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
Gravitational Couplings for y-Gop-Planes
Giraldo, Juan Fernando Ospina
2000-01-01
The Wess-Zumino action for y deformed and generalized orientifold planes (yGOp-planes) is presented and one power expantion is realized from which processes that involves yGOp-planes, RR-forms, gravitons and gaugeons, are obtained. Finally non-standard yGOp-planes are showed.
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.
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
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
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
Gravitational Couplings for Gop-Planes and y-Op-Planes
Giraldo, Juan Fernando Ospina
2000-01-01
The Wess-Zumino actions for generalized orientifold planes (GOp-planes) and y-deformed orientifold planes (yOp-planes) are presented and two series power expantions are realized from whiches processes that involves GOp-planes,yOp-planes, RR-forms, gravitons and gaugeons, are obtained. Finally non-standard GOp-planes and y-Op-planes are showed.
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.
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
Early Opening of Seychelles and India: the Gop Basin Revisited
Dyment, J.; Vadakkeyakath, Y.; Bhattacharya, G.
2012-12-01
The deep offshore region located between the India-Pakistan continental margin and the Laxmi Ridge continental sliver contains valuable imprints of the early oceanic opening phase between India and the Seychelles. The acquisition of wide-angle deep seismic data by British scientists in 2003 provided new information about the deep structure and nature of the crust [1,2]. These data complement the large amount of seismic reflection profiles, altimetry-derived gravity and marine magnetic data which allow mapping the structure and determining the age of the oceanic crust [3,4,5]. Although these authors all agree on the oceanic nature of the Gop Basin, they surprisingly differ on the extent of the oceanic crust, the location of the extinct spreading center and the age of the basin. Here we re-evaluate published interpretations of the Gop Basin in light of all available data. The major discrepancy between [1,2,4] and [5] is the location of the extinct spreading center. [1,2,4] place it on an unnamed basement high located at 19°55'N, whereas [5] identify it with the Palitana Ridge at 19°25'N. Checking the location of the basement high of [1,2,4] on the basement isobath map of [3], based on many seismic reflection profiles, reveals that this basement high actually is an isolated feature of limited extent, which at best can be considered as part of a NE-SW trending basement high zone. This basement high locally coincides with a strong positive magnetic anomaly and a narrow gravity anomaly low but the trend of these anomalies is E-W, in contrast to the NE-SW trend of the basement in this area. For these reasons, this basement high probably is not the location of the Gop Basin extinct spreading center. Conversely, on the basement isobath map of [3], the Palitana Ridge appears as a prominent E-W high, located in the middle of a broad E-W graben, the Gop Basin. It extends over 200 km and is flanked on both sides by basement 2000 m deeper. On free air gravity anomaly maps, the
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.
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)
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)
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.
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
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
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
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.
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
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...
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.
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.
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 ...
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
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
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)
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.
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)
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
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
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...
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...
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.
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
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.
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)
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.
Is the Gop rift oceanic? A reevaluation of the Seychelles-India conjugate margins
Guan, Huixin; Werner, Philippe; Geoffroy, Laurent
2016-04-01
Recent studies reevaluated the timing and evolution of the breakup process between the Seychelles continental ridge and India, and the relationship between this evolution and mantle melting associated with the Deccan Igneous Province1,2,3. Those studies, mainly based on gravity and seismic refraction surveys, point that the oceanic domain located between the Seychelles and the Laxmi Ridge (here designed as the Carlsberg Basin) is the youngest oceanic domain between India and the Seychelles. To the East of the Laxmi Ridge, the aborted Gop Rift is considered as an older highly magmatic extensional continental system with magmatism, breakup and oceanic spreading being coeval with or even predating the emplacement of the major pulse of the Deccan trapps. This interpretation on the oceanic nature of the Gop Rift conflicts with other extensive surveys based on magnetic and seismic reflection data4 which suggest that the Gop Rift is an extended syn-magmatic continental domain. In our work based (a) on the existing data, (b) on new deep-seismic reflection surveys (already published by Misra5) down to the Moho and underlying mantle and (c) on new concepts on the geometry of volcanic passive margins, we propose a distinct interpretation of the Seychelles-India system. As proposed by former authors6,7, the Indian margin suffered some continental stretching and thinning before the onset of the Deccan traps during the Mesozoic. Thus continental crust thickness cannot be used easily as a proxy of syn-magmatic stretching-thinning processes or even to infer the presence or not of oceanic-type crust based, solely, on crustal thickness. However, some remarkable features appear on some of the deep penetration seismic lines we studied. We illustrate that the whole Seychelles/India system, before the opening of the present-day "Carlsberg Basin" may simply be regarded as a pair of sub-symmetric conjugate volcanic passive margins (VPMs) with inner and outer SDR wedges dipping towards the
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
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
Jiang, Guangli; Liu, Leibo; Zhu, Wenping; Yin, Shouyi; Wei, Shaojun
2015-09-04
This paper proposes a real-time feature extraction VLSI architecture for high-resolution images based on the accelerated KAZE algorithm. Firstly, a new system architecture is proposed. It increases the system throughput, provides flexibility in image resolution, and offers trade-offs between speed and scaling robustness. The architecture consists of a two-dimensional pipeline array that fully utilizes computational similarities in octaves. Secondly, a substructure (block-serial discrete-time cellular neural network) that can realize a nonlinear filter is proposed. This structure decreases the memory demand through the removal of data dependency. Thirdly, a hardware-friendly descriptor is introduced in order to overcome the hardware design bottleneck through the polar sample pattern; a simplified method to realize rotation invariance is also presented. Finally, the proposed architecture is designed in TSMC 65 nm CMOS technology. The experimental results show a performance of 127 fps in full HD resolution at 200 MHz frequency. The peak performance reaches 181 GOPS and the throughput is double the speed of other state-of-the-art architectures.
Directory of Open Access Journals (Sweden)
Guangli Jiang
2015-09-01
Full Text Available This paper proposes a real-time feature extraction VLSI architecture for high-resolution images based on the accelerated KAZE algorithm. Firstly, a new system architecture is proposed. It increases the system throughput, provides flexibility in image resolution, and offers trade-offs between speed and scaling robustness. The architecture consists of a two-dimensional pipeline array that fully utilizes computational similarities in octaves. Secondly, a substructure (block-serial discrete-time cellular neural network that can realize a nonlinear filter is proposed. This structure decreases the memory demand through the removal of data dependency. Thirdly, a hardware-friendly descriptor is introduced in order to overcome the hardware design bottleneck through the polar sample pattern; a simplified method to realize rotation invariance is also presented. Finally, the proposed architecture is designed in TSMC 65 nm CMOS technology. The experimental results show a performance of 127 fps in full HD resolution at 200 MHz frequency. The peak performance reaches 181 GOPS and the throughput is double the speed of other state-of-the-art architectures.
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.)
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
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)
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)
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)
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
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)
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
Tropospheric products of the second GOP European GNSS reprocessing (1996-2014)
Dousa, Jan; Vaclavovic, Pavel; Elias, Michal
2017-09-01
In this paper, we present results of the second reprocessing of all data from 1996 to 2014 from all stations in International Association of Geodesy (IAG) Reference Frame Sub-Commission for Europe (EUREF) Permanent Network (EPN) as performed at the Geodetic Observatory Pecný (GOP). While the original goal of this research was to ultimately contribute to the realization of a new European Terrestrial Reference System (ETRS), we also aim to provide a new set of GNSS (Global Navigation Satellite System) tropospheric parameter time series with possible applications to climate research. To achieve these goals, we improved a strategy to guarantee the continuity of these tropospheric parameters and we prepared several variants of troposphere modelling. We then assessed all solutions in terms of the repeatability of coordinates as an internal evaluation of applied models and strategies and in terms of zenith tropospheric delays (ZTDs) and horizontal gradients with those of the ERA-Interim numerical weather model (NWM) reanalysis. When compared to the GOP Repro1 (first EUREF reprocessing) solution, the results of the GOP Repro2 (second EUREF reprocessing) yielded improvements of approximately 50 and 25 % in the repeatability of the horizontal and vertical components, respectively, and of approximately 9 % in tropospheric parameters. Vertical repeatability was reduced from 4.14 to 3.73 mm when using the VMF1 mapping function, a priori ZHD (zenith hydrostatic delay), and non-tidal atmospheric loading corrections from actual weather data. Raising the elevation cut-off angle from 3 to 7° and then to 10° increased RMS from coordinates' repeatability, which was then confirmed by independently comparing GNSS tropospheric parameters with the NWM reanalysis. The assessment of tropospheric horizontal gradients with respect to the ERA-Interim revealed a strong sensitivity of estimated gradients to the quality of GNSS antenna tracking performance. This impact was demonstrated at the
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
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)
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...
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
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
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.
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)
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.
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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.
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).
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
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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
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
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)
Application of Multistage Homotopy Perturbation Method to the Chaotic Genesio System
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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.
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.
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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).
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.)
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
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)
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
A discrete homotopy perturbation method for non-linear Schrodinger equation
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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.
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)
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
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...
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
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.
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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.
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)
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
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.
A Newton-Based Extremum Seeking MPPT Method for Photovoltaic Systems with Stochastic Perturbations
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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.
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)
Quality control and validation of the new IOP and GOP ocean products from CryoSat-2
Calafat, Francisco M.; Cipollini, Paolo; Snaith, Helen; Bouffard, Jérôme; Féménias, Pierre; Parrinello, Tommaso
2015-04-01
CryoSat-2 is a huge asset to the oceanographic community, and the exploitation of its data over the ocean represents a welcome additional return for ESA's investment in a mission whose primary objective is to monitor the cryosphere. The CryoSat Project has approved, in the frame of the CryoSat routine phase, the generation of additional ocean products which are available since April 2014. These are the Interim Ocean Products (IOP), normally available within 2-3 day from acquisition, and the Geophysical Ocean Products (GOP), with consolidated orbits and available 30 days after acquisition. To enable their full exploitation by the scientific and operational oceanographic communities, these new ocean products need to be thoroughly quality-controlled and validated. Here we present the results of the scientific quality control performed at the UK National Oceanography Centre (NOC) within the framework of the CryOcean-QCV project. The assessment and quality control of the data is conducted both daily and monthly on a global scale for the L2 IOP and GOP products and includes coverage/completeness, data flow and latency analysis, along-track and crossover analysis, and estimation of error levels and measurement precision. Diagnostics are computed for the sea surface height (SSH), significant wave height (SWH), radar backscatter coefficient (sigma0), wind speed and mispointing parameters. In addition we present an absolute validation of the altimetric SSH for the GOP product against sea level observations from high-quality tide gauges equipped with Global Positioning System (GPS) receivers. Finally, the validation is extended by comparing the SSH from CryoSat-2 with that from other altimetric missions (Envisat, Jason-1 and Jason-2).
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)
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.
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.
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
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)
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.
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.
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)
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.
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
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
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.
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
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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.
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
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.
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
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.
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
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)
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.
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...
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.
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.
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)
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.
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.
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
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.
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.
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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
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.
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.
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)
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)
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
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
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)
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
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
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
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
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
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
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)
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
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.
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
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
Stanek, Magdalena; Dąbrowski, Janusz; Różański, Szymon; Janicki, Bogdan; Długosz, Jacek
2017-06-01
The aim of the present work was to assess the concentrations of metals in the abdominal muscle and exoskeleton of 3-year-old males and 4-year-old females and males of spiny-cheek crayfish (Orconectes limosus) collected from Lake Gopło. A total of 93 males and 35 females were collected in autumn (October 2014). The analyzes of heavy metals were conducted by means of atomic absorption spectroscopy with a PU9100X spectrometer. The content of mercury was determined using AMA 254 mercury analyser. As analyses indicated heavy metals accumulated in the muscle and exoskeleton in the following sequence: Zn > Cu > Pb > Mn > Ni > Hg and Mn > Pb > Zn > Ni > Cu > Hg, respectively. Statistically significant differences between 3- and 4-year-old males were found for all analyzed metals. Gender dependent differences were calculated only for Ni in the muscle tissue and for Mn and Hg in the exoskeleton. In comparison with the study carried out 2 years ago notably higher concentrations of Pb were found in the muscle and a higher content of Zn, Pb, Mn and Ni was determined in the exoskeleton.
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
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.
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)
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.
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
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
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
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
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
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)
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.
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.
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.)
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)
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.
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)
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.
A 60 GOPS/W, -1.8 V to 0.9 V body bias ULP cluster in 28 nm UTBB FD-SOI technology
Rossi, Davide; Pullini, Antonio; Loi, Igor; Gautschi, Michael; Gürkaynak, Frank K.; Bartolini, Andrea; Flatresse, Philippe; Benini, Luca
2016-03-01
Ultra-low power operation and extreme energy efficiency are strong requirements for a number of high-growth application areas, such as E-health, Internet of Things, and wearable Human-Computer Interfaces. A promising approach to achieve up to one order of magnitude of improvement in energy efficiency over current generation of integrated circuits is near-threshold computing. However, frequency degradation due to aggressive voltage scaling may not be acceptable across all performance-constrained applications. Thread-level parallelism over multiple cores can be used to overcome the performance degradation at low voltage. Moreover, enabling the processors to operate on-demand and over a wide supply voltage and body bias ranges allows to achieve the best possible energy efficiency while satisfying a large spectrum of computational demands. In this work we present the first ever implementation of a 4-core cluster fabricated using conventional-well 28 nm UTBB FD-SOI technology. The multi-core architecture we present in this work is able to operate on a wide range of supply voltages starting from 0.44 V to 1.2 V. In addition, the architecture allows a wide range of body bias to be applied from -1.8 V to 0.9 V. The peak energy efficiency 60 GOPS/W is achieved at 0.5 V supply voltage and 0.5 V forward body bias. Thanks to the extended body bias range of conventional-well FD-SOI technology, high energy efficiency can be guaranteed for a wide range of process and environmental conditions. We demonstrate the ability to compensate for up to 99.7% of chips for process variation with only ±0.2 V of body biasing, and compensate temperature variation in the range -40 °C to 120 °C exploiting -1.1 V to 0.8 V body biasing. When compared to leading-edge near-threshold RISC processors optimized for extremely low power applications, the multi-core architecture we propose has 144× more performance at comparable energy efficiency levels. Even when compared to other low-power processors
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)
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.
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)
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)
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.
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
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
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...
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
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.
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.
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
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
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
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
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
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.
Kato expansion in quantum canonical perturbation theory
Energy Technology Data Exchange (ETDEWEB)
Nikolaev, Andrey, E-mail: Andrey.Nikolaev@rdtex.ru [Institute of Computing for Physics and Technology, Protvino, Moscow Region, Russia and RDTeX LTD, Moscow (Russian Federation)
2016-06-15
This work establishes a connection between canonical perturbation series in quantum mechanics and a Kato expansion for the resolvent of the Liouville superoperator. Our approach leads to an explicit expression for a generator of a block-diagonalizing Dyson’s ordered exponential in arbitrary perturbation order. Unitary intertwining of perturbed and unperturbed averaging superprojectors allows for a description of ambiguities in the generator and block-diagonalized Hamiltonian. We compare the efficiency of the corresponding computational algorithm with the efficiencies of the Van Vleck and Magnus methods for high perturbative orders.
Kato expansion in quantum canonical perturbation theory
International Nuclear Information System (INIS)
Nikolaev, Andrey
2016-01-01
This work establishes a connection between canonical perturbation series in quantum mechanics and a Kato expansion for the resolvent of the Liouville superoperator. Our approach leads to an explicit expression for a generator of a block-diagonalizing Dyson’s ordered exponential in arbitrary perturbation order. Unitary intertwining of perturbed and unperturbed averaging superprojectors allows for a description of ambiguities in the generator and block-diagonalized Hamiltonian. We compare the efficiency of the corresponding computational algorithm with the efficiencies of the Van Vleck and Magnus methods for high perturbative orders.
On adiabatic perturbations in the ekpyrotic scenario
International Nuclear Information System (INIS)
Linde, A.; Mukhanov, V.; Vikman, A.
2010-01-01
In a recent paper, Khoury and Steinhardt proposed a way to generate adiabatic cosmological perturbations with a nearly flat spectrum in a contracting Universe. To produce these perturbations they used a regime in which the equation of state exponentially rapidly changed during a short time interval. Leaving aside the singularity problem and the difficult question about the possibility to transmit these perturbations from a contracting Universe to the expanding phase, we will show that the methods used in Khoury are inapplicable for the description of the cosmological evolution and of the process of generation of perturbations in this scenario
Yepez-Martinez, Tochtli; Civitarese, Osvaldo; Hess, Peter O.
2018-02-01
Starting from an algebraic model based on the QCD-Hamiltonian and previously applied to study meson states, we have developed an extension of it in order to explore the structure of baryon states. In developing our approach we have adapted concepts taken from group theory and non-perturbative many-body methods to describe states built from effective quarks and anti-quarks degrees of freedom. As a Hamiltonian we have used the QCD Hamiltonian written in the Coulomb Gauge, and expressed it in terms of effective quark-antiquark, di-quarks and di-antiquark excitations. To gain some insights about the relevant interactions of quarks in hadronic states, the Hamiltonian was approximately diagonalized by mapping quark-antiquark pairs and di-quarks (di-antiquarks) onto phonon states. In dealing with the structure of the vacuum of the theory, color-scalar and color-vector states are introduced to account for ground-state correlations. While the use of a purely color-scalar ground state is an obvious choice, so that colorless hadrons contain at least three quarks, the presence of coupled color-vector pairs in the ground state allows for colorless excitations resulting from the action of color objects upon it.
Arslanturk, Cihat
2011-02-01
Although tapered fins transfer more rate of heat per unit volume, they are not found in every practical application because of the difficulty in manufacturing and fabrications. Therefore, there is a scope to modify the geometry of a constant thickness fin in view of the less difficulty in manufacturing and fabrication as well as betterment of heat transfer rate per unit volume of the fin material. For the better utilization of fin material, it is proposed a modified geometry of new fin with a step change in thickness (SF) in the literature. In the present paper, the homotopy perturbation method has been used to evaluate the temperature distribution within the straight radiating fins with a step change in thickness and variable thermal conductivity. The temperature profile has an abrupt change in the temperature gradient where the step change in thickness occurs and thermal conductivity parameter describing the variation of thermal conductivity has an important role on the temperature profile and the heat transfer rate. The optimum geometry which maximizes the heat transfer rate for a given fin volume has been found. The derived condition of optimality gives an open choice to the designer.
Guo, Yang
2018-01-04
In this communication, an improved perturbative triples correction (T) algorithm for domain based local pair-natural orbital singles and doubles coupled cluster (DLPNO-CCSD) theory is reported. In our previous implementation, the semi-canonical approximation was used and linear scaling was achieved for both the DLPNO-CCSD and (T) parts of the calculation. In this work, we refer to this previous method as DLPNO-CCSD(T0) to emphasize the semi-canonical approximation. It is well-established that the DLPNO-CCSD method can predict very accurate absolute and relative energies with respect to the parent canonical CCSD method. However, the (T0) approximation may introduce significant errors in absolute energies as the triples correction grows up in magnitude. In the majority of cases, the relative energies from (T0) are as accurate as the canonical (T) results of themselves. Unfortunately, in rare cases and in particular for small gap systems, the (T0) approximation breaks down and relative energies show large deviations from the parent canonical CCSD(T) results. To address this problem, an iterative (T) algorithm based on the previous DLPNO-CCSD(T0) algorithm has been implemented [abbreviated here as DLPNO-CCSD(T)]. Using triples natural orbitals to represent the virtual spaces for triples amplitudes, storage bottlenecks are avoided. Various carefully designed approximations ease the computational burden such that overall, the increase in the DLPNO-(T) calculation time over DLPNO-(T0) only amounts to a factor of about two (depending on the basis set). Benchmark calculations for the GMTKN30 database show that compared to DLPNO-CCSD(T0), the errors in absolute energies are greatly reduced and relative energies are moderately improved. The particularly problematic case of cumulene chains of increasing lengths is also successfully addressed by DLPNO-CCSD(T).
