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Sample records for well-posedness linear perturbations

  1. Well-posedness of the second-order linear singular Dirichlet problem

    Czech Academy of Sciences Publication Activity Database

    Lomtatidze, Alexander; Opluštil, Z.

    2015-01-01

    Roč. 22, č. 3 (2015), s. 409-419 ISSN 1072-947X Institutional support: RVO:67985840 Keywords : singular Dirichlet problem * well-posedness Subject RIV: BA - General Mathematics Impact factor: 0.417, year: 2015 http://www.degruyter.com/view/j/gmj.2015.22.issue-3/gmj-2015-0023/gmj-2015-0023. xml

  2. Well-posedness of (N = 1) classical supergravity

    International Nuclear Information System (INIS)

    Bao, D.; Choquet-Bruhat, Y.; Isenberg, J.; Yasskin, P.B.

    1985-01-01

    In this paper we investigate whether classical (N = 1) supergravity has a well-posed locally causal Cauchy problem. We define well-posedness to mean that any choice of initial data (from an appropriate function space) which satisfies the supergravity constraint equations and a set of gauge conditions can be continuously developed into a space-time solution of the supergravity field equations around the initial surface. Local causality means that the domains of dependence of the evolution equations coincide with those determined by the light cones. We show that when the fields of classical supergravity are treated as formal objects, the field equations are (under certain gauge conditions) equivalent to a coupled system of quasilinear nondiagonal second-order partial differential equations which is formally nonstrictly hyperbolic (in the sense of Leray--Ohya). Hence, if the fields were numerical valued, there would be an applicable existence theorem leading to well-posedness. We shall observe that well-posedness is assured if the fields are taken to be Grassmann (i.e., exterior algebra) valued, for then the second-order system decouples into the vacuum Einstein equation and a sequence of numerical valued linear diagonal strictly hyperbolic partial differential equations which can be solved successively

  3. Well-posedness and exponential stability for a wave equation with nonlocal time-delay condition

    Directory of Open Access Journals (Sweden)

    Carlos Alberto Raposo

    2017-11-01

    Full Text Available Well-posedness and exponential stability of nonlocal time-delayed of a wave equation with a integral conditions of the 1st kind forms the center of this work. Through semigroup theory we prove the well-posedness by the Hille-Yosida theorem and the exponential stability exploring the dissipative properties of the linear operator associated to damped model using the Gearhart-Huang-Pruss theorem.

  4. Well-posedness of one-dimensional Korteweg models

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    Sylvie Benzoni-Gavage

    2006-05-01

    Full Text Available We investigate the initial-value problem for one-dimensional compressible fluids endowed with internal capillarity. We focus on the isothermal inviscid case with variable capillarity. The resulting equations for the density and the velocity, consisting of the mass conservation law and the momentum conservation with Korteweg stress, are a system of third order nonlinear dispersive partial differential equations. Additionally, this system is Hamiltonian and admits travelling solutions, representing propagating phase boundaries with internal structure. By change of unknown, it roughly reduces to a quasilinear Schrodinger equation. This new formulation enables us to prove local well-posedness for smooth perturbations of travelling profiles and almost-global existence for small enough perturbations. A blow-up criterion is also derived.

  5. The Hartree Equation for Infinitely Many Particles I. Well-Posedness Theory

    Science.gov (United States)

    Lewin, Mathieu; Sabin, Julien

    2015-02-01

    We show local and global well-posedness results for the Hartree equation where γ is a bounded self-adjoint operator on , ρ γ ( x) = γ( x, x) and w is a smooth short-range interaction potential. The initial datum γ(0) is assumed to be a perturbation of a translation-invariant state γ f = f(-Δ) which describes a quantum system with an infinite number of particles, such as the Fermi sea at zero temperature, or the Fermi-Dirac and Bose-Einstein gases at positive temperature. Global well-posedness follows from the conservation of the relative (free) energy of the state γ( t), counted relatively to the stationary state γ f . We indeed use a general notion of relative entropy, which allows us to treat a wide class of stationary states f(-Δ). Our results are based on a Lieb-Thirring inequality at positive density and on a recent Strichartz inequality for orthonormal functions, which are both due to Frank, Lieb, Seiringer and the first author of this article.

  6. LP Well-Posedness for Bilevel Vector Equilibrium and Optimization Problems with Equilibrium Constraints

    OpenAIRE

    Khanh, Phan Quoc; Plubtieng, Somyot; Sombut, Kamonrat

    2014-01-01

    The purpose of this paper is introduce several types of Levitin-Polyak well-posedness for bilevel vector equilibrium and optimization problems with equilibrium constraints. Base on criterion and characterizations for these types of Levitin-Polyak well-posedness we argue on diameters and Kuratowski’s, Hausdorff’s, or Istrǎtescus measures of noncompactness of approximate solution sets under suitable conditions, and we prove the Levitin-Polyak well-posedness for bilevel vector equilibrium and op...

  7. Perturbed asymptotically linear problems

    OpenAIRE

    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...

  8. On well-posedness of variational models of charged drops.

    Science.gov (United States)

    Muratov, Cyrill B; Novaga, Matteo

    2016-03-01

    Electrified liquids are well known to be prone to a variety of interfacial instabilities that result in the onset of apparent interfacial singularities and liquid fragmentation. In the case of electrically conducting liquids, one of the basic models describing the equilibrium interfacial configurations and the onset of instability assumes the liquid to be equipotential and interprets those configurations as local minimizers of the energy consisting of the sum of the surface energy and the electrostatic energy. Here we show that, surprisingly, this classical geometric variational model is mathematically ill-posed irrespective of the degree to which the liquid is electrified. Specifically, we demonstrate that an isolated spherical droplet is never a local minimizer, no matter how small is the total charge on the droplet, as the energy can always be lowered by a smooth, arbitrarily small distortion of the droplet's surface. This is in sharp contrast to the experimental observations that a critical amount of charge is needed in order to destabilize a spherical droplet. We discuss several possible regularization mechanisms for the considered free boundary problem and argue that well-posedness can be restored by the inclusion of the entropic effects resulting in finite screening of free charges.

  9. Hyperbolic systems with analytic coefficients well-posedness of the Cauchy problem

    CERN Document Server

    Nishitani, Tatsuo

    2014-01-01

    This monograph focuses on the well-posedness of the Cauchy problem for linear hyperbolic systems with matrix coefficients. Mainly two questions are discussed: (A) Under which conditions on lower order terms is the Cauchy problem well posed? (B) When is the Cauchy problem well posed for any lower order term? For first order two by two systems with two independent variables with real analytic coefficients, we present complete answers for both (A) and (B). For first order systems with real analytic coefficients we prove general necessary conditions for question (B) in terms of minors of the principal symbols. With regard to sufficient conditions for (B), we introduce hyperbolic systems with nondegenerate characteristics, which contains strictly hyperbolic systems, and prove that the Cauchy problem for hyperbolic systems with nondegenerate characteristics is well posed for any lower order term. We also prove that any hyperbolic system which is close to a hyperbolic system with a nondegenerate characteristic of mu...

  10. Well-Posedness of Nonlocal Parabolic Differential Problems with Dependent Operators

    Directory of Open Access Journals (Sweden)

    Allaberen Ashyralyev

    2014-01-01

    Full Text Available The nonlocal boundary value problem for the parabolic differential equation v'(t+A(tv(t=f(t  (0≤t≤T,  v(0=v(λ+φ,  0<λ≤T in an arbitrary Banach space E with the dependent linear positive operator A(t is investigated. The well-posedness of this problem is established in Banach spaces C0β,γ(Eα-β of all Eα-β-valued continuous functions φ(t on [0,T] satisfying a Hölder condition with a weight (t+τγ. New Schauder type exact estimates in Hölder norms for the solution of two nonlocal boundary value problems for parabolic equations with dependent coefficients are established.

  11. Semiclassical limit and well-posedness of nonlinear Schrodinger-Poisson systems

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    Hailiang Li

    2003-09-01

    Full Text Available This paper concerns the well-posedness and semiclassical limit of nonlinear Schrodinger-Poisson systems. We show the local well-posedness and the existence of semiclassical limit of the two models for initial data with Sobolev regularity, before shocks appear in the limit system. We establish the existence of a global solution and show the time-asymptotic behavior of a classical solutions of Schrodinger-Poisson system for a fixed re-scaled Planck constant.

  12. Well-posedness and accuracy of the ensemble Kalman filter in discrete and continuous time

    KAUST Repository

    Kelly, D. T B

    2014-09-22

    The ensemble Kalman filter (EnKF) is a method for combining a dynamical model with data in a sequential fashion. Despite its widespread use, there has been little analysis of its theoretical properties. Many of the algorithmic innovations associated with the filter, which are required to make a useable algorithm in practice, are derived in an ad hoc fashion. The aim of this paper is to initiate the development of a systematic analysis of the EnKF, in particular to do so for small ensemble size. The perspective is to view the method as a state estimator, and not as an algorithm which approximates the true filtering distribution. The perturbed observation version of the algorithm is studied, without and with variance inflation. Without variance inflation well-posedness of the filter is established; with variance inflation accuracy of the filter, with respect to the true signal underlying the data, is established. The algorithm is considered in discrete time, and also for a continuous time limit arising when observations are frequent and subject to large noise. The underlying dynamical model, and assumptions about it, is sufficiently general to include the Lorenz \\'63 and \\'96 models, together with the incompressible Navier-Stokes equation on a two-dimensional torus. The analysis is limited to the case of complete observation of the signal with additive white noise. Numerical results are presented for the Navier-Stokes equation on a two-dimensional torus for both complete and partial observations of the signal with additive white noise.

