation is not noticeably different from the one obtained in general relativity
Constraints on stress-energy perturbations in general relativity
International Nuclear Information System (INIS)
Traschen, J.
1985-01-01
Conditions are found for the existence of integral constraints on stress-energy perturbations in general relativity. The integral constraints can be thought of as a general-relativistic generalization of the conservation of energy and momentum of matter perturbations in special relativity. The constraints are stated in terms of a vector field V, and the Robertson-Walker spacetimes are shown to have such constraint vectors. Although in general V is not a Killing vector, in a vacuum spacetime the constraint vectors are precisely the Killing vectors
Reactor perturbation calculations by Monte Carlo methods
International Nuclear Information System (INIS)
Gubbins, M.E.
1965-09-01
Whilst Monte Carlo methods are useful for reactor calculations involving complicated geometry, it is difficult to apply them to the calculation of perturbation worths because of the large amount of computing time needed to obtain good accuracy. Various ways of overcoming these difficulties are investigated in this report, with the problem of estimating absorbing control rod worths particularly in mind. As a basis for discussion a method of carrying out multigroup reactor calculations by Monte Carlo methods is described. Two methods of estimating a perturbation worth directly, without differencing two quantities of like magnitude, are examined closely but are passed over in favour of a third method based on a correlation technique. This correlation method is described, and demonstrated by a limited range of calculations for absorbing control rods in a fast reactor. In these calculations control rod worths of between 1% and 7% in reactivity are estimated to an accuracy better than 10% (3 standard errors) in about one hour's computing time on the English Electric KDF.9 digital computer. (author)
Methods and applications of analytical perturbation theory
International Nuclear Information System (INIS)
Kirchgraber, U.; Stiefel, E.
1978-01-01
This monograph on perturbation theory is based on various courses and lectures held by the authors at the ETH, Zurich and at the University of Texas, Austin. Its principal intention is to inform application-minded mathematicians, physicists and engineers about recent developments in this field. The reader is not assumed to have mathematical knowledge beyond what is presented in standard courses on analysis and linear algebra. Chapter I treats the transformations of systems of differential equations and the integration of perturbed systems in a formal way. These tools are applied in Chapter II to celestial mechanics and to the theory of tops and gyroscopic motion. Chapter III is devoted to the discussion of Hamiltonian systems of differential equations and exposes the algebraic aspects of perturbation theory showing also the necessary modifications of the theory in case of singularities. The last chapter gives the mathematical justification for the methods developed in the previous chapters and investigates important questions such as error estimations for the solutions and asymptotic stability. Each chapter ends with useful comments and an extensive reference to the original literature. (HJ) [de
Generalizing genetical genomics: getting added value from environmental perturbation.
Li, Yang; Breitling, Rainer; Jansen, Ritsert C
2008-10-01
Genetical genomics is a useful approach for studying the effect of genetic perturbations on biological systems at the molecular level. However, molecular networks depend on the environmental conditions and, thus, a comprehensive understanding of biological systems requires studying them across multiple environments. We propose a generalization of genetical genomics, which combines genetic and sensibly chosen environmental perturbations, to study the plasticity of molecular networks. This strategy forms a crucial step toward understanding why individuals respond differently to drugs, toxins, pathogens, nutrients and other environmental influences. Here we outline a strategy for selecting and allocating individuals to particular treatments, and we discuss the promises and pitfalls of the generalized genetical genomics approach.
Evolution of curvature perturbation in generalized gravity theories
International Nuclear Information System (INIS)
Matsuda, Tomohiro
2009-01-01
Using the cosmological perturbation theory in terms of the δN formalism, we find the simple formulation of the evolution of the curvature perturbation in generalized gravity theories. Compared with the standard gravity theory, a crucial difference appears in the end-boundary of the inflationary stage, which is due to the non-ideal form of the energy-momentum tensor that depends explicitly on the curvature scalar. Recent study shows that ultraviolet-complete quantum theory of gravity (Horava-Lifshitz gravity) can be approximated by using a generalized gravity action. Our paper may give an important step in understanding the evolution of the curvature perturbation during inflation, where the energy-momentum tensor may not be given by the ideal form due to the corrections from the fundamental theory.
A Theory of the Perturbed Consumer with General Budgets
DEFF Research Database (Denmark)
McFadden, Daniel L; Fosgerau, Mogens
We consider demand systems for utility-maximizing consumers facing general budget constraints whose utilities are perturbed by additive linear shifts in marginal utilities. Budgets are required to be compact but are not required to be convex. We define demand generating functions (DGF) whose...... subgradients with respect to these perturbations are convex hulls of the utility-maximizing demands. We give necessary as well as sufficient conditions for DGF to be consistent with utility maximization, and establish under quite general conditions that utility-maximizing demands are almost everywhere single......-valued and smooth in their arguments. We also give sufficient conditions for integrability of perturbed demand. Our analysis provides a foundation for applications of consumer theory to problems with nonlinear budget constraints....
A Generalized and Refined Perturbed Version of Ostrowski Type Inequalities
Directory of Open Access Journals (Sweden)
M. Z. Sarikaya
2017-01-01
Full Text Available In this paper, we first obtain a new identity for twice differentiable mappings. Then, we establish generalized and improved perturbed version of Ostrowski type inequalities for functions whose derivatives are of bounded variation or second derivatives are either bounded or Lipschitzian.
Generalized perturbation theory using two-dimensional, discrete ordinates transport theory
International Nuclear Information System (INIS)
Childs, R.L.
1979-01-01
Perturbation theory for changes in linear and bilinear functionals of the forward and adjoint fluxes in a critical reactor has been implemented using two-dimensional discrete ordinates transport theory. The computer program DOT IV was modified to calculate the generalized functions Λ and Λ*. Demonstration calculations were performed for changes in a reaction-rate ratio and a reactivity worth caused by system perturbations. The perturbation theory predictions agreed with direct calculations to within about 2%. A method has been developed for calculating higher lambda eigenvalues and eigenfunctions using techniques similar to those developed for generalized functions. Demonstration calculations have been performed to obtain these eigenfunctions
New Methods in Non-Perturbative QCD
Energy Technology Data Exchange (ETDEWEB)
Unsal, Mithat [North Carolina State Univ., Raleigh, NC (United States)
2017-01-31
In this work, we investigate the properties of quantum chromodynamics (QCD), by using newly developing mathematics and physics formalisms. Almost all of the mass in the visible universe emerges from a quantum chromodynamics (QCD), which has a completely negligible microscopic mass content. An intimately related issue in QCD is the quark confinement problem. Answers to non-perturbative questions in QCD remained largely elusive despite much effort over the years. It is also believed that the usual perturbation theory is inadequate to address these kinds of problems. Perturbation theory gives a divergent asymptotic series (even when the theory is properly renormalized), and there are non-perturbative phenomena which never appear at any order in perturbation theory. Recently, a fascinating bridge between perturbation theory and non-perturbative effects has been found: a formalism called resurgence theory in mathematics tells us that perturbative data and non-perturbative data are intimately related. Translating this to the language of quantum field theory, it turns out that non-perturbative information is present in a coded form in perturbation theory and it can be decoded. We take advantage of this feature, which is particularly useful to understand some unresolved mysteries of QCD from first principles. In particular, we use: a) Circle compactifications which provide a semi-classical window to study confinement and mass gap problems, and calculable prototypes of the deconfinement phase transition; b) Resurgence theory and transseries which provide a unified framework for perturbative and non-perturbative expansion; c) Analytic continuation of path integrals and Lefschetz thimbles which may be useful to address sign problem in QCD at finite density.
A general-model-space diagrammatic perturbation theory
International Nuclear Information System (INIS)
Hose, G.; Kaldor, U.
1980-01-01
A diagrammatic many-body perturbation theory applicable to arbitrary model spaces is presented. The necessity of having a complete model space (all possible occupancies of the partially-filled shells) is avoided. This requirement may be troublesome for systems with several well-spaced open shells, such as most atomic and molecular excited states, as a complete model space spans a very broad energy range and leaves out states within that range, leading to poor or no convergence of the perturbation series. The method presented here would be particularly useful for such states. The solution of a model problem (He 2 excited Σ + sub(g) states) is demonstrated. (Auth.)
Chiral perturbation theory for nucleon generalized parton distributions
Energy Technology Data Exchange (ETDEWEB)
Diehl, M. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Manashov, A. [Regensburg Univ. (Germany). Inst. fuer Physik 1 - Theoretische Physik]|[Sankt-Petersburg State Univ. (Russian Federation). Dept. of Theoretical Physics; Schaefer, A. [Regensburg Univ. (Germany). Inst. fuer Physik 1 - Theoretische Physik
2006-08-15
We analyze the moments of the isosinglet generalized parton distributions H, E, H, E of the nucleon in one-loop order of heavy-baryon chiral perturbation theory. We discuss in detail the construction of the operators in the effective theory that are required to obtain all corrections to a given order in the chiral power counting. The results will serve to improve the extrapolation of lattice results to the chiral limit. (orig.)
Canonical perturbation theory in linearized general relativity theory
International Nuclear Information System (INIS)
Gonzales, R.; Pavlenko, Yu.G.
1986-01-01
Canonical perturbation theory in linearized general relativity theory is developed. It is shown that the evolution of arbitrary dynamic value, conditioned by the interaction of particles, gravitation and electromagnetic fields, can be presented in the form of a series, each member of it corresponding to the contribution of certain spontaneous or induced process. The main concepts of the approach are presented in the approximation of a weak gravitational field
Existence of Generalized Homoclinic Solutions of Lotka-Volterra System under a Small Perturbation
Mi, Yuzhen
2016-01-01
This paper investigates Lotka-Volterra system under a small perturbation vxx=-μ(1-a2u-v)v+ϵf(ϵ,v,vx,u,ux), uxx=-(1-u-a1v)u+ϵg(ϵ,v,vx,u,ux). By the Fourier series expansion technique method, the fixed point theorem, the perturbation theorem, and the reversibility, we prove that near μ=0 the system has a generalized homoclinic solution exponentially approaching a periodic solution.
Existence of Generalized Homoclinic Solutions of Lotka-Volterra System under a Small Perturbation
Directory of Open Access Journals (Sweden)
Yuzhen Mi
2016-01-01
Full Text Available This paper investigates Lotka-Volterra system under a small perturbation vxx=-μ(1-a2u-vv+ϵf(ϵ,v,vx,u,ux, uxx=-(1-u-a1vu+ϵg(ϵ,v,vx,u,ux. By the Fourier series expansion technique method, the fixed point theorem, the perturbation theorem, and the reversibility, we prove that near μ=0 the system has a generalized homoclinic solution exponentially approaching a periodic solution.
Neoclassical toroidal viscosity in perturbed equilibria with general tokamak geometry
Energy Technology Data Exchange (ETDEWEB)
Logan, Nikolas C.; Park, Jong-Kyu; Kim, Kimin; Wang, Zhirui [Plasma Physics Laboratory, Princeton University, Princeton, New Jersey 08543 (United States); Berkery, John W. [Department of Applied Physics and Applied Mathematics, Columbia University, New York, New York 10027 (United States)
2013-12-15
This paper presents a calculation of neoclassical toroidal viscous torque independent of large-aspect-ratio expansions across kinetic regimes. The Perturbed Equilibrium Nonambipolar Transport (PENT) code was developed for this purpose, and is compared to previous combined regime models as well as regime specific limits and a drift kinetic δf guiding center code. It is shown that retaining general expressions, without circular large-aspect-ratio or other orbit approximations, can be important at experimentally relevant aspect ratio and shaping. The superbanana plateau, a kinetic resonance effect recently recognized for its relevance to ITER, is recovered by the PENT calculations and shown to require highly accurate treatment of geometric effects.
The General Necessary Condition for the Validity of Dirac's Transition Perturbation Theory
Quang, Nguyen Vinh
1996-01-01
For the first time, from the natural requirements for the successive approximation the general necessary condition of validity of the Dirac's method is explicitly established. It is proved that the conception of 'the transition probability per unit time' is not valid. The 'super-platinium rules' for calculating the transition probability are derived for the arbitrarily strong time-independent perturbation case.
International Nuclear Information System (INIS)
Franca Walter, F.L.; Alvim, A.C.M.; Silva, F.C. da; Melo e Frutuoso, P.F.
1995-01-01
The application of the GPT methodology to a reliability engineering problem of great practical interest is discussed: that of the analysis of the influence of the demand rate on the accident rate of a process plant equipped with a single protective channel. This problem has been solved in the literature by traditional methods, that is, for each demand rate value the system of differential equations that governs the system behavior (derived from a Markovian reliability model) is solved and the resulting points are employed to generate the desired curve. This sensitivity analysis has been performed by means of a GPT approach in order to show how it could simplify the calculations. Although an analytical solution is available for the above equations, the application of the GPT approach needed the solution of the system for a few points (reference solutions) and the results agree very well with those published. (author). 9 refs, 4 figs
Small-sample-worth perturbation methods
International Nuclear Information System (INIS)
1985-01-01
It has been assumed that the perturbed region, R/sub p/, is large enough so that: (1) even without a great deal of biasing there is a substantial probability that an average source-neutron will enter it; and (2) once having entered, the neutron is likely to make several collisions in R/sub p/ during its lifetime. Unfortunately neither assumption is valid for the typical configurations one encounters in small-sample-worth experiments. In such experiments one measures the reactivity change which is induced when a very small void in a critical assembly is filled with a sample of some test-material. Only a minute fraction of the fission-source neutrons ever gets into the sample and, of those neutrons that do, most emerge uncollided. Monte Carlo small-sample perturbations computations are described
A Parameter Robust Method for Singularly Perturbed Delay Differential Equations
Directory of Open Access Journals (Sweden)
Erdogan Fevzi
2010-01-01
Full Text Available Uniform finite difference methods are constructed via nonstandard finite difference methods for the numerical solution of singularly perturbed quasilinear initial value problem for delay differential equations. A numerical method is constructed for this problem which involves the appropriate Bakhvalov meshes on each time subinterval. The method is shown to be uniformly convergent with respect to the perturbation parameter. A numerical example is solved using the presented method, and the computed result is compared with exact solution of the problem.
Performance prediction of electrohydrodynamic thrusters by the perturbation method
International Nuclear Information System (INIS)
Shibata, H.; Watanabe, Y.; Suzuki, K.
2016-01-01
In this paper, we present a novel method for analyzing electrohydrodynamic (EHD) thrusters. The method is based on a perturbation technique applied to a set of drift-diffusion equations, similar to the one introduced in our previous study on estimating breakdown voltage. The thrust-to-current ratio is generalized to represent the performance of EHD thrusters. We have compared the thrust-to-current ratio obtained theoretically with that obtained from the proposed method under atmospheric air conditions, and we have obtained good quantitative agreement. Also, we have conducted a numerical simulation in more complex thruster geometries, such as the dual-stage thruster developed by Masuyama and Barrett [Proc. R. Soc. A 469, 20120623 (2013)]. We quantitatively clarify the fact that if the magnitude of a third electrode voltage is low, the effective gap distance shortens, whereas if the magnitude of the third electrode voltage is sufficiently high, the effective gap distance lengthens.
Developing feasible loading patterns using perturbation theory methods
International Nuclear Information System (INIS)
White, J.R.; Avila, K.M.
1990-01-01
This work illustrates an approach to core reload design that combines the power of integer programming with the efficiency of generalized perturbation theory. The main use of the method is as a tool to help the design engineer identify feasible loading patterns with minimum time and effort. The technique is highly successful for the burnable poison (BP) loading problem, but the unpredictable behavior of the branch-and-bound algorithm degrades overall performance for large problems. Unfortunately, the combined fuel shuffling plus BP optimization problem falls into this latter classification. Overall, however, the method shows great promise for significantly reducing the manpower time required for the reload design process. And it may even give the further benefit of better designs and improved performance
Exact-to-precision generalized perturbation theory for source-driven systems
International Nuclear Information System (INIS)
Wang Congjian; Abdel-Khalik, Hany S.
2011-01-01
Highlights: ► We present a new development in higher order generalized perturbation theory. ► The method addresses the explosion in the flux phase space, input parameters, and responses. ► The method hybridizes first-order GPT and proper orthogonal decomposition snapshots method. ► A simplified 1D and realistic 2D assembly models demonstrate applicability of the method. ► The accuracy of the method is compared to exact direct perturbations and first-order GPT. - Abstract: Presented in this manuscript are new developments to perturbation theory which are intended to extend its applicability to estimate, with quantifiable accuracy, the exact variations in all responses calculated by the model with respect to all possible perturbations in the model's input parameters. The new developments place high premium on reducing the associated computational overhead in order to enable the use of perturbation theory in routine reactor design calculations. By way of examples, these developments could be employed in core simulation to accurately estimate the few-group cross-sections variations resulting from perturbations in neutronics and thermal-hydraulics core conditions. These variations are currently being described using a look-up table approach, where thousands of assembly calculations are performed to capture few-group cross-sections variations for the downstream core calculations. Other applications include the efficient evaluation of surrogates for applications that require repeated model runs such as design optimization, inverse studies, uncertainty quantification, and online core monitoring. The theoretical background of these developments applied to source-driven systems and supporting numerical experiments are presented in this manuscript. Extension to eigenvalue problems will be presented in a future article.
Solitary wave solution to a singularly perturbed generalized Gardner ...
Indian Academy of Sciences (India)
2017-03-24
Mar 24, 2017 ... Abstract. This paper is concerned with the existence of travelling wave solutions to a singularly perturbed gen- eralized Gardner equation with nonlinear terms of any order. By using geometric singular perturbation theory and based on the relation between solitary wave solution and homoclinic orbits of the ...
Perturbative methods applied for sensitive coefficients calculations in thermal-hydraulic systems
International Nuclear Information System (INIS)
Andrade Lima, F.R. de
1993-01-01
The differential formalism and the Generalized Perturbation Theory (GPT) are applied to sensitivity analysis of thermal-hydraulics problems related to pressurized water reactor cores. The equations describing the thermal-hydraulic behavior of these reactors cores, used in COBRA-IV-I code, are conveniently written. The importance function related to the response of interest and the sensitivity coefficient of this response with respect to various selected parameters are obtained by using Differential and Generalized Perturbation Theory. The comparison among the results obtained with the application of these perturbative methods and those obtained directly with the model developed in COBRA-IV-I code shows a very good agreement. (author)
Generalized polarizabilities of the nucleon in baryon chiral perturbation theory
Energy Technology Data Exchange (ETDEWEB)
Lensky, Vadim [Johannes Gutenberg Universitaet Mainz, Institut fuer Kernphysik, Cluster of Excellence PRISMA, Mainz (Germany); Institute for Theoretical and Experimental Physics, Moscow (Russian Federation); National Research Nuclear University MEPhI (Moscow Engineering Physics Institute), Moscow (Russian Federation); Pascalutsa, Vladimir; Vanderhaeghen, Marc [Johannes Gutenberg Universitaet Mainz, Institut fuer Kernphysik, Cluster of Excellence PRISMA, Mainz (Germany)
2017-02-15
The nucleon generalized polarizabilities (GPs), probed in virtual Compton scattering (VCS), describe the spatial distribution of the polarization density in a nucleon. They are accessed experimentally via the process of electron-proton bremsstrahlung (ep → epγ) at electron-beam facilities, such as MIT-Bates, CEBAF (Jefferson Lab), and MAMI (Mainz). We present the calculation of the nucleon GPs and VCS observables at next-to-leading order in baryon chiral perturbation theory (BχPT), and confront the results with the empirical information. At this order our results are predictions, in the sense that all the parameters are well known from elsewhere. Within the relatively large uncertainties of our calculation we find good agreement with the experimental observations of VCS and the empirical extractions of the GPs. We find large discrepancies with previous chiral calculations - all done in heavy-baryon χPT (HBχPT) - and discuss the differences between BχPT and HBχPT responsible for these discrepancies. (orig.)
Stringy horizons and generalized FZZ duality in perturbation theory
Energy Technology Data Exchange (ETDEWEB)
Giribet, Gaston [Martin Fisher School of Physics, Brandeis University,Waltham, Massachusetts 02453 (United States); Departamento de Física, Universidad de Buenos Aires FCEN-UBA and IFIBA-CONICET,Ciudad Universitaria, Pabellón I, 1428, Buenos Aires (Argentina)
2017-02-14
We study scattering amplitudes in two-dimensional string theory on a black hole bakground. We start with a simple derivation of the Fateev-Zamolodchikov-Zamolodchikov (FZZ) duality, which associates correlation functions of the sine-Liouville integrable model on the Riemann sphere to tree-level string amplitudes on the Euclidean two-dimensional black hole. This derivation of FZZ duality is based on perturbation theory, and it relies on a trick originally due to Fateev, which involves duality relations between different Selberg type integrals. This enables us to rewrite the correlation functions of sine-Liouville theory in terms of a special set of correlators in the gauged Wess-Zumino-Witten (WZW) theory, and use this to perform further consistency checks of the recently conjectured Generalized FZZ (GFZZ) duality. In particular, we prove that n-point correlation functions in sine-Liouville theory involving n−2 winding modes actually coincide with the correlation functions in the SL(2,ℝ)/U(1) gauged WZW model that include n−2 oscillator operators of the type described by Giveon, Itzhaki and Kutasov in reference https://www.doi.org/10.1007/JHEP10(2016)157. This proves the GFZZ duality for the case of tree level maximally winding violating n-point amplitudes with arbitrary n. We also comment on the connection between GFZZ and other marginal deformations previously considered in the literature.
Energy Technology Data Exchange (ETDEWEB)
Bozkaya, Uğur, E-mail: ugur.bozkaya@atauni.edu.tr [Department of Chemistry, Atatürk University, Erzurum 25240, Turkey and Department of Chemistry, Middle East Technical University, Ankara 06800 (Turkey)
2014-09-28
General analytic gradient expressions (with the frozen-core approximation) are presented for density-fitted post-HF methods. An efficient implementation of frozen-core analytic gradients for the second-order Møller–Plesset perturbation theory (MP2) with the density-fitting (DF) approximation (applying to both reference and correlation energies), which is denoted as DF-MP2, is reported. The DF-MP2 method is applied to a set of alkanes, conjugated dienes, and noncovalent interaction complexes to compare the computational cost of single point analytic gradients with MP2 with the resolution of the identity approach (RI-MP2) [F. Weigend and M. Häser, Theor. Chem. Acc. 97, 331 (1997); R. A. Distasio, R. P. Steele, Y. M. Rhee, Y. Shao, and M. Head-Gordon, J. Comput. Chem. 28, 839 (2007)]. In the RI-MP2 method, the DF approach is used only for the correlation energy. Our results demonstrate that the DF-MP2 method substantially accelerate the RI-MP2 method for analytic gradient computations due to the reduced input/output (I/O) time. Because in the DF-MP2 method the DF approach is used for both reference and correlation energies, the storage of 4-index electron repulsion integrals (ERIs) are avoided, 3-index ERI tensors are employed instead. Further, as in case of integrals, our gradient equation is completely avoid construction or storage of the 4-index two-particle density matrix (TPDM), instead we use 2- and 3-index TPDMs. Hence, the I/O bottleneck of a gradient computation is significantly overcome. Therefore, the cost of the generalized-Fock matrix (GFM), TPDM, solution of Z-vector equations, the back transformation of TPDM, and integral derivatives are substantially reduced when the DF approach is used for the entire energy expression. Further application results show that the DF approach introduce negligible errors for closed-shell reaction energies and equilibrium bond lengths.
A perturbation method for dark solitons based on a complete set of the squared Jost solutions
International Nuclear Information System (INIS)
Ao Shengmei; Yan Jiaren
2005-01-01
A perturbation method for dark solitons is developed, which is based on the construction and the rigorous proof of the complete set of squared Jost solutions. The general procedure solving the adiabatic solution of perturbed nonlinear Schroedinger + equation, the time-evolution equation of dark soliton parameters and a formula for calculating the first-order correction are given. The method can also overcome the difficulties resulting from the non-vanishing boundary condition
Generalized perturbation theory error control within PWR core-loading pattern optimization
International Nuclear Information System (INIS)
Imbriani, J.S.; Turinsky, P.J.; Kropaczek, D.J.
1995-01-01
The fuel management optimization code FORMOSA-P has been developed to determine the family of near-optimum loading patterns for PWR reactors. The code couples the optimization technique of simulated annealing (SA) with a generalized perturbation theory (GPT) model for evaluating core physics characteristics. To ensure the accuracy of the GPT predictions, as well as to maximize the efficient of the SA search, a GPT error control method has been developed
Generalizing genetical genomics : getting added value from environmental perturbation
Li, Yang; Breitling, Rainer; Jansen, Ritsert C.
2008-01-01
Genetical genomics is a useful approach for studying the effect of genetic perturbations on biological systems at the molecular level. However, molecular networks depend on the environmental conditions and, thus, a comprehensive understanding of biological systems requires studying them across
On the resolvents methods in quantum perturbation calculations
International Nuclear Information System (INIS)
Burzynski, A.
1979-01-01
This paper gives a systematic review of resolvent methods in quantum perturbation calculations. The case of discrete spectrum of hamiltonian is considered specially (in the literature this is the fewest considered case). The topics of calculations of quantum transitions by using of the resolvent formalism, quantum transitions between states from particular subspaces, the shifts of energy levels, are shown. The main ideas of stationary perturbation theory developed by Lippmann and Schwinger are considered too. (author)
International Nuclear Information System (INIS)
Kates, R.E.
1979-01-01
This thesis shows that a small body with possibly strong internal gravity moves through an empty region of a curved, and not necessarily asymptotically flat, external spacetime on an approximate geodesic. By approximate geodesic, the following is meant: Suppose the ratio epsilon = m/L 1 - where m is the body's mass and L is a curvature reference length of the external field - is a small parameter. Then the body's worldline deviates from a geodesic only by distances of at most THETA(epsilon) L over times of order L. The worldline is calculated directly from the Einstein field equation using a singular perturbation technique that has been generalized from the method of matched asymptotic expansions. The need for singular perturbation techniques has long been appreciated in fluid mechanics, where they are now standard procedure in problems in which the straightforward expansion in powers of a small parameter fails to give a correct qualitative picture. In part I of this thesis, singular perturbations on manifolds are formulated in a coordinate-free way suitable for treating problems in general relativity and other field theories. Most importantly for this thesis, the coordinate-free formulation of singular perturbations given in part I is essential for treatment of the problem of motion in part II
International Nuclear Information System (INIS)
Santos, Adimir dos; Borges, A.A.
2000-01-01
A new method for the calculation of sensitivity coefficients is developed. The new method is a combination of two methodologies used for calculating these coefficients, which are the differential and the generalized perturbation theory methods. The proposed method utilizes as integral parameter the average flux in an arbitrary region of the system. Thus, the sensitivity coefficient contains only the component corresponding to the neutron flux. To obtain the new sensitivity coefficient, the derivates of the integral parameter, φ(ξ), with respect to σ are calculated using the perturbation method and the functional derivates of this generic integral parameter with respect to σ and φ are calculated using the differential method. The new method merges the advantages of the differential and generalized perturbation theory methods and eliminates their disadvantages. (author)
Perturbation method for periodic solutions of nonlinear jerk equations
International Nuclear Information System (INIS)
Hu, H.
2008-01-01
A Lindstedt-Poincare type perturbation method with bookkeeping parameters is presented for determining accurate analytical approximate periodic solutions of some third-order (jerk) differential equations with cubic nonlinearities. In the process of the solution, higher-order approximate angular frequencies are obtained by Newton's method. A typical example is given to illustrate the effectiveness and simplicity of the proposed method
A semi perturbative method for QED
Jora, Renata; Schechter, Joseph
2014-01-01
We compute the QED beta function using a new method of functional integration. It turns out that in this procedure the beta function contains only the first two orders coefficients and thus corresponds to a new renormalization scheme, long time supposed to exist.
International Nuclear Information System (INIS)
Moore, B.R.; Turinsky, P.J.
1998-01-01
Boiling water reactor (BWR) loading pattern assessment requires solving the two-group, nodal form of the neutron diffusion equation and drift-flux form of the fluid equations simultaneously because these equation sets are strongly coupled via nonlinear feedback. To reduce the computational burden associated with the calculation of the core attributes (that is, core eigenvalue and thermal margins) of a perturbed BWR loading pattern, the analytical and numerical aspects of a higher order generalized perturbation theory (GPT) method, which correctly addresses the strong nonlinear feedbacks of two-phase flow, have been established. Inclusion of Jacobian information in the definition of the generalized flux adjoints provides for a rapidly convergent iterative method for solution of the power distribution and eigenvalue of a loading pattern perturbed from a reference state. Results show that the computational speedup of GPT compared with conventional forward solution methods demanding consistent accuracy is highly dependent on the number of spatial nodes utilized by the core simulator, varying from superior to inferior performance as the number of nodes increases
International Nuclear Information System (INIS)
Borges, Antonio Andrade
1998-01-01
A new method for the calculation of sensitivity coefficients is developed. The new method is a combination of two methodologies used for calculating theses coefficients, which are the differential and the generalized perturbation theory methods. The method utilizes as integral parameter the average flux in an arbitrary region of the system. Thus, the sensitivity coefficient contains only the component corresponding to the neutron flux. To obtain the new sensitivity coefficient, the derivatives of the integral parameter, Φ, with respect to σ are calculated using the perturbation method and the functional derivatives of this generic integral parameter with respect to σ and Φ are calculated using the differential method. (author)
Uncertainty Analysis of Few Group Cross Sections Based on Generalized Perturbation Theory
International Nuclear Information System (INIS)
Han, Tae Young; Lee, Hyun Chul; Noh, Jae Man
2014-01-01
In this paper, the methodology of the sensitivity and uncertainty analysis code based on GPT was described and the preliminary verification calculations on the PMR200 pin cell problem were carried out. As a result, they are in a good agreement when compared with the results by TSUNAMI. From this study, it is expected that MUSAD code based on GPT can produce the uncertainty of the homogenized few group microscopic cross sections for a core simulator. For sensitivity and uncertainty analyses for general core responses, a two-step method is available and it utilizes the generalized perturbation theory (GPT) for homogenized few group cross sections in the first step and stochastic sampling method for general core responses in the second step. The uncertainty analysis procedure based on GPT in the first step needs the generalized adjoint solution from a cell or lattice code. For this, the generalized adjoint solver has been integrated into DeCART in our previous work. In this paper, MUSAD (Modues of Uncertainty and Sensitivity Analysis for DeCART) code based on the classical perturbation theory was expanded to the function of the sensitivity and uncertainty analysis for few group cross sections based on GPT. First, the uncertainty analysis method based on GPT was described and, in the next section, the preliminary results of the verification calculation on a VHTR pin cell problem were compared with the results by TSUNAMI of SCALE 6.1
An Operator Perturbation Method of Polarized Line Transfer V ...
Indian Academy of Sciences (India)
tribpo
imate Lambda Iteration) method to the resonance scattering in spectral lines formed in the presence of weak magnetic fields. The method is based on an operator perturbation approach, and can efficiently give solutions for oriented vector magnetic fields in the solar atmosphere. Key words. ... 1999 for observational.
expansion method and travelling wave solutions for the perturbed ...
Indian Academy of Sciences (India)
Abstract. In this paper, we construct the travelling wave solutions to the perturbed nonlinear. Schrödinger's equation (NLSE) with Kerr law non-linearity by the extended (G /G)-expansion method. Based on this method, we obtain abundant exact travelling wave solutions of NLSE with. Kerr law nonlinearity with arbitrary ...
Non-perturbative methods applied to multiphoton ionization
International Nuclear Information System (INIS)
Brandi, H.S.; Davidovich, L.; Zagury, N.
1982-09-01
The use of non-perturbative methods in the treatment of atomic ionization is discussed. Particular attention is given to schemes of the type proposed by Keldysh where multiphoton ionization and tunnel auto-ionization occur for high intensity fields. These methods are shown to correspond to a certain type of expansion of the T-matrix in the intra-atomic potential; in this manner a criterium concerning the range of application of these non-perturbative schemes is suggested. A brief comparison between the ionization rate of atoms in the presence of linearly and circularly polarized light is presented. (Author) [pt
International Nuclear Information System (INIS)
Garcia, Juan Matias
2005-01-01
Perturbation Methods represent a powerful tool to do sensitivity analysis, and they found many aplications in nuclear engineering.As an introduction to this kind of analysis, we develope a program that apply the Generalized Perturbation Theory or GPT Method to bidimensional system of rectangular geometry.We first consider an homogeneous system of non-multiplying material and then an heterogeneous system with region of multiplying material, with the intention of make concret aplications of perturbation method to nuclear engineering problems.The program, that we called Pert, determines neutron fluxes and importance functions applying the Multigroup Diffusion Theory; and also solves the integrals required to calculate sensitivity coefficients.Using this perturbation methods we could verify the low computational cost required to make this kind of analysis and the simplicity of the equations systems involved, allowing us to make elaborates sensitivity analysis for the responses of our interest
Second-Order Perturbation Theory for Generalized Active Space Self-Consistent-Field Wave Functions.
Ma, Dongxia; Li Manni, Giovanni; Olsen, Jeppe; Gagliardi, Laura
2016-07-12
A multireference second-order perturbation theory approach based on the generalized active space self-consistent-field (GASSCF) wave function is presented. Compared with the complete active space (CAS) and restricted active space (RAS) wave functions, GAS wave functions are more flexible and can employ larger active spaces and/or different truncations of the configuration interaction expansion. With GASSCF, one can explore chemical systems that are not affordable with either CASSCF or RASSCF. Perturbation theory to second order on top of GAS wave functions (GASPT2) has been implemented to recover the remaining electron correlation. The method has been benchmarked by computing the chromium dimer ground-state potential energy curve. These calculations show that GASPT2 gives results similar to CASPT2 even with a configuration interaction expansion much smaller than the corresponding CAS expansion.
International Nuclear Information System (INIS)
Lima, Fernando R.A.; Lira, Carlos A.B.O.; Gandini, Augusto
1995-01-01
During the last two decades perturbative methods became an efficient tool to perform sensitivity analysis in nuclear reactor safety problems. In this paper, a comparative study taking into account perturbation formalisms (Diferential and Matricial Mthods and generalized Perturbation Theory - GPT) is considered. Then a few number of applications are described to analyze the sensitivity of some functions relavant to thermal hydraulics designs or safety analysis of nuclear reactor cores and steam generators. The behaviours of the nuclear reactor cores and steam generators are simulated, respectively, by the COBRA-IV-I and GEVAP codes. Results of sensitivity calculations have shown a good agreement when compared to those obtained directly by using the mentioned codes. So, a significative computational time safe can be obtained with perturbative methods performing sensitivity analysis in nuclear power plants. (author). 25 refs., 5 tabs
Variational configuration interaction methods and comparison with perturbation theory
International Nuclear Information System (INIS)
Pople, J.A.; Seeger, R.; Krishnan, R.
1977-01-01
A configuration interaction (CI) procedure which includes all single and double substitutions from an unrestricted Hartree-Fock single determinant is described. This has the feature that Moller-Plesset perturbation results to second and third order are obtained in the first CI iterative cycle. The procedure also avoids the necessity of a full two-electron integral transformation. A simple expression for correcting the final CI energy for lack of size consistency is proposed. Finally, calculations on a series of small molecules are presented to compare these CI methods with perturbation theory
Perturbation method for calculating impurity binding energy in an ...
Indian Academy of Sciences (India)
Nilanjan Sil
2017-12-18
Dec 18, 2017 ... Abstract. In the present paper, we have studied the binding energy of the shallow donor hydrogenic impurity, which is confined in an inhomogeneous cylindrical quantum dot (CQD) of GaAs-AlxGa1−xAs. Perturbation method is used to calculate the binding energy within the framework of effective mass ...
Application of New Variational Homotopy Perturbation Method For ...
African Journals Online (AJOL)
This paper discusses the application of the New Variational Homotopy Perturbation Method (NVHPM) for solving integro-differential equations. The advantage of the new Scheme is that it does not require discretization, linearization or any restrictive assumption of any form be fore it is applied. Several test problems are ...
Diagrammatic perturbation methods in networks and sports ranking combinatorics
International Nuclear Information System (INIS)
Park, Juyong
2010-01-01
Analytic and computational tools developed in statistical physics are being increasingly applied to the study of complex networks. Here we present recent developments in the diagrammatic perturbation methods for the exponential random graph models, and apply them to the combinatoric problem of determining the ranking of nodes in directed networks that represent pairwise competitions
Singular perturbations introduction to system order reduction methods with applications
Shchepakina, Elena; Mortell, Michael P
2014-01-01
These lecture notes provide a fresh approach to investigating singularly perturbed systems using asymptotic and geometrical techniques. It gives many examples and step-by-step techniques, which will help beginners move to a more advanced level. Singularly perturbed systems appear naturally in the modelling of many processes that are characterized by slow and fast motions simultaneously, for example, in fluid dynamics and nonlinear mechanics. This book’s approach consists in separating out the slow motions of the system under investigation. The result is a reduced differential system of lesser order. However, it inherits the essential elements of the qualitative behaviour of the original system. Singular Perturbations differs from other literature on the subject due to its methods and wide range of applications. It is a valuable reference for specialists in the areas of applied mathematics, engineering, physics, biology, as well as advanced undergraduates for the earlier parts of the book, and graduate stude...
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.
Born approximation to a perturbative numerical method for the solution of the Schroedinger equation
International Nuclear Information System (INIS)
Adam, Gh.
1978-01-01
A step function perturbative numerical method (SF-PN method) is developed for the solution of the Cauchy problem for the second order liniar differential equation in normal form. An important point stressed in the present paper, which seems to have been previously ignored in the literature devoted to the PN methods, is the close connection between the first order perturbation theory of the PN approach and the wellknown Born approximation, and, in general, the connection between the varjous orders of the PN corrections and the Neumann series. (author)
On the treatment of nonlinear local feedbacks within advanced nodal generalized perturbation theory
International Nuclear Information System (INIS)
Maldonado, G.I.; Turinsky, P.J.; Kropaczek, D.J.
1993-01-01
Recent efforts to upgrade the underlying neutronics formulations within the in-core nuclear fuel management optimization code FORMOSA (Ref. 1) have produced two important developments; first, a computationally efficient and second-order-accurate advanced nodal generalized perturbation theory (GPT) model [derived from the nonlinear iterative nodal expansion method (NEM)] for evaluating core attributes (i.e., k eff and power distribution versus cycle burnup), and second, an equally efficient and accurate treatment of local thermal-hydraulic and fission product feedbacks embedded within NEM GPT. The latter development is the focus of this paper
Green's functions in quantum chemistry - I. The Σ perturbation method
International Nuclear Information System (INIS)
Sebastian, K.L.
1978-01-01
As an improvement over the Hartree-Fock approximation, a Green's Function method - the Σ perturbation method - is investigated for molecular calculations. The method is applied to the hydrogen molecule and to the π-electron system of ethylene under PPP approximation. It is found that when the algebraic approximation is used, the energy obtained is better than that of the HF approach, but is not as good as that of the configuration-interaction method. The main advantage of this procedure is that it is devoid of the most serious defect of HF method, viz. incorrect dissociation limits. (K.B.)
Sound Attenuation in Elliptic Mufflers Using a Regular Perturbation Method
Banerjee, Subhabrata; Jacobi, Anthony M.
2012-01-01
The study of sound attenuation in an elliptical chamber involves the solution of the Helmholtz equation in elliptic coordinate systems. The Eigen solutions for such problems involve the Mathieu and the modified Mathieu functions. The computation of such functions poses considerable challenge. An alternative method to solve such problems had been proposed in this paper. The elliptical cross-section of the muffler has been treated as a perturbed circle, enabling the use of a regular perturbatio...
Green's function method for perturbed Korteweg-de Vries equation
International Nuclear Information System (INIS)
Cai Hao; Huang Nianning
2003-01-01
The x-derivatives of squared Jost solution are the eigenfunctions with the zero eigenvalue of the linearized equation derived from the perturbed Korteweg-de Vries equation. A method similar to Green's function formalism is introduced to show the completeness of the squared Jost solutions in multi-soliton cases. It is not related to Lax equations directly, and thus it is beneficial to deal with the nonlinear equations with complicated Lax pair
International Nuclear Information System (INIS)
Kwok, K.S.; Bernard, J.A.; Lanning, D.D.
1992-01-01
The perturbed reactivity method is a general technique for the estimation of reactivity. It is particularly suited to the determination of a reactor's initial degree of subcriticality and was developed to facilitate the automated startup of both spacecraft and multi-modular reactors using model-based control laws. It entails perturbing a shutdown reactor by the insertion of reactivity at a known rate and then estimating the initial degree of subcriticality from observation of the resulting reactor period. While similar to inverse kinetics, the perturbed reactivity method differs in that the net reactivity present in the core is treated as two separate entities. The first is that associated with the known perturbation. This quantity, together with the observed period and the reactor's describing parameters, are the inputs to the method's implementing algorithm. The second entity, which is the algorithm;s output, is the sum of all other reactivities including those resulting from inherent feedback and the initial degree of subcriticality. During an automated startup, feedback effects will be minimal. Hence, when applied to a shutdown reactor, the output of the perturbed reactivity method will be a constant that is equal to the initial degree of subcriticality. This is a major advantage because repeated estimates can be made of this one quantity and signal smoothing techniques can be applied to enhance accuracy. In addition to describing the theoretical basis for the perturbed reactivity method, factors involved in its implementation such as the movement of control devices other than those used to create the perturbation, source estimation, and techniques for data smoothing are presented
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.)
Stochastic Recursive Algorithms for Optimization Simultaneous Perturbation Methods
Bhatnagar, S; Prashanth, L A
2013-01-01
Stochastic Recursive Algorithms for Optimization presents algorithms for constrained and unconstrained optimization and for reinforcement learning. Efficient perturbation approaches form a thread unifying all the algorithms considered. Simultaneous perturbation stochastic approximation and smooth fractional estimators for gradient- and Hessian-based methods are presented. These algorithms: • are easily implemented; • do not require an explicit system model; and • work with real or simulated data. Chapters on their application in service systems, vehicular traffic control and communications networks illustrate this point. The book is self-contained with necessary mathematical results placed in an appendix. The text provides easy-to-use, off-the-shelf algorithms that are given detailed mathematical treatment so the material presented will be of significant interest to practitioners, academic researchers and graduate students alike. The breadth of applications makes the book appropriate for reader from sim...
DeVille, R. E. Lee; Harkin, Anthony; Holzer, Matt; Josić, Krešimir; Kaper, Tasso J.
2008-06-01
For singular perturbation problems, the renormalization group (RG) method of Chen, Goldenfeld, and Oono [Phys. Rev. E. 49 (1994) 4502-4511] has been shown to be an effective general approach for deriving reduced or amplitude equations that govern the long time dynamics of the system. It has been applied to a variety of problems traditionally analyzed using disparate methods, including the method of multiple scales, boundary layer theory, the WKBJ method, the Poincaré-Lindstedt method, the method of averaging, and others. In this article, we show how the RG method may be used to generate normal forms for large classes of ordinary differential equations. First, we apply the RG method to systems with autonomous perturbations, and we show that the reduced or amplitude equations generated by the RG method are equivalent to the classical Poincaré-Birkhoff normal forms for these systems up to and including terms of O(ɛ2), where ɛ is the perturbation parameter. This analysis establishes our approach and generalizes to higher order. Second, we apply the RG method to systems with nonautonomous perturbations, and we show that the reduced or amplitude equations so generated constitute time-asymptotic normal forms, which are based on KBM averages. Moreover, for both classes of problems, we show that the main coordinate changes are equivalent, up to translations between the spaces in which they are defined. In this manner, our results show that the RG method offers a new approach for deriving normal forms for nonautonomous systems, and it offers advantages since one can typically more readily identify resonant terms from naive perturbation expansions than from the nonautonomous vector fields themselves. Finally, we establish how well the solution to the RG equations approximates the solution of the original equations on time scales of O(1/ɛ).
International Nuclear Information System (INIS)
Silverman, J.N.
1983-01-01
A generalized Euler transformation (GET) is introduced which provides a powerful alternative method of accurately summing strongly divergent Rayleigh-Schroedinger (RS) perturbation series when other summability methods fail or are difficult to apply. The GET is simple to implement and, unlike a number of other summation procedures, requires no a priori knowledge of the analytic properties of the function underlying the RS series. Application of the GET to the difficult problem of the RS weak-field ground-state eigenvalue series of the hydrogen atom in a magnetic field (quadratic Zeeman effect) yields sums of good accuracy over a very wide range of field strengths up to the most intense fields of 10 14 G. The GET results are compared with those obtained by other summing methods
Block correlated second order perturbation theory with a generalized valence bond reference function
International Nuclear Information System (INIS)
Xu, Enhua; Li, Shuhua
2013-01-01
The block correlated second-order perturbation theory with a generalized valence bond (GVB) reference (GVB-BCPT2) is proposed. In this approach, each geminal in the GVB reference is considered as a “multi-orbital” block (a subset of spin orbitals), and each occupied or virtual spin orbital is also taken as a single block. The zeroth-order Hamiltonian is set to be the summation of the individual Hamiltonians of all blocks (with explicit two-electron operators within each geminal) so that the GVB reference function and all excited configuration functions are its eigenfunctions. The GVB-BCPT2 energy can be directly obtained without iteration, just like the second order Møller–Plesset perturbation method (MP2), both of which are size consistent. We have applied this GVB-BCPT2 method to investigate the equilibrium distances and spectroscopic constants of 7 diatomic molecules, conformational energy differences of 8 small molecules, and bond-breaking potential energy profiles in 3 systems. GVB-BCPT2 is demonstrated to have noticeably better performance than MP2 for systems with significant multi-reference character, and provide reasonably accurate results for some systems with large active spaces, which are beyond the capability of all CASSCF-based methods
Xu, Enhua; Li, Shuhua
2013-11-07
The block correlated second-order perturbation theory with a generalized valence bond (GVB) reference (GVB-BCPT2) is proposed. In this approach, each geminal in the GVB reference is considered as a "multi-orbital" block (a subset of spin orbitals), and each occupied or virtual spin orbital is also taken as a single block. The zeroth-order Hamiltonian is set to be the summation of the individual Hamiltonians of all blocks (with explicit two-electron operators within each geminal) so that the GVB reference function and all excited configuration functions are its eigenfunctions. The GVB-BCPT2 energy can be directly obtained without iteration, just like the second order Mo̸ller-Plesset perturbation method (MP2), both of which are size consistent. We have applied this GVB-BCPT2 method to investigate the equilibrium distances and spectroscopic constants of 7 diatomic molecules, conformational energy differences of 8 small molecules, and bond-breaking potential energy profiles in 3 systems. GVB-BCPT2 is demonstrated to have noticeably better performance than MP2 for systems with significant multi-reference character, and provide reasonably accurate results for some systems with large active spaces, which are beyond the capability of all CASSCF-based methods.
Core design and operation optimization methods based on time-dependent perturbation theory
International Nuclear Information System (INIS)
Greenspan, E.
1983-08-01
A general approach for the optimization of nuclear reactor core design and operation is outlined; it is based on two cornerstones: a newly developed time-dependent (or burnup-dependent) perturbation theory for nonlinear problems and a succesive iteration technique. The resulting approach is capable of handling realistic reactor models using computational methods of any degree of sophistication desired, while accounting for all the constraints imposed. Three general optimization strategies, different in the way for handling the constraints, are formulated. (author)
International Nuclear Information System (INIS)
Kim, Do Heon; Choi, Hang Bok
2001-03-01
A user's guide for GENOVA, a GENeralized perturbation theory (GPT)-based Optimization and uncertainty analysis program for Canada deuterium uranium (CANDU) physics VAriables, was prepared. The program was developed under the framework of CANDU physics design and analysis code RFSP. The generalized perturbation method was implemented in GENOVA to estimate the zone controller unit (ZCU) level upon refueling operation and calculate various sensitivity coefficients for fuel management study and uncertainty analyses, respectively. This documentation contains descriptions and directions of four major modules of GENOVA such as ADJOINT, GADJINT, PERTURB, and PERTXS so that it can be used as a practical guide for GENOVA users. This documentation includes sample inputs for the ZCU level estimation and sensitivity coefficient calculation, which are the main application of GENOVA. The GENOVA can be used as a supplementary tool of the current CANDU physics design code for advanced CANDU core analysis and fuel development
Second-order generalized perturbation theory for source-driven systems
International Nuclear Information System (INIS)
Greenspan, E.; Gilai, D.; Oblow, E.M.
1978-01-01
A second-order generalized perturbation theory (GPT) for the effect of multiple system variations on a general flux functional in source-driven systems is derived. The derivation is based on a functional Taylor series in which second-order derivatives are retained. The resulting formulation accounts for the nonlinear effect of a given variation accurate to third order in the flux and adjoint perturbations. It also accounts for the effect of interaction between any number of variations. The new formulation is compared with exact perturbation theory as well as with perturbation theory for altered systems. The usefulnes of the second-order GPT formulation is illustrated by applying it to optimization problems. Its applicability to areas of cross-section sensitivity analysis and system design and evaluation is also discussed
State of the art in HGPT (Heuristically Based Generalized Perturbation) methodology
International Nuclear Information System (INIS)
Gandini, A.
1993-01-01
A distinctive feature of heuristically based generalized perturbation theory (HGPT) methodology consists in the systematic use of importance conservation concepts. As well known, this use leads to fundamental reciprocity relationships from which perturbation, or sensitivity, expressions can be derived. The state of the art of the HGPT methodology is here illustrated. The application to a number of specific nonlinear fields of interest is commented. (author)
Foundations of quantum chromodynamics: Perturbative methods in gauge theories
International Nuclear Information System (INIS)
Muta, T.
1986-01-01
This volume develops the techniques of perturbative QCD in great detail starting with field theory. Aside from extensive treatments of the renormalization group technique, the operator product expansion formalism and their applications to short-distance reactions, this book provides a comprehensive introduction to gauge field theories. Examples and exercises are provided to amplify the discussions on important topics. Contents: Introduction; Elements of Quantum Chromodynamics; The Renormalization Group Method; Asymptotic Freedom; Operator Product Expansion Formalism; Applications; Renormalization Scheme Dependence; Factorization Theorem; Further Applications; Power Corrections; Infrared Problem. Power Correlations; Infrared Problem
Approximate solution fuzzy pantograph equation by using homotopy perturbation method
Jameel, A. F.; Saaban, A.; Ahadkulov, H.; Alipiah, F. M.
2017-09-01
In this paper, Homotopy Perturbation Method (HPM) is modified and formulated to find the approximate solution for its employment to solve (FDDEs) involving a fuzzy pantograph equation. The solution that can be obtained by using HPM is in the form of infinite series that converge to the actual solution of the FDDE and this is one of the benefits of this method In addition, it can be used for solving high order fuzzy delay differential equations directly without reduction to a first order system. Moreover, the accuracy of HPM can be detected without needing the exact solution. The HPM is studied for fuzzy initial value problems involving pantograph equation. Using the properties of fuzzy set theory, we reformulate the standard approximate method of HPM and obtain the approximate solutions. The effectiveness of the proposed method is demonstrated for third order fuzzy pantograph equation.