Guo, Yang; Riplinger, Christoph; Becker, Ute; Liakos, Dimitrios G.; Minenkov, Yury; Cavallo, Luigi; Neese, Frank
2018-01-01
In this communication, an improved perturbative triples correction (T) algorithm for domain based local pair-natural orbital singles and doubles coupled cluster (DLPNO-CCSD) theory is reported. In our previous implementation, the semi-canonical approximation was used and linear scaling was achieved for both the DLPNO-CCSD and (T) parts of the calculation. In this work, we refer to this previous method as DLPNO-CCSD(T0) to emphasize the semi-canonical approximation. It is well-established that the DLPNO-CCSD method can predict very accurate absolute and relative energies with respect to the parent canonical CCSD method. However, the (T0) approximation may introduce significant errors in absolute energies as the triples correction grows up in magnitude. In the majority of cases, the relative energies from (T0) are as accurate as the canonical (T) results of themselves. Unfortunately, in rare cases and in particular for small gap systems, the (T0) approximation breaks down and relative energies show large deviations from the parent canonical CCSD(T) results. To address this problem, an iterative (T) algorithm based on the previous DLPNO-CCSD(T0) algorithm has been implemented [abbreviated here as DLPNO-CCSD(T)]. Using triples natural orbitals to represent the virtual spaces for triples amplitudes, storage bottlenecks are avoided. Various carefully designed approximations ease the computational burden such that overall, the increase in the DLPNO-(T) calculation time over DLPNO-(T0) only amounts to a factor of about two (depending on the basis set). Benchmark calculations for the GMTKN30 database show that compared to DLPNO-CCSD(T0), the errors in absolute energies are greatly reduced and relative energies are moderately improved. The particularly problematic case of cumulene chains of increasing lengths is also successfully addressed by DLPNO-CCSD(T).
An integral equation for the continuation of perturbative expansions
International Nuclear Information System (INIS)
Ciulli, S.
1984-01-01
It is shown how a procedure for analytic continuation, based on methods of functional analysis, can be used to extend the results of a perturbative calculation to yield nonperturbative information which could not be obtained directly from a perturbative expansion
Bounded Perturbation Regularization for Linear Least Squares Estimation
Ballal, Tarig; Suliman, Mohamed Abdalla Elhag; Al-Naffouri, Tareq Y.
2017-01-01
This paper addresses the problem of selecting the regularization parameter for linear least-squares estimation. We propose a new technique called bounded perturbation regularization (BPR). In the proposed BPR method, a perturbation with a bounded
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.
International Nuclear Information System (INIS)
Mueller, A.H.
1986-03-01
A brief review of some of the recent progress in perturbative QCD is given (heavy quark production, small-x physics, minijets and related topics, classical simulations in high energy reactions, coherence and the string effect)
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
Discrete state perturbation theory via Green's functions
International Nuclear Information System (INIS)
Rubinson, W.
1975-01-01
The exposition of stationary-state perturbation theory via the Green's function method in Goldberger and Watson's Collision Theory is reworked in a way that makes explicit its mathematical basis. It is stressed that the theory consists of the construction of, and manipulations on, a mathematical identity. The perturbation series fall out of the identity almost immediately. The logical status of the method is commented on
Monte Carlo technique for local perturbations in multiplying systems
International Nuclear Information System (INIS)
Bernnat, W.
1974-01-01
The use of the Monte Carlo method for the calculation of reactivity perturbations in multiplying systems due to changes in geometry or composition requires a correlated sampling technique to make such calculations economical or in the case of very small perturbations even feasible. The technique discussed here is suitable for local perturbations. Very small perturbation regions will be treated by an adjoint mode. The perturbation of the source distribution due to the changed system and its reaction on the reactivity worth or other values of interest is taken into account by a fission matrix method. The formulation of the method and its application are discussed. 10 references. (U.S.)
International Nuclear Information System (INIS)
Dasnieres de Veigy, A.; Ouvry, S.; Paris-6 Univ., 75
1992-06-01
The problem of the statistical mechanics of an anyon gas is addressed. A perturbative analysis in the anyonic coupling constant α is reviewed, and the thermodynamical potential is computed at first and second order. An adequate second quantized formalism (field theory at finite temperature) is proposed. At first order in perturbation theory, the results are strikingly simple: only the second virial coefficient close to bosonic statistics is corrected. At second order, however, the complexity of the anyon model appears. One can compute exactly the perturbative correction to each cluster coefficient. However, and contrary to first order, a closed expression for the equation of state seems out of reach. As an illustration, the perturbative expressions of a 3 , a 4 , a 5 and a 6 are given at second order. Finally, using the same formalism, the equation of state of an anyon gas in a constant magnetic field is analyzed at first order in perturbation theory. (K.A.) 16 refs.; 3 figs.; 7 tabs
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)
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)
Cylindrical dust acoustic waves with transverse perturbation
International Nuclear Information System (INIS)
Xue Jukui
2003-01-01
The nonlinear dust acoustic waves in dusty plasmas with the combined effects of bounded cylindrical geometry and the transverse perturbation are studied. Using the perturbation method, a cylindrical Kadomtsev-Petviashvili (CKP) equation that describes the dust acoustic waves is deduced for the first time. A particular solution of this CKP equation is also obtained. It is shown that the dust acoustic solitary waves can exist in the CKP equation
Alternative perturbation approaches in classical mechanics
International Nuclear Information System (INIS)
Amore, Paolo; Raya, Alfredo; Fernandez, Francisco M
2005-01-01
We discuss two alternative methods, based on the Lindstedt-Poincare technique, for the removal of secular terms from the equations of perturbation theory. We calculate the period of an anharmonic oscillator by means of both approaches and show that one of them is more accurate for all values of the coupling constant. We believe that present discussion and comparison may be a suitable exercise for teaching perturbation theory in advanced undergraduate courses on classical mechanics
Preheating curvaton perturbations
International Nuclear Information System (INIS)
Bastero-Gil, M.; Di Clemente, V.; King, S.F.
2005-01-01
We discuss the potentially important role played by preheating in certain variants of the curvaton mechanism in which isocurvature perturbations of a D-flat (and F-flat) direction become converted to curvature perturbations during reheating. We discover that parametric resonance of the isocurvature components amplifies the superhorizon fluctuations by a significant amount. As an example of these effects we develop a particle physics motivated model which involves hybrid inflation with the waterfall field N being responsible for generating the μ term, the right-handed neutrino mass scale, and the Peccei-Quinn symmetry breaking scale. The role of the curvaton field can be played either by usual Higgs field, or the lightest right-handed sneutrino. Our new results show that it is possible to achieve the correct curvature perturbations for initial values of the curvaton fields of order the weak scale. In this model we show that the prediction for the spectral index of the final curvature perturbation only depends on the mass of the curvaton during inflation, where consistency with current observational data requires the ratio of this mass to the Hubble constant to be 0.3
String perturbation theory diverges
International Nuclear Information System (INIS)
Gross, D.J.; Periwal, V.
1988-01-01
We prove that perturbation theory for the bosonic string diverges for arbitrary values of the coupling constant and is not Borel summable. This divergence is independent of the existence of the infinities that occur in the theory due to the presence of tachyons and dilaton tadpoles. We discuss the physical implications of such a divergence
Instantaneous stochastic perturbation theory
International Nuclear Information System (INIS)
Lüscher, Martin
2015-01-01
A form of stochastic perturbation theory is described, where the representative stochastic fields are generated instantaneously rather than through a Markov process. The correctness of the procedure is established to all orders of the expansion and for a wide class of field theories that includes all common formulations of lattice QCD.
Cosmological perturbations in antigravity
Oltean, Marius; Brandenberger, Robert
2014-10-01
We compute the evolution of cosmological perturbations in a recently proposed Weyl-symmetric theory of two scalar fields with oppositely signed conformal couplings to Einstein gravity. It is motivated from the minimal conformal extension of the standard model, such that one of these scalar fields is the Higgs while the other is a new particle, the dilaton, introduced to make the Higgs mass conformally symmetric. At the background level, the theory admits novel geodesically complete cyclic cosmological solutions characterized by a brief period of repulsive gravity, or "antigravity," during each successive transition from a big crunch to a big bang. For simplicity, we consider scalar perturbations in the absence of anisotropies, with potential set to zero and without any radiation. We show that despite the necessarily wrong-signed kinetic term of the dilaton in the full action, these perturbations are neither ghostlike nor tachyonic in the limit of strongly repulsive gravity. On this basis, we argue—pending a future analysis of vector and tensor perturbations—that, with respect to perturbative stability, the cosmological solutions of this theory are viable.
Solan, Eilon; Vieille, Nicolas
2015-01-01
We study irreducible time-homogenous Markov chains with finite state space in discrete time. We obtain results on the sensitivity of the stationary distribution and other statistical quantities with respect to perturbations of the transition matrix. We define a new closeness relation between transition matrices, and use graph-theoretic techniques, in contrast with the matrix analysis techniques previously used.
Scalar cosmological perturbations
International Nuclear Information System (INIS)
Uggla, Claes; Wainwright, John
2012-01-01
Scalar perturbations of Friedmann-Lemaitre cosmologies can be analyzed in a variety of ways using Einstein's field equations, the Ricci and Bianchi identities, or the conservation equations for the stress-energy tensor, and possibly introducing a timelike reference congruence. The common ground is the use of gauge invariants derived from the metric tensor, the stress-energy tensor, or from vectors associated with a reference congruence, as basic variables. Although there is a complication in that there is no unique choice of gauge invariants, we will show that this can be used to advantage. With this in mind our first goal is to present an efficient way of constructing dimensionless gauge invariants associated with the tensors that are involved, and of determining their inter-relationships. Our second goal is to give a unified treatment of the various ways of writing the governing equations in dimensionless form using gauge-invariant variables, showing how simplicity can be achieved by a suitable choice of variables and normalization factors. Our third goal is to elucidate the connection between the metric-based approach and the so-called 1 + 3 gauge-invariant approach to cosmological perturbations. We restrict our considerations to linear perturbations, but our intent is to set the stage for the extension to second-order perturbations. (paper)
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
DEFF Research Database (Denmark)
jora, Renata; Schechter, Joseph; Naeem Shahid, M.
2009-01-01
We study the effects of the perturbation which violates the permutation symmetry of three Majorana neutrinos but preserves the well known (23) interchange symmetry. This is done in the presenceof an arbitrary Majorana phase which serves to insure the degeneracy of the three neutrinos at the unper...... at the unperturbed level....
On the singular perturbations for fractional differential equation.
Atangana, Abdon
2014-01-01
The goal of this paper is to examine the possible extension of the singular perturbation differential equation to the concept of fractional order derivative. To achieve this, we presented a review of the concept of fractional calculus. We make use of the Laplace transform operator to derive exact solution of singular perturbation fractional linear differential equations. We make use of the methodology of three analytical methods to present exact and approximate solution of the singular perturbation fractional, nonlinear, nonhomogeneous differential equation. These methods are including the regular perturbation method, the new development of the variational iteration method, and the homotopy decomposition method.
On the Singular Perturbations for Fractional Differential Equation
Directory of Open Access Journals (Sweden)
Abdon Atangana
2014-01-01
Full Text Available The goal of this paper is to examine the possible extension of the singular perturbation differential equation to the concept of fractional order derivative. To achieve this, we presented a review of the concept of fractional calculus. We make use of the Laplace transform operator to derive exact solution of singular perturbation fractional linear differential equations. We make use of the methodology of three analytical methods to present exact and approximate solution of the singular perturbation fractional, nonlinear, nonhomogeneous differential equation. These methods are including the regular perturbation method, the new development of the variational iteration method, and the homotopy decomposition method.
International Nuclear Information System (INIS)
Mynick, H.E.
1993-01-01
Recent work has developed an analytic theory for the stochastic transport of passing MeV ions due to low-n magnetic perturbations, valid for frequencies from ω = 0 to ω ∼ ω TAE ∼ 100 kHz, and for modes with multiple harmonics and nontrivial radial structure, which predicts stochastic thresholds in agreement with guiding-center (GC) results. Obtaining GC results is time consuming, typically requiring hours of computer time to obtain loss results for a single point in parameter space. Along with earlier theory developed for the stochastic transport of trapped particles in such perturbations, this theory gives the basis for a far more rapid means of numerically assessing energetic ion loss in a given configuration, somewhat akin to the RIPLOS code for rapid evaluation of loss due to TF ripple. The authors present the details of implementing such a code, now being developed. The implementation also raises some further theoretical issues. The currently available stochastic thresholds for passing and trapped particles are not the same, and an analytic understanding of the transition between them awaits development
Application of depletion perturbation theory to fuel cycle burnup analysis
International Nuclear Information System (INIS)
White, J.R.
1979-01-01
Over the past several years static perturbation theory methods have been increasingly used for reactor analysis in lieu of more detailed and costly direct computations. Recently, perturbation methods incorporating time dependence have also received attention, and several authors have demonstrated their applicability to fuel burnup analysis. The objective of the work described here is to demonstrate that a time-dependent perturbation method can be easily and accurately applied to realistic depletion problems
Stability under persistent perturbation by white noise
International Nuclear Information System (INIS)
Kalyakin, L
2014-01-01
Deterministic dynamical system which has an asymptotical stable equilibrium is considered under persistent perturbation by white noise. It is well known that if the perturbation does not vanish in the equilibrium position then there is not Lyapunov's stability. The trajectories of the perturbed system diverge from the equilibrium to arbitrarily large distances with probability 1 in finite time. New concept of stability on a large time interval is discussed. The length of interval agrees the reciprocal quantity of the perturbation parameter. The measure of stability is the expectation of the square distance from the trajectory till the equilibrium position. The method of parabolic equation is applied to both estimate the expectation and prove such stability. The main breakthrough is the barrier function derived for the parabolic equation. The barrier is constructed by using the Lyapunov function of the unperturbed system
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.)
Perturbation calculations with Wilson loop
International Nuclear Information System (INIS)
Peixoto Junior, L.B.
1984-01-01
We present perturbative calculations with the Wilson loop (WL). The dimensional regularization method is used with a special attention concerning to the problem of divergences in the WL expansion in second and fourth orders, in three and four dimensions. We show that the residue in the pole, in 4d, of the fourth order graphs contribution sum is important for the charge renormalization. We compute up to second order the exact expression of the WL, in three-dimensional gauge theories with topological mass as well as its assimptotic behaviour for small and large distances. the author [pt
Nonperturbative perturbation theory
International Nuclear Information System (INIS)
Bender, C.M.
1989-01-01
In this talk we describe a recently proposed graphical perturbative calculational scheme for quantum field theory. The basic idea is to expand in the power of the interaction term. For example, to solve a λφ 4 theory in d-dimensional space-time, we introduce a small parameter δ and consider a λ(φ 2 ) 1+δ field theory. We show how to expand such a theory as a series in powers of δ. The resulting perturbation series appears to have a finite radius of convergence and numerical results for low-dimensional models are good. We have computed the two-point and four-point Green's functions to second order in powers of δ and the 2n-point Green's functions (n>2) to order δ. We explain how to renormalize the theory and show that, to first order in powers of δ, when δ>0 and d≥4 the theory is free. This conclusion remains valid to second order in powers of δ, and we believe that it remains valid to all orders in powers of δ. The new perturbative scheme is consistent with global supersymmetry invariance. We examine a two-dimensional supersymmetric quantum field theory in which we do not know of any other means for doing analytical calculations. We illustrate the power of this new technique by computing the ground-state energy density E to second order in this new perturbation theory. We show that there is a beautiful and delicate cancellation between infinite classes of graphs which leads to the result that E=0. (orig.)
Perturbed asymptotically linear problems
Bartolo, R.; Candela, A. M.; Salvatore, A.
2012-01-01
The aim of this paper is investigating the existence of solutions of some semilinear elliptic problems on open bounded domains when the nonlinearity is subcritical and asymptotically linear at infinity and there is a perturbation term which is just continuous. Also in the case when the problem has not a variational structure, suitable procedures and estimates allow us to prove that the number of distinct crtitical levels of the functional associated to the unperturbed problem is "stable" unde...
Twisting perturbed parafermions
Directory of Open Access Journals (Sweden)
A.V. Belitsky
2017-07-01
Full Text Available The near-collinear expansion of scattering amplitudes in maximally supersymmetric Yang–Mills theory at strong coupling is governed by the dynamics of stings propagating on the five sphere. The pentagon transitions in the operator product expansion which systematize the series get reformulated in terms of matrix elements of branch-point twist operators in the two-dimensional O(6 nonlinear sigma model. The facts that the latter is an asymptotically free field theory and that there exists no local realization of twist fields prevents one from explicit calculation of their scaling dimensions and operator product expansion coefficients. This complication is bypassed making use of the equivalence of the sigma model to the infinite-level limit of WZNW models perturbed by current–current interactions, such that one can use conformal symmetry and conformal perturbation theory for systematic calculations. Presently, to set up the formalism, we consider the O(3 sigma model which is reformulated as perturbed parafermions.
Qualitative reasoning for biological network inference from systematic perturbation experiments.
Badaloni, Silvana; Di Camillo, Barbara; Sambo, Francesco
2012-01-01
The systematic perturbation of the components of a biological system has been proven among the most informative experimental setups for the identification of causal relations between the components. In this paper, we present Systematic Perturbation-Qualitative Reasoning (SPQR), a novel Qualitative Reasoning approach to automate the interpretation of the results of systematic perturbation experiments. Our method is based on a qualitative abstraction of the experimental data: for each perturbation experiment, measured values of the observed variables are modeled as lower, equal or higher than the measurements in the wild type condition, when no perturbation is applied. The algorithm exploits a set of IF-THEN rules to infer causal relations between the variables, analyzing the patterns of propagation of the perturbation signals through the biological network, and is specifically designed to minimize the rate of false positives among the inferred relations. Tested on both simulated and real perturbation data, SPQR indeed exhibits a significantly higher precision than the state of the art.
On algebraically special perturbations of black holes
International Nuclear Information System (INIS)
Chandrasekhar, S.
1984-01-01
Algebraically special perturbations of black holes excite gravitational waves that are either purely ingoing or purely outgoing. Solutions, appropriate to such perturbations of the Kerr, the Schwarzschild, and the Reissner-Nordstroem black-holes, are obtained in explicit forms by different methods. The different methods illustrate the remarkable inner relations among different facets of the mathematical theory. In the context of the Kerr black-hole they derive from the different ways in which the explicit value of the Starobinsky constant emerges, and in the context of the Schwarzschild and the Reissner-Nordstroem black-holes they derive from the potential barriers surrounding them belonging to a special class. (author)
Non-Perturbative Renormalization
Mastropietro, Vieri
2008-01-01
The notion of renormalization is at the core of several spectacular achievements of contemporary physics, and in the last years powerful techniques have been developed allowing to put renormalization on a firm mathematical basis. This book provides a self-consistent and accessible introduction to the sophisticated tools used in the modern theory of non-perturbative renormalization, allowing an unified and rigorous treatment of Quantum Field Theory, Statistical Physics and Condensed Matter models. In particular the first part of this book is devoted to Constructive Quantum Field Theory, providi
Perturbative quantum chromodynamics
1989-01-01
This book will be of great interest to advanced students and researchers in the area of high energy theoretical physics. Being the most complete and updated review volume on Perturbative QCD, it serves as an extremely useful textbook or reference book. Some of the reviews in this volume are the best that have been written on the subject anywhere. Contents: Factorization of Hard Processes in QCD (J C Collins, D E Soper & G Sterman); Exclusive Processes in Quantum Chromodynamics (S J Brodsky & G P Lepage); Coherence and Physics of QCD Jets (Yu L Dokshitzer, V A Khoze & S I Troyan); Pomeron in Qu
Khoshgoftar, M. J.; Mirzaali, M. J.; Rahimi, G. H.