  13. Global Well-Posedness for Cubic NLS with Nonlinear Damping

    KAUST Repository

    Antonelli, Paolo

    2010-11-04

    We study the Cauchy problem for the cubic nonlinear Schrödinger equation, perturbed by (higher order) dissipative nonlinearities. We prove global in-time existence of solutions for general initial data in the energy space. In particular we treat the energy-critical case of a quintic dissipation in three space dimensions. © Taylor & Francis Group, LLC.

  14. Global well-posedness for Schrödinger equation with derivative in H(R)

    Science.gov (United States)

    Miao, Changxing; Wu, Yifei; Xu, Guixiang

    In this paper, we consider the Cauchy problem of the cubic nonlinear Schrödinger equation with derivative in H(R). This equation was known to be the local well-posedness for s⩾1/2 > (Takaoka, 1999 [27]), ill-posedness for s (Biagioni and Linares, 2001 [1], etc.) and global well-posedness for s>1/2 > (I-team, 2002 [10]). In this paper, we show that it is global well-posedness in the endpoint space H(R), which remained open previously. The main approach is the third generation I-method combined with a new resonant decomposition technique. The resonant decomposition is applied to control the singularity coming from the resonant interaction.

  15. Cosmological perturbations beyond linear order

    CERN Multimedia

    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.

  16. Well-posedness and accuracy of the ensemble Kalman filter in discrete and continuous time

    International Nuclear Information System (INIS)

    Kelly, D T B; Stuart, A M; Law, K J H

    2014-01-01

    The ensemble Kalman filter (EnKF) is a method for combining a dynamical model with data in a sequential fashion. Despite its widespread use, there has been little analysis of its theoretical properties. Many of the algorithmic innovations associated with the filter, which are required to make a useable algorithm in practice, are derived in an ad hoc fashion. The aim of this paper is to initiate the development of a systematic analysis of the EnKF, in particular to do so for small ensemble size. The perspective is to view the method as a state estimator, and not as an algorithm which approximates the true filtering distribution. The perturbed observation version of the algorithm is studied, without and with variance inflation. Without variance inflation well-posedness of the filter is established; with variance inflation accuracy of the filter, with respect to the true signal underlying the data, is established. The algorithm is considered in discrete time, and also for a continuous time limit arising when observations are frequent and subject to large noise. The underlying dynamical model, and assumptions about it, is sufficiently general to include the Lorenz '63 and '96 models, together with the incompressible Navier–Stokes equation on a two-dimensional torus. The analysis is limited to the case of complete observation of the signal with additive white noise. Numerical results are presented for the Navier–Stokes equation on a two-dimensional torus for both complete and partial observations of the signal with additive white noise. (paper)

  17. Well-posedness of inverse problems for systems with time dependent parameters

    DEFF Research Database (Denmark)

    Banks, H. T.; Pedersen, Michael

    2009-01-01

    on the data of the problem. We also consider well-posedness as well as finite element type approximations in associated inverse problems. The problem above is a weak formulation that includes models in abstract differential operator form that include plate, beam and shell equations with several important...

  18. Global well-posedness for passively transported nonlinear moisture dynamics with phase changes

    Science.gov (United States)

    Hittmeir, Sabine; Klein, Rupert; Li, Jinkai; Titi, Edriss S.

    2017-10-01

    We study a moisture model for warm clouds that has been used by Klein and Majda (2006 Theor. Comput. Fluid Dyn. 20 525-551) as a basis for multiscale asymptotic expansions for deep convective phenomena. These moisture balance equations correspond to a bulk microphysics closure in the spirit of Kessler (1969 Meteorol. Monogr. 10 1-84) and Grabowski and Smolarkiewicz (1996 Mon. Weather Rev. 124 487-97), in which water is present in the gaseous state as water vapor and in the liquid phase as cloud water and rain water. It thereby contains closures for the phase changes condensation and evaporation, as well as the processes of autoconversion of cloud water into rainwater and the collection of cloud water by the falling rain droplets. Phase changes are associated with enormous amounts of latent heat and therefore provide a strong coupling to the thermodynamic equation. In this work we assume the velocity field to be given and prove rigorously the global existence and uniqueness of uniformly bounded solutions of the moisture model with viscosity, diffusion and heat conduction. To guarantee local well-posedness we first need to establish local existence results for linear parabolic equations, subject to the Robin boundary conditions on the cylindric type of domains under consideration. We then derive a priori estimates, for proving the maximum principle, using the Stampacchia method, as well as the iterative method by Alikakos (1979 J. Differ. Equ. 33 201-25) to obtain uniform boundedness. The evaporation term is of power law type, with an exponent in general less or equal to one and therefore making the proof of uniqueness more challenging. However, these difficulties can be circumvented by introducing new unknowns, which satisfy the required cancellation and monotonicity properties in the source terms.

  19. Sufficient conditions for Hadamard well-posedness of a coupled thermo-chemo-poroelastic system

    Directory of Open Access Journals (Sweden)

    Tetyana Malysheva

    2016-01-01

    Full Text Available This article addresses the well-posedness of a coupled parabolic-elliptic system modeling fully coupled thermal, chemical, hydraulic, and mechanical processes in porous formations that impact drilling and borehole stability. The underlying thermo-chemo-poroelastic model is a system of time-dependent parabolic equations describing thermal, solute, and fluid diffusions coupled with Navier-type elliptic equations that attempt to capture the elastic behavior of rock around a borehole. An existence and uniqueness theory for a corresponding initial-boundary value problem is an open problem in the field. We give sufficient conditions for the well-posedness in the sense of Hadamard of a weak solution to a fully coupled parabolic-elliptic initial-boundary value problem describing homogeneous and isotropic media.

  20. Well-posedness for Semi-relativistic Hartree Equations of Critical Type

    International Nuclear Information System (INIS)

    Lenzmann, Enno

    2007-01-01

    We prove local and global well-posedness for semi-relativistic, nonlinear Schroedinger equations with initial data in H s (R 3 ). Here F(u) is a critical Hartree nonlinearity that corresponds to Coulomb or Yukawa type self-interactions. For focusing F(u), which arise in the quantum theory of boson stars, we derive global-in-time existence for small initial data, where the smallness condition is expressed in terms of the L 2 -norm of solitary wave ground states. Our proof of well-posedness does not rely on Strichartz type estimates. As a major benefit from this, our method enables us to consider external potentials of a quite general class

  1. Global Well-Posedness of the NLS System for Infinitely Many Fermions

    Science.gov (United States)

    Chen, Thomas; Hong, Younghun; Pavlović, Nataša

    2017-04-01

    In this paper, we study the mean field quantum fluctuation dynamics for a system of infinitely many fermions with delta pair interactions in the vicinity of an equilibrium solution (the Fermi sea) at zero temperature, in dimensions d = 2, 3, and prove global well-posedness of the corresponding Cauchy problem. Our work extends some of the recent important results obtained by Lewin and Sabin in [33,34], who addressed this problem for more regular pair interactions.

  2. Well-posedness of a thermo-mechanical model for shape memory alloys under tension

    Czech Academy of Sciences Publication Activity Database

    Krejčí, Pavel; Stefanelli, U.

    2010-01-01

    Roč. 44, č. 6 (2010), s. 1239-1253 ISSN 0764-583X R&D Projects: GA ČR GAP201/10/2315 Institutional research plan: CEZ:AV0Z10190503 Keywords : shape memory alloys * thermo-mechanics * well-posedness * hysteresis operator Subject RIV: BA - General Mathematics Impact factor: 1.202, year: 2010 http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=8129335

  3. On the local well-posedness of Lovelock and Horndeski theories

    Science.gov (United States)

    Papallo, Giuseppe; Reall, Harvey S.

    2017-08-01

    We investigate local well-posedness of the initial value problem for Lovelock and Horndeski theories of gravity. A necessary condition for local well-posedness is strong hyperbolicity of the equations of motion. Even weak hyperbolicity can fail for strong fields so we restrict to weak fields. The Einstein equation is known to be strongly hyperbolic in harmonic gauge so we study Lovelock theories in harmonic gauge. We show that the equation of motion is always weakly hyperbolic for weak fields but, in a generic weak-field background, it is not strongly hyperbolic. For Horndeski theories, we prove that, for weak fields, the equation of motion is always weakly hyperbolic in any generalized harmonic gauge. For some Horndeski theories there exists a generalized harmonic gauge for which the equation of motion is strongly hyperbolic in a weak-field background. This includes "k-essence" like theories. However, for more general Horndeski theories, there is no generalized harmonic gauge for which the equation of motion is strongly hyperbolic in a generic weak-field background. Our results show that the standard method used to establish local well-posedness of the Einstein equation does not extend to Lovelock or general Horndeski theories. This raises the possibility that these theories may not admit a well-posed initial value problem even for weak fields.