Hybrid perturbation methods based on statistical time series models
San-Juan, Juan Félix; San-Martín, Montserrat; Pérez, Iván; López, Rosario
2016-04-01
In this work we present a new methodology for orbit propagation, the hybrid perturbation theory, based on the combination of an integration method and a prediction technique. The former, which can be a numerical, analytical or semianalytical theory, generates an initial approximation that contains some inaccuracies derived from the fact that, in order to simplify the expressions and subsequent computations, not all the involved forces are taken into account and only low-order terms are considered, not to mention the fact that mathematical models of perturbations not always reproduce physical phenomena with absolute precision. The prediction technique, which can be based on either statistical time series models or computational intelligence methods, is aimed at modelling and reproducing missing dynamics in the previously integrated approximation. This combination results in the precision improvement of conventional numerical, analytical and semianalytical theories for determining the position and velocity of any artificial satellite or space debris object. In order to validate this methodology, we present a family of three hybrid orbit propagators formed by the combination of three different orders of approximation of an analytical theory and a statistical time series model, and analyse their capability to process the effect produced by the flattening of the Earth. The three considered analytical components are the integration of the Kepler problem, a first-order and a second-order analytical theories, whereas the prediction technique is the same in the three cases, namely an additive Holt-Winters method.
International Nuclear Information System (INIS)
Gurjao, Emir Candeia
1996-02-01
The differential and GPT (Generalized Perturbation Theory) formalisms of the Perturbation Theory were applied in this work to a simplified U-tubes steam generator model to perform sensitivity analysis. The adjoint and importance equations, with the corresponding expressions for the sensitivity coefficients, were derived for this steam generator model. The system was numerically was numerically solved in a Fortran program, called GEVADJ, in order to calculate the sensitivity coefficients. A transient loss of forced primary coolant in the nuclear power plant Angra-1 was used as example case. The average and final values of functionals: secondary pressure and enthalpy were studied in relation to changes in the secondary feedwater flow, enthalpy and total volume in secondary circuit. Absolute variations in the above functionals were calculated using the perturbative methods, considering the variations in the feedwater flow and total secondary volume. Comparison with the same variations obtained via direct model showed in general good agreement, demonstrating the potentiality of perturbative methods for sensitivity analysis of nuclear systems. (author)
Beyond perturbation introduction to the homotopy analysis method
Liao, Shijun
2003-01-01
Solving nonlinear problems is inherently difficult, and the stronger the nonlinearity, the more intractable solutions become. Analytic approximations often break down as nonlinearity becomes strong, and even perturbation approximations are valid only for problems with weak nonlinearity.This book introduces a powerful new analytic method for nonlinear problems-homotopy analysis-that remains valid even with strong nonlinearity. In Part I, the author starts with a very simple example, then presents the basic ideas, detailed procedures, and the advantages (and limitations) of homotopy analysis. Part II illustrates the application of homotopy analysis to many interesting nonlinear problems. These range from simple bifurcations of a nonlinear boundary-value problem to the Thomas-Fermi atom model, Volterra''s population model, Von Kármán swirling viscous flow, and nonlinear progressive waves in deep water.Although the homotopy analysis method has been verified in a number of prestigious journals, it has yet to be ...
Developments in perturbation theory
International Nuclear Information System (INIS)
Greenspan, E.
1976-01-01
Included are sections dealing with perturbation expressions for reactivity, methods for the calculation of perturbed fluxes, integral transport theory formulations for reactivity, generalized perturbation theory, sensitivity and optimization studies, multigroup calculations of bilinear functionals, and solution of inhomogeneous Boltzmann equations with singular operators
Directory of Open Access Journals (Sweden)
Yun-zhi Zou
2012-01-01
Full Text Available A new class of generalized dynamical systems involving generalized f-projection operators is introduced and studied in Banach spaces. By using the fixed-point theorem due to Nadler, the equilibrium points set of this class of generalized global dynamical systems is proved to be nonempty and closed under some suitable conditions. Moreover, the solutions set of the systems with set-valued perturbation is showed to be continuous with respect to the initial value.
Application of a perturbation method for realistic dynamic simulation of industrial robots
Waiboer, R.R.; Aarts, Ronald G.K.M.; Jonker, Jan B.
2005-01-01
This paper presents the application of a perturbation method for the closed-loop dynamic simulation of a rigid-link manipulator with joint friction. In this method the perturbed motion of the manipulator is modelled as a first-order perturbation of the nominal manipulator motion. A non-linear finite
Formulation of nonlinear chromaticity in circular accelerators by canonical perturbation method
International Nuclear Information System (INIS)
Takao, Masaru
2005-01-01
The formulation of nonlinear chromaticity in circular accelerators based on the canonical perturbation method is presented. Since the canonical perturbation method directly relates the tune shift to the perturbation Hamiltonian, it greatly simplifies the calculation of the nonlinear chromaticity. The obtained integral representation for nonlinear chromaticity can be systematically extended to higher orders
Acoustofluidics 13: Analysis of acoustic streaming by perturbation methods.
Sadhal, S S
2012-07-07
In this Part 13 of the tutorial series "Acoustofluidics--exploiting ultrasonic standing waves forces and acoustic streaming in microfluidic systems for cell and particle manipulation," the streaming phenomenon is presented from an analytical standpoint, and perturbation methods are developed for analyzing such flows. Acoustic streaming is the phenomenon that takes place when a steady flow field is generated by the absorption of an oscillatory field. This can happen either by attenuation (quartz wind) or by interaction with a boundary. The latter type of streaming can also be generated by an oscillating solid in an otherwise still fluid medium or vibrating enclosure of a fluid body. While we address the first kind of streaming, our focus is largely on the second kind from a practical standpoint for application to microfluidic systems. In this Focus article, we limit the analysis to one- and two-dimensional problems in order to understand the analytical techniques with examples that most-easily illustrate the streaming phenomenon.
Stability Analysis of Nonuniform Rectangular Beams Using Homotopy Perturbation Method
Directory of Open Access Journals (Sweden)
Seval Pinarbasi
2012-01-01
Full Text Available The design of slender beams, that is, beams with large laterally unsupported lengths, is commonly controlled by stability limit states. Beam buckling, also called “lateral torsional buckling,” is different from column buckling in that a beam not only displaces laterally but also twists about its axis during buckling. The coupling between twist and lateral displacement makes stability analysis of beams more complex than that of columns. For this reason, most of the analytical studies in the literature on beam stability are concentrated on simple cases: uniform beams with ideal boundary conditions and simple loadings. This paper shows that complex beam stability problems, such as lateral torsional buckling of rectangular beams with variable cross-sections, can successfully be solved using homotopy perturbation method (HPM.
Homogenized parameters of light water fuel elements computed by a perturbative (perturbation) method
International Nuclear Information System (INIS)
Koide, Maria da Conceicao Michiyo
2000-01-01
A new analytic formulation for material parameters homogenization of the two dimensional and two energy-groups diffusion model has been successfully used as a fast computational tool for recovering the detailed group fluxes in full reactor cores. The homogenization method which has been proposed does not require the solution of the diffusion problem by a numerical method. As it is generally recognized that currents at assembly boundaries must be computed accurately, a simple numerical procedure designed to improve the values of currents obtained by nodal calculations is also presented. (author)
Energy Technology Data Exchange (ETDEWEB)
Geemert, R. van E-mail: rene.vangeemert@psi.ch; Hoogenboom, J.E. E-mail: j.e.hoogenboom@iri.tudelft.nl
2001-09-01
As nuclear fuel economy is basically a multi-cycle issue, a fair way of evaluating reload patterns is to consider their performance in the case of an equilibrium cycle. The equilibrium cycle associated with a reload pattern is defined as the limit fuel cycle that eventually emerges after multiple successive periodic refueling, each time implementing the same reload scheme. Since the equilibrium cycle is the solution of a reload operation invariance equation, it can in principle be found with sufficient accuracy only by applying an iterative procedure, simulating the emergence of the limit cycle. For a design purpose such as the optimization of reload patterns, in which many different equilibrium cycle perturbations (resulting from many different limited changes in the reload operator) must be evaluated, this requires far too much computational effort. However, for very fast calculation of these many different equilibrium cycle perturbations it is also possible to set up a generalized variational approach. This approach results in an iterative scheme that yields the exact perturbation in the equilibrium cycle solution as well, in an accelerated way. Furthermore, both the solution of the adjoint equations occurring in the perturbation theory formalism and the implementation of the optimization algorithm have been parallellized and executed on a massively parallel machine. The combination of parallellism and generalized perturbation theory offers the opportunity to perform very exhaustive, fast and accurate sampling of the solution space for the equilibrium cycle reload pattern optimization problem.
A discrete homotopy perturbation method for non-linear Schrodinger equation
Directory of Open Access Journals (Sweden)
H. A. Wahab
2015-12-01
Full Text Available A general analysis is made by homotopy perturbation method while taking the advantages of the initial guess, appearance of the embedding parameter, different choices of the linear operator to the approximated solution to the non-linear Schrodinger equation. We are not dependent upon the Adomian polynomials and find the linear forms of the components without these calculations. The discretised forms of the nonlinear Schrodinger equation allow us whether to apply any numerical technique on the discritisation forms or proceed for perturbation solution of the problem. The discretised forms obtained by constructed homotopy provide the linear parts of the components of the solution series and hence a new discretised form is obtained. The general discretised form for the NLSE allows us to choose any initial guess and the solution in the closed form.
Numerical perturbative methods in the quantum theory of physical systems
International Nuclear Information System (INIS)
Adam, G.
1980-01-01
During the last two decades, development of digital electronic computers has led to the deployment of new, distinct methods in theoretical physics. These methods, based on the advances of modern numerical analysis as well as on specific equations describing physical processes, enabled to perform precise calculations of high complexity which have completed and sometimes changed our image of many physical phenomena. Our efforts have concentrated on the development of numerical methods with such intrinsic performances as to allow a successful approach of some Key issues in present theoretical physics on smaller computation systems. The basic principle of such methods is to translate, in numerical analysis language, the theory of perturbations which is suited to numerical rather than to analytical computation. This idea has been illustrated by working out two problems which arise from the time independent Schroedinger equation in the non-relativistic approximation, within both quantum systems with a small number of particles and systems with a large number of particles, respectively. In the first case, we are led to the numerical solution of some quadratic ordinary differential equations (first section of the thesis) and in the second case, to the solution of some secular equations in the Brillouin area (second section). (author)
The Generalized Sturmian Method
DEFF Research Database (Denmark)
Avery, James Emil
2011-01-01
these ideas clearly so that they become more accessible. By bringing together these non-standard methods, the book intends to inspire graduate students, postdoctoral researchers and academics to think of novel approaches. Is there a method out there that we have not thought of yet? Can we design a new method...... generations of researchers were left to work out how to achieve this ambitious goal for molecular systems of ever-increasing size. This book focuses on non-mainstream methods to solve the molecular electronic Schrödinger equation. Each method is based on a set of core ideas and this volume aims to explain...
International Nuclear Information System (INIS)
Takac, S.M.
1972-01-01
The method is based on perturbation of the reactor cell from a few up to few tens of percent. Measurements were performed for square lattice calls of zero power reactors Anna, NORA and RB, with metal uranium and uranium oxide fuel elements, water, heavy water and graphite moderators. Character and functional dependence of perturbations were obtained from the experimental results. Zero perturbation was determined by extrapolation thus obtaining the real physical neutron flux distribution in the reactor cell. Simple diffusion theory for partial plate cell perturbation was developed for verification of the perturbation method. The results of these calculation proved that introducing the perturbation sample in the fuel results in flattening the thermal neutron density dependent on the amplitude of the applied perturbation. Extrapolation applied for perturbed distributions was found to be justified
Global Melnikov Theory in Hamiltonian Systems with General Time-Dependent Perturbations
Gidea, Marian; de la Llave, Rafael
2018-04-01
We consider a mechanical system consisting of n-penduli and a d-degree-of-freedom rotator. The phase space of the rotator defines a normally hyperbolic invariant manifold Λ _0 . We apply a time-dependent perturbation, which is not assumed to be either Hamiltonian, or periodic, or quasi-periodic, as we allow for rather general time dependence. The strength of the perturbation is given by a parameter ɛ \\in R . For all |ɛ | sufficiently small, the augmented flow—obtained by making the time into a new variable—has a normally hyperbolic locally invariant manifold \\tilde{Λ }_ɛ . For ɛ =0 , \\tilde{Λ }_0=Λ _0× R . We define a Melnikov-type vector, which gives the first-order expansion of the displacement of the stable and unstable manifolds of \\tilde{Λ }_0 under the perturbation. We provide an explicit formula for the Melnikov vector in terms of convergent improper integrals of the perturbation along homoclinic orbits of the unperturbed system. We show that if the perturbation satisfies some explicit non-degeneracy conditions, then the stable and unstable manifolds of \\tilde{Λ }_ɛ , W^s(\\tilde{Λ }_ɛ ) and W^u(\\tilde{Λ }_ɛ ) , respectively, intersect along a transverse homoclinic manifold, and, moreover, the splitting of W^s(\\tilde{Λ }_ɛ ) and W^u(\\tilde{Λ }_ɛ ) can be explicitly computed, up to the first order, in terms of the Melnikov-type vector. This implies that the excursions along some homoclinic trajectories yield a non-trivial increase of order O(ɛ ) in the action variables of the rotator, for all sufficiently small perturbations. The formulas that we obtain are independent of the unperturbed motions in Λ _0 , and give, at the same time, the effects on periodic, quasi-periodic, or general-type orbits. When the perturbation is Hamiltonian, we express the effects of the perturbation, up to the first order, in terms of a Melnikov potential. In addition, if the perturbation is periodic, we obtain that the non-degeneracy conditions on
Toshmatov, Bobir; Stuchlík, Zdeněk; Schee, Jan; Ahmedov, Bobomurat
2018-04-01
The electromagnetic (EM) perturbations of the black hole solutions in general relativity coupled to nonlinear electrodynamics (NED) are studied for both electrically and magnetically charged black holes, assuming that the EM perturbations do not alter the spacetime geometry. It is shown that the effective potentials of the electrically and magnetically charged black holes related to test perturbative NED EM fields are related to the effective metric governing the photon motion, contrary to the effective potential of the linear electrodynamic (Maxwell) field that is related to the spacetime metric. Consequently, corresponding quasinormal (QN) frequencies differ as well. As a special case, we study new family of the NED black hole solutions which tend in the weak field limit to the Maxwell field, giving the Reissner-Nordström (RN) black hole solution. We compare the NED Maxwellian black hole QN spectra with the RN black hole QN spectra.
International Nuclear Information System (INIS)
Hwang, Jai-chan; Noh, Hyerim
2005-01-01
We consider a general relativistic zero-pressure irrotational cosmological medium perturbed to the third order. We assume a flat Friedmann background but include the cosmological constant. We ignore the rotational perturbation which decays in expanding phase. In our previous studies we discovered that, to the second-order perturbation, except for the gravitational wave contributions, the relativistic equations coincide exactly with the previously known Newtonian ones. Since the Newtonian second-order equations are fully nonlinear, any nonvanishing third- and higher-order terms in the relativistic analyses are supposed to be pure relativistic corrections. In this work, we derive such correction terms appearing in the third order. Continuing our success in the second-order perturbations, we take the comoving gauge. We discover that the third-order correction terms are of φ v order higher than the second-order terms where φ v is a gauge-invariant combination related to the three-space curvature perturbation in the comoving gauge; compared with the Newtonian potential, we have δΦ∼(3/5)φ v to the linear order. Therefore, the pure general relativistic effects are of φ v order higher than the Newtonian ones. The corrections terms are independent of the horizon scale and depend only on the linear-order gravitational potential (curvature) perturbation strength. From the temperature anisotropy of cosmic microwave background, we have (δT/T)∼(1/3)δΦ∼(1/5)φ v ∼10 -5 . Therefore, our present result reinforces our previous important practical implication that near the current era one can use the large-scale Newtonian numerical simulation more reliably even as the simulation scale approaches near (and goes beyond) the horizon
Energy Technology Data Exchange (ETDEWEB)
Garcia, Vanessa S. [Universidade Federal Fluminense (EEIMVR/UFF-RJ), Volta Redonda, RJ (Brazil). Escola de Engenharia Industrial e Metalurgica. Programa de Pos-Graduacao em Modelagem Computacional em Ciencia e Tecnologia; Silva, Fernando C.; Silva, Ademir X., E-mail: fernando@con.ufrj.b, E-mail: ademir@con.ufrj.b [Coordenacao dos Programas de Pos-Graduacao de Engenharia (PEN/COPPE/UFRJ), Rio de Janeiro, RJ (Brazil). Programa de Engenharia Nuclear; Alvarez, Gustavo B. [Universidade Federal Fluminense (EEIMVR/UFF-RJ), Volta Redonda, RJ (Brazil). Escola de Engenharia Industrial e Metalurgica. Dept. de Ciencias Exatas
2011-07-01
Boron neutron capture therapy - BNCT - is a binary cancer treatment used in brain tumors. The tumor is loaded with a boron compound and subsequently irradiated by thermal neutrons. The therapy is based on the {sup 10}B (n, {alpha}) {sup 7}Li nuclear reaction, which emits two types of high-energy particles, {alpha} particle and the {sup 7}Li nuclei. The total kinetic energy released in this nuclear reaction, when deposited in the tumor region, destroys the cancer cells. Since the success of the BNCT is linked to the different selectivity between the tumor and healthy tissue, it is necessary to carry out a sensitivity analysis to determinate the boron concentration. Computational simulations are very important in this context because they help in the treatment planning by calculating the lowest effective absorbed dose rate to reduce the damage to healthy tissue. The objective of this paper is to present a deterministic method based on generalized perturbation theory (GPT) to perform sensitivity analysis with respect to the {sup 10}B concentration and to estimate the absorbed dose rate by patients undergoing this therapy. The advantage of the method is a significant reduction in computational time required to perform these calculations. To simulate the neutron flux in all brain regions, the method relies on a two-dimensional neutron transport equation whose spatial, angular and energy variables are discretized by the diamond difference method, the discrete ordinate method and multigroup formulation, respectively. The results obtained through GPT are consistent with those obtained using other methods, demonstrating the efficacy of the proposed method. (author)
International Nuclear Information System (INIS)
Garcia, Vanessa S.; Silva, Fernando C.; Silva, Ademir X.; Alvarez, Gustavo B.
2011-01-01
Boron neutron capture therapy - BNCT - is a binary cancer treatment used in brain tumors. The tumor is loaded with a boron compound and subsequently irradiated by thermal neutrons. The therapy is based on the 10 B (n, α) 7 Li nuclear reaction, which emits two types of high-energy particles, α particle and the 7 Li nuclei. The total kinetic energy released in this nuclear reaction, when deposited in the tumor region, destroys the cancer cells. Since the success of the BNCT is linked to the different selectivity between the tumor and healthy tissue, it is necessary to carry out a sensitivity analysis to determinate the boron concentration. Computational simulations are very important in this context because they help in the treatment planning by calculating the lowest effective absorbed dose rate to reduce the damage to healthy tissue. The objective of this paper is to present a deterministic method based on generalized perturbation theory (GPT) to perform sensitivity analysis with respect to the 10 B concentration and to estimate the absorbed dose rate by patients undergoing this therapy. The advantage of the method is a significant reduction in computational time required to perform these calculations. To simulate the neutron flux in all brain regions, the method relies on a two-dimensional neutron transport equation whose spatial, angular and energy variables are discretized by the diamond difference method, the discrete ordinate method and multigroup formulation, respectively. The results obtained through GPT are consistent with those obtained using other methods, demonstrating the efficacy of the proposed method. (author)
Generalized subspace correction methods
Energy Technology Data Exchange (ETDEWEB)
Kolm, P. [Royal Institute of Technology, Stockholm (Sweden); Arbenz, P.; Gander, W. [Eidgenoessiche Technische Hochschule, Zuerich (Switzerland)
1996-12-31
A fundamental problem in scientific computing is the solution of large sparse systems of linear equations. Often these systems arise from the discretization of differential equations by finite difference, finite volume or finite element methods. Iterative methods exploiting these sparse structures have proven to be very effective on conventional computers for a wide area of applications. Due to the rapid development and increasing demand for the large computing powers of parallel computers, it has become important to design iterative methods specialized for these new architectures.
International Nuclear Information System (INIS)
Fathizadeh, M.; Aroujalian, A.
2012-01-01
The boundary layer convective heat transfer equations with low pressure gradient over a flat plate are solved using Homotopy Perturbation Method, which is one of the semi-exact methods. The nonlinear equations of momentum and energy solved simultaneously via Homotopy Perturbation Method are in good agreement with results obtained from numerical methods. Using this method, a general equation in terms of Pr number and pressure gradient (λ) is derived which can be used to investigate velocity and temperature profiles in the boundary layer.
A complete basis for a perturbation expansion of the general N-body problem
International Nuclear Information System (INIS)
Laing, W Blake; Kelle, David W; Dunn, Martin; Watson, Deborah K
2009-01-01
We discuss a basis set developed to calculate perturbation coefficients in an expansion of the general N-body problem. This basis has two advantages. First, the basis is complete order-by-order for the perturbation series. Second, the number of independent basis tensors spanning the space for a given order does not scale with N, the number of particles, despite the generality of the problem. At first order, the number of basis tensors is 25 for all N, i.e. the problem scales as N 0 , although one would initially expect an N 6 scaling at first order. The perturbation series is expanded in inverse powers of the spatial dimension. This results in a maximally symmetric configuration at lowest order which has a point group isomorphic with the symmetric group, S N . The resulting perturbation series is order-by-order invariant under the N! operations of the S N point group which is responsible for the slower than exponential growth of the basis. In this paper, we demonstrate the completeness of the basis and perform the first test of this formalism through first order by comparing to an exactly solvable fully interacting problem of N particles with a two-body harmonic interaction potential
Perturbation Method of Analysis Applied to Substitution Measurements of Buckling
Energy Technology Data Exchange (ETDEWEB)
Persson, Rolf
1966-11-15
Calculations with two-group perturbation theory on substitution experiments with homogenized regions show that a condensation of the results into a one-group formula is possible, provided that a transition region is introduced in a proper way. In heterogeneous cores the transition region comes in as a consequence of a new cell concept. By making use of progressive substitutions the properties of the transition region can be regarded as fitting parameters in the evaluation procedure. The thickness of the region is approximately equal to the sum of 1/(1/{tau} + 1/L{sup 2}){sup 1/2} for the test and reference regions. Consequently a region where L{sup 2} >> {tau}, e.g. D{sub 2}O, contributes with {radical}{tau} to the thickness. In cores where {tau} >> L{sup 2} , e.g. H{sub 2}O assemblies, the thickness of the transition region is determined by L. Experiments on rod lattices in D{sub 2}O and on test regions of D{sub 2}O alone (where B{sup 2} = - 1/L{sup 2} ) are analysed. The lattice measurements, where the pitches differed by a factor of {radical}2, gave excellent results, whereas the determination of the diffusion length in D{sub 2}O by this method was not quite successful. Even regions containing only one test element can be used in a meaningful way in the analysis.
Perturbation methods and closure approximations in nonlinear systems
International Nuclear Information System (INIS)
Dubin, D.H.E.
1984-01-01
In the first section of this thesis, Hamiltonian theories of guiding center and gyro-center motion are developed using modern symplectic methods and Lie transformations. Littlejohn's techniques, combined with the theory of resonant interaction and island overlap, are used to explore the problem of adiabatic invariance and onset of stochasticity. As an example, the breakdown of invariance due to resonance between drift motion and gyromotion in a tokamak is considered. A Hamiltonian is developed for motion in a straight magnetic field with electrostatic perturbations in the gyrokinetic ordering, from which nonlinear gyrokinetic equations are constructed which have the property of phase-space preservation, useful for computer simulation. Energy invariants are found and various limits of the equations are considered. In the second section, statistical closure theories are applied to simple dynamical systems. The logistic map is used as an example because of its universal properties and simple quadratic nonlinearity. The first closure considered is the direct interaction approximation of Kraichnan, which is found to fail when applied to the logistic map because it cannot approximate the bounded support of the map's equilibrium distribution. By imposing a periodically constraint on a Langevin form of the DIA a new stable closure is developed
International Nuclear Information System (INIS)
Noack, K.
1982-01-01
The perturbation source method may be a powerful Monte-Carlo means to calculate small effects in a particle field. In a preceding paper we have formulated this methos in inhomogeneous linear particle transport problems describing the particle fields by solutions of Fredholm integral equations and have derived formulae for the second moment of the difference event point estimator. In the present paper we analyse the general structure of its variance, point out the variance peculiarities, discuss the dependence on certain transport games and on generation procedures of the auxiliary particles and draw conclusions to improve this method
Time-Sliced Perturbation Theory for Large Scale Structure I: General Formalism
Blas, Diego; Ivanov, Mikhail M.; Sibiryakov, Sergey
2016-01-01
We present a new analytic approach to describe large scale structure formation in the mildly non-linear regime. The central object of the method is the time-dependent probability distribution function generating correlators of the cosmological observables at a given moment of time. Expanding the distribution function around the Gaussian weight we formulate a perturbative technique to calculate non-linear corrections to cosmological correlators, similar to the diagrammatic expansion in a three-dimensional Euclidean quantum field theory, with time playing the role of an external parameter. For the physically relevant case of cold dark matter in an Einstein--de Sitter universe, the time evolution of the distribution function can be found exactly and is encapsulated by a time-dependent coupling constant controlling the perturbative expansion. We show that all building blocks of the expansion are free from spurious infrared enhanced contributions that plague the standard cosmological perturbation theory. This pave...
DEFF Research Database (Denmark)
Farrokhzad, F.; Mowlaee, P.; Barari, Amin
2011-01-01
The beam deformation equation has very wide applications in structural engineering. As a differential equation, it has its own problem concerning existence, uniqueness and methods of solutions. Often, original forms of governing differential equations used in engineering problems are simplified...... Method (OHAM). The comparisons of the results reveal that these methods are very effective, convenient and quite accurate to systems of non-linear differential equation......., and this process produces noise in the obtained answers. This paper deals with solution of second order of differential equation governing beam deformation using four analytical approximate methods, namely the Homotopy Perturbation Method (HPM), Variational Iteration Method (VIM) and Optimal Homotopy Asymptotic...
Angular momentum in general relativity. II. Perturbations of a rotating black hole
Energy Technology Data Exchange (ETDEWEB)
Prior, C R [Cambridge Univ. (UK). Dept. of Applied Mathematics and Theoretical Physics
1977-06-30
The definition of angular momentum proposed in part I of this series (Prior. Proc. R. Soc. Lond.; A354:379 (1977)) is investigated when applied to rotating black holes. It is shown how to use the formula to evaluate the angular momentum of a stationary black hole. This acts as a description of a background space on which the effect of first matter and then gravitational perturbations is considered. The latter are of most interest and the rate of change of angular momentum, dJ/dt, is found as an expression in the shear induced in the event horizon by the perturbation and in its time integral. Teukolsky's solutions (Astrophys. J.; 185:635 (1973)) for the perturbed component of the Weyl tensor are then used to find this shear and hence to give an exact answer for dJ/dt. One of the implications of the result is a direct verification of Bekenstein's formula (Phys. Rev.; 7D:949 (1973)) relating in a simple way the rate of change of angular momentum to the rate of change of mass caused by a plane wave. A more general expression is also given for dM/dt. Considering only stationary perturbations, it is shown how to generalize the definition of angular momentum so as to include information about its direction as well. Three problems are particularly discussed - a single moon, two or more moons and a ring of matter causing the perturbation - since they provide illustrations of all the main features of the black hole's behaviour. In every case it is found that the black hole realigns its axis of rotation so that the final configuration is axisymmetric if possible; otherwise is slows down completely to reach a static state.
Robust Trajectory Design in Highly Perturbed Environments Leveraging Continuation Methods, Phase I
National Aeronautics and Space Administration — Research is proposed to investigate continuation methods to improve the robustness of trajectory design algorithms for spacecraft in highly perturbed dynamical...
Extinction and Permanence of a General Predator-Prey System with Impulsive Perturbations
Directory of Open Access Journals (Sweden)
Xianning Liu
2012-01-01
Full Text Available A general predator-prey system is studied in a scheme where there is periodic impulsive perturbations. This scheme has the potential to protect the predator from extinction but under some conditions may also serve to lead to extinction of the prey. Conditions for extinction and permanence are obtained via the comparison methods involving monotone theory of impulsive systems and multiple Liapunov functions, which establish explicit bounds on solutions. The existence of a positive periodic solution is also studied by the bifurcation theory. Application is given to a Lotka-Volterra predator-prey system with periodic impulsive immigration of the predator. It is shown that the results are quite different from the corresponding system without impulsive immigration, where extinction of the prey can never be achieved. The prey will be extinct or permanent independent of whether the system without impulsive effect immigration is permanent or not. The model and its results suggest an approach of pest control which proves more effective than the classical one.
International Nuclear Information System (INIS)
Maldonado, G.I.; Turinsky, P.J.
1995-01-01
The determination of the family of optimum core loading patterns for pressurized water reactors (PWRs) involves the assessment of the core attributes for thousands of candidate loading patterns. For this reason, the computational capability to efficiently and accurately evaluate a reactor core's eigenvalue and power distribution versus burnup using a nodal diffusion generalized perturbation theory (GPT) model is developed. The GPT model is derived from the forward nonlinear iterative nodal expansion method (NEM) to explicitly enable the preservation of the finite difference matrix structure. This key feature considerably simplifies the mathematical formulation of NEM GPT and results in reduced memory storage and CPU time requirements versus the traditional response-matrix approach to NEM. In addition, a treatment within NEM GPT can account for localized nonlinear feedbacks, such as that due to fission product buildup and thermal-hydraulic effects. When compared with a standard nonlinear iterative NEM forward flux solve with feedbacks, the NEM GPT model can execute between 8 and 12 times faster. These developments are implemented within the PWR in-core nuclear fuel management optimization code FORMOSA-P, combining the robustness of its adaptive simulated annealing stochastic optimization algorithm with an NEM GPT neutronics model that efficiently and accurately evaluates core attributes associated with objective functions and constraints of candidate loading patterns
Application of Classical and Lie Transform Methods to Zonal Perturbation in the Artificial Satellite
San-Juan, J. F.; San-Martin, M.; Perez, I.; Lopez-Ochoa, L. M.
2013-08-01
A scalable second-order analytical orbit propagator program is being carried out. This analytical orbit propagator combines modern perturbation methods, based on the canonical frame of the Lie transform, and classical perturbation methods in function of orbit types or the requirements needed for a space mission, such as catalog maintenance operations, long period evolution, and so on. As a first step on the validation of part of our orbit propagator, in this work we only consider the perturbation produced by zonal harmonic coefficients in the Earth's gravity potential, so that it is possible to analyze the behaviour of the perturbation methods involved in the corresponding analytical theories.
Optimal Monotonicity-Preserving Perturbations of a Given Runge–Kutta Method
Higueras, Inmaculada
2018-02-14
Perturbed Runge–Kutta methods (also referred to as downwind Runge–Kutta methods) can guarantee monotonicity preservation under larger step sizes relative to their traditional Runge–Kutta counterparts. In this paper we study the question of how to optimally perturb a given method in order to increase the radius of absolute monotonicity (a.m.). We prove that for methods with zero radius of a.m., it is always possible to give a perturbation with positive radius. We first study methods for linear problems and then methods for nonlinear problems. In each case, we prove upper bounds on the radius of a.m., and provide algorithms to compute optimal perturbations. We also provide optimal perturbations for many known methods.
Optimal Monotonicity-Preserving Perturbations of a Given Runge–Kutta Method
Higueras, Inmaculada; Ketcheson, David I.; Kocsis, Tihamé r A.
2018-01-01
Perturbed Runge–Kutta methods (also referred to as downwind Runge–Kutta methods) can guarantee monotonicity preservation under larger step sizes relative to their traditional Runge–Kutta counterparts. In this paper we study the question of how to optimally perturb a given method in order to increase the radius of absolute monotonicity (a.m.). We prove that for methods with zero radius of a.m., it is always possible to give a perturbation with positive radius. We first study methods for linear problems and then methods for nonlinear problems. In each case, we prove upper bounds on the radius of a.m., and provide algorithms to compute optimal perturbations. We also provide optimal perturbations for many known methods.
A Newton-Based Extremum Seeking MPPT Method for Photovoltaic Systems with Stochastic Perturbations
Directory of Open Access Journals (Sweden)
Heng Li
2014-01-01
Full Text Available Microcontroller based maximum power point tracking (MPPT has been the most popular MPPT approach in photovoltaic systems due to its high flexibility and efficiency in different photovoltaic systems. It is well known that PV systems typically operate under a range of uncertain environmental parameters and disturbances, which implies that MPPT controllers generally suffer from some unknown stochastic perturbations. To address this issue, a novel Newton-based stochastic extremum seeking MPPT method is proposed. Treating stochastic perturbations as excitation signals, the proposed MPPT controller has a good tolerance of stochastic perturbations in nature. Different from conventional gradient-based extremum seeking MPPT algorithm, the convergence rate of the proposed controller can be totally user-assignable rather than determined by unknown power map. The stability and convergence of the proposed controller are rigorously proved. We further discuss the effects of partial shading and PV module ageing on the proposed controller. Numerical simulations and experiments are conducted to show the effectiveness of the proposed MPPT algorithm.
Comparison of two perturbation methods to estimate the land surface modeling uncertainty
Su, H.; Houser, P.; Tian, Y.; Kumar, S.; Geiger, J.; Belvedere, D.
2007-12-01
In land surface modeling, it is almost impossible to simulate the land surface processes without any error because the earth system is highly complex and the physics of the land processes has not yet been understood sufficiently. In most cases, people want to know not only the model output but also the uncertainty in the modeling, to estimate how reliable the modeling is. Ensemble perturbation is an effective way to estimate the uncertainty in land surface modeling, since land surface models are highly nonlinear which makes the analytical approach not applicable in this estimation. The ideal perturbation noise is zero mean Gaussian distribution, however, this requirement can't be satisfied if the perturbed variables in land surface model have physical boundaries because part of the perturbation noises has to be removed to feed the land surface models properly. Two different perturbation methods are employed in our study to investigate their impact on quantifying land surface modeling uncertainty base on the Land Information System (LIS) framework developed by NASA/GSFC land team. One perturbation method is the built-in algorithm named "STATIC" in LIS version 5; the other is a new perturbation algorithm which was recently developed to minimize the overall bias in the perturbation by incorporating additional information from the whole time series for the perturbed variable. The statistical properties of the perturbation noise generated by the two different algorithms are investigated thoroughly by using a large ensemble size on a NASA supercomputer and then the corresponding uncertainty estimates based on the two perturbation methods are compared. Their further impacts on data assimilation are also discussed. Finally, an optimal perturbation method is suggested.
Xia, Ya-Rong; Zhang, Shun-Li; Xin, Xiang-Peng
2018-03-01
In this paper, we propose the concept of the perturbed invariant subspaces (PISs), and study the approximate generalized functional variable separation solution for the nonlinear diffusion-convection equation with weak source by the approximate generalized conditional symmetries (AGCSs) related to the PISs. Complete classification of the perturbed equations which admit the approximate generalized functional separable solutions (AGFSSs) is obtained. As a consequence, some AGFSSs to the resulting equations are explicitly constructed by way of examples.
A perturbation-based susbtep method for coupled depletion Monte-Carlo codes
International Nuclear Information System (INIS)
Kotlyar, Dan; Aufiero, Manuele; Shwageraus, Eugene; Fratoni, Massimiliano
2017-01-01
Highlights: • The GPT method allows to calculate the sensitivity coefficients to any perturbation. • Full Jacobian of sensitivities, cross sections (XS) to concentrations, may be obtained. • The time dependent XS is obtained by combining the GPT and substep methods. • The proposed GPT substep method considerably reduces the time discretization error. • No additional MC transport solutions are required within the time step. - Abstract: Coupled Monte Carlo (MC) methods are becoming widely used in reactor physics analysis and design. Many research groups therefore, developed their own coupled MC depletion codes. Typically, in such coupled code systems, neutron fluxes and cross sections are provided to the depletion module by solving a static neutron transport problem. These fluxes and cross sections are representative only of a specific time-point. In reality however, both quantities would change through the depletion time interval. Recently, Generalized Perturbation Theory (GPT) equivalent method that relies on collision history approach was implemented in Serpent MC code. This method was used here to calculate the sensitivity of each nuclide and reaction cross section due to the change in concentration of every isotope in the system. The coupling method proposed in this study also uses the substep approach, which incorporates these sensitivity coefficients to account for temporal changes in cross sections. As a result, a notable improvement in time dependent cross section behavior was obtained. The method was implemented in a wrapper script that couples Serpent with an external depletion solver. The performance of this method was compared with other existing methods. The results indicate that the proposed method requires substantially less MC transport solutions to achieve the same accuracy.
An Introduction to Perturbative Methods in Gauge Theories
International Nuclear Information System (INIS)
T Muta
1998-01-01
This volume develops the techniques of perturbative QCD in great pedagogical detail starting with field theory. Aside from extensive treatments of the renormalization group technique, the operator product expansion formalism and their applications to short-distance reactions, this book provides a comprehensive introduction to gauge theories. Examples and exercises are provided to amplify the discussions on important topics. This is an ideal textbook on the subject of quantum chromodynamics and is essential for researchers and graduate students in high energy physics, nuclear physics and mathematical physics
Directory of Open Access Journals (Sweden)
Mustafa Kemal BAHAR
2010-06-01
Full Text Available In this study, the effects of applied electric field on the isolated square quantum well was investigated by analytic and perturbative method. The energy eigen values and wave functions in quantum well were found by perturbative method. Later, the electric field effects were investigated by analytic method, the results of perturbative and analytic method were compared. As well as both of results fit with each other, it was observed that externally applied electric field changed importantly electronic properties of the system.
International Nuclear Information System (INIS)
Rossi, Lubianka Ferrari Russo
2014-01-01
The main target of this study is to introduce a new method for calculating the coefficients of sensibility through the union of differential method and generalized perturbation theory, which are the two methods generally used in reactor physics to obtain such variables. These two methods, separated, have some issues turning the sensibility coefficients calculation slower or computationally exhaustive. However, putting them together, it is possible to repair these issues and build a new equation for the coefficient of sensibility. The method introduced in this study was applied in a PWR reactor, where it was performed the sensibility analysis for the production and 239 Pu conversion rate during 120 days (1 cycle) of burnup. The computational code used for both burnup and sensibility analysis, the CINEW, was developed in this study and all the results were compared with codes widely used in reactor physics, such as CINDER and SERPENT. The new mathematical method for calculating the sensibility coefficients and the code CINEW provide good numerical agility and also good efficiency and security, once the new method, when compared with traditional ones, provide satisfactory results, even when the other methods use different mathematical approaches. The burnup analysis, performed using the code CINEW, was compared with the code CINDER, showing an acceptable variation, though CINDER presents some computational issues due to the period it was built. The originality of this study is the application of such method in problems involving temporal dependence and, not least, the elaboration of the first national code for burnup and sensitivity analysis. (author)
Time-sliced perturbation theory for large scale structure I: general formalism
Energy Technology Data Exchange (ETDEWEB)
Blas, Diego; Garny, Mathias; Sibiryakov, Sergey [Theory Division, CERN, CH-1211 Genève 23 (Switzerland); Ivanov, Mikhail M., E-mail: diego.blas@cern.ch, E-mail: mathias.garny@cern.ch, E-mail: mikhail.ivanov@cern.ch, E-mail: sergey.sibiryakov@cern.ch [FSB/ITP/LPPC, École Polytechnique Fédérale de Lausanne, CH-1015, Lausanne (Switzerland)
2016-07-01
We present a new analytic approach to describe large scale structure formation in the mildly non-linear regime. The central object of the method is the time-dependent probability distribution function generating correlators of the cosmological observables at a given moment of time. Expanding the distribution function around the Gaussian weight we formulate a perturbative technique to calculate non-linear corrections to cosmological correlators, similar to the diagrammatic expansion in a three-dimensional Euclidean quantum field theory, with time playing the role of an external parameter. For the physically relevant case of cold dark matter in an Einstein-de Sitter universe, the time evolution of the distribution function can be found exactly and is encapsulated by a time-dependent coupling constant controlling the perturbative expansion. We show that all building blocks of the expansion are free from spurious infrared enhanced contributions that plague the standard cosmological perturbation theory. This paves the way towards the systematic resummation of infrared effects in large scale structure formation. We also argue that the approach proposed here provides a natural framework to account for the influence of short-scale dynamics on larger scales along the lines of effective field theory.
International Nuclear Information System (INIS)
Dehghan, Mehdi; Shakeri, Fatemeh
2007-01-01
In this work, the solution of an inverse problem concerning a diffusion equation with source control parameters is presented. The homotopy perturbation method is employed to solve this equation. This method changes a difficult problem into a simple problem which can be easily solved. In this procedure, according to the homotopy technique, a homotopy with an embedding parameter p element of [0,1] is constructed, and this parameter is considered a 'small parameter', so the method is called the homotopy perturbation method, which can take full advantage of the traditional perturbation method and homotopy technique. The approximations obtained by the proposed method are uniformly valid not only for small parameters, but also for very large parameters. The fact that this technique, in contrast to the traditional perturbation methods, does not require a small parameter in the system, leads to wide applications in nonlinear equations
International Nuclear Information System (INIS)
Gandini, A.
1996-01-01
The heuristically based generalized perturbation theory (HGPT), to first and higher order, applied to the neutron field of a reactor system, is discussed in relation to the criticality reset procedure. This procedure is implicit within the GPT methodology, corresponding to the so called filtering of the importance function relevant to the neutron field from the fundamental mode contamination. It is common practice to use the so called ''lambda''-mode filter. In order to account for any possible reset option, a general definition is introduced of an intensive control variable (ρ) entering into the governing equations, and correspondingly a fundamental ρ-mode filtering of the importance function is defined, relevant to the real criticality reset (control) mechanism adopted. A simple example illustrates the need to take into account the correct filtering, so as to avoid significant inaccuracies in the sensitivity calculation results. The extension of this filtering technique to other functions entering into the GPT perturbative formulations at first and higher order is also discussed. (author)
The role of the control variable in the heuristically based generalized perturbation theory (HGPT)
International Nuclear Information System (INIS)
Gandini, A.
1995-01-01
The heuristically based generalized perturbation theory (HGPT) applied to the neutron field of a reactor system is discussed in relation to the criticality reset procedure. This procedure is implicit within the GPT methodology, corresponding to the so called filtering of the importance function relevant to the neutron field from the fundamental mode contamination. It is common practice to use the so called γ-mode filter. In order to account for any possible reset option, a general definition is introduced of an intensive control variable (ρ) entering into the governing equations, and correspondingly a fundamental ρ-mode filtering of the importance function is defined, relevant to the real criticality reset mechanism (control) adopted. A simple example illustrates the need in many circumstances of interest of taking into proper account the correct filtering so to avoid significant inaccuracies in the sensitivity calculation results
Commutator perturbation method in the study of vibrational-rotational spectra of diatomic molecules
International Nuclear Information System (INIS)
Matamala-Vasquez, A.; Karwowski, J.
2000-01-01
The commutator perturbation method, an algebraic version of the Van Vleck-Primas perturbation method, expressed in terms of ladder operators, has been applied to solving the eigenvalue problem of the Hamiltonian describing the vibrational-rotational motion of a diatomic molecule. The physical model used in this work is based on Dunham's approach. The method facilitates obtaining both energies and eigenvectors in an algebraic way
The perturbed angular correlation method - a modern technique in studying solids
International Nuclear Information System (INIS)
Unterricker, S.; Hunger, H.J.
1979-01-01
Starting from theoretical fundamentals the differential perturbed angular correlation method has been explained. By using the probe nucleus 111 Cd the magnetic dipole interaction in Fesub(x)Alsub(1-x) alloys and the electric quadrupole interaction in Cd have been measured. The perturbed angular correlation method is a modern nuclear measuring method and can be applied in studying ordering processes, phase transformations and radiation damages in metals, semiconductors and insulators
Generalized perturbation theory for LWR depletion analysis and core design applications
International Nuclear Information System (INIS)
White, J.R.; Frank, B.R.
1986-01-01
A comprehensive time-dependent perturbation theory formulation that includes macroscopic depletion, thermal-hydraulic and poison feedback effects, and a criticality reset mechanism is developed. The methodology is compatible with most current LWR design codes. This new development allows GTP/DTP methods to be used quantitatively in a variety of realistic LWR physics applications that were not possible prior to this work. A GTP-based optimization technique for incore fuel management analyses is addressed as a promising application of the new formulation
Perturbative method for the derivation of quantum kinetic theory based on closed-time-path formalism
International Nuclear Information System (INIS)
Koide, Jun
2002-01-01
Within the closed-time-path formalism, a perturbative method is presented, which reduces the microscopic field theory to the quantum kinetic theory. In order to make this reduction, the expectation value of a physical quantity must be calculated under the condition that the Wigner distribution function is fixed, because it is the independent dynamical variable in the quantum kinetic theory. It is shown that when a nonequilibrium Green function in the form of the generalized Kadanoff-Baym ansatz is utilized, this condition appears as a cancellation of a certain part of contributions in the diagrammatic expression of the expectation value. Together with the quantum kinetic equation, which can be derived in the closed-time-path formalism, this method provides a basis for the kinetic-theoretical description
Covariant second-order perturbations in generalized two-field inflation
International Nuclear Information System (INIS)
Tzavara, Eleftheria; Tent, Bartjan van; Mizuno, Shuntaro
2014-01-01
We examine the covariant properties of generalized models of two-field inflation, with non-canonical kinetic terms and a possibly non-trivial field metric. We demonstrate that kinetic-term derivatives and covariant field derivatives do commute in a proper covariant framework, which was not realized before in the literature. We also define a set of generalized slow-roll parameters, using a unified notation. Within this framework, we study the most general class of models that allows for well-defined adiabatic and entropic sound speeds, which we identify as the models with parallel momentum and field velocity vectors. For these models we write the exact cubic action in terms of the adiabatic and isocurvature perturbations. We thus provide the tool to calculate the exact non-Gaussianity beyond slow-roll and at any scale for these generalized models. We illustrate our general results by considering their long-wavelength limit, as well as with the example of two-field DBI inflation
Araneda, Bernardo
2018-04-01
We present weighted covariant derivatives and wave operators for perturbations of certain algebraically special Einstein spacetimes in arbitrary dimensions, under which the Teukolsky and related equations become weighted wave equations. We show that the higher dimensional generalization of the principal null directions are weighted conformal Killing vectors with respect to the modified covariant derivative. We also introduce a modified Laplace–de Rham-like operator acting on tensor-valued differential forms, and show that the wave-like equations are, at the linear level, appropriate projections off shell of this operator acting on the curvature tensor; the projection tensors being made out of weighted conformal Killing–Yano tensors. We give off shell operator identities that map the Einstein and Maxwell equations into weighted scalar equations, and using adjoint operators we construct solutions of the original field equations in a compact form from solutions of the wave-like equations. We study the extreme and zero boost weight cases; extreme boost corresponding to perturbations of Kundt spacetimes (which includes near horizon geometries of extreme black holes), and zero boost to static black holes in arbitrary dimensions. In 4D our results apply to Einstein spacetimes of Petrov type D and make use of weighted Killing spinors.
International Nuclear Information System (INIS)
Killingbeck, J.
1979-01-01
By using the methods of perturbation theory it is possible to construct simple formulae for the numerical integration of the Schroedinger equation, and also to calculate expectation values solely by means of simple eigenvalue calculations. (Auth.)
Application of perturbation theory to lattice calculations based on method of cyclic characteristics
Assawaroongruengchot, Monchai
Perturbation theory is a technique used for the estimation of changes in performance functionals, such as linear reaction rate ratio and eigenvalue affected by small variations in reactor core compositions. Here the algorithm of perturbation theory is developed for the multigroup integral neutron transport problems in 2D fuel assemblies with isotropic scattering. The integral transport equation is used in the perturbative formulation because it represents the interconnecting neutronic systems of the lattice assemblies via the tracking lines. When the integral neutron transport equation is used in the formulation, one needs to solve the resulting integral transport equations for the flux importance and generalized flux importance functions. The relationship between the generalized flux importance and generalized source importance functions is defined in order to transform the generalized flux importance transport equations into the integro-differential equations for the generalized adjoints. Next we develop the adjoint and generalized adjoint transport solution algorithms based on the method of cyclic characteristics (MOCC) in DRAGON code. In the MOCC method, the adjoint characteristics equations associated with a cyclic tracking line are formulated in such a way that a closed form for the adjoint angular function can be obtained. The MOCC method then requires only one cycle of scanning over the cyclic tracking lines in each spatial iteration. We also show that the source importance function by CP method is mathematically equivalent to the adjoint function by MOCC method. In order to speed up the MOCC solution algorithm, a group-reduction and group-splitting techniques based on the structure of the adjoint scattering matrix are implemented. A combined forward flux/adjoint function iteration scheme, based on the group-splitting technique and the common use of a large number of variables storing tracking-line data and exponential values, is proposed to reduce the
Application of perturbation theory to lattice calculations based on method of cyclic characteristics
Energy Technology Data Exchange (ETDEWEB)
Assawaroongruengchot, M
2007-07-01
Perturbation theory is a technique used for the estimation of changes in performance functionals, such as linear reaction rate ratio and eigenvalue affected by small variations in reactor core compositions. Here the algorithm of perturbation theory is developed for the multigroup integral neutron transport problems in 2D fuel assemblies with isotropic scattering. The integral transport equation is used in the perturbative formulation because it represents the interconnecting neutronic systems of the lattice assemblies via the tracking lines. When the integral neutron transport equation is used in the formulation, one needs to solve the resulting integral transport equations for the flux importance and generalized flux importance functions. The relationship between the generalized flux importance and generalized source importance functions is defined in order to transform the generalized flux importance transport equations into the integro-differential equations for the generalized adjoints. Next we develop the adjoint and generalized adjoint transport solution algorithms based on the method of cyclic characteristics (MOCC) in DRAGON code. In the MOCC method, the adjoint characteristics equations associated with a cyclic tracking line are formulated in such a way that a closed form for the adjoint angular function can be obtained. The MOCC method then requires only one cycle of scanning over the cyclic tracking lines in each spatial iteration. We also show that the source importance function by CP method is mathematically equivalent to the adjoint function by MOCC method. In order to speed up the MOCC solution algorithm, a group-reduction and group-splitting techniques based on the structure of the adjoint scattering matrix are implemented. A combined forward flux/adjoint function iteration scheme, based on the group-splitting technique and the common use of a large number of variables storing tracking-line data and exponential values, is proposed to reduce the
Application of perturbation theory to lattice calculations based on method of cyclic characteristics
International Nuclear Information System (INIS)
Assawaroongruengchot, M.