2015-11-01
Recently application of functionally graded materials(FGMs) have attracted a great deal of interest. These materials are composed of various materials with different micro-structures which can vary spatially in FGMs. Such composites with varying thickness and non-uniform pressure can be used in the aerospace engineering. Therefore, analysis of such composite is of high importance in engineering problems. Thermoelastic analysis of functionally graded cylinder with variable thickness under non-uniform pressure is considered. First order shear deformation theory and total potential energy approach is applied to obtain the governing equations of non-homogeneous cylinder. Considering the inner and outer solutions, perturbation series are applied to solve the governing equations. Outer solution for out of boundaries and more sensitive variable in inner solution at the boundaries are considered. Combining of inner and outer solution for near and far points from boundaries leads to high accurate displacement field distribution. The main aim of this paper is to show the capability of matched asymptotic solution for different non-homogeneous cylinders with different shapes and different non-uniform pressures. The results can be used to design the optimum thickness of the cylinder and also some properties such as high temperature residence by applying non-homogeneous material.
Reddy, M Rami; Erion, Mark D
2009-12-01
Molecular dynamics (MD) simulations in conjunction with thermodynamic perturbation approach was used to calculate relative solvation free energies of five pairs of small molecules, namely; (1) methanol to ethane, (2) acetone to acetamide, (3) phenol to benzene, (4) 1,1,1 trichloroethane to ethane, and (5) phenylalanine to isoleucine. Two studies were performed to evaluate the dependence of the convergence of these calculations on MD simulation length and starting configuration. In the first study, each transformation started from the same well-equilibrated configuration and the simulation length was varied from 230 to 2,540 ps. The results indicated that for transformations involving small structural changes, a simulation length of 860 ps is sufficient to obtain satisfactory convergence. In contrast, transformations involving relatively large structural changes, such as phenylalanine to isoleucine, require a significantly longer simulation length (>2,540 ps) to obtain satisfactory convergence. In the second study, the transformation was completed starting from three different configurations and using in each case 860 ps of MD simulation. The results from this study suggest that performing one long simulation may be better than averaging results from three different simulations using a shorter simulation length and three different starting configurations.
Stepping stability: effects of sensory perturbation
Directory of Open Access Journals (Sweden)
Krebs David E
2005-05-01
Full Text Available Abstract Background Few tools exist for quantifying locomotor stability in balance impaired populations. The objective of this study was to develop and evaluate a technique for quantifying stability of stepping in healthy people and people with peripheral (vestibular hypofunction, VH and central (cerebellar pathology, CB balance dysfunction by means a sensory (auditory perturbation test. Methods Balance impaired and healthy subjects performed a repeated bench stepping task. The perturbation was applied by suddenly changing the cadence of the metronome (100 beat/min to 80 beat/min at a predetermined time (but unpredictable by the subject during the trial. Perturbation response was quantified by computing the Euclidian distance, expressed as a fractional error, between the anterior-posterior center of gravity attractor trajectory before and after the perturbation was applied. The error immediately after the perturbation (Emax, error after recovery (Emin and the recovery response (Edif were documented for each participant, and groups were compared with ANOVA. Results Both balance impaired groups exhibited significantly higher Emax (p = .019 and Emin (p = .028 fractional errors compared to the healthy (HE subjects, but there were no significant differences between CB and VH groups. Although response recovery was slower for CB and VH groups compared to the HE group, the difference was not significant (p = .051. Conclusion The findings suggest that individuals with balance impairment have reduced ability to stabilize locomotor patterns following perturbation, revealing the fragility of their impairment adaptations and compensations. These data suggest that auditory perturbations applied during a challenging stepping task may be useful for measuring rehabilitation outcomes.
Acoustic anisotropic wavefields through perturbation theory
Alkhalifah, Tariq Ali
2013-09-01
Solving the anisotropic acoustic wave equation numerically using finite-difference methods introduces many problems and media restriction requirements, and it rarely contributes to the ability to resolve the anisotropy parameters. Among these restrictions are the inability to handle media with η<0 and the presence of shear-wave artifacts in the solution. Both limitations do not exist in the solution of the elliptical anisotropic acoustic wave equation. Using perturbation theory in developing the solution of the anisotropic acoustic wave equation allows direct access to the desired limitation-free solutions, that is, solutions perturbed from the elliptical anisotropic background medium. It also provides a platform for parameter estimation because of the ability to isolate the wavefield dependency on the perturbed anisotropy parameters. As a result, I derive partial differential equations that relate changes in the wavefield to perturbations in the anisotropy parameters. The solutions of the perturbation equations represented the coefficients of a Taylor-series-type expansion of the wavefield as a function of the perturbed parameter, which is in this case η or the tilt of the symmetry axis. The expansion with respect to the symmetry axis allows use of an acoustic transversely isotropic media with a vertical symmetry axis (VTI) kernel to estimate the background wavefield and the corresponding perturbation coefficients. The VTI extrapolation kernel is about one-fourth the cost of the transversely isotropic model with a tilt in the symmetry axis kernel. Thus, for a small symmetry axis tilt, the cost of migration using a first-order expansion can be reduced. The effectiveness of the approach was demonstrated on the Marmousi model.
Non-perturbative versus perturbative renormalization of lattice operators
International Nuclear Information System (INIS)
Goeckeler, M.; Technische Hochschule Aachen; Horsley, R.; Ilgenfritz, E.M.; Oelrich, H.; Forschungszentrum Juelich GmbH; Schierholz, G.; Forschungszentrum Juelich GmbH; Perlt, H.; Schiller, A.; Rakow, P.
1995-09-01
Our objective is to compute the moments of the deep-inelastic structure functions of the nucleon on the lattice. A major source of uncertainty is the renormalization of the lattice operators that enter the calculation. In this talk we compare the renormalization constants of the most relevant twist-two bilinear quark operators which we have computed non-perturbatively and perturbatively to one loop order. Furthermore, we discuss the use of tadpole improved perturbation theory. (orig.)
Physico-chemical properties of perturbed water: facts and enigmas
Vittorio Elia
2012-01-01
Background The study of extremely diluted and agitated substances and solutions is strictly linked with the analysis of properties of water perturbed using different systems. This study is about the determination of the physical-chemical parameters of water, after the perturbations described. Methods The perturbed water was obtained using the three different protocols: Ã‚Â· EDS (Extremely Diluted Solutions). Obtained through an iterative process of ...
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)
Perturbation studies on KAHTER
Energy Technology Data Exchange (ETDEWEB)
Rueckert, M.; Jonas, H.; Neef, R. D.
1974-10-15
The paper describes experimental and analytical results by both transport theory and diffusion theory calculations of perturbation tests in the KAHTER pebble bed critical experiment. The fission-weighted adjoint flux is measured from in-core detector responses by introducing a Cf-source into the core. Adjoint-weighted reactivities are calculated and compared to reactivity measurements for the introduction of a fuel and graphite pebble onto the top of the critical pile, the central rod worth, and the effect of replacing B4C with varying amounts of HfC in the central rod. In addition, analytical studies were made of the sensitivity of criticality to the fuel to graphite pebble ratio as measured in tests and of the effect of the upper void cavity as simulated in tests by placing cadmium layer across the top of the pebble pile to force a zero flux boundary condition.
Perturbation theory with instantons
International Nuclear Information System (INIS)
Carruthers, P.; Pinsky, S.S.; Zachariasen, F.
1977-05-01
''Perturbation theory'' rules are developed for calculating the effect of instantons in a pure Yang-Mills theory with no fermions, in the ''dilute gas'' approximation in which the N-instanton solution is assumed to be the sum of N widely separated one-instanton solutions. These rules are then used to compute the gluon propagator and proper vertex function including all orders of the instanton interaction but only to lowest order in the gluon coupling. It is to be expected that such an approximation is valid only for momenta q larger than the physical mass μ. The result is that in this regime instantons cause variations in the propagator and vertex of the form (μ 2 /q 2 )/sup -8π 2 b/ where b is the coefficient in the expansion of the β function: β = bg 3 +...
Non-perturbative QCD and hadron physics
International Nuclear Information System (INIS)
Cobos-Martínez, J J
2016-01-01
A brief exposition of contemporary non-perturbative methods based on the Schwinger-Dyson (SDE) and Bethe-Salpeter equations (BSE) of Quantum Chromodynamics (QCD) and their application to hadron physics is given. These equations provide a non-perturbative continuum formulation of QCD and are a powerful and promising tool for the study of hadron physics. Results on some properties of hadrons based on this approach, with particular attention to the pion distribution amplitude, elastic, and transition electromagnetic form factors, and their comparison to experimental data are presented. (paper)
Death to perturbative QCD in exclusive processes?
Energy Technology Data Exchange (ETDEWEB)
Eckardt, R.; Hansper, J.; Gari, M.F. [Institut fuer Theoretische Physik, Bochum (Germany)
1994-04-01
The authors discuss the question of whether perturbative QCD is applicable in calculations of exclusive processes at available momentum transfers. They show that the currently used method of determining hadronic quark distribution amplitudes from QCD sum rules yields wave functions which are completely undetermined because the polynomial expansion diverges. Because of the indeterminacy of the wave functions no statement can be made at present as to whether perturbative QCD is valid. The authors emphasize the necessity of a rigorous discussion of the subject and the importance of experimental data in the range of interest.
Perturbative and nonperturbative renormalization in lattice QCD
Energy Technology Data Exchange (ETDEWEB)
Goeckeler, M. [Regensburg Univ. (Germany). Institut fuer Theoretische Physik; Horsley, R. [University of Edinburgh (United Kingdom). School of Physics and Astronomy; Perlt, H. [Leipzig Univ. (DE). Institut fuer Theoretische Physik] (and others)
2010-03-15
We investigate the perturbative and nonperturbative renormalization of composite operators in lattice QCD restricting ourselves to operators that are bilinear in the quark fields (quark-antiquark operators). These include operators which are relevant to the calculation of moments of hadronic structure functions. The nonperturbative computations are based on Monte Carlo simulations with two flavors of clover fermions and utilize the Rome-Southampton method also known as the RI-MOM scheme. We compare the results of this approach with various estimates from lattice perturbation theory, in particular with recent two-loop calculations. (orig.)
Perturbations of normally solvable nonlinear operators, I
Directory of Open Access Journals (Sweden)
William O. Ray
1985-01-01
Full Text Available Let X and Y be Banach spaces and let ℱ and be Gateaux differentiable mappings from X to Y In this note we study when the operator ℱ+ is surjective for sufficiently small perturbations of a surjective operator ℱ The methods extend previous results in the area of normal solvability for nonlinear operators.
MCNP perturbation technique for criticality analysis
International Nuclear Information System (INIS)
McKinney, G.W.; Iverson, J.L.
1995-01-01
The differential operator perturbation technique has been incorporated into the Monte Carlo N-Particle transport code MCNP and will become a standard feature of future releases. This feature includes first and/or second order terms of the Taylor Series expansion for response perturbations related to cross-section data (i.e., density, composition, etc.). Criticality analyses can benefit from this technique in that predicted changes in the track-length tally estimator of K eff may be obtained for multiple perturbations in a single run. A key advantage of this method is that a precise estimate of a small change in response (i.e., < 1%) is easily obtained. This technique can also offer acceptable accuracy, to within a few percent, for up to 20-30% changes in a response
Gravitational perturbation theory and synchrotron radiation
Energy Technology Data Exchange (ETDEWEB)
Breuer, R A [Max-Planck-Institut fuer Physik und Astrophysik, Muenchen (F.R. Germany). Inst. fuer Astrophysik
1975-01-01
This article presents methods and results for a gravitational perturbation theory which treats massless fields as linearized perturbations of an arbitrary gravitational vacuum background spacetime. The formalism is outlined for perturbations of type (22) spacetimes. As an application, high-frequency radiation emitted by particles moving approximately on relativistic circular geodesic orbits is computed. More precisely, the test particle assumption is made; throughout it is therefore assumed that the reaction of the radiation on the particle motion is negligible. In particular, these orbits are studied in the gravitational field of a spherically symmetric (Schwarzschild-) black hole as well as of a rotating (Kerr-) black hole. In this model, the outgoing radiation is highly focussed and of much higher fequency than the orbital frequency, i.e. one is dealing with 'gravitational synchrotron radiation'.
Gribov ambiguity, perturbation theory, and confinement
International Nuclear Information System (INIS)
Greensite, J.P.
1978-01-01
The generating functional proposed for gauge theories by Bender, Eguchi, and Pagels (BEP) is shown to be equivalent to a truncated form of the functional integral, in which only one field configuration from each gauge-equivalent Gribov set contributes to the functional integration. The standard perturbation technique provides a method of realizing this truncation condition. It is shown that any gauge-covariant quantity (such as the quark N-point functions), evaluated by perturbating around a field configuration gauge-equivalent to A = 0, is related by a gauge transformation to the same quantity evaluated perturbatively around the trivial vacuum. It follows that, contrary to the conclusion of BEP, the existence of degeneracies in the Coulomb gauge-fixing condition (the Gribov ambiguity) is not directly related to the physics of confinement
Jonker, Jan B.; van Essen, T.G.; van Essen, T.G.
1997-01-01
A finite element based method has been developed for computing time-averaged fluid-induced radial excitation forces and rotor dynamic forces on a two-dimensional centrifugal impeller rotating and whirling in a volute casing. In this method potential flow theory is used, which implies the assumption
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
Energy Technology Data Exchange (ETDEWEB)
Guo, Yang; Sivalingam, Kantharuban; Neese, Frank, E-mail: Frank.Neese@cec.mpg.de [Max Planck Institut für Chemische Energiekonversion, Stiftstr. 34-36, D-45470 Mülheim an der Ruhr (Germany); Valeev, Edward F. [Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24014 (United States)
2016-03-07
Multi-reference (MR) electronic structure methods, such as MR configuration interaction or MR perturbation theory, can provide reliable energies and properties for many molecular phenomena like bond breaking, excited states, transition states or magnetic properties of transition metal complexes and clusters. However, owing to their inherent complexity, most MR methods are still too computationally expensive for large systems. Therefore the development of more computationally attractive MR approaches is necessary to enable routine application for large-scale chemical systems. Among the state-of-the-art MR methods, second-order N-electron valence state perturbation theory (NEVPT2) is an efficient, size-consistent, and intruder-state-free method. However, there are still two important bottlenecks in practical applications of NEVPT2 to large systems: (a) the high computational cost of NEVPT2 for large molecules, even with moderate active spaces and (b) the prohibitive cost for treating large active spaces. In this work, we address problem (a) by developing a linear scaling “partially contracted” NEVPT2 method. This development uses the idea of domain-based local pair natural orbitals (DLPNOs) to form a highly efficient algorithm. As shown previously in the framework of single-reference methods, the DLPNO concept leads to an enormous reduction in computational effort while at the same time providing high accuracy (approaching 99.9% of the correlation energy), robustness, and black-box character. In the DLPNO approach, the virtual space is spanned by pair natural orbitals that are expanded in terms of projected atomic orbitals in large orbital domains, while the inactive space is spanned by localized orbitals. The active orbitals are left untouched. Our implementation features a highly efficient “electron pair prescreening” that skips the negligible inactive pairs. The surviving pairs are treated using the partially contracted NEVPT2 formalism. A detailed
Synchronizing the noise-perturbed Lue chaotic system
International Nuclear Information System (INIS)
Zhang Yan; Chen Shihua; Zhou Hong
2009-01-01
In this paper, synchronization between unidirectionally coupled Lue chaotic systems with noise perturbation is investigated theoretically and numerically. Sufficient conditions of synchronization between these noise-perturbed systems are established by means of the so-called sliding mode control method. Some numerical simulations are also included to visualize the effectiveness and the feasibility of the developed approach.
International Nuclear Information System (INIS)
Harada, Masayasu
2009-01-01
Chiral perturbation theory has been used for great number of phenomenological analyses in low energy QCD as well as the lattice QCD analyses since the creation of the theory by Weinberg in 1979 followed by its consolidation by Gasser and Leutwyler in 1984 and 85. The theory is now the highly established one as the approach based on the effective field theory to search for Green function including quantum correlations in the frame of the systematic expansion technique using Lagrangian which includes all of the terms allowed by the symmetry. This review has been intended to describe how systematically physical quantities are calculated in the framework of the chiral symmetry. Consequently many of the various phenomenological analyses are not taken up here for which other reports are to be referred. Further views are foreseen to be developed based on the theory in addition to numbers of results reported up to the present. Finally π-π scattering is taken up to discuss to what energy scale the theory is available. (S. Funahashi)
International Nuclear Information System (INIS)
Fabris, J.D.
1977-01-01
The electric quadrupolar interaction in some hafnium complexes, measured at the metal nucleus level is studied. For that purpose, the technique of γ-γ perturbed angular correlation is used: the frequencies of quadrupolar interaction are compared with some hafnium α-hydroxicarboxilates, namely glycolate, lactate, mandelate and benzylate; the influence of the temperature on the quadrupolar coupling on the hafnium tetramandelate is studied; finally, the effects associated with the capture of thermal neutrons by hafnium tetramandelate are examined locally at the nuclear level. The first group of results shows significant differences in a series of complexes derived from glycolic acid. On the other hand, the substitution of the protons in hafnium tetramandelate structure by some alkaline cations permits to verify a correlation between the variations in the quadrupolar coupling and the electronegativities of the substituent elements. Measurements at high temperatures show that this complex is thermally stable at 100 and 150 0 C. It is possible to see the appearance of two distinct sites for the probe nucleus, after heating the sample at 100 0 C for prolonged time. This fact is attributed to a probable interconversion among the postulated structural isomers for the octacoordinated compounds. Finally, measurements of angular correlation on the irradiated complex show that there is an effective destruction of the target molecule by neutron capture [pt
Perturbative quantum chromodynamics
International Nuclear Information System (INIS)
Brodsky, S.J.
1979-12-01
The application of QCD to hadron dynamics at short distances, where asymptotic freedom allows a systematic perturbative approach, is addressed. The main theme of the approach is to incorporate systematically the effects of the hadronic wave function in large momentum transfer exclusive and inclusive reactions. Although it is conventional to treat the hadron as a classical source of on-shell quarks, there are important dynamical effects due to hadronic constituent structure which lead to a broader testing ground for QCD. QCD predictions are discussed for exclusive processes and form factors at large momentum transfer in which the short-distance behavior and the finite compositeness of the hadronic wave functions play crucial roles. Many of the standard tests of QCD are reviewed including the predictions for R = sigma/sub e + e - →had//sigma/sub e + e - →μ + μ - /, the structure functions of hadrons and photons, jet phenomena, and the QCD corrections to deep inelastic processes. The exclusive-inclusive connection in QCD, the effects of power-law scale-breaking contributions, and the important role of the available energy in controlling logarithmic scale violations are also discussed. 150 references, 44 figures
Lattice regularized chiral perturbation theory
International Nuclear Information System (INIS)
Borasoy, Bugra; Lewis, Randy; Ouimet, Pierre-Philippe A.