  4. Existence and Hadamard well-posedness of a system of simultaneous generalized vector quasi-equilibrium problems

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    Wenyan Zhang

    2017-03-01

    Full Text Available Abstract An existence result for the solution set of a system of simultaneous generalized vector quasi-equilibrium problems (for short, (SSGVQEP is obtained, which improves Theorem 3.1 of the work of Ansari et al. (J. Optim. Theory Appl. 127:27-44, 2005. Moreover, a definition of Hadamard-type well-posedness for (SSGVQEP is introduced and sufficient conditions for Hadamard well-posedness of (SSGVQEP are established.

  5. Dispersive estimates for rational symbols and local well-posedness of the nonzero energy NV equation. II

    Science.gov (United States)

    Kazeykina, Anna; Muñoz, Claudio

    2018-04-01

    We continue our study on the Cauchy problem for the two-dimensional Novikov-Veselov (NV) equation, integrable via the inverse scattering transform for the two dimensional Schrödinger operator at a fixed energy parameter. This work is concerned with the more involved case of a positive energy parameter. For the solution of the linearized equation we derive smoothing and Strichartz estimates by combining new estimates for two different frequency regimes, extending our previous results for the negative energy case [18]. The low frequency regime, which our previous result was not able to treat, is studied in detail. At non-low frequencies we also derive improved smoothing estimates with gain of almost one derivative. Then we combine the linear estimates with a Fourier decomposition method and Xs,b spaces to obtain local well-posedness of NV at positive energy in Hs, s > 1/2. Our result implies, in particular, that at least for s > 1/2, NV does not change its behavior from semilinear to quasilinear as energy changes sign, in contrast to the closely related Kadomtsev-Petviashvili equations. As a complement to our LWP results, we also provide some new explicit solutions of NV at zero energy, generalizations of the lumps solutions, which exhibit new and nonstandard long time behavior. In particular, these solutions blow up in infinite time in L2.

  6. Global Well-Posedness of the Boltzmann Equation with Large Amplitude Initial Data

    Science.gov (United States)

    Duan, Renjun; Huang, Feimin; Wang, Yong; Yang, Tong

    2017-07-01

    The global well-posedness of the Boltzmann equation with initial data of large amplitude has remained a long-standing open problem. In this paper, by developing a new {L^∞_xL^1v\\cap L^∞_{x,v}} approach, we prove the global existence and uniqueness of mild solutions to the Boltzmann equation in the whole space or torus for a class of initial data with bounded velocity-weighted {L^∞} norm under some smallness condition on the {L^1_xL^∞_v} norm as well as defect mass, energy and entropy so that the initial data allow large amplitude oscillations. Both the hard and soft potentials with angular cut-off are considered, and the large time behavior of solutions in the {L^∞_{x,v}} norm with explicit rates of convergence are also studied.

  7. Population density models of integrate-and-fire neurons with jumps: well-posedness.

    Science.gov (United States)

    Dumont, Grégory; Henry, Jacques

    2013-09-01

    In this paper we study the well-posedness of different models of population of leaky integrate-and-fire neurons with a population density approach. The synaptic interaction between neurons is modeled by a potential jump at the reception of a spike. We study populations that are self excitatory or self inhibitory. We distinguish the cases where this interaction is instantaneous from the one where there is a repartition of conduction delays. In the case of a bounded density of delays both excitatory and inhibitory population models are shown to be well-posed. But without conduction delay the solution of the model of self excitatory neurons may blow up. We analyze the different behaviours of the model with jumps compared to its diffusion approximation.

  8. Perturbation analysis of linear control problems

    International Nuclear Information System (INIS)

    Petkov, Petko; Konstantinov, Mihail

    2017-01-01

    The paper presents a brief overview of the technique of splitting operators, proposed by the authors and intended for perturbation analysis of control problems involving unitary and orthogonal matrices. Combined with the technique of Lyapunov majorants and the implementation of the Banach and Schauder fixed point principles, it allows to obtain rigorous non-local perturbation bounds for a set of sensitivity analysis problems. Among them are the reduction of linear systems into orthogonal canonical forms, the feedback synthesis problem and pole assignment problem in particular, as well as other important problems in control theory and linear algebra. Key words: perturbation analysis, canonical forms, feedback synthesis

  9. Study on the well-posedness, convergence and the stability of the semi-implicit upwind numerical solver for the multi-fluid model

    International Nuclear Information System (INIS)

    Lee, S. Y.; Park, C. E.; Hibiki, T.; Ishii, M.; Ransom, V. H.

    2012-01-01

    conditions for well-posedness are met. To study the non-linear stability and the convergence, various runs with the torus problem using the SPACE code are utilized to confirm the frequency cascading effects that augment non-linear stability. A robust mechanism for the flow regime change is also a very important factor for developing non-linearly stable and convergent code. A open pipe flow problem is also simulated to investigate the non-linear stability effects in a flow geometry more typical of real safety code applications. (authors)

  10. Well-posedness of the Cauchy problem for models of large amplitude internal waves

    International Nuclear Information System (INIS)

    Guyenne, Philippe; Lannes, David; Saut, Jean-Claude

    2010-01-01

    We consider in this paper the 'shallow-water/shallow-water' asymptotic model obtained in Choi and Camassa (1999 J. Fluid Mech. 396 1–36), Craig et al (2005 Commun. Pure. Appl. Math. 58 1587–641) (one-dimensional interface) and Bona et al (2008 J. Math. Pures Appl. 89 538–66) (two-dimensional interface) from the two-layer system with rigid lid, for the description of large amplitude internal waves at the interface of two layers of immiscible fluids of different densities. For one-dimensional interfaces, this system is of hyperbolic type and its local well-posedness does not raise serious difficulties, although other issues (blow-up, loss of hyperbolicity, etc) turn out to be delicate. For two-dimensional interfaces, the system is nonlocal. Nevertheless, we prove that it conserves some properties of 'hyperbolic type' and show that the associated Cauchy problem is locally well posed in suitable Sobolev classes provided some natural restrictions are imposed on the data. These results are illustrated by numerical simulations with emphasis on the formation of shock waves

  11. Mathematical well-posedness of a two-fluid equations for bubbly two-phase flows

    International Nuclear Information System (INIS)

    Okawa, Tomio; Kataoka, Isao

    2000-01-01

    It is widely known that two-fluid equations used in most engineering applications do not satisfy the necessary condition for being mathematical well-posed as initial-value problems. In the case of stratified two-phase flows, several researchers have revealed that differential models satisfying the necessary condition are to be derived if the pressure difference between the phases is related to the spatial gradient of the void fraction through the effects of gravity or surface tension. While, in the case of dispersed two-phase flows, no physically reasonable method to derive mathematically well-posed two-fluid model has been proposed. In the present study, particularly focusing on the effect of interfacial pressure terms, we derived the mathematically closed form of the volume-averaged two-fluid model for bubbly two-phase flows. As a result of characteristic analyses, it was shown that the proposed two-fluid equations satisfy the necessary condition of mathematical well-posedness if the void fraction is sufficiently small. (author)

  12. Well-Posedness and Primal-Dual Analysis of Some Convex Separable Optimization Problems

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    Stefan M. Stefanov

    2013-01-01

    Full Text Available We focus on some convex separable optimization problems, considered by the author in previous papers, for which problems, necessary and sufficient conditions or sufficient conditions have been proved, and convergent algorithms of polynomial computational complexity have been proposed for solving these problems. The concepts of well-posedness of optimization problems in the sense of Tychonov, Hadamard, and in a generalized sense, as well as calmness in the sense of Clarke, are discussed. It is shown that the convex separable optimization problems under consideration are calm in the sense of Clarke. The concept of stability of the set of saddle points of the Lagrangian in the sense of Gol'shtein is also discussed, and it is shown that this set is not stable for the “classical” Lagrangian. However, it turns out that despite this instability, due to the specificity of the approach, suggested by the author for solving problems under consideration, it is not necessary to use modified Lagrangians but only the “classical” Lagrangians. Also, a primal-dual analysis for problems under consideration in view of methods for solving them is presented.

  13. Well-Posedness of a fully coupled thermo-chemo-poroelastic system with applications to petroleum rock mechanics

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    Tetyana Malysheva

    2017-05-01

    Full Text Available We consider a system of fully coupled parabolic and elliptic equations constituting the general model of chemical thermo-poroelasticity for a fluid-saturated porous media. The main result of this paper is the developed well-posedness theory for the corresponding initial-boundary problem arising from petroleum rock mechanics applications. Using the proposed pseudo-decoupling method, we establish, subject to some natural assumptions imposed on matrices of diffusion coefficients, the existence, uniqueness, and continuous dependence on initial and boundary data of a weak solution to the problem. Numerical experiments confirm the applicability of the obtained well-posedness results for thermo-chemo-poroelastic models with real-data parameters.

  14. Well-posedness of the conductivity reconstruction from an interior current density in terms of Schauder theory

    KAUST Repository

    Kim, Yong-Jung

    2015-06-23

    We show the well-posedness of the conductivity image reconstruction problem with a single set of interior electrical current data and boundary conductivity data. Isotropic conductivity is considered in two space dimensions. Uniqueness for similar conductivity reconstruction problems has been known for several cases. However, the existence and the stability are obtained in this paper for the first time. The main tool of the proof is the method of characteristics of a related curl equation.