2007-01-01
Perturbation theory is a technique used for the estimation of changes in performance functionals, such as linear reaction rate ratio and eigenvalue affected by small variations in reactor core compositions. Here the algorithm of perturbation theory is developed for the multigroup integral neutron transport problems in 2D fuel assemblies with isotropic scattering. The integral transport equation is used in the perturbative formulation because it represents the interconnecting neutronic systems of the lattice assemblies via the tracking lines. When the integral neutron transport equation is used in the formulation, one needs to solve the resulting integral transport equations for the flux importance and generalized flux importance functions. The relationship between the generalized flux importance and generalized source importance functions is defined in order to transform the generalized flux importance transport equations into the integro-differential equations for the generalized adjoints. Next we develop the adjoint and generalized adjoint transport solution algorithms based on the method of cyclic characteristics (MOCC) in DRAGON code. In the MOCC method, the adjoint characteristics equations associated with a cyclic tracking line are formulated in such a way that a closed form for the adjoint angular function can be obtained. The MOCC method then requires only one cycle of scanning over the cyclic tracking lines in each spatial iteration. We also show that the source importance function by CP method is mathematically equivalent to the adjoint function by MOCC method. In order to speed up the MOCC solution algorithm, a group-reduction and group-splitting techniques based on the structure of the adjoint scattering matrix are implemented. A combined forward flux/adjoint function iteration scheme, based on the group-splitting technique and the common use of a large number of variables storing tracking-line data and exponential values, is proposed to reduce the
International Nuclear Information System (INIS)
Matsuda, Tomohiro
2009-01-01
The δN formalism is considered to calculate the evolution of the curvature perturbation in generalized multi-field inflation models. The result is consistent with the usual calculation of the standard kinetic term. For the calculation of the generalized kinetic term, we improved the definition of the adiabatic field. Our calculation improves the usual calculation of R . based on the field equations and the perturbations, giving a very simple and intuitive argument for the evolution equations in terms of the perturbations of the inflaton velocity. Significance of non-equilibrium corrections are also discussed, which is caused by the small-scale (decaying) inhomogeneities. This formalism based on the modulated inflation scenario (i.e., calculation based on the perturbations related to the inflaton velocity) provides a powerful tool for investigating the signature of moduli that may appear in string theory.
New predictions for generalized spin polarizabilities from heavy baryon chiral perturbation theory
International Nuclear Information System (INIS)
Chung-Wen Kao; Barbara Pasquini; Marc Vanderhaeghen
2004-01-01
We extract the next-to-next-to-leading order results for spin-flip generalized polarizabilities (GPs) of the nucleon from the spin-dependent amplitudes for virtual Compton scattering (VCS) at Ο(p 4 ) in heavy baryon chiral perturbation theory. At this order, no unknown low energy constants enter the theory, allowing us to make absolute predictions for all spin-flip GPs. Furthermore, by using constraint equations between the GPs due to nucleon crossing combined with charge conjugation symmetry of the VCS amplitudes, we get a next-to-next-to-next-to-leading order prediction for one of the GPs. We provide estimates for forthcoming double polarization experiments which allow to access these spin-flip GPs of the nucleon
Chiral perturbation theory for generalized parton distributions and baryon distribution amplitudes
Energy Technology Data Exchange (ETDEWEB)
Wein, Philipp
2016-05-06
In this thesis we apply low-energy effective field theory to the first moments of generalized parton distributions and to baryon distribution amplitudes, which are both highly relevant for the parametrization of the nonperturbative part in hard processes. These quantities yield complementary information on hadron structure, since the former treat hadrons as a whole and, thus, give information about the (angular) momentum carried by an entire parton species on average, while the latter parametrize the momentum distribution within an individual Fock state. By performing one-loop calculations within covariant baryon chiral perturbation theory, we obtain sensible parametrizations of the quark mass dependence that are ideally suited for the subsequent analysis of lattice QCD data.
International Nuclear Information System (INIS)
Hughes, S.
1977-01-01
An expression is derived for the solar radiation pressure disturbing function on an Earth satellite orbit which takes into account the variation of the solar radiation flux with distance from the Sun's centre and the absorption of radiation by the satellite. This expression is then expanded in terms of the Keplerian elements of the satellite and solar orbits using Kaula's method (Astr. J.; 67:300 (1962)). The Kaula inclination functions are replaced by an equivalent set of modified Allan (Proc. R. Soc. A.; 288:60 (1965)) inclination functions. The resulting expression reduces to the form commonly used in solar radiation pressure perturbation studies (e.g. Aksnes, Cel. Mech.; 13:89 (1976)), when certain terms are neglected. If, as happens quite often in practice, a satellite's orbit is in near-resonance with certain of these neglected terms, these near-resonant terms can cause changes in the satellite's orbital elements comparable to those produced by the largest term in Aksnes's expression. A new expression for the solar radiation pressure disturbing function expansion is suggested for use in future studies of satellite orbits perturbed by solar radiation pressure. (author)
A perturbation method in strongly correlated fermion systems
International Nuclear Information System (INIS)
Keiter, H.; Oberbach, S.; Kilic, S.
1998-01-01
We present a new expression for the grand partition function of a many-body system which contains a generalized Feenberg energy formula. In addition a form of the momentum distribution function of the Luttinger model is derived and non Fermi liquid behaviour is demonstrated. (Copyright (1998) World Scientific Publishing Co. Pte. Ltd)
Directory of Open Access Journals (Sweden)
Muhammad Aslam Noor
2008-01-01
Full Text Available We suggest and analyze a technique by combining the variational iteration method and the homotopy perturbation method. This method is called the variational homotopy perturbation method (VHPM. We use this method for solving higher dimensional initial boundary value problems with variable coefficients. The developed algorithm is quite efficient and is practically well suited for use in these problems. The proposed scheme finds the solution without any discritization, transformation, or restrictive assumptions and avoids the round-off errors. Several examples are given to check the reliability and efficiency of the proposed technique.
Extended Krenciglowa-Kuo method and perturbation expansion of Q-box
International Nuclear Information System (INIS)
Shimizu, Genki; Otsuka, Takaharu; Takayanagi, Kazuo
2015-01-01
The Extended Krenciglowa-Kuo (EKK) method is a microscopic method to construct the energy-independent effective Hamiltonian H eff ; provided with an exact Q-box of the system, we can show which eigenstates are described by H eff given by the EKK method. In actual calculations, however, we can calculate the Q-box only up to a finite order in the perturbation theory. In this work, we examine the EKK method with the approximate Q-box, and show that the perturbative calculation of the Q-box does not harm the convergence properties of the EKK iterative method. (author)
Generalized atmospheric Rosenbluth methods (GARM)
International Nuclear Information System (INIS)
Rechnitzer, A; Janse van Rensburg, E J
2008-01-01
We show that the classical Rosenbluth method for sampling self-avoiding walks (Hammersley and Morton 1954 J. R. Stat. Soc. B 16 23, Rosenbluth and Rosenbluth 1955 J. Chem. Phys. 23 356) can be extended to a general algorithm for sampling many families of objects, including self-avoiding polygons. The implementation relies on an elementary move which is a generalization of kinetic growth; rather than only appending edges to the endpoint, edges may be inserted at any vertex provided the resulting objects still lie within the same family. This gives, for the first time, a kinetic growth algorithm for sampling self-avoiding polygons. We implement this method using pruning and enrichment (Grassberger 1997 Phys. Rev. E 56 3682) to sample self-avoiding walks and polygons. The algorithm can be further extended by mixing it with length-preserving moves, such as pivots and crank-shaft moves. (fast track communication)
Hybridization of the probability perturbation method with gradient information
DEFF Research Database (Denmark)
Johansen, Kent; Caers, J.; Suzuki, S.
2007-01-01
Geostatistically based history-matching methods make it possible to devise history-matching strategies that will honor geologic knowledge about the reservoir. However, the performance of these methods is known to be impeded by slow convergence rates resulting from the stochastic nature of the alg...
Deriving average soliton equations with a perturbative method
International Nuclear Information System (INIS)
Ballantyne, G.J.; Gough, P.T.; Taylor, D.P.
1995-01-01
The method of multiple scales is applied to periodically amplified, lossy media described by either the nonlinear Schroedinger (NLS) equation or the Korteweg--de Vries (KdV) equation. An existing result for the NLS equation, derived in the context of nonlinear optical communications, is confirmed. The method is then applied to the KdV equation and the result is confirmed numerically
Utilization of the perturbation method for determination of the buckling heterogenous reactors
International Nuclear Information System (INIS)
Gheorghe, R.
1975-01-01
Evaluation of material buckling for heterogenous nulcear reactors is a key-problem for reactor people. In this direction several methods have been elaborated: bi-group method, heterogenous method and perturbation methods. Out of them, mostly employed is the perturbation method which is also presented in this paper and is applied in some parameter calculations of a new cell type for which fuel is positioned in the marginal area and the moderator is in the centre. It is based on the technique of progressive substitution. Advantages of the method: buckling comes out clearly, high level defects due to differences between O perturbated fluxes and the unperturbated flux Osub(o) can be corrected by an iterative procedure; using a modified bi-group theory, one can clearly describe effects of other parameters
International Nuclear Information System (INIS)
Maldonado, G.I.; Turinsky, P.J.; Kropaczek, D.J.
1993-01-01
The computational capability of efficiently and accurately evaluate reactor core attributes (i.e., k eff and power distributions as a function of cycle burnup) utilizing a second-order accurate advanced nodal Generalized Perturbation Theory (GPT) model has been developed. The GPT model is derived from the forward non-linear iterative Nodal Expansion Method (NEM) strategy, thereby extending its inherent savings in memory storage and high computational efficiency to also encompass GPT via the preservation of the finite-difference matrix structure. The above development was easily implemented into the existing coarse-mesh finite-difference GPT-based in-core fuel management optimization code FORMOSA-P, thus combining the proven robustness of its adaptive Simulated Annealing (SA) multiple-objective optimization algorithm with a high-fidelity NEM GPT neutronics model to produce a powerful computational tool used to generate families of near-optimum loading patterns for PWRs. (orig.)
Perturbation methods and the Melnikov functions for slowly varying oscillators
International Nuclear Information System (INIS)
Lakrad, Faouzi; Charafi, Moulay Mustapha
2005-01-01
A new approach to obtaining the Melnikov function for homoclinic orbits in slowly varying oscillators is proposed. The present method applies the Lindstedt-Poincare method to determine an approximation of homoclinic solutions. It is shown that the resultant Melnikov condition is the same as that obtained in the usual way involving distance functions in three dimensions by Wiggins and Holmes [Homoclinic orbits in slowly varying oscillators. SIAM J Math Anal 1987;18(3):612
González-Díaz, Humberto; Arrasate, Sonia; Gómez-SanJuan, Asier; Sotomayor, Nuria; Lete, Esther; Besada-Porto, Lina; Ruso, Juan M
2013-01-01
In general perturbation methods starts with a known exact solution of a problem and add "small" variation terms in order to approach to a solution for a related problem without known exact solution. Perturbation theory has been widely used in almost all areas of science. Bhor's quantum model, Heisenberg's matrix mechanincs, Feyman diagrams, and Poincare's chaos model or "butterfly effect" in complex systems are examples of perturbation theories. On the other hand, the study of Quantitative Structure-Property Relationships (QSPR) in molecular complex systems is an ideal area for the application of perturbation theory. There are several problems with exact experimental solutions (new chemical reactions, physicochemical properties, drug activity and distribution, metabolic networks, etc.) in public databases like CHEMBL. However, in all these cases, we have an even larger list of related problems without known solutions. We need to know the change in all these properties after a perturbation of initial boundary conditions. It means, when we test large sets of similar, but different, compounds and/or chemical reactions under the slightly different conditions (temperature, time, solvents, enzymes, assays, protein targets, tissues, partition systems, organisms, etc.). However, to the best of our knowledge, there is no QSPR general-purpose perturbation theory to solve this problem. In this work, firstly we review general aspects and applications of both perturbation theory and QSPR models. Secondly, we formulate a general-purpose perturbation theory for multiple-boundary QSPR problems. Last, we develop three new QSPR-Perturbation theory models. The first model classify correctly >100,000 pairs of intra-molecular carbolithiations with 75-95% of Accuracy (Ac), Sensitivity (Sn), and Specificity (Sp). The model predicts probabilities of variations in the yield and enantiomeric excess of reactions due to at least one perturbation in boundary conditions (solvent, temperature
Enhanced Multistage Homotopy Perturbation Method: Approximate Solutions of Nonlinear Dynamic Systems
Directory of Open Access Journals (Sweden)
Daniel Olvera
2014-01-01
Full Text Available We introduce a new approach called the enhanced multistage homotopy perturbation method (EMHPM that is based on the homotopy perturbation method (HPM and the usage of time subintervals to find the approximate solution of differential equations with strong nonlinearities. We also study the convergence of our proposed EMHPM approach based on the value of the control parameter h by following the homotopy analysis method (HAM. At the end of the paper, we compare the derived EMHPM approximate solutions of some nonlinear physical systems with their corresponding numerical integration solutions obtained by using the classical fourth order Runge-Kutta method via the amplitude-time response curves.
International Nuclear Information System (INIS)
Belendez, A.; Hernandez, A.; Belendez, T.; Neipp, C.; Marquez, A.
2008-01-01
He's homotopy perturbation method is used to calculate higher-order approximate periodic solutions of a nonlinear oscillator with discontinuity for which the elastic force term is proportional to sgn(x). We find He's homotopy perturbation method works very well for the whole range of initial amplitudes, and the excellent agreement of the approximate frequencies and periodic solutions with the exact ones has been demonstrated and discussed. Only one iteration leads to high accuracy of the solutions with a maximal relative error for the approximate period of less than 1.56% for all values of oscillation amplitude, while this relative error is 0.30% for the second iteration and as low as 0.057% when the third-order approximation is considered. Comparison of the result obtained using this method with those obtained by different harmonic balance methods reveals that He's homotopy perturbation method is very effective and convenient
Analysis of Diffusion Problems using Homotopy Perturbation and Variational Iteration Methods
DEFF Research Database (Denmark)
Barari, Amin; Poor, A. Tahmasebi; Jorjani, A.
2010-01-01
In this paper, variational iteration method and homotopy perturbation method are applied to different forms of diffusion equation. The diffusion equations have found wide applications in heat transfer problems, theory of consolidation and many other problems in engineering. The methods proposed...
International Nuclear Information System (INIS)
Biazar, J.; Eslami, M.; Aminikhah, H.
2009-01-01
In this article, an application of He's homotopy perturbation method is applied to solve systems of Volterra integral equations of the first kind. Some non-linear examples are prepared to illustrate the efficiency and simplicity of the method. Applying the method for linear systems is so easily that it does not worth to have any example.
International Nuclear Information System (INIS)
Biazar, J.; Ghazvini, H.
2009-01-01
In this paper, the He's homotopy perturbation method is applied to solve systems of Volterra integral equations of the second kind. Some examples are presented to illustrate the ability of the method for linear and non-linear such systems. The results reveal that the method is very effective and simple.
Application of homotopy-perturbation method to nonlinear population dynamics models
International Nuclear Information System (INIS)
Chowdhury, M.S.H.; Hashim, I.; Abdulaziz, O.
2007-01-01
In this Letter, the homotopy-perturbation method (HPM) is employed to derive approximate series solutions of nonlinear population dynamics models. The nonlinear models considered are the multispecies Lotka-Volterra equations. The accuracy of this method is examined by comparison with the available exact and the fourth-order Runge-Kutta method (RK4)
Stochastic Generalized Method of Moments
Yin, Guosheng; Ma, Yanyuan; Liang, Faming; Yuan, Ying
2011-01-01
The generalized method of moments (GMM) is a very popular estimation and inference procedure based on moment conditions. When likelihood-based methods are difficult to implement, one can often derive various moment conditions and construct the GMM objective function. However, minimization of the objective function in the GMM may be challenging, especially over a large parameter space. Due to the special structure of the GMM, we propose a new sampling-based algorithm, the stochastic GMM sampler, which replaces the multivariate minimization problem by a series of conditional sampling procedures. We develop the theoretical properties of the proposed iterative Monte Carlo method, and demonstrate its superior performance over other GMM estimation procedures in simulation studies. As an illustration, we apply the stochastic GMM sampler to a Medfly life longevity study. Supplemental materials for the article are available online. © 2011 American Statistical Association.
Stochastic Generalized Method of Moments
Yin, Guosheng
2011-08-16
The generalized method of moments (GMM) is a very popular estimation and inference procedure based on moment conditions. When likelihood-based methods are difficult to implement, one can often derive various moment conditions and construct the GMM objective function. However, minimization of the objective function in the GMM may be challenging, especially over a large parameter space. Due to the special structure of the GMM, we propose a new sampling-based algorithm, the stochastic GMM sampler, which replaces the multivariate minimization problem by a series of conditional sampling procedures. We develop the theoretical properties of the proposed iterative Monte Carlo method, and demonstrate its superior performance over other GMM estimation procedures in simulation studies. As an illustration, we apply the stochastic GMM sampler to a Medfly life longevity study. Supplemental materials for the article are available online. © 2011 American Statistical Association.
Application of a Perturbation Method for Realistic Dynamic Simulation of Industrial Robots
International Nuclear Information System (INIS)
Waiboer, R. R.; Aarts, R. G. K. M.; Jonker, J. B.
2005-01-01
This paper presents the application of a perturbation method for the closed-loop dynamic simulation of a rigid-link manipulator with joint friction. In this method the perturbed motion of the manipulator is modelled as a first-order perturbation of the nominal manipulator motion. A non-linear finite element method is used to formulate the dynamic equations of the manipulator mechanism. In a closed-loop simulation the driving torques are generated by the control system. Friction torques at the actuator joints are introduced at the stage of perturbed dynamics. For a mathematical model of the friction torques we implemented the LuGre friction model that accounts both for the sliding and pre-sliding regime. To illustrate the method, the motion of a six-axes industrial Staeubli robot is simulated. The manipulation task implies transferring a laser spot along a straight line with a trapezoidal velocity profile. The computed trajectory tracking errors are compared with measured values, where in both cases the tip position is computed from the joint angles using a nominal kinematic robot model. It is found that a closed-loop simulation using a non-linear finite element model of this robot is very time-consuming due to the small time step of the discrete controller. Using the perturbation method with the linearised model a substantial reduction of the computer time is achieved without loss of accuracy
Energy Technology Data Exchange (ETDEWEB)
Garcia-Ravelo, J.; Trujillo, A. L. [Escuela Superior de Fisica y Matematicas, Instituto Politecnico Nacional, Unidad Profesional Adolfo Lopez Mateos, Zacatenco, 07738 Mexico D.F. (Mexico); Schulze-Halberg, A. [Department of Mathematics and Actuarial Science, Indiana University Northwest, 3400 Broadway, Gary, Indiana 46408 (United States)
2012-10-15
We obtain explicit formulas for perturbative corrections of the infinite quantum well model. The formulas we obtain are based on a class of matrix elements that we construct by means of two-parameter ladder operators associated with the infinite quantum well system. Our approach can be used to construct solutions to Schroedinger-type equations that involve generalized harmonic perturbations of their potentials, such as cosine powers, Fourier series, and more general functions. As a particular case, we obtain characteristic values for odd periodic solutions of the Mathieu equation.
International Nuclear Information System (INIS)
García-Ravelo, J.; Trujillo, A. L.; Schulze-Halberg, A.
2012-01-01
We obtain explicit formulas for perturbative corrections of the infinite quantum well model. The formulas we obtain are based on a class of matrix elements that we construct by means of two-parameter ladder operators associated with the infinite quantum well system. Our approach can be used to construct solutions to Schrödinger-type equations that involve generalized harmonic perturbations of their potentials, such as cosine powers, Fourier series, and more general functions. As a particular case, we obtain characteristic values for odd periodic solutions of the Mathieu equation.
Lattice field theories: non-perturbative methods of analysis
International Nuclear Information System (INIS)
Weinstein, M.
1978-01-01
A lecture is given on the possible extraction of interesting physical information from quantum field theories by studying their semiclassical versions. From the beginning the problem of solving for the spectrum states of any given continuum quantum field theory is considered as a giant Schroedinger problem, and then some nonperturbative methods for diagonalizing the Hamiltonian of the theory are explained without recourse to semiclassical approximations. The notion of a lattice appears as an artifice to handle the problems associated with the familiar infrared and ultraviolet divergences of continuum quantum field theory and in fact for all but gauge theories. 18 references
The comparison of MCNP perturbation technique with MCNP difference method in critical calculation
International Nuclear Information System (INIS)
Liu Bin; Lv Xuefeng; Zhao Wei; Wang Kai; Tu Jing; Ouyang Xiaoping
2010-01-01
For a nuclear fission system, we calculated Δk eff , which arise from system material composition changes, by two different approaches, the MCNP perturbation technique and the MCNP difference method. For every material composition change, we made four different runs, each run with different cycles or each cycle generating different neutrons, then we compared the two Δk eff that are obtained by two different approaches. As a material composition change in any particular cell of the nuclear fission system is small compared to the material compositions in the whole nuclear fission system, in other words, this composition change can be treated as a small perturbation, the Δk eff results obtained from the MCNP perturbation technique are much quicker, much more efficient and reliable than the results from the MCNP difference method. When a material composition change in any particular cell of the nuclear fission system is significant compared to the material compositions in the whole nuclear fission system, both the MCNP perturbation technique and the MCNP difference method can give satisfactory results. But for the run with the same cycles and each cycle generating the same neutrons, the results obtained from the MCNP perturbation technique are systemically less than the results obtained from the MCNP difference method. To further confirm our calculation results from the MCNP4C, we run the exact same MCNP4C input file in MCNP5, the calculation results from MCNP5 are the same as the calculation results from MCNP4C. We need caution when using the MCNP perturbation technique to calculate the Δk eff as the material composition change is large compared to the material compositions in the whole nuclear fission system, even though the material composition changes of any particular cell of the fission system still meet the criteria of MCNP perturbation technique.
The multistage homotopy-perturbation method: A powerful scheme for handling the Lorenz system
International Nuclear Information System (INIS)
Chowdhury, M.S.H.; Hashim, I.; Momani, S.
2009-01-01
In this paper, a new reliable algorithm based on an adaptation of the standard homotopy-perturbation method (HPM) is presented. The HPM is treated as an algorithm in a sequence of intervals (i.e. time step) for finding accurate approximate solutions to the famous Lorenz system. Numerical comparisons between the multistage homotopy-perturbation method (MHPM) and the classical fourth-order Runge-Kutta (RK4) method reveal that the new technique is a promising tool for the nonlinear systems of ODEs.
Born approximation to a perturbative numerical method for the solution of the Schrodinger equation
International Nuclear Information System (INIS)
Adam, Gh.
1978-05-01
A perturbative numerical (PN) method is given for the solution of a regular one-dimensional Cauchy problem arising from the Schroedinger equation. The present method uses a step function approximation for the potential. Global, free of scaling difficulty, forward and backward PN algorithms are derived within first order perturbation theory (Born approximation). A rigorous analysis of the local truncation errors is performed. This shows that the order of accuracy of the method is equal to four. In between the mesh points, the global formula for the wavefunction is accurate within O(h 4 ), while that for the first order derivative is accurate within O(h 3 ). (author)
New numerical method for iterative or perturbative solution of quantum field theory
International Nuclear Information System (INIS)
Hahn, S.C.; Guralnik, G.S.
1999-01-01
A new computational idea for continuum quantum Field theories is outlined. This approach is based on the lattice source Galerkin methods developed by Garcia, Guralnik and Lawson. The method has many promising features including treating fermions on a relatively symmetric footing with bosons. As a spin-off of the technology developed for 'exact' solutions, the numerical methods used have a special case application to perturbation theory. We are in the process of developing an entirely numerical approach to evaluating graphs to high perturbative order. (authors)
Preparation of Stable Amyloid-β Oligomers Without Perturbative Methods.
Kotler, Samuel A; Ramamoorthy, Ayyalusamy
2018-01-01
Soluble amyloid-β (Aβ) oligomers have become a focal point in the study of Alzheimer's disease due to their ability to elicit cytotoxicity. A number of recent studies have concentrated on the structural characterization of soluble Aβ oligomers to gain insight into their mechanism of toxicity. Consequently, providing reproducible protocols for the preparation of such oligomers is of utmost importance. The method presented in this chapter details a protocol for preparing an Aβ oligomer, with a primarily disordered secondary structure, without the need for chemical modification or amino acid substitution. Due to the stability of these disordered Aβ oligomers and the reproducibility with which they form, they are amenable for biophysical and high-resolution structural characterization.
International Nuclear Information System (INIS)
White, J.R.
1986-01-01
A new approach for the physics design and analysis of LWR reload cores is developed and demonstrated through several practical applications. The new design philosophy uses first- and second-order response derivatives to predict the important reactor performance characteristics (power peaking, reactivity coefficients, etc.) for any number of possible material configurations (assembly shuffling and burnable poison loadings). The response derivatives are computed using generalized perturbation theory (GPT) techniques. This report describes in detail an idealized GPT-based design system. The idealized system would contain individual modules to generate the required first-order and higher-order sensitivity data. It would also contain at least two major application codes; one for core design optimization and the other for evaluation of several safety parameters of interest in off-normal situations. This ideal system would be fully automated, user-friendly, and quite flexible in its ability to provide a variety of design and analysis capabilities. Information gained form these three studies gives a good foundation for the development of a complete integrated design package
Directory of Open Access Journals (Sweden)
R. Darzi
2010-01-01
Full Text Available We applied the variational iteration method and the homotopy perturbation method to solve Sturm-Liouville eigenvalue and boundary value problems. The main advantage of these methods is the flexibility to give approximate and exact solutions to both linear and nonlinear problems without linearization or discretization. The results show that both methods are simple and effective.
Darzi R; Neamaty A
2010-01-01
We applied the variational iteration method and the homotopy perturbation method to solve Sturm-Liouville eigenvalue and boundary value problems. The main advantage of these methods is the flexibility to give approximate and exact solutions to both linear and nonlinear problems without linearization or discretization. The results show that both methods are simple and effective.
International Nuclear Information System (INIS)
Kim, Do Heon; Choi, Hang Bok
2001-01-01
A generalized perturbation theory (GPT) program, GENOVA, has been developed for the purpose of various applications to Canadian deuterium uranium (CANDU) reactor physics analyses. GENOVA was written under the framework of CANDU physics design and analysis code, RFSP. A sensitivity method based on the GPT was implemented in GENOVA to estimate various sensitivity coefficients related to the movement of zone controller units (ZCUs) existing in the CANDU reactor. The numerical algorithm for the sensitivity method was verified by a simple 2 x 2 node problem. The capability of predicting ZCU levels upon a refueling perturbation was validated for a CANDU-6 reactor problem. The applicability of GENOVA to the CANDU-6 core physics analysis has been demonstrated with the optimum refueling simulation and the uncertainty analysis problems. For the optimum refueling simulation, an optimum channel selection strategy has been proposed, using the ZCU level predicted by GENOVA. The refueling simulation of a CANDU-6 natural uranium core has shown that the ZCU levels are successfully controlled within the operating range while the channel and bundle powers are satisfying the license limits. An uncertainty analysis has been performed for the fuel composition heterogeneity of a CANDU DUPIC core, using the sensitivity coefficients generated by GENOVA. The results have shown that the uncertainty of the core performance parameter can be reduced appreciably when the contents of the major fissile isotopes are tightly controlled. GENOVA code has been successfully explored to supplement the weak points of the current design and analysis code, such as the incapacity of performing an optimum refueling simulation and uncertainty analysis. The sample calculations have shown that GENOVA has strong potential to be used for CANDU core analysis combined with the current design and analysis code, RFSP, especially for the development of advanced CANDU fuels
The method of rigged spaces in singular perturbation theory of self-adjoint operators
Koshmanenko, Volodymyr; Koshmanenko, Nataliia
2016-01-01
This monograph presents the newly developed method of rigged Hilbert spaces as a modern approach in singular perturbation theory. A key notion of this approach is the Lax-Berezansky triple of Hilbert spaces embedded one into another, which specifies the well-known Gelfand topological triple. All kinds of singular interactions described by potentials supported on small sets (like the Dirac δ-potentials, fractals, singular measures, high degree super-singular expressions) admit a rigorous treatment only in terms of the equipped spaces and their scales. The main idea of the method is to use singular perturbations to change inner products in the starting rigged space, and the construction of the perturbed operator by the Berezansky canonical isomorphism (which connects the positive and negative spaces from a new rigged triplet). The approach combines three powerful tools of functional analysis based on the Birman-Krein-Vishik theory of self-adjoint extensions of symmetric operators, the theory of singular quadra...
Yield strength measurement of shock-loaded metal by flyer-impact perturbation method
Ma, Xiaojuan; Shi, Zhan
2018-06-01
Yield strength is one of the most important physical properties of a solid material, especially far from its melting line. The flyer-impact perturbation method measures material yield strength on the basis of correlation between the yield strength under shock compression and the damping of oscillatory perturbations in the shape of a shock front passing through the material. We used flyer-impact experiments on targets with machined grooves on the impact surface of shock 6061-T6 aluminum to between 32 and 61 GPa and recorded the evolution of the shock front perturbation amplitude in the sample with electric pins. Simulations using the elastic-plastic model can be matched to the experiments, explaining well the form of the perturbation decay and constraining the yield strength of 6061-T6 aluminum to be 1.31-1.75 GPa. These results are in agreement with values obtained from reshock and release wave profiles. We conclude that the flyer-impact perturbation method is indeed a new means to measure material strength.
Application of the perturbation iteration method to boundary layer type problems.
Pakdemirli, Mehmet
2016-01-01
The recently developed perturbation iteration method is applied to boundary layer type singular problems for the first time. As a preliminary work on the topic, the simplest algorithm of PIA(1,1) is employed in the calculations. Linear and nonlinear problems are solved to outline the basic ideas of the new solution technique. The inner and outer solutions are determined with the iteration algorithm and matched to construct a composite expansion valid within all parts of the domain. The solutions are contrasted with the available exact or numerical solutions. It is shown that the perturbation-iteration algorithm can be effectively used for solving boundary layer type problems.
Non-standard perturbative methods for the effective potential in λφ4 QFT
International Nuclear Information System (INIS)
Okopinska, A.
1986-07-01
The effective potential in scalar QFT is calculated in the non-standard perturbative methods and compared with the conventional loop expansion. In the space time dimensions 0 and 1 the results are compared with the ''exact'' effective potential obtained numerically. In 4 dimensions we show that λφ 4 theory is non-interacting. (author)
A Double Perturbation Method for Reducing Dynamical Degradation of the Digital Baker Map
Liu, Lingfeng; Lin, Jun; Miao, Suoxia; Liu, Bocheng
2017-06-01
The digital Baker map is widely used in different kinds of cryptosystems, especially for image encryption. However, any chaotic map which is realized on the finite precision device (e.g. computer) will suffer from dynamical degradation, which refers to short cycle lengths, low complexity and strong correlations. In this paper, a novel double perturbation method is proposed for reducing the dynamical degradation of the digital Baker map. Both state variables and system parameters are perturbed by the digital logistic map. Numerical experiments show that the perturbed Baker map can achieve good statistical and cryptographic properties. Furthermore, a new image encryption algorithm is provided as a simple application. With a rather simple algorithm, the encrypted image can achieve high security, which is competitive to the recently proposed image encryption algorithms.
Perturbation method for calculation of narrow-band impedance and trapped modes
International Nuclear Information System (INIS)
Heifets, S.A.
1987-01-01
An iterative method for calculation of the narrow-band impedance is described for a system with a small variation in boundary conditions, so that the variation can be considered as a perturbation. The results are compared with numeric calculations. The method is used to relate the origin of the trapped modes with the degeneracy of the spectrum of an unperturbed system. The method also can be applied to transverse impedance calculations. 6 refs., 6 figs., 1 tab
Directory of Open Access Journals (Sweden)
Abdoul R. Ghotbi
2008-01-01
Full Text Available Due to wide range of interest in use of bioeconomic models to gain insight into the scientific management of renewable resources like fisheries and forestry, homotopy perturbation method is employed to approximate the solution of the ratio-dependent predator-prey system with constant effort prey harvesting. The results are compared with the results obtained by Adomian decomposition method. The results show that, in new model, there are less computations needed in comparison to Adomian decomposition method.
Regularization and computational methods for precise solution of perturbed orbit transfer problems
Woollands, Robyn Michele
The author has developed a suite of algorithms for solving the perturbed Lambert's problem in celestial mechanics. These algorithms have been implemented as a parallel computation tool that has broad applicability. This tool is composed of four component algorithms and each provides unique benefits for solving a particular type of orbit transfer problem. The first one utilizes a Keplerian solver (a-iteration) for solving the unperturbed Lambert's problem. This algorithm not only provides a "warm start" for solving the perturbed problem but is also used to identify which of several perturbed solvers is best suited for the job. The second algorithm solves the perturbed Lambert's problem using a variant of the modified Chebyshev-Picard iteration initial value solver that solves two-point boundary value problems. This method converges over about one third of an orbit and does not require a Newton-type shooting method and thus no state transition matrix needs to be computed. The third algorithm makes use of regularization of the differential equations through the Kustaanheimo-Stiefel transformation and extends the domain of convergence over which the modified Chebyshev-Picard iteration two-point boundary value solver will converge, from about one third of an orbit to almost a full orbit. This algorithm also does not require a Newton-type shooting method. The fourth algorithm uses the method of particular solutions and the modified Chebyshev-Picard iteration initial value solver to solve the perturbed two-impulse Lambert problem over multiple revolutions. The method of particular solutions is a shooting method but differs from the Newton-type shooting methods in that it does not require integration of the state transition matrix. The mathematical developments that underlie these four algorithms are derived in the chapters of this dissertation. For each of the algorithms, some orbit transfer test cases are included to provide insight on accuracy and efficiency of these
Supersingular quantum perturbations
International Nuclear Information System (INIS)
Detwiler, L.C.; Klauder, J.R.
1975-01-01
A perturbation potential is called supersingular whenever generally every matrix element of the perturbation in the unperturbed eigenstates is infinite. It follows that supersingular perturbations do not have conventional perturbation expansions, say for energy eigenvalues. By invoking variational arguments, we determine the asymptotic behavior of the energy eigenvalues for asymptotically small values of the coupling constant of the supersingular perturbation
Improved Monte Carlo-perturbation method for estimation of control rod worths in a research reactor
International Nuclear Information System (INIS)
Kalcheva, Silva; Koonen, Edgar
2009-01-01
A hybrid method dedicated to improve the experimental technique for estimation of control rod worths in a research reactor is presented. The method uses a combination of Monte Carlo technique and perturbation theory. Perturbation method is used to obtain the equation for the relative efficiency of control rod insertion. A series of coefficients, describing the axial absorption profile are used to correct the equation for a composite rod, having a complicated burn-up irradiation history. These coefficients have to be determined - by experiment or by using some theoretical/numerical method. In the present paper they are derived from the macroscopic absorption cross-sections, obtained from detailed Monte Carlo calculations by MCNPX 2.6.F of the axial burn-up profile during control rod life. The method is validated on measurements of control rod worths at the BR2 reactor. Comparison with direct MCNPX evaluations of control rod worths is also presented
Perturbed Strong Stability Preserving Time-Stepping Methods For Hyperbolic PDEs
Hadjimichael, Yiannis
2017-09-30
A plethora of physical phenomena are modelled by hyperbolic partial differential equations, for which the exact solution is usually not known. Numerical methods are employed to approximate the solution to hyperbolic problems; however, in many cases it is difficult to satisfy certain physical properties while maintaining high order of accuracy. In this thesis, we develop high-order time-stepping methods that are capable of maintaining stability constraints of the solution, when coupled with suitable spatial discretizations. Such methods are called strong stability preserving (SSP) time integrators, and we mainly focus on perturbed methods that use both upwind- and downwind-biased spatial discretizations. Firstly, we introduce a new family of third-order implicit Runge–Kuttas methods with arbitrarily large SSP coefficient. We investigate the stability and accuracy of these methods and we show that they perform well on hyperbolic problems with large CFL numbers. Moreover, we extend the analysis of SSP linear multistep methods to semi-discretized problems for which different terms on the right-hand side of the initial value problem satisfy different forward Euler (or circle) conditions. Optimal perturbed and additive monotonicity-preserving linear multistep methods are studied in the context of such problems. Optimal perturbed methods attain augmented monotonicity-preserving step sizes when the different forward Euler conditions are taken into account. On the other hand, we show that optimal SSP additive methods achieve a monotonicity-preserving step-size restriction no better than that of the corresponding non-additive SSP linear multistep methods. Furthermore, we develop the first SSP linear multistep methods of order two and three with variable step size, and study their optimality. We describe an optimal step-size strategy and demonstrate the effectiveness of these methods on various one- and multi-dimensional problems. Finally, we establish necessary conditions
Application of Multistage Homotopy Perturbation Method to the Chaotic Genesio System
Directory of Open Access Journals (Sweden)
M. S. H. Chowdhury
2012-01-01
Full Text Available Finding accurate solution of chaotic system by using efficient existing numerical methods is very hard for its complex dynamical behaviors. In this paper, the multistage homotopy-perturbation method (MHPM is applied to the Chaotic Genesio system. The MHPM is a simple reliable modification based on an adaptation of the standard homotopy-perturbation method (HPM. The HPM is treated as an algorithm in a sequence of intervals for finding accurate approximate solutions to the Chaotic Genesio system. Numerical comparisons between the MHPM and the classical fourth-order Runge-Kutta (RK4 solutions are made. The results reveal that the new technique is a promising tool for the nonlinear chaotic systems of ordinary differential equations.
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Jing Wang
2013-01-01
Full Text Available The image reconstruction for electrical impedance tomography (EIT mathematically is a typed nonlinear ill-posed inverse problem. In this paper, a novel iteration regularization scheme based on the homotopy perturbation technique, namely, homotopy perturbation inversion method, is applied to investigate the EIT image reconstruction problem. To verify the feasibility and effectiveness, simulations of image reconstruction have been performed in terms of considering different locations, sizes, and numbers of the inclusions, as well as robustness to data noise. Numerical results indicate that this method can overcome the numerical instability and is robust to data noise in the EIT image reconstruction. Moreover, compared with the classical Landweber iteration method, our approach improves the convergence rate. The results are promising.
International Nuclear Information System (INIS)
Hojjati, M.H.; Jafari, S.
2008-01-01
In this work, two powerful analytical methods, namely homotopy perturbation method (HPM) and Adomian's decomposition method (ADM), are introduced to obtain distributions of stresses and displacements in rotating annular elastic disks with uniform and variable thicknesses and densities. The results obtained by these methods are then compared with the verified variational iteration method (VIM) solution. He's homotopy perturbation method which does not require a 'small parameter' has been used and a homotopy with an imbedding parameter p element of [0,1] is constructed. The method takes the full advantage of the traditional perturbation methods and the homotopy techniques and yields a very rapid convergence of the solution. Adomian's decomposition method is an iterative method which provides analytical approximate solutions in the form of an infinite power series for nonlinear equations without linearization, perturbation or discretization. Variational iteration method, on the other hand, is based on the incorporation of a general Lagrange multiplier in the construction of correction functional for the equation. This study demonstrates the ability of the methods for the solution of those complicated rotating disk cases with either no or difficult to find fairly exact solutions without the need to use commercial finite element analysis software. The comparison among these methods shows that although the numerical results are almost the same, HPM is much easier, more convenient and efficient than ADM and VIM
Nikazad, T; Davidi, R; Herman, G T
2012-03-01
We study the convergence of a class of accelerated perturbation-resilient block-iterative projection methods for solving systems of linear equations. We prove convergence to a fixed point of an operator even in the presence of summable perturbations of the iterates, irrespective of the consistency of the linear system. For a consistent system, the limit point is a solution of the system. In the inconsistent case, the symmetric version of our method converges to a weighted least squares solution. Perturbation resilience is utilized to approximate the minimum of a convex functional subject to the equations. A main contribution, as compared to previously published approaches to achieving similar aims, is a more than an order of magnitude speed-up, as demonstrated by applying the methods to problems of image reconstruction from projections. In addition, the accelerated algorithms are illustrated to be better, in a strict sense provided by the method of statistical hypothesis testing, than their unaccelerated versions for the task of detecting small tumors in the brain from X-ray CT projection data.
International Nuclear Information System (INIS)
Cuce, Erdem; Cuce, Pinar Mert
2015-01-01
Highlights: • Homotopy perturbation method has been applied to porous fins. • Dimensionless efficiency and effectiveness expressions have been firstly developed. • Effects of porous and convection parameters on thermal analysis have been clarified. • Ratio of porous fin to solid fin heat transfer rate has been given for various cases. • Reliability and practicality of homotopy perturbation method has been illustrated. - Abstract: In our previous works, thermal performance of straight fins with both constant and temperature-dependent thermal conductivity has been investigated in detail and dimensionless analytical expressions of fin efficiency and fin effectiveness have been developed for the first time in literature via homotopy perturbation method. In this study, previous works have been extended to porous fins. Governing equations have been formulated by performing Darcy’s model. Dimensionless temperature distribution along the length of porous fin has been determined as a function of porosity and convection parameters. The ratio of porous fin to solid fin heat transfer rate has also been evaluated as a function of thermo-geometric fin parameter. The results have been compared with those of finite difference method for a specific case and an excellent agreement has been observed. The expressions developed are beneficial for thermal engineers for preliminary assessment of thermophysical systems instead of consuming time in heat conduction problems governed by strongly nonlinear differential equations
Homotopy perturbation method for free vibration analysis of beams on elastic foundation
International Nuclear Information System (INIS)
Ozturk, Baki; Coskun, Safa Bozkurt; Koc, Mehmet Zahid; Atay, Mehmet Tarik
2010-01-01
In this study, the homotopy perturbation method (HPM) is applied for free vibration analysis of beam on elastic foundation. This numerical method is applied on a previously available case study. Analytical solutions and frequency factors are evaluated for different ratios of axial load N acting on the beam to Euler buckling load, N r . The application of HPM for the particular problem in this study gives results which are in excellent agreement with both analytical solutions and the variational iteration method (VIM) solutions for the case considered in this study and the differential transform method (DTM) results available in the literature.
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seyd ghasem enayati
2017-01-01
Full Text Available In this paper, two powerful analytical methods known as modified homotopy perturbation method and Amplitude Frequency Formulation called respectively MHPM and AFF, are introduced to derive approximate solutions of a system of ordinary differential equations appear in mechanical applications. These methods convert a difficult problem into a simple one, which can be easily handled. The obtained solutions are compared with numerical fourth order runge-kutta method to show the applicability and accuracy of both MHPM and AFF in solving this sample problem. The results attained in this paper confirm the idea that MHPM and AFF are powerful mathematical tools and they can be applied to linear and nonlinear problems.
Continuity and general perturbation of the Drazin inverse for closed linear operators
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N. Castro González
2002-01-01
Full Text Available We study perturbations and continuity of the Drazin inverse of a closed linear operator A and obtain explicit error estimates in terms of the gap between closed operators and the gap between ranges and nullspaces of operators. The results are used to derive a theorem on the continuity of the Drazin inverse for closed operators and to describe the asymptotic behavior of operator semigroups.
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Anant Kant Shukla
2014-11-01
Full Text Available We obtain approximate analytical solutions of two mathematical models of the dynamics of tobacco use and relapse including peer pressure using the homotopy perturbation method (HPM and the homotopy analysis method (HAM. To enlarge the domain of convergence we apply the Padé approximation to the HPM and HAM series solutions. We show graphically that the results obtained by both methods are very accurate in comparison with the numerical solution for a period of 30 years.
Determination of the most reactivity control rod by pseudo-harmonics perturbation method
International Nuclear Information System (INIS)
Freire, Fernando S.; Silva, Fernando C.; Martinez, Aquilino S.
2005-01-01
Frequently it is necessary to compute the change in core multiplication caused by a change in the core temperature or composition. Even when this perturbation is localized, such as a control rod inserted into the core, one does not have to repeat the original criticality calculation, but instead we can use the well-known pseudo-harmonics perturbation method to express the corresponding change in the multiplication factor in terms of the neutron flux expanded in the basis vectors characterizing the unperturbed core. Therefore we may compute the control rod worth to find the most reactivity control rod to calculate the fast shutdown margin. In this thesis we propose a simple and precise method to identify the most reactivity control rod. (author)
Energy Technology Data Exchange (ETDEWEB)
Perruchot-Triboulet, S.; Sanchez, R.
1997-12-01
The modification of the isotopic composition, the temperature or even accounting for across section uncertainties in one part of a nuclear reactor core, affects the value of the effective multiplication factor. A new tool allows the analysis of the reactivity effect generated by the modification of the system. With the help of the direct and adjoint fluxes, a detailed balance of reactivity, between the compared systems, is done for each isotopic cross section. After the presentation of the direct and adjoint transport equations in the context of the multigroup code transport APOLLO2, this note describes the method, based on perturbation theory, for the analysis of the reactivity variation. An example application is also given. (author).
Perturbation method utilization in the analysis of the Convertible Spectral Shift Reactor (RCVS)
International Nuclear Information System (INIS)
Bruna, G.B; Legendre, J.F.; Porta, J.; Doriath, J.Y.
1988-01-01
In the framework of the preliminary faisability studies on a new core concept, techniques derived from perturbation theory show-up very useful in the calculation and physical analysis of project parameters. We show, in the present work, some applications of these methods to the RCVS (Reacteur Convertible a Variation de Spectre - Convertible Spectral Shift Reactor) Concept studies. Actually, we present here the search of a few group project type energy structure and the splitting of reactivity effects into individual components [fr
Soliton solutions of the two-dimensional KdV-Burgers equation by homotopy perturbation method
International Nuclear Information System (INIS)
Molabahrami, A.; Khani, F.; Hamedi-Nezhad, S.
2007-01-01
In this Letter, the He's homotopy perturbation method (HPM) to finding the soliton solutions of the two-dimensional Korteweg-de Vries Burgers' equation (tdKdVB) for the initial conditions was applied. Numerical solutions of the equation were obtained. The obtained solutions, in comparison with the exact solutions admit a remarkable accuracy. The results reveal that the HPM is very effective and simple
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
Analysis of radionuclide transport through fissured porous media with a perturbation method
Energy Technology Data Exchange (ETDEWEB)
Banat, M [JGC Corp., Tokyo (Japan)
1995-04-01
This paper presents a specific procedure for obtaining solutions for the transport of radionuclides in a fissured porous media. The concentration profiles are deduced for a wide range of Peclet numbers using a perturbation method with a multiscale of time. Results show clearly that because of an increase of longitudinal dispersion, the radionuclide moves faster with respect to the case of zero dispersion (i.e. an infinite Peclet number). The main purpose of this paper is to demonstrate the practical advantage of the present calculation method with respect to the classical numerical and analytical methods used for radionuclide transport. (author).
International Nuclear Information System (INIS)
Claro, L.H.; Alvim, A.C.M.; Thome, Z.D.
1988-08-01
The objective of this work is to stydy the effect of intense perturbations, such as control rod insertion in the core of PWR reactors, through a perturbation approach consisting of a modified version of the pseudo-harmonics method. A typical one-dimensional PWR reactor model was used as a reference state, from which two perturbations were imposed, simulation gray and black control rod insertion. In the first case, eigenvalue convergence was achieved with the eighth order of approximation approximation and perturbed fluxes and eigenvalue estimates agreed very well with direct calculation results. The second case tested represents a very intense localized perturbation. Oscillation in keff were observed er of approximation increased and the method failed to converge. Results obtained indicate that the pseudo-harmonics method can be used to compute 2 group fluxes and fundamental eigenvalue of perturbated states resulting from gray control rod insertion in PWR reactors. The method is limited, however, by perturbation intensity, as other perturbation methods are. (author) [pt
International Nuclear Information System (INIS)
Gómez-Valent, Adrià; Karimkhani, Elahe; Solà, Joan
2015-01-01
We determine the Hubble expansion and the general cosmic perturbation equations for a general system consisting of self-conserved matter, ρ m , and self-conserved dark energy (DE), ρ D . While at the background level the two components are non-interacting, they do interact at the perturbations level. We show that the coupled system of matter and DE perturbations can be transformed into a single, third order, matter perturbation equation, which reduces to the (derivative of the) standard one in the case that the DE is just a cosmological constant. As a nontrivial application we analyze a class of dynamical models whose DE density ρ D (H) consists of a constant term, C 0 , and a series of powers of the Hubble rate. These models were previously analyzed from the point of view of dynamical vacuum models, but here we treat them as self-conserved DE models with a dynamical equation of state. We fit them to the wealth of expansion history and linear structure formation data and compare their fit quality with that of the concordance ΛCDM model. Those with C 0 =0 include the so-called ''entropic-force'' and ''QCD-ghost'' DE models, as well as the pure linear model ρ D ∼H, all of which appear strongly disfavored. The models with C 0 ≠0 , in contrast, emerge as promising dynamical DE candidates whose phenomenological performance is highly competitive with the rigid Λ-term inherent to the ΛCDM
Energy Technology Data Exchange (ETDEWEB)
Gómez-Valent, Adrià; Karimkhani, Elahe; Solà, Joan, E-mail: adriagova@ecm.ub.edu, E-mail: e.karimkhani91@basu.ac.ir, E-mail: sola@ecm.ub.edu [High Energy Physics Group, Dept. ECM, and Institut de Ciències del Cosmos (ICC), Universitat de Barcelona, Av. Diagonal 647, E-08028 Barcelona, Catalonia (Spain)
2015-12-01
We determine the Hubble expansion and the general cosmic perturbation equations for a general system consisting of self-conserved matter, ρ{sub m}, and self-conserved dark energy (DE), ρ{sub D}. While at the background level the two components are non-interacting, they do interact at the perturbations level. We show that the coupled system of matter and DE perturbations can be transformed into a single, third order, matter perturbation equation, which reduces to the (derivative of the) standard one in the case that the DE is just a cosmological constant. As a nontrivial application we analyze a class of dynamical models whose DE density ρ{sub D}(H) consists of a constant term, C{sub 0}, and a series of powers of the Hubble rate. These models were previously analyzed from the point of view of dynamical vacuum models, but here we treat them as self-conserved DE models with a dynamical equation of state. We fit them to the wealth of expansion history and linear structure formation data and compare their fit quality with that of the concordance ΛCDM model. Those with C{sub 0}=0 include the so-called ''entropic-force'' and ''QCD-ghost'' DE models, as well as the pure linear model ρ{sub D}∼H, all of which appear strongly disfavored. The models with C{sub 0}≠0 , in contrast, emerge as promising dynamical DE candidates whose phenomenological performance is highly competitive with the rigid Λ-term inherent to the ΛCDM.