2004-01-01
Chiral perturbation theory can be defined and regularized on a spacetime lattice. A few motivations are discussed here, and an explicit lattice Lagrangian is reviewed. A particular aspect of the connection between lattice chiral perturbation theory and lattice QCD is explored through a study of the Wess-Zumino-Witten term
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.
Propagation of Ion Acoustic Perturbations
DEFF Research Database (Denmark)
Pécseli, Hans
1975-01-01
Equations describing the propagation of ion acoustic perturbations are considered, using the assumption that the electrons are Boltzman distributed and isothermal at all times. Quasi-neutrality is also considered.......Equations describing the propagation of ion acoustic perturbations are considered, using the assumption that the electrons are Boltzman distributed and isothermal at all times. Quasi-neutrality is also considered....
Continual integral in perturbation theory
International Nuclear Information System (INIS)
Slavnov, A.A.
1975-01-01
It is shown that all results obtained by means of continual integration within the framework of perturbation theory are completely equivalent to those obtained by the usual diagram technique and are therfore just as rigorous. A rigorous justification is given for the rules for operating with continual integrals in perturbation theory. (author)
Bozkaya, Uǧur; Turney, Justin M.; Yamaguchi, Yukio; Schaefer, Henry F.; Sherrill, C. David
2011-09-01
Using a Lagrangian-based approach, we present a more elegant derivation of the equations necessary for the variational optimization of the molecular orbitals (MOs) for the coupled-cluster doubles (CCD) method and second-order Møller-Plesset perturbation theory (MP2). These orbital-optimized theories are referred to as OO-CCD and OO-MP2 (or simply "OD" and "OMP2" for short), respectively. We also present an improved algorithm for orbital optimization in these methods. Explicit equations for response density matrices, the MO gradient, and the MO Hessian are reported both in spin-orbital and closed-shell spin-adapted forms. The Newton-Raphson algorithm is used for the optimization procedure using the MO gradient and Hessian. Further, orbital stability analyses are also carried out at correlated levels. The OD and OMP2 approaches are compared with the standard MP2, CCD, CCSD, and CCSD(T) methods. All these methods are applied to H2O, three diatomics, and the O_4^+ molecule. Results demonstrate that the CCSD and OD methods give nearly identical results for H2O and diatomics; however, in symmetry-breaking problems as exemplified by O_4^+, the OD method provides better results for vibrational frequencies. The OD method has further advantages over CCSD: its analytic gradients are easier to compute since there is no need to solve the coupled-perturbed equations for the orbital response, the computation of one-electron properties are easier because there is no response contribution to the particle density matrices, the variational optimized orbitals can be readily extended to allow inactive orbitals, it avoids spurious second-order poles in its response function, and its transition dipole moments are gauge invariant. The OMP2 has these same advantages over canonical MP2, making it promising for excited state properties via linear response theory. The quadratically convergent orbital-optimization procedure converges quickly for OMP2, and provides molecular properties that
Characterizing heterogeneous cellular responses to perturbations.
Slack, Michael D; Martinez, Elisabeth D; Wu, Lani F; Altschuler, Steven J
2008-12-09
Cellular populations have been widely observed to respond heterogeneously to perturbation. However, interpreting the observed heterogeneity is an extremely challenging problem because of the complexity of possible cellular phenotypes, the large dimension of potential perturbations, and the lack of methods for separating meaningful biological information from noise. Here, we develop an image-based approach to characterize cellular phenotypes based on patterns of signaling marker colocalization. Heterogeneous cellular populations are characterized as mixtures of phenotypically distinct subpopulations, and responses to perturbations are summarized succinctly as probabilistic redistributions of these mixtures. We apply our method to characterize the heterogeneous responses of cancer cells to a panel of drugs. We find that cells treated with drugs of (dis-)similar mechanism exhibit (dis-)similar patterns of heterogeneity. Despite the observed phenotypic diversity of cells observed within our data, low-complexity models of heterogeneity were sufficient to distinguish most classes of drug mechanism. Our approach offers a computational framework for assessing the complexity of cellular heterogeneity, investigating the degree to which perturbations induce redistributions of a limited, but nontrivial, repertoire of underlying states and revealing functional significance contained within distinct patterns of heterogeneous responses.
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.
Word Embedding Perturbation for Sentence Classification
Zhang, Dongxu; Yang, Zhichao
2018-01-01
In this technique report, we aim to mitigate the overfitting problem of natural language by applying data augmentation methods. Specifically, we attempt several types of noise to perturb the input word embedding, such as Gaussian noise, Bernoulli noise, and adversarial noise, etc. We also apply several constraints on different types of noise. By implementing these proposed data augmentation methods, the baseline models can gain improvements on several sentence classification tasks.
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
Chiral perturbation theory with nucleons
International Nuclear Information System (INIS)
Meissner, U.G.
1991-09-01
I review the constraints posed on the interactions of pions, nucleons and photons by the spontaneously broken chiral symmetry of QCD. The framework to perform these calculations, chiral perturbation theory, is briefly discussed in the meson sector. The method is a simultaneous expansion of the Greens functions in powers of external moments and quark masses around the massless case, the chiral limit. To perform this expansion, use is made of a phenomenological Lagrangian which encodes the Ward-identities and pertinent symmetries of QCD. The concept of chiral power counting is introduced. The main part of the lectures of consists in describing how to include baryons (nucleons) and how the chiral structure is modified by the fact that the nucleon mass in the chiral limit does not vanish. Particular emphasis is put on working out applications to show the strengths and limitations of the methods. Some processes which are discussed are threshold photopion production, low-energy compton scattering off nucleons, πN scattering and the σ-term. The implications of the broken chiral symmetry on the nuclear forces are briefly described. An alternative approach, in which the baryons are treated as very heavy fields, is touched upon
Non-Perturbative Asymptotic Improvement of Perturbation Theory and Mellin-Barnes Representation
Directory of Open Access Journals (Sweden)
Samuel Friot
2010-10-01
Full Text Available Using a method mixing Mellin-Barnes representation and Borel resummation we show how to obtain hyperasymptotic expansions from the (divergent formal power series which follow from the perturbative evaluation of arbitrary ''N-point'' functions for the simple case of zero-dimensional φ4 field theory. This hyperasymptotic improvement appears from an iterative procedure, based on inverse factorial expansions, and gives birth to interwoven non-perturbative partial sums whose coefficients are related to the perturbative ones by an interesting resurgence phenomenon. It is a non-perturbative improvement in the sense that, for some optimal truncations of the partial sums, the remainder at a given hyperasymptotic level is exponentially suppressed compared to the remainder at the preceding hyperasymptotic level. The Mellin-Barnes representation allows our results to be automatically valid for a wide range of the phase of the complex coupling constant, including Stokes lines. A numerical analysis is performed to emphasize the improved accuracy that this method allows to reach compared to the usual perturbative approach, and the importance of hyperasymptotic optimal truncation schemes.
Perturbative Gaussianizing transforms for cosmological fields
Hall, Alex; Mead, Alexander
2018-01-01
Constraints on cosmological parameters from large-scale structure have traditionally been obtained from two-point statistics. However, non-linear structure formation renders these statistics insufficient in capturing the full information content available, necessitating the measurement of higher order moments to recover information which would otherwise be lost. We construct quantities based on non-linear and non-local transformations of weakly non-Gaussian fields that Gaussianize the full multivariate distribution at a given order in perturbation theory. Our approach does not require a model of the fields themselves and takes as input only the first few polyspectra, which could be modelled or measured from simulations or data, making our method particularly suited to observables lacking a robust perturbative description such as the weak-lensing shear. We apply our method to simulated density fields, finding a significantly reduced bispectrum and an enhanced correlation with the initial field. We demonstrate that our method reconstructs a large proportion of the linear baryon acoustic oscillations, improving the information content over the raw field by 35 per cent. We apply the transform to toy 21 cm intensity maps, showing that our method still performs well in the presence of complications such as redshift-space distortions, beam smoothing, pixel noise and foreground subtraction. We discuss how this method might provide a route to constructing a perturbative model of the fully non-Gaussian multivariate likelihood function.
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
Privacy Is Become with, Data Perturbation
Singh, Er. Niranjan; Singhai, Niky
2011-06-01
Privacy is becoming an increasingly important issue in many data mining applications that deal with health care, security, finance, behavior and other types of sensitive data. Is particularly becoming important in counterterrorism and homeland security-related applications. We touch upon several techniques of masking the data, namely random distortion, including the uniform and Gaussian noise, applied to the data in order to protect it. These perturbation schemes are equivalent to additive perturbation after the logarithmic Transformation. Due to the large volume of research in deriving private information from the additive noise perturbed data, the security of these perturbation schemes is questionable Many artificial intelligence and statistical methods exist for data analysis interpretation, Identifying and measuring the interestingness of patterns and rules discovered, or to be discovered is essential for the evaluation of the mined knowledge and the KDD process as a whole. While some concrete measurements exist, assessing the interestingness of discovered knowledge is still an important research issue. As the tool for the algorithm implementations we chose the language of choice in industrial world MATLAB.
Cosmological perturbations beyond linear order
CERN. Geneva
2013-01-01
Cosmological perturbation theory is the standard tool to understand the formation of the large scale structure in the Universe. However, its degree of applicability is limited by the growth of the amplitude of the matter perturbations with time. This problem can be tackled with by using N-body simulations or analytical techniques that go beyond the linear calculation. In my talk, I'll summarise some recent efforts in the latter that ameliorate the bad convergence of the standard perturbative expansion. The new techniques allow better analytical control on observables (as the matter power spectrum) over scales very relevant to understand the expansion history and formation of structure in the Universe.
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.
Perturbation theory of effective Hamiltonians
International Nuclear Information System (INIS)
Brandow, B.H.
1975-01-01
This paper constitutes a review of the many papers which have used perturbation theory to derive ''effective'' or ''model'' Hamiltonians. It begins with a brief review of nondegenerate and non-many-body perturbation theory, and then considers the degenerate but non-many-body problem in some detail. It turns out that the degenerate perturbation problem is not uniquely defined, but there are some practical criteria for choosing among the various possibilities. Finally, the literature dealing with the linked-cluster aspects of open-shell many-body systems is reviewed. (U.S.)
The power of perturbation theory
Energy Technology Data Exchange (ETDEWEB)
Serone, Marco [SISSA International School for Advanced Studies and INFN Trieste, Via Bonomea 265, 34136, Trieste (Italy); Abdus Salam International Centre for Theoretical Physics, Strada Costiera 11, 34151, Trieste (Italy); Spada, Gabriele [SISSA International School for Advanced Studies and INFN Trieste, Via Bonomea 265, 34136, Trieste (Italy); Villadoro, Giovanni [Abdus Salam International Centre for Theoretical Physics, Strada Costiera 11, 34151, Trieste (Italy)
2017-05-10
We study quantum mechanical systems with a discrete spectrum. We show that the asymptotic series associated to certain paths of steepest-descent (Lefschetz thimbles) are Borel resummable to the full result. Using a geometrical approach based on the Picard-Lefschetz theory we characterize the conditions under which perturbative expansions lead to exact results. Even when such conditions are not met, we explain how to define a different perturbative expansion that reproduces the full answer without the need of transseries, i.e. non-perturbative effects, such as real (or complex) instantons. Applications to several quantum mechanical systems are presented.
Ngo, Son Tung; Mai, Binh Khanh; Hiep, Dinh Minh; Li, Mai Suan
2015-10-01
The binding mechanism of AC1NX476 to HIV-1 protease wild type and mutations was studied by the docking and molecular dynamics simulations. The binding free energy was calculated using the double-annihilation binding free energy method. It is shown that the binding affinity of AC1NX476 to wild type is higher than not only ritonavir but also darunavir, making AC1NX476 become attractive candidate for HIV treatment. Our theoretical results are in excellent agreement with the experimental data as the correlation coefficient between calculated and experimentally measured binding free energies R = 0.993. Residues Asp25-A, Asp29-A, Asp30-A, Ile47-A, Gly48-A, and Val50-A from chain A, and Asp25-B from chain B play a crucial role in the ligand binding. The mutations were found to reduce the receptor-ligand interaction by widening the binding cavity, and the binding propensity is mainly driven by the van der Waals interaction. Our finding may be useful for designing potential drugs to combat with HIV. © 2015 John Wiley & Sons A/S.
Tunnelling instability via perturbation theory
Energy Technology Data Exchange (ETDEWEB)
Graffi, S. (Bologna Univ. (Italy). Dip. di Matematica); Grecchi, V. (Moderna Univ. (Italy). Dip. di Matematica); Jona-Lasinio, G. (Paris-11 Univ., 91 - Orsay (France). Lab. de Physique Theorique et Hautes Energies)
1984-10-21
The semiclassical limit of low lying states in a multiwell potential is studied by rigorous perturbative techniques. In particular tunnelling instability and localisation of wave functions is obtained in a simple way under small deformations of symmetric potentials.
Perturbation theory of quantum resonances
Czech Academy of Sciences Publication Activity Database
Durand, P.; Paidarová, Ivana
2016-01-01
Roč. 135, č. 7 (2016), s. 159 ISSN 1432-2234 Institutional support: RVO:61388955 Keywords : Partitioning technique * Analytic continuation * Perturbative expansion Subject RIV: CF - Physical ; Theoretical Chemistry
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...
Perturbative tests of quantum chromodynamics
International Nuclear Information System (INIS)
Michael, C.
1978-01-01
A review is given of perturbation theory results for quantum chromodynamics and of tests in deep inelastic lepton scattering, electron-positron annihilation, hadronic production of massive dileptons and hadronic large-momentum-transfer processes. (author)
Review of chiral perturbation theory
Indian Academy of Sciences (India)
Abstract. A review of chiral perturbation theory and recent developments on the comparison of its predictions with experiment is presented. Some interesting topics with scope for further elaboration are touched upon.
Perturbation theory in light-cone gauge
International Nuclear Information System (INIS)
Vianello, Eliana
2000-01-01
Perturbation calculations are presented for the light-cone gauge Schwinger model. Eigenstates can be calculated perturbatively but the perturbation theory is nonstandard. We hope to extend the work to QCD 2 to resolve some outstanding issues in those theories
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 angular correlations and distributions
International Nuclear Information System (INIS)
Makaryunas, K.
1976-01-01
The present index comprises original works and review papers on the perturbed angular correlations (PAC) and distributions (PAD). The articles published in the Soviet and foreign journals as well as the materials of conferences, monographs and collections published in the USSR and abroad, the preprints produced by various institutes and abstracts of disertations are included from 1948 up to 1973. The whole material compiled in this index is divided into three parts. Part one is a bibliographic index. All papers in this part are divided into three sections. Section one comprises the papers devoted to the theoretical works on PAC, review papers, monographs, materials of conferences. Section two deals with the works of methodical character where correlation spectrometers as well as the treatment of experimental data are described. In section three experimental works with concrete nuclei are compiled. Part two gives the characteristic of works performed with concrete nuclei. This part is presented in the form of the table in which the works are systematized according to the chemical elements and isotopes. The table shows the characteristics of the nuclear levels used in the investigations by PAC as well as brief characteristics of experiments and results obtained. Part three - appendix contains alphabetic index of the authors, the list of the used editions with the abbreviations of the titles of these editions. The lists indicating the dynamic of the quantity of works on PAC and the distribution according to the literature sources are also given
Noise Reduction in High-Throughput Gene Perturbation Screens
Motivation: Accurate interpretation of perturbation screens is essential for a successful functional investigation. However, the screened phenotypes are often distorted by noise, and their analysis requires specialized statistical analysis tools. The number and scope of statistical methods available...
Acoustic wavefield evolution as a function of source location perturbation
Alkhalifah, Tariq Ali
2010-01-01
differential equations have the same structure as the wave equation with a source function that depends on the background (original source) wavefield. The similarity in form implies that we can use familiar numerical methods to solve the perturbation equations
International Nuclear Information System (INIS)
Junqueira, Astrogildo de Carvalho
1999-01-01
The electric field gradient (efg) at the Nb site in the intermetallic compounds Nb 3 M (M = Al, Si, Ge, Sn) and at the T site in the intermetallic compounds T 3 Al (T = Ti, Zr, Hf, V, Nb, Ta) was measured by Perturbed Angular Correlation (PAC) method using the well known gamma-gamma cascade of 133-482 keV in 181 Ta from the β - decay of 181 Hf. The compounds were prepared by arc melting the constituent elements under argon atmosphere along with radioactive 181 Hf substituting approximately 0.1 atomic percent of Nb and T elements. The PAC measurements were carried out at 295 K for all compounds and the efg was obtained for each alloy. The results for the efg in the T 3 Al compounds showed a strong correlation with the number of conduction electrons, while for the Nbs M compounds the efg behavior is influenced mainly by the p electrons of the M elements. The so-called universal correlation between the electronic and lattice contribution for the efg in metals was not verified in this work for all studied compounds. Measurements of the quadrupole frequency in the range of 100 to 1210 K for the Nb 3 Al compound showed a linear behaviour with the temperature. Superconducting properties of this alloys may probably be related with this observed behaviour. The efg results are compared to those reported for other binary alloys and discussed with the help of ab-initio methods. (author)
Directory of Open Access Journals (Sweden)
Elham Azimzadeh
2013-01-01
Full Text Available Objectives: Falling is a main cause of mortality in elderly. Balance training exercises can help to prevent falls in older adults. According to the principle of specificity of training, the perturbation-based trainings are more similar to the real world. So these training programs can improve balance in elderly. Furthermore, exercising in an aquatic environment can reduce the limitations for balance training rather than a non-aquatic on. The aim of this study is comparing the effectiveness of perturbed and non-perturbed balance training programs in water on static and dynamic balance in aforementioned population group. Methods & Materials: 37 old women (age 80-65, were randomized to the following groups: perturbation-based training (n=12, non-perturbation-based training (n=12 and control (n=13 groups. Static and dynamic balance had been tested before and after the eight weeks of training by the postural stability test of the Biodex balance system using dynamic (level 4 and static platform. The data were analyzed by one sample paired t-test, Independent t-test and ANOVA. Results: There was a significant improvement for all indexes of static and dynamic balance in perturbation-based training (P<0.05. However, in non-perturbed group, all indexes were improved except ML (P<0.05. ANOVA showed that perturbed training was more effective than non-perturbed training on both static and dynamic balances. Conclusion: The findings confirmed the specificity principle of training. Although balance training can improve balance abilities, these kinds of trainings are not such specific for improving balance neuromuscular activities.The perturbation-based trainings can activate postural compensatory responses and reduce falling risk. According to results, we can conclude that hydrotherapy especially with perturbation-based programs will be useful for rehabilitation interventions in elderly .
International Nuclear Information System (INIS)
Seregin, A.S.
2000-01-01
In the paper the formulae for perturbation theory functionals calculation are given and equations are based on improved coarse mesh discretization of diffusion problem in 3-dimensional geometry (Hex-Z). Expressions for the reactivity effect components and reactivity coefficients, written in the framework of the first order perturbation theory, are presented. On this basis the formulae for estimation of the sensitivity coefficients of different reactivity effects group cross-sections were derived. Expressions for the reactivity effect and its components obtained in the framework of the strict perturbation theory, are also presented in the paper. (author)
Perturbation Solutions of the Quintic Duffing Equation with Strong Nonlinearities
Directory of Open Access Journals (Sweden)
Mehmet Pakdemirli
Full Text Available The quintic Duffing equation with strong nonlinearities is considered. Perturbation solutions are constructed using two different techniques: The classical multiple scales method (MS and the newly developed multiple scales Lindstedt Poincare method (MSLP. The validity criteria for admissible solutions are derived. Both approximate solutions are contrasted with the numerical solutions. It is found that MSLP provides compatible solution with the numerical solution for strong nonlinearities whereas MS solution fail to produce physically acceptable solution for large perturbation parameters.