  15. Non-local PDEs with discrete state-dependent delays: Well-posedness in a metric space

    Czech Academy of Sciences Publication Activity Database

    Rezunenko, Oleksandr; Zagalak, Petr

    2013-01-01

    Roč. 33, č. 2 (2013), s. 819-835 ISSN 1078-0947 R&D Projects: GA ČR(CZ) GAP103/12/2431 Institutional support: RVO:67985556 Keywords : Partial differential equations with delay s * well-posedness * metric space Subject RIV: BC - Control Systems Theory Impact factor: 0.923, year: 2013 http://library.utia.cas.cz/separaty/2012/AS/zagalak-0381969.pdf

  16. Well-posedness for the Cauchy problem of the Klein-Gordon-Zakharov system in 2D

    OpenAIRE

    Kinoshita, Shinya

    2016-01-01

    This paper is concerned with the Cauchy problem of $2$D Klein-Gordon-Zakharov system with very low regularity initial data. We prove the bilinear estimates which are crucial to get the local in time well-posedness. The estimates are established by the Fourier restriction norm method. We utilize the bilinear Strichartz estimates and the nonlinear version of the classical Loomis-Whitney inequality which was applied to Zakharov system.

  17. Well-posedness of the conductivity reconstruction from an interior current density in terms of Schauder theory

    KAUST Repository

    Kim, Yong-Jung; Lee, Min-Gi

    2015-01-01

    We show the well-posedness of the conductivity image reconstruction problem with a single set of interior electrical current data and boundary conductivity data. Isotropic conductivity is considered in two space dimensions. Uniqueness for similar conductivity reconstruction problems has been known for several cases. However, the existence and the stability are obtained in this paper for the first time. The main tool of the proof is the method of characteristics of a related curl equation.

  18. Global well-posedness for the radial defocusing cubic wave equation on $R^3$ and for rough data

    Directory of Open Access Journals (Sweden)

    Tristan Roy

    2007-11-01

    Full Text Available We prove global well-posedness for the radial defocusing cubic wave equation $$displaylines{ partial_{tt} u - Delta u = -u^{3} cr u(0,x = u_{0}(x cr partial_{t} u(0,x = u_{1}(x }$$ with data $(u_0, u_1 in H^{s} imes H^{s-1}$, $1 > s >7/10$. The proof relies upon a Morawetz-Strauss-type inequality that allows us to control the growth of an almost conserved quantity.

  19. Global well-posedness and scattering for the focusing nonlinear Schrödinger equation in the nonradial case

    Directory of Open Access Journals (Sweden)

    Pigong Han

    2012-01-01

    Full Text Available The energy-critical, focusing nonlinear Schrödinger equation in the nonradial case reads as follows: \\[i\\partial_t u = -\\Delta u -|u|^{\\frac{4}{N-2}}u,\\quad (x,0=u_0 \\in H^1 (\\mathbb{R}^N,\\quad N\\geq 3.\\] Under a suitable assumption on the maximal strong solution, using a compactness argument and a virial identity, we establish the global well-posedness and scattering in the nonradial case, which gives a positive answer to one open problem proposed by Kenig and Merle [Invent. Math. 166 (2006, 645–675].

  20. Running vacuum cosmological models: linear scalar perturbations

    Energy Technology Data Exchange (ETDEWEB)

    Perico, E.L.D. [Instituto de Física, Universidade de São Paulo, Rua do Matão 1371, CEP 05508-090, São Paulo, SP (Brazil); Tamayo, D.A., E-mail: elduartep@usp.br, E-mail: tamayo@if.usp.br [Departamento de Astronomia, Universidade de São Paulo, Rua do Matão 1226, CEP 05508-900, São Paulo, SP (Brazil)

    2017-08-01

    In cosmology, phenomenologically motivated expressions for running vacuum are commonly parameterized as linear functions typically denoted by Λ( H {sup 2}) or Λ( R ). Such models assume an equation of state for the vacuum given by P-bar {sub Λ} = - ρ-bar {sub Λ}, relating its background pressure P-bar {sub Λ} with its mean energy density ρ-bar {sub Λ} ≡ Λ/8π G . This equation of state suggests that the vacuum dynamics is due to an interaction with the matter content of the universe. Most of the approaches studying the observational impact of these models only consider the interaction between the vacuum and the transient dominant matter component of the universe. We extend such models by assuming that the running vacuum is the sum of independent contributions, namely ρ-bar {sub Λ} = Σ {sub i} ρ-bar {sub Λ} {sub i} . Each Λ i vacuum component is associated and interacting with one of the i matter components in both the background and perturbation levels. We derive the evolution equations for the linear scalar vacuum and matter perturbations in those two scenarios, and identify the running vacuum imprints on the cosmic microwave background anisotropies as well as on the matter power spectrum. In the Λ( H {sup 2}) scenario the vacuum is coupled with every matter component, whereas the Λ( R ) description only leads to a coupling between vacuum and non-relativistic matter, producing different effects on the matter power spectrum.

  1. Well-posedness and ill-posedness of the fifth-order modified KdV equation

    Directory of Open Access Journals (Sweden)

    Soonsik Kwon

    2008-01-01

    Full Text Available We consider the initial value problem of the fifth-order modified KdV equation on the Sobolev spaces. $$displaylines{ partial_t u - partial_x^5u + c_1partial_x^3(u^3 + c_2upartial_x upartial_x^2 u + c_3uupartial_x^3 u =0cr u(x,0= u_0(x }$$ where $u:mathbb{R}imesmathbb{R} o mathbb{R} $ and $c_j$'s are real. We show the local well-posedness in $H^s(mathbb{R}$ for $sgeq 3/4$ via the contraction principle on $X^{s,b}$ space. Also, we show that the solution map from data to the solutions fails to be uniformly continuous below $H^{3/4}(mathbb{R}$. The counter example is obtained by approximating the fifth order mKdV equation by the cubic NLS equation.

  2. A necessary and sufficient condition for well-posedness of initial value problems of retarded functional differential equations

    Science.gov (United States)

    Nishiguchi, Junya

    2017-09-01

    We introduce the retarded functional differential equations (RFDEs) with general delay structure to treat various delay differential equations (DDEs) in a unified way and to clarify the delay structure in those dynamics. We are interested in the question as to which space of histories is suitable for the dynamics of each DDE, and investigate the well-posedness of the initial value problems (IVPs) of the RFDEs. A main theorem is that the IVP is well-posed for any ;admissible; history functional if and only if the semigroup determined by the trivial RFDE x ˙ = 0 is continuous. We clarify the meaning of the Hale-Kato axiom (Hale & Kato [12]) by applying this result to RFDEs with infinite delay. We also apply the result to DDEs with unbounded time- and state-dependent delays.

  3. Bounded Perturbation Regularization for Linear Least Squares Estimation

    KAUST Repository

    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

  4. 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

  5. Global well-posedness and asymptotic behavior of solutions for the three-dimensional MHD equations with Hall and ion-slip effects

    Science.gov (United States)

    Zhao, Xiaopeng; Zhu, Mingxuan

    2018-04-01

    In this paper, we consider the small initial data global well-posedness of solutions for the magnetohydrodynamics with Hall and ion-slip effects in R^3. In addition, we also establish the temporal decay estimates for the weak solutions. With these estimates in hand, we study the algebraic time decay for higher-order Sobolev norms of small initial data solutions.

  6. Non-linear perturbations of a spherically collapsing star

    International Nuclear Information System (INIS)

    Brizuela, David

    2009-01-01

    Linear perturbation theory has been a successful tool in General Relativity, and can be considered as complementary to full nonlinear simulations. Going to second and higher perturbative orders improves the approximation and offers a controlled way to analyze the nonlinearities of the theory, though the problem becomes much harder computationally. We present a systematic approach to the treatment of high order metric perturbations, focusing on the scenario of nonspherical perturbations of a dynamical spherical background. It is based on the combination of adapted geometrical variables and the use of efficient computer algebra techniques. After dealing with a number of theoretical issues, like the construction of gauge invariants, we apply the formalism to the particular case of a perfect fluid star surrounded by a vacuum exterior. We describe the regularization of the divergences of the perturbations at null infinity and the matching conditions through the surface of the star.

  7. Expressions for linearized perturbations in ideal-fluid cosmological models

    International Nuclear Information System (INIS)

    Ratra, B.

    1988-01-01

    We present closed-form solutions of the relativistic linear perturbation equations (in synchronous gauge) that govern the evolution of inhomogeneities in homogeneous, spatially flat, ideal-fluid, cosmological models. These expressions, which are valid for irregularities on any scale, allow one to analytically interpolate between the known approximate solutions which are valid at early times and at late times

  8. 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.