Local and accumulated truncation errors in a class of perturbative numerical methods
International Nuclear Information System (INIS)
Adam, G.; Adam, S.; Corciovei, A.
1980-01-01
The approach to the solution of the radial Schroedinger equation using piecewise perturbative theory with a step function reference potential leads to a class of powerful numerical methods, conveniently abridged as SF-PNM(K), where K denotes the order at which the perturbation series was truncated. In the present paper rigorous results are given for the local truncation errors and bounds are derived for the accumulated truncated errors associated to SF-PNM(K), K = 0, 1, 2. They allow us to establish the smoothness conditions which have to be fulfilled by the potential in order to ensure a safe use of SF-PNM(K), and to understand the experimentally observed behaviour of the numerical results with the step size h. (author)
Conformal methods in general relativity
Valiente Kroon, Juan A
2016-01-01
This book offers a systematic exposition of conformal methods and how they can be used to study the global properties of solutions to the equations of Einstein's theory of gravity. It shows that combining these ideas with differential geometry can elucidate the existence and stability of the basic solutions of the theory. Introducing the differential geometric, spinorial and PDE background required to gain a deep understanding of conformal methods, this text provides an accessible account of key results in mathematical relativity over the last thirty years, including the stability of de Sitter and Minkowski spacetimes. For graduate students and researchers, this self-contained account includes useful visual models to help the reader grasp abstract concepts and a list of further reading, making this the perfect reference companion on the topic.
International Nuclear Information System (INIS)
Noack, K.
1981-01-01
The perturbation source method is used in the Monte Carlo method in calculating small effects in a particle field. It offers primising possibilities for introducing positive correlation between subtracting estimates even in the cases where other methods fail, in the case of geometrical variations of a given arrangement. The perturbation source method is formulated on the basis of integral equations for the particle fields. The formulae for the second moment of the difference of events are derived. Explicity a certain class of transport games and different procedures for generating the so-called perturbation particles are considered [ru
Penkov, V. B.; Ivanychev, D. A.; Novikova, O. S.; Levina, L. V.
2018-03-01
The article substantiates the possibility of building full parametric analytical solutions of mathematical physics problems in arbitrary regions by means of computer systems. The suggested effective means for such solutions is the method of boundary states with perturbations, which aptly incorporates all parameters of an orthotropic medium in a general solution. We performed check calculations of elastic fields of an anisotropic rectangular region (test and calculation problems) for a generalized plane stress state.
DEFF Research Database (Denmark)
Reck, Kasper; Thomsen, Erik Vilain; Hansen, Ole
2011-01-01
. The solution of the mapped Helmholtz equation is found by solving an infinite series of Poisson equations using two dimensional Fourier series. The solution is entirely based on analytical expressions and is not mesh dependent. The analytical results are compared to a numerical (finite element method) solution......The scalar wave equation, or Helmholtz equation, describes within a certain approximation the electromagnetic field distribution in a given system. In this paper we show how to solve the Helmholtz equation in complex geometries using conformal mapping and the homotopy perturbation method...
Determination of Periodic Solution for Tapered Beams with Modified Iteration Perturbation Method
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Mohammad Mehdi Mashinchi Joubari
2015-01-01
Full Text Available In this paper, we implemented the Modified Iteration Perturbation Method (MIPM for approximating the periodic behavior of a tapered beam. This problem is formulated as a nonlinear ordinary differential equation with linear and nonlinear terms. The solution is quickly convergent and does not need to complicated calculations. Comparing the results of the MIPM with the exact solution shows that this method is effective and convenient. Also, it is predicated that MIPM can be potentially used in the analysis of strongly nonlinear oscillation problems accurately.
Directory of Open Access Journals (Sweden)
Claude Rodrigue Bambe Moutsinga
2018-01-01
Full Text Available Most existing multivariate models in finance are based on diffusion models. These models typically lead to the need of solving systems of Riccati differential equations. In this paper, we introduce an efficient method for solving systems of stiff Riccati differential equations. In this technique, a combination of Laplace transform and homotopy perturbation methods is considered as an algorithm to the exact solution of the nonlinear Riccati equations. The resulting technique is applied to solving stiff diffusion model problems that include interest rates models as well as two and three-factor stochastic volatility models. We show that the present approach is relatively easy, efficient and highly accurate.
Laplace transform homotopy perturbation method for the approximation of variational problems.
Filobello-Nino, U; Vazquez-Leal, H; Rashidi, M M; Sedighi, H M; Perez-Sesma, A; Sandoval-Hernandez, M; Sarmiento-Reyes, A; Contreras-Hernandez, A D; Pereyra-Diaz, D; Hoyos-Reyes, C; Jimenez-Fernandez, V M; Huerta-Chua, J; Castro-Gonzalez, F; Laguna-Camacho, J R
2016-01-01
This article proposes the application of Laplace Transform-Homotopy Perturbation Method and some of its modifications in order to find analytical approximate solutions for the linear and nonlinear differential equations which arise from some variational problems. As case study we will solve four ordinary differential equations, and we will show that the proposed solutions have good accuracy, even we will obtain an exact solution. In the sequel, we will see that the square residual error for the approximate solutions, belongs to the interval [0.001918936920, 0.06334882582], which confirms the accuracy of the proposed methods, taking into account the complexity and difficulty of variational problems.
Numerical simulation of the regularized long wave equation by He's homotopy perturbation method
Energy Technology Data Exchange (ETDEWEB)
Inc, Mustafa [Department of Mathematics, Firat University, 23119 Elazig (Turkey)], E-mail: minc@firat.edu.tr; Ugurlu, Yavuz [Department of Mathematics, Firat University, 23119 Elazig (Turkey)
2007-09-17
In this Letter, we present the homotopy perturbation method (shortly HPM) for obtaining the numerical solution of the RLW equation. We obtain the exact and numerical solutions of the Regularized Long Wave (RLW) equation for certain initial condition. The initial approximation can be freely chosen with possible unknown constants which can be determined by imposing the boundary and initial conditions. Comparison of the results with those of other methods have led us to significant consequences. The numerical solutions are compared with the known analytical solutions.
Numerical simulation of the regularized long wave equation by He's homotopy perturbation method
International Nuclear Information System (INIS)
Inc, Mustafa; Ugurlu, Yavuz
2007-01-01
In this Letter, we present the homotopy perturbation method (shortly HPM) for obtaining the numerical solution of the RLW equation. We obtain the exact and numerical solutions of the Regularized Long Wave (RLW) equation for certain initial condition. The initial approximation can be freely chosen with possible unknown constants which can be determined by imposing the boundary and initial conditions. Comparison of the results with those of other methods have led us to significant consequences. The numerical solutions are compared with the known analytical solutions
GENERAL METHOD OF STOCKS AUDIT
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Iryna Galushchak
2017-03-01
Full Text Available The article deals with the organization and methodology of accounting and auditing inventory enterprises. Suggestions for improvement of accounting permit to raise processing and presenting economic information to a higher level for making the economic and management decisions. Theory and practice problems of stocks audit were investigated. The basic directions of improvement of stock audit were defined. The auditor can form an opinion about the state of business transactions of accounting of goods, define shortcomings in its organization and possible directions of elimination of violations and abuses. Program of audit of operations accounting with stocks should include the investigation of the preservation of property, valuation and posting costs, correct evaluation of purchased tangible assets, using of stocks in production. It is worth to use techniques and methods of verification such as inventory, comparative control, comparison of documentary evidence, counter check, check arithmetic for audit of goods. Keywords: audit, stocks, activities of the company.
Shen, Tonghao; Su, Neil Qiang; Wu, Anan; Xu, Xin
2014-03-05
In this work, we first review the perturbative treatment of an oscillator with cubic anharmonicity. It is shown that there is a quantum-classical correspondence in terms of mean displacement, mean-squared displacement, and the corresponding variance in the first-order perturbation theory, provided that the amplitude of the classical oscillator is fixed at the zeroth-order energy of quantum mechanics EQM (0). This correspondence condition is realized by proposing the extended Langevin dynamics (XLD), where the key is to construct a proper driving force. It is assumed that the driving force adopts a simple harmonic form with its amplitude chosen according to EQM (0), while the driving frequency chosen as the harmonic frequency. The latter can be improved by using the natural frequency of the system in response to the potential if its anharmonicity is strong. By comparing to the accurate numeric results from discrete variable representation calculations for a set of diatomic species, it is shown that the present method is able to capture the large part of anharmonicity, being competitive with the wave function-based vibrational second-order perturbation theory, for the whole frequency range from ∼4400 cm(-1) (H2 ) to ∼160 cm(-1) (Na2 ). XLD shows a substantial improvement over the classical molecular dynamics which ceases to work for hard mode when zero-point energy effects are significant. Copyright © 2013 Wiley Periodicals, Inc.
Analysis of 2D reactor core using linear perturbation theory and nodal finite element methods
International Nuclear Information System (INIS)
Adrian Mugica; Edmundo del Valle
2005-01-01
In this work the multigroup steady state neutron diffusion equations are solved using the nodal finite element method (NFEM) and the Linear Perturbation Theory (LPT) for XY geometry. The NFEM used corresponds to the Raviart-Thomas schemes RT0 and RT1, interpolating 5 and 12 parameters respectively in each node of the space discretization. The accuracy of these methods is related with the dimension of the space approximation and the mesh size. Therefore, using fine meshes and the RT0 or RT1 nodal methods leads to a large an interesting eigenvalue problem. The finite element method used to discretize the weak formulation of the diffusion equations is the Galerkin one. The algebraic structure of the discrete eigenvalue problem is obtained and solved using the Wielandt technique and the BGSTAB iterative method using the SPARSKIT package developed by Yousef Saad. The results obtained with LPT show good agreement with the results obtained directly for the perturbed problem. In fact, the cpu time to solve a single problem, the unperturbed and the perturbed one, is practically the same but when one is focused in shuffling many times two different assemblies in the core then the LPT technique becomes quite useful to get good approximations in a short time. This particular problem was solved for one quarter-core with NFEM. Thus, the computer program based on LPT can be used to perform like an analysis tool in the fuel reload optimization or combinatory analysis to get reload patterns in nuclear power plants once that it had been incorporated with the thermohydraulic aspects needed to simulate accurately a real problem. The maximum differences between the NFEM and LPT for the three LWR reactor cores are about 250 pcm. This quantity is considered an acceptable value for this kind of analysis. (authors)
Lagos, Macarena; Bellini, Emilio; Noller, Johannes; Ferreira, Pedro G.; Baker, Tessa
2018-03-01
We analyse cosmological perturbations around a homogeneous and isotropic background for scalar-tensor, vector-tensor and bimetric theories of gravity. Building on previous results, we propose a unified view of the effective parameters of all these theories. Based on this structure, we explore the viable space of parameters for each family of models by imposing the absence of ghosts and gradient instabilities. We then focus on the quasistatic regime and confirm that all these theories can be approximated by the phenomenological two-parameter model described by an effective Newton's constant and the gravitational slip. Within the quasistatic regime we pinpoint signatures which can distinguish between the broad classes of models (scalar-tensor, vector-tensor or bimetric). Finally, we present the equations of motion for our unified approach in such a way that they can be implemented in Einstein-Boltzmann solvers.
International Nuclear Information System (INIS)
Kalcheva, Silva; Koonen, Edgar
2008-01-01
A hybrid method dedicated to improve the experimental technique for estimation of control rod worths in a research reactor is presented. The method uses a combination of Monte Carlo technique and perturbation theory. The perturbation theory is used to obtain the relation between the relative rod efficiency and the buckling of the reactor with partially inserted rod. A series of coefficients, describing the axial absorption profile are used to correct the buckling for an arbitrary composite rod, having complicated burn up irradiation history. These coefficients have to be determined - by experiment or by using some theoretical/numerical method. In the present paper they are derived from the macroscopic absorption cross sections, obtained from detailed Monte Carlo calculations by MCNPX 2.6.F of the axial burn up profile during control rod life. The method is validated on measurements of control rod worths at the BR2 reactor. Comparison with direct Monte Carlo evaluations of control rod worths is also presented. The uncertainties, arising from the used approximations in the presented hybrid method are discussed. (authors)
Directory of Open Access Journals (Sweden)
Rabounski D.
2007-07-01
Full Text Available We consider the Podkletnov effect — the weight loss of an object located over a superconducting disc in air due to support by an alternating magnetic field. We consider this problem using the mathematical methods of General Relativity. We show via Einstein’s equations and the geodesic equations in a space perturbed by a disc undergoing oscillatory bounces orthogonal to its own plane, that there is no r ˆ ole of superconductivity; the Podkletnov effect is due to the fact that the field of the background space non-holonomity (the basic non-othogonality of time lines to the spatial section, being perturbed by such an oscillating disc produces energy and momentum flow in order to compensate the perturbation in itself. Such a momentum flow is directed above the disc in Podkletnov’s experiment, so it works like negative gravity (anti-gravity. We propose a simple mechanical system which, simulating the Podkletnov effect, is an experimental test of the whole theory. The theory allows for other “anti-gravity devices”, which simulate the Podkletnov effect without use of very costly superconductor technology. Such devices could be applied to be used as a cheap source of new energy, and could have implications to air and space travel.
International Nuclear Information System (INIS)
Zhang Honghao; Yan Wenbin; Li Xuesong
2008-01-01
By using combinatorics, we give a new proof for the recurrence relations of the characteristic polynomial coefficients, and we further obtain an explicit expression for the generic term of the coefficient sequence, which yields the trace formulae of the Cayley-Hamilton's theorem with all coefficients explicitly given. This implies a byproduct, a complete expression for the determinant of any finite-dimensional matrix in terms of the traces of its successive powers. And we discuss some of their applications to chiral perturbation theory and general relativity
Non perturbative method for radiative corrections applied to lepton-proton scattering
International Nuclear Information System (INIS)
Chahine, C.
1979-01-01
We present a new, non perturbative method to effect radiative corrections in lepton (electron or muon)-nucleon scattering, useful for existing or planned experiments. This method relies on a spectral function derived in a previous paper, which takes into account both real soft photons and virtual ones and hence is free from infrared divergence. Hard effects are computed perturbatively and then included in the form of 'hard factors' in the non peturbative soft formulas. Practical computations are effected using the Gauss-Jacobi integration method which reduce the relevant integrals to a rapidly converging sequence. For the simple problem of the radiative quasi-elastic peak, we get an exponentiated form conjectured by Schwinger and found by Yennie, Frautschi and Suura. We compare also our results with the peaking approximation, which we derive independantly, and with the exact one-photon emission formula of Mo and Tsai. Applications of our method to the continuous spectrum include the radiative tail of the Δ 33 resonance in e + p scattering and radiative corrections to the Feynman scale invariant F 2 structure function for the kinematics of two recent high energy muon experiments
Generalized Time-Limited Balanced Reduction Method
DEFF Research Database (Denmark)
Shaker, Hamid Reza; Shaker, Fatemeh
2013-01-01
In this paper, a new method for model reduction of bilinear systems is presented. The proposed technique is from the family of gramian-based model reduction methods. The method uses time-interval generalized gramians in the reduction procedure rather than the ordinary generalized gramians...... and in such a way it improves the accuracy of the approximation within the time-interval which the method is applied. The time-interval generalized gramians are the solutions to the generalized time-interval Lyapunov equations. The conditions for these equations to be solvable are derived and an algorithm...
International Nuclear Information System (INIS)
Gratreau, P.
1987-01-01
The motion of charged particles in a magnetized plasma column, such as that of a magnetic mirror trap or a tokamak, is determined in the framework of the canonical perturbation theory through a method of variation of constants which preserves the energy conservation and the symmetry invariance. The choice of a frame of coordinates close to that of the magnetic coordinates allows a relatively precise determination of the guiding-center motion with a low-ordered approximation in the adiabatic parameter. A Hamiltonian formulation of the motion equations is obtained
Energy Technology Data Exchange (ETDEWEB)
Takac, S M; Krcevinac, S B [Institute of nuclear sciences Boris Kidric, Vinca, Beograd (Yugoslavia)
1966-07-15
Measurements of thermal neutron density distributions were carried out in a variety of reactor cells by the newly developed cell perturbation method. The big geometrical and nuclear differences between the considered cells served as a very good testing ground for both the theory and experiments. The final experimental results are compared with a 'THERMOS'-type of calculation and in one case with the K-7 TRANSPO. In lattices L-1, L-2 and L-3 a very good agreement was reached with the results of K-7 THERMOS, while in lattice L-4, because of its complexity, the agreement was within the quoted errors (author)
The generalized approximation method and nonlinear heat transfer equations
Directory of Open Access Journals (Sweden)
Rahmat Khan
2009-01-01
Full Text Available Generalized approximation technique for a solution of one-dimensional steady state heat transfer problem in a slab made of a material with temperature dependent thermal conductivity, is developed. The results obtained by the generalized approximation method (GAM are compared with those studied via homotopy perturbation method (HPM. For this problem, the results obtained by the GAM are more accurate as compared to the HPM. Moreover, our (GAM generate a sequence of solutions of linear problems that converges monotonically and rapidly to a solution of the original nonlinear problem. Each approximate solution is obtained as the solution of a linear problem. We present numerical simulations to illustrate and confirm the theoretical results.
Wang, Yajie; Shi, Yunbo; Yu, Xiaoyu; Liu, Yongjie
2016-01-01
Currently, tracking in photovoltaic (PV) systems suffers from some problems such as high energy consumption, poor anti-interference performance, and large tracking errors. This paper presents a solar PV tracking system on the basis of an improved perturbation and observation method, which maximizes photoelectric conversion efficiency. According to the projection principle, we design a sensor module with a light-intensity-detection module for environmental light-intensity measurement. The effect of environmental factors on the system operation is reduced, and intelligent identification of the weather is realized. This system adopts the discrete-type tracking method to reduce power consumption. A mechanical structure with a level-pitch double-degree-of-freedom is designed, and attitude correction is performed by closed-loop control. A worm-and-gear mechanism is added, and the reliability, stability, and precision of the system are improved. Finally, the perturbation and observation method designed and improved by this study was tested by simulated experiments. The experiments verified that the photoelectric sensor resolution can reach 0.344°, the tracking error is less than 2.5°, the largest improvement in the charge efficiency can reach 44.5%, and the system steadily and reliably works. PMID:27327657
Directory of Open Access Journals (Sweden)
Yajie Wang
Full Text Available Currently, tracking in photovoltaic (PV systems suffers from some problems such as high energy consumption, poor anti-interference performance, and large tracking errors. This paper presents a solar PV tracking system on the basis of an improved perturbation and observation method, which maximizes photoelectric conversion efficiency. According to the projection principle, we design a sensor module with a light-intensity-detection module for environmental light-intensity measurement. The effect of environmental factors on the system operation is reduced, and intelligent identification of the weather is realized. This system adopts the discrete-type tracking method to reduce power consumption. A mechanical structure with a level-pitch double-degree-of-freedom is designed, and attitude correction is performed by closed-loop control. A worm-and-gear mechanism is added, and the reliability, stability, and precision of the system are improved. Finally, the perturbation and observation method designed and improved by this study was tested by simulated experiments. The experiments verified that the photoelectric sensor resolution can reach 0.344°, the tracking error is less than 2.5°, the largest improvement in the charge efficiency can reach 44.5%, and the system steadily and reliably works.
Wang, Yajie; Shi, Yunbo; Yu, Xiaoyu; Liu, Yongjie
2016-01-01
Currently, tracking in photovoltaic (PV) systems suffers from some problems such as high energy consumption, poor anti-interference performance, and large tracking errors. This paper presents a solar PV tracking system on the basis of an improved perturbation and observation method, which maximizes photoelectric conversion efficiency. According to the projection principle, we design a sensor module with a light-intensity-detection module for environmental light-intensity measurement. The effect of environmental factors on the system operation is reduced, and intelligent identification of the weather is realized. This system adopts the discrete-type tracking method to reduce power consumption. A mechanical structure with a level-pitch double-degree-of-freedom is designed, and attitude correction is performed by closed-loop control. A worm-and-gear mechanism is added, and the reliability, stability, and precision of the system are improved. Finally, the perturbation and observation method designed and improved by this study was tested by simulated experiments. The experiments verified that the photoelectric sensor resolution can reach 0.344°, the tracking error is less than 2.5°, the largest improvement in the charge efficiency can reach 44.5%, and the system steadily and reliably works.
Energy Technology Data Exchange (ETDEWEB)
Schunert, Sebastian; Wang, Congjian; Wang, Yaqi; Kong, Fande; Ortensi, Javier; Baker, Benjamin; Gleicher, Frederick; DeHart, Mark; Martineau, Richard
2017-04-01
Rattlesnake and MAMMOTH are the designated TREAT analysis tools currently being developed at the Idaho National Laboratory. Concurrent with development of the multi-physics, multi-scale capabilities, sensitivity analysis and uncertainty quantification (SA/UQ) capabilities are required for predicitive modeling of the TREAT reactor. For steady-state SA/UQ, that is essential for setting initial conditions for the transients, generalized perturbation theory (GPT) will be used. This work describes the implementation of a PETSc based solver for the generalized adjoint equations that constitute a inhomogeneous, rank deficient problem. The standard approach is to use an outer iteration strategy with repeated removal of the fundamental mode contamination. The described GPT algorithm directly solves the GPT equations without the need of an outer iteration procedure by using Krylov subspaces that are orthogonal to the operator’s nullspace. Three test problems are solved and provide sufficient verification for the Rattlesnake’s GPT capability. We conclude with a preliminary example evaluating the impact of the Boron distribution in the TREAT reactor using perturbation theory.
Directory of Open Access Journals (Sweden)
P. J. Irvine
2013-09-01
Full Text Available We present a simple method to generate a perturbed parameter ensemble (PPE of a fully-coupled atmosphere-ocean general circulation model (AOGCM, HadCM3, without requiring flux-adjustment. The aim was to produce an ensemble that samples parametric uncertainty in some key variables and gives a plausible representation of the climate. Six atmospheric parameters, a sea-ice parameter and an ocean parameter were jointly perturbed within a reasonable range to generate an initial group of 200 members. To screen out implausible ensemble members, 20 yr pre-industrial control simulations were run and members whose temperature responses to the parameter perturbations were projected to be outside the range of 13.6 ± 2 °C, i.e. near to the observed pre-industrial global mean, were discarded. Twenty-one members, including the standard unperturbed model, were accepted, covering almost the entire span of the eight parameters, challenging the argument that without flux-adjustment parameter ranges would be unduly restricted. This ensemble was used in 2 experiments; an 800 yr pre-industrial and a 150 yr quadrupled CO2 simulation. The behaviour of the PPE for the pre-industrial control compared well to ERA-40 reanalysis data and the CMIP3 ensemble for a number of surface and atmospheric column variables with the exception of a few members in the Tropics. However, we find that members of the PPE with low values of the entrainment rate coefficient show very large increases in upper tropospheric and stratospheric water vapour concentrations in response to elevated CO2 and one member showed an implausible nonlinear climate response, and as such will be excluded from future experiments with this ensemble. The outcome of this study is a PPE of a fully-coupled AOGCM which samples parametric uncertainty and a simple methodology which would be applicable to other GCMs.
Investigation of collisional excitation-transfer processes in a plasma by laser perturbation method
International Nuclear Information System (INIS)
Sakurai, Takeki
1983-01-01
The theoretical background and the experimental method of the laser perturbation method applied to the study of collisional excitation transfer process in plasma are explained. The atomic density at some specified level can be evaluated theoretically. By using the theoretical results and the experimentally obtained data, the total attenuation probability, the collisional transfer probability and natural emission probability were estimated. For the experiments, continuous wave laser (cw) and pulse laser are employed. It is possible by using pulse dye laser to observe the attenuation curve directly, and to bring in resonance to any atomic spectra. At the beginning, the experimental studies were made on He-Ne discharge. The pulse dye laser has been used for the excitation of alkali atoms. The first application of pulse laser to the study of plasma physics was the study on He. The cross section of disalignment has also been studied by the laser perturbation. The alignment of atoms, step and cascade transfer, the confinement of radiation and optogalvanic effect are discussed in this paper. (Kato, T.)
Manzoni, Francesco; Ryde, Ulf
2018-03-01
We have calculated relative binding affinities for eight tetrafluorophenyl-triazole-thiogalactoside inhibitors of galectin-3 with the alchemical free-energy perturbation approach. We obtain a mean absolute deviation from experimental estimates of only 2-3 kJ/mol and a correlation coefficient (R 2) of 0.5-0.8 for seven relative affinities spanning a range of up to 11 kJ/mol. We also studied the effect of using different methods to calculate the charges of the inhibitor and different sizes of the perturbed group (the atoms that are described by soft-core potentials and are allowed to have differing coordinates). However, the various approaches gave rather similar results and it is not possible to point out one approach as consistently and significantly better than the others. Instead, we suggest that such small and reasonable variations in the computational method can be used to check how stable the calculated results are and to obtain a more accurate estimate of the uncertainty than if performing only one calculation with a single computational setup.
Fourth-order perturbative extension of the single-double excitation coupled-cluster method
International Nuclear Information System (INIS)
Derevianko, Andrei; Emmons, Erik D.
2002-01-01
Fourth-order many-body corrections to matrix elements for atoms with one valence electron are derived. The obtained diagrams are classified using coupled-cluster-inspired separation into contributions from n-particle excitations from the lowest-order wave function. The complete set of fourth-order diagrams involves only connected single, double, and triple excitations and disconnected quadruple excitations. Approximately half of the fourth-order diagrams are not accounted for by the popular coupled-cluster method truncated at single and double excitations (CCSD). Explicit formulas are tabulated for the entire set of fourth-order diagrams missed by the CCSD method and its linearized version, i.e., contributions from connected triple and disconnected quadruple excitations. A partial summation scheme of the derived fourth-order contributions to all orders of perturbation theory is proposed
Directory of Open Access Journals (Sweden)
Wenzhen Chen
2013-01-01
Full Text Available The singularly perturbed method (SPM is proposed to obtain the analytical solution for the delayed supercritical process of nuclear reactor with temperature feedback and small step reactivity inserted. The relation between the reactivity and time is derived. Also, the neutron density (or power and the average density of delayed neutron precursors as the function of reactivity are presented. The variations of neutron density (or power and temperature with time are calculated and plotted and compared with those by accurate solution and other analytical methods. It is shown that the results by the SPM are valid and accurate in the large range and the SPM is simpler than those in the previous literature.
A perturbation method to the tent map based on Lyapunov exponent and its application
Cao, Lv-Chen; Luo, Yu-Ling; Qiu, Sen-Hui; Liu, Jun-Xiu
2015-10-01
Perturbation imposed on a chaos system is an effective way to maintain its chaotic features. A novel parameter perturbation method for the tent map based on the Lyapunov exponent is proposed in this paper. The pseudo-random sequence generated by the tent map is sent to another chaos function — the Chebyshev map for the post processing. If the output value of the Chebyshev map falls into a certain range, it will be sent back to replace the parameter of the tent map. As a result, the parameter of the tent map keeps changing dynamically. The statistical analysis and experimental results prove that the disturbed tent map has a highly random distribution and achieves good cryptographic properties of a pseudo-random sequence. As a result, it weakens the phenomenon of strong correlation caused by the finite precision and effectively compensates for the digital chaos system dynamics degradation. Project supported by the Guangxi Provincial Natural Science Foundation, China (Grant No. 2014GXNSFBA118271), the Research Project of Guangxi University, China (Grant No. ZD2014022), the Fund from Guangxi Provincial Key Laboratory of Multi-source Information Mining & Security, China (Grant No. MIMS14-04), the Fund from the Guangxi Provincial Key Laboratory of Wireless Wideband Communication & Signal Processing, China (Grant No. GXKL0614205), the Education Development Foundation and the Doctoral Research Foundation of Guangxi Normal University, the State Scholarship Fund of China Scholarship Council (Grant No. [2014]3012), and the Innovation Project of Guangxi Graduate Education, China (Grant No. YCSZ2015102).
International Nuclear Information System (INIS)
Sakane, Shinichi; Yezdimer, Eric M.; Liu, Wenbin; Barriocanal, Jose A.; Doren, Douglas J.; Wood, Robert H.
2000-01-01
The ab initio/classical free energy perturbation (ABC-FEP) method proposed previously by Wood et al. [J. Chem. Phys. 110, 1329 (1999)] uses classical simulations to calculate solvation free energies within an empirical potential model, then applies free energy perturbation theory to determine the effect of changing the empirical solute-solvent interactions to corresponding interactions calculated from ab initio methods. This approach allows accurate calculation of solvation free energies using an atomistic description of the solvent and solute, with interactions calculated from first principles. Results can be obtained at a feasible computational cost without making use of approximations such as a continuum solvent or an empirical cavity formation energy. As such, the method can be used far from ambient conditions, where the empirical parameters needed for approximate theories of solvation may not be available. The sources of error in the ABC-FEP method are the approximations in the ab initio method, the finite sample of configurations, and the classical solvent model. This article explores the accuracy of various approximations used in the ABC-FEP method by comparing to the experimentally well-known free energy of hydration of water at two state points (ambient conditions, and 973.15 K and 600 kg/m3). The TIP4P-FQ model [J. Chem. Phys. 101, 6141 (1994)] is found to be a reliable solvent model for use with this method, even at supercritical conditions. Results depend strongly on the ab initio method used: a gradient-corrected density functional theory is not adequate, but a localized MP2 method yields excellent agreement with experiment. Computational costs are reduced by using a cluster approximation, in which ab initio pair interaction energies are calculated between the solute and up to 60 solvent molecules, while multi-body interactions are calculated with only a small cluster (5 to 12 solvent molecules). Sampling errors for the ab initio contribution to
Generalization of the ERIT Principle and Method
International Nuclear Information System (INIS)
Ruggiero, A.
2008-01-01
The paper describes the generalization of the method to produce secondary particles with a low-energy and low-intensity primary beam circulating in a Storage Ring with the Emittance-Recovery by Internal-Target (ERIT)
On dark energy isocurvature perturbation
International Nuclear Information System (INIS)
Liu, Jie; Zhang, Xinmin; Li, Mingzhe
2011-01-01
Determining the equation of state of dark energy with astronomical observations is crucially important to understand the nature of dark energy. In performing a likelihood analysis of the data, especially of the cosmic microwave background and large scale structure data the dark energy perturbations have to be taken into account both for theoretical consistency and for numerical accuracy. Usually, one assumes in the global fitting analysis that the dark energy perturbations are adiabatic. In this paper, we study the dark energy isocurvature perturbation analytically and discuss its implications for the cosmic microwave background radiation and large scale structure. Furthermore, with the current astronomical observational data and by employing Markov Chain Monte Carlo method, we perform a global analysis of cosmological parameters assuming general initial conditions for the dark energy perturbations. The results show that the dark energy isocurvature perturbations are very weakly constrained and that purely adiabatic initial conditions are consistent with the data
Energy Technology Data Exchange (ETDEWEB)
Fang, Xiao; Blazek, Jonathan A.; McEwen, Joseph E.; Hirata, Christopher M., E-mail: fang.307@osu.edu, E-mail: blazek@berkeley.edu, E-mail: mcewen.24@osu.edu, E-mail: hirata.10@osu.edu [Center for Cosmology and AstroParticle Physics, Department of Physics, The Ohio State University, 191 W Woodruff Ave, Columbus OH 43210 (United States)
2017-02-01
Cosmological perturbation theory is a powerful tool to predict the statistics of large-scale structure in the weakly non-linear regime, but even at 1-loop order it results in computationally expensive mode-coupling integrals. Here we present a fast algorithm for computing 1-loop power spectra of quantities that depend on the observer's orientation, thereby generalizing the FAST-PT framework (McEwen et al., 2016) that was originally developed for scalars such as the matter density. This algorithm works for an arbitrary input power spectrum and substantially reduces the time required for numerical evaluation. We apply the algorithm to four examples: intrinsic alignments of galaxies in the tidal torque model; the Ostriker-Vishniac effect; the secondary CMB polarization due to baryon flows; and the 1-loop matter power spectrum in redshift space. Code implementing this algorithm and these applications is publicly available at https://github.com/JoeMcEwen/FAST-PT.
Directory of Open Access Journals (Sweden)
Stefan Hollands
2009-09-01
Full Text Available In this paper, we propose a new framework for quantum field theory in terms of consistency conditions. The consistency conditions that we consider are ''associativity'' or ''factorization'' conditions on the operator product expansion (OPE of the theory, and are proposed to be the defining property of any quantum field theory. Our framework is presented in the Euclidean setting, and is applicable in principle to any quantum field theory, including non-conformal ones. In our framework, we obtain a characterization of perturbations of a given quantum field theory in terms of a certain cohomology ring of Hochschild-type. We illustrate our framework by the free field, but our constructions are general and apply also to interacting quantum field theories. For such theories, we propose a new scheme to construct the OPE which is based on the use of non-linear quantized field equations.
DEFF Research Database (Denmark)
Sørup, Hjalte Jomo Danielsen; Georgiadis, Stylianos; Gregersen, Ida Bülow
2017-01-01
Urban water infrastructure has very long planning horizons, and planning is thus very dependent on reliable estimates of the impacts of climate change. Many urban water systems are designed using time series with a high temporal resolution. To assess the impact of climate change on these systems......, similarly high-resolution precipitation time series for future climate are necessary. Climate models cannot at their current resolutions provide these time series at the relevant scales. Known methods for stochastic downscaling of climate change to urban hydrological scales have known shortcomings...... in constructing realistic climate-changed precipitation time series at the sub-hourly scale. In the present study we present a deterministic methodology to perturb historical precipitation time series at the minute scale to reflect non-linear expectations to climate change. The methodology shows good skill...
''Use of perturbative methods to break down the variation of reactivity between two systems''
International Nuclear Information System (INIS)
Perruchot-Triboulet, S.; Sanchez, R.
1997-01-01
The modification of the isotopic composition, the temperature or even accounting for across section uncertainties in one part of a nuclear reactor core, affects the value of the effective multiplication factor. A new tool allows the analysis of the reactivity effect generated by the modification of the system. With the help of the direct and adjoint fluxes, a detailed balance of reactivity, between the compared systems, is done for each isotopic cross section. After the presentation of the direct and adjoint transport equations in the context of the multigroup code transport APOLLO2, this note describes the method, based on perturbation theory, for the analysis of the reactivity variation. An example application is also given. (author)
A Modified Computational Scheme for the Stochastic Perturbation Finite Element Method
Directory of Open Access Journals (Sweden)
Feng Wu
Full Text Available Abstract A modified computational scheme of the stochastic perturbation finite element method (SPFEM is developed for structures with low-level uncertainties. The proposed scheme can provide second-order estimates of the mean and variance without differentiating the system matrices with respect to the random variables. When the proposed scheme is used, it involves finite analyses of deterministic systems. In the case of one random variable with a symmetric probability density function, the proposed computational scheme can even provide a result with fifth-order accuracy. Compared with the traditional computational scheme of SPFEM, the proposed scheme is more convenient for numerical implementation. Four numerical examples demonstrate that the proposed scheme can be used in linear or nonlinear structures with correlated or uncorrelated random variables.
International Nuclear Information System (INIS)
Bertschinger, E.
1987-01-01
Path integrals may be used to describe the statistical properties of a random field such as the primordial density perturbation field. In this framework the probability distribution is given for a Gaussian random field subjected to constraints such as the presence of a protovoid or supercluster at a specific location in the initial conditions. An algorithm has been constructed for generating samples of a constrained Gaussian random field on a lattice using Monte Carlo techniques. The method makes possible a systematic study of the density field around peaks or other constrained regions in the biased galaxy formation scenario, and it is effective for generating initial conditions for N-body simulations with rare objects in the computational volume. 21 references
Directory of Open Access Journals (Sweden)
D. Sarsri
2016-03-01
Full Text Available This paper presents a methodological approach to compute the stochastic eigenmodes of large FE models with parameter uncertainties based on coupling of second order perturbation method and component mode synthesis methods. Various component mode synthesis methods are used to optimally reduce the size of the model. The statistical first two moments of dynamic response of the reduced system are obtained by the second order perturbation method. Numerical results illustrating the accuracy and efficiency of the proposed coupled methodological procedures for large FE models with uncertain parameters are presented.
Directory of Open Access Journals (Sweden)
Reza Mohammadyari
2015-08-01
Full Text Available The problem of solid particle settling is a well known problem in mechanic of fluids. The parametrized Perturbation Method is applied to analytically solve the unsteady motion of a spherical particle falling in a Newtonian fluid using the drag of the form given by Oseen/Ferreira, for a range of Reynolds numbers. Particle equation of motion involved added mass term and ignored the Basset term. By using this new kind of perturbation method called parameterized perturbation method (PPM, analytical expressions for the instantaneous velocity, acceleration and position of the particle were derived. The presented results show the effectiveness of PPM and high rate of convergency of the method to achieve acceptable answers.
General method for designing wave shape transformers.
Ma, Hua; Qu, Shaobo; Xu, Zhuo; Wang, Jiafu
2008-12-22
An effective method for designing wave shape transformers (WSTs) is investigated by adopting the coordinate transformation theory. Following this method, the devices employed to transform electromagnetic (EM) wave fronts from one style with arbitrary shape and size to another style, can be designed. To verify this method, three examples in 2D spaces are also presented. Compared with the methods proposed in other literatures, this method offers the general procedure in designing WSTs, and thus is of great importance for the potential and practical applications possessed by such kinds of devices.
Energy Technology Data Exchange (ETDEWEB)
Borges, Antonio Andrade
1998-07-01
A new method for the calculation of sensitivity coefficients is developed. The new method is a combination of two methodologies used for calculating theses coefficients, which are the differential and the generalized perturbation theory methods. The method utilizes as integral parameter the average flux in an arbitrary region of the system. Thus, the sensitivity coefficient contains only the component corresponding to the neutron flux. To obtain the new sensitivity coefficient, the derivatives of the integral parameter, {phi}, with respect to {sigma} are calculated using the perturbation method and the functional derivatives of this generic integral parameter with respect to {sigma} and {phi} are calculated using the differential method. (author)
Energy Technology Data Exchange (ETDEWEB)
Takac, S M [Institute of Nuclear Sciences Boris Kidric, Vinca, Beograd (Yugoslavia)
1972-07-01
The method is based on perturbation of the reactor cell from a few up to few tens of percent. Measurements were performed for square lattice calls of zero power reactors ANNA, NORA and RB, with metal uranium and uranium oxide fuel elements, water, heavy water and graphite moderators. Character and functional dependence of perturbations were obtained from the experimental results. Zero perturbation was determined by extrapolation thus obtaining the real physical neutron flux distribution in the reactor cell. Simple diffusion theory for partial plate cell perturbation was developed for verification of the perturbation method. The results of these calculation proved that introducing the perturbation sample in the fuel results in flattening the thermal neutron density dependent on the amplitude of the applied perturbation. Extrapolation applied for perturbed distributions was found to be justified.
Application of He's homotopy perturbation method to conservative truly nonlinear oscillators
International Nuclear Information System (INIS)
Belendez, A.; Belendez, T.; Marquez, A.; Neipp, C.
2008-01-01
We apply He's homotopy perturbation method to find improved approximate solutions to conservative truly nonlinear oscillators. This approach gives us not only a truly periodic solution but also the period of the motion as a function of the amplitude of oscillation. We find that this method works very well for the whole range of parameters in the case of the cubic oscillator, and excellent agreement of the approximate frequencies with the exact one has been demonstrated and discussed. For the second order approximation we have shown that the relative error in the analytical approximate frequency is approximately 0.03% for any parameter values involved. We also compared the analytical approximate solutions and the Fourier series expansion of the exact solution. This has allowed us to compare the coefficients for the different harmonic terms in these solutions. The most significant features of this method are its simplicity and its excellent accuracy for the whole range of oscillation amplitude values and the results reveal that this technique is very effective and convenient for solving conservative truly nonlinear oscillatory systems
International Nuclear Information System (INIS)
Esmaeilpour, M.; Ganji, D.D.
2007-01-01
In this Letter, the problem of forced convection over a horizontal flat plate is presented and the homotopy perturbation method (HPM) is employed to compute an approximation to the solution of the system of nonlinear differential equations governing on the problem. It has been attempted to show the capabilities and wide-range applications of the homotopy perturbation method in comparison with the previous ones in solving heat transfer problems. The obtained solutions, in comparison with the exact solutions admit a remarkable accuracy. A clear conclusion can be drawn from the numerical results that the HPM provides highly accurate numerical solutions for nonlinear differential equations
DEFF Research Database (Denmark)
Ganji, D.D; Miansari, Mo; B, Ganjavi
2008-01-01
In this paper, homotopy-perturbation method (HPM) is introduced to solve nonlinear equations of ozone decomposition in aqueous solutions. HPM deforms a di¢ cult problem into a simple problem which can be easily solved. The effects of some parameters such as temperature to the solutions are consid......In this paper, homotopy-perturbation method (HPM) is introduced to solve nonlinear equations of ozone decomposition in aqueous solutions. HPM deforms a di¢ cult problem into a simple problem which can be easily solved. The effects of some parameters such as temperature to the solutions...
Eshkuvatov, Z K; Zulkarnain, F S; Nik Long, N M A; Muminov, Z
2016-01-01
Modified homotopy perturbation method (HPM) was used to solve the hypersingular integral equations (HSIEs) of the first kind on the interval [-1,1] with the assumption that the kernel of the hypersingular integral is constant on the diagonal of the domain. Existence of inverse of hypersingular integral operator leads to the convergence of HPM in certain cases. Modified HPM and its norm convergence are obtained in Hilbert space. Comparisons between modified HPM, standard HPM, Bernstein polynomials approach Mandal and Bhattacharya (Appl Math Comput 190:1707-1716, 2007), Chebyshev expansion method Mahiub et al. (Int J Pure Appl Math 69(3):265-274, 2011) and reproducing kernel Chen and Zhou (Appl Math Lett 24:636-641, 2011) are made by solving five examples. Theoretical and practical examples revealed that the modified HPM dominates the standard HPM and others. Finally, it is found that the modified HPM is exact, if the solution of the problem is a product of weights and polynomial functions. For rational solution the absolute error decreases very fast by increasing the number of collocation points.
Perturbation theory corrections to the two-particle reduced density matrix variational method.
Juhasz, Tamas; Mazziotti, David A
2004-07-15
In the variational 2-particle-reduced-density-matrix (2-RDM) method, the ground-state energy is minimized with respect to the 2-particle reduced density matrix, constrained by N-representability conditions. Consider the N-electron Hamiltonian H(lambda) as a function of the parameter lambda where we recover the Fock Hamiltonian at lambda=0 and we recover the fully correlated Hamiltonian at lambda=1. We explore using the accuracy of perturbation theory at small lambda to correct the 2-RDM variational energies at lambda=1 where the Hamiltonian represents correlated atoms and molecules. A key assumption in the correction is that the 2-RDM method will capture a fairly constant percentage of the correlation energy for lambda in (0,1] because the nonperturbative 2-RDM approach depends more significantly upon the nature rather than the strength of the two-body Hamiltonian interaction. For a variety of molecules we observe that this correction improves the 2-RDM energies in the equilibrium bonding region, while the 2-RDM energies at stretched or nearly dissociated geometries, already highly accurate, are not significantly changed. At equilibrium geometries the corrected 2-RDM energies are similar in accuracy to those from coupled-cluster singles and doubles (CCSD), but at nonequilibrium geometries the 2-RDM energies are often dramatically more accurate as shown in the bond stretching and dissociation data for water and nitrogen. (c) 2004 American Institute of Physics.
International Nuclear Information System (INIS)
Etter, S.
1982-01-01
By current ultrasonic flow measuring equipment (UFME) the mean velocity is measured for one or two measuring paths. This mean velocity is not equal to the velocity averaged over the flow cross-section, by means of which the flow rate is calculated. This difference will be found already for axially symmetrical, fully developed velocity profiles and, to a larger extent, for disturbed profiles varying in flow direction and for nonsteady flow. Corrective factors are defined for steady and nonsteady flows. These factors can be derived from the flow profiles within the UFME. By mathematical simulation of the entrainment effect the influence of cross and swirl flows on various ultrasonic measuring methods is studied. The applied UFME with crossed measuring paths is shown to be largely independent of cross and swirl flows. For evaluation in a computer of velocity network measurements in circular cross-sections the equations for interpolation and integration are derived. Results of the mathematical method are the isotach profile, the flow rate and, for fully developed flow, directly the corrective factor. In the experimental part corrective factors are determined in nonsteady flow in a measuring plane before and in form measuring planes behind a perturbation. (orig./RW) [de
Large-order perturbation theory
International Nuclear Information System (INIS)
Wu, T.T.
1982-01-01
The original motivation for studying the asymptotic behavior of the coefficients of perturbation series came from quantum field theory. An overview is given of some of the attempts to understand quantum field theory beyond finite-order perturbation series. At least is the case of the Thirring model and probably in general, the full content of a relativistic quantum field theory cannot be recovered from its perturbation series. This difficulty, however, does not occur in quantum mechanics, and the anharmonic oscillator is used to illustrate the methods used in large-order perturbation theory. Two completely different methods are discussed, the first one using the WKB approximation, and a second one involving the statistical analysis of Feynman diagrams. The first one is well developed and gives detailed information about the desired asymptotic behavior, while the second one is still in its infancy and gives instead information about the distribution of vertices of the Feynman diagrams
International Nuclear Information System (INIS)
Sabouri, Pouya
2013-01-01
This thesis presents a comprehensive study of sensitivity/uncertainty analysis for reactor performance parameters (e.g. the k-effective) to the base nuclear data from which they are computed. The analysis starts at the fundamental step, the Evaluated Nuclear Data File and the uncertainties inherently associated with the data they contain, available in the form of variance/covariance matrices. We show that when a methodical and consistent computation of sensitivity is performed, conventional deterministic formalisms can be sufficient to propagate nuclear data uncertainties with the level of accuracy obtained by the most advanced tools, such as state-of-the-art Monte Carlo codes. By applying our developed methodology to three exercises proposed by the OECD (Uncertainty Analysis for Criticality Safety Assessment Benchmarks), we provide insights of the underlying physical phenomena associated with the used formalisms. (author)
Energy Technology Data Exchange (ETDEWEB)
Zolfaghari, M; Ghaderi, R; Sheikhol Eslami, A; Hosseinnia, S H; Sadati, J [Intelligent System Research Group, Faculty of Electrical and Computer Engineering, Babol, Noushirvani University of Technology, PO Box 47135-484, Babol (Iran, Islamic Republic of); Ranjbar, A [Golestan University, Gorgan (Iran, Islamic Republic of); Momani, S [Department of Mathematics, Mutah University, PO Box 7, Al-Karak (Jordan)], E-mail: h.hoseinnia@stu.nit.ac.ir, E-mail: a.ranjbar@nit.ac.ir, E-mail: shahermm@yahoo.com
2009-10-15
The enhanced homotopy perturbation method (EHPM) is applied for finding improved approximate solutions of the well-known Bagley-Torvik equation for three different cases. The main characteristic of the EHPM is using a stabilized linear part, which guarantees the stability and convergence of the overall solution. The results are finally compared with the Adams-Bashforth-Moulton numerical method, the Adomian decomposition method (ADM) and the fractional differential transform method (FDTM) to verify the performance of the EHPM.
International Nuclear Information System (INIS)
Zolfaghari, M; Ghaderi, R; Sheikhol Eslami, A; Hosseinnia, S H; Sadati, J; Ranjbar, A; Momani, S
2009-01-01
The enhanced homotopy perturbation method (EHPM) is applied for finding improved approximate solutions of the well-known Bagley-Torvik equation for three different cases. The main characteristic of the EHPM is using a stabilized linear part, which guarantees the stability and convergence of the overall solution. The results are finally compared with the Adams-Bashforth-Moulton numerical method, the Adomian decomposition method (ADM) and the fractional differential transform method (FDTM) to verify the performance of the EHPM.
Zolfaghari, M.; Ghaderi, R.; Sheikhol Eslami, A.; Ranjbar, A.; Hosseinnia, S. H.; Momani, S.; Sadati, J.
2009-10-01
The enhanced homotopy perturbation method (EHPM) is applied for finding improved approximate solutions of the well-known Bagley-Torvik equation for three different cases. The main characteristic of the EHPM is using a stabilized linear part, which guarantees the stability and convergence of the overall solution. The results are finally compared with the Adams-Bashforth-Moulton numerical method, the Adomian decomposition method (ADM) and the fractional differential transform method (FDTM) to verify the performance of the EHPM.
Directory of Open Access Journals (Sweden)
U. Filobello-Nino
2015-01-01
Full Text Available We propose an approximate solution of T-F equation, obtained by using the nonlinearities distribution homotopy perturbation method (NDHPM. Besides, we show a table of comparison, between this proposed approximate solution and a numerical of T-F, by establishing the accuracy of the results.
A computational chemistry analysis of six unique tautomers of cyromazine, a pesticide used for fly control, was performed with density functional theory (DFT) and canonical second order Møller–Plesset perturbation theory (MP2) methods to gain insight into the contributions of molecular structure to ...
Directory of Open Access Journals (Sweden)
Aboozar Heydari
2017-09-01
Full Text Available In this paper, the effects of nonlinear forces due to the electromagnetic field of bearing and the unbalancing force on nonlinear vibration behavior of a rotor is investigated. The rotor is modeled as a rigid body that is supported by two magnetic bearings with eight-polar structures. The governing dynamics equations of the system that are coupled nonlinear second order ordinary differential equations (ODEs are derived, and for solving these equations, the homotopy perturbation method (HPM is used. By applying HPM, the possibility of presenting a harmonic semi-analytical solution, is provided. In fact, with equality the coefficient of auxiliary parameter (p, the system of coupled nonlinear second order and non-homogenous differential equations are obtained so that consists of unbalancing effects. By considering some initial condition for displacement and velocity in the horizontal and vertical directions, free vibration analysis is done and next, the forced vibration analysis under the effect of harmonic forces also is investigated. Likewise, various parameters on the vibration behavior of rotor are studied. Changes in amplitude and response phase per excitation frequency are investigated. Results show that by increasing excitation frequency, the motion amplitude is also increases and by passing the critical speed, it decreases. Also it shows that the magnetic bearing system performance is in stable maintenance of rotor. The parameters affecting on vibration behavior, has been studied and by comparison the results with the other references, which have a good precision up to 2nd order of embedding parameter, it implies the accuracy of this method in current research.
The 'Falling Box' method in general relativity
International Nuclear Information System (INIS)
Gladush, V.D.