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
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.
Base case and perturbation scenarios
Energy Technology Data Exchange (ETDEWEB)
Edmunds, T
1998-10-01
This report describes fourteen energy factors that could affect electricity markets in the future (demand, process, source mix, etc.). These fourteen factors are believed to have the most influence on the State's energy environment. A base case, or most probable, characterization is given for each of these fourteen factors over a twenty year time horizon. The base case characterization is derived from quantitative and qualitative information provided by State of California government agencies, where possible. Federal government databases are nsed where needed to supplement the California data. It is envisioned that a initial selection of issue areas will be based upon an evaluation of them under base case conditions. For most of the fourteen factors, the report identities possible perturbations from base case values or assumptions that may be used to construct additional scenarios. Only those perturbations that are plausible and would have a significant effect on energy markets are included in the table. The fourteen factors and potential perturbations of the factors are listed in Table 1.1. These perturbations can be combined to generate internally consist.ent. combinations of perturbations relative to the base case. For example, a low natural gas price perturbation should be combined with a high natural gas demand perturbation. The factor perturbations are based upon alternative quantitative forecasts provided by other institutions (the Department of Energy - Energy Information Administration in some cases), changes in assumptions that drive the quantitative forecasts, or changes in assumptions about the structure of the California energy markets. The perturbations are intended to be used for a qualitative reexamination of issue areas after an initial evaluation under the base case. The perturbation information would be used as a "tiebreaker;" to make decisions regarding those issue areas that were marginally accepted or rejected under the base case. Hf a
Infrared problems in field perturbation theory
International Nuclear Information System (INIS)
David, Francois.
1982-12-01
The work presented mainly covers questions related to the presence of ''infrared'' divergences in perturbation expansions of the Green functions of certain massless field theories. It is important to determine the mathematical status of perturbation expansions in field theory in order to define the region in which they are valid. Renormalization and the symmetry of a theory are important factors in infrared problems. The main object of this thesis resides in the mathematical techniques employed: integral representations of the Feynman amplitudes; methods for desingularization, regularization and dimensional renormalization. Nonlinear two dimensional space-time sigma models describing Goldstone's low energy boson dynamics associated with a breaking of continuous symmetry are studied. Random surface models are then investigated followed by infrared divergences in super-renormalizable theories. Finally, nonperturbation effects in massless theories are studied by expanding the two-dimensional nonlinear sigma model in 1/N [fr
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.)
Forecasting with the Standardized Self-Perturbed Kalman Filter
DEFF Research Database (Denmark)
Grassi, Stefano; Nonejad, Nima; Santucci de Magistris, Paolo
We propose and study the finite-sample properties of a modified version of the self-perturbed Kalman filter of Park and Jun (1992) for the on-line estimation of models subject to parameter instability. The perturbation term in the updating equation of the state covariance matrix is now weighted...... compared to other on-line, classical and Bayesian methods. The standardized self-perturbed Kalman filter is adopted to forecast the equity premium on the S&P500 index under several model specifications, and to investigate to what extent and how realized variance can be exploited to predict excess returns....
Effect of perturbation in low β proton accelerating structures
International Nuclear Information System (INIS)
Jule, W.E.; Baggett, D; Wechsler, P.; Gluckstern, R.L.
1976-01-01
In the first tank of the LAMPF 201 Linac it is desired to have a linear field distribution. One tries to achieve this by perturbing the first and last cells of the tank. A discussion is given of how perturbations in cell geometry in a periodic structure affect the field distribution in structures which correspond to low to intermediate values of β. It is shown that a geometric perturbation in one cell couples to many cells, and a method to obtain the coupling distribution from the geometric model is described. The necessary criteria to achieve the desired field distribution at LAMPF are discussed
Analytic continuation in perturbative QCD
International Nuclear Information System (INIS)
Caprini, Irinel
2002-01-01
We discuss some attempts to improve standard perturbative expansion in QCD by using the analytic continuation in the momentum and the Borel complex planes. We first analyse the momentum-plane analyticity properties of the Borel-summed Green functions in perturbative QCD and the connection between the Landau singularities and the infrared renormalons. By using the analytic continuation in the Borel complex plane, we propose a new perturbative series replacing the standard expansion in powers of the normalized coupling constant a. The new expansion functions have branch point and essential singularities at the origin of the complex a-plane and divergent Taylor expansions in powers of a. On the other hand the modified expansion of the QCD correlators is convergent under rather conservative conditions. (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.
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.
New perturbative approach to renormalizable field theories
International Nuclear Information System (INIS)
Dhar, A.; Gupta, V.
1984-01-01
A new method for obtaining perturbative predictions in quantum field theory is developed. Our method gives finite predictions, which are free from scheme ambiguities, for any quantity of interest (like a cross section or a Green's function) starting directly from the bare regularized Lagrangian. The central idea in our approach is to incorporate directly the consequences of dimensional transmutation for the predictions of the theory. We thus completely bypass the conventional renormalization procedure and the ambiguities associated with it. The case of massless theories with a single dimensionless coupling constant is treated in detail to illustrate our approach
A hybrid perturbation-Galerkin technique for partial differential equations
Geer, James F.; Anderson, Carl M.
1990-01-01
A two-step hybrid perturbation-Galerkin technique for improving the usefulness of perturbation solutions to partial differential equations which contain a parameter is presented and discussed. In the first step of the method, the leading terms in the asymptotic expansion(s) of the solution about one or more values of the perturbation parameter are obtained using standard perturbation methods. In the second step, the perturbation functions obtained in the first step are used as trial functions in a Bubnov-Galerkin approximation. This semi-analytical, semi-numerical hybrid technique appears to overcome some of the drawbacks of the perturbation and Galerkin methods when they are applied by themselves, while combining some of the good features of each. The technique is illustrated first by a simple example. It is then applied to the problem of determining the flow of a slightly compressible fluid past a circular cylinder and to the problem of determining the shape of a free surface due to a sink above the surface. Solutions obtained by the hybrid method are compared with other approximate solutions, and its possible application to certain problems associated with domain decomposition is discussed.
Coupling-parameter expansion in thermodynamic perturbation theory.
Ramana, A Sai Venkata; Menon, S V G
2013-02-01
An approach to the coupling-parameter expansion in the liquid state theory of simple fluids is presented by combining the ideas of thermodynamic perturbation theory and integral equation theories. This hybrid scheme avoids the problems of the latter in the two phase region. A method to compute the perturbation series to any arbitrary order is developed and applied to square well fluids. Apart from the Helmholtz free energy, the method also gives the radial distribution function and the direct correlation function of the perturbed system. The theory is applied for square well fluids of variable ranges and compared with simulation data. While the convergence of perturbation series and the overall performance of the theory is good, improvements are needed for potentials with shorter ranges. Possible directions for further developments in the coupling-parameter expansion are indicated.
Cosmological perturbation theory and quantum gravity
Energy Technology Data Exchange (ETDEWEB)
Brunetti, Romeo [Dipartimento di Matematica, Università di Trento,Via Sommarive 14, 38123 Povo TN (Italy); Fredenhagen, Klaus [II Institute für Theoretische Physik, Universität Hamburg,Luruper Chaussee 149, 22761 Hamburg (Germany); Hack, Thomas-Paul [Institute für Theoretische Physik, Universität Leipzig,Brüderstr. 16, 04103 Leipzig (Germany); Pinamonti, Nicola [Dipartimento di Matematica, Università di Genova,Via Dodecaneso 35, 16146 Genova (Italy); INFN, Sezione di Genova,Via Dodecaneso 33, 16146 Genova (Italy); Rejzner, Katarzyna [Department of Mathematics, University of York,Heslington, York YO10 5DD (United Kingdom)
2016-08-04
It is shown how cosmological perturbation theory arises from a fully quantized perturbative theory of quantum gravity. Central for the derivation is a non-perturbative concept of gauge-invariant local observables by means of which perturbative invariant expressions of arbitrary order are generated. In particular, in the linearised theory, first order gauge-invariant observables familiar from cosmological perturbation theory are recovered. Explicit expressions of second order quantities are presented as well.
Chaotic inflation with metric and matter perturbations
International Nuclear Information System (INIS)
Feldman, H.A.; Brandenberger, R.H.
1989-01-01
A perturbative scheme to analyze the evolution of both metric and scalar field perturbations in an expanding universe is developed. The scheme is applied to study chaotic inflation with initial metric and scalar field perturbations present. It is shown that initial gravitational perturbations with wavelength smaller than the Hubble radius rapidly decay. The metric simultaneously picks up small perturbations determined by the matter inhomogeneities. Both are frozen in once the wavelength exceeds the Hubble radius. (orig.)
Process for computing geometric perturbations for probabilistic analysis
Fitch, Simeon H. K. [Charlottesville, VA; Riha, David S [San Antonio, TX; Thacker, Ben H [San Antonio, TX
2012-04-10
A method for computing geometric perturbations for probabilistic analysis. The probabilistic analysis is based on finite element modeling, in which uncertainties in the modeled system are represented by changes in the nominal geometry of the model, referred to as "perturbations". These changes are accomplished using displacement vectors, which are computed for each node of a region of interest and are based on mean-value coordinate calculations.
Perturbed Motion of Airplane and Safe Store Separation
S. C. Raisinghani; S. Rao
1983-01-01
A method is presented to predict the perturbed motion of an airplane following stores jettisoning. The mass, moment of inertia, forces, and moments acting on the airplane are suitable split into contributions from the stores and the rest of the airplane parts. The seperation of stores is assumed to result in a step change of mass, moment of intertai, forces, and moments contributed by stores. The resulting set of perturbed state equations of motion are solved for two illustrative airplane str...
Basics of QCD perturbation theory
International Nuclear Information System (INIS)
Soper, D.E.
1997-01-01
This is an introduction to the use of QCD perturbation theory, emphasizing generic features of the theory that enable one to separate short-time and long-time effects. The author also covers some important classes of applications: electron-positron annihilation to hadrons, deeply inelastic scattering, and hard processes in hadron-hadron collisions. 31 refs., 38 figs
Current issues in perturbative QCD
International Nuclear Information System (INIS)
Hinchliffe, I.
1994-12-01
This review talk discusses some issues of active research in perturbative QCD. The following topics are discussed: (1) current value of αs; (2) heavy quark production in hadron collisions; (3) production of Ψ and Υ in p anti p collisions; (4) prompt photon production; (5) small-x and related phenomena; and (6) particle multiplicity in heavy quark jets
New results in perturbative QCD
International Nuclear Information System (INIS)
Ellis, R.K.
1986-01-01
Three topics in perturbative QCD important for Super-collider physics are reviewed. The topics are: 1. (2 → 2) jet phenomena calculated in O(αs 3 ). 2. New techniques for the calculation of tree graphs. 3. Color coherence in jet phenomena. 31 references, 6 figures
Seven topics in perturbative QCD
International Nuclear Information System (INIS)
Buras, A.J.
1980-09-01
The following topics of perturbative QCD are discussed: (1) deep inelastic scattering; (2) higher order corrections to e + e - annihilation, to photon structure functions and to quarkonia decays; (3) higher order corrections to fragmentation functions and to various semi-inclusive processes; (4) higher twist contributions; (5) exclusive processes; (6) transverse momentum effects; (7) jet and photon physics
Reggeon interactions in perturbative QCD
International Nuclear Information System (INIS)
Kirschner, R.
1994-08-01
We study the pairwise interaction of reggeized gluons and quarks in the Regge limit of perturbative QCD. The interactions are represented as integral kernels in the transverse momentum space and as operators in the impact parameter space. We observe conformal symmetry and holomorphic factorization in all cases. (orig.)
Basics of QCD perturbation theory
Energy Technology Data Exchange (ETDEWEB)
Soper, D.E. [Univ. of Oregon, Eugene, OR (United States). Inst. of Theoretical Science
1997-06-01
This is an introduction to the use of QCD perturbation theory, emphasizing generic features of the theory that enable one to separate short-time and long-time effects. The author also covers some important classes of applications: electron-positron annihilation to hadrons, deeply inelastic scattering, and hard processes in hadron-hadron collisions. 31 refs., 38 figs.
Status of chiral perturbation theory
International Nuclear Information System (INIS)
Ecker, G.
1996-10-01
A survey is made of semileptonic and nonleptonic kaon decays in the framework of chiral perturbation theory. The emphasis is on what has been done rather than how it was done. The theoretical predictions are compared with available experimental results. (author)
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
Perturbative QCD and exclusive processes
International Nuclear Information System (INIS)
Bennett, J.; Hawes, F.; Zhao, M.; Zyla, P.
1991-01-01
The authors discuss perturbation theory as applied to particle physics calculations. In particle physics one is generally interested in the scattering amplitude for a system going from some initial state to a final state. The intermediate state or states are unknown. To get the scattering amplitude it is necessary to sum the contributions from processes which pass through all possible intermediate states. Intermediate states involve the exchange of intermediate vector bosons between the particles, and with this interaction is associated a coupling constant α. Each additional boson exchange involves an additional contribution of α to the coupling. If α is less than 1, one can see that the relative contribution of higher order processes is less and less important as α falls. In QCD the gluons serve as the intermediate vector bosons exchanged by quarks and gluons, and the interaction constant is not really a constant, but depends upon the distance between the particles. At short distances the coupling is small, and one can assume perturbative expansions may converge rapidly. Exclusive scattering processes, as opposed to inclusive, are those in which all of the final state products are detected. The authors then discuss the application of perturbative QCD to the deuteron. The issues of chiral conservation and color transparancy are also discussed, in the scheme of large Q 2 interations, where perturbative QCD should be applicable
Perturbative treatment of nuclear rotations
International Nuclear Information System (INIS)
Civitarese, O.
1980-01-01
In this work, it is described the case corresponding to perturbative quantum treatment of a fermion system in free rotation and the divergences which resulted from the 'break' in symmetry, associated by the adoption of a deformed basis as a non pertubed solution. (A.C.A.S.) [pt
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.
Energy Technology Data Exchange (ETDEWEB)
Le Cocq, A
1998-11-23
The aim of this work is the performances improvement of the Monte-Carlo codes for the criticality studies. MORET IV is especially concerned. With multigroup approximations, the anisotropy equations are very irregular and show quick variations. In a Monte-Carlo codes, they are estimated only by the first coefficients of Legendre polynomials development. Many methods have been characterised using variable number of these coefficients, allowing their reconstruction. So reference representations were defined. Thus they showed that the approximation by only one Dirac could lead to a reactivity under-evaluations. Referring to these representations, new methods have been introduced in MORET IV and instructions have been proposed. Two methods (the correlated samples method and the derivatives sampling method) have been studied to define the divergence between two closely configurations result. A few variance formula of the collision density variation for an infinite medium to an energy group, have been established. These formula have been perfected by simulation for a finite medium. (A.L.B.)
Energy Technology Data Exchange (ETDEWEB)
Le Cocq, A
1998-11-23
The aim of this work is the performances improvement of the Monte-Carlo codes for the criticality studies. MORET IV is especially concerned. With multigroup approximations, the anisotropy equations are very irregular and show quick variations. In a Monte-Carlo codes, they are estimated only by the first coefficients of Legendre polynomials development. Many methods have been characterised using variable number of these coefficients, allowing their reconstruction. So reference representations were defined. Thus they showed that the approximation by only one Dirac could lead to a reactivity under-evaluations. Referring to these representations, new methods have been introduced in MORET IV and instructions have been proposed. Two methods (the correlated samples method and the derivatives sampling method) have been studied to define the divergence between two closely configurations result. A few variance formula of the collision density variation for an infinite medium to an energy group, have been established. These formula have been perfected by simulation for a finite medium. (A.L.B.)
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.
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
A perturbation-based model for rectifier circuits
Directory of Open Access Journals (Sweden)
Vipin B. Vats
2006-01-01
Full Text Available A perturbation-theoretic analysis of rectifier circuits is presented. The governing differential equation of the half-wave rectifier with capacitor filter is analyzed by expanding the output voltage as a Taylor series with respect to an artificially introduced parameter in the nonlinearity of the diode characteristic as is done in quantum theory. The perturbation parameter introduced in the analysis is independent of the circuit components as compared to the method presented by multiple scales. The various terms appearing in the perturbation series are then modeled in the form of an equivalent circuit. This model is subsequently used in the analysis of full-wave rectifier. Matlab simulation results are included which confirm the validity of the theoretical formulations. Perturbation analysis acts a helpful tool in analyzing time-varying systems and chaotic systems.
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.)
Invariant Solutions for a Class of Perturbed Nonlinear Wave Equations
Directory of Open Access Journals (Sweden)
Waheed A. Ahmed
2017-11-01
Full Text Available Approximate symmetries of a class of perturbed nonlinear wave equations are computed using two newly-developed methods. Invariant solutions associated with the approximate symmetries are constructed for both methods. Symmetries and solutions are compared through discussing the advantages and disadvantages of each method.
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
A non-perturbative approach to strings
International Nuclear Information System (INIS)
Orland, P.
1986-03-01
After briefly reviewing the theory of strings in the light-cone gauge, a lattice regularized path integral for the amplitudes is discussed. The emphasis is put on a toy string model; the U(N) Veneziano model in the limit as N->infinite with g 0 2 N fixed. The lattice methods of Giles and Thorn are used extensively, but are found to require modification beyond perturbation theory. The twenty-six-dimensional toy string model is recast as a two-dimensional spin system. (orig.)
A non-perturbative approach to strings
International Nuclear Information System (INIS)
Orland, P.
1986-01-01
After briefly reviewing the theory of strings in the light-cone gauge, a lattice regularized path integral for the amplitudes is discussed. The emphasis is put on a toy string model; the U(N) Veneziano model in the limit as N → ∞, with g/sup 2//sub o/N fixed. The lattice methods of Giles and Thorn are used extensively, but are found to require modification beyond perturbation theory. The twenty-six-dimensional toy string model is recast as a two-dimensional spin system
Homological Perturbation Theory for Nonperturbative Integrals
Johnson-Freyd, Theo
2015-11-01
We use the homological perturbation lemma to produce explicit formulas computing the class in the twisted de Rham complex represented by an arbitrary polynomial. This is a non-asymptotic version of the method of Feynman diagrams. In particular, we explain that phenomena usually thought of as particular to asymptotic integrals in fact also occur exactly: integrals of the type appearing in quantum field theory can be reduced in a totally algebraic fashion to integrals over an Euler-Lagrange locus, provided this locus is understood in the scheme-theoretic sense, so that imaginary critical points and multiplicities of degenerate critical points contribute.
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.
Perturbations in electromagnetic dark energy
International Nuclear Information System (INIS)
Jiménez, Jose Beltrán; Maroto, Antonio L.; Koivisto, Tomi S.; Mota, David F.
2009-01-01
It has been recently proposed that the presence of a temporal electromagnetic field on cosmological scales could explain the phase of accelerated expansion that the universe is currently undergoing. The field contributes as a cosmological constant and therefore, the homogeneous cosmology produced by such a model is exactly the same as that of ΛCDM. However, unlike a cosmological constant term, electromagnetic fields can acquire perturbations which in principle could affect CMB anisotropies and structure formation. In this work, we study the evolution of inhomogeneous scalar perturbations in this model. We show that provided the initial electromagnetic fluctuations generated during inflation are small, the model is perfectly compatible with both CMB and large scale structure observations at the same level of accuracy as ΛCDM
Perturbative instabilities in Horava gravity
International Nuclear Information System (INIS)
Bogdanos, Charalampos; Saridakis, Emmanuel N
2010-01-01
We investigate the scalar and tensor perturbations in Horava gravity, with and without detailed balance, around a flat background. Once both types of perturbations are taken into account, it is revealed that the theory is plagued by ghost-like scalar instabilities in the range of parameters which would render it power-counting renormalizable, that cannot be overcome by simple tricks such as analytic continuation. Implementing a consistent flow between the UV and IR limits seems thus more challenging than initially presumed, regardless of whether the theory approaches general relativity at low energies or not. Even in the phenomenologically viable parameter space, the tensor sector leads to additional potential problems, such as fine-tunings and super-luminal propagation.