  9. EDITORIAL: Non-linear and non-Gaussian cosmological perturbations Non-linear and non-Gaussian cosmological perturbations

    Science.gov (United States)

    Sasaki, Misao; Wands, David

    2010-06-01

    In recent years there has been a resurgence of interest in the study of non-linear perturbations of cosmological models. This has been the result of both theoretical developments and observational advances. New theoretical challenges arise at second and higher order due to mode coupling and the need to develop new gauge-invariant variables beyond first order. In particular, non-linear interactions lead to deviations from a Gaussian distribution of primordial perturbations even if initial vacuum fluctuations are exactly Gaussian. These non-Gaussianities provide an important probe of models for the origin of structure in the very early universe. We now have a detailed picture of the primordial distribution of matter from surveys of the cosmic microwave background, notably NASA's WMAP satellite. The situation will continue to improve with future data from the ESA Planck satellite launched in 2009. To fully exploit these data cosmologists need to extend non-linear cosmological perturbation theory beyond the linear theory that has previously been sufficient on cosmological scales. Another recent development has been the realization that large-scale structure, revealed in high-redshift galaxy surveys, could also be sensitive to non-linearities in the primordial curvature perturbation. This focus section brings together a collection of invited papers which explore several topical issues in this subject. We hope it will be of interest to theoretical physicists and astrophysicists alike interested in understanding and interpreting recent developments in cosmological perturbation theory and models of the early universe. Of course it is only an incomplete snapshot of a rapidly developing field and we hope the reader will be inspired to read further work on the subject and, perhaps, fill in some of the missing pieces. This focus section is dedicated to the memory of Lev Kofman (1957-2009), an enthusiastic pioneer of inflationary cosmology and non-Gaussian perturbations.

  10. Canonical perturbation theory in linearized general relativity theory

    International Nuclear Information System (INIS)

    Gonzales, R.; Pavlenko, Yu.G.

    1986-01-01

    Canonical perturbation theory in linearized general relativity theory is developed. It is shown that the evolution of arbitrary dynamic value, conditioned by the interaction of particles, gravitation and electromagnetic fields, can be presented in the form of a series, each member of it corresponding to the contribution of certain spontaneous or induced process. The main concepts of the approach are presented in the approximation of a weak gravitational field

  11. Uniform in N global well-posedness of the time-dependent Hartree-Fock-Bogoliubov equations in R^{1+1}

    Science.gov (United States)

    Chong, Jacky Jia Wei

    2018-04-01

    We prove the global well-posedness of the time-dependent Hartree-Fock-Bogoliubov (TDHFB) equations in R^{1+1} with two-body interaction potential of the form N^{-1}v_N(x) = N^{β -1} v(N^β x) where v≥0 is a sufficiently regular radial function, i.e., v \\in L^1(R)\\cap C^∞ (R) . In particular, using methods of dispersive PDEs similar to the ones used in Grillakis and Machedon (Commun Partial Differ Equ 42:24-67, 2017), we are able to show for any scaling parameter β >0 the TDHFB equations are globally well-posed in some Strichartz-type spaces independent of N, cf. (Bach et al. in The time-dependent Hartree-Fock-Bogoliubov equations for Bosons, 2016. arXiv:1602.05171).

  12. Well-posedness and exact controllability of a fourth order Schrodinger equation with variable coefficients and Neumann boundary control and collocated observation

    Directory of Open Access Journals (Sweden)

    Ruili Wen

    2016-08-01

    Full Text Available We consider an open-loop system of a fourth order Schrodinger equation with variable coefficients and Neumann boundary control and collocated observation. Using the multiplier method on Riemannian manifold we show that that the system is well-posed in the sense of Salamon. This implies that the exponential stability of the closed-loop system under the direct proportional output feedback control and the exact controllability of open-loop system are equivalent. So in order to conclude feedback stabilization from well-posedness, we study the exact controllability under a uniqueness assumption by presenting the observability inequality for the dual system. In addition, we show that the system is regular in the sense of Weiss, and that the feedthrough operator is zero.

  13. Bounded Perturbation Regularization for Linear Least Squares Estimation

    KAUST Repository

    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.

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

    CERN Document Server

    Sung Il Kwon

    2002-01-01

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

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

    International Nuclear Information System (INIS)

    SUNG-IL KWON; AMY H. REGAN

    2002-01-01

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

  16. Bounds and estimates for the linearly perturbed eigenvalue problem

    International Nuclear Information System (INIS)

    Raddatz, W.D.

    1983-01-01

    This thesis considers the problem of bounding and estimating the discrete portion of the spectrum of a linearly perturbed self-adjoint operator, M(x). It is supposed that one knows an incomplete set of data consisting in the first few coefficients of the Taylor series expansions of one or more of the eigenvalues of M(x) about x = 0. The foundations of the variational study of eigen-values are first presented. These are then used to construct the best possible upper bounds and estimates using various sets of given information. Lower bounds are obtained by estimating the error in the upper bounds. The extension of these bounds and estimates to the eigenvalues of the doubly-perturbed operator M(x,y) is discussed. The results presented have numerous practical application in the physical sciences, including problems in atomic physics and the theory of vibrations of acoustical and mechanical systems

  17. Large data well-posedness in the energy space of the Chern-Simons-Schrödinger system

    Science.gov (United States)

    Lim, Zhuo Min

    2018-02-01

    We consider the initial-value problem for the Chern-Simons-Schrödinger system, which is a gauge-covariant Schrödinger system in Rt × Rx2 with a long-range electromagnetic field. We show that, in the Coulomb gauge, it is locally well-posed in Hs for s ⩾ 1, and the solution map satisfies a local-in-time weak Lipschitz bound. By energy conservation, we also obtain a global regularity result. The key is to retain the non-perturbative part of the derivative nonlinearity in the principal operator, and exploit the dispersive properties of the resulting paradifferential-type principal operator using adapted Up and Vp spaces.

  18. Exact non-linear equations for cosmological perturbations

    Energy Technology Data Exchange (ETDEWEB)

    Gong, Jinn-Ouk [Asia Pacific Center for Theoretical Physics, Pohang 37673 (Korea, Republic of); Hwang, Jai-chan [Department of Astronomy and Atmospheric Sciences, Kyungpook National University, Daegu 41566 (Korea, Republic of); Noh, Hyerim [Korea Astronomy and Space Science Institute, Daejeon 34055 (Korea, Republic of); Wu, David Chan Lon; Yoo, Jaiyul, E-mail: jinn-ouk.gong@apctp.org, E-mail: jchan@knu.ac.kr, E-mail: hr@kasi.re.kr, E-mail: clwu@physik.uzh.ch, E-mail: jyoo@physik.uzh.ch [Center for Theoretical Astrophysics and Cosmology, Institute for Computational Science, Universität Zürich, CH-8057 Zürich (Switzerland)

    2017-10-01

    We present a complete set of exact and fully non-linear equations describing all three types of cosmological perturbations—scalar, vector and tensor perturbations. We derive the equations in a thoroughly gauge-ready manner, so that any spatial and temporal gauge conditions can be employed. The equations are completely general without any physical restriction except that we assume a flat homogeneous and isotropic universe as a background. We also comment briefly on the application of our formulation to the non-expanding Minkowski background.

  19. Linear Perturbation Adaptive Control of Hydraulically Driven Manipulators

    DEFF Research Database (Denmark)

    Andersen, T.O.; Hansen, M.R.; Conrad, Finn

    2004-01-01

    control.Using the Lyapunov approach, under slowly time-varying assumptions, it is shown that the tracking error and the parameter error remain bounded. This bound is a function of the ideal parameters and a bounded disturbance. The control algorithm decouples and linearizes the manipulator so that each......A method for synthesis of a robust adaptive scheme for a hydraulically driven manipulator, that takes full advantage of any known system dynamics to simplify the adaptive control problem for the unknown portion of the dynamics is presented. The control method is based on adaptive perturbation...

  20. On the non-linear scale of cosmological perturbation theory

    CERN Document Server

    Blas, Diego; Konstandin, Thomas

    2013-01-01

    We discuss the convergence of cosmological perturbation theory. We prove that the polynomial enhancement of the non-linear corrections expected from the effects of soft modes is absent in equal-time correlators like the power or bispectrum. We first show this at leading order by resumming the most important corrections of soft modes to an arbitrary skeleton of hard fluctuations. We derive the same result in the eikonal approximation, which also allows us to show the absence of enhancement at any order. We complement the proof by an explicit calculation of the power spectrum at two-loop order, and by further numerical checks at higher orders. Using these insights, we argue that the modification of the power spectrum from soft modes corresponds at most to logarithmic corrections. Finally, we discuss the asymptotic behavior in the large and small momentum regimes and identify the expansion parameter pertinent to non-linear corrections.

  1. On the non-linear scale of cosmological perturbation theory

    International Nuclear Information System (INIS)

    Blas, Diego; Garny, Mathias; Konstandin, Thomas

    2013-04-01

    We discuss the convergence of cosmological perturbation theory. We prove that the polynomial enhancement of the non-linear corrections expected from the effects of soft modes is absent in equal-time correlators like the power or bispectrum. We first show this at leading order by resumming the most important corrections of soft modes to an arbitrary skeleton of hard fluctuations. We derive the same result in the eikonal approximation, which also allows us to show the absence of enhancement at any order. We complement the proof by an explicit calculation of the power spectrum at two-loop order, and by further numerical checks at higher orders. Using these insights, we argue that the modification of the power spectrum from soft modes corresponds at most to logarithmic corrections. Finally, we discuss the asymptotic behavior in the large and small momentum regimes and identify the expansion parameter pertinent to non-linear corrections.