1998-01-01
The problems of justification, generalization, and applicability of the 'falling box' method to obtained some exact solutions of the vacuum Einstein equations are investigated. The 'physical' inference of the Reissner-Nordstrom-de Sitter and Kerr metrics is shown. Explanation is given for the well-known relativistic phenomenon which consists in that gravity is created by the double density of the electrical field energy
International Nuclear Information System (INIS)
Nieves, Jose F.; Pal, Palash B.
2006-01-01
We consider the calculation of amplitudes for processes that take place in a constant background magnetic field, first using the standard method for the calculation of an amplitude in an external field, and second utilizing the Schwinger propagator for charged particles in a magnetic field. We show that there are processes for which the Schwinger-propagator method does not yield the total amplitude. We explain why the two methods yield equivalent results in some cases and indicate when we can expect the equivalence to hold. We show these results in fairly general terms and illustrate them with specific examples as well
Linear perturbation renormalization group method for Ising-like spin systems
Directory of Open Access Journals (Sweden)
J. Sznajd
2013-03-01
Full Text Available The linear perturbation group transformation (LPRG is used to study the thermodynamics of the axial next-nearest-neighbor Ising model with four spin interactions (extended ANNNI in a field. The LPRG for weakly interacting Ising chains is presented. The method is used to study finite field para-ferrimagnetic phase transitions observed in layered uranium compounds, UAs1-xSex, UPd2Si2 or UNi2Si2. The above-mentioned systems are made of ferromagnetic layers and the spins from the nearest-neighbor and next-nearest-neighbor layers are coupled by the antiferromagnetic interactions J121-xSex the para-ferri phase transition is of the first order as expected from the symmetry reason, in UT2Si2 (T=Pd, Ni this transition seems to be a continuous one, at least in the vicinity of the multicritical point. Within the MFA, the critical character of the finite field para-ferrimagnetic transition at least at one isolated point can be described by the ANNNI model supplemented by an additional, e.g., four-spin interaction. However, in LPRG approximation for the ratio κ = J2/J1 around 0.5 there is a critical value of the field for which an isolated critical point also exists in the original ANNNI model. The positive four-spin interaction shifts the critical point towards higher fields and changes the shape of the specific heat curve. In the latter case for the fields small enough, the specific heat exhibits two-peak structure in the paramagnetic phase.
On the partitioning method and the perturbation quantum theory - discrete spectra
International Nuclear Information System (INIS)
Logrado, P.G.
1982-05-01
Lower and upper bounds to eigenvalues of the Schroedinger equation H Ψ = E Ψ (H = H 0 + V) and the convergence condition, in Schonberg's perturbation theory, are presented. These results are obtained using the partitioning technique. It is presented for the first time a perturbation treatment obtained when the reference function in the partitioning technique is chosen to be a true eigenfunction Ψ. The convergence condition and upper and lower bounds for the true eigenvalues E are derived in this formulation. The concept of the reaction and wave operators is also discussed. (author)
A Generalized Slave-Particle Method
Georgescu, Alexandru Bogdan; Ismail-Beigi, Sohrab
2015-03-01
Two slave-particle methods, namely the slave-rotor and the slave-spin approaches, have been of recent interest in the computational correlated electron community. Both methods solve Hubbard-type models and go beyond the single-particle approximations by describing aspects of correlated electron behavior in a computationally efficient manner. We present a generalized slave-particle formalism that connects the the two while reproducing the results of each method in the appropriate limit. The framework automatically corrects the problematic small U behavior of the slave-rotor approach while reproducing its behavior in situations where it has been found physically relevant (e.g., for nickelate heterostructures). This work is supported by the National Science Foundation through Grant MRSEC NSF DMR-1119826.
Dinesh Kumar, S.; Nageshwar Rao, R.; Pramod Chakravarthy, P.
2017-11-01
In this paper, we consider a boundary value problem for a singularly perturbed delay differential equation of reaction-diffusion type. We construct an exponentially fitted numerical method using Numerov finite difference scheme, which resolves not only the boundary layers but also the interior layers arising from the delay term. An extensive amount of computational work has been carried out to demonstrate the applicability of the proposed method.
Tarumi, Moto; Kobayashi, Masato; Nakai, Hiromi
2012-11-13
The antisymmetric product of strongly orthogonal geminals (APSG) method is a wave function theory that can effectively treat the static electron correlation. Recently, we proposed the open-shell APSG method using one-electron orbitals for open-shell parts. In this paper, we have extended the perturbation correction to the open-shell APSG calculations through Møller-Plesset-type multiconfiguration perturbation theory (MP-MCPT). Numerical applications demonstrate that the present open-shell MP-MCPT can reasonably reproduce the dissociation energies or equilibrium distances for open-shell systems.
International Nuclear Information System (INIS)
Balino, Jorge L.; Larreteguy, Axel E.; Andrade Lima, Fernando R.
1995-01-01
The differential method was applied to the sensitivity analysis for water hammer problems in hydraulic networks. Starting from the classical water hammer equations in a single-phase liquid with friction, the state vector comprising the piezometric head and the velocity was defined. Applying the differential method the adjoint operator, the adjoint equations with the general form of their boundary conditions, and the general form of the bilinear concomitant were calculated. The discretized adjoint equations and the corresponding boundary conditions were programmed and solved by using the so called method of characteristics. As an example, a constant-level tank connected through a pipe to a valve discharging to atmosphere was considered. The bilinear concomitant was calculated for this particular case. The corresponding sensitivity coefficients due to the variation of different parameters by using both the differential method and the response surface generated by the computer code WHAT were also calculated. The results obtained with these methods show excellent agreement. (author). 11 refs, 2 figs, 2 tabs
Generalized multiscale finite element methods: Oversampling strategies
Efendiev, Yalchin R.; Galvis, Juan; Li, Guanglian; Presho, Michael
2014-01-01
In this paper, we propose oversampling strategies in the generalized multiscale finite element method (GMsFEM) framework. The GMsFEM, which has been recently introduced in Efendiev et al. (2013b) [Generalized Multiscale Finite Element Methods, J. Comput. Phys., vol. 251, pp. 116-135, 2013], allows solving multiscale parameter-dependent problems at a reduced computational cost by constructing a reduced-order representation of the solution on a coarse grid. The main idea of the method consists of (1) the construction of snapshot space, (2) the construction of the offline space, and (3) construction of the online space (the latter for parameter-dependent problems). In Efendiev et al. (2013b) [Generalized Multiscale Finite Element Methods, J. Comput. Phys., vol. 251, pp. 116-135, 2013], it was shown that the GMsFEM provides a flexible tool to solve multiscale problems with a complex input space by generating appropriate snapshot, offline, and online spaces. In this paper, we develop oversampling techniques to be used in this context (see Hou and Wu (1997) where oversampling is introduced for multiscale finite element methods). It is known (see Hou and Wu (1997)) that the oversampling can improve the accuracy of multiscale methods. In particular, the oversampling technique uses larger regions (larger than the target coarse block) in constructing local basis functions. Our motivation stems from the analysis presented in this paper, which shows that when using oversampling techniques in the construction of the snapshot space and offline space, GMsFEM will converge independent of small scales and high contrast under certain assumptions. We consider the use of a multiple eigenvalue problems to improve the convergence and discuss their relation to single spectral problems that use oversampled regions. The oversampling procedures proposed in this paper differ from those in Hou and Wu (1997). In particular, the oversampling domains are partially used in constructing local
On the Perturb-and-Observe and Incremental Conductance MPPT methods for PV systems
DEFF Research Database (Denmark)
Sera, Dezso; Mathe, Laszlo; Kerekes, Tamas
2013-01-01
This paper presents a detailed analysis of the two most well-known hill-climbing MPPT algorithms, the Perturb-and-Observe (P&O) and Incremental Conductance (INC). The purpose of the analysis is to clarify some common misconceptions in the literature regarding these two trackers, therefore helping...
Generalized Analysis of a Distribution Separation Method
Directory of Open Access Journals (Sweden)
Peng Zhang
2016-04-01
Full Text Available Separating two probability distributions from a mixture model that is made up of the combinations of the two is essential to a wide range of applications. For example, in information retrieval (IR, there often exists a mixture distribution consisting of a relevance distribution that we need to estimate and an irrelevance distribution that we hope to get rid of. Recently, a distribution separation method (DSM was proposed to approximate the relevance distribution, by separating a seed irrelevance distribution from the mixture distribution. It was successfully applied to an IR task, namely pseudo-relevance feedback (PRF, where the query expansion model is often a mixture term distribution. Although initially developed in the context of IR, DSM is indeed a general mathematical formulation for probability distribution separation. Thus, it is important to further generalize its basic analysis and to explore its connections to other related methods. In this article, we first extend DSM’s theoretical analysis, which was originally based on the Pearson correlation coefficient, to entropy-related measures, including the KL-divergence (Kullback–Leibler divergence, the symmetrized KL-divergence and the JS-divergence (Jensen–Shannon divergence. Second, we investigate the distribution separation idea in a well-known method, namely the mixture model feedback (MMF approach. We prove that MMF also complies with the linear combination assumption, and then, DSM’s linear separation algorithm can largely simplify the EM algorithm in MMF. These theoretical analyses, as well as further empirical evaluation results demonstrate the advantages of our DSM approach.
Energy Technology Data Exchange (ETDEWEB)
Hong, Youngjoon, E-mail: hongy@uic.edu; Nicholls, David P., E-mail: davidn@uic.edu
2017-02-01
The accurate numerical simulation of linear waves interacting with periodic layered media is a crucial capability in engineering applications. In this contribution we study the stable and high-order accurate numerical simulation of the interaction of linear, time-harmonic waves with a periodic, triply layered medium with irregular interfaces. In contrast with volumetric approaches, High-Order Perturbation of Surfaces (HOPS) algorithms are inexpensive interfacial methods which rapidly and recursively estimate scattering returns by perturbation of the interface shape. In comparison with Boundary Integral/Element Methods, the stable HOPS algorithm we describe here does not require specialized quadrature rules, periodization strategies, or the solution of dense non-symmetric positive definite linear systems. In addition, the algorithm is provably stable as opposed to other classical HOPS approaches. With numerical experiments we show the remarkable efficiency, fidelity, and accuracy one can achieve with an implementation of this algorithm.
Instantons and large N an introduction to non-perturbative methods in quantum field theory
Marino, Marcos
2015-01-01
This highly pedagogical textbook for graduate students in particle, theoretical and mathematical physics, explores advanced topics of quantum field theory. Clearly divided into two parts; the first focuses on instantons with a detailed exposition of instantons in quantum mechanics, supersymmetric quantum mechanics, the large order behavior of perturbation theory, and Yang-Mills theories, before moving on to examine the large N expansion in quantum field theory. The organised presentation style, in addition to detailed mathematical derivations, worked examples and applications throughout, enables students to gain practical experience with the tools necessary to start research. The author includes recent developments on the large order behaviour of perturbation theory and on large N instantons, and updates existing treatments of classic topics, to ensure that this is a practical and contemporary guide for students developing their understanding of the intricacies of quantum field theory.
Forner-Cordero, Arturo; Ackermann, Marko; de Lima Freitas, Mateus
2011-01-01
Perturbations during human gait such as a trip or a slip can result in a fall, especially among frail populations such as the elderly. In order to recover from a trip or a stumble during gait, humans perform different types of recovery strategies. It is very useful to uncover the mechanisms of the recovery to improve training methods for populations at risk of falling. Moreover, human recovery strategies could be applied to implement controllers for bipedal robot walker, as an application of biomimetic design. A biomechanical model of the response to a trip during gait might uncover the control mechanisms underlying the different recovery strategies and the adaptation of the responses found during the execution of successive perturbation trials. This paper introduces a model of stumble in the multibody system framework. This model is used to assess different feedforward strategies to recover from a trip. First of all, normal gait patterns for the musculoskeletal system model are obtained by solving an optimal control problem. Secondly, the reference gait is perturbed by the application of forces on the swinging foot in different ways: as an instantaneous inelastic collision of the foot with an obstacle, as an impulsive horizontal force or using a force curve measured experimentally during gait perturbation experiments. The influence of the type of perturbation, the timing of the collision with respect to the gait cycle, as well as of the coefficient of restitution was investigated previously. Finally, in order to test the effects of different muscle excitation levels on the initial phases of the recovery response, several muscle excitations were added to selected muscles of the legs, thus providing a simulation of the recovery reactions. These results pave the way for future analysis and modeling of the control mechanisms of gait.
Fundamental parameters of QCD from non-perturbative methods for two and four flavors
International Nuclear Information System (INIS)
Marinkovic, Marina
2013-01-01
The non-perturbative formulation of Quantumchromodynamics (QCD) on a four dimensional space-time Euclidean lattice together with the finite size techniques enable us to perform the renormalization of the QCD parameters non-perturbatively. In order to obtain precise predictions from lattice QCD, one needs to include the dynamical fermions into lattice QCD simulations. We consider QCD with two and four mass degenerate flavors of O(a) improved Wilson quarks. In this thesis, we improve the existing determinations of the fundamental parameters of two and four flavor QCD. In four flavor theory, we compute the precise value of the Λ parameter in the units of the scale L max defined in the hadronic regime. We also give the precise determination of the Schroedinger functional running coupling in four flavour theory and compare it to the perturbative results. The Monte Carlo simulations of lattice QCD within the Schroedinger Functional framework were performed with a platform independent program package Schroedinger Funktional Mass Preconditioned Hybrid Monte Carlo (SF-MP-HMC), developed as a part of this project. Finally, we compute the strange quark mass and the Λ parameter in two flavour theory, performing a well-controlled continuum limit and chiral extrapolation. To achieve this, we developed a universal program package for simulating two flavours of Wilson fermions, Mass Preconditioned Hybrid Monte Carlo (MP-HMC), which we used to run large scale simulations on small lattice spacings and on pion masses close to the physical value.
A fast and accurate method for perturbative resummation of transverse momentum-dependent observables
Kang, Daekyoung; Lee, Christopher; Vaidya, Varun
2018-04-01
We propose a novel strategy for the perturbative resummation of transverse momentum-dependent (TMD) observables, using the q T spectra of gauge bosons ( γ ∗, Higgs) in pp collisions in the regime of low (but perturbative) transverse momentum q T as a specific example. First we introduce a scheme to choose the factorization scale for virtuality in momentum space instead of in impact parameter space, allowing us to avoid integrating over (or cutting off) a Landau pole in the inverse Fourier transform of the latter to the former. The factorization scale for rapidity is still chosen as a function of impact parameter b, but in such a way designed to obtain a Gaussian form (in ln b) for the exponentiated rapidity evolution kernel, guaranteeing convergence of the b integral. We then apply this scheme to obtain the q T spectra for Drell-Yan and Higgs production at NNLL accuracy. In addition, using this scheme we are able to obtain a fast semi-analytic formula for the perturbative resummed cross sections in momentum space: analytic in its dependence on all physical variables at each order of logarithmic accuracy, up to a numerical expansion for the pure mathematical Bessel function in the inverse Fourier transform that needs to be performed just once for all observables and kinematics, to any desired accuracy.
Performances improvement of maximum power point tracking perturb and observe method
Energy Technology Data Exchange (ETDEWEB)
Egiziano, L.; Femia, N.; Granozio, D.; Petrone, G.; Spagnuolo, G. [Salermo Univ., Salermo (Italy); Vitelli, M. [Seconda Univ. di Napoli, Napoli (Italy)
2006-07-01
Perturb and observe best operation conditions were investigated in order to identify edge efficiency performance capabilities of a maximum power point (MPP) tracking technique for photovoltaic (PV) applications. The strategy was developed to ensure a 3-points behavior across the MPP under a fixed irradiation level with a central point blocked on the MPP and 2 operating points operating at voltage values that guaranteed the same power levels. The system was also devised to quickly detect the MPP movement in the presence of varying atmospheric conditions by increasing the perturbation so that the MPP was guaranteed within a few sampling periods. A perturbation equation was selected where amplitude was represented as a function of the actual power drawn from the PV field together with the adoption of a parabolic interpolation of the sequence of the final 3 acquired voltage power couples corresponding to as many operating points. The technique was developed to ensure that the power difference between 2 consecutive operating points was higher than the power quantization error. Simulations were conducted to demonstrate that the proposed technique arranged operating points symmetrically around the MPP. The average power of the 3-points set was achieved by means of the parabolic prediction. Experiments conducted to validate the simulation showed a reduced power oscillation below the MPP and a real power gain. 2 refs., 8 figs.
Directory of Open Access Journals (Sweden)
Pranab Kanti Roy
2015-09-01
Full Text Available This work aimed at studying the effects of environmental temperature and surface emissivity parameter on the temperature distribution, efficiency and heat transfer rate of a conductive–radiative fin. The Homotopy Perturbation Method (HPM being one of the semi-numerical methods for highly nonlinear and inhomogeneous equations, the local temperature distribution efficiencies and heat transfer rates are obtained using HPM in which Newton–Raphson method is used for the insulated boundary condition. It is found that the results of the present works are in good agreement with results available in the literature.
Xi, Qing; Li, Zhao-Fu; Luo, Chuan
2014-05-01
Sensitivity analysis of hydrology and water quality parameters has a great significance for integrated model's construction and application. Based on AnnAGNPS model's mechanism, terrain, hydrology and meteorology, field management, soil and other four major categories of 31 parameters were selected for the sensitivity analysis in Zhongtian river watershed which is a typical small watershed of hilly region in the Taihu Lake, and then used the perturbation method to evaluate the sensitivity of the parameters to the model's simulation results. The results showed that: in the 11 terrain parameters, LS was sensitive to all the model results, RMN, RS and RVC were generally sensitive and less sensitive to the output of sediment but insensitive to the remaining results. For hydrometeorological parameters, CN was more sensitive to runoff and sediment and relatively sensitive for the rest results. In field management, fertilizer and vegetation parameters, CCC, CRM and RR were less sensitive to sediment and particulate pollutants, the six fertilizer parameters (FR, FD, FID, FOD, FIP, FOP) were particularly sensitive for nitrogen and phosphorus nutrients. For soil parameters, K is quite sensitive to all the results except the runoff, the four parameters of the soil's nitrogen and phosphorus ratio (SONR, SINR, SOPR, SIPR) were less sensitive to the corresponding results. The simulation and verification results of runoff in Zhongtian watershed show a good accuracy with the deviation less than 10% during 2005- 2010. Research results have a direct reference value on AnnAGNPS model's parameter selection and calibration adjustment. The runoff simulation results of the study area also proved that the sensitivity analysis was practicable to the parameter's adjustment and showed the adaptability to the hydrology simulation in the Taihu Lake basin's hilly region and provide reference for the model's promotion in China.
Cumulants in perturbation expansions for non-equilibrium field theory
International Nuclear Information System (INIS)
Fauser, R.
1995-11-01
The formulation of perturbation expansions for a quantum field theory of strongly interacting systems in a general non-equilibrium state is discussed. Non-vanishing initial correlations are included in the formulation of the perturbation expansion in terms of cumulants. The cumulants are shown to be the suitable candidate for summing up the perturbation expansion. Also a linked-cluster theorem for the perturbation series with cumulants is presented. Finally a generating functional of the perturbation series with initial correlations is studied. We apply the methods to a simple model of a fermion-boson system. (orig.)
Perturbative coherence in field theory
International Nuclear Information System (INIS)
Aldrovandi, R.; Kraenkel, R.A.
1987-01-01
A general condition for coherent quantization by perturbative methods is given, because the basic field equations of a fild theory are not always derivable from a Lagrangian. It's seen that non-lagrangian models way have well defined vertices, provided they satisfy what they call the 'coherence condition', which is less stringent than the condition for the existence of a Lagrangian. They note that Lagrangian theories are perturbatively coherent, in the sense that they have well defined vertices, and that they satisfy automatically that condition. (G.D.F.) [pt
Woollands, Robyn M.; Read, Julie L.; Probe, Austin B.; Junkins, John L.
2017-12-01
We present a new method for solving the multiple revolution perturbed Lambert problem using the method of particular solutions and modified Chebyshev-Picard iteration. The method of particular solutions differs from the well-known Newton-shooting method in that integration of the state transition matrix (36 additional differential equations) is not required, and instead it makes use of a reference trajectory and a set of n particular solutions. Any numerical integrator can be used for solving two-point boundary problems with the method of particular solutions, however we show that using modified Chebyshev-Picard iteration affords an avenue for increased efficiency that is not available with other step-by-step integrators. We take advantage of the path approximation nature of modified Chebyshev-Picard iteration (nodes iteratively converge to fixed points in space) and utilize a variable fidelity force model for propagating the reference trajectory. Remarkably, we demonstrate that computing the particular solutions with only low fidelity function evaluations greatly increases the efficiency of the algorithm while maintaining machine precision accuracy. Our study reveals that solving the perturbed Lambert's problem using the method of particular solutions with modified Chebyshev-Picard iteration is about an order of magnitude faster compared with the classical shooting method and a tenth-twelfth order Runge-Kutta integrator. It is well known that the solution to Lambert's problem over multiple revolutions is not unique and to ensure that all possible solutions are considered we make use of a reliable preexisting Keplerian Lambert solver to warm start our perturbed algorithm.
Yaşar, Elif; Yıldırım, Yakup; Yaşar, Emrullah
2018-06-01
This paper devotes to conformable fractional space-time perturbed Gerdjikov-Ivanov (GI) equation which appears in nonlinear fiber optics and photonic crystal fibers (PCF). We consider the model with full nonlinearity in order to give a generalized flavor. The sine-Gordon equation approach is carried out to model equation for retrieving the dark, bright, dark-bright, singular and combined singular optical solitons. The constraint conditions are also reported for guaranteeing the existence of these solitons. We also present some graphical simulations of the solutions for better understanding the physical phenomena of the behind the considered model.
International Nuclear Information System (INIS)
Suck Salk, S.H.
1985-01-01
With the use of projection operators, the formal expressions of distorted-wave and coupled-channel-wave transition amplitudes for rearrangement collisions are derived. Use of projection operators (for the transition amplitudes) sharpens our understanding of the structural differences between the two transition amplitudes. The merit of each representation of the transition amplitudes is discussed. Derived perturbation potentials are found to have different structures. The rigorously derived distorted-wave Born-approximation (DWBA) transition amplitude is shown to be a generalization of the earlier DWBA expression obtained from the assumption of the dominance of elastic scattering in rearrangement collisions
Method for comparison of tokamak divertor strike point data with magnetic perturbation models
Czech Academy of Sciences Publication Activity Database
Cahyna, Pavel; Peterka, Matěj; Nardon, E.; Frerichs, H.; Pánek, Radomír
2014-01-01
Roč. 54, č. 6 (2014), 064002-064002 ISSN 0029-5515. [International Workshop on Stochasticity in Fusion Plasmas /6./. Jülich, 18.03.2013-20.03.2013] R&D Projects: GA ČR GAP205/11/2341 Institutional support: RVO:61389021 Keywords : divertor * resonant magnetic perturbation Subject RIV: BL - Plasma and Gas Discharge Physics Impact factor: 3.062, year: 2014 http://iopscience.iop.org/0029-5515/54/6/064002/pdf/0029-5515_54_6_064002.pdf
Energy Technology Data Exchange (ETDEWEB)
Casoli, Pierre; Authier, Nicolas [Commissariat a l' Energie Atomique, Centre d' Etudes de Valduc, 21120 Is-Sur-Tille (France)
2008-07-01
Reactivity worth measurements of material samples put in the central cavities of nuclear reactors allow to test cross section nuclear databases or to extract information about the critical masses of fissile elements. Such experiments have already been completed on the Caliban and Silene experimental reactors operated by the Criticality and Neutronics Research Laboratory of Valduc (CEA, France) using the perturbation measurement technique. Calculations have been performed to prepare future experiments on new materials, such as light elements, structure materials, fission products or actinides. (authors)
Fan, Zhichao; Hwang, Keh-Chih; Rogers, John A.; Huang, Yonggang; Zhang, Yihui
2018-02-01
Mechanically-guided 3D assembly based on controlled, compressive buckling represents a promising, emerging approach for forming complex 3D mesostructures in advanced materials. Due to the versatile applicability to a broad set of material types (including device-grade single-crystal silicon) over length scales from nanometers to centimeters, a wide range of novel applications have been demonstrated in soft electronic systems, interactive bio-interfaces as well as tunable electromagnetic devices. Previously reported 3D designs relied mainly on finite element analyses (FEA) as a guide, but the massive numerical simulations and computational efforts necessary to obtain the assembly parameters for a targeted 3D geometry prevent rapid exploration of engineering options. A systematic understanding of the relationship between a 3D shape and the associated parameters for assembly requires the development of a general theory for the postbuckling process. In this paper, a double perturbation method is established for the postbuckling analyses of planar curved beams, of direct relevance to the assembly of ribbon-shaped 3D mesostructures. By introducing two perturbation parameters related to the initial configuration and the deformation, the highly nonlinear governing equations can be transformed into a series of solvable, linear equations that give analytic solutions to the displacements and curvatures during postbuckling. Systematic analyses of postbuckling in three representative ribbon shapes (sinusoidal, polynomial and arc configurations) illustrate the validity of theoretical method, through comparisons to the results of experiment and FEA. These results shed light on the relationship between the important deformation quantities (e.g., mode ratio and maximum strain) and the assembly parameters (e.g., initial configuration and the applied strain). This double perturbation method provides an attractive route to the inverse design of ribbon-shaped 3D geometries, as
Directory of Open Access Journals (Sweden)
Norhasimah Mahiddin
2014-01-01
Full Text Available The modified decomposition method (MDM and homotopy perturbation method (HPM are applied to obtain the approximate solution of the nonlinear model of tumour invasion and metastasis. The study highlights the significant features of the employed methods and their ability to handle nonlinear partial differential equations. The methods do not need linearization and weak nonlinearity assumptions. Although the main difference between MDM and Adomian decomposition method (ADM is a slight variation in the definition of the initial condition, modification eliminates massive computation work. The approximate analytical solution obtained by MDM logically contains the solution obtained by HPM. It shows that HPM does not involve the Adomian polynomials when dealing with nonlinear problems.
Algebraic renormalization. Perturbative renormalization, symmetries and anomalies
International Nuclear Information System (INIS)
Piguet, O.
1995-01-01
This book is an introduction to the algebraic method in the perturbative renormalization of relativistic quantum field theory. After a general introduction to renormalized perturbation theory the quantum action principle and Ward identities are described. Then Yang-Mills gauge theories are considered. Thereafter the BRS cohomology and descent equations are described. Then nonrenormalization theorems and topological field theories are considered. Finally an application to the bosonic string is described. (HSI)
Directory of Open Access Journals (Sweden)
D. Olvera
2015-01-01
Full Text Available We expand the application of the enhanced multistage homotopy perturbation method (EMHPM to solve delay differential equations (DDEs with constant and variable coefficients. This EMHPM is based on a sequence of subintervals that provide approximate solutions that require less CPU time than those computed from the dde23 MATLAB numerical integration algorithm solutions. To address the accuracy of our proposed approach, we examine the solutions of several DDEs having constant and variable coefficients, finding predictions with a good match relative to the corresponding numerical integration solutions.
Directory of Open Access Journals (Sweden)
Saeed Dinarvand
2012-01-01
Full Text Available The steady three-dimensional flow of condensation or spraying on inclined spinning disk is studied analytically. The governing nonlinear equations and their associated boundary conditions are transformed into the system of nonlinear ordinary differential equations. The series solution of the problem is obtained by utilizing the homotopy perturbation method (HPM. The velocity and temperature profiles are shown and the influence of Prandtl number on the heat transfer and Nusselt number is discussed in detail. The validity of our solutions is verified by the numerical results. Unlike free surface flows on an incline, this through flow is highly affected by the spray rate and the rotation of the disk.
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.
General methods for analyzing bounded proportion data
Hossain, Abu
2017-01-01
This thesis introduces two general classes of models for analyzing proportion response variable when the response variable Y can take values between zero and one, inclusive of zero and/or one. The models are inflated GAMLSS model and generalized Tobit GAMLSS model. The inflated GAMLSS model extends the flexibility of beta inflated models by allowing the distribution on (0,1) of the continuous component of the dependent variable to come from any explicit or transformed (i.e. logit or truncated...
Tripathi, Rajnee; Mishra, Hradyesh Kumar
2016-01-01
In this communication, we describe the Homotopy Perturbation Method with Laplace Transform (LT-HPM), which is used to solve the Lane-Emden type differential equations. It's very difficult to solve numerically the Lane-Emden types of the differential equation. Here we implemented this method for two linear homogeneous, two linear nonhomogeneous, and four nonlinear homogeneous Lane-Emden type differential equations and use their appropriate comparisons with exact solutions. In the current study, some examples are better than other existing methods with their nearer results in the form of power series. The Laplace transform used to accelerate the convergence of power series and the results are shown in the tables and graphs which have good agreement with the other existing method in the literature. The results show that LT-HPM is very effective and easy to implement.
International Nuclear Information System (INIS)
Carta, M.; Bianchini, G.; Peluso, V.; Gandini, A.; Fabrizio, V.; Ricci, L.
2013-01-01
Conclusions: • GPT methodologies can provide a codified “key to reading” to the properties of some GUINEVERE integral characteristics respect to analogous characteristics in MYRRHA. • The present work has been focused on the analysis, by numerical simulations, of the representativeness, with respect to the MYRRHA situation assumed as reference system, of the behaviour in GUINEVERE of the spectral indexes F9/F5, F8/F5 and F7/F5 following a localized (core shell) or global (whole active core) lead (GUINEVERE) or lead-bismuth (MYRRHA) 20% density reduction. • The analysis, carried out by means of GPT methodologies implemented into the ERANOS French neutronic code, and using the US dispersion matrix BOLNA, provided encouraging results concerning the correlation for all the spectral indexes taken into account
Generalization of the Moszkovski-Scott method
International Nuclear Information System (INIS)
Balbutsev, E.B.
1976-01-01
A constant separation parameter is proposed to be used in the Moszkovski-Scott method for solving the Bethe-Goldstone equation. After such a modification one can apply the method to odd states of relative motion, not only to even ones. Some essential inaccuracies of the original method are eliminated, as well
International Nuclear Information System (INIS)
Collins, J.C.
1985-01-01
Progress in quantum chromodynamics in the past year is reviewed in these specific areas: proof of factorization for hadron-hadron collisions, fast calculation of higher order graphs, perturbative Monte Carlo calculations for hadron-hadron scattering, applicability of perturbative methods to heavy quark production, and understanding of the small-x problem. 22 refs
International Nuclear Information System (INIS)
Bartlett, R.; Kirtman, B.; Davidson, E.R.
1978-01-01
After noting some advantages of using perturbation theory some of the various types are related on a chart and described, including many-body nonlinear summations, quartic force-field fit for geometry, fourth-order correlation approximations, and a survey of some recent work. Alternative initial approximations in perturbation theory are also discussed. 25 references
Şenol, Mehmet; Alquran, Marwan; Kasmaei, Hamed Daei
2018-06-01
In this paper, we present analytic-approximate solution of time-fractional Zakharov-Kuznetsov equation. This model demonstrates the behavior of weakly nonlinear ion acoustic waves in a plasma bearing cold ions and hot isothermal electrons in the presence of a uniform magnetic field. Basic definitions of fractional derivatives are described in the Caputo sense. Perturbation-iteration algorithm (PIA) and residual power series method (RPSM) are applied to solve this equation with success. The convergence analysis is also presented for both methods. Numerical results are given and then they are compared with the exact solutions. Comparison of the results reveal that both methods are competitive, powerful, reliable, simple to use and ready to apply to wide range of fractional partial differential equations.
Energy Technology Data Exchange (ETDEWEB)
Gurjao, Emir Candeia
1996-02-01
The differential and GPT (Generalized Perturbation Theory) formalisms of the Perturbation Theory were applied in this work to a simplified U-tubes steam generator model to perform sensitivity analysis. The adjoint and importance equations, with the corresponding expressions for the sensitivity coefficients, were derived for this steam generator model. The system was numerically was numerically solved in a Fortran program, called GEVADJ, in order to calculate the sensitivity coefficients. A transient loss of forced primary coolant in the nuclear power plant Angra-1 was used as example case. The average and final values of functionals: secondary pressure and enthalpy were studied in relation to changes in the secondary feedwater flow, enthalpy and total volume in secondary circuit. Absolute variations in the above functionals were calculated using the perturbative methods, considering the variations in the feedwater flow and total secondary volume. Comparison with the same variations obtained via direct model showed in general good agreement, demonstrating the potentiality of perturbative methods for sensitivity analysis of nuclear systems. (author) 22 refs., 7 figs., 8 tabs.
Perturbative and constructive renormalization
International Nuclear Information System (INIS)
Veiga, P.A. Faria da
2000-01-01
These notes are a survey of the material treated in a series of lectures delivered at the X Summer School Jorge Andre Swieca. They are concerned with renormalization in Quantum Field Theories. At the level of perturbation series, we review classical results as Feynman graphs, ultraviolet and infrared divergences of Feynman integrals. Weinberg's theorem and Hepp's theorem, the renormalization group and the Callan-Symanzik equation, the large order behavior and the divergence of most perturbation series. Out of the perturbative regime, as an example of a constructive method, we review Borel summability and point out how it is possible to circumvent the perturbation diseases. These lectures are a preparation for the joint course given by professor V. Rivasseau at the same school, where more sophisticated non-perturbative analytical methods based on rigorous renormalization group techniques are presented, aiming at furthering our understanding about the subject and bringing field theoretical models to a satisfactory mathematical level. (author)
First general methods toward aldehyde enolphosphates.
Barthes, Nicolas; Grison, Claude
2012-02-01
We herein report two innovative methods toward aldehyde enolphosphates and the first saccharidic aldehyde enolphosphates. Aldehyde enolphosphate function is worthwhile to be considered as a good phosphoenolpyruvate analogue. Copyright © 2011 Elsevier Inc. All rights reserved.
General method of quantitative spectrographic analysis
International Nuclear Information System (INIS)
Capdevila, C.; Roca, M.
1966-01-01
A spectrographic method was developed to determine 23 elements in a wide range of concentrations; the method can be applied to metallic or refractory samples. Previous melting with lithium tetraborate and germanium oxide is done in order to avoid the influence of matrix composition and crystalline structure. Germanium oxide is also employed as internal standard. The resulting beads ar mixed with graphite powder (1:1) and excited in a 10 amperes direct current arc. (Author) 12 refs
International Nuclear Information System (INIS)
Zeppenfeld, D.
1984-01-01
The present thesis deals with the construction and the analysis of mesonic bound states in SU(N) gauge theories in a two-dimensional space-time. The based field theory can thereby be considered as a simplified version of the QCD, the theory of the strong interactions. After an extensive discussion of the quantization in the temporal gauge and after the Poincare invariance of the theory has been shown mesonic bound states and the meson spectrum for different ranges of the free parameters of the theory (quark mass, coupling constant, and index N of the gauge group) are treated. The spectrum is given by a boundary value problem which in the perturbative limit is solved analytically. For massless quarks gauge-invariant annihilation operators are constructed which permit an exact solution of the energy eigenvalue equation. The energy eigenstates so found described massive interacting mesons which are surrounded by a cloud of massless free particles. (orig.) [de
Directory of Open Access Journals (Sweden)
FAHIM GOHARAWAN
2017-04-01
Full Text Available Techniques for the cavity measurement of the electrical characteristics of the materials are well established using the approximate method due to its simplicity in material insertion and fabrication. However, the exact method which requires more comprehensive mathematical analysis as well, owing to the practical difficulties for the material insertion, is not mostly used while performing the measurements as compared to approximate method in most of the works. In this work the comparative analysis of both the approximate as well as Exact method is performed and accuracy of the Exact method is established by performing the measurements of non-magnetic material Teflon within the cavity.
International Nuclear Information System (INIS)
Awan, F.G.; Sheikh, N.A.; Qureshi, S.A.; Sheikh, N.M.
2017-01-01
Techniques for the cavity measurement of the electrical characteristics of the materials are well established using the approximate method due to its simplicity in material insertion and fabrication. However, the exact method which requires more comprehensive mathematical analysis as well, owing to the practical difficulties for the material insertion, is not mostly used while performing the measurements as compared to approximate method in most of the works. In this work the comparative analysis of both the approximate as well as Exact method is performed and accuracy of the Exact method is established by performing the measurements of non-magnetic material Teflon within the cavity. (author)
Discounted Markov games : generalized policy iteration method
Wal, van der J.
1978-01-01
In this paper, we consider two-person zero-sum discounted Markov games with finite state and action spaces. We show that the Newton-Raphson or policy iteration method as presented by Pollats-chek and Avi-Itzhak does not necessarily converge, contradicting a proof of Rao, Chandrasekaran, and Nair.
Methods for summing general Kapteyn series
Energy Technology Data Exchange (ETDEWEB)
Tautz, R C [Zentrum fuer Astronomie und Astrophysik, Technische Universitaet Berlin, Hardenbergstrasse 36, D-10623 Berlin (Germany); Lerche, I [Institut fuer Geowissenschaften, Naturwissenschaftliche Fakultaet III, Martin-Luther-Universitaet Halle, D-06099 Halle (Germany); Dominici, D, E-mail: rct@gmx.eu, E-mail: lercheian@yahoo.com, E-mail: dominicd@newpaltz.edu [Department of Mathematics, State University of New York at New Paltz, 1 Hawk Dr, New Paltz, NY 12561-2443 (United States)
2011-09-23
The general features and characteristics of Kapteyn series, which are a special type of series involving the Bessel function, are investigated. For many applications in physics, astrophysics and mathematics, it is crucial to have closed-form expressions in order to determine their functional structure and parametric behavior. The closed-form expressions of Kapteyn series have mostly been limited to special cases, even though there are often similarities in the approaches used to reduce the series to analytically tractable forms. The goal of this paper is to review the previous work in the area and to show that Kapteyn series can be expressed as trigonometric or gamma function series, which can be evaluated in a closed form for specific parameters. Two examples with a similar structure are given, showing the complexity of Kapteyn series. (paper)
Prospect on general software of Monte Carlo method
International Nuclear Information System (INIS)
Pei Lucheng
1992-01-01
This is a short paper on the prospect of Monte Carlo general software. The content consists of cluster sampling method, zero variance technique, self-improved method, and vectorized Monte Carlo method
Chabab, M.; El Batoul, A.; Lahbas, A.; Oulne, M.
2018-05-01
Based on the minimal length concept, inspired by Heisenberg algebra, a closed analytical formula is derived for the energy spectrum of the prolate γ-rigid Bohr-Mottelson Hamiltonian of nuclei, within a quantum perturbation method (QPM), by considering a scaled Davidson potential in β shape variable. In the resulting solution, called X(3)-D-ML, the ground state and the first β-band are all studied as a function of the free parameters. The fact of introducing the minimal length concept with a QPM makes the model very flexible and a powerful approach to describe nuclear collective excitations of a variety of vibrational-like nuclei. The introduction of scaling parameters in the Davidson potential enables us to get a physical minimum of this latter in comparison with previous works. The analysis of the corrected wave function, as well as the probability density distribution, shows that the minimal length parameter has a physical upper bound limit.
International Nuclear Information System (INIS)
Campolina, Daniel de A.M.; Pereira, Claubia; Veloso, Maria Auxiliadora F.
2013-01-01
For all the physical components that comprise a nuclear system there is an uncertainty. Assessing the impact of uncertainties in the simulation of fissionable material systems is essential for a best estimate calculation that has been replacing the conservative model calculations as the computational power increases. The propagation of uncertainty in a simulation using sampling based method is recent because of the huge computational effort required. In this work a sample space of MCNP calculations were used as a black box model to propagate the uncertainty of system parameters. The efficiency of the method was compared to a conservative method. Uncertainties in input parameters of the reactor considered non-neutronic uncertainties, including geometry dimensions and density. The effect of the uncertainties on the effective multiplication factor of the system was analyzed respect to the possibility of using many uncertainties in the same input. If the case includes more than 46 parameters with uncertainty in the same input, the sampling based method is proved to be more efficient than the conservative method. (author)
International Nuclear Information System (INIS)
Passos, E.M.J. de
1976-01-01
The relationship between the Johnson-Baranger time-dependent folded diagram (JBFD) expansion, and the time independent methods of perturbation theory, are investigated. In the nondegenerate case, the JBFD expansion and the Rayleigh-Schroedinger perturbation expansion, for the ground state energy, are identical. On the other hand, in the degenerate case, for the nonhermitian effective interaction considered, the JBFD expansion, of the effective interaction, is equal to the perturbative expansion of the effective interaction of the nonhermitian eigenvalue problem of Bloch and Brandow-Des Cloizeaux. For the two hermitian effective interactions, the JBFD expansion of the effective interaction differs from the perturbation expansion of the effective interaction of the hermitian eigenvalue problem of Des Cloizeaux [pt
Pedesseau, Laurent; Jouanna, Paul
2004-12-01
The SASP (semianalytical stochastic perturbations) method is an original mixed macro-nano-approach dedicated to the mass equilibrium of multispecies phases, periphases, and interphases. This general method, applied here to the reflexive relation Ck⇔μk between the concentrations Ck and the chemical potentials μk of k species within a fluid in equilibrium, leads to the distribution of the particles at the atomic scale. The macroaspects of the method, based on analytical Taylor's developments of chemical potentials, are intimately mixed with the nanoaspects of molecular mechanics computations on stochastically perturbed states. This numerical approach, directly linked to definitions, is universal by comparison with current approaches, DLVO Derjaguin-Landau-Verwey-Overbeek, grand canonical Monte Carlo, etc., without any restriction on the number of species, concentrations, or boundary conditions. The determination of the relation Ck⇔μk implies in fact two problems: a direct problem Ck⇒μk and an inverse problem μk⇒Ck. Validation of the method is demonstrated in case studies A and B which treat, respectively, a direct problem and an inverse problem within a free saturated gypsum solution. The flexibility of the method is illustrated in case study C dealing with an inverse problem within a solution interphase, confined between two (120) gypsum faces, remaining in connection with a reference solution. This last inverse problem leads to the mass equilibrium of ions and water molecules within a 3 Å thick gypsum interface. The major unexpected observation is the repulsion of SO42- ions towards the reference solution and the attraction of Ca2+ ions from the reference solution, the concentration being 50 times higher within the interphase as compared to the free solution. The SASP method is today the unique approach able to tackle the simulation of the number and distribution of ions plus water molecules in such extreme confined conditions. This result is of prime
International Nuclear Information System (INIS)
Sakai, Shiro; Arita, Ryotaro; Aoki, Hideo
2006-01-01
We propose a new quantum Monte Carlo method especially intended to couple with the dynamical mean-field theory. The algorithm is not only much more efficient than the conventional Hirsch-Fye algorithm, but is applicable to multiorbital systems having an SU(2)-symmetric Hund's coupling as well
Energy Technology Data Exchange (ETDEWEB)
Nelms, Benjamin E. [Canis Lupus LLC, Merrimac, Wisconsin 53561 (United States); Opp, Daniel; Zhang, Geoffrey; Moros, Eduardo; Feygelman, Vladimir, E-mail: vladimir.feygelman@moffitt.org [Department of Radiation Oncology, Moffitt Cancer Center, Tampa, Florida 33612 (United States)
2014-06-15
Purpose: In this work, the feasibility of implementing a motion-perturbation approach to accurately estimate volumetric dose in the presence of organ motion—previously demonstrated for VMAT-–is studied for static gantry IMRT. The method's accuracy is improved for the voxels that have very low planned dose but acquire appreciable dose due to motion. The study describes the modified algorithm and its experimental validation and provides an example of a clinical application. Methods: A contoured region-of-interest is propagated according to the predefined motion kernel throughout time-resolved 4D phantom dose grids. This timed series of 3D dose grids is produced by the measurement-guided dose reconstruction algorithm, based on an irradiation of a staticARCCHECK (AC) helical dosimeter array (Sun Nuclear Corp., Melbourne, FL). Each moving voxel collects dose over the dynamic simulation. The difference in dose-to-moving voxel vs dose-to-static voxel in-phantom forms the basis of a motion perturbation correction that is applied to the corresponding voxel in the patient dataset. A new method to synchronize the accelerator and dosimeter clocks, applicable to fixed-gantry IMRT, was developed. Refinements to the algorithm account for the excursion of low dose voxels into high dose regions, causing appreciable dose increase due to motion (LDVE correction). For experimental validation, four plans using TG-119 structure sets and objectives were produced using segmented IMRT direct machine parameters optimization in Pinnacle treatment planning system (v. 9.6, Philips Radiation Oncology Systems, Fitchburg, WI). All beams were delivered with the gantry angle of 0°. Each beam was delivered three times: (1) to the static AC centered on the room lasers; (2) to a static phantom containing a MAPCHECK2 (MC2) planar diode array dosimeter (Sun Nuclear); and (3) to the moving MC2 phantom. The motion trajectory was an ellipse in the IEC XY plane, with 3 and 1.5 cm axes. The period
International Nuclear Information System (INIS)
Druzhinina, O V; Shestakov, A A
2002-01-01
A generalized direct Lyapunov method is put forward for the study of stability and attraction in general time systems of the following types: the classical dynamical system in the sense of Birkhoff, the general system in the sense of Zubov, the general system in the sense of Seibert, the general system with delay, and the general 'input-output' system. For such systems, with the help of generalized Lyapunov functions with respect to two filters, two quasifilters, or two filter bases, necessary and sufficient conditions for stability and attraction are obtained under minimal assumptions about the mathematical structure of the general system
Method and Apparatus for Performance Optimization Through Physical Perturbation of Task Elements
Prinzel, Lawrence J., III (Inventor); Pope, Alan T. (Inventor); Palsson, Olafur S. (Inventor); Turner, Marsha J. (Inventor)
2016-01-01
The invention is an apparatus and method of biofeedback training for attaining a physiological state optimally consistent with the successful performance of a task, wherein the probability of successfully completing the task is made is inversely proportional to a physiological difference value, computed as the absolute value of the difference between at least one physiological signal optimally consistent with the successful performance of the task and at least one corresponding measured physiological signal of a trainee performing the task. The probability of successfully completing the task is made inversely proportional to the physiological difference value by making one or more measurable physical attributes of the environment in which the task is performed, and upon which completion of the task depends, vary in inverse proportion to the physiological difference value.
International Nuclear Information System (INIS)
Green, T.A.
1978-10-01
For one-electron heteropolar systems, the wave-theoretic Lagrangian of Paper I 2 is simplified in two distinct approximations. The first is semiclassical; the second is quantal, for velocities below those for which the semiclassical treatment is reliable. For each approximation, unitarity and detailed balancing are discussed. Then, the variational method as described by Demkov is used to determine the coupled equations for the radial functions and the Euler-Lagrange equations for the translational factors which are part of the theory. Specific semiclassical formulae for the translational factors are given in a many-state approximation. Low-velocity quantal formulae are obtained in a one-state approximation. The one-state results of both approximations agree with an earlier determination by Riley. 14 references
A generalized resonating group method with absorptive interaction
International Nuclear Information System (INIS)
Hernandez, E.; Mondragon, A.; Instituto Nacional de Investigaciones Nucleares, Mexico City)
1981-01-01
A generalized Hill-Wheeler equation for the elastic collision at two composite nuclei is obtained projecting the complete many-body Schroedinger equation on the subspace of model internal wave functions and on its orthogonal complement. We get a new, non hermitian (absorptive) interaction term W which takes into account the flux loss in the elastic channel, besides the usual RGM effective Hamiltonian and normalization kernels. A perturbation series expansion for W containing only linked diagrams is given. Finally, the antisymmetrized product of internal wave functions of the fragments that appear in the projection operator is expressed in terms of complex generator coordinates, then the terms appearing in effective interaction can be written as matrix elements of the microscopic interactions and/or the antisymmetrizer between two center shell model states. (author)
International Nuclear Information System (INIS)
Du Zeng-Ji; Lin Wan-Tao; Mo Jia-Qi
2012-01-01
The EI Niño-southern oscillation (ENSO) is an interannual phenomenon involved in tropical Pacific ocean-atmosphere interactions. In this paper, we develop an asymptotic method of solving the nonlinear equation using the ENSO model. Based on a class of the oscillator of the ENSO model, a approximate solution of the corresponding problem is studied employing the perturbation method
On Self-Adaptive Method for General Mixed Variational Inequalities
Directory of Open Access Journals (Sweden)
Abdellah Bnouhachem
2008-01-01
Full Text Available We suggest and analyze a new self-adaptive method for solving general mixed variational inequalities, which can be viewed as an improvement of the method of (Noor 2003. Global convergence of the new method is proved under the same assumptions as Noor's method. Some preliminary computational results are given to illustrate the efficiency of the proposed method. Since the general mixed variational inequalities include general variational inequalities, quasivariational inequalities, and nonlinear (implicit complementarity problems as special cases, results proved in this paper continue to hold for these problems.
A Generalized Autocovariance Least-Squares Method for Covariance Estimation
DEFF Research Database (Denmark)
Åkesson, Bernt Magnus; Jørgensen, John Bagterp; Poulsen, Niels Kjølstad
2007-01-01
A generalization of the autocovariance least- squares method for estimating noise covariances is presented. The method can estimate mutually correlated system and sensor noise and can be used with both the predicting and the filtering form of the Kalman filter.......A generalization of the autocovariance least- squares method for estimating noise covariances is presented. The method can estimate mutually correlated system and sensor noise and can be used with both the predicting and the filtering form of the Kalman filter....
C. Colloca TS/FM
2004-01-01
TS/FM group informs you that, for the progress of the works at the Prévessin site entrance, some perturbation of the traffic may occur during the week between the 14th and 18th of June for a short duration. Access will be assured at any time. For more information, please contact 160239. C. Colloca TS/FM
International Nuclear Information System (INIS)
Truchet, G.; Leconte, P.; Peneliau, Y.; Santamarina, A.
2013-01-01
The first goal of this paper is to present an exact method able to precisely evaluate very small reactivity effects with a Monte Carlo code (<10 pcm). it has been decided to implement the exact perturbation theory in TRIPOLI-4 and, consequently, to calculate a continuous-energy adjoint flux. The Iterated Fission Probability (IFP) method was chosen because it has shown great results in some other Monte Carlo codes. The IFP method uses a forward calculation to compute the adjoint flux, and consequently, it does not rely on complex code modifications but on the physical definition of the adjoint flux as a phase-space neutron importance. In the first part of this paper, the IFP method implemented in TRIPOLI-4 is described. To illustrate the efficiency of the method, several adjoint fluxes are calculated and compared with their equivalent obtained by the deterministic code APOLLO-2. The new implementation can calculate angular adjoint flux. In the second part, a procedure to carry out an exact perturbation calculation is described. A single cell benchmark has been used to test the accuracy of the method, compared with the 'direct' estimation of the perturbation. Once again the method based on the IFP shows good agreement for a calculation time far more inferior to the 'direct' method. The main advantage of the method is that the relative accuracy of the reactivity variation does not depend on the magnitude of the variation itself, which allows us to calculate very small reactivity perturbations with high precision. It offers the possibility to split reactivity contributions on both isotopes and reactions. Other applications of this perturbation method are presented and tested like the calculation of exact kinetic parameters (βeff, Λeff) or sensitivity parameters
Directory of Open Access Journals (Sweden)
Magdy A. El-Tawil
2009-01-01
Full Text Available A perturbing nonlinear Schrodinger equation is studied under general complex nonhomogeneities and complex initial conditions for zero boundary conditions. The perturbation method together with the eigenfunction expansion and variational parameters methods are used to introduce an approximate solution for the perturbative nonlinear case for which a power series solution is proved to exist. Using Mathematica, the symbolic solution algorithm is tested through computing the possible approximations under truncation procedures. The method of solution is illustrated through case studies and figures.