The status of perturbative QCD
International Nuclear Information System (INIS)
Ellis, R.K.
1988-10-01
The advances in perturbative QCD are reviewed. The status of determinations of the coupling constant α/sub S/ and the parton distribution functions is presented. New theoretical results on the spin dependent structure functions of the proton are also reviewed. The theoretical description of the production of vector bosons, jets and heavy quarks is outlined with special emphasis on new results. Expected rates for top quark production at hadronic colliders are presented. 111 refs., 8 figs
Scalar perturbations and conformal transformation
International Nuclear Information System (INIS)
Fabris, J.C.; Tossa, J.
1995-11-01
The non-minimal coupling of gravity to a scalar field can be transformed into a minimal coupling through a conformal transformation. We show how to connect the results of a perturbation calculation, performed around a Friedman-Robertson-Walker background solution, before and after the conformal transformation. We work in the synchronous gauge, but we discuss the implications of employing other frames. (author). 16 refs
Perturbative QCD at finite temperature
International Nuclear Information System (INIS)
Altherr, T.
1989-03-01
We discuss an application of finite temperature QCD to lepton-pair production in a quark-gluon plasma. The perturbative calculation is performed within the realtime formalism. After cancellation of infrared and mass singularities, the corrections at O (α s ) are found to be very small in the region where the mass of the Drell-Yan pair is much larger than the temperature of the plasma. Interesting effects, however, appear at the annihilation threshold of the thermalized quarks
1983-01-01
disturbance theory . The main feature of the method is the use of measured pressure along lines in the flow direction near the tunnel walls. This method...disturbance theory , then $can be written ( , = qo( , ) .@ (:. S-in(.t + 0.( or s CO (8) Defining cw as co S . ^(9) gives Sin= C, f(4,.) + OCr,z)co.s(0t...AUTHOR (S)/ AUTEUR (S) H. Sawada, visiting scientist 2nd Aerodynamics Division, National Aerospace Laboratory, Japan SERIES/SERIE Aeronautical Note 6
Gauge-invariant cosmological density perturbations
International Nuclear Information System (INIS)
Sasaki, Misao.
1986-06-01
Gauge-invariant formulation of cosmological density perturbation theory is reviewed with special emphasis on its geometrical aspects. Then the gauge-invariant measure of the magnitude of a given perturbation is presented. (author)
Perturbation of an exact strong gravity solution
International Nuclear Information System (INIS)
Baran, S.A.
1982-10-01
Perturbations of an exact strong gravity solution are investigated. It is shown, by using the new multipole expansions previously presented, that this exact and static spherically symmetric solution is stable under odd parity perturbations. (author)
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
Modélisation de l'imagerie biomédicale hybride par perturbations mécaniques
Seppecher , Laurent
2014-01-01
This thesis aims at developing an original mathematical approach for modeling hybrid biomedical imaging modalities. The core idea is to run an ill-posed imaging method while perturbing the medium using mechanical displacements. These displacements described by an elastic wave equation perturb the collected measurements. Using these perturbed measurements and taking advantage of the perturbation localizing e↵ect, it is possible to significantly overcome the resolution of the basic method. The ...
Perturbation theory in nuclear fuel management optimization
International Nuclear Information System (INIS)
Ho, L.W.; Rohach, A.F.
1982-01-01
Perturbation theory along with a binary fuel shuffling technique is applied to predict the effects of various core configurations and, hence, the optimization of in-core fuel management. The computer code FULMNT has been developed to shuffle the fuel assemblies in search of the lowest possible power peaking factor. An iteration approach is used in the search routine. A two-group diffusion theory method is used to obtain the power distribution for the iterations. A comparison of the results of this method with other methods shows that this approach can save computer time and obtain better power peaking factors. The code also has a burnup capability that can be used to check power peaking throughout the core life
Resummation of perturbative QCD by pade approximants
International Nuclear Information System (INIS)
Gardi, E.
1997-01-01
In this lecture I present some of the new developments concerning the use of Pade Approximants (PA's) for resuming perturbative series in QCD. It is shown that PA's tend to reduce the renormalization scale and scheme dependence as compared to truncated series. In particular it is proven that in the limit where the β function is dominated by the 1-loop contribution, there is an exact symmetry that guarantees invariance of diagonal PA's under changing the renormalization scale. In addition it is shown that in the large β 0 approximation diagonal PA's can be interpreted as a systematic method for approximating the flow of momentum in Feynman diagrams. This corresponds to a new multiple scale generalization of the Brodsky-Lepage-Mackenzie (BLM) method to higher orders. I illustrate the method with the Bjorken sum rule and the vacuum polarization function. (author)
Multiplicative perturbations of local C-semigroups
Indian Academy of Sciences (India)
2016-08-26
Aug 26, 2016 ... In this paper, we establish some left and right multiplicative perturbation theorems concerning local -semigroups when the generator of a perturbed local -semigroup S(⋅) may not be densely defined and the perturbation operator is a bounded linear operator from ¯D(A) into () such that = ...
Multiplicative perturbations of local C-semigroups
Indian Academy of Sciences (India)
In this paper, we establish some left and right multiplicative perturbation theorems concerning local -semigroups when the generator of a perturbed local -semigroup S ( ⋅ ) may not be densely defined and the perturbation operator is a bounded linear operator from D ( A ) ¯ into () such that = on D ( A ) ¯ ...
FRW Cosmological Perturbations in Massive Bigravity
Comelli, D; Pilo, L
2014-01-01
Cosmological perturbations of FRW solutions in ghost free massive bigravity, including also a second matter sector, are studied in detail. At early time, we find that sub horizon exponential instabilities are unavoidable and they lead to a premature departure from the perturbative regime of cosmological perturbations.
Perturbation theories for the dipolar fluids
International Nuclear Information System (INIS)
Lee, L.L.; Chung, T.H.
1983-01-01
We derive here four different perturbation equations for the calculation of the angular pair correlation functions of dipolar fluids; namely, the first order y-expansion, the modified Percus--Yevik (MPY) expansion, the modified hypernetted chain (MHNC) expansion, and the modified linearized hypernetted chain (MLHNC) equation. Both the method of the functional expansion and the method of the cluster integrals are utilized. Comparison with other perturbation theories (e.g., the Melnyk--Smith equation) is made. While none of the theories is exact, as shown by the cluster diagrams, the MLHNC and the MHNC contain more diagrams than, say, the MPY and y-expansion. The y-expansion equation can be improved by including the correction terms to the Kirkwood superposition approximation for the triplet correlation function. For example, the inclusion of the correction term rho∫d4h(14)h(24)h(34) in a formula given by Henderson, is shown to improve substantially the y-expansion equation. We examine the performance of two of the theories: the y-expansion and the MLHNC equation for a Stockmayer (dipolar) fluid with a reduced dipole moment μ/sup asterisk2/ [ = μ 2 /(epsilonsigma 3 )] = 1.0. Comparison with Monte Carlo simulation results of Adams et al. and with other theories (e.g., the QHNC equation) shows that our results are reasonable. Further improvements of the equations are also pointed out
Nonlinearly perturbed semi-Markov processes
Silvestrov, Dmitrii
2017-01-01
The book presents new methods of asymptotic analysis for nonlinearly perturbed semi-Markov processes with a finite phase space. These methods are based on special time-space screening procedures for sequential phase space reduction of semi-Markov processes combined with the systematical use of operational calculus for Laurent asymptotic expansions. Effective recurrent algorithms are composed for getting asymptotic expansions, without and with explicit upper bounds for remainders, for power moments of hitting times, stationary and conditional quasi-stationary distributions for nonlinearly perturbed semi-Markov processes. These results are illustrated by asymptotic expansions for birth-death-type semi-Markov processes, which play an important role in various applications. The book will be a useful contribution to the continuing intensive studies in the area. It is an essential reference for theoretical and applied researchers in the field of stochastic processes and their applications that will cont...
A parabolic singular perturbation problem with an internal layer
Grasman, J.; Shih, S.D.
2004-01-01
A method is presented to approximate with singular perturbation methods a parabolic differential equation for the quarter plane with a discontinuity at the corner. This discontinuity gives rise to an internal layer. It is necessary to match the local solution in this layer with the one in a corner
An intermolecular perturbation theory for the region of moderate overlap
International Nuclear Information System (INIS)
Hayes, I.C.; Stone, A.J.
1984-01-01
A perturbational method is described for calculating the interaction energy of two molecules in the region where the overlap between their wave-functions is significant. By working directly with a basis of determinants constructed from the SCF orbitals of the separated molecules, without orthogonalization, it is possible to avoid many of the disadvantages of other methods. (author)
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
The classification of diagrams in perturbation theory
International Nuclear Information System (INIS)
Phillips, D.R.; Afnan, I.R.
1995-01-01
The derivation of scattering equations connecting the amplitudes obtained from diagrammatic expansions is of interest in many branches of physics. One method for deriving such equations is the classification-of-diagrams technique of Taylor. However, as we shall explain in this paper, there are certain points of Taylor's method which require clarification. First, it is not clear whether Taylor's original method is equivlant to the simpler classification-of-diagrams scheme used by Thomas, Rinat, Afnan, and Blankleider (TRAB). Second, when the Taylor method is applied to certain problems in a time-dependent perturbation theory it leads to the over-counting of some diagrams. This paper first restates Taylor's method, in the process uncovering reasons why certain diagrams might be double-counted in the Taylor method. In then explores how far Taylor's method is equivalent to the simpler TRAB method. Finally, it examines precisely why the double-counting occurs in Taylor's method and derives corrections which compensate for this double-counting. copyright 1995 Academic Press, Inc
Hadronic Structure from Perturbative Dressing
Energy Technology Data Exchange (ETDEWEB)
Arash, Firooz [Physics Department, Tafresh University, Tafresh, Iran and Center for theoretical physics and Mathematics, AEOI, P.O. Box 11365-8486, Tehran (Iran, Islamic Republic of)]. E-mail: farash@cic.aut.ac.ir
2005-09-15
Perturbative dressing of a valence quark in QCD produces the internal structure of an extended object, the so-called Valon. The valon structure is universal and independent of the hosting hadron. Polarized and unpolarized proton and pion structure functions are calculated in the valon representation. One finds that although all the available data on g{sub 1}{sup p,n,d} are easily reproduced, a sizable orbital angular momentum associated with the partonic structure of the valon is required in order to have a spin 1/2 valon.
Perturbations in loop quantum cosmology
International Nuclear Information System (INIS)
Nelson, W; Agullo, I; Ashtekar, A
2014-01-01
The era of precision cosmology has allowed us to accurately determine many important cosmological parameters, in particular via the CMB. Confronting Loop Quantum Cosmology with these observations provides us with a powerful test of the theory. For this to be possible, we need a detailed understanding of the generation and evolution of inhomogeneous perturbations during the early, quantum gravity phase of the universe. Here, we have described how Loop Quantum Cosmology provides a completion of the inflationary paradigm, that is consistent with the observed power spectra of the CMB
Mobile ankle and knee perturbator.
Andersen, Jacob Buus; Sinkjaer, Thomas
2003-10-01
A mobile ankle and knee perturbator has been developed. It consists of a functional joint with an integrated clutch. Four Bowden wires connect the joint to a powerful motor and a double pneumatic cylinder. When needed during any time of the gait cycle, it is possible to impose an ankle rotation by engaging the clutch and rotating the ankle or knee joint with a predefined displacement. The system is designed to investigate electrophysiological and biomechanical features of the human ankle or knee joint during gait.
Perturbatively improving RI-MOM renormalization constants
Energy Technology Data Exchange (ETDEWEB)
Constantinou, M.; Costa, M.; Panagopoulos, H. [Cyprus Univ. (Cyprus). Dept. of Physics; Goeckeler, M. [Regensburg Univ. (Germany). Institut fuer Theoretische Physik; Horsley, R. [Edinburgh Univ. (United Kingdom). School of Physics; Perlt, H.; Schiller, A. [Leipzig Univ. (Germany). Inst. fuer Theoretische Physik; Rakow, P.E.L. [Liverpool Univ. (United Kingdom). Dept. of Mathematical Sciences; Schhierholz, G. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)
2013-03-15
The determination of renormalization factors is of crucial importance in lattice QCD. They relate the observables obtained on the lattice to their measured counterparts in the continuum in a suitable renormalization scheme. Therefore, they have to be computed as precisely as possible. A widely used approach is the nonperturbative Rome-Southampton method. It requires, however, a careful treatment of lattice artifacts. In this paper we investigate a method to suppress these artifacts by subtracting one-loop contributions to renormalization factors calculated in lattice perturbation theory. We compare results obtained from a complete one-loop subtraction with those calculated for a subtraction of contributions proportional to the square of the lattice spacing.
Simultaneous perturbation stochastic approximation for tidal models
Altaf, M.U.
2011-05-12
The Dutch continental shelf model (DCSM) is a shallow sea model of entire continental shelf which is used operationally in the Netherlands to forecast the storm surges in the North Sea. The forecasts are necessary to support the decision of the timely closure of the moveable storm surge barriers to protect the land. In this study, an automated model calibration method, simultaneous perturbation stochastic approximation (SPSA) is implemented for tidal calibration of the DCSM. The method uses objective function evaluations to obtain the gradient approximations. The gradient approximation for the central difference method uses only two objective function evaluation independent of the number of parameters being optimized. The calibration parameter in this study is the model bathymetry. A number of calibration experiments is performed. The effectiveness of the algorithm is evaluated in terms of the accuracy of the final results as well as the computational costs required to produce these results. In doing so, comparison is made with a traditional steepest descent method and also with a newly developed proper orthogonal decompositionbased calibration method. The main findings are: (1) The SPSA method gives comparable results to steepest descent method with little computational cost. (2) The SPSA method with little computational cost can be used to estimate large number of parameters.
Simultaneous perturbation stochastic approximation for tidal models
Altaf, M.U.; Heemink, A.W.; Verlaan, M.; Hoteit, Ibrahim
2011-01-01
The Dutch continental shelf model (DCSM) is a shallow sea model of entire continental shelf which is used operationally in the Netherlands to forecast the storm surges in the North Sea. The forecasts are necessary to support the decision of the timely closure of the moveable storm surge barriers to protect the land. In this study, an automated model calibration method, simultaneous perturbation stochastic approximation (SPSA) is implemented for tidal calibration of the DCSM. The method uses objective function evaluations to obtain the gradient approximations. The gradient approximation for the central difference method uses only two objective function evaluation independent of the number of parameters being optimized. The calibration parameter in this study is the model bathymetry. A number of calibration experiments is performed. The effectiveness of the algorithm is evaluated in terms of the accuracy of the final results as well as the computational costs required to produce these results. In doing so, comparison is made with a traditional steepest descent method and also with a newly developed proper orthogonal decompositionbased calibration method. The main findings are: (1) The SPSA method gives comparable results to steepest descent method with little computational cost. (2) The SPSA method with little computational cost can be used to estimate large number of parameters.
"Phonon" scattering beyond perturbation theory
Qiu, WuJie; Ke, XueZhi; Xi, LiLi; Wu, LiHua; Yang, Jiong; Zhang, WenQing
2016-02-01
Searching and designing materials with intrinsically low lattice thermal conductivity (LTC) have attracted extensive consideration in thermoelectrics and thermal management community. The concept of part-crystalline part-liquid state, or even part-crystalline part-amorphous state, has recently been proposed to describe the exotic structure of materials with chemical- bond hierarchy, in which a set of atoms is weakly bonded to the rest species while the other sublattices retain relatively strong rigidity. The whole system inherently manifests the coexistence of rigid crystalline sublattices and fluctuating noncrystalline substructures. Representative materials in the unusual state can be classified into two categories, i.e., caged and non-caged ones. LTCs in both systems deviate from the traditional T -1 relationship ( T, the absolute temperature), which can hardly be described by small-parameter-based perturbation approaches. Beyond the classical perturbation theory, an extra rattling-like scattering should be considered to interpret the liquid-like and sublattice-amorphization-induced heat transport. Such a kind of compounds could be promising high-performance thermoelectric materials, due to the extremely low LTCs. Other physical properties for these part-crystalline substances should also exhibit certain novelty and deserve further exploration.
Perturbation theory for Alfven wave
International Nuclear Information System (INIS)
Yoshida, Z.; Mahajan, S.M.
1995-01-01
The Alfven wave is the dominant low frequency transverse mode of a magnetized plasma. The Alfven wave propagation along the magnetic field, and displays a continuous spectrum even in a bounded plasma. This is essentially due to the degeneracy of the wave characteristics, i.e. the frequency (ω) is primarily determined by the wave number in the direction parallel to the ambient magnetic field (k parallel ) and is independent of the perpendicular wavenumbers. The characteristics, that are the direction along which the wave energy propagates, are identical to the ambient magnetic field lines. Therefore, the spectral structure of the Alfven wave has a close relationship with the geometric structure of the magnetic field lines. In an inhomogeneous plasma, the Alfven resonance constitutes a singularity for the defining wave equation; this results in a singular eigenfunction corresponding to the continuous spectrum. The aim of this review is to present an overview of the perturbation theory for the Alfven wave. Emphasis is placed on those perturbations of the continuous spectrum which lead to the creation of point spectra. Such qualitative changes in the spectrum are relevant to many plasma phenomena
Research on perturbation based Monte Carlo reactor criticality search
International Nuclear Information System (INIS)
Li Zeguang; Wang Kan; Li Yangliu; Deng Jingkang
2013-01-01
Criticality search is a very important aspect in reactor physics analysis. Due to the advantages of Monte Carlo method and the development of computer technologies, Monte Carlo criticality search is becoming more and more necessary and feasible. Traditional Monte Carlo criticality search method is suffered from large amount of individual criticality runs and uncertainty and fluctuation of Monte Carlo results. A new Monte Carlo criticality search method based on perturbation calculation is put forward in this paper to overcome the disadvantages of traditional method. By using only one criticality run to get initial k_e_f_f and differential coefficients of concerned parameter, the polynomial estimator of k_e_f_f changing function is solved to get the critical value of concerned parameter. The feasibility of this method was tested. The results show that the accuracy and efficiency of perturbation based criticality search method are quite inspiring and the method overcomes the disadvantages of traditional one. (authors)
Perturbations i have Known and Loved
Field, Robert W.