  2. On the non-linear scale of cosmological perturbation theory

    Energy Technology Data Exchange (ETDEWEB)

    Blas, Diego [European Organization for Nuclear Research (CERN), Geneva (Switzerland); Garny, Mathias; Konstandin, Thomas [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)

    2013-04-15

    We discuss the convergence of cosmological perturbation theory. We prove that the polynomial enhancement of the non-linear corrections expected from the effects of soft modes is absent in equal-time correlators like the power or bispectrum. We first show this at leading order by resumming the most important corrections of soft modes to an arbitrary skeleton of hard fluctuations. We derive the same result in the eikonal approximation, which also allows us to show the absence of enhancement at any order. We complement the proof by an explicit calculation of the power spectrum at two-loop order, and by further numerical checks at higher orders. Using these insights, we argue that the modification of the power spectrum from soft modes corresponds at most to logarithmic corrections. Finally, we discuss the asymptotic behavior in the large and small momentum regimes and identify the expansion parameter pertinent to non-linear corrections.

  3. Linear perturbations of a self-similar solution of hydrodynamics with non-linear heat conduction

    International Nuclear Information System (INIS)

    Dubois-Boudesocque, Carine

    2000-01-01

    The stability of an ablative flow, where a shock wave is located upstream a thermal front, is of importance in inertial confinement fusion. The present model considers an exact self-similar solution to the hydrodynamic equations with non-linear heat conduction for a semi-infinite slab. For lack of an analytical solution, a high resolution numerical procedure is devised, which couples a finite difference method with a relaxation algorithm using a two-domain pseudo-spectral method. Stability of this solution is studied by introducing linear perturbation method within a Lagrangian-Eulerian framework. The initial and boundary value problem is solved by a splitting of the equations between a hyperbolic system and a parabolic equation. The boundary conditions of the hyperbolic system are treated, in the case of spectral methods, according to Thompson's approach. The parabolic equation is solved by an influence matrix method. These numerical procedures have been tested versus exact solutions. Considering a boundary heat flux perturbation, the space-time evolution of density, velocity and temperature are shown. (author) [fr

  4. Linear and non-linear amplification of high-mode perturbations at the ablation front in HiPER targets

    Energy Technology Data Exchange (ETDEWEB)

    Olazabal-Loume, M; Breil, J; Hallo, L; Ribeyre, X [CELIA, UMR 5107 Universite Bordeaux 1-CNRS-CEA, 351 cours de la Liberation, 33405 Talence (France); Sanz, J, E-mail: olazabal@celia.u-bordeaux1.f [ETSI Aeronauticos, Universidad Politecnica de Madrid, Madrid 28040 (Spain)

    2011-01-15

    The linear and non-linear sensitivity of the 180 kJ baseline HiPER target to high-mode perturbations, i.e. surface roughness, is addressed using two-dimensional simulations and a complementary analysis by linear and non-linear ablative Rayleigh-Taylor models. Simulations provide an assessment of an early non-linear stage leading to a significant deformation of the ablation surface for modes of maximum linear growth factor. A design using a picket prepulse evidences an improvement in the target stability inducing a delay of the non-linear behavior. Perturbation evolution and shape, evidenced by simulations of the non-linear stage, are analyzed with existing self-consistent non-linear theory.

  5. Dynamics of linear perturbations in f(R) gravity

    International Nuclear Information System (INIS)

    Bean, Rachel; Bernat, David; Pogosian, Levon; Silvestri, Alessandra; Trodden, Mark

    2007-01-01

    We consider predictions for structure formation from modifications to general relativity in which the Einstein-Hilbert action is replaced by a general function of the Ricci scalar. We work without fixing a gauge, as well as in explicit popular coordinate choices, appropriate for the modification of existing cosmological code. We present the framework in a comprehensive and practical form that can be directly compared to standard perturbation analyses. By considering the full evolution equations, we resolve perceived instabilities previously suggested, and instead find a suppression of perturbations. This result presents significant challenges for agreement with current cosmological structure formation observations. The findings apply to a broad range of forms of f(R) for which the modification becomes important at low curvatures, disfavoring them in comparison with the ΛCDM scenario. As such, these results provide a powerful method to rule out a wide class of modified gravity models aimed at providing an alternative explanation to the dark energy problem

  6. The non-linear Perron-Frobenius theorem : Perturbations and aggregation

    NARCIS (Netherlands)

    Dietzenbacher, E

    The dominant eigenvalue and the corresponding eigenvector (or Perron vector) of a non-linear eigensystem are considered. We discuss the effects upon these, of perturbations and of aggregation of the underlying mapping. The results are applied to study the sensivity of the outputs in a non-linear

  7. How pathogens use linear motifs to perturb host cell networks

    KAUST Repository

    Via, Allegra; Uyar, Bora; Brun, Christine; Zanzoni, Andreas

    2015-01-01

    Molecular mimicry is one of the powerful stratagems that pathogens employ to colonise their hosts and take advantage of host cell functions to guarantee their replication and dissemination. In particular, several viruses have evolved the ability to interact with host cell components through protein short linear motifs (SLiMs) that mimic host SLiMs, thus facilitating their internalisation and the manipulation of a wide range of cellular networks. Here we present convincing evidence from the literature that motif mimicry also represents an effective, widespread hijacking strategy in prokaryotic and eukaryotic parasites. Further insights into host motif mimicry would be of great help in the elucidation of the molecular mechanisms behind host cell invasion and the development of anti-infective therapeutic strategies.

  8. Application of linear programming and perturbation theory in optimization of fuel utilization in a nuclear reactor

    International Nuclear Information System (INIS)

    Zavaljevski, N.

    1985-01-01

    Proposed optimization procedure is fast due to application of linear programming. Non-linear constraints which demand iterative application of linear programming are slowing down the calculation. Linearization can be done by different procedures starting from simple empirical rules for fuel in-core management to complicated general perturbation theory with higher order of corrections. A mathematical model was formulated for optimization of improved fuel cycle. A detailed algorithm for determining minimum of fresh fuel at the beginning of each fuel cycle is shown and the problem is linearized by first order perturbation theory and it is optimized by linear programming. Numerical illustration of the proposed method was done for the experimental reactor mostly for saving computer time

  9. Connection between perturbation theory, projection-operator techniques, and statistical linearization for nonlinear systems

    International Nuclear Information System (INIS)

    Budgor, A.B.; West, B.J.

    1978-01-01

    We employ the equivalence between Zwanzig's projection-operator formalism and perturbation theory to demonstrate that the approximate-solution technique of statistical linearization for nonlinear stochastic differential equations corresponds to the lowest-order β truncation in both the consolidated perturbation expansions and in the ''mass operator'' of a renormalized Green's function equation. Other consolidated equations can be obtained by selectively modifying this mass operator. We particularize the results of this paper to the Duffing anharmonic oscillator equation

  10. Absorption line profiles in a moving atmosphere - A single scattering linear perturbation theory

    Science.gov (United States)

    Hays, P. B.; Abreu, V. J.

    1989-01-01

    An integral equation is derived which linearly relates Doppler perturbations in the spectrum of atmospheric absorption features to the wind system which creates them. The perturbation theory is developed using a single scattering model, which is validated against a multiple scattering calculation. The nature and basic properties of the kernels in the integral equation are examined. It is concluded that the kernels are well behaved and that wind velocity profiles can be recovered using standard inversion techniques.

  11. Linear analysis on the growth of non-spherical perturbations in supersonic accretion flows

    Energy Technology Data Exchange (ETDEWEB)

    Takahashi, Kazuya; Yamada, Shoichi, E-mail: ktakahashi@heap.phys.waseda.ac.jp [Advanced Research Institute for Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku 169-8555 (Japan)

    2014-10-20

    We analyzed the growth of non-spherical perturbations in supersonic accretion flows. We have in mind an application to the post-bounce phase of core-collapse supernovae (CCSNe). Such non-spherical perturbations have been suggested by a series of papers by Arnett, who has numerically investigated violent convections in the outer layers of pre-collapse stars. Moreover, Couch and Ott demonstrated in their numerical simulations that such perturbations may lead to a successful supernova even for a progenitor that fails to explode without fluctuations. This study investigated the linear growth of perturbations during the infall onto a stalled shock wave. The linearized equations are solved as an initial and boundary value problem with the use of a Laplace transform. The background is a Bondi accretion flow whose parameters are chosen to mimic the 15 M {sub ☉} progenitor model by Woosley and Heger, which is supposed to be a typical progenitor of CCSNe. We found that the perturbations that are given at a large radius grow as they flow down to the shock radius; the density perturbations can be amplified by a factor of 30, for example. We analytically show that the growth rate is proportional to l, the index of the spherical harmonics. We also found that the perturbations oscillate in time with frequencies that are similar to those of the standing accretion shock instability. This may have an implication for shock revival in CCSNe, which will be investigated in our forthcoming paper in more detail.

  12. Linear theory of density perturbations in a neutrino+baryon universe

    International Nuclear Information System (INIS)

    Wasserman, I.