Primal Interior Point Method for Minimization of Generalized Minimax Functions
Czech Academy of Sciences Publication Activity Database
Lukšan, Ladislav; Matonoha, Ctirad; Vlček, Jan
2010-01-01
Roč. 46, č. 4 (2010), s. 697-721 ISSN 0023-5954 R&D Projects: GA ČR GA201/09/1957 Institutional research plan: CEZ:AV0Z10300504 Keywords : unconstrained optimization * large-scale optimization * nonsmooth optimization * generalized minimax optimization * interior-point methods * modified Newton methods * variable metric methods * global convergence * computational experiments Subject RIV: BA - General Mathematics Impact factor: 0.461, year: 2010 http://dml.cz/handle/10338.dmlcz/140779
An iterative method for the canard explosion in general planar systems
DEFF Research Database (Denmark)
Brøns, Morten
2013-01-01
The canard explosion is the change of amplitude and period of a limit cycle born in a Hopf bifurcation in a very narrow parameter interval. The phenomenon is well understood in singular perturbation problems where a small parameter controls the slow/fast dynamics. However, canard explosions are a...... on the van der Pol equation, showing that the asymptotics of the method is correct, and on a templator model for a self-replicating system....... are also observed in systems where no such parameter can obviously be identied. Here we show how the iterative method of Roussel and Fraser, devised to construct regular slow manifolds, can be used to determine a canard point in a general planar system of nonlinear ODEs. We demonstrate the method...
Lu, Chao; Li, Xubin; Wu, Dongsheng; Zheng, Lianqing; Yang, Wei
2016-01-12
In aqueous solution, solute conformational transitions are governed by intimate interplays of the fluctuations of solute-solute, solute-water, and water-water interactions. To promote molecular fluctuations to enhance sampling of essential conformational changes, a common strategy is to construct an expanded Hamiltonian through a series of Hamiltonian perturbations and thereby broaden the distribution of certain interactions of focus. Due to a lack of active sampling of configuration response to Hamiltonian transitions, it is challenging for common expanded Hamiltonian methods to robustly explore solvent mediated rare conformational events. The orthogonal space sampling (OSS) scheme, as exemplified by the orthogonal space random walk and orthogonal space tempering methods, provides a general framework for synchronous acceleration of slow configuration responses. To more effectively sample conformational transitions in aqueous solution, in this work, we devised a generalized orthogonal space tempering (gOST) algorithm. Specifically, in the Hamiltonian perturbation part, a solvent-accessible-surface-area-dependent term is introduced to implicitly perturb near-solute water-water fluctuations; more importantly in the orthogonal space response part, the generalized force order parameter is generalized as a two-dimension order parameter set, in which essential solute-solvent and solute-solute components are separately treated. The gOST algorithm is evaluated through a molecular dynamics simulation study on the explicitly solvated deca-alanine (Ala10) peptide. On the basis of a fully automated sampling protocol, the gOST simulation enabled repetitive folding and unfolding of the solvated peptide within a single continuous trajectory and allowed for detailed constructions of Ala10 folding/unfolding free energy surfaces. The gOST result reveals that solvent cooperative fluctuations play a pivotal role in Ala10 folding/unfolding transitions. In addition, our assessment
International Nuclear Information System (INIS)
Zhu Shengyun; Li Anli; Gou Zhenghui; Zheng Shengnan; Li Guangsheng
1994-01-01
The g-factor hence the magnetic moment, of the isomeric state 43 Sc(19/2 - , 3.1232 MeV) has been measured by the time differential perturbed angular distribution method. The measured values are g = 0.3279(19) and μ/μN = 3.108(18) nm
Studies od radioactive decay after-effects by the method of perturbed angular γγ-correlation
International Nuclear Information System (INIS)
Shpinkova, L.G.
2002-01-01
One of the methods applied for electron capture (Ec) after-effects studied is the time differential perturbed angular γγ-correlation (Tdpa( technique, which allows investigating hyperfine interactions of electromagnetic moments of nuclei with extranuclear fields created by electrons and ions around the probe atom in the studied matrix. After-effects can differentially affect the observed angular correlation and, thus, be studied by this method. The experiments performed so far with different nuclei in different matrixes showed that the after-effects are not important in TDPAC studies of metallic systems because of a considerable lag caused by a finite lifetime of the initial state of the γγ-cascade and the fast relaxation due to conduction electrons. In insulators and oxides. the after-effects should be taken into account while interpreting experimental data . A problem of molecular dynamic studies in liquids obscured by after-effects was also mentioned in the literature. A possibility of molecule disintegration caused by EC after-effects, initiated by the Auger-process was studied for 111 In-complexes with diethylenetriaminepentaacetic acid in neutral aqueous solutions. The results of the work showed directly that the AC after-effects could cause the metal-legand complexes disintegration. The observation of the non-equilibrium fraction with presumably high transient gradients caused by both a relaxation from the highly ionised state od 111 Cd (the daughter nucleus in the EC decay of 111 In) and rearrangement of the chemical bonds allowed assessing the time required for these transient processes (before complex disintegration or complex relaxation to the equilibrium state)
International Nuclear Information System (INIS)
Ecker, G.
1996-06-01
After a general introduction to the structure of effective field theories, the main ingredients of chiral perturbation theory are reviewed. Applications include the light quark mass ratios and pion-pion scattering to two-loop accuracy. In the pion-nucleon system, the linear σ model is contrasted with chiral perturbation theory. The heavy-nucleon expansion is used to construct the effective pion-nucleon Lagrangian to third order in the low-energy expansion, with applications to nucleon Compton scattering. (author)
Generalized differential transform method to differential-difference equation
International Nuclear Information System (INIS)
Zou Li; Wang Zhen; Zong Zhi
2009-01-01
In this Letter, we generalize the differential transform method to solve differential-difference equation for the first time. Two simple but typical examples are applied to illustrate the validity and the great potential of the generalized differential transform method in solving differential-difference equation. A Pade technique is also introduced and combined with GDTM in aim of extending the convergence area of presented series solutions. Comparisons are made between the results of the proposed method and exact solutions. Then we apply the differential transform method to the discrete KdV equation and the discrete mKdV equation, and successfully obtain solitary wave solutions. The results reveal that the proposed method is very effective and simple. We should point out that generalized differential transform method is also easy to be applied to other nonlinear differential-difference equation.
A hyperpower iterative method for computing the generalized Drazin ...
Indian Academy of Sciences (India)
Shwetabh Srivastava
[6, 7]. A number of direct and iterative methods for com- putation of the Drazin inverse were developed in [8–12]. Its extension to Banach algebras is known as the generalized Drazin inverse and was established in [13]. Let J denote the complex. Banach algebra with the unit 1. The generalized Drazin inverse of an element ...
Generalized empirical likelihood methods for analyzing longitudinal data
Wang, S.; Qian, L.; Carroll, R. J.
2010-01-01
Efficient estimation of parameters is a major objective in analyzing longitudinal data. We propose two generalized empirical likelihood based methods that take into consideration within-subject correlations. A nonparametric version of the Wilks
Perturbative renormalization of composite operators via flow equations. Pt. 1
Energy Technology Data Exchange (ETDEWEB)
Keller, G. (Max-Planck-Institut fuer Physik und Astrophysik, Muenchen (Germany). Werner-Heisenberg-Inst. fuer Physik); Kopper, C. (Goettingen Univ. (Germany). Inst. fuer Theoretische Physik)
1992-09-01
We apply the general framework of the continuous renormalization group, whose significance for perturbative quantum field theories was recognized by Polchinski, to investigate by new and mathematically simple methods the perturbative renormalization of composite operators. In this paper we demonstrate the perturbative renormalizability of the Green functions of the Euclidean massive {Phi}{sub 4}{sup 4} theory with one insertion of a (possibly oversubtracted, in the BPHZ language) composite operator. Moreover we show that our method admits an easy proof of the Zimmermann identities and of the Lowenstein rule. (orig.).
Perturbative renormalization of composite operators via flow equations. Pt. 1
International Nuclear Information System (INIS)
Keller, G.; Kopper, C.
1992-01-01
We apply the general framework of the continuous renormalization group, whose significance for perturbative quantum field theories was recognized by Polchinski, to investigate by new and mathematically simple methods the perturbative renormalization of composite operators. In this paper we demonstrate the perturbative renormalizability of the Green functions of the Euclidean massive Φ 4 4 theory with one insertion of a (possibly oversubtracted, in the BPHZ language) composite operator. Moreover we show that our method admits an easy proof of the Zimmermann identities and of the Lowenstein rule. (orig.)
Perturbed effects at radiation physics
International Nuclear Information System (INIS)
Külahcı, Fatih; Şen, Zekâi
2013-01-01
Perturbation methodology is applied in order to assess the linear attenuation coefficient, mass attenuation coefficient and cross-section behavior with random components in the basic variables such as the radiation amounts frequently used in the radiation physics and chemistry. Additionally, layer attenuation coefficient (LAC) and perturbed LAC (PLAC) are proposed for different contact materials. Perturbation methodology provides opportunity to obtain results with random deviations from the average behavior of each variable that enters the whole mathematical expression. The basic photon intensity variation expression as the inverse exponential power law (as Beer–Lambert's law) is adopted for perturbation method exposition. Perturbed results are presented not only in terms of the mean but additionally the standard deviation and the correlation coefficients. Such perturbation expressions provide one to assess small random variability in basic variables. - Highlights: • Perturbation methodology is applied to Radiation Physics. • Layer attenuation coefficient (LAC) and perturbed LAC are proposed for contact materials. • Perturbed linear attenuation coefficient is proposed. • Perturbed mass attenuation coefficient (PMAC) is proposed. • Perturbed cross-section is proposed
CERN. Geneva
2013-01-01
Perturbative QCD is the general theoretical framework for describing hard scattering processes yielding multiparticle production at hadron colliders. In these lectures, we shall introduce fundamental features of perturbative QCD and describe its application to several high energy collider processes, including jet production in electron-positron annihilation, deep inelastic scattering, Higgs boson and gauge boson production at the LHC.
Edge detection methods based on generalized type-2 fuzzy logic
Gonzalez, Claudia I; Castro, Juan R; Castillo, Oscar
2017-01-01
In this book four new methods are proposed. In the first method the generalized type-2 fuzzy logic is combined with the morphological gra-dient technique. The second method combines the general type-2 fuzzy systems (GT2 FSs) and the Sobel operator; in the third approach the me-thodology based on Sobel operator and GT2 FSs is improved to be applied on color images. In the fourth approach, we proposed a novel edge detec-tion method where, a digital image is converted a generalized type-2 fuzzy image. In this book it is also included a comparative study of type-1, inter-val type-2 and generalized type-2 fuzzy systems as tools to enhance edge detection in digital images when used in conjunction with the morphologi-cal gradient and the Sobel operator. The proposed generalized type-2 fuzzy edge detection methods were tested with benchmark images and synthetic images, in a grayscale and color format. Another contribution in this book is that the generalized type-2 fuzzy edge detector method is applied in the preproc...
Generalized empirical likelihood methods for analyzing longitudinal data
Wang, S.
2010-02-16
Efficient estimation of parameters is a major objective in analyzing longitudinal data. We propose two generalized empirical likelihood based methods that take into consideration within-subject correlations. A nonparametric version of the Wilks theorem for the limiting distributions of the empirical likelihood ratios is derived. It is shown that one of the proposed methods is locally efficient among a class of within-subject variance-covariance matrices. A simulation study is conducted to investigate the finite sample properties of the proposed methods and compare them with the block empirical likelihood method by You et al. (2006) and the normal approximation with a correctly estimated variance-covariance. The results suggest that the proposed methods are generally more efficient than existing methods which ignore the correlation structure, and better in coverage compared to the normal approximation with correctly specified within-subject correlation. An application illustrating our methods and supporting the simulation study results is also presented.
Directory of Open Access Journals (Sweden)
D. S. Vakhlyarskiy
2016-01-01
Full Text Available This paper proposes a method to calculate the splitting of natural frequency of the shell of hemispherical resonator gyro. (HRG. The paper considers splitting that arises from the small defect of the middle surface, which makes the resonator different from the rotary shell. The presented method is a combination of the perturbation method and the finite element method. The method allows us to find the frequency splitting caused by defects in shape, arbitrary distributed in the circumferential direction. This is achieved by calculating the perturbations of multiple natural frequencies of the second and higher orders. The proposed method allows us to calculate the splitting of multiple frequencies for the shell with the meridian of arbitrary shape.A developed finite element is an annular element of the shell and has two nodes. Projections of movements are used on the axis of the global cylindrical system of coordinates, as the unknown. To approximate the movements are used polynomials of the second degree. Within the finite element the geometric characteristics are arranged in a series according to the small parameter of perturbations of the middle surface geometry.Movements on the final element are arranged in series according to the small parameter, and in a series according to circumferential angle. With computer used to implement the method, three-dimensional arrays are used to store the perturbed quantities. This allows the use of regular expressions for the mass and stiffness matrices, when building the finite element, instead of analytic dependencies for each perturbation of these matrices of the required order with desirable mathematical operations redefined in accordance with the perturbation method.As a test task, is calculated frequency splitting of non-circular cylindrical resonator with Navier boundary conditions. The discrepancy between the results and semi-analytic solution to this problem is less than 1%. For a cylindrical shell is
Generalized Row-Action Methods for Tomographic Imaging
DEFF Research Database (Denmark)
Andersen, Martin Skovgaard; Hansen, Per Christian
2014-01-01
Row-action methods play an important role in tomographic image reconstruction. Many such methods can be viewed as incremental gradient methods for minimizing a sum of a large number of convex functions, and despite their relatively poor global rate of convergence, these methods often exhibit fast...... initial convergence which is desirable in applications where a low-accuracy solution is acceptable. In this paper, we propose relaxed variants of a class of incremental proximal gradient methods, and these variants generalize many existing row-action methods for tomographic imaging. Moreover, they allow...
New Implicit General Linear Method | Ibrahim | Journal of the ...
African Journals Online (AJOL)
A New implicit general linear method is designed for the numerical olution of stiff differential Equations. The coefficients matrix is derived from the stability function. The method combines the single-implicitness or diagonal implicitness with property that the first two rows are implicit and third and fourth row are explicit.
Generalized spectral method for near-field optical microscopy
Energy Technology Data Exchange (ETDEWEB)
Jiang, B.-Y.; Zhang, L. M.; Basov, D. N.; Fogler, M. M. [Department of Physics, University of California San Diego, 9500 Gilman Drive, La Jolla, California 92093 (United States); Castro Neto, A. H. [Department of Physics, Boston University, 590 Commonwealth Avenue, Boston, Massachusetts 02215 (United States); Centre for Advanced 2D Materials and Graphene Research Centre, National University of Singapore, Singapore, Singapore 117542 (Singapore)
2016-02-07
Electromagnetic interaction between a sub-wavelength particle (the “probe”) and a material surface (the “sample”) is studied theoretically. The interaction is shown to be governed by a series of resonances corresponding to surface polariton modes localized near the probe. The resonance parameters depend on the dielectric function and geometry of the probe as well as on the surface reflectivity of the material. Calculation of such resonances is carried out for several types of axisymmetric probes: spherical, spheroidal, and pear-shaped. For spheroids, an efficient numerical method is developed, capable of handling cases of large or strongly momentum-dependent surface reflectivity. Application of the method to highly resonant materials, such as aluminum oxide (by itself or covered with graphene), reveals a rich structure of multi-peak spectra and nonmonotonic approach curves, i.e., the probe-sample distance dependence. These features also strongly depend on the probe shape and optical constants of the model. For less resonant materials such as silicon oxide, the dependence is weak, so that the spheroidal model is reliable. The calculations are done within the quasistatic approximation with radiative damping included perturbatively.
Generalized Truncated Methods for an Efficient Solution of Retrial Systems
Directory of Open Access Journals (Sweden)
Ma Jose Domenech-Benlloch
2008-01-01
Full Text Available We are concerned with the analytic solution of multiserver retrial queues including the impatience phenomenon. As there are not closed-form solutions to these systems, approximate methods are required. We propose two different generalized truncated methods to effectively solve this type of systems. The methods proposed are based on the homogenization of the state space beyond a given number of users in the retrial orbit. We compare the proposed methods with the most well-known methods appeared in the literature in a wide range of scenarios. We conclude that the proposed methods generally outperform previous proposals in terms of accuracy for the most common performance parameters used in retrial systems with a moderated growth in the computational cost.
A generalized endogenous grid method for discrete-continuous choice
John Rust; Bertel Schjerning; Fedor Iskhakov
2012-01-01
This paper extends Carroll's endogenous grid method (2006 "The method of endogenous gridpoints for solving dynamic stochastic optimization problems", Economic Letters) for models with sequential discrete and continuous choice. Unlike existing generalizations, we propose solution algorithm that inherits both advantages of the original method, namely it avoids all root finding operations, and also efficiently deals with restrictions on the continuous decision variable. To further speed up the s...
A Generalized Runge-Kutta Method of order three
DEFF Research Database (Denmark)
Thomsen, Per Grove
2002-01-01
The report presents a numerical method for the solution of stiff systems of ODE's and index one DAE's. The type of method is a 4- stage Generalized Linear Method that is reformulated in a special Semi Implicit Runge Kutta Method of SDIRK type. Error estimation is by imbedding a method of order 4...... based on the same stages as the method and the coefficients are selected for ease of implementation. The method has 4 stages and the stage-order is 2. For purposes of generating dense output and for initializing the iteration in the internal stages a continuous extension is derived. The method is A......-stable and we present the region of absolute stability and the order star of the order 3 method that is used for computing the solution....
Learning with Generalization Capability by Kernel Methods of Bounded Complexity
Czech Academy of Sciences Publication Activity Database
Kůrková, Věra; Sanguineti, M.
2005-01-01
Roč. 21, č. 3 (2005), s. 350-367 ISSN 0885-064X R&D Projects: GA AV ČR 1ET100300419 Institutional research plan: CEZ:AV0Z10300504 Keywords : supervised learning * generalization * model complexity * kernel methods * minimization of regularized empirical errors * upper bounds on rates of approximate optimization Subject RIV: BA - General Mathematics Impact factor: 1.186, year: 2005
Equivalence of the generalized and complex Kohn variational methods
Energy Technology Data Exchange (ETDEWEB)
Cooper, J N; Armour, E A G [School of Mathematical Sciences, University Park, Nottingham NG7 2RD (United Kingdom); Plummer, M, E-mail: pmxjnc@googlemail.co [STFC Daresbury Laboratory, Daresbury, Warrington, Cheshire WA4 4AD (United Kingdom)
2010-04-30
For Kohn variational calculations on low energy (e{sup +} - H{sub 2}) elastic scattering, we prove that the phase shift approximation, obtained using the complex Kohn method, is precisely equal to a value which can be obtained immediately via the real-generalized Kohn method. Our treatment is sufficiently general to be applied directly to arbitrary potential scattering or single open channel scattering problems, with exchange if required. In the course of our analysis, we develop a framework formally to describe the anomalous behaviour of our generalized Kohn calculations in the regions of the well-known Schwartz singularities. This framework also explains the mathematical origin of the anomaly-free singularities we reported in a previous article. Moreover, we demonstrate a novelty: that explicit solutions of the Kohn equations are not required in order to calculate optimal phase shift approximations. We relate our rigorous framework to earlier descriptions of the Kohn-type methods.
Equivalence of the generalized and complex Kohn variational methods
International Nuclear Information System (INIS)
Cooper, J N; Armour, E A G; Plummer, M
2010-01-01
For Kohn variational calculations on low energy (e + - H 2 ) elastic scattering, we prove that the phase shift approximation, obtained using the complex Kohn method, is precisely equal to a value which can be obtained immediately via the real-generalized Kohn method. Our treatment is sufficiently general to be applied directly to arbitrary potential scattering or single open channel scattering problems, with exchange if required. In the course of our analysis, we develop a framework formally to describe the anomalous behaviour of our generalized Kohn calculations in the regions of the well-known Schwartz singularities. This framework also explains the mathematical origin of the anomaly-free singularities we reported in a previous article. Moreover, we demonstrate a novelty: that explicit solutions of the Kohn equations are not required in order to calculate optimal phase shift approximations. We relate our rigorous framework to earlier descriptions of the Kohn-type methods.
Multiple-time-stepping generalized hybrid Monte Carlo methods
Energy Technology Data Exchange (ETDEWEB)
Escribano, Bruno, E-mail: bescribano@bcamath.org [BCAM—Basque Center for Applied Mathematics, E-48009 Bilbao (Spain); Akhmatskaya, Elena [BCAM—Basque Center for Applied Mathematics, E-48009 Bilbao (Spain); IKERBASQUE, Basque Foundation for Science, E-48013 Bilbao (Spain); Reich, Sebastian [Universität Potsdam, Institut für Mathematik, D-14469 Potsdam (Germany); Azpiroz, Jon M. [Kimika Fakultatea, Euskal Herriko Unibertsitatea (UPV/EHU) and Donostia International Physics Center (DIPC), P.K. 1072, Donostia (Spain)
2015-01-01
Performance of the generalized shadow hybrid Monte Carlo (GSHMC) method [1], which proved to be superior in sampling efficiency over its predecessors [2–4], molecular dynamics and hybrid Monte Carlo, can be further improved by combining it with multi-time-stepping (MTS) and mollification of slow forces. We demonstrate that the comparatively simple modifications of the method not only lead to better performance of GSHMC itself but also allow for beating the best performed methods, which use the similar force splitting schemes. In addition we show that the same ideas can be successfully applied to the conventional generalized hybrid Monte Carlo method (GHMC). The resulting methods, MTS-GHMC and MTS-GSHMC, provide accurate reproduction of thermodynamic and dynamical properties, exact temperature control during simulation and computational robustness and efficiency. MTS-GHMC uses a generalized momentum update to achieve weak stochastic stabilization to the molecular dynamics (MD) integrator. MTS-GSHMC adds the use of a shadow (modified) Hamiltonian to filter the MD trajectories in the HMC scheme. We introduce a new shadow Hamiltonian formulation adapted to force-splitting methods. The use of such Hamiltonians improves the acceptance rate of trajectories and has a strong impact on the sampling efficiency of the method. Both methods were implemented in the open-source MD package ProtoMol and were tested on a water and a protein systems. Results were compared to those obtained using a Langevin Molly (LM) method [5] on the same systems. The test results demonstrate the superiority of the new methods over LM in terms of stability, accuracy and sampling efficiency. This suggests that putting the MTS approach in the framework of hybrid Monte Carlo and using the natural stochasticity offered by the generalized hybrid Monte Carlo lead to improving stability of MTS and allow for achieving larger step sizes in the simulation of complex systems.
Optimized Perturbation Theory for Wave Functions of Quantum Systems
International Nuclear Information System (INIS)
Hatsuda, T.; Tanaka, T.; Kunihiro, T.
1997-01-01
The notion of the optimized perturbation, which has been successfully applied to energy eigenvalues, is generalized to treat wave functions of quantum systems. The key ingredient is to construct an envelope of a set of perturbative wave functions. This leads to a condition similar to that obtained from the principle of minimal sensitivity. Applications of the method to the quantum anharmonic oscillator and the double well potential show that uniformly valid wave functions with correct asymptotic behavior are obtained in the first-order optimized perturbation even for strong couplings. copyright 1997 The American Physical Society
Resummation of the QCD perturbative series for hard processes
International Nuclear Information System (INIS)
Catani, S.
1989-01-01
We study the region of inhibited radiation in hard hadronic processes, as for jet cross sections and heavy flavour production near threshold. The cases of deep inelastic scattering and Drell-Yan annihilation are explicitly considered. A general method to exponentiate leading and next-to-leading logarithms to all orders in perturbation theory is developed. A complete formula for the large N-moments is given and shown to agree with previous two-loop calculations. The resummation procedure suggests how to connect the perturbative and nonperturbative regions. The natural limit within the perturbative phase is shown to be the intrinsic transverse momentum. (orig.)
Energy Technology Data Exchange (ETDEWEB)
Freire, Fernando S.; Silva, Fernando C.; Martinez, Aquilino S. [Universidade Federal, Rio de Janeiro, RJ (Brazil). Coordenacao dos Programas de Pos-graduacao de Engenharia. Programa de Engenharia Nuclear]. E-mail: ffreire@con.ufrj.br; fernando@con.ufrj.br; aquilino@.con.ufrj.br
2005-07-01
Frequently it is necessary to compute the change in core multiplication caused by a change in the core temperature or composition. Even when this perturbation is localized, such as a control rod inserted into the core, one does not have to repeat the original criticality calculation, but instead we can use the well-known pseudo-harmonics perturbation method to express the corresponding change in the multiplication factor in terms of the neutron flux expanded in the basis vectors characterizing the unperturbed core. Therefore we may compute the control rod worth to find the most reactivity control rod to calculate the fast shutdown margin. In this thesis we propose a simple and precise method to identify the most reactivity control rod. (author)
Renormalized Lie perturbation theory
International Nuclear Information System (INIS)
Rosengaus, E.; Dewar, R.L.
1981-07-01
A Lie operator method for constructing action-angle transformations continuously connected to the identity is developed for area preserving mappings. By a simple change of variable from action to angular frequency a perturbation expansion is obtained in which the small denominators have been renormalized. The method is shown to lead to the same series as the Lagrangian perturbation method of Greene and Percival, which converges on KAM surfaces. The method is not superconvergent, but yields simple recursion relations which allow automatic algebraic manipulation techniques to be used to develop the series to high order. It is argued that the operator method can be justified by analytically continuing from the complex angular frequency plane onto the real line. The resulting picture is one where preserved primary KAM surfaces are continuously connected to one another
Computation of Optimal Monotonicity Preserving General Linear Methods
Ketcheson, David I.
2009-07-01
Monotonicity preserving numerical methods for ordinary differential equations prevent the growth of propagated errors and preserve convex boundedness properties of the solution. We formulate the problem of finding optimal monotonicity preserving general linear methods for linear autonomous equations, and propose an efficient algorithm for its solution. This algorithm reliably finds optimal methods even among classes involving very high order accuracy and that use many steps and/or stages. The optimality of some recently proposed methods is verified, and many more efficient methods are found. We use similar algorithms to find optimal strong stability preserving linear multistep methods of both explicit and implicit type, including methods for hyperbolic PDEs that use downwind-biased operators.
Generalization of the influence function method in mining subsidence
International Nuclear Information System (INIS)
Bello Garcia, A.; Mendendez Diaz, A.; Ordieres Mere, J.B.; Gonzalez Nicieza, C.
1996-01-01
A generic approach to subsidence prediction based on the influence function method is presented. The changes proposed to the classical approach are the result of a previous analysis stage where a generalization to the 3D problem was made. In addition other hypothesis in order to relax the structural principles of the classical model are suggested. The quantitative results of this process and a brief discussion of its method of employment is presented. 13 refs., 8 figs., 5 tabs
Generalized series method in the theory of atomic nucleus
International Nuclear Information System (INIS)
Gorbatov, A.M.
1991-01-01
On a hypersphere of a prescribed radius the so-called genealogical basis has been constructed. By making use of this basis, the many-body Schroedinger equation has been obtained for bound states of various physical systems. The genealogical series method, being in general outline the extension of the angular potential functions method, deals with the potential harmonics of any generation needed. The new approach provides an exact numerical description of the hadron systems with two-body higher interaction
On summation of perturbation expansions
International Nuclear Information System (INIS)
Horzela, A.
1985-04-01
The problem of the restoration of physical quantities defined by divergent perturbation expansions is analysed. The Pad'e and Borel summability is proved for alternating perturbation expansions with factorially growing coefficients. The proof is based on the methods of the classical moments theory. 17 refs. (author)
Exploring Gender Biases in a General Methods Class.
Quinn, Robert J.; Obenchain, Kathryn M.
1999-01-01
Describes how students in a general secondary methods course responded to a gender-neutral exam question by consistently assuming that the student in the hypothetical scenario was male. Describes the follow-up class discussion, noting students' assumptions, defensive responses, subconscious decision making, and awareness/nonawareness of their own…
Recursive form of general limited memory variable metric methods
Czech Academy of Sciences Publication Activity Database
Lukšan, Ladislav; Vlček, Jan
2013-01-01
Roč. 49, č. 2 (2013), s. 224-235 ISSN 0023-5954 Institutional support: RVO:67985807 Keywords : unconstrained optimization * large scale optimization * limited memory methods * variable metric updates * recursive matrix formulation * algorithms Subject RIV: BA - General Mathematics Impact factor: 0.563, year: 2013 http://dml.cz/handle/10338.dmlcz/143365
Heavy meson mass spectra by general relativistic methods
International Nuclear Information System (INIS)
Italiano, A.; Lattuada, M.; Maccarrone, G.D.; Recami, E.; Riggi, F.; Vinciguerra, D.
1984-01-01
By applying the classical methods of general relativity to elementary particles one can get, in a natural way, the observed confinement of their constituents, avoiding any recourse to phenome-nological models such as bag model and allowing the deduction of the heavy meson (i.e. charmonium (J/psi) and bottomium (UPSILON)) mass spectra
A general method to coat colloidal particles with titiana
Demirors, A.F.; van Blaaderen, A.; Imhof, A.
2010-01-01
We describe a general one-pot method for coating colloidal particles with amorphous titania. Various colloidal particles such as silica particles, large silver colloids, gibbsite platelets, and polystyrene spheres were successfully coated with a titania shell. Although there are several ways of
General Anisotropy Identification of Paperboard with Virtual Fields Method
J.M. Considine; F. Pierron; K.T. Turner; D.W. Vahey
2014-01-01
This work extends previous efforts in plate bending of Virtual Fields Method (VFM) parameter identification to include a general 2-D anisotropicmaterial. Such an extension was needed for instances in which material principal directions are unknown or when specimen orientation is not aligned with material principal directions. A new fixture with a multiaxial force...
A hyperpower iterative method for computing the generalized Drazin ...
Indian Academy of Sciences (India)
A quadratically convergent Newton-type iterative scheme is proposed for approximating the generalized Drazin inverse bd of the Banach algebra element b. Further, its extension into the form of the hyperpower iterative method of arbitrary order p ≤ 2 is presented. Convergence criteria along with the estimation of error ...
Directory of Open Access Journals (Sweden)
X. Zhao
2012-01-01
Full Text Available A combined interior point homotopy continuation method is proposed for solving general multiobjective programming problem. We prove the existence and convergence of a smooth homotopy path from almost any interior initial interior point to a solution of the KKT system under some basic assumptions.
Madigan, Michael L; Aviles, Jessica; Allin, Leigh J; Nussbaum, Maury A; Alexander, Neil B
2018-04-16
A growing number of studies are using modified treadmills to train reactive balance after trip-like perturbations that require multiple steps to recover balance. The goal of this study was thus to develop and validate a low-tech reactive balance rating method in the context of trip-like treadmill perturbations to facilitate the implementation of this training outside the research setting. Thirty-five residents of five senior congregate housing facilities participated in the study. Subjects completed a series of reactive balance tests on a modified treadmill from which the reactive balance rating was determined, along with a battery of standard clinical balance and mobility tests that predict fall risk. We investigated the strength of correlation between the reactive balance rating and reactive balance kinematics. We compared the strength of correlation between the reactive balance rating and clinical tests predictive of fall risk, with the strength of correlation between reactive balance kinematics and the same clinical tests. We also compared the reactive balance rating between subjects predicted to be at a high or low risk of falling. The reactive balance rating was correlated with reactive balance kinematics (Spearman's rho squared = .04 - .30), exhibited stronger correlations with clinical tests than most kinematic measures (Spearman's rho squared = .00 - .23), and was 42-60% lower among subjects predicted to be at a high risk for falling. The reactive balance rating method may provide a low-tech, valid measure of reactive balance kinematics, and an indicator of fall risk, after trip-like postural perturbations.
Institute of Scientific and Technical Information of China (English)
朱卫平; 黄黔
2002-01-01
In order to analyze bellows effectively and practically, the finite-element-displacement-perturbation method (FEDPM) is proposed for the geometric nonlinearbehaviors of shells of revolution subjected to pure bending moments or lateral forces in one of their meridional planes. The formulations are mainly based upon the idea of perturba-tion that the nodal displacement vector and the nodal force vector of each finite elementare expanded by taking root-mean-square value of circumferential strains of the shells as aperturbation parameter. The load steps and the iteration times are not cs arbitrary andunpredictable as in usual nonlinear analysis. Instead, there are certain relations betweenthe load steps and the displacement increments, and no need of iteration for each loadstep. Besides, in the formulations, the shell is idealized into a series of conical frusta for the convenience of practice, Sander' s nonlinear geometric equations of moderate smallrotation are used, and the shell made of more than one material ply is also considered.
Generalized Pseudospectral Method and Zeros of Orthogonal Polynomials
Directory of Open Access Journals (Sweden)
Oksana Bihun
2018-01-01
Full Text Available Via a generalization of the pseudospectral method for numerical solution of differential equations, a family of nonlinear algebraic identities satisfied by the zeros of a wide class of orthogonal polynomials is derived. The generalization is based on a modification of pseudospectral matrix representations of linear differential operators proposed in the paper, which allows these representations to depend on two, rather than one, sets of interpolation nodes. The identities hold for every polynomial family pνxν=0∞ orthogonal with respect to a measure supported on the real line that satisfies some standard assumptions, as long as the polynomials in the family satisfy differential equations Apν(x=qν(xpν(x, where A is a linear differential operator and each qν(x is a polynomial of degree at most n0∈N; n0 does not depend on ν. The proposed identities generalize known identities for classical and Krall orthogonal polynomials, to the case of the nonclassical orthogonal polynomials that belong to the class described above. The generalized pseudospectral representations of the differential operator A for the case of the Sonin-Markov orthogonal polynomials, also known as generalized Hermite polynomials, are presented. The general result is illustrated by new algebraic relations satisfied by the zeros of the Sonin-Markov polynomials.
Bortz, John; Shatz, Narkis
2011-04-01
The recently developed generalized functional method provides a means of designing nonimaging concentrators and luminaires for use with extended sources and receivers. We explore the mathematical relationships between optical designs produced using the generalized functional method and edge-ray, aplanatic, and simultaneous multiple surface (SMS) designs. Edge-ray and dual-surface aplanatic designs are shown to be special cases of generalized functional designs. In addition, it is shown that dual-surface SMS designs are closely related to generalized functional designs and that certain computational advantages accrue when the two design methods are combined. A number of examples are provided. © 2011 Optical Society of America
Geometric perturbation theory and plasma physics
International Nuclear Information System (INIS)
Omohundro, S.M.
1985-01-01
Modern differential geometric techniques are used to unify the physical asymptotics underlying mechanics, wave theory, and statistical mechanics. The approach gives new insights into the structure of physical theories and is suited to the needs of modern large-scale computer simulation and symbol manipulation systems. A coordinate-free formulation of non-singular perturbation theory is given, from which a new Hamiltonian perturbation structure is derived and related to the unperturbed structure in five different ways. The theory of perturbations in the presence of symmetry is developed, and the method of averaging is related to reduction by a circle-group action. The pseudo-forces and magnetic Poisson bracket terms due to reduction are given a natural asymptotic interpretation. Similar terms due to changing reference frames are related to the method of variation of parameters, which is also given a Hamiltonian formulation. These methods are used to answer a long-standing question posed by Kruskal about nearly periodic systems. The answer leads to a new secular perturbation theory that contains no adhoc elements, which is then applied to gyromotion. Eikonal wave theory is given a Hamiltonian formulation that generalizes Whitham's Lagrangian approach. The evolution of wave action density on ray phase space is given a Hamiltonian structure using a Lie-Poisson bracket. The relationship between dissipative and Hamiltonian systems is discussed. A theory motivated by free electron lasers gives new restrictions on the change of area of projected parallelepipeds under canonical transformations
Balaji, Nidish Narayanaa; Krishna, I. R. Praveen; Padmanabhan, C.
2018-05-01
The Harmonic Balance Method (HBM) is a frequency-domain based approximation approach used for obtaining the steady state periodic behavior of forced dynamical systems. Intrinsically these systems are non-autonomous and the method offers many computational advantages over time-domain methods when the fundamental period of oscillation is known (generally fixed as the forcing period itself or a corresponding sub-harmonic if such behavior is expected). In the current study, a modified approach, based on He's Energy Balance Method (EBM), is applied to obtain the periodic solutions of conservative systems. It is shown that by this approach, periodic solutions of conservative systems on iso-energy manifolds in the phase space can be obtained very efficiently. The energy level provides the additional constraint on the HBM formulation, which enables the determination of the period of the solutions. The method is applied to the linear harmonic oscillator, a couple of nonlinear oscillators, the elastic pendulum and the Henon-Heiles system. The approach is used to trace the bifurcations of the periodic solutions of the last two, being 2 degree-of-freedom systems demonstrating very rich dynamical behavior. In the process, the advantages offered by the current formulation of the energy balance is brought out. A harmonic perturbation approach is used to evaluate the stability of the solutions for the bifurcation diagram.
Random 2D Composites and the Generalized Method of Schwarz
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Vladimir Mityushev
2015-01-01
Full Text Available Two-phase composites with nonoverlapping inclusions randomly embedded in matrix are investigated. A straightforward approach is applied to estimate the effective properties of random 2D composites. First, deterministic boundary value problems are solved for all locations of inclusions, that is, for all events of the considered probabilistic space C by the generalized method of Schwarz. Second, the effective properties are calculated in analytical form and averaged over C. This method is related to the traditional method based on the average probabilistic values involving the n-point correlation functions. However, we avoid computation of the correlation functions and compute their weighted moments of high orders by an indirect method which does not address the correlation functions. The effective properties are exactly expressed through these moments. It is proved that the generalized method of Schwarz converges for an arbitrary multiply connected doubly periodic domain and for an arbitrary contrast parameter. The proposed method yields an algorithm which can be applied with symbolic computations. The Torquato-Milton parameter ζ1 is exactly written for circular inclusions.
Energy Technology Data Exchange (ETDEWEB)
Rossi, Lubianka Ferrari Russo
2014-07-01
The main target of this study is to introduce a new method for calculating the coefficients of sensibility through the union of differential method and generalized perturbation theory, which are the two methods generally used in reactor physics to obtain such variables. These two methods, separated, have some issues turning the sensibility coefficients calculation slower or computationally exhaustive. However, putting them together, it is possible to repair these issues and build a new equation for the coefficient of sensibility. The method introduced in this study was applied in a PWR reactor, where it was performed the sensibility analysis for the production and {sup 239}Pu conversion rate during 120 days (1 cycle) of burnup. The computational code used for both burnup and sensibility analysis, the CINEW, was developed in this study and all the results were compared with codes widely used in reactor physics, such as CINDER and SERPENT. The new mathematical method for calculating the sensibility coefficients and the code CINEW provide good numerical agility and also good efficiency and security, once the new method, when compared with traditional ones, provide satisfactory results, even when the other methods use different mathematical approaches. The burnup analysis, performed using the code CINEW, was compared with the code CINDER, showing an acceptable variation, though CINDER presents some computational issues due to the period it was built. The originality of this study is the application of such method in problems involving temporal dependence and, not least, the elaboration of the first national code for burnup and sensitivity analysis. (author)
International Nuclear Information System (INIS)
Suslov, I.M.
2005-01-01
Various perturbation series are factorially divergent. The behavior of their high-order terms can be determined by Lipatov's method, which involves the use of instanton configurations of appropriate functional integrals. When the Lipatov asymptotic form is known and several lowest order terms of the perturbation series are found by direct calculation of diagrams, one can gain insight into the behavior of the remaining terms of the series, which can be resummed to solve various strong-coupling problems in a certain approximation. This approach is demonstrated by determining the Gell-Mann-Low functions in φ 4 theory, QED, and QCD with arbitrary coupling constants. An overview of the mathematical theory of divergent series is presented, and interpretation of perturbation series is discussed. Explicit derivations of the Lipatov asymptotic form are presented for some basic problems in theoretical physics. A solution is proposed to the problem of renormalon contributions, which hampered progress in this field in the late 1970s. Practical perturbation-series summation schemes are described both for a coupling constant of order unity and in the strong-coupling limit. An interpretation of the Borel integral is given for 'non-Borel-summable' series. Higher order corrections to the Lipatov asymptotic form are discussed
Automated general temperature correction method for dielectric soil moisture sensors
Kapilaratne, R. G. C. Jeewantinie; Lu, Minjiao
2017-08-01
An effective temperature correction method for dielectric sensors is important to ensure the accuracy of soil water content (SWC) measurements of local to regional-scale soil moisture monitoring networks. These networks are extensively using highly temperature sensitive dielectric sensors due to their low cost, ease of use and less power consumption. Yet there is no general temperature correction method for dielectric sensors, instead sensor or site dependent correction algorithms are employed. Such methods become ineffective at soil moisture monitoring networks with different sensor setups and those that cover diverse climatic conditions and soil types. This study attempted to develop a general temperature correction method for dielectric sensors which can be commonly used regardless of the differences in sensor type, climatic conditions and soil type without rainfall data. In this work an automated general temperature correction method was developed by adopting previously developed temperature correction algorithms using time domain reflectometry (TDR) measurements to ThetaProbe ML2X, Stevens Hydra probe II and Decagon Devices EC-TM sensor measurements. The rainy day effects removal procedure from SWC data was automated by incorporating a statistical inference technique with temperature correction algorithms. The temperature correction method was evaluated using 34 stations from the International Soil Moisture Monitoring Network and another nine stations from a local soil moisture monitoring network in Mongolia. Soil moisture monitoring networks used in this study cover four major climates and six major soil types. Results indicated that the automated temperature correction algorithms developed in this study can eliminate temperature effects from dielectric sensor measurements successfully even without on-site rainfall data. Furthermore, it has been found that actual daily average of SWC has been changed due to temperature effects of dielectric sensors with a
Instabilities in mimetic matter perturbations
Energy Technology Data Exchange (ETDEWEB)
Firouzjahi, Hassan; Gorji, Mohammad Ali [School of Astronomy, Institute for Research in Fundamental Sciences (IPM), P.O. Box 19395-5531, Tehran (Iran, Islamic Republic of); Mansoori, Seyed Ali Hosseini, E-mail: firouz@ipm.ir, E-mail: gorji@ipm.ir, E-mail: shosseini@shahroodut.ac.ir, E-mail: shossein@ipm.ir [Physics Department, Shahrood University of Technology, P.O. Box 3619995161 Shahrood (Iran, Islamic Republic of)
2017-07-01
We study cosmological perturbations in mimetic matter scenario with a general higher derivative function. We calculate the quadratic action and show that both the kinetic term and the gradient term have the wrong sings. We perform the analysis in both comoving and Newtonian gauges and confirm that the Hamiltonians and the associated instabilities are consistent with each other in both gauges. The existence of instabilities is independent of the specific form of higher derivative function which generates gradients for mimetic field perturbations. It is verified that the ghost instability in mimetic perturbations is not associated with the higher derivative instabilities such as the Ostrogradsky ghost.
A general first-order global sensitivity analysis method
International Nuclear Information System (INIS)
Xu Chonggang; Gertner, George Zdzislaw
2008-01-01
Fourier amplitude sensitivity test (FAST) is one of the most popular global sensitivity analysis techniques. The main mechanism of FAST is to assign each parameter with a characteristic frequency through a search function. Then, for a specific parameter, the variance contribution can be singled out of the model output by the characteristic frequency. Although FAST has been widely applied, there are two limitations: (1) the aliasing effect among parameters by using integer characteristic frequencies and (2) the suitability for only models with independent parameters. In this paper, we synthesize the improvement to overcome the aliasing effect limitation [Tarantola S, Gatelli D, Mara TA. Random balance designs for the estimation of first order global sensitivity indices. Reliab Eng Syst Safety 2006; 91(6):717-27] and the improvement to overcome the independence limitation [Xu C, Gertner G. Extending a global sensitivity analysis technique to models with correlated parameters. Comput Stat Data Anal 2007, accepted for publication]. In this way, FAST can be a general first-order global sensitivity analysis method for linear/nonlinear models with as many correlated/uncorrelated parameters as the user specifies. We apply the general FAST to four test cases with correlated parameters. The results show that the sensitivity indices derived by the general FAST are in good agreement with the sensitivity indices derived by the correlation ratio method, which is a non-parametric method for models with correlated parameters
A perturbed martingale approach to global optimization
Energy Technology Data Exchange (ETDEWEB)
Sarkar, Saikat [Computational Mechanics Lab, Department of Civil Engineering, Indian Institute of Science, Bangalore 560012 (India); Roy, Debasish, E-mail: royd@civil.iisc.ernet.in [Computational Mechanics Lab, Department of Civil Engineering, Indian Institute of Science, Bangalore 560012 (India); Vasu, Ram Mohan [Department of Instrumentation and Applied Physics, Indian Institute of Science, Bangalore 560012 (India)
2014-08-01
A new global stochastic search, guided mainly through derivative-free directional information computable from the sample statistical moments of the design variables within a Monte Carlo setup, is proposed. The search is aided by imparting to the directional update term additional layers of random perturbations referred to as ‘coalescence’ and ‘scrambling’. A selection step, constituting yet another avenue for random perturbation, completes the global search. The direction-driven nature of the search is manifest in the local extremization and coalescence components, which are posed as martingale problems that yield gain-like update terms upon discretization. As anticipated and numerically demonstrated, to a limited extent, against the problem of parameter recovery given the chaotic response histories of a couple of nonlinear oscillators, the proposed method appears to offer a more rational, more accurate and faster alternative to most available evolutionary schemes, prominently the particle swarm optimization. - Highlights: • Evolutionary global optimization is posed as a perturbed martingale problem. • Resulting search via additive updates is a generalization over Gateaux derivatives. • Additional layers of random perturbation help avoid trapping at local extrema. • The approach ensures efficient design space exploration and high accuracy. • The method is numerically assessed via parameter recovery of chaotic oscillators.
Generalized hybrid Monte Carlo - CMFD methods for fission source convergence
International Nuclear Information System (INIS)
Wolters, Emily R.; Larsen, Edward W.; Martin, William R.
2011-01-01
In this paper, we generalize the recently published 'CMFD-Accelerated Monte Carlo' method and present two new methods that reduce the statistical error in CMFD-Accelerated Monte Carlo. The CMFD-Accelerated Monte Carlo method uses Monte Carlo to estimate nonlinear functionals used in low-order CMFD equations for the eigenfunction and eigenvalue. The Monte Carlo fission source is then modified to match the resulting CMFD fission source in a 'feedback' procedure. The two proposed methods differ from CMFD-Accelerated Monte Carlo in the definition of the required nonlinear functionals, but they have identical CMFD equations. The proposed methods are compared with CMFD-Accelerated Monte Carlo on a high dominance ratio test problem. All hybrid methods converge the Monte Carlo fission source almost immediately, leading to a large reduction in the number of inactive cycles required. The proposed methods stabilize the fission source more efficiently than CMFD-Accelerated Monte Carlo, leading to a reduction in the number of active cycles required. Finally, as in CMFD-Accelerated Monte Carlo, the apparent variance of the eigenfunction is approximately equal to the real variance, so the real error is well-estimated from a single calculation. This is an advantage over standard Monte Carlo, in which the real error can be underestimated due to inter-cycle correlation. (author)
International Nuclear Information System (INIS)
Kemshell, P.B.; Wright, W.V.; Sanders, L.G.
1984-01-01
DUCKPOND, the sensitivity option of the Monte Carlo code McBEND, is being used to study the effect of environmental perturbations on the response of a dual detector neutron porosity logging tool. Using a detailed model of an actual tool, calculations have been performed for a 19% porosity limestone rock sample in the API Test Pit. Within a single computer run, the tool response, or near-to-far detector count ratio, and the sensitivity of this response to the concentration of each isotope present in the formation have been estimated. The calculated tool response underestimates the measured value by about 10%, which is equal to 1.5 ''standard errors'', but this apparent discrepancy is shown to be within the spread of calculated values arising from uncertainties on the rock composition
Directory of Open Access Journals (Sweden)
Domingues M. O.
2013-12-01
Full Text Available We present a new adaptive multiresoltion method for the numerical simulation of ideal magnetohydrodynamics. The governing equations, i.e., the compressible Euler equations coupled with the Maxwell equations are discretized using a finite volume scheme on a two-dimensional Cartesian mesh. Adaptivity in space is obtained via Harten’s cell average multiresolution analysis, which allows the reliable introduction of a locally refined mesh while controlling the error. The explicit time discretization uses a compact Runge–Kutta method for local time stepping and an embedded Runge-Kutta scheme for automatic time step control. An extended generalized Lagrangian multiplier approach with the mixed hyperbolic-parabolic correction type is used to control the incompressibility of the magnetic field. Applications to a two-dimensional problem illustrate the properties of the method. Memory savings and numerical divergences of magnetic field are reported and the accuracy of the adaptive computations is assessed by comparing with the available exact solution.
Generalized multiscale finite element methods. nonlinear elliptic equations
Efendiev, Yalchin R.; Galvis, Juan; Li, Guanglian; Presho, Michael
2013-01-01
In this paper we use the Generalized Multiscale Finite Element Method (GMsFEM) framework, introduced in [26], in order to solve nonlinear elliptic equations with high-contrast coefficients. The proposed solution method involves linearizing the equation so that coarse-grid quantities of previous solution iterates can be regarded as auxiliary parameters within the problem formulation. With this convention, we systematically construct respective coarse solution spaces that lend themselves to either continuous Galerkin (CG) or discontinuous Galerkin (DG) global formulations. Here, we use Symmetric Interior Penalty Discontinuous Galerkin approach. Both methods yield a predictable error decline that depends on the respective coarse space dimension, and we illustrate the effectiveness of the CG and DG formulations by offering a variety of numerical examples. © 2014 Global-Science Press.