2011-06-01
A spectroscopic perturbation is a disruption of a ^1Σ-^1Σ-like regular pattern that can embody level-shifts, extra lines, and intensity anomalies. Once upon a time, when a band was labeled ``perturbed,'' it was considered worthless because it could at best yield molecular constants unsuited for archival tables. Nevertheless, a few brave spectroscopists, notably Albin Lagerqvist and Richard Barrow, collected perturbations because they knew that the pattern of multiple perturbations formed an intricate puzzle that would eventually reveal the presence and electronic symmetry of otherwise unobservable electronic states. There are many kinds of patterns of broken patterns. In my PhD thesis I showed how to determine absolute vibrational assignments for the perturber from patterns among the observed values of perturbation matrix elements. When a ^3Π state is perturbed, its six (Ω, parity) components capture a pattern of level shifts and intensity anomalies that reveals more about the nature of the perturber than a simple perturbation of the single component of a ^1Σ state. In perturbation-facilitated OODR, a perturbed singlet level acts as a spectroscopic doorway through which the entire triplet manifold may be systematically explored. For polyatomic molecule vibrations, a vibrational polyad (a group of mutually perturbing vibrational levels, among which the perturbation matrix elements are expected to follow harmonic oscillator scaling rules) can contain more components than a ^3Π state and intrapolyad patterns can be exquisitely sensitive not merely to the nature of an interloper within the polyad but also to the eigenvector character of the vibronic state from which the polyad is viewed. Variation of scaled polyad interaction parameters from one polyad to the next, a pattern of patterns, can signal proximity to an isomerization barrier. Everything in Rydberg-land seems to scale as N⋆-3, yet a trespassing valence state causes all scaling and propensity rules go
Perturbativity in the seesaw mechanism
International Nuclear Information System (INIS)
Asaka, Takehiko; Tsuyuki, Takanao
2016-01-01
We consider the Standard Model extended by right-handed neutrinos to explain massive neutrinos through the seesaw mechanism. The new fermion can be observed when it has a sufficiently small mass and large mixings to left-handed neutrinos. If such a particle is the lightest right-handed neutrino, its contribution to the mass matrix of active neutrinos needs to be canceled by that of a heavier one. Yukawa couplings of the heavier one are then larger than those of the lightest one. We show that the perturbativity condition gives a severe upper bound on the mixing of the lightest right-handed neutrino, depending on the masses of heavier ones. Models of high energy phenomena, such as leptogenesis, can be constrained by low energy experiments.
Initial conditions for cosmological perturbations
Ashtekar, Abhay; Gupt, Brajesh
2017-02-01
Penrose proposed that the big bang singularity should be constrained by requiring that the Weyl curvature vanishes there. The idea behind this past hypothesis is attractive because it constrains the initial conditions for the universe in geometric terms and is not confined to a specific early universe paradigm. However, the precise statement of Penrose’s hypothesis is tied to classical space-times and furthermore restricts only the gravitational degrees of freedom. These are encapsulated only in the tensor modes of the commonly used cosmological perturbation theory. Drawing inspiration from the underlying idea, we propose a quantum generalization of Penrose’s hypothesis using the Planck regime in place of the big bang, and simultaneously incorporating tensor as well as scalar modes. Initial conditions selected by this generalization constrain the universe to be as homogeneous and isotropic in the Planck regime as permitted by the Heisenberg uncertainty relations.
Initial conditions for cosmological perturbations
International Nuclear Information System (INIS)
Ashtekar, Abhay; Gupt, Brajesh
2017-01-01
Penrose proposed that the big bang singularity should be constrained by requiring that the Weyl curvature vanishes there. The idea behind this past hypothesis is attractive because it constrains the initial conditions for the universe in geometric terms and is not confined to a specific early universe paradigm. However, the precise statement of Penrose’s hypothesis is tied to classical space-times and furthermore restricts only the gravitational degrees of freedom. These are encapsulated only in the tensor modes of the commonly used cosmological perturbation theory. Drawing inspiration from the underlying idea, we propose a quantum generalization of Penrose’s hypothesis using the Planck regime in place of the big bang, and simultaneously incorporating tensor as well as scalar modes. Initial conditions selected by this generalization constrain the universe to be as homogeneous and isotropic in the Planck regime as permitted by the Heisenberg uncertainty relations . (paper)
Curvature perturbations from dimensional decoupling
Giovannini, Massimo
2005-01-01
The scalar modes of the geometry induced by dimensional decoupling are investigated. In the context of the low energy string effective action, solutions can be found where the spatial part of the background geometry is the direct product of two maximally symmetric Euclidean manifolds whose related scale factors evolve at a dual rate so that the expanding dimensions first accelerate and then decelerate while the internal dimensions always contract. After introducing the perturbative treatment of the inhomogeneities, a class of five-dimensional geometries is discussed in detail. Quasi-normal modes of the system are derived and the numerical solution for the evolution of the metric inhomogeneities shows that the fluctuations of the internal dimensions provide a term that can be interpreted, in analogy with the well-known four-dimensional situation, as a non-adiabatic pressure density variation. Implications of this result are discussed with particular attention to string cosmological scenarios.
Perturbation Biology: Inferring Signaling Networks in Cellular Systems
Miller, Martin L.; Gauthier, Nicholas P.; Jing, Xiaohong; Kaushik, Poorvi; He, Qin; Mills, Gordon; Solit, David B.; Pratilas, Christine A.; Weigt, Martin; Braunstein, Alfredo; Pagnani, Andrea; Zecchina, Riccardo; Sander, Chris
2013-01-01
We present a powerful experimental-computational technology for inferring network models that predict the response of cells to perturbations, and that may be useful in the design of combinatorial therapy against cancer. The experiments are systematic series of perturbations of cancer cell lines by targeted drugs, singly or in combination. The response to perturbation is quantified in terms of relative changes in the measured levels of proteins, phospho-proteins and cellular phenotypes such as viability. Computational network models are derived de novo, i.e., without prior knowledge of signaling pathways, and are based on simple non-linear differential equations. The prohibitively large solution space of all possible network models is explored efficiently using a probabilistic algorithm, Belief Propagation (BP), which is three orders of magnitude faster than standard Monte Carlo methods. Explicit executable models are derived for a set of perturbation experiments in SKMEL-133 melanoma cell lines, which are resistant to the therapeutically important inhibitor of RAF kinase. The resulting network models reproduce and extend known pathway biology. They empower potential discoveries of new molecular interactions and predict efficacious novel drug perturbations, such as the inhibition of PLK1, which is verified experimentally. This technology is suitable for application to larger systems in diverse areas of molecular biology. PMID:24367245
Acoustic wavefield evolution as a function of source location perturbation
Alkhalifah, Tariq Ali
2010-12-01
The wavefield is typically simulated for seismic exploration applications through solving the wave equation for a specific seismic source location. The direct relation between the form (or shape) of the wavefield and the source location can provide insights useful for velocity estimation and interpolation. As a result, I derive partial differential equations that relate changes in the wavefield shape to perturbations in the source location, especially along the Earth\\'s surface. These partial differential equations have the same structure as the wave equation with a source function that depends on the background (original source) wavefield. The similarity in form implies that we can use familiar numerical methods to solve the perturbation equations, including finite difference and downward continuation. In fact, we can use the same Green\\'s function to solve the wave equation and its source perturbations by simply incorporating source functions derived from the background field. The solutions of the perturbation equations represent the coefficients of a Taylor\\'s series type expansion of the wavefield as a function of source location. As a result, we can speed up the wavefield calculation as we approximate the wavefield shape for sources in the vicinity of the original source. The new formula introduces changes to the background wavefield only in the presence of lateral velocity variation or in general terms velocity variations in the perturbation direction. The approach is demonstrated on the smoothed Marmousi model.
The Hill-determinant perturbation theory with triangular propagators
International Nuclear Information System (INIS)
Znojil, M.
1996-01-01
A new version of the Rayleigh-Schroedinger perturbation prescription is proposed. Its main formal feature lies in an unusual choice of the model space and unperturbed H 0 and in a resulting lower-triangular matrix structure of its propagators. Within the framework of the so-called Hill-determinant method, an admissibility of any incompletely solvable zero-order Hamiltonian is achieved in this way. As a consequence, the range of practical applicability of our new perturbative formalism may be expected to incorporate many new phenomenological interactions with a strongly anharmonic character. 18 refs
Charged scalar perturbations around Garfinkle–Horowitz–Strominger black holes
Directory of Open Access Journals (Sweden)
Cheng-Yong Zhang
2015-10-01
Full Text Available We examine the stability of the Garfinkle–Horowitz–Strominger (GHS black hole under charged scalar perturbations. Employing the appropriate numerical methods, we show that the GHS black hole is always stable against charged scalar perturbations. This is different from the results obtained in the de Sitter and anti-de Sitter black holes. Furthermore, we argue that in the GHS black hole background there is no amplification of the incident charged scalar wave to cause the superradiance, so that the superradiant instability cannot exist in this spacetime.
Perturbative approach to non-Markovian stochastic Schroedinger equations
International Nuclear Information System (INIS)
Gambetta, Jay; Wiseman, H.M.
2002-01-01
In this paper we present a perturbative procedure that allows one to numerically solve diffusive non-Markovian stochastic Schroedinger equations, for a wide range of memory functions. To illustrate this procedure numerical results are presented for a classically driven two-level atom immersed in an environment with a simple memory function. It is observed that as the order of the perturbation is increased the numerical results for the ensemble average state ρ red (t) approach the exact reduced state found via Imamog-barlu ' s enlarged system method [Phys. Rev. A 50, 3650 (1994)
Alien calculus and non perturbative effects in Quantum Field Theory
Bellon, Marc P.
2016-12-01
In many domains of physics, methods for dealing with non-perturbative aspects are required. Here, I want to argue that a good approach for this is to work on the Borel transforms of the quantities of interest, the singularities of which give non-perturbative contributions. These singularities in many cases can be largely determined by using the alien calculus developed by Jean Écalle. My main example will be the two point function of a massless theory given as a solution of a renormalization group equation.
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.)
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
Perturbative analysis for Kaplan's lattice chiral fermions
International Nuclear Information System (INIS)
Aoki, S.; Hirose, H.
1994-01-01
Perturbation theory for lattice fermions with domain wall mass terms is developed and is applied to investigate the chiral Schwinger model formulated on the lattice by Kaplan's method. We calculate the effective action for gauge fields to one loop, and find that it contains a longitudinal component even for anomaly-free cases. From the effective action we obtain gauge anomalies and Chern-Simons currents without ambiguity. We also show that the current corresponding to the fermion number has a nonzero divergence and it flows off the wall into the extra dimension. Similar results are obtained for a proposal by Shamir, who used a constant mass term with free boundaries instead of domain walls
Introduction to non-perturbative quantum chromodynamics
International Nuclear Information System (INIS)
Pene, O.
1995-01-01
Quantum chromodynamics is considered to be the theory of strong interaction. The main peculiarity of this theory is that its asymptotic states (hadrons) are different from its elementary fields (quarks and gluons). This property plays a great part in any physical process involving small momentum-energy transfers. In such a range perturbative methods are no longer allowed. This work focuses on other tools such as QCD symmetry, the quark model, Green functions and the sum rules. To get hadron characteristics numerically, QCD on lattices is used but only in the case of simple process involving no more than one hadron in the initial and final states because of the complexity of the Green function. Some examples using a Monte-Carlo simulation are given. (A.C.)
Perturbative analysis in higher-spin theories
Energy Technology Data Exchange (ETDEWEB)
Didenko, V.E. [I.E. Tamm Department of Theoretical Physics, Lebedev Physical Institute,Leninsky prospect 53, 119991, Moscow (Russian Federation); Misuna, N.G. [Moscow Institute of Physics and Technology,Institutsky lane 9, 141700, Dolgoprudny, Moscow region (Russian Federation); Vasiliev, M.A. [I.E. Tamm Department of Theoretical Physics, Lebedev Physical Institute,Leninsky prospect 53, 119991, Moscow (Russian Federation)
2016-07-28
A new scheme of the perturbative analysis of the nonlinear HS equations is developed giving directly the final result for the successive application of the homotopy integrations which appear in the standard approach. It drastically simplifies the analysis and results from the application of the standard spectral sequence approach to the higher-spin covariant derivatives, allowing us in particular to reduce multiple homotopy integrals resulting from the successive application of the homotopy trick to a single integral. Efficiency of the proposed method is illustrated by various examples. In particular, it is shown how the Central on-shell theorem of the free theory immediately results from the nonlinear HS field equations with no intermediate computations.
Customer-oriented finite perturbation analysis for queueing networks
Heidergott, B.F.
2000-01-01
We consider queueing networks for which the performance measureJ ( ) depends on a parameter , which can be a service time parameter or a buffer size, and we are interested in sensitivity analysis of J ( ) with respect to . We introduce a new method, called customer-oriented finite perturbation
A Variational Approach to Perturbed Discrete Anisotropic Equations
Directory of Open Access Journals (Sweden)
Amjad Salari
2016-01-01
Full Text Available We continue the study of discrete anisotropic equations and we will provide new multiplicity results of the solutions for a discrete anisotropic equation. We investigate the existence of infinitely many solutions for a perturbed discrete anisotropic boundary value problem. The approach is based on variational methods and critical point theory.
On some perturbation techniques for quasi-linear parabolic equations
Directory of Open Access Journals (Sweden)
Igor Malyshev
1990-01-01
Full Text Available We study a nonhomogeneous quasi-linear parabolic equation and introduce a method that allows us to find the solution of a nonlinear boundary value problem in explicit form. This task is accomplished by perturbing the original equation with a source function, which is then found as a solution of some nonlinear operator equation.
Finite perturbation studies of magnetic susceptibility and shielding with GIAO
International Nuclear Information System (INIS)
Zaucer, M.; Pumpernik, D.; Hladnik, M.; Azman, A.
1977-01-01
The magnetic susceptibility tensor and proton and fluorine magnetic shielding tensors are calculated for F 2 and (FHF) - using an ab initio finite perturbation method with gauge-invariant atomic orbitals (GIAO). The discussion of the basis set deficiency shows that the calculated values for the susceptibilities are reliable. Simple additivity (Pascal rule) for the susceptibility is confirmed. (orig.) [de
Perturbative evolution: a different approach at small x
Energy Technology Data Exchange (ETDEWEB)
Donnachie, A. [University of Manchester, School of Physics and Astromony, Manchester (United Kingdom); Landshoff, P.V. [DAMTP, Cambridge University, Cambridge (United Kingdom)
2017-08-15
We propose an approach to DGLAP evolution at small x that circumvents the usual problem that a perturbation expansion is not valid there. The data for the charm structure function are important to motivate the method, and it describes them much more successfully than the conventional approach. (orig.)
Learning gene networks under SNP perturbations using eQTL datasets.
Directory of Open Access Journals (Sweden)
Lingxue Zhang
2014-02-01
Full Text Available The standard approach for identifying gene networks is based on experimental perturbations of gene regulatory systems such as gene knock-out experiments, followed by a genome-wide profiling of differential gene expressions. However, this approach is significantly limited in that it is not possible to perturb more than one or two genes simultaneously to discover complex gene interactions or to distinguish between direct and indirect downstream regulations of the differentially-expressed genes. As an alternative, genetical genomics study has been proposed to treat naturally-occurring genetic variants as potential perturbants of gene regulatory system and to recover gene networks via analysis of population gene-expression and genotype data. Despite many advantages of genetical genomics data analysis, the computational challenge that the effects of multifactorial genetic perturbations should be decoded simultaneously from data has prevented a widespread application of genetical genomics analysis. In this article, we propose a statistical framework for learning gene networks that overcomes the limitations of experimental perturbation methods and addresses the challenges of genetical genomics analysis. We introduce a new statistical model, called a sparse conditional Gaussian graphical model, and describe an efficient learning algorithm that simultaneously decodes the perturbations of gene regulatory system by a large number of SNPs to identify a gene network along with expression quantitative trait loci (eQTLs that perturb this network. While our statistical model captures direct genetic perturbations of gene network, by performing inference on the probabilistic graphical model, we obtain detailed characterizations of how the direct SNP perturbation effects propagate through the gene network to perturb other genes indirectly. We demonstrate our statistical method using HapMap-simulated and yeast eQTL datasets. In particular, the yeast gene network
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...
Perturbative algebraic quantum field theory at finite temperature
Energy Technology Data Exchange (ETDEWEB)
Lindner, Falk
2013-08-15
We present the algebraic approach to perturbative quantum field theory for the real scalar field in Minkowski spacetime. In this work we put a special emphasis on the inherent state-independence of the framework and provide a detailed analysis of the state space. The dynamics of the interacting system is constructed in a novel way by virtue of the time-slice axiom in causal perturbation theory. This method sheds new light in the connection between quantum statistical dynamics and perturbative quantum field theory. In particular it allows the explicit construction of the KMS and vacuum state for the interacting, massive Klein-Gordon field which implies the absence of infrared divergences of the interacting theory at finite temperature, in particular for the interacting Wightman and time-ordered functions.
Melnikov processes and chaos in randomly perturbed dynamical systems
Yagasaki, Kazuyuki
2018-07-01
We consider a wide class of randomly perturbed systems subjected to stationary Gaussian processes and show that chaotic orbits exist almost surely under some nondegenerate condition, no matter how small the random forcing terms are. This result is very contrasting to the deterministic forcing case, in which chaotic orbits exist only if the influence of the forcing terms overcomes that of the other terms in the perturbations. To obtain the result, we extend Melnikov’s method and prove that the corresponding Melnikov functions, which we call the Melnikov processes, have infinitely many zeros, so that infinitely many transverse homoclinic orbits exist. In addition, a theorem on the existence and smoothness of stable and unstable manifolds is given and the Smale–Birkhoff homoclinic theorem is extended in an appropriate form for randomly perturbed systems. We illustrate our theory for the Duffing oscillator subjected to the Ornstein–Uhlenbeck process parametrically.
Singular perturbation analysis of relaxation oscillations in reactor systems
International Nuclear Information System (INIS)
Ward, M.E.; Lee, J.C.
1987-01-01
A singular perturbation method for the analysis of large power oscillations in nuclear reactors is applied to obtain phase-plane solutions of the Ergen-Weinberg model. The system equations, recast in an appropriate form, directly give a first approximation to the closed trajectory in which the system behaviour is idealized as relaxation oscillations. Further approximations in the phase plane are determined using separate perturbation series on individual parts of the oscillation, with variations in the assignment of dependent and independent variables to consistently obtain convergent series. The accuracy of each order of the phase-plane solution increases with the magnitude of the power pulse in the actual physical situation. For realistic reactor conditions, both the trajectory and period of oscillation are well predicted using the first two terms of each perturbation series
Two-scale approach to oscillatory singularly perturbed transport equations
Frénod, Emmanuel
2017-01-01
This book presents the classical results of the two-scale convergence theory and explains – using several figures – why it works. It then shows how to use this theory to homogenize ordinary differential equations with oscillating coefficients as well as oscillatory singularly perturbed ordinary differential equations. In addition, it explores the homogenization of hyperbolic partial differential equations with oscillating coefficients and linear oscillatory singularly perturbed hyperbolic partial differential equations. Further, it introduces readers to the two-scale numerical methods that can be built from the previous approaches to solve oscillatory singularly perturbed transport equations (ODE and hyperbolic PDE) and demonstrates how they can be used efficiently. This book appeals to master’s and PhD students interested in homogenization and numerics, as well as to the Iter community.