    1981-01-01

    Various aspects of the linear theory of density perturbations in a universe containing a significant population of massive neutrinos are calculated. Because linear perturbations in the neutrino density are subject to nonviscous damping on length scales smaller than the effective neutrino Jeans length, the fluctuation spectrum of the neutrino density perturbations just after photon decoupling is expected to peak near the maximum neutrino Jeans mass. The gravitational effects of nonneutrino species are included in calculating the maximum neutrino Jeans mass, which is found to be [M/sub J/(t)]/sub max/approx.10 17 M/sub sun//[m/sub ν/(eV)] 2 , about an order of magnitude smaller than is obtained when nonneutrino species are ignored. An explicit expression for the nonviscous damping of neutrino density perturbations less massive than the maximum neutrino Jeans mass is derived. The linear evolution of density perturbations after photon decoupling is discussed. Of particular interest is the possibility that fluctuations in the neutrino density induce baryon density perturbations after photon decoupling and that the maximum neutrino Jeans determines the characteristic bound mass of galaxy clusters

  13. Optimal Linear Responses for Markov Chains and Stochastically Perturbed Dynamical Systems

    Science.gov (United States)

    Antown, Fadi; Dragičević, Davor; Froyland, Gary

    2018-03-01

    The linear response of a dynamical system refers to changes to properties of the system when small external perturbations are applied. We consider the little-studied question of selecting an optimal perturbation so as to (i) maximise the linear response of the equilibrium distribution of the system, (ii) maximise the linear response of the expectation of a specified observable, and (iii) maximise the linear response of the rate of convergence of the system to the equilibrium distribution. We also consider the inhomogeneous, sequential, or time-dependent situation where the governing dynamics is not stationary and one wishes to select a sequence of small perturbations so as to maximise the overall linear response at some terminal time. We develop the theory for finite-state Markov chains, provide explicit solutions for some illustrative examples, and numerically apply our theory to stochastically perturbed dynamical systems, where the Markov chain is replaced by a matrix representation of an approximate annealed transfer operator for the random dynamical system.

  14. A discrete homotopy perturbation method for non-linear Schrodinger equation

    Directory of Open Access Journals (Sweden)

    H. A. Wahab

    2015-12-01

    Full Text Available A general analysis is made by homotopy perturbation method while taking the advantages of the initial guess, appearance of the embedding parameter, different choices of the linear operator to the approximated solution to the non-linear Schrodinger equation. We are not dependent upon the Adomian polynomials and find the linear forms of the components without these calculations. The discretised forms of the nonlinear Schrodinger equation allow us whether to apply any numerical technique on the discritisation forms or proceed for perturbation solution of the problem. The discretised forms obtained by constructed homotopy provide the linear parts of the components of the solution series and hence a new discretised form is obtained. The general discretised form for the NLSE allows us to choose any initial guess and the solution in the closed form.

  15. A Homotopy-Perturbation analysis of the non-linear contaminant ...

    African Journals Online (AJOL)

    In this research work, a Homotopy-perturbation analysis of a non –linear contaminant flow equation with an initial continuous point source is provided. The equation is characterized by advection, diffusion and adsorption. We assume that the adsorption term is modeled by Freudlich Isotherm. We provide an approximation of ...

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

    Directory of Open Access Journals (Sweden)

    Yoshitsugu Takei

    2015-01-01

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

  17. Linear perturbation growth at the trailing edge of a rarefaction wave

    International Nuclear Information System (INIS)

    Wouchuk, J.G.; Carretero, R.

    2003-01-01

    An analytic model for the perturbation growth inside a rarefaction wave is presented. The objective of the work is to calculate the growth of the perturbations at the trailing edge of a simple expanding wave in planar geometry. Previous numerical and analytical works have shown that the ripples at the rarefaction tail exhibit linear growth asymptotically in time [Yang et al., Phys. Fluids 6, 1856 (1994), A. Velikovich and L. Phillips, ibid. 8, 1107 (1996)]. However, closed expressions for the asymptotic value of the perturbed velocity of the trailing edge have not been reported before, except for very weak rarefactions. Explicit analytic solutions for the perturbations growing at the rarefaction trailing edge as a function of time and also for the asymptotic perturbed velocity are given, for fluids with γ<3. The limits of weak and strong rarefactions are considered and the corresponding scaling laws are given. A semi-qualitative discussion of the late time linear growth at the trailing edge ripple is presented and it is seen that the lateral mass flow induced by the sound wave fluctuations is solely responsible for that behavior. Only the rarefactions generated after the interaction of a shock wave with a contact discontinuity are considered

  18. Perturbations of linear delay differential equations at the verge of instability.

    Science.gov (United States)

    Lingala, N; Namachchivaya, N Sri

    2016-06-01

    The characteristic equation for a linear delay differential equation (DDE) has countably infinite roots on the complex plane. This paper considers linear DDEs that are on the verge of instability, i.e., a pair of roots of the characteristic equation lies on the imaginary axis of the complex plane and all other roots have negative real parts. It is shown that when small noise perturbations are present, the probability distribution of the dynamics can be approximated by the probability distribution of a certain one-dimensional stochastic differential equation (SDE) without delay. This is advantageous because equations without delay are easier to simulate and one-dimensional SDEs are analytically tractable. When the perturbations are also linear, it is shown that the stability depends on a specific complex number. The theory is applied to study oscillators with delayed feedback. Some errors in other articles that use multiscale approach are pointed out.

  19. Particle linear theory on a self-gravitating perturbed cubic Bravais lattice

    International Nuclear Information System (INIS)

    Marcos, B.

    2008-01-01

    Discreteness effects are a source of uncontrolled systematic errors of N-body simulations, which are used to compute the evolution of a self-gravitating fluid. We have already developed the so-called ''particle linear theory''(PLT), which describes the evolution of the position of self-gravitating particles located on a perturbed simple cubic lattice. It is the discrete analogue of the well-known (Lagrangian) linear theory of a self-gravitating fluid. Comparing both theories permits us to quantify precisely discreteness effects in the linear regime. It is useful to develop the PLT also for other perturbed lattices because they represent different discretizations of the same continuous system. In this paper we detail how to implement the PLT for perturbed cubic Bravais lattices (simple, body, and face-centered) in a cubic simulation box. As an application, we will study the discreteness effects--in the linear regime--of N-body simulations for which initial conditions have been set up using these different lattices.

  20. The correlation function for density perturbations in an expanding universe. I - Linear theory

    Science.gov (United States)

    Mcclelland, J.; Silk, J.

    1977-01-01

    The evolution of the two-point correlation function for adiabatic density perturbations in the early universe is studied. Analytical solutions are obtained for the evolution of linearized spherically symmetric adiabatic density perturbations and the two-point correlation function for these perturbations in the radiation-dominated portion of the early universe. The results are then extended to the regime after decoupling. It is found that: (1) adiabatic spherically symmetric perturbations comparable in scale with the maximum Jeans length would survive the radiation-dominated regime; (2) irregular fluctuations are smoothed out up to the scale of the maximum Jeans length in the radiation era, but regular fluctuations might survive on smaller scales; (3) in general, the only surviving structures for irregularly shaped adiabatic density perturbations of arbitrary but finite scale in the radiation regime are the size of or larger than the maximum Jeans length in that regime; (4) infinite plane waves with a wavelength smaller than the maximum Jeans length but larger than the critical dissipative damping scale could survive the radiation regime; and (5) black holes would also survive the radiation regime and might accrete sufficient mass after decoupling to nucleate the formation of galaxies.

  1. New hybrid non-linear transformations of divergent perturbation series for quadratic Zeeman effects

    International Nuclear Information System (INIS)

    Belkic, D.

    1989-01-01

    The problem of hydrogen atoms in an external uniform magnetic field (quadratic Zeeman effect) is studied by means of perturbation theory. The power series for the ground-state energy in terms of magnetic-field strength B is divergent. Nevertheless, it is possible to induce convergence of this divergent series by applying various non-linear transformations. These transformations of originally divergent perturbation series yield new sequences, which then converge. The induced convergence is, however, quite slow. A new hybrid Shanks-Levin non-linear transform is devised here for accelerating these slowly converging series and sequences. Significant improvement in the convergence rate is obtained. Agreement with the exact results is excellent. (author)

  2. Optimal Control Strategies in a Two Dimensional Differential Game Using Linear Equation under a Perturbed System

    Directory of Open Access Journals (Sweden)

    Musa Danjuma SHEHU

    2008-06-01

    Full Text Available This paper lays emphasis on formulation of two dimensional differential games via optimal control theory and consideration of control systems whose dynamics is described by a system of Ordinary Differential equation in the form of linear equation under the influence of two controls U(. and V(.. Base on this, strategies were constructed. Hence we determine the optimal strategy for a control say U(. under a perturbation generated by the second control V(. within a given manifold M.

  3. Continuity and general perturbation of the Drazin inverse for closed linear operators

    Directory of Open Access Journals (Sweden)

    N. Castro González

    2002-01-01

    Full Text Available We study perturbations and continuity of the Drazin inverse of a closed linear operator A and obtain explicit error estimates in terms of the gap between closed operators and the gap between ranges and nullspaces of operators. The results are used to derive a theorem on the continuity of the Drazin inverse for closed operators and to describe the asymptotic behavior of operator semigroups.

  4. A Lie-Deprit perturbation algorithm for linear differential equations with periodic coefficients

    OpenAIRE

    Casas Pérez, Fernando; Chiralt Monleon, Cristina

    2014-01-01

    A perturbative procedure based on the Lie-Deprit algorithm of classical mechanics is proposed to compute analytic approximations to the fundamental matrix of linear di erential equations with periodic coe cients. These approximations reproduce the structure assured by the Floquet theorem. Alternatively, the algorithm provides explicit approximations to the Lyapunov transformation reducing the original periodic problem to an autonomous sys- tem and also to its characteristic ...

  5. Solution to the Diffusion equation for multi groups in X Y geometry using Linear Perturbation theory

    International Nuclear Information System (INIS)

    Mugica R, C.A.