Methods of checking general safety criteria in UML statechart specifications
International Nuclear Information System (INIS)
Pap, Zsigmond; Majzik, Istvan; Pataricza, Andras; Szegi, Andras
2005-01-01
This paper describes methods and tools for safety analysis of UML statechart specifications. A comprehensive set of general safety criteria including completeness and consistency is applied in automated analysis. Analysis techniques are based on OCL expressions, graph transformations and reachability analysis. Two canonical intermediate representations of the statechart specification are introduced. They are suitable for straightforward implementation of checker methods and for the support of the proof of the correctness and soundness of the applied analysis. One of them also serves as a basis of the metamodel of a variant of UML statecharts proposed for the specification of safety-critical control systems. The analysis is extended to object-oriented specifications. Examples illustrate the application of the checker methods implemented by an automated tool-set
Some Convergence Strategies for the Alternating Generalized Projection Method
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Maricarmen Andrade
2013-11-01
Full Text Available In this paper we extend the application of the alternating projection algorithm to solve the problem of finding a point in the intersection of $n$ sets ($n\\geq2$, which are not all of them convex sets. Here we term such method as alternating generalized projection (AGP method. In particular, we are interested in addressing the problem of avoiding the so-called trap points, which may prevent an algorithm to obtain a feasible solution in two or more sets not all convex. Some strategies that allow us to reach the feasible solution are established and conjectured. Finally, we present simple numerical results that illustrate the efficiency of the iterative methods considered.
Cross section recondensation method via generalized energy condensation theory
International Nuclear Information System (INIS)
Douglass, Steven; Rahnema, Farzad
2011-01-01
Highlights: → A new method is presented which corrects for core environment error from specular boundaries at the lattice cell level. → Solution obtained with generalized energy condensation provides improved approximation to the core level fine-group flux. → Iterative recondensation of the cross sections and unfolding of the flux provides on-the-fly updating of the core cross sections. → Precomputation of energy integrals and fine-group cross sections allows for easy implementation and efficient solution. → Method has been implemented in 1D and shown to correct the environment error, particularly in strongly heterogeneous cores. - Abstract: The standard multigroup method used in whole-core reactor analysis relies on energy condensed (coarse-group) cross sections generated from single lattice cell calculations, typically with specular reflective boundary conditions. Because these boundary conditions are an approximation and not representative of the core environment for that lattice, an error is introduced in the core solution (both eigenvalue and flux). As current and next generation reactors trend toward increasing assembly and core heterogeneity, this error becomes more significant. The method presented here corrects for this error by generating updated coarse-group cross sections on-the-fly within whole-core reactor calculations without resorting to additional cell calculations. In this paper, the fine-group core flux is unfolded by making use of the recently published Generalized Condensation Theory and the cross sections are recondensed at the whole-core level. By iteratively performing this recondensation, an improved core solution is found in which the core-environment has been fully taken into account. This recondensation method is both easy to implement and computationally very efficient because it requires precomputation and storage of only the energy integrals and fine-group cross sections. In this work, the theoretical basis and development
Nonequilibrium Statistical Operator Method and Generalized Kinetic Equations
Kuzemsky, A. L.
2018-01-01
We consider some principal problems of nonequilibrium statistical thermodynamics in the framework of the Zubarev nonequilibrium statistical operator approach. We present a brief comparative analysis of some approaches to describing irreversible processes based on the concept of nonequilibrium Gibbs ensembles and their applicability to describing nonequilibrium processes. We discuss the derivation of generalized kinetic equations for a system in a heat bath. We obtain and analyze a damped Schrödinger-type equation for a dynamical system in a heat bath. We study the dynamical behavior of a particle in a medium taking the dissipation effects into account. We consider the scattering problem for neutrons in a nonequilibrium medium and derive a generalized Van Hove formula. We show that the nonequilibrium statistical operator method is an effective, convenient tool for describing irreversible processes in condensed matter.
Soil-structure interaction - a general method to calculate soil impedance
International Nuclear Information System (INIS)
Farvacque, M.; Gantenbein, F.
1983-01-01
A correct analysis of the seismic response of nuclear power plant buildings needs to take into account the soil structure interaction. The most classical and simple method consists in characterizing the soil by a stiffness and a damping function for each component of the translation and rotation of the foundation. In a more exact way an impedance function of the frequency may be introduced. Literature provides data to estimate these coefficients for simple soil and foundation configurations and using linear hypothesis. This paper presents a general method to calculate soil impedances which is based on the computation of the impulsive response of the soil using an axisymmetric 2D finite element Code (INCA). The Fourier transform of this response is made in the time interval before the return of the reflected waves on the boundaries of the F.E. domain. This procedure which limits the perturbing effects of the reflections is improved by introducing absorbing boundary elements. A parametric study for homogeneous and layered soils has been carried out using this method. (orig.)
Song, Yun S; Steinrücken, Matthias
2012-03-01
The transition density function of the Wright-Fisher diffusion describes the evolution of population-wide allele frequencies over time. This function has important practical applications in population genetics, but finding an explicit formula under a general diploid selection model has remained a difficult open problem. In this article, we develop a new computational method to tackle this classic problem. Specifically, our method explicitly finds the eigenvalues and eigenfunctions of the diffusion generator associated with the Wright-Fisher diffusion with recurrent mutation and arbitrary diploid selection, thus allowing one to obtain an accurate spectral representation of the transition density function. Simplicity is one of the appealing features of our approach. Although our derivation involves somewhat advanced mathematical concepts, the resulting algorithm is quite simple and efficient, only involving standard linear algebra. Furthermore, unlike previous approaches based on perturbation, which is applicable only when the population-scaled selection coefficient is small, our method is nonperturbative and is valid for a broad range of parameter values. As a by-product of our work, we obtain the rate of convergence to the stationary distribution under mutation-selection balance.
Directory of Open Access Journals (Sweden)
I-Chung Liu
2012-01-01
Full Text Available We have analyzed the effects of variable heat flux and internal heat generation on the flow and heat transfer in a thin film on a horizontal sheet in the presence of thermal radiation. Similarity transformations are used to transform the governing equations to a set of coupled nonlinear ordinary differential equations. The obtained differential equations are solved approximately by the homotopy perturbation method (HPM. The effects of various parameters governing the flow and heat transfer in this study are discussed and presented graphically. Comparison of numerical results is made with the earlier published results under limiting cases.
Disformal transformation of cosmological perturbations
Directory of Open Access Journals (Sweden)
Masato Minamitsuji
2014-10-01
Full Text Available We investigate the gauge-invariant cosmological perturbations in the gravity and matter frames in the general scalar–tensor theory where two frames are related by the disformal transformation. The gravity and matter frames are the extensions of the Einstein and Jordan frames in the scalar–tensor theory where two frames are related by the conformal transformation, respectively. First, it is shown that the curvature perturbation in the comoving gauge to the scalar field is disformally invariant as well as conformally invariant, which gives the predictions from the cosmological model where the scalar field is responsible both for inflation and cosmological perturbations. Second, in case that the disformally coupled matter sector also contributes to curvature perturbations, we derive the evolution equations of the curvature perturbation in the uniform matter energy density gauge from the energy (nonconservation in the matter sector, which are independent of the choice of the gravity sector. While in the matter frame the curvature perturbation in the uniform matter energy density gauge is conserved on superhorizon scales for the vanishing nonadiabatic pressure, in the gravity frame it is not conserved even if the nonadiabatic pressure vanishes. The formula relating two frames gives the amplitude of the curvature perturbation in the matter frame, once it is evaluated in the gravity frame.
Disformal transformation of cosmological perturbations
International Nuclear Information System (INIS)
Minamitsuji, Masato
2014-01-01
We investigate the gauge-invariant cosmological perturbations in the gravity and matter frames in the general scalar–tensor theory where two frames are related by the disformal transformation. The gravity and matter frames are the extensions of the Einstein and Jordan frames in the scalar–tensor theory where two frames are related by the conformal transformation, respectively. First, it is shown that the curvature perturbation in the comoving gauge to the scalar field is disformally invariant as well as conformally invariant, which gives the predictions from the cosmological model where the scalar field is responsible both for inflation and cosmological perturbations. Second, in case that the disformally coupled matter sector also contributes to curvature perturbations, we derive the evolution equations of the curvature perturbation in the uniform matter energy density gauge from the energy (non)conservation in the matter sector, which are independent of the choice of the gravity sector. While in the matter frame the curvature perturbation in the uniform matter energy density gauge is conserved on superhorizon scales for the vanishing nonadiabatic pressure, in the gravity frame it is not conserved even if the nonadiabatic pressure vanishes. The formula relating two frames gives the amplitude of the curvature perturbation in the matter frame, once it is evaluated in the gravity frame
Koopmans' theorem in the Hartree-Fock method. General formulation
Plakhutin, Boris N.
2018-03-01
This work presents a general formulation of Koopmans' theorem (KT) in the Hartree-Fock (HF) method which is applicable to molecular and atomic systems with arbitrary orbital occupancies and total electronic spin including orbitally degenerate (OD) systems. The new formulation is based on the full set of variational conditions imposed upon the HF orbitals by the variational principle for the total energy and the conditions imposed by KT on the orbitals of an ionized electronic shell [B. N. Plakhutin and E. R. Davidson, J. Chem. Phys. 140, 014102 (2014)]. Based on these conditions, a general form of the restricted open-shell HF method is developed, whose eigenvalues (orbital energies) obey KT for the whole energy spectrum. Particular attention is paid to the treatment of OD systems, for which the new method gives a number of unexpected results. For example, the present method gives four different orbital energies for the triply degenerate atomic level 2p in the second row atoms B to F. Based on both KT conditions and a parallel treatment of atoms B to F within a limited configuration interaction approach, we prove that these four orbital energies, each of which is triply degenerate, are related via KT to the energies of different spin-dependent ionization and electron attachment processes (2p)N → (2p ) N ±1. A discussion is also presented of specific limitations of the validity of KT in the HF method which arise in OD systems. The practical applicability of the theory is verified by comparing KT estimates of the ionization potentials I2s and I2p for the second row open-shell atoms Li to F with the relevant experimental data.
Generalized multiscale finite element methods (GMsFEM)
Efendiev, Yalchin R.; Galvis, Juan; Hou, Thomasyizhao
2013-01-01
In this paper, we propose a general approach called Generalized Multiscale Finite Element Method (GMsFEM) for performing multiscale simulations for problems without scale separation over a complex input space. As in multiscale finite element methods (MsFEMs), the main idea of the proposed approach is to construct a small dimensional local solution space that can be used to generate an efficient and accurate approximation to the multiscale solution with a potentially high dimensional input parameter space. In the proposed approach, we present a general procedure to construct the offline space that is used for a systematic enrichment of the coarse solution space in the online stage. The enrichment in the online stage is performed based on a spectral decomposition of the offline space. In the online stage, for any input parameter, a multiscale space is constructed to solve the global problem on a coarse grid. The online space is constructed via a spectral decomposition of the offline space and by choosing the eigenvectors corresponding to the largest eigenvalues. The computational saving is due to the fact that the construction of the online multiscale space for any input parameter is fast and this space can be re-used for solving the forward problem with any forcing and boundary condition. Compared with the other approaches where global snapshots are used, the local approach that we present in this paper allows us to eliminate unnecessary degrees of freedom on a coarse-grid level. We present various examples in the paper and some numerical results to demonstrate the effectiveness of our method. © 2013 Elsevier Inc.
Generalized multiscale finite element methods (GMsFEM)
Efendiev, Yalchin R.
2013-10-01
In this paper, we propose a general approach called Generalized Multiscale Finite Element Method (GMsFEM) for performing multiscale simulations for problems without scale separation over a complex input space. As in multiscale finite element methods (MsFEMs), the main idea of the proposed approach is to construct a small dimensional local solution space that can be used to generate an efficient and accurate approximation to the multiscale solution with a potentially high dimensional input parameter space. In the proposed approach, we present a general procedure to construct the offline space that is used for a systematic enrichment of the coarse solution space in the online stage. The enrichment in the online stage is performed based on a spectral decomposition of the offline space. In the online stage, for any input parameter, a multiscale space is constructed to solve the global problem on a coarse grid. The online space is constructed via a spectral decomposition of the offline space and by choosing the eigenvectors corresponding to the largest eigenvalues. The computational saving is due to the fact that the construction of the online multiscale space for any input parameter is fast and this space can be re-used for solving the forward problem with any forcing and boundary condition. Compared with the other approaches where global snapshots are used, the local approach that we present in this paper allows us to eliminate unnecessary degrees of freedom on a coarse-grid level. We present various examples in the paper and some numerical results to demonstrate the effectiveness of our method. © 2013 Elsevier Inc.
Geometric Hamiltonian structures and perturbation theory
International Nuclear Information System (INIS)
Omohundro, S.
1984-08-01
We have been engaged in a program of investigating the Hamiltonian structure of the various perturbation theories used in practice. We describe the geometry of a Hamiltonian structure for non-singular perturbation theory applied to Hamiltonian systems on symplectic manifolds and the connection with singular perturbation techniques based on the method of averaging
Guo, Yang; Becker, Ute; Neese, Frank
2018-03-01
Local correlation theories have been developed in two main flavors: (1) "direct" local correlation methods apply local approximation to the canonical equations and (2) fragment based methods reconstruct the correlation energy from a series of smaller calculations on subsystems. The present work serves two purposes. First, we investigate the relative efficiencies of the two approaches using the domain-based local pair natural orbital (DLPNO) approach as the "direct" method and the cluster in molecule (CIM) approach as the fragment based approach. Both approaches are applied in conjunction with second-order many-body perturbation theory (MP2) as well as coupled-cluster theory with single-, double- and perturbative triple excitations [CCSD(T)]. Second, we have investigated the possible merits of combining the two approaches by performing CIM calculations with DLPNO methods serving as the method of choice for performing the subsystem calculations. Our cluster-in-molecule approach is closely related to but slightly deviates from approaches in the literature since we have avoided real space cutoffs. Moreover, the neglected distant pair correlations in the previous CIM approach are considered approximately. Six very large molecules (503-2380 atoms) were studied. At both MP2 and CCSD(T) levels of theory, the CIM and DLPNO methods show similar efficiency. However, DLPNO methods are more accurate for 3-dimensional systems. While we have found only little incentive for the combination of CIM with DLPNO-MP2, the situation is different for CIM-DLPNO-CCSD(T). This combination is attractive because (1) the better parallelization opportunities offered by CIM; (2) the methodology is less memory intensive than the genuine DLPNO-CCSD(T) method and, hence, allows for large calculations on more modest hardware; and (3) the methodology is applicable and efficient in the frequently met cases, where the largest subsystem calculation is too large for the canonical CCSD(T) method.
Investigation on generalized Variational Nodal Methods for heterogeneous nodes
International Nuclear Information System (INIS)
Wang, Yongping; Wu, Hongchun; Li, Yunzhao; Cao, Liangzhi; Shen, Wei
2017-01-01
Highlights: • We developed two heterogeneous nodal methods based on the Variational Nodal Method. • Four problems were solved to evaluate the two heterogeneous nodal methods. • The function expansion method is good at treating continuous-changing heterogeneity. • The finite sub-element method is good at treating discontinuous-changing heterogeneity. - Abstract: The Variational Nodal Method (VNM) is generalized for heterogeneous nodes and applied to four kinds of problems including Molten Salt Reactor (MSR) core problem with continuous cross section profile, Pressurized Water Reactor (PWR) control rod cusping effect problem, PWR whole-core pin-by-pin problem, and heterogeneous PWR core problem without fuel-coolant homogenization in each pin cell. Two approaches have been investigated for the treatment of the nodal heterogeneity in this paper. To concentrate on spatial heterogeneity, diffusion approximation was adopted for the angular variable in neutron transport equation. To provide demonstrative numerical results, the codes in this paper were developed in slab geometry. The first method, named as function expansion (FE) method, expands nodal flux by orthogonal polynomials and the nodal cross sections are also expressed as spatial depended functions. The second path, named as finite sub-element (FS) method, takes advantage of the finite-element method by dividing each node into numbers of homogeneous sub-elements and expanding nodal flux into the combination of linear sub-element trial functions. Numerical tests have been carried out to evaluate the ability of the two nodal (coarse-mesh) heterogeneous VNMs by comparing with the fine-mesh homogeneous VNM. It has been demonstrated that both heterogeneous approaches can handle heterogeneous nodes. The FE method is good at continuous-changing heterogeneity as in the MSR core problem, while the FS method is good at discontinuous-changing heterogeneity such as the PWR pin-by-pin problem and heterogeneous PWR core
Higher order perturbation theory - An example for discussion
International Nuclear Information System (INIS)
Lewins, J.D.; Parks, G.; Babb, A.L.
1986-01-01
Higher order perturbation theory is developed in the form of a Taylor series expansion to third order to calculate the thermal utilization of a nonuniform cell. The development takes advantage of the self-adjoint property of the diffusion operator to provide a simple development of this illustration of generalized perturbation theory employing scalar perturbation parameters. The results show how a designer might employ a second-order theory to quantify proposed design improvements, together with the limitations of second- and third-order theory. The chosen example has an exact optimization solution and thus provides a clear understanding of the role of perturbation theory at its various orders. Convergence and the computational advantages and disadvantages of the method are discussed
On the systematic construction of convergent perturbation series
International Nuclear Information System (INIS)
Schmidt, C.
1993-12-01
Starting from the general decomposition of the many-body Hamiltonian parametrized by an operator Λwe derive the class of 'Λ-transformed' perturbation series. Aiming at practical applications we consider many-body perturbation theory of atoms and molecules in finite dimensional Hilbert spaces. Investigation of the analyticity properties of the eigenvalues and eigenstates of the Hamiltonian as functions of the coupling parameter defined by the particular decomposition of H allows for the construction of (minimal) Λoperators mapping an originally divergent series to a convergent one. There exists an operator Λ opt leading to the exact results in first order. Further improvements of the above mentioned minimal Λoperators can be achieved by approximations of Λ opt leading to fast convergent perturbation series. As the size of the remaining perturbation is given by the Λoperator chosen this method provides an a priori estimate of the convergence properties. (orig.)
Dhage Iteration Method for Generalized Quadratic Functional Integral Equations
Directory of Open Access Journals (Sweden)
Bapurao C. Dhage
2015-01-01
Full Text Available In this paper we prove the existence as well as approximations of the solutions for a certain nonlinear generalized quadratic functional integral equation. An algorithm for the solutions is developed and it is shown that the sequence of successive approximations starting at a lower or upper solution converges monotonically to the solutions of related quadratic functional integral equation under some suitable mixed hybrid conditions. We rely our main result on Dhage iteration method embodied in a recent hybrid fixed point theorem of Dhage (2014 in partially ordered normed linear spaces. An example is also provided to illustrate the abstract theory developed in the paper.
Studying the perturbative Reggeon
International Nuclear Information System (INIS)
Griffiths, S.; Ross, D.A.
2000-01-01
We consider the flavour non-singlet Reggeon within the context of perturbative QCD. This consists of ladders built out of ''reggeized'' quarks. We propose a method for the numerical solution of the integro-differential equation for the amplitude describing the exchange of such a Reggeon. The solution is known to have a sharp rise at low values of Bjorken-x when applied to non-singlet quantities in deep-inelastic scattering. We show that when the running of the coupling is taken into account this sharp rise is further enhanced, although the Q 2 dependence is suppressed by the introduction of the running coupling. We also investigate the effects of simulating non-perturbative physics by introducing a constituent mass for the soft quarks and an effective mass for the soft gluons exchanged in the t-channel. (orig.)
Robust fractional order differentiators using generalized modulating functions method
Liu, Dayan; Laleg-Kirati, Taous-Meriem
2015-01-01
This paper aims at designing a fractional order differentiator for a class of signals satisfying a linear differential equation with unknown parameters. A generalized modulating functions method is proposed first to estimate the unknown parameters, then to derive accurate integral formulae for the left-sided Riemann-Liouville fractional derivatives of the studied signal. Unlike the improper integral in the definition of the left-sided Riemann-Liouville fractional derivative, the integrals in the proposed formulae can be proper and be considered as a low-pass filter by choosing appropriate modulating functions. Hence, digital fractional order differentiators applicable for on-line applications are deduced using a numerical integration method in discrete noisy case. Moreover, some error analysis are given for noise error contributions due to a class of stochastic processes. Finally, numerical examples are given to show the accuracy and robustness of the proposed fractional order differentiators.
Integrating Multiple Teaching Methods into a General Chemistry Classroom
Francisco, Joseph S.; Nicoll, Gayle; Trautmann, Marcella
1998-02-01
In addition to the traditional lecture format, three other teaching strategies (class discussions, concept maps, and cooperative learning) were incorporated into a freshman level general chemistry course. Student perceptions of their involvement in each of the teaching methods, as well as their perceptions of the utility of each method were used to assess the effectiveness of the integration of the teaching strategies as received by the students. Results suggest that each strategy serves a unique purpose for the students and increased student involvement in the course. These results indicate that the multiple teaching strategies were well received by the students and that all teaching strategies are necessary for students to get the most out of the course.
A generalized trial solution method for solving the aerosol equation
International Nuclear Information System (INIS)
Simons, S.; Simpson, D.R.
1988-01-01
It is shown how the introduction of orthogonal functions together with a time-dependent scaling factor may be used to develop a generalized trial solution method for tackling the aerosol equation. The approach is worked out in detail for the case where the initial particle size spectrum follows a γ-distribution, and it is shown to be a viable technique as long as the initial volume fraction of particulate material is not too large. The method is applied to several situations of interest, and is shown to give more accurate results (with marginally shorter computing times) than are given by the three-parameter log-normal or γ distribution trial functions. (author)
Robust fractional order differentiators using generalized modulating functions method
Liu, Dayan
2015-02-01
This paper aims at designing a fractional order differentiator for a class of signals satisfying a linear differential equation with unknown parameters. A generalized modulating functions method is proposed first to estimate the unknown parameters, then to derive accurate integral formulae for the left-sided Riemann-Liouville fractional derivatives of the studied signal. Unlike the improper integral in the definition of the left-sided Riemann-Liouville fractional derivative, the integrals in the proposed formulae can be proper and be considered as a low-pass filter by choosing appropriate modulating functions. Hence, digital fractional order differentiators applicable for on-line applications are deduced using a numerical integration method in discrete noisy case. Moreover, some error analysis are given for noise error contributions due to a class of stochastic processes. Finally, numerical examples are given to show the accuracy and robustness of the proposed fractional order differentiators.
The spectral method and ergodic theorems for general Markov chains
International Nuclear Information System (INIS)
Nagaev, S V
2015-01-01
We study the ergodic properties of Markov chains with an arbitrary state space and prove a geometric ergodic theorem. The method of the proof is new: it may be described as an operator method. Our main result is an ergodic theorem for Harris-Markov chains in the case when the return time to some fixed set has finite expectation. Our conditions for the transition function are more general than those used by Athreya-Ney and Nummelin. Unlike them, we impose restrictions not on the original transition function but on the transition function of an embedded Markov chain constructed from the return times to the fixed set mentioned above. The proof uses the spectral theory of linear operators on a Banach space
General methods for alarm reduction; Larmsanering med generella metoder
Energy Technology Data Exchange (ETDEWEB)
Ahnlund, Jonas; Bergquist, Tord; Raaberg, Martin [Lund Univ. (Sweden). Dept. of Information Technology
2003-10-01
The information in the control rooms has increased due to the technological advances in process control. Large industries produce large data quantities, where some information is unnecessary or even incorrect. The operator needs support from an advanced and well-adjusted alarm system to be able to separate a real event from a minor disturbance. The alarms must be of assistance and not a nuisance. An enhanced alarm situation qualifies an increased efficiency with fewer production disturbances and an improved safety. Yet, it is still unusual that actions are taken to improve the situation. An alarm cleanup with general methods can shortly be described as taking advantage of the control systems built-in functions, the possibility to modify or create function blocks and fine-tune the settings in the alarm system. In this project, we make use of an intelligent software, Alarm Cleanup Toolbox, that simulate different signal processing methods and tries to find improved settings on all the signals in the process. This is a fast and cost-efficient way to improve the overall alarm situation, and lays a foundation for more advanced alarm systems. An alarm cleanup has been carried out at Flintraennan district heating plant in Malmoe, where various signal processing methods has been implemented in a parallel alarm system. This made it possible to compare the two systems under the same conditions. The result is very promising, and shows that a lot of improvements can be achieved with very little effort. An analysis of the alarm system at Vattenreningen (the water purification process) at Heleneholmsverket in Malmoe has been carried out. Alarm Cleanup Toolbox has, besides suggesting improved settings, also found logical errors in the alarm system. Here, no implementation was carried out and therefore the results are analytical, but they validate the efficiency of the general methods. The project has shown that an alarm cleanup with general methods is cost-efficient, and that the
Modularity and the spread of perturbations in complex dynamical systems.
Kolchinsky, Artemy; Gates, Alexander J; Rocha, Luis M
2015-12-01
We propose a method to decompose dynamical systems based on the idea that modules constrain the spread of perturbations. We find partitions of system variables that maximize "perturbation modularity," defined as the autocovariance of coarse-grained perturbed trajectories. The measure effectively separates the fast intramodular from the slow intermodular dynamics of perturbation spreading (in this respect, it is a generalization of the "Markov stability" method of network community detection). Our approach captures variation of modular organization across different system states, time scales, and in response to different kinds of perturbations: aspects of modularity which are all relevant to real-world dynamical systems. It offers a principled alternative to detecting communities in networks of statistical dependencies between system variables (e.g., "relevance networks" or "functional networks"). Using coupled logistic maps, we demonstrate that the method uncovers hierarchical modular organization planted in a system's coupling matrix. Additionally, in homogeneously coupled map lattices, it identifies the presence of self-organized modularity that depends on the initial state, dynamical parameters, and type of perturbations. Our approach offers a powerful tool for exploring the modular organization of complex dynamical systems.
Perturbation Theory of Embedded Eigenvalues
DEFF Research Database (Denmark)
Engelmann, Matthias
project gives a general and systematic approach to analytic perturbation theory of embedded eigenvalues. The spectral deformation technique originally developed in the theory of dilation analytic potentials in the context of Schrödinger operators is systematized by the use of Mourre theory. The group...... of dilations is thereby replaced by the unitary group generated y the conjugate operator. This then allows to treat the perturbation problem with the usual Kato theory.......We study problems connected to perturbation theory of embedded eigenvalues in two different setups. The first part deals with second order perturbation theory of mass shells in massive translation invariant Nelson type models. To this end an expansion of the eigenvalues w.r.t. fiber parameter up...
The theory of singular perturbations
De Jager, E M
1996-01-01
The subject of this textbook is the mathematical theory of singular perturbations, which despite its respectable history is still in a state of vigorous development. Singular perturbations of cumulative and of boundary layer type are presented. Attention has been given to composite expansions of solutions of initial and boundary value problems for ordinary and partial differential equations, linear as well as quasilinear; also turning points are discussed. The main emphasis lies on several methods of approximation for solutions of singularly perturbed differential equations and on the mathemat
International Nuclear Information System (INIS)
Saitovitch, H.
1979-01-01
This work is based on our quadrupolar interaction (QI) measurements on intercalated 2H-TaS sub(2) coumponds. As intercalating elements we used the alcalines - Li, Na, K, Cs -as well as the NH sub(3) (ammonia) and C sub(6) H sub(5) N (pyridine) molecules. The (QI) measurements were performed via the differential perturbed angular correlation (DPAC) technique, using Ta sup(181) as the probe isotope, on the hydrated and anhidrous phases of the intercalated systems. Our results happened to be in better agreement with the ionic model, one of the accepted models used to describe the intercalation process, as well as the transfered charges quantities and its distribution in the intercalated systems. And by its side the measured quantities, quadrupole interaction frequencies (QIF) and their distributions δ, contributed to support and to improve the ionic model. A strong charge dynamics between the 2H-TaS sub(2) sandwiches was observed and a relation between the (QIF) changes and amount of transfered charge (e sup(-)/Ta) was established. The attempt to specify the numerical contributions to the (QI) changes arriving from the different components of the 2H-TaS sub(2) intercalated systems put in evidence the probable orbitals involved in the systems bonds. Finally the kinetics of the intercalation process to form the 2H-TaS sub(2) (Li) sub(x) system was followed continuously by the (DPAC) measurements. (author)
Generalized Hartree-Fock method for electron-atom scattering
International Nuclear Information System (INIS)
Rosenberg, L.
1997-01-01
In the widely used Hartree-Fock procedure for atomic structure calculations, trial functions in the form of linear combinations of Slater determinants are constructed and the Rayleigh-Ritz minimum principle is applied to determine the best in that class. A generalization of this approach, applicable to low-energy electron-atom scattering, is developed here. The method is based on a unique decomposition of the scattering wave function into open- and closed-channel components, so chosen that an approximation to the closed-channel component may be obtained by adopting it as a trial function in a minimum principle, whose rigor can be maintained even when the target wave functions are imprecisely known. Given a closed-channel trial function, the full scattering function may be determined from the solution of an effective one-body Schroedinger equation. Alternatively, in a generalized Hartree-Fock approach, the minimum principle leads to coupled integrodifferential equations to be satisfied by the basis functions appearing in a Slater-determinant representation of the closed-channel wave function; it also provides a procedure for optimizing the choice of nonlinear parameters in a variational determination of these basis functions. Inclusion of additional Slater determinants in the closed-channel trial function allows for systematic improvement of that function, as well as the calculated scattering parameters, with the possibility of spurious singularities avoided. Electron-electron correlations can be important in accounting for long-range forces and resonances. These correlation effects can be included explicitly by suitable choice of one component of the closed-channel wave function; the remaining component may then be determined by the generalized Hartree-Fock procedure. As a simple test, the method is applied to s-wave scattering of positrons by hydrogen. copyright 1997 The American Physical Society
General Methods for Evolutionary Quantitative Genetic Inference from Generalized Mixed Models.
de Villemereuil, Pierre; Schielzeth, Holger; Nakagawa, Shinichi; Morrissey, Michael
2016-11-01
Methods for inference and interpretation of evolutionary quantitative genetic parameters, and for prediction of the response to selection, are best developed for traits with normal distributions. Many traits of evolutionary interest, including many life history and behavioral traits, have inherently nonnormal distributions. The generalized linear mixed model (GLMM) framework has become a widely used tool for estimating quantitative genetic parameters for nonnormal traits. However, whereas GLMMs provide inference on a statistically convenient latent scale, it is often desirable to express quantitative genetic parameters on the scale upon which traits are measured. The parameters of fitted GLMMs, despite being on a latent scale, fully determine all quantities of potential interest on the scale on which traits are expressed. We provide expressions for deriving each of such quantities, including population means, phenotypic (co)variances, variance components including additive genetic (co)variances, and parameters such as heritability. We demonstrate that fixed effects have a strong impact on those parameters and show how to deal with this by averaging or integrating over fixed effects. The expressions require integration of quantities determined by the link function, over distributions of latent values. In general cases, the required integrals must be solved numerically, but efficient methods are available and we provide an implementation in an R package, QGglmm. We show that known formulas for quantities such as heritability of traits with binomial and Poisson distributions are special cases of our expressions. Additionally, we show how fitted GLMM can be incorporated into existing methods for predicting evolutionary trajectories. We demonstrate the accuracy of the resulting method for evolutionary prediction by simulation and apply our approach to data from a wild pedigreed vertebrate population. Copyright © 2016 de Villemereuil et al.
FATAL, General Experiment Fitting Program by Nonlinear Regression Method
International Nuclear Information System (INIS)
Salmon, L.; Budd, T.; Marshall, M.
1982-01-01
1 - Description of problem or function: A generalized fitting program with a free-format keyword interface to the user. It permits experimental data to be fitted by non-linear regression methods to any function describable by the user. The user requires the minimum of computer experience but needs to provide a subroutine to define his function. Some statistical output is included as well as 'best' estimates of the function's parameters. 2 - Method of solution: The regression method used is based on a minimization technique devised by Powell (Harwell Subroutine Library VA05A, 1972) which does not require the use of analytical derivatives. The method employs a quasi-Newton procedure balanced with a steepest descent correction. Experience shows this to be efficient for a very wide range of application. 3 - Restrictions on the complexity of the problem: The current version of the program permits functions to be defined with up to 20 parameters. The function may be fitted to a maximum of 400 points, preferably with estimated values of weight given
Amyloid oligomer structure characterization from simulations: A general method
Energy Technology Data Exchange (ETDEWEB)
Nguyen, Phuong H., E-mail: phuong.nguyen@ibpc.fr [Laboratoire de Biochimie Théorique, UPR 9080, CNRS Université Denis Diderot, Sorbonne Paris Cité IBPC, 13 rue Pierre et Marie Curie, 75005 Paris (France); Li, Mai Suan [Institute of Physics, Polish Academy of Sciences, Al. Lotnikow 32/46, 02-668 Warsaw (Poland); Derreumaux, Philippe, E-mail: philippe.derreumaux@ibpc.fr [Laboratoire de Biochimie Théorique, UPR 9080, CNRS Université Denis Diderot, Sorbonne Paris Cité IBPC, 13 rue Pierre et Marie Curie, 75005 Paris (France); Institut Universitaire de France, 103 Bvd Saint-Germain, 75005 Paris (France)
2014-03-07
Amyloid oligomers and plaques are composed of multiple chemically identical proteins. Therefore, one of the first fundamental problems in the characterization of structures from simulations is the treatment of the degeneracy, i.e., the permutation of the molecules. Second, the intramolecular and intermolecular degrees of freedom of the various molecules must be taken into account. Currently, the well-known dihedral principal component analysis method only considers the intramolecular degrees of freedom, and other methods employing collective variables can only describe intermolecular degrees of freedom at the global level. With this in mind, we propose a general method that identifies all the structures accurately. The basis idea is that the intramolecular and intermolecular states are described in terms of combinations of single-molecule and double-molecule states, respectively, and the overall structures of oligomers are the product basis of the intramolecular and intermolecular states. This way, the degeneracy is automatically avoided. The method is illustrated on the conformational ensemble of the tetramer of the Alzheimer's peptide Aβ{sub 9−40}, resulting from two atomistic molecular dynamics simulations in explicit solvent, each of 200 ns, starting from two distinct structures.
Generalized Bootstrap Method for Assessment of Uncertainty in Semivariogram Inference
Olea, R.A.; Pardo-Iguzquiza, E.
2011-01-01
The semivariogram and its related function, the covariance, play a central role in classical geostatistics for modeling the average continuity of spatially correlated attributes. Whereas all methods are formulated in terms of the true semivariogram, in practice what can be used are estimated semivariograms and models based on samples. A generalized form of the bootstrap method to properly model spatially correlated data is used to advance knowledge about the reliability of empirical semivariograms and semivariogram models based on a single sample. Among several methods available to generate spatially correlated resamples, we selected a method based on the LU decomposition and used several examples to illustrate the approach. The first one is a synthetic, isotropic, exhaustive sample following a normal distribution, the second example is also a synthetic but following a non-Gaussian random field, and a third empirical sample consists of actual raingauge measurements. Results show wider confidence intervals than those found previously by others with inadequate application of the bootstrap. Also, even for the Gaussian example, distributions for estimated semivariogram values and model parameters are positively skewed. In this sense, bootstrap percentile confidence intervals, which are not centered around the empirical semivariogram and do not require distributional assumptions for its construction, provide an achieved coverage similar to the nominal coverage. The latter cannot be achieved by symmetrical confidence intervals based on the standard error, regardless if the standard error is estimated from a parametric equation or from bootstrap. ?? 2010 International Association for Mathematical Geosciences.
GENP-2, Program System for Integral Reactor Perturbation
International Nuclear Information System (INIS)
Boioli, A.; Cecchini, G.P.
1975-01-01
1 - Description of problem or function: GENP-2 is a system of programs that use 'generalized perturbation theory' to calculate the perturbations of reactor integral characteristics which can be expressed by means of ratios between linear or bilinear functionals of the real and/or adjoint fluxes (e.g. reaction rate ratios), due to cross section perturbations. 2 - Method of solution: GENP-2 consists of the following codes: DDV, SORCI, CIAP-PMN and GLOBP-2D. DDV calculates the real or adjoint fluxes and power distribution using multigroup diffusion theory in 2-dimensions. SORCI uses the fluxes from DDV to calculate the real and/or adjoint general perturbation sources. CIAP-PMN reads the sources from SORCI and uses them in the real or adjoint generalised importance calculations (2 dimensions, multi- group diffusion). GLOBP-2D uses the importance calculated by CIAP-PMN, and the fluxes calculated by DDV, in generalised perturbation expressions to calculate the perturbation in the quantity of interest. 3 - Restrictions on the complexity of the problem: DDV although variably dimensioned has the following restrictions: - max. number of mesh points 6400; - max. number of mesh points in 1-dimension 81; - max. number of regions 6400; - max. number of energy groups 100; - if power distribution calculated, product of number of groups and number of regions 2500. The other programs have the same restrictions if applicable
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.
International Nuclear Information System (INIS)
Belendez, A.; Belendez, T.; Neipp, C.; Hernandez, A.; Alvarez, M.L.
2009-01-01
The homotopy perturbation method is used to solve the nonlinear differential equation that governs the nonlinear oscillations of a system typified as a mass attached to a stretched elastic wire. The restoring force for this oscillator has an irrational term with a parameter λ that characterizes the system (0 ≤ λ ≤ 1). For λ = 1 and small values of x, the restoring force does not have a dominant term proportional to x. We find this perturbation method works very well for the whole range of parameters involved, and excellent agreement of the approximate frequencies and periodic solutions with the exact ones has been demonstrated and discussed. Only one iteration leads to high accuracy of the solutions and the maximal relative error for the approximate frequency is less than 2.2% for small and large values of oscillation amplitude. This error corresponds to λ = 1, while for λ < 1 the relative error is much lower. For example, its value is as low as 0.062% for λ = 0.5.
Energy Technology Data Exchange (ETDEWEB)
Faisal, F H.M. [Bielefeld Univ. (Germany, F.R.). Fakultaet fuer Physik
1976-06-11
In this work the perturbation theory for multiphoton processes at high intensities is investigated and it is described an analytical method of summing the perturbation series to extract the contribution from all terms that give rise to the absorption of N photons by an atomic system. The method is first applied to the solution of a simple model problem and the result is confirmed by direct integration of the model Schroedinger equation. The usual lowest (nonvanishing)-order perturbation-theoretical calculation is also carried out for this model to demonstrate explicitly that the full result correctly reproduces that of the lowest-order theory in the limit of low intensity. The method is then extended to the case of an atomic system with well-developed spectrum (e.g. H atom) and the N-photon T-matrix is derived in terms of a ''photon matrix'' asub(N), for which a three-term recurrence relation is established. Next, from the vantage point of the general result obtained here, A probe is made into the nature of several approximate nonperturbative solutions that have appeared in the literature in the past. It is shown here that their applicability is severely restricted by the requirement of the essential spectral degeneracy of the atomic system. Finally, appendix A outlines a prescription of computing the photon matrix asub(N), which (as in the usual lowest-order perturbation-theoretical calculation)requires a knowledge of the eigenfunctions and eigenvalues of the atomic Hamiltonian only.
Adaptive Elastic Net for Generalized Methods of Moments.
Caner, Mehmet; Zhang, Hao Helen
2014-01-30
Model selection and estimation are crucial parts of econometrics. This paper introduces a new technique that can simultaneously estimate and select the model in generalized method of moments (GMM) context. The GMM is particularly powerful for analyzing complex data sets such as longitudinal and panel data, and it has wide applications in econometrics. This paper extends the least squares based adaptive elastic net estimator of Zou and Zhang (2009) to nonlinear equation systems with endogenous variables. The extension is not trivial and involves a new proof technique due to estimators lack of closed form solutions. Compared to Bridge-GMM of Caner (2009), we allow for the number of parameters to diverge to infinity as well as collinearity among a large number of variables, also the redundant parameters set to zero via a data dependent technique. This method has the oracle property, meaning that we can estimate nonzero parameters with their standard limit and the redundant parameters are dropped from the equations simultaneously. Numerical examples are used to illustrate the performance of the new method.
An efficient iterative method for the generalized Stokes problem
Energy Technology Data Exchange (ETDEWEB)
Sameh, A. [Univ. of Minnesota, Twin Cities, MN (United States); Sarin, V. [Univ. of Illinois, Urbana, IL (United States)
1996-12-31
This paper presents an efficient iterative scheme for the generalized Stokes problem, which arises frequently in the simulation of time-dependent Navier-Stokes equations for incompressible fluid flow. The general form of the linear system is where A = {alpha}M + vT is an n x n symmetric positive definite matrix, in which M is the mass matrix, T is the discrete Laplace operator, {alpha} and {nu} are positive constants proportional to the inverses of the time-step {Delta}t and the Reynolds number Re respectively, and B is the discrete gradient operator of size n x k (k < n). Even though the matrix A is symmetric and positive definite, the system is indefinite due to the incompressibility constraint (B{sup T}u = 0). This causes difficulties both for iterative methods and commonly used preconditioners. Moreover, depending on the ratio {alpha}/{nu}, A behaves like the mass matrix M at one extreme and the Laplace operator T at the other, thus complicating the issue of preconditioning.
Comparative phylogeography: concepts, methods and general patterns in neotropical birds
International Nuclear Information System (INIS)
Arbelaez Cortes, Enrique
2012-01-01
Understanding the patterns and processes involved in intraspecific lineages diversification in time and space is the aim of phylogeography. The comparison of those phylogeographic patterns among co-distributed species shows insights of a community history. Here I review the concepts and methodologies of comparative phylogeography, an active research field that has heterogeneous analytical methods. In order to present a framework for phylogeography in the neotropics, I comment the general phylogeographic patterns of the birds from this region. this review is based on more than 100 studies conducted during the last 25 years and indicate that despite different co-distributed species seem to share some points in their phylogeographic pattern they have idiosyncratic aspects, indicating an unique history for each one.
On the existence of perturbed Robertson-Walker universes
International Nuclear Information System (INIS)
D'Eath, P.D.
1976-01-01
Solutions of the full nonlinear field equations of general relativity near the Robertson-Walker universes are examined, together with their relation to linearized perturbations. A method due to Choquet-Bruhat and Deser is used to prove existence theorems for solutions near Robertson-Walker constraint data of the constraint equations on a spacelike hypersurface. These theorems allow one to regard the matter fluctuations as independent quantities, ranging over certain function spaces. In the k=-1 case the existence theory describes perturbations which may vary within uniform bounds throughout space. When k=+1 a modification of the method leads to a theorem which clarifies some unusual features of these constraint perturbations. The k=0 existence theorem refers only to perturbations which die away at large distances. The connection between linearized constraint solutions and solutions of the full constraints is discussed. For k= +- 1 backgrounds, solutions of the linearized constraints are analyzed using transverse-traceless decompositions of symmetric tensors. Finally the time-evolution of perturbed constraint data and the validity of linearized perturbation theory for Robertson-Walker universes are considered
Hong, Youngjoon; Nicholls, David P.
2017-09-01
The capability to rapidly and robustly simulate the scattering of linear waves by periodic, multiply layered media in two and three dimensions is crucial in many engineering applications. In this regard, we present a High-Order Perturbation of Surfaces method for linear wave scattering in a multiply layered periodic medium to find an accurate numerical solution of the governing Helmholtz equations. For this we truncate the bi-infinite computational domain to a finite one with artificial boundaries, above and below the structure, and enforce transparent boundary conditions there via Dirichlet-Neumann Operators. This is followed by a Transformed Field Expansion resulting in a Fourier collocation, Legendre-Galerkin, Taylor series method for solving the problem in a transformed set of coordinates. Assorted numerical simulations display the spectral convergence of the proposed algorithm.
Salgado, Iván; Mera-Hernández, Manuel; Chairez, Isaac
2017-11-01
This study addresses the problem of designing an output-based controller to stabilize multi-input multi-output (MIMO) systems in the presence of parametric disturbances as well as uncertainties in the state model and output noise measurements. The controller design includes a linear state transformation which separates uncertainties matched to the control input and the unmatched ones. A differential neural network (DNN) observer produces a nonlinear approximation of the matched perturbation and the unknown states simultaneously in the transformed coordinates. This study proposes the use of the Attractive Ellipsoid Method (AEM) to optimize the gains of the controller and the gain observer in the DNN structure. As a consequence, the obtained control input minimizes the convergence zone for the estimation error. Moreover, the control design uses the estimated disturbance provided by the DNN to obtain a better performance in the stabilization task in comparison with a quasi-minimal output feedback controller based on a Luenberger observer and a sliding mode controller. Numerical results pointed out the advantages obtained by the nonlinear control based on the DNN observer. The first example deals with the stabilization of an academic linear MIMO perturbed system and the second example stabilizes the trajectories of a DC-motor into a predefined operation point. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.
Mixed Generalized Multiscale Finite Element Methods and Applications
Chung, Eric T.
2015-03-03
In this paper, we present a mixed generalized multiscale finite element method (GMsFEM) for solving flow in heterogeneous media. Our approach constructs multiscale basis functions following a GMsFEM framework and couples these basis functions using a mixed finite element method, which allows us to obtain a mass conservative velocity field. To construct multiscale basis functions for each coarse edge, we design a snapshot space that consists of fine-scale velocity fields supported in a union of two coarse regions that share the common interface. The snapshot vectors have zero Neumann boundary conditions on the outer boundaries, and we prescribe their values on the common interface. We describe several spectral decompositions in the snapshot space motivated by the analysis. In the paper, we also study oversampling approaches that enhance the accuracy of mixed GMsFEM. A main idea of oversampling techniques is to introduce a small dimensional snapshot space. We present numerical results for two-phase flow and transport, without updating basis functions in time. Our numerical results show that one can achieve good accuracy with a few basis functions per coarse edge if one selects appropriate offline spaces. © 2015 Society for Industrial and Applied Mathematics.
Generalized multiscale finite element method for elasticity equations
Chung, Eric T.
2014-10-05
In this paper, we discuss the application of generalized multiscale finite element method (GMsFEM) to elasticity equation in heterogeneous media. We consider steady state elasticity equations though some of our applications are motivated by elastic wave propagation in subsurface where the subsurface properties can be highly heterogeneous and have high contrast. We present the construction of main ingredients for GMsFEM such as the snapshot space and offline spaces. The latter is constructed using local spectral decomposition in the snapshot space. The spectral decomposition is based on the analysis which is provided in the paper. We consider both continuous Galerkin and discontinuous Galerkin coupling of basis functions. Both approaches have their cons and pros. Continuous Galerkin methods allow avoiding penalty parameters though they involve partition of unity functions which can alter the properties of multiscale basis functions. On the other hand, discontinuous Galerkin techniques allow gluing multiscale basis functions without any modifications. Because basis functions are constructed independently from each other, this approach provides an advantage. We discuss the use of oversampling techniques that use snapshots in larger regions to construct the offline space. We provide numerical results to show that one can accurately approximate the solution using reduced number of degrees of freedom.
Randomized Oversampling for Generalized Multiscale Finite Element Methods
Calo, Victor M.
2016-03-23
In this paper, we develop efficient multiscale methods for flows in heterogeneous media. We use the generalized multiscale finite element (GMsFEM) framework. GMsFEM approximates the solution space locally using a few multiscale basis functions. This approximation selects an appropriate snapshot space and a local spectral decomposition, e.g., the use of oversampled regions, in order to achieve an efficient model reduction. However, the successful construction of snapshot spaces may be costly if too many local problems need to be solved in order to obtain these spaces. We use a moderate quantity of local solutions (or snapshot vectors) with random boundary conditions on oversampled regions with zero forcing to deliver an efficient methodology. Motivated by the randomized algorithm presented in [P. G. Martinsson, V. Rokhlin, and M. Tygert, A Randomized Algorithm for the approximation of Matrices, YALEU/DCS/TR-1361, Yale University, 2006], we consider a snapshot space which consists of harmonic extensions of random boundary conditions defined in a domain larger than the target region. Furthermore, we perform an eigenvalue decomposition in this small space. We study the application of randomized sampling for GMsFEM in conjunction with adaptivity, where local multiscale spaces are adaptively enriched. Convergence analysis is provided. We present representative numerical results to validate the method proposed.
Perturbation theory from stochastic quantization
International Nuclear Information System (INIS)
Hueffel, H.
1984-01-01
By using a diagrammatical method it is shown that in scalar theories the stochastic quantization method of Parisi and Wu gives the usual perturbation series in Feynman diagrams. It is further explained how to apply the diagrammatical method to gauge theories, discussing the origin of ghost effects. (Author)
Directory of Open Access Journals (Sweden)
H. Wan
2014-09-01
Full Text Available This paper explores the feasibility of an experimentation strategy for investigating sensitivities in fast components of atmospheric general circulation models. The basic idea is to replace the traditional serial-in-time long-term climate integrations by representative ensembles of shorter simulations. The key advantage of the proposed method lies in its efficiency: since fewer days of simulation are needed, the computational cost is less, and because individual realizations are independent and can be integrated simultaneously, the new dimension of parallelism can dramatically reduce the turnaround time in benchmark tests, sensitivities studies, and model tuning exercises. The strategy is not appropriate for exploring sensitivity of all model features, but it is very effective in many situations. Two examples are presented using the Community Atmosphere Model, version 5. In the first example, the method is used to characterize sensitivities of the simulated clouds to time-step length. Results show that 3-day ensembles of 20 to 50 members are sufficient to reproduce the main signals revealed by traditional 5-year simulations. A nudging technique is applied to an additional set of simulations to help understand the contribution of physics–dynamics interaction to the detected time-step sensitivity. In the second example, multiple empirical parameters related to cloud microphysics and aerosol life cycle are perturbed simultaneously in order to find out which parameters have the largest impact on the simulated global mean top-of-atmosphere radiation balance. It turns out that 12-member ensembles of 10-day simulations are able to reveal the same sensitivities as seen in 4-year simulations performed in a previous study. In both cases, the ensemble method reduces the total computational time by a factor of about 15, and the turnaround time by a factor of several hundred. The efficiency of the method makes it particularly useful for the development of
Generalization of mixed multiscale finite element methods with applications
Energy Technology Data Exchange (ETDEWEB)
Lee, C S [Texas A & M Univ., College Station, TX (United States)
2016-08-01
Many science and engineering problems exhibit scale disparity and high contrast. The small scale features cannot be omitted in the physical models because they can affect the macroscopic behavior of the problems. However, resolving all the scales in these problems can be prohibitively expensive. As a consequence, some types of model reduction techniques are required to design efficient solution algorithms. For practical purpose, we are interested in mixed finite element problems as they produce solutions with certain conservative properties. Existing multiscale methods for such problems include the mixed multiscale finite element methods. We show that for complicated problems, the mixed multiscale finite element methods may not be able to produce reliable approximations. This motivates the need of enrichment for coarse spaces. Two enrichment approaches are proposed, one is based on generalized multiscale finte element metthods (GMsFEM), while the other is based on spectral element-based algebraic multigrid (rAMGe). The former one, which is called mixed GMsFEM, is developed for both Darcy’s flow and linear elasticity. Application of the algorithm in two-phase flow simulations are demonstrated. For linear elasticity, the algorithm is subtly modified due to the symmetry requirement of the stress tensor. The latter enrichment approach is based on rAMGe. The algorithm differs from GMsFEM in that both of the velocity and pressure spaces are coarsened. Due the multigrid nature of the algorithm, recursive application is available, which results in an efficient multilevel construction of the coarse spaces. Stability, convergence analysis, and exhaustive numerical experiments are carried out to validate the proposed enrichment approaches. iii
Glutarimides: Biological activity, general synthetic methods and physicochemical properties
Directory of Open Access Journals (Sweden)
Popović-Đorđević Jelena B.