Non-perturbative power corrections to ghost and gluon propagators
International Nuclear Information System (INIS)
Boucaud, Philippe; Leroy, Jean-Pierre; Yaouanc, Alain Le; Lokhov, Alexey; Micheli, Jacques; Pene, Olivier; RodrIguez-Quintero, Jose; Roiesnel, Claude
2006-01-01
We study the dominant non-perturbative power corrections to the ghost and gluon propagators in Landau gauge pure Yang-Mills theory using OPE and lattice simulations. The leading order Wilson coefficients are proven to be the same for both propagators. The ratio of the ghost and gluon propagators is thus free from this dominant power correction. Indeed, a purely perturbative fit of this ratio gives smaller value ( ≅ 270MeV) of Λ M-barS-bar than the one obtained from the propagators separately( ≅ 320MeV). This argues in favour of significant non-perturbative ∼ 1/q 2 power corrections in the ghost and gluon propagators. We check the self-consistency of the method
Constraints on perturbative RG flows in six dimensions
Energy Technology Data Exchange (ETDEWEB)
Stergiou, Andreas [Department of Physics, Yale University,217 Prospect St, New Haven, CT 06520 (United States); Stone, David [INFN, Sezione di Roma,Piazzale A. Moro 2, I-00185 Roma (Italy); Vitale, Lorenzo G. [Institut de Théorie des Phènoménes Physiques, EPFL,Route Cantonale, CH-1015 Lausanne (Switzerland)
2016-08-01
When conformal field theories (CFTs) are perturbed by marginally relevant deformations, renormalization group (RG) flows ensue that can be studied with perturbative methods, at least as long as they remain close to the original CFT. In this work we study such RG flows in the vicinity of six-dimensional unitary CFTs. Neglecting effects of scalar operators of dimension two and four, we use Weyl consistency conditions to prove the a-theorem in perturbation theory, and establish that scale implies conformal invariance. We identify a quantity that monotonically decreases in the flow to the infrared due to unitarity, showing that it does not agree with the one studied recently in the literature on the six-dimensional ϕ{sup 3} theory.
Perturbative algebraic quantum field theory at finite temperature
International Nuclear Information System (INIS)
Lindner, Falk
2013-08-01
We present the algebraic approach to perturbative quantum field theory for the real scalar field in Minkowski spacetime. In this work we put a special emphasis on the inherent state-independence of the framework and provide a detailed analysis of the state space. The dynamics of the interacting system is constructed in a novel way by virtue of the time-slice axiom in causal perturbation theory. This method sheds new light in the connection between quantum statistical dynamics and perturbative quantum field theory. In particular it allows the explicit construction of the KMS and vacuum state for the interacting, massive Klein-Gordon field which implies the absence of infrared divergences of the interacting theory at finite temperature, in particular for the interacting Wightman and time-ordered functions.
Closed form bound-state perturbation theory
Directory of Open Access Journals (Sweden)
Ollie J. Rose
1980-01-01
Full Text Available The perturbed Schrödinger eigenvalue problem for bound states is cast into integral form using Green's Functions. A systematic algorithm is developed and applied to the resulting equation giving rise to approximate solutions expressed as functions of the given perturbation parameter. As a by-product, convergence radii for the traditional Rayleigh-Schrödinger and Brillouin-Wigner perturbation theories emerge in a natural way.
Perturbative spacetimes from Yang-Mills theory
Energy Technology Data Exchange (ETDEWEB)
Luna, Andrés [School of Physics and Astronomy, University of Glasgow,Glasgow G12 8QQ, Scotland (United Kingdom); Monteiro, Ricardo [Theoretical Physics Department, CERN,Geneva (Switzerland); Nicholson, Isobel; Ochirov, Alexander; O’Connell, Donal [Higgs Centre for Theoretical Physics,School of Physics and Astronomy, The University of Edinburgh,Edinburgh EH9 3JZ, Scotland (United Kingdom); Westerberg, Niclas [Institute of Photonics and Quantum Sciences,School of Engineering and Physical Sciences, Heriot-Watt University,Edinburgh (United Kingdom); Higgs Centre for Theoretical Physics,School of Physics and Astronomy, The University of Edinburgh,Edinburgh EH9 3JZ, Scotland (United Kingdom); White, Chris D. [Centre for Research in String Theory,School of Physics and Astronomy, Queen Mary University of London,327 Mile End Road, London E1 4NS (United Kingdom)
2017-04-12
The double copy relates scattering amplitudes in gauge and gravity theories. In this paper, we expand the scope of the double copy to construct spacetime metrics through a systematic perturbative expansion. The perturbative procedure is based on direct calculation in Yang-Mills theory, followed by squaring the numerator of certain perturbative diagrams as specified by the double-copy algorithm. The simplest spherically symmetric, stationary spacetime from the point of view of this procedure is a particular member of the Janis-Newman-Winicour family of naked singularities. Our work paves the way for applications of the double copy to physically interesting problems such as perturbative black-hole scattering.
International Nuclear Information System (INIS)
Dai, H.L.; Wang, X.
2006-01-01
In this paper, an analytical method is introduced to solve the problem for the dynamic stress-focusing and centred-effect of perturbation of the magnetic field vector in orthotropic cylinders under thermal and mechanical shock loads. Analytical expressions for the dynamic stresses and the perturbation of the magnetic field vector are obtained by means of finite Hankel transforms and Laplace transforms. The response histories of dynamic stresses and the perturbation of the field vector are also obtained. In practical examples, the dynamic focusing effect on both magnetoelastic stress and perturbation of the axial magnetic field vector in an orthotropic cylinder subjected to various shock loads is presented and discussed
Dynamically constrained ensemble perturbations – application to tides on the West Florida Shelf
Directory of Open Access Journals (Sweden)
F. Lenartz
2009-07-01
Full Text Available A method is presented to create an ensemble of perturbations that satisfies linear dynamical constraints. A cost function is formulated defining the probability of each perturbation. It is shown that the perturbations created with this approach take the land-sea mask into account in a similar way as variational analysis techniques. The impact of the land-sea mask is illustrated with an idealized configuration of a barrier island. Perturbations with a spatially variable correlation length can be also created by this approach. The method is applied to a realistic configuration of the West Florida Shelf to create perturbations of the M2 tidal parameters for elevation and depth-averaged currents. The perturbations are weakly constrained to satisfy the linear shallow-water equations. Despite that the constraint is derived from an idealized assumption, it is shown that this approach is applicable to a non-linear and baroclinic model. The amplitude of spurious transient motions created by constrained perturbations of initial and boundary conditions is significantly lower compared to perturbing the variables independently or to using only the momentum equation to compute the velocity perturbations from the elevation.
A convergent reformulation of perturbative QCD
International Nuclear Information System (INIS)
Alves, R.J.G.
2000-10-01
We present and explore a new formulation of perturbative QCD based not on the renormalised coupling but on the dimensional transmutation parameter of the theory and the property of asymptotic scaling. The approach yields a continued function, the iterated function being that involved in the solution of the two-loop β-function equation. In the so-called large-b limit the continued function reduces to a continued fraction and the successive approximants are diagonal Pade approximants. We investigate numerically the convergence of successive approximants using the leading-b approximation, motivated by renormalons, to model the all-orders result. We consider the Adler D-function of vacuum polarisation, the Polarised Bjorken and Gross-LIewellyn Smith sum rules, the (unpolarised) Bjorken sum rule, and the Minkowskian quantities R τ and the R-ratio of e + e - annihilation. In contrast to diagonal Pade approximants the truncated continued function method gives remarkably stable large-order approximants in cases where infrared renormalon effects are important. We also use the new approach to determine the QCD fundamental parameters from the R τ and the R-ratio measurements, where we find Λ-tilde (3)/MS = 516 ± 48 MeV (which yields α s (μ = m τ ) = 0.360 -0.020 +0.021 ), and Λ-tilde (5)/MS = 299 -7 +6 MeV (which yields α s (μ = m z 0 ) = 0.1218 ± 0.0004), respectively. The evolution of the former value to the m z 0 energy results in α s (μ = m z 0 ) = 0.123 ± 0.002. These values are in line with other determinations available in the literature. We implement the Complete Renormalisation Group Improvement (CORGI) scheme throughout all the calculations. We report on how the mathematical concept of Stieltjes series can be used to assess the convergence of Pade approximants of perturbative series. We find that the combinations of UV renormalons which occur in perturbative QCD may or may not be Stieltjes series depending on the renormalisation scheme used. (author)
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)
Fedosov quantization and perturbative quantum field theory
Energy Technology Data Exchange (ETDEWEB)
Collini, Giovanni
2016-12-12
Fedosov has described a geometro-algebraic method to construct in a canonical way a deformation of the Poisson algebra associated with a finite-dimensional symplectic manifold (''phase space''). His algorithm gives a non-commutative, but associative, product (a so-called ''star-product'') between smooth phase space functions parameterized by Planck's constant ℎ, which is treated as a deformation parameter. In the limit as ℎ goes to zero, the star product commutator goes to ℎ times the Poisson bracket, so in this sense his method provides a quantization of the algebra of classical observables. In this work, a generalization of Fedosov's method is developed which applies to the infinite-dimensional symplectic ''manifolds'' that occur in Lagrangian field theories. We show that the procedure remains mathematically well-defined, and we explain the relationship of the method to more standard perturbative quantization schemes in quantum field theory.
Photoionization cross sections and Auger rates calculated by many-body perturbation theory
International Nuclear Information System (INIS)
Kelly, H.P.
1976-01-01
Methods for applying the many body perturbation theory to atomic calculations are discussed with particular emphasis on calculation of photoionization cross sections and Auger rates. Topics covered include: Rayleigh--Schroedinger theory; many body perturbation theory; calculations of photoionization cross sections; and Auger rates
The Heun equation and the Calogero-Moser-Sutherland system II: Perturbation and algebraic solution
Directory of Open Access Journals (Sweden)
Kouichi Takemura
2004-02-01
Full Text Available We apply a method of perturbation for the $BC_1$ Inozemtsev model from the trigonometric model and show the holomorphy of perturbation. Consequently, the convergence of eigenvalues and eigenfuncions which are expressed as formal power series is proved. We investigate also the relationship between $L^2$ space and some finite dimensional space of elliptic functions.
Non-perturbative calculation of equilibrium polarization of stored electron beams
International Nuclear Information System (INIS)
Yokoya, Kaoru.
1992-05-01
Stored electron/positron beams polarize spontaneously owing to the spin-flip synchrotron radiation. In the existing computer codes, the degree of the equilibrium polarization has been calculated using perturbation expansions in terms of the orbital oscillation amplitudes. In this paper a new numerical method is presented which does not employ the perturbation expansion. (author)
Massive states in chiral perturbation theory
Energy Technology Data Exchange (ETDEWEB)
Mallik, S [Saha Inst. of Nuclear Physics, Calcutta (India)
1995-08-01
It is shown that the chiral nonanalytic terms generated by {Delta}{sub 33} resonance in the nucleon self-energy is reproduced in chiral perturbation theory by perturbing appropriate local operators contained in the pion-nucleon effective Lagrangian itself. (orig.)
On the non-perturbative effects
International Nuclear Information System (INIS)
Manjavidze, J.; Voronyuk, V.
2004-01-01
The quantum correspondence principle based on the time reversibility is adopted to take into account the non-Abelian symmetry constrains. The main properties of the new strong-coupling perturbation theory which take into account non-perturbative effects are described. (author)
Scalar Quantum Electrodynamics: Perturbation Theory and Beyond
International Nuclear Information System (INIS)
Bashir, A.; Gutierrez-Guerrero, L. X.; Concha-Sanchez, Y.
2006-01-01
In this article, we calculate scalar propagator in arbitrary dimensions and gauge and the three-point scalar-photon vertex in arbitrary dimensions and Feynman gauge, both at the one loop level. We also discuss constraints on their non perturbative structure imposed by requirements of gauge invariance and perturbation theory
Sensitivity calculations of integral parameters by a generalyzed perturbation theory
International Nuclear Information System (INIS)
Santo, A.C.F. de.
1981-12-01
In this work, we first revise some concepts, concerning the neutron transport in nuclear systems. We derive the balance and importance equation. Then we discuss the neutron importance in subcritical, critical and supercritical systems. The adjoint flux is estabilished as the neutron importance for the fission process. The conventional perturbation theory is later presented. We developed a sistematic perturbative formulation in the first order variation in the distribution functions calculate the reactivity due to a system perturbation. We present in detail the flux difference and generalized functions methos. The above formulation is then extended for altered systems. We consider integral parameters of the type ratio of bilinear functionals (for which the reactivity is a particular case). We define sensitivity coeficients, for any integral parameter, corresponding to a especific system alterations. Possible aplication of the method are also discussed. In the last part of this work, we apply the perturbative formulation to the doppler reacitivity sensibility calculation, utilizing the generalized functions method. We describe in detail the compiler program written for this and some other possible aplications. (Author) [pt
Reconstructing the ideal results of a perturbed analog quantum simulator
Schwenk, Iris; Reiner, Jan-Michael; Zanker, Sebastian; Tian, Lin; Leppäkangas, Juha; Marthaler, Michael
2018-04-01
Well-controlled quantum systems can potentially be used as quantum simulators. However, a quantum simulator is inevitably perturbed by coupling to additional degrees of freedom. This constitutes a major roadblock to useful quantum simulations. So far there are only limited means to understand the effect of perturbation on the results of quantum simulation. Here we present a method which, in certain circumstances, allows for the reconstruction of the ideal result from measurements on a perturbed quantum simulator. We consider extracting the value of the correlator 〈Ôi(t ) Ôj(0 ) 〉 from the simulated system, where Ôi are the operators which couple the system to its environment. The ideal correlator can be straightforwardly reconstructed by using statistical knowledge of the environment, if any n -time correlator of operators Ôi of the ideal system can be written as products of two-time correlators. We give an approach to verify the validity of this assumption experimentally by additional measurements on the perturbed quantum simulator. The proposed method can allow for reliable quantum simulations with systems subjected to environmental noise without adding an overhead to the quantum system.
Perturbation theory in nuclear fuel management optimization
International Nuclear Information System (INIS)
Ho, L.W.
1981-01-01
Nuclear in-core fuel management involves all the physical aspects which allow optimal operation of the nuclear fuel within the reactor core. In most nuclear power reactors, fuel loading patterns which have a minimum power peak are economically desirable to allow the reactors to operate at the highest power density and to minimize the possibility of fuel failure. In this study, perturbation theory along with a binary fuel shuffling technique is applied to predict the effects of various core configurations, and hence, the optimization of in-core fuel management. The computer code FULMNT has been developed to shuffle the fuel assemblies in search of the lowest possible power peaking factor. An iteration approach is used in the search routine. A two-group diffusion theory method is used to obtain the power distribution for the iterations. A comparison of the results of this method with other methods shows that this approach can save computer time. The code also has a burnup capability which can be used to check power peaking throughout the core life
An Improved Perturb and Observe Algorithm for Photovoltaic Motion Carriers
Peng, Lele; Xu, Wei; Li, Liming; Zheng, Shubin
2018-03-01
An improved perturbation and observation algorithm for photovoltaic motion carriers is proposed in this paper. The model of the proposed algorithm is given by using Lambert W function and tangent error method. Moreover, by using matlab and experiment of photovoltaic system, the tracking performance of the proposed algorithm is tested. And the results demonstrate that the improved algorithm has fast tracking speed and high efficiency. Furthermore, the energy conversion efficiency by the improved method has increased by nearly 8.2%.
Makarewicz, Emilia; Gordon, Agnieszka J; Mierzwicki, Krzysztof; Latajka, Zdzislaw; Berski, Slawomir
2014-06-05
Quantum chemistry methods have been applied to study the influence of the Xe atom inserted into the hydrogen-bromine bond (HBr → HXeBr), particularly on the nature of atomic interactions in the HBr···CO2 and HXeBr···CO2 complexes. Detailed analysis of the nature of chemical bonds has been carried out using topological analysis of the electron localization function, while topological analysis of electron density was used to gain insight into the nature of weak nonbonding interactions. Symmetry-adapted perturbation theory within the orbital approach was applied for greater understanding of the physical contributions to the total interaction energy.
Bounded Perturbation Regularization for Linear Least Squares Estimation
Ballal, Tarig
2017-10-18
This paper addresses the problem of selecting the regularization parameter for linear least-squares estimation. We propose a new technique called bounded perturbation regularization (BPR). In the proposed BPR method, a perturbation with a bounded norm is allowed into the linear transformation matrix to improve the singular-value structure. Following this, the problem is formulated as a min-max optimization problem. Next, the min-max problem is converted to an equivalent minimization problem to estimate the unknown vector quantity. The solution of the minimization problem is shown to converge to that of the ℓ2 -regularized least squares problem, with the unknown regularizer related to the norm bound of the introduced perturbation through a nonlinear constraint. A procedure is proposed that combines the constraint equation with the mean squared error (MSE) criterion to develop an approximately optimal regularization parameter selection algorithm. Both direct and indirect applications of the proposed method are considered. Comparisons with different Tikhonov regularization parameter selection methods, as well as with other relevant methods, are carried out. Numerical results demonstrate that the proposed method provides significant improvement over state-of-the-art methods.
Shishkin, G. I.
2015-11-01
An initial-boundary value problem is considered for a singularly perturbed parabolic convection-diffusion equation with a perturbation parameter ɛ (ɛ ∈ (0, 1]) multiplying the highest order derivative. The stability of a standard difference scheme based on monotone approximations of the problem on a uniform mesh is analyzed, and the behavior of discrete solutions in the presence of perturbations is examined. The scheme does not converge ɛ-uniformly in the maximum norm as the number of its grid nodes is increased. When the solution of the difference scheme converges, which occurs if N -1 ≪ ɛ and N -1 0 ≪ 1, where N and N 0 are the numbers of grid intervals in x and t, respectively, the scheme is not ɛ-uniformly well conditioned or stable to data perturbations in the grid problem and to computer perturbations. For the standard difference scheme in the presence of data perturbations in the grid problem and/or computer perturbations, conditions on the "parameters" of the difference scheme and of the computer (namely, on ɛ, N, N 0, admissible data perturbations in the grid problem, and admissible computer perturbations) are obtained that ensure the convergence of the perturbed solutions. Additionally, the conditions are obtained under which the perturbed numerical solution has the same order of convergence as the solution of the unperturbed standard difference scheme.
International Nuclear Information System (INIS)
Tan, Jianhao; Tong, Dechun; Gu, Qiang; Fang, Wencheng; Zhao, Zhentang
2016-01-01
A tuning method augmented by the bead-pull technique based on nonresonant perturbation field distribution measurements has been widely applied for traveling-wave (TW) accelerating structures. The method is also suitable for deflecting structures, but some key considerations of the field components of the HEM_1_1 mode and the selection of bead merit discussion. A “cage”-type perturbing object has been designed, fabricated and applied in nonresonant perturbation measurements. Measurements on an S-band TW deflecting structure are carried out, and the measurement and tuning method will be used on the newly developed X-band deflecting structure at Shanghai Institute of Applied Physics.
Energy Technology Data Exchange (ETDEWEB)
Tan, Jianhao [Shanghai Institute of Applied Physics, Chinese Academy of Science, Shanghai 201800 (China); Shanghai Science Research Center, Chinese Academy of Science, Shanghai 201204 (China); Tong, Dechun [Department of Engineering Physics, Tsinghua University, Beijing 100084 (China); Gu, Qiang; Fang, Wencheng [Shanghai Institute of Applied Physics, Chinese Academy of Science, Shanghai 201800 (China); Shanghai Science Research Center, Chinese Academy of Science, Shanghai 201204 (China); Zhao, Zhentang, E-mail: zhaozhentang@sinap.ac.cn [Shanghai Institute of Applied Physics, Chinese Academy of Science, Shanghai 201800 (China); Shanghai Key Laboratory of Cryogenics & Superconducting RF Technology, Shanghai 201800 (China); Shanghai Science Research Center, Chinese Academy of Science, Shanghai 201204 (China)
2016-11-01
A tuning method augmented by the bead-pull technique based on nonresonant perturbation field distribution measurements has been widely applied for traveling-wave (TW) accelerating structures. The method is also suitable for deflecting structures, but some key considerations of the field components of the HEM{sub 11} mode and the selection of bead merit discussion. A “cage”-type perturbing object has been designed, fabricated and applied in nonresonant perturbation measurements. Measurements on an S-band TW deflecting structure are carried out, and the measurement and tuning method will be used on the newly developed X-band deflecting structure at Shanghai Institute of Applied Physics.