    2004-01-01

    Diverse methods exist to solve numerically the neutron diffusion equation for several energy groups in stationary state among those that highlight those of finite elements. In this work the numerical solution of this equation is presented using Raviart-Thomas nodal methods type finite element, the RT0 and RT1, in combination with iterative techniques that allow to obtain the approached solution in a quick form. Nevertheless the above mentioned, the precision of a method is intimately bound to the dimension of the approach space by cell, 5 for the case RT0 and 12 for the RT1, and/or to the mesh refinement, that makes the order of the problem of own value to solve to grow considerably. By this way if it wants to know an acceptable approach to the value of the effective multiplication factor of the system when this it has experimented a small perturbation it was appeal to the Linear perturbation theory with which is possible to determine it starting from the neutron flow and of the effective multiplication factor of the not perturbed case. Results are presented for a reference problem in which a perturbation is introduced in an assemble that simulates changes in the control bar. (Author)

  6. Tangent Orbital Rendezvous Using Linear Relative Motion with J2 Perturbations

    Directory of Open Access Journals (Sweden)

    Gang Zhang

    2013-01-01

    Full Text Available The tangent-impulse coplanar orbit rendezvous problem is studied based on the linear relative motion for J2-perturbed elliptic orbits. There are three cases: (1 only the first impulse is tangent; (2 only the second impulse is tangent; (3 both impulses are tangent. For a given initial impulse point, the first two problems can be transformed into finding all roots of a single variable function about the transfer time, which can be done by the secant method. The bitangent rendezvous problem requires the same solution for the first two problems. By considering the initial coasting time, the bitangent rendezvous solution is obtained with a difference function. A numerical example for two coplanar elliptic orbits with J2 perturbations is given to verify the efficiency of these proposed techniques.

  7. Perturbation Solutions for Random Linear Structural Systems subject to Random Excitation using Stochastic Differential Equations

    DEFF Research Database (Denmark)

    Köyluoglu, H.U.; Nielsen, Søren R.K.; Cakmak, A.S.

    1994-01-01

    perturbation method using stochastic differential equations. The joint statistical moments entering the perturbation solution are determined by considering an augmented dynamic system with state variables made up of the displacement and velocity vector and their first and second derivatives with respect......The paper deals with the first and second order statistical moments of the response of linear systems with random parameters subject to random excitation modelled as white-noise multiplied by an envelope function with random parameters. The method of analysis is basically a second order...... to the random parameters of the problem. Equations for partial derivatives are obtained from the partial differentiation of the equations of motion. The zero time-lag joint statistical moment equations for the augmented state vector are derived from the Itô differential formula. General formulation is given...

  8. Linear perturbation of spherically symmetric flows: a first-order upwind scheme for the gas dynamics equations in Lagrangian coordinates

    International Nuclear Information System (INIS)

    Clarisse, J.M.

    2007-01-01

    A numerical scheme for computing linear Lagrangian perturbations of spherically symmetric flows of gas dynamics is proposed. This explicit first-order scheme uses the Roe method in Lagrangian coordinates, for computing the radial spherically symmetric mean flow, and its linearized version, for treating the three-dimensional linear perturbations. Fulfillment of the geometric conservation law discrete formulations for both the mean flow and its perturbation is ensured. This scheme capabilities are illustrated by the computation of free-surface mode evolutions at the boundaries of a spherical hollow shell undergoing an homogeneous cumulative compression, showing excellent agreement with reference results. (author)

  9. Analysis of perturbations of moments associated with orthogonality linear functionals through the Szegö transformation

    Directory of Open Access Journals (Sweden)

    Edinson Fuentes

    2015-06-01

    Full Text Available In this paper, we consider perturbations to a sequence of moments associated with an orthogonality linear functional that is represented by a positive measure supported in [−1, 1]. In particular, given a perturbation to such a measure on the real line, we analyze the perturbation obtained on the corresponding measure on the unit circle, when both measures are related through the Szeg´´o transformation. A similar perturbation is analyzed through the inverse Szeg´´o transformation. In both cases, we show that the applied perturbation can be expressed in terms of the singular part of the measures, and also in terms of the corresponding sequences of moments. Resumen. En el presente trabajo, analizamos las perturbaciones a una sucesión de momentos asociada a un funcional lineal de ortogonalidad que se representa por una medida positiva con soporte en [−1, 1]. En particular, dada una cierta perturbación a dicha medida en la recta real, analizamos la perturbación obtenida en la correspondiente medida en la circunferencia unidad, cuando dichas medidas están relacionadas por la transformación de Szeg´´o. También se analiza una perturbación similar a través de la transformación inversa de Szeg´´o. En ambos casos, se muestra que la perturbación aplicada puede ser expresada en términos de la parte singular de las medidas, y también a través de las correspondientes sucesiones de momentos.

  10. Nu shifts in betatron oscillations from uniform perturbations in the presence of non-linear magnetic guide fields

    International Nuclear Information System (INIS)

    Crebbin, K.C.

    1985-05-01

    Uniform magnetic field perturbations cause a closed orbit distortion in a circular accelerator. If the magnetic guide field is non-linear these perturbations can also cause a Nu shift in the betatron oscillations. Such a shift in radial Nu values has been observed in the Bevalac while studying the low energy resonant extraction system. In the Bevalac, the radial perturbation comes from the quadrants being magnetically about 0.8% longer than 90 0 . The normal effect of this type of perturbation is a radial closed orbit shift and orbit distortion. The Nu shift, associated with this type of perturbation in the presence of a non-linear guide field, is discussed in this paper. A method of handling the non-linear n values is discussed as well as the mechanism for the associated Nu shift. Computer calculations are compared to measurements. 2 refs., 4 figs

  11. Black hole nonmodal linear stability under odd perturbations: The Reissner-Nordström case

    Science.gov (United States)

    Fernández Tío, Julián M.; Dotti, Gustavo

    2017-06-01

    Following a program on black hole nonmodal linear stability initiated by one of the authors [Phys. Rev. Lett. 112, 191101 (2014), 10.1103/PhysRevLett.112.191101], we study odd linear perturbations of the Einstein-Maxwell equations around a Reissner-Nordström anti-de Sitter black hole. We show that all the gauge invariant information in the metric and Maxwell field perturbations is encoded in the spacetime scalars F =δ (Fαβ *Fα β) and Q =δ (1/48 Cαβ γ δ *Cα β γ δ), where Cα β γ δ is the Weyl tensor, Fα β is the Maxwell field, a star denotes Hodge dual, and δ means first order variation, and that the linearized Einstein-Maxwell equations are equivalent to a coupled system of wave equations for F and Q . For a non-negative cosmological constant we prove that F and Q are pointwise bounded on the outer static region. The fields are shown to diverge as the Cauchy horizon is approached from the inner dynamical region, providing evidence supporting strong cosmic censorship. In the asymptotically anti-de Sitter case the dynamics depends on the boundary condition at the conformal timelike boundary, and there are instabilities if Robin boundary conditions are chosen.

  12. Variance analysis of the Monte-Carlo perturbation source method in inhomogeneous linear particle transport problems

    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

  13. On a finite moment perturbation of linear functionals and the inverse Szegö transformation

    Directory of Open Access Journals (Sweden)

    Edinson Fuentes

    2016-05-01

    Full Text Available Given a sequence of moments $\\{c_{n}\\}_{n\\in\\ze}$ associated with an Hermitian linear functional $\\mathcal{L}$ defined in the space of Laurent polynomials, we study a new functional $\\mathcal{L}_{\\Omega}$ which is a perturbation of $\\mathcal{L}$ in such a way that a finite number of moments are perturbed. Necessary and sufficient conditions are given for the regularity of $\\mathcal{L}_{\\Omega}$, and a connection formula between the corresponding families of orthogonal polynomials is obtained. On the other hand, assuming $\\mathcal{L}_{\\Omega}$ is positive definite, the perturbation is analyzed through the inverse Szegö transformation. Resumen. Dada una sucesión de momentos $\\{c_{n}\\}_{n\\in\\ze}$ asociada a un funcional lineal hermitiano $\\mathcal{L}$ definido en el espacio de los polinomios de Laurent, estudiamos un nuevo funcional $\\mathcal{L}_{\\Omega}$ que consiste en una perturbación de $\\mathcal{L}$ de tal forma que se perturba un número finito de momentos de la sucesión. Se encuentran condiciones necesarias y suficientes para la regularidad de $\\mathcal{L}_{\\Omega}$, y se obtiene una fórmula de conexión que relaciona las familias de polinomios ortogonales correspondientes. Por otro lado, suponiendo que $\\mathcal{L}_{\\Omega}$ es definido positivo, se analiza la perturbación mediante de la transformación inversa de Szegö.

  14. Comparisons of linear and nonlinear plasma response models for non-axisymmetric perturbations

    Energy Technology Data Exchange (ETDEWEB)

    Turnbull, A. D.; Ferraro, N. M.; Lao, L. L.; Lanctot, M. J. [General Atomics, P.O. Box 85608, San Diego, California 92186-5608 (United States); Izzo, V. A. [University of California-San Diego, 9500 Gilman Dr., La Jolla, California 92093-0417 (United States); Lazarus, E. A.; Hirshman, S. P. [Oak Ridge National Laboratory