2015-01-01
Full Text Available Glutarimides, 2,6-dioxopiperidines are compounds that rarely occur in natural sources, but so far isolated ones exert widespread pharmacological activities, which makes them valuable as potential pharmacotherapeutics. Glutarimides act as androgen receptor antagonists, anti-inflammatory, anxiolytics, antibacterials, and tumor suppressing agents. Some synthetic glutarimide derivatives are already in use as immunosuppressive and sedative (e.g., thalidomide or anxiolytics (buspirone drugs. The wide applicability of this class of compounds, justify the interest of scientists to explore new pathways for its syntheses. General methods for synthesis of six-membered imide ring, are presented in this paper. These methods include: a reaction of dicarboxylic acids with ammonia or primary amine, b reactions of cyclization: amido-acids, diamides, dinitriles, nitrilo-acids, amido-nitriles, amido-esters, amidoacyl-chlorides or diacyl-chlorides, c adition of carbon-monoxide on a,b-unsaturated amides, d oxidation reactions, e Michael adition of active methylen compounds on methacrylamide or conjugated amides. Some of the described methods are used for closing glutarimide ring in syntheses of farmacological active compounds sesbanimide and aldose reductase inhibitors (ARI. Analyses of the geometry, as well as, the spectroscopic analyses (NMR and FT-IR of some glutarimides are presented because of their broad spectrum of pharmacological activity. To elucidate structures of glutarimides, geometrical parameters of newly synthesized tert-pentyl-1-benzyl-4-methyl-glutarimide-3-carboxylate (PBMG are analyzed and compared with the experimental data from X-ray analysis for glutarimide. Moreover, molecular electrostatic potential (MEP surface which is plotted over the optimized geometry to elucidate the reactivity of PBMG molecule is analyzed. The electronic properties of glutarimide derivatives are explained on the example of thalidomide. The Frontier Molecular Orbital
Perturbative quantum chromodynamics
International Nuclear Information System (INIS)
Radyushkin, A.V.
1987-01-01
The latest achievements in perturbative quantum chromodynamics (QCD) relating to the progress in factorization of small and large distances are presented. The following problems are concerned: Development of the theory of Sudakov effects on the basis of mean contour formalism. Development of nonlocal condensate formalism. Calculation of hadron wave functions and hadron distribution functions using QCD method of sum rules. Development of the theory of Regge behaviour in QCD, behaviour of structure functions at small x. Study of polarization effects in hadron processes with high momentum transfer
International Nuclear Information System (INIS)
Ixaru, G.L.
1978-03-01
The method developed in the previous paper (preprint, C.I.Ph. (Bucharest), MC-2-78, 1978) is here investigated from computational point of view. Special emphasis is paid to the two basic descriptors of the efficiency: the volume of memory required and the computational effort (timing). Next, two experimental cases are reported. They (i) confirm the theoretical estimates for the rate cf convergence of each version of the present method and (ii) show that the present method is substantially faster than the others. Specifically, it is found that for typical physical problems it is faster by a factor of ten up to twenty than the methods commonly used, viz. Numerov and de Vogelaere. The data reported also allow an inUirect comparison with the method of Gordon. I l/ allow an indirect comparison with the method of Gordon. It is shown that, while this exhibits the same rate as our basic, lowest order version, the computational effort for the latter is, in case of systems with nine equations, only half than for the method of Gordon. At the end of the paper some types of physical problems are suggested which should be the most benefitting if solved numerically with the present method. (author)
Gauge-invariant perturbations in a spatially flat anisotropic universe
International Nuclear Information System (INIS)
Den, Mitsue.
1986-12-01
The gauge-invariant perturbations in a spatially flat anisotropic universe with an arbitrary dimension (= N) are studied. In a previous paper the equations for the perturbations with a wave vector k a in one of the axial directions were derived and their solutions were shown. In this paper the perturbations with k a in arbitrary directions are treated. The remarkable properties are that all three types (scalar, vector, and tensor) of perturbations are generally coupled, so that a density perturbation can be produced also by vector or tensor perturbations. The formulation is quite general, but the behavior of the perturbations is discussed in a simple case such that N = 4 and k a is orthogonal to one of the axial directions. In this case, the perturbations are divided into two groups which are dynamically decoupled from each other. The asymptotic behavior of the perturbations in the group containing the density perturbation is discussed. (author)
Non-perturbative description of quantum systems
Feranchuk, Ilya; Le, Van-Hoang; Ulyanenkov, Alexander
2015-01-01
This book introduces systematically the operator method for the solution of the Schrödinger equation. This method permits to describe the states of quantum systems in the entire range of parameters of Hamiltonian with a predefined accuracy. The operator method is unique compared with other non-perturbative methods due to its ability to deliver in zeroth approximation the uniformly suitable estimate for both ground and excited states of quantum system. The method has been generalized for the application to quantum statistics and quantum field theory. In this book, the numerous applications of operator method for various physical systems are demonstrated. Simple models are used to illustrate the basic principles of the method which are further used for the solution of complex problems of quantum theory for many-particle systems. The results obtained are supplemented by numerical calculations, presented as tables and figures.
Chiral symmetry in perturbative QCD
International Nuclear Information System (INIS)
Trueman, T.L.
1979-04-01
The chiral symmetry of quantum chromodynamics with massless quarks is unbroken in perturbation theory. Dimensional regularization is used. The ratio of the vector and axial vector renormalization constante is shown to be independent of the renormalization mass. The general results are explicitly verified to fourth order in g, the QCD coupling constant
The spherical harmonics method, 1 (general development of the theory)
International Nuclear Information System (INIS)
Mark, C.
1957-02-01
A method of obtaining approximate solutions of the transport equation is presented in a form applicable in principle to any geometry. The approximation will give good results in cases where the angular distribution is not very anisotropic. The basis of the approximation is to expand the density per unit solid angle Ψ(→/r, →/Ω) in spherical harmonic tensors formed from →/Ω the unit vector in the direction of velocity, and to break off the expansion. A differential equation whose degree increases with the order of the approximation is obtained for the total density Ψ (o) (r). This equation has the form where the numbers ν i depend on the order of the approximation and on the value of the parameter a of the medium, but not at all on the geometry. When the equation for the total density is an ordinary equation, we simulate the physical condition of continuity of Ψ(→/r, →/Ω) at a boundary in a multi-medium problem by requiring that the spherical harmonic moments of Ψ(→/r, →/Ω) which we retain be continuous; and this determines the constants in the solution for Ψ (o) (→/r. The form of the solution for the total density and the necessary moments in an approximation of general order is given explicitly for plane and spherical symmetry; and for cylindrical symmetry the solution is given for two low-order approximations. In a later report (CRT-338, Revised) the application of the method to several problems involving plane and spherical symmetry will be discussed in detail and the results of a number of examples already worked will also be given. (author)
The spherical harmonics method, 1 (general development of the theory)
Energy Technology Data Exchange (ETDEWEB)
Mark, C
1957-02-15
A method of obtaining approximate solutions of the transport equation is presented in a form applicable in principle to any geometry. The approximation will give good results in cases where the angular distribution is not very anisotropic. The basis of the approximation is to expand the density per unit solid angle {Psi}({yields}/r, {yields}/{Omega}) in spherical harmonic tensors formed from {yields}/{Omega} the unit vector in the direction of velocity, and to break off the expansion. A differential equation whose degree increases with the order of the approximation is obtained for the total density {Psi}{sup (o)}(r). This equation has the form where the numbers {nu}{sub i} depend on the order of the approximation and on the value of the parameter a of the medium, but not at all on the geometry. When the equation for the total density is an ordinary equation, we simulate the physical condition of continuity of {Psi}({yields}/r, {yields}/{Omega}) at a boundary in a multi-medium problem by requiring that the spherical harmonic moments of {Psi}({yields}/r, {yields}/{Omega}) which we retain be continuous; and this determines the constants in the solution for {Psi}{sup (o)}({yields}/r. The form of the solution for the total density and the necessary moments in an approximation of general order is given explicitly for plane and spherical symmetry; and for cylindrical symmetry the solution is given for two low-order approximations. In a later report (CRT-338, Revised) the application of the method to several problems involving plane and spherical symmetry will be discussed in detail and the results of a number of examples already worked will also be given. (author)
Cluster-cell calculation using the method of generalized homogenization
International Nuclear Information System (INIS)
Laletin, N.I.; Boyarinov, V.F.
1988-01-01
The generalized-homogenization method (GHM), used for solving the neutron transfer equation, was applied to calculating the neutron distribution in the cluster cell with a series of cylindrical cells with cylindrically coaxial zones. Single-group calculations of the technological channel of the cell of an RBMK reactor were performed using GHM. The technological channel was understood to be the reactor channel, comprised of the zirconium rod, the water or steam-water mixture, the uranium dioxide fuel element, and the zirconium tube, together with the adjacent graphite layer. Calculations were performed for channels with no internal sources and with unit incoming current at the external boundary as well as for channels with internal sources and zero current at the external boundary. The PRAKTINETs program was used to calculate the symmetric neutron distributions in the microcell and in channels with homogenized annular zones. The ORAR-TsM program was used to calculate the antisymmetric distribution in the microcell. The accuracy of the calculations were compared for the two channel versions
Abou-zeid, Mohamed Y.; Mohamed, Mona A. A.
2017-09-01
This article is an analytic discussion for the motion of power-law nanofluid with heat transfer under the effect of viscous dissipation, radiation, and internal heat generation. The governing equations are discussed under the assumptions of long wavelength and low Reynolds number. The solutions for temperature and nanoparticle profiles are obtained by using homotopy perturbation method. Results for the behaviours of the axial velocity, temperature, and nanoparticles as well as the skin friction coefficient, reduced Nusselt number, and Sherwood number with other physical parameters are obtained graphically and analytically. It is found that as the power-law exponent increases, both the axial velocity and temperature increase, whereas nanoparticles decreases. These results may have applicable importance in the research discussions of nanofluid flow in channels with small diameters under the effect of different temperature distributions.
Energy Technology Data Exchange (ETDEWEB)
Wan, Hui; Rasch, Philip J.; Zhang, Kai; Qian, Yun; Yan, Huiping; Zhao, Chun
2014-09-08
This paper explores the feasibility of an experimentation strategy for investigating sensitivities in fast components of atmospheric general circulation models. The basic idea is to replace the traditional serial-in-time long-term climate integrations by representative ensembles of shorter simulations. The key advantage of the proposed method lies in its efficiency: since fewer days of simulation are needed, the computational cost is less, and because individual realizations are independent and can be integrated simultaneously, the new dimension of parallelism can dramatically reduce the turnaround time in benchmark tests, sensitivities studies, and model tuning exercises. The strategy is not appropriate for exploring sensitivity of all model features, but it is very effective in many situations. Two examples are presented using the Community Atmosphere Model version 5. The first example demonstrates that the method is capable of characterizing the model cloud and precipitation sensitivity to time step length. A nudging technique is also applied to an additional set of simulations to help understand the contribution of physics-dynamics interaction to the detected time step sensitivity. In the second example, multiple empirical parameters related to cloud microphysics and aerosol lifecycle are perturbed simultaneously in order to explore which parameters have the largest impact on the simulated global mean top-of-atmosphere radiation balance. Results show that in both examples, short ensembles are able to correctly reproduce the main signals of model sensitivities revealed by traditional long-term climate simulations for fast processes in the climate system. The efficiency of the ensemble method makes it particularly useful for the development of high-resolution, costly and complex climate models.
Geometric perturbation theory and plasma physics
Energy Technology Data Exchange (ETDEWEB)
Omohundro, S.M.
1985-04-04
Modern differential geometric techniques are used to unify the physical asymptotics underlying mechanics, wave theory and statistical mechanics. The approach gives new insights into the structure of physical theories and is suited to the needs of modern large-scale computer simulation and symbol manipulation systems. A coordinate-free formulation of non-singular perturbation theory is given, from which a new Hamiltonian perturbation structure is derived and related to the unperturbed structure. The theory of perturbations in the presence of symmetry is developed, and the method of averaging is related to reduction by a circle group action. The pseudo-forces and magnetic Poisson bracket terms due to reduction are given a natural asymptotic interpretation. Similar terms due to changing reference frames are related to the method of variation of parameters, which is also given a Hamiltonian formulation. These methods are used to answer a question about nearly periodic systems. The answer leads to a new secular perturbation theory that contains no ad hoc elements. Eikonal wave theory is given a Hamiltonian formulation that generalizes Whitham's Lagrangian approach. The evolution of wave action density on ray phase space is given a Hamiltonian structure using a Lie-Poisson bracket. The relationship between dissipative and Hamiltonian systems is discussed. A new type of attractor is defined which attracts both forward and backward in time and is shown to occur in infinite-dimensional Hamiltonian systems with dissipative behavior. The theory of Smale horseshoes is applied to gyromotion in the neighborhood of a magnetic field reversal and the phenomenon of reinsertion in area-preserving horseshoes is introduced. The central limit theorem is proved by renormalization group techniques. A natural symplectic structure for thermodynamics is shown to arise asymptotically from the maximum entropy formalism.
Geometric perturbation theory and plasma physics
International Nuclear Information System (INIS)
Omohundro, S.M.
1985-01-01
Modern differential geometric techniques are used to unify the physical asymptotics underlying mechanics, wave theory and statistical mechanics. The approach gives new insights into the structure of physical theories and is suited to the needs of modern large-scale computer simulation and symbol manipulation systems. A coordinate-free formulation of non-singular perturbation theory is given, from which a new Hamiltonian perturbation structure is derived and related to the unperturbed structure. The theory of perturbations in the presence of symmetry is developed, and the method of averaging is related to reduction by a circle group action. The pseudo-forces and magnetic Poisson bracket terms due to reduction are given a natural asymptotic interpretation. Similar terms due to changing reference frames are related to the method of variation of parameters, which is also given a Hamiltonian formulation. These methods are used to answer a question about nearly periodic systems. The answer leads to a new secular perturbation theory that contains no ad hoc elements. Eikonal wave theory is given a Hamiltonian formulation that generalizes Whitham's Lagrangian approach. The evolution of wave action density on ray phase space is given a Hamiltonian structure using a Lie-Poisson bracket. The relationship between dissipative and Hamiltonian systems is discussed. A new type of attractor is defined which attracts both forward and backward in time and is shown to occur in infinite-dimensional Hamiltonian systems with dissipative behavior. The theory of Smale horseshoes is applied to gyromotion in the neighborhood of a magnetic field reversal and the phenomenon of reinsertion in area-preserving horseshoes is introduced. The central limit theorem is proved by renormalization group techniques. A natural symplectic structure for thermodynamics is shown to arise asymptotically from the maximum entropy formalism
Application of linear and higher perturbation theory in reactor physics
International Nuclear Information System (INIS)
Woerner, D.
1978-01-01
For small perturbations in the material composition of a reactor according to the first approximation of perturbation theory the eigenvalue perturbation is proportional to the perturbation of the system. This assumption is true for the neutron flux not influenced by the perturbance. The two-dimensional code LINESTO developed for such problems in this paper on the basis of diffusion theory determines the relative change of the multiplication constant. For perturbations varying the neutron flux in the space of energy and position the eigenvalue perturbation is also influenced by this changed neutron flux. In such cases linear perturbation theory yields larger errors. Starting from the methods of calculus of variations there is additionally developed in this paper a perturbation method of calculation permitting in a quick and simple manner to assess the influence of flux perturbation on the eigenvalue perturbation. While the source of perturbations is evaluated in isotropic approximation of diffusion theory the associated inhomogeneous equation may be used to determine the flux perturbation by means of diffusion or transport theory. Possibilities of application and limitations of this method are studied in further systematic investigations on local perturbations. It is shown that with the integrated code system developed in this paper a number of local perturbations may be checked requiring little computing time. With it flux perturbations in first approximation and perturbations of the multiplication constant in second approximation can be evaluated. (orig./RW) [de
Principles of chiral perturbation theory
International Nuclear Information System (INIS)
Leutwyler, H.
1995-01-01
An elementary discussion of the main concepts used in chiral perturbation theory is given in textbooks and a more detailed picture of the applications may be obtained from the reviews. Concerning the foundations of the method, the literature is comparatively scarce. So, I will concentrate on the basic concepts and explain why the method works. (author)
Wickman, J.; Diehl, S.; Blasius, B.; Klausmeier, C.; Ryabov, A.; Brännström, Å.
2017-01-01
Spatial structure can decisively influence the way evolutionary processes unfold. Several methods have thus far been used to study evolution in spatial systems, including population genetics, quantitative genetics, momentclosure approximations, and individual-based models. Here we extend the study of spatial evolutionary dynamics to eco-evolutionary models based on reaction-diffusion equations and adaptive dynamics. Specifically, we derive expressions for the strength of directional and stabi...
Confinement and hadron-hadron interactions by general relativistic methods
Recami, Erasmo
By postulating covariance of physical laws under global dilations, one can describe gravitational and strong interactions in a unified way. Namely, in terms of the new discrete dilational degree of freedom, our cosmos and hadrons can be regarded as finite, similar systems. And a discrete hierarchy of finite ``universes'' may be defined, which are governed by fields with strengths inversally proportional to their radii; in each universe an Equivalence Principle holds, so that the relevant field can be there geometrized. Scaled-down Einstein equations -with cosmological term- are assumed to hold inside hadrons (= strong micro-cosmoses); and they yield in a natural way classical confinement, as well as ``asymptotic freedom'', of the hadron constituents. In other words, the association of strong micro-universes of Friedmann type with hadrons (i.e., applying the methods of General Relativity to subnuclear particle physics) allows avoiding recourse to phenomenological models such as the Bag Model. Inside hadrons we have to deal with a tensorial field (= strong gravity), and hadron constituents are supposed to exchange spin-2 ``gluons''. Our approach allows us also to write down a tensorial, bi-scale field theory of hadron-hadron interactions, based on modified Einstein-type equations here proposed for strong interactions in our space. We obtain in particular: (i) the correct Yukawa behaviour of the strong scalar potential at the static limit and for r>~l fm; (ii) the value of hadron radii. As a byproduct, we derive a whole ``numerology'', connecting our gravitational cosmos with the strong micro-cosmoses (hadrons), such that it does imply no variation of G with the epoch. Finally, since a structute of the ``micro-universe'' type seems to be characteristic even of leptons, a hope for the future is including also weak interactions in our classical unification of the fundamental forces.
Residual-driven online generalized multiscale finite element methods
Chung, Eric T.
2015-09-08
The construction of local reduced-order models via multiscale basis functions has been an area of active research. In this paper, we propose online multiscale basis functions which are constructed using the offline space and the current residual. Online multiscale basis functions are constructed adaptively in some selected regions based on our error indicators. We derive an error estimator which shows that one needs to have an offline space with certain properties to guarantee that additional online multiscale basis function will decrease the error. This error decrease is independent of physical parameters, such as the contrast and multiple scales in the problem. The offline spaces are constructed using Generalized Multiscale Finite Element Methods (GMsFEM). We show that if one chooses a sufficient number of offline basis functions, one can guarantee that additional online multiscale basis functions will reduce the error independent of contrast. We note that the construction of online basis functions is motivated by the fact that the offline space construction does not take into account distant effects. Using the residual information, we can incorporate the distant information provided the offline approximation satisfies certain properties. In the paper, theoretical and numerical results are presented. Our numerical results show that if the offline space is sufficiently large (in terms of the dimension) such that the coarse space contains all multiscale spectral basis functions that correspond to small eigenvalues, then the error reduction by adding online multiscale basis function is independent of the contrast. We discuss various ways computing online multiscale basis functions which include a use of small dimensional offline spaces.
Directory of Open Access Journals (Sweden)
Suheel Abdullah Malik
Full Text Available In this paper, a new heuristic scheme for the approximate solution of the generalized Burgers'-Fisher equation is proposed. The scheme is based on the hybridization of Exp-function method with nature inspired algorithm. The given nonlinear partial differential equation (NPDE through substitution is converted into a nonlinear ordinary differential equation (NODE. The travelling wave solution is approximated by the Exp-function method with unknown parameters. The unknown parameters are estimated by transforming the NODE into an equivalent global error minimization problem by using a fitness function. The popular genetic algorithm (GA is used to solve the minimization problem, and to achieve the unknown parameters. The proposed scheme is successfully implemented to solve the generalized Burgers'-Fisher equation. The comparison of numerical results with the exact solutions, and the solutions obtained using some traditional methods, including adomian decomposition method (ADM, homotopy perturbation method (HPM, and optimal homotopy asymptotic method (OHAM, show that the suggested scheme is fairly accurate and viable for solving such problems.
Malik, Suheel Abdullah; Qureshi, Ijaz Mansoor; Amir, Muhammad; Malik, Aqdas Naveed; Haq, Ihsanul
2015-01-01
In this paper, a new heuristic scheme for the approximate solution of the generalized Burgers'-Fisher equation is proposed. The scheme is based on the hybridization of Exp-function method with nature inspired algorithm. The given nonlinear partial differential equation (NPDE) through substitution is converted into a nonlinear ordinary differential equation (NODE). The travelling wave solution is approximated by the Exp-function method with unknown parameters. The unknown parameters are estimated by transforming the NODE into an equivalent global error minimization problem by using a fitness function. The popular genetic algorithm (GA) is used to solve the minimization problem, and to achieve the unknown parameters. The proposed scheme is successfully implemented to solve the generalized Burgers'-Fisher equation. The comparison of numerical results with the exact solutions, and the solutions obtained using some traditional methods, including adomian decomposition method (ADM), homotopy perturbation method (HPM), and optimal homotopy asymptotic method (OHAM), show that the suggested scheme is fairly accurate and viable for solving such problems.
Energy Technology Data Exchange (ETDEWEB)
Feygelman, Vladimir, E-mail: vladimir.feygelman@moffitt.org; Tonner, Brian; Hunt, Dylan; Zhang, Geoffrey; Moros, Eduardo [Department of Radiation Oncology, Moffitt Cancer Center, Tampa, Florida 33612 (United States); Stambaugh, Cassandra [Department of Physics, University of South Florida, Tampa, Florida 33612 (United States); Nelms, Benjamin E. [Canis Lupus LLC, Merrimac, Wisconsin 53561 (United States)
2015-11-15
Purpose: Previous studies show that dose to a moving target can be estimated using 4D measurement-guided dose reconstruction based on a process called virtual motion simulation, or VMS. A potential extension of VMS is to estimate dose during dynamic multileaf collimator (MLC)-tracking treatments. The authors introduce a modified VMS method and quantify its performance as proof-of-concept for tracking applications. Methods: Direct measurements with a moving biplanar diode array were used to verify accuracy of the VMS dose estimates. A tracking environment for variably sized circular MLC apertures was simulated by sending preprogrammed control points to the MLC while simultaneously moving the accelerator treatment table. Sensitivity of the method to simulated tracking latency (0–700 ms) was also studied. Potential applicability of VMS to fast changing beam apertures was evaluated by modeling, based on the demonstrated dependence of the cumulative dose on the temporal dose gradient. Results: When physical and virtual latencies were matched, the agreement rates (2% global/2 mm gamma) between the VMS and the biplanar dosimeter were above 96%. When compared to their own reference dose (0 induced latency), the agreement rates for VMS and biplanar array track closely up to 200 ms of induced latency with 10% low-dose cutoff threshold and 300 ms with 50% cutoff. Time-resolved measurements suggest that even in the modulated beams, the error in the cumulative dose introduced by the 200 ms VMS time resolution is not likely to exceed 0.5%. Conclusions: Based on current results and prior benchmarks of VMS accuracy, the authors postulate that this approach should be applicable to any MLC-tracking treatments where leaf speeds do not exceed those of the current Varian accelerators.
International Nuclear Information System (INIS)
Feygelman, Vladimir; Tonner, Brian; Hunt, Dylan; Zhang, Geoffrey; Moros, Eduardo; Stambaugh, Cassandra; Nelms, Benjamin E.
2015-01-01
Purpose: Previous studies show that dose to a moving target can be estimated using 4D measurement-guided dose reconstruction based on a process called virtual motion simulation, or VMS. A potential extension of VMS is to estimate dose during dynamic multileaf collimator (MLC)-tracking treatments. The authors introduce a modified VMS method and quantify its performance as proof-of-concept for tracking applications. Methods: Direct measurements with a moving biplanar diode array were used to verify accuracy of the VMS dose estimates. A tracking environment for variably sized circular MLC apertures was simulated by sending preprogrammed control points to the MLC while simultaneously moving the accelerator treatment table. Sensitivity of the method to simulated tracking latency (0–700 ms) was also studied. Potential applicability of VMS to fast changing beam apertures was evaluated by modeling, based on the demonstrated dependence of the cumulative dose on the temporal dose gradient. Results: When physical and virtual latencies were matched, the agreement rates (2% global/2 mm gamma) between the VMS and the biplanar dosimeter were above 96%. When compared to their own reference dose (0 induced latency), the agreement rates for VMS and biplanar array track closely up to 200 ms of induced latency with 10% low-dose cutoff threshold and 300 ms with 50% cutoff. Time-resolved measurements suggest that even in the modulated beams, the error in the cumulative dose introduced by the 200 ms VMS time resolution is not likely to exceed 0.5%. Conclusions: Based on current results and prior benchmarks of VMS accuracy, the authors postulate that this approach should be applicable to any MLC-tracking treatments where leaf speeds do not exceed those of the current Varian accelerators
International Nuclear Information System (INIS)
Doriath, J.Y.
1983-05-01
The need for increasingly accurate nuclear reactor performance data has led to increasingly sophisticated methods for solving the Boltzmann transport equation. This work has revealed the need for analyzing the functional signatures of the neutron flux using pattern recognition techniques to relate the local and overall phases of reactor calculations according to the desired parameters. This approach makes it possible to develop procedures based on a reference calculations and designed to evaluate the disturbances due to changes in physical media and to media interface modifications [fr
Eisenbeis, J.; Roy, C.; Bland, E. C.; Occhipinti, G.
2017-12-01
Most recent methods in ionospheric tomography are based on the inversion of the total electron content measured by ground-based GPS receivers. As a consequence of the high frequency of the GPS signal and the absence of horizontal raypaths, the electron density structure is mainly reconstructed in the F2 region (300 km), where the ionosphere reaches the maximum of ionization, and is not sensitive to the lower ionospheric structure. We propose here a new tomographic method of the lower ionosphere (Roy et al., 2014), based on the full inversion of over-the-horizon (OTH) radar data and applicable to SuperDarn data. The major advantage of our methodology is taking into account, numerically and jointly, the effect that the electron density perturbations induce not only in the speed of electromagnetic waves but also on the raypath geometry. This last point is extremely critical for OTH/SuperDarn data inversions as the emitted signal propagates through the ionosphere between a fixed starting point (the radar) and an unknown end point on the Earth surface where the signal is backscattered. We detail our ionospheric tomography method with the aid of benchmark tests in order to highlight the sensitivity of the radar related to the explored observational parameters: frequencies, elevations, azimuths. Having proved the necessity to take into account both effects simultaneously, we apply our method to real backscattered data from Super Darn and OTH radar. The preliminary solution obtained with the Hokkaido East SuperDARN with only two frequencies (10MHz and 11MHz), showed here, is stable and push us to deeply explore a more complete dataset that we will present at the AGU 2017. This is, in our knowledge, the first time that an ionospheric tomography has been estimated with SuperDarn backscattered data. Reference: Roy, C., G. Occhipinti, L. Boschi, J.-P. Moliné, and M. Wieczorek (2014), Effect of ray and speed perturbations on ionospheric tomography by over-the-horizon radar: A
General Quality Control (QC) Guidelines for SAM Methods
Learn more about quality control guidelines and recommendations for the analysis of samples using the methods listed in EPA's Selected Analytical Methods for Environmental Remediation and Recovery (SAM).
International Nuclear Information System (INIS)
Chen, Yong; Shanghai Jiao-Tong Univ., Shangai; Chinese Academy of sciences, Beijing
2005-01-01
A general method to uniformly construct exact solutions in terms of special function of nonlinear partial differential equations is presented by means of a more general ansatz and symbolic computation. Making use of the general method, we can successfully obtain the solutions found by the method proposed by Fan (J. Phys. A., 36 (2003) 7009) and find other new and more general solutions, which include polynomial solutions, exponential solutions, rational solutions, triangular periodic wave solution, soliton solutions, soliton-like solutions and Jacobi, Weierstrass doubly periodic wave solutions. A general variable-coefficient two-dimensional KdV equation is chosen to illustrate the method. As a result, some new exact soliton-like solutions are obtained. planets. The numerical results are given in tables. The results are discussed in the conclusion
Directory of Open Access Journals (Sweden)
Li Wang
2017-02-01
Full Text Available The ability to obtain appropriate parameters for an advanced pressurized water reactor (PWR unit model is of great significance for power system analysis. The attributes of that ability include the following: nonlinear relationships, long transition time, intercoupled parameters and difficult obtainment from practical test, posed complexity and difficult parameter identification. In this paper, a model and a parameter identification method for the PWR primary loop system were investigated. A parameter identification process was proposed, using a particle swarm optimization (PSO algorithm that is based on random perturbation (RP-PSO. The identification process included model variable initialization based on the differential equations of each sub-module and program setting method, parameter obtainment through sub-module identification in the Matlab/Simulink Software (Math Works Inc., Natick, MA, USA as well as adaptation analysis for an integrated model. A lot of parameter identification work was carried out, the results of which verified the effectiveness of the method. It was found that the change of some parameters, like the fuel temperature and coolant temperature feedback coefficients, changed the model gain, of which the trajectory sensitivities were not zero. Thus, obtaining their appropriate values had significant effects on the simulation results. The trajectory sensitivities of some parameters in the core neutron dynamic module were interrelated, causing the parameters to be difficult to identify. The model parameter sensitivity could be different, which would be influenced by the model input conditions, reflecting the parameter identifiability difficulty degree for various input conditions.
An iterative method for the canard explosion in general planar systems
DEFF Research Database (Denmark)
Brøns, Morten
2012-01-01
The canard explosion is the change of amplitude and period of a limit cycle born in a Hopf bifurcation in a very narrow parameter interval. The phenomenon is well understood in singular perturbation problems where a small parameter controls the slow/fast dynamics. However, canard explosions are a...... equation, showing that the asymptotics of the method is correct, and on a templator model for a self-replicating system....
Wickman, Jonas; Diehl, Sebastian; Blasius, Bernd; Klausmeier, Christopher A; Ryabov, Alexey B; Brännström, Åke
2017-04-01
Spatial structure can decisively influence the way evolutionary processes unfold. To date, several methods have been used to study evolution in spatial systems, including population genetics, quantitative genetics, moment-closure approximations, and individual-based models. Here we extend the study of spatial evolutionary dynamics to eco-evolutionary models based on reaction-diffusion equations and adaptive dynamics. Specifically, we derive expressions for the strength of directional and stabilizing/disruptive selection that apply both in continuous space and to metacommunities with symmetrical dispersal between patches. For directional selection on a quantitative trait, this yields a way to integrate local directional selection across space and determine whether the trait value will increase or decrease. The robustness of this prediction is validated against quantitative genetics. For stabilizing/disruptive selection, we show that spatial heterogeneity always contributes to disruptive selection and hence always promotes evolutionary branching. The expression for directional selection is numerically very efficient and hence lends itself to simulation studies of evolutionary community assembly. We illustrate the application and utility of the expressions for this purpose with two examples of the evolution of resource utilization. Finally, we outline the domain of applicability of reaction-diffusion equations as a modeling framework and discuss their limitations.
Site investigations. Investigation methods and general execution programme
International Nuclear Information System (INIS)
2001-01-01
at least one deep chemistry-prioritized cored borehole, and start of long-term monitoring of chemical parameters in new selected sampling points. Fracture-filling mineral investigations are initiated during the final phase of the initial site investigation. The transport properties of the rock are estimated mainly on the basis of the hydrogeological and hydrogeochemical description, combined with generic, non-site-specific information. Furthermore, supplementary measurements of groundwater flow are performed in one of the first deep boreholes. In cases where mineralogy and/or groundwater chemistry differs significantly from the generic database, certain time-consuming laboratory investigations such as through diffusion measurements will be initiated. A large number of methods are used to investigate the geology of the site. They can be described in general terms under the headings: geophysics, surface geology, soil geology, bedrock geology, borehole investigations and geodetic measurements. The thermal properties of the rock are determined primarily on the basis of mineral composition and by means of laboratory studies of recovered rock cores. The determination of the transport properties of the rock is based on generic, non-site-specific data, combined with he hydrogeological and hydrogeochemical description of the rock. Laboratory measurements on drill cores and rock material are used to determine/verify sorption values and diffusivities. Diffusion tests and tracer tests in and between boreholes can be used to verify the reasonableness of estimated parameter values. The discipline surface ecosystems includes both the living environment, i.e. animals and plants, and their interactions with the non-living environment, e.g. climate and water. The characterization includes both hydrogeological and hydrogeochemical characterization of soil strata and surface waters and inventory/characterization of flora and fauna
Extending the alias Monte Carlo sampling method to general distributions
International Nuclear Information System (INIS)
Edwards, A.L.; Rathkopf, J.A.; Smidt, R.K.
1991-01-01
The alias method is a Monte Carlo sampling technique that offers significant advantages over more traditional methods. It equals the accuracy of table lookup and the speed of equal probable bins. The original formulation of this method sampled from discrete distributions and was easily extended to histogram distributions. We have extended the method further to applications more germane to Monte Carlo particle transport codes: continuous distributions. This paper presents the alias method as originally derived and our extensions to simple continuous distributions represented by piecewise linear functions. We also present a method to interpolate accurately between distributions tabulated at points other than the point of interest. We present timing studies that demonstrate the method's increased efficiency over table lookup and show further speedup achieved through vectorization. 6 refs., 12 figs., 2 tabs
Quantum theory of anharmonic oscillators - a variational and systematic general approximation method
International Nuclear Information System (INIS)
Yamazaki, K.; Kyoto Univ.
1984-01-01
The paper investigates the energy levels and wavefunctions of an anharmonic oscillator characterised by the potential 1/2ω 2 q 2 +lambdaq 4 . As a lowest-order approximation an extremely simple formula for energy levels, Esub(i)sup(0) = (i+1/2)1/4(3/αsub(i)+αsub(i)), is derived (i being the quantum number of the energy level). This formula reproduces the exact energy levels within an error of about 1%. Systematically higher orders of the present perturbation theory are developed. The present second-order perturbation theory reduces the errors of the lowest-order results by a factor of about 1/5 in general. Various ranges (large, intermediate, small) of (i, lambda) are investigated and compared with the exact values obtained by other workers. For i = 0, 1, even the fourth-order perturbation calculation can be elaborated explicitly, which reduces the error to about 0.01% for any lambda. For small lambda it gives correct numerical coefficients up to lambda 4 terms, as it should. (author)
Generalized WKB method through an appropriate canonical transformation giving an exact invariant
International Nuclear Information System (INIS)
Guyard, J.; Nadeau, A.
1976-01-01
The solution of differential equations of the type d 2 q/dtau 2 +ω 2 (tau)q=0 is of great interest in Physics. Authors often introduce an auxiliary function w, solution of a differential equation which can be solved by a perturbation method. In fact this approach is nothing but an extension of the well known WKB method. Lewis has found an exact invariant of the motion given in closed form in terms in a much easier way. This method can now be used as a natural way of introducing the WKB extension [fr
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...
Site investigations. Investigation methods and general execution programme
Energy Technology Data Exchange (ETDEWEB)
NONE
2001-01-01
SKB plans to commence site investigations in 2002. The present report is a broadening of the general programme and describes the execution of the investigations in so-called discipline-specific programmes for the disciplines geology, rock mechanics, thermal properties, hydrogeology, hydro geochemistry, transport properties of the rock and surface ecosystems. It also describes various technical aspects of drilling, which comprises a significant portion of the investigations. Based on this possible programme, site-specific programmes will then be prepared and adapted to the site-specific questions and conditions on the specific candidate area. The main product of the investigations is a site description. This document presents an integrated description of the site (geosphere and biosphere) and its regional environs with respect to current state and naturally ongoing processes. Provided that the initial site investigation shows that the site is still favourable, complete investigations are commenced. Primary investigation data are stored in SKB's database SICADA. The database's primary data mainly represent parameter values for single measurement points or limited measurement objects. Primary data are subjected to both discipline-specific and integrated analysis and interpretation in order to be able to subdivide the site into suitable geometric units and to assign discipline-specific properties to these geometric units. In this way a three-dimensional, primarily geo scientific, site-descriptive model of rock and ground is built. The site-descriptive model is represented with the aid of both geographic information systems (GIS) and above all SKB's CAD-based computer tool, Rock Visualization System (RVS). RVS is also used as an active instrument in the interpretation of information, especially to be able to judge the relative locations of different deformation zones. When the site has been selected, the investigations are focused on characterizing
Vich, M.; Romero, R.; Richard, E.; Arbogast, P.; Maynard, K.
2010-09-01
Heavy precipitation events occur regularly in the western Mediterranean region. These events often have a high impact on the society due to economic and personal losses. The improvement of the mesoscale numerical forecasts of these events can be used to prevent or minimize their impact on the society. In previous studies, two ensemble prediction systems (EPSs) based on perturbing the model initial and boundary conditions were developed and tested for a collection of high-impact MEDEX cyclonic episodes. These EPSs perturb the initial and boundary potential vorticity (PV) field through a PV inversion algorithm. This technique ensures modifications of all the meteorological fields without compromising the mass-wind balance. One EPS introduces the perturbations along the zones of the three-dimensional PV structure presenting the local most intense values and gradients of the field (a semi-objective choice, PV-gradient), while the other perturbs the PV field over the MM5 adjoint model calculated sensitivity zones (an objective method, PV-adjoint). The PV perturbations are set from a PV error climatology (PVEC) that characterizes typical PV errors in the ECMWF forecasts, both in intensity and displacement. This intensity and displacement perturbation of the PV field is chosen randomly, while its location is given by the perturbation zones defined in each ensemble generation method. Encouraged by the good results obtained by these two EPSs that perturb the PV field, a new approach based on a manual perturbation of the PV field has been tested and compared with the previous results. This technique uses the satellite water vapor (WV) observations to guide the correction of initial PV structures. The correction of the PV field intents to improve the match between the PV distribution and the WV image, taking advantage of the relation between dark and bright features of WV images and PV anomalies, under some assumptions. Afterwards, the PV inversion algorithm is applied to run
Karian, Zaven A
2000-01-01
Throughout the physical and social sciences, researchers face the challenge of fitting statistical distributions to their data. Although the study of statistical modelling has made great strides in recent years, the number and variety of distributions to choose from-all with their own formulas, tables, diagrams, and general properties-continue to create problems. For a specific application, which of the dozens of distributions should one use? What if none of them fit well?Fitting Statistical Distributions helps answer those questions. Focusing on techniques used successfully across many fields, the authors present all of the relevant results related to the Generalized Lambda Distribution (GLD), the Generalized Bootstrap (GB), and Monte Carlo simulation (MC). They provide the tables, algorithms, and computer programs needed for fitting continuous probability distributions to data in a wide variety of circumstances-covering bivariate as well as univariate distributions, and including situations where moments do...
Rubin's CMS reduction method for general state-space models
Kraker, de A.; Campen, van D.H.
1996-01-01
In this paper the Rubin CMS procedure for the reduction and successive coupling of undamped structural subsystems with symmetric system matrices will be modified for the case of general damping. The final coordinate transformation is based on the use of complex (residual) flexibility modes,
The generalized Mayer theorem in the approximating hamiltonian method
International Nuclear Information System (INIS)
Bakulev, A.P.; Bogoliubov, N.N. Jr.; Kurbatov, A.M.
1982-07-01
With the help of the generalized Mayer theorem we obtain the improved inequality for free energies of model and approximating systems, where only ''connected parts'' over the approximating hamiltonian are taken into account. For the concrete system we discuss the problem of convergency of appropriate series of ''connected parts''. (author)
Jacobi-Davidson methods for generalized MHD-eigenvalue problems
J.G.L. Booten; D.R. Fokkema; G.L.G. Sleijpen; H.A. van der Vorst (Henk)
1995-01-01
textabstractA Jacobi-Davidson algorithm for computing selected eigenvalues and associated eigenvectors of the generalized eigenvalue problem $Ax = lambda Bx$ is presented. In this paper the emphasis is put on the case where one of the matrices, say the B-matrix, is Hermitian positive definite. The
Perturbation theory in large order
International Nuclear Information System (INIS)
Bender, C.M.
1978-01-01
For many quantum mechanical models, the behavior of perturbation theory in large order is strikingly simple. For example, in the quantum anharmonic oscillator, which is defined by -y'' + (x 2 /4 + ex 4 /4 - E) y = 0, y ( +- infinity) = 0, the perturbation coefficients, A/sub n/, in the expansion for the ground-state energy, E(ground state) approx. EPSILON/sub n = 0//sup infinity/ A/sub n/epsilon/sup n/, simplify dramatically as n → infinity: A/sub n/ approx. (6/π 3 )/sup 1/2/(-3)/sup n/GAMMA(n + 1/2). Methods of applied mathematics are used to investigate the nature of perturbation theory in quantum mechanics and show that its large-order behavior is determined by the semiclassical content of the theory. In quantum field theory the perturbation coefficients are computed by summing Feynman graphs. A statistical procedure in a simple lambda phi 4 model for summing the set of all graphs as the number of vertices → infinity is presented. Finally, the connection between the large-order behavior of perturbation theory in quantum electrodynamics and the value of α, the charge on the electron, is discussed. 7 figures
Non-perturbative background field calculations
International Nuclear Information System (INIS)
Stephens, C.R.; Department of Physics, University of Utah, Salt Lake City, Utah 84112)
1988-01-01
New methods are developed for calculating one loop functional determinants in quantum field theory. Instead of relying on a calculation of all the eigenvalues of the small fluctuation equation, these techniques exploit the ability of the proper time formalism to reformulate an infinite dimensional field theoretic problem into a finite dimensional covariant quantum mechanical analog, thereby allowing powerful tools such as the method of Jacobi fields to be used advantageously in a field theory setting. More generally the methods developed herein should be extremely valuable when calculating quantum processes in non-constant background fields, offering a utilitarian alternative to the two standard methods of calculation: perturbation theory in the background field or taking the background field into account exactly. The formalism developed also allows for the approximate calculation of covariances of partial differential equations from a knowledge of the solutions of a homogeneous ordinary differential equation. copyright 1988 Academic Press, Inc
Non-perturbative background field calculations
Stephens, C. R.
1988-01-01
New methods are developed for calculating one loop functional determinants in quantum field theory. Instead of relying on a calculation of all the eigenvalues of the small fluctuation equation, these techniques exploit the ability of the proper time formalism to reformulate an infinite dimensional field theoretic problem into a finite dimensional covariant quantum mechanical analog, thereby allowing powerful tools such as the method of Jacobi fields to be used advantageously in a field theory setting. More generally the methods developed herein should be extremely valuable when calculating quantum processes in non-constant background fields, offering a utilitarian alternative to the two standard methods of calculation—perturbation theory in the background field or taking the background field into account exactly. The formalism developed also allows for the approximate calculation of covariances of partial differential equations from a knowledge of the solutions of a homogeneous ordinary differential equation.
Superfield perturbation theory and renormalization
International Nuclear Information System (INIS)
Delbourgo, R.
1975-01-01
The perturbation theory graphs and divergences in super-symmetric Lagrangian models are studied by using superfield techniques. In super PHI 3 -theory very little effort is needed to arrive at the single infinite (wave function) renormalization counterterm, while in PHI 4 -theory the method indicates the counter-Lagrangians needed at the one-loop level and possibly beyond
Factorization theorems in perturbative quantum field theory
International Nuclear Information System (INIS)
Date, G.D.
1982-01-01
This dissertation deals with factorization properties of Green functions and cross-sections in perturbation theory. It consists of two parts. Part I deals with the factorization theorem for the Drell-Yan cross-section. The new approach developed for this purpose is based upon a renormalization group equation with a generalized anomalous dimension. Using an alternate form of factorization for the Drell-Yan cross-section, derived in perturbation theory, a corresponding generalized anomalous dimension is defined, and explicit Feynman rules for its calculation are given. The resultant renormalization group equation is solved by a formal solution which is exhibited explicitly. Simple, explicit calculations are performed which verify Mueller's conjecture for the recovery of the usual parton model results for the Drell-Yan cross-section. The approach developed in this work offers a general framework to analyze the role played by the group factors in the cancellation of the soft divergences, and study their influence on the asymptotic behavior. Part II deals with factorization properties of the Green functions in position space. In this part, a Landau equation analysis is carried out for the singularities of the position space Green fucntions, in perturbation theory with the theta 4 interaction Lagrangian. A physical picture interpretation is given for the corresponding Landau equations. It is used to suggest a light-cone expansion. Using a power counting method, a formal derivation of the light-cone expansion for the two point function, the three point function and a product of two currents, is given without assuming a short distance expansion. Possible extensions to other theories is also considered
Perturbations of the Friedmann universe
International Nuclear Information System (INIS)
Novello, M.; Salim, J.M.; Heintzmann, H.
1982-01-01
Correcting and extending previous work by Hawking (1966) and Olson (1976) the complete set of perturbation equations of a Friedmann Universe in the quasi-Maxwellian form is derived and analized. The formalism is then applied to scalar, vector and tensor perturbations of a phenomenological fluid, which is modelled such as to comprise shear and heat flux. Depending on the equation of state of the background it is found that there exist unstable (growing) modes of purely rotational character. It is further found that (to linear order at least) any vortex perturbation is equivalent to a certain heat flux vector. The equation for the gravitational waves are derived in a completely equivalent method as in case of the propagation, in a curved space-time, of electromagnetic waves in a plasma endowed with some definite constitutive relations. (Author) [pt
Linearly convergent stochastic heavy ball method for minimizing generalization error
Loizou, Nicolas; Richtarik, Peter
2017-01-01
In this work we establish the first linear convergence result for the stochastic heavy ball method. The method performs SGD steps with a fixed stepsize, amended by a heavy ball momentum term. In the analysis, we focus on minimizing the expected loss
James, Andrew J A; Konik, Robert M; Lecheminant, Philippe; Robinson, Neil J; Tsvelik, Alexei M
2018-02-26
We review two important non-perturbative approaches for extracting the physics of low-dimensional strongly correlated quantum systems. Firstly, we start by providing a comprehensive review of non-Abelian bosonization. This includes an introduction to the basic elements of conformal field theory as applied to systems with a current algebra, and we orient the reader by presenting a number of applications of non-Abelian bosonization to models with large symmetries. We then tie this technique into recent advances in the ability of cold atomic systems to realize complex symmetries. Secondly, we discuss truncated spectrum methods for the numerical study of systems in one and two dimensions. For one-dimensional systems we provide the reader with considerable insight into the methodology by reviewing canonical applications of the technique to the Ising model (and its variants) and the sine-Gordon model. Following this we review recent work on the development of renormalization groups, both numerical and analytical, that alleviate the effects of truncating the spectrum. Using these technologies, we consider a number of applications to one-dimensional systems: properties of carbon nanotubes, quenches in the Lieb-Liniger model, 1 + 1D quantum chromodynamics, as well as Landau-Ginzburg theories. In the final part we move our attention to consider truncated spectrum methods applied to two-dimensional systems. This involves combining truncated spectrum methods with matrix product state algorithms. We describe applications of this method to two-dimensional systems of free fermions and the quantum Ising model, including their non-equilibrium dynamics.
James, Andrew J. A.; Konik, Robert M.; Lecheminant, Philippe; Robinson, Neil J.; Tsvelik, Alexei M.
2018-04-01
We review two important non-perturbative approaches for extracting the physics of low-dimensional strongly correlated quantum systems. Firstly, we start by providing a comprehensive review of non-Abelian bosonization. This includes an introduction to the basic elements of conformal field theory as applied to systems with a current algebra, and we orient the reader by presenting a number of applications of non-Abelian bosonization to models with large symmetries. We then tie this technique into recent advances in the ability of cold atomic systems to realize complex symmetries. Secondly, we discuss truncated spectrum methods for the numerical study of systems in one and two dimensions. For one-dimensional systems we provide the reader with considerable insight into the methodology by reviewing canonical applications of the technique to the Ising model (and its variants) and the sine-Gordon model. Following this we review recent work on the development of renormalization groups, both numerical and analytical, that alleviate the effects of truncating the spectrum. Using these technologies, we consider a number of applications to one-dimensional systems: properties of carbon nanotubes, quenches in the Lieb–Liniger model, 1 + 1D quantum chromodynamics, as well as Landau–Ginzburg theories. In the final part we move our attention to consider truncated spectrum methods applied to two-dimensional systems. This involves combining truncated spectrum methods with matrix product state algorithms. We describe applications of this method to two-dimensional systems of free fermions and the quantum Ising model, including their non-equilibrium dynamics.
Generalized dilatation operator method for non-relativistic holography
Energy Technology Data Exchange (ETDEWEB)
Chemissany, Wissam, E-mail: wissam@stanford.edu [Department of Physics and SITP, Stanford University, Stanford, CA 94305 (United States); Papadimitriou, Ioannis, E-mail: ioannis.papadimitriou@csic.es [Instituto de Física Teórica UAM/CSIC, Universidad Autónoma de Madrid, Madrid 28049 (Spain)
2014-10-07
We present a general algorithm for constructing the holographic dictionary for Lifshitz and hyperscaling violating Lifshitz backgrounds for any value of the dynamical exponent z and any value of the hyperscaling violation parameter θ compatible with the null energy condition. The objective of the algorithm is the construction of the general asymptotic solution of the radial Hamilton–Jacobi equation subject to the desired boundary conditions, from which the full dictionary can be subsequently derived. Contrary to the relativistic case, we find that a fully covariant construction of the asymptotic solution for running non-relativistic theories necessitates an expansion in the eigenfunctions of two commuting operators instead of one. This provides a covariant but non-relativistic grading of the expansion, according to the number of time derivatives.
A general method for enclosing solutions of interval linear equations
Czech Academy of Sciences Publication Activity Database
Rohn, Jiří
2012-01-01
Roč. 6, č. 4 (2012), s. 709-717 ISSN 1862-4472 R&D Projects: GA ČR GA201/09/1957; GA ČR GC201/08/J020 Institutional research plan: CEZ:AV0Z10300504 Keywords : interval linear equations * solution set * enclosure * absolute value inequality Subject RIV: BA - General Mathematics Impact factor: 1.654, year: 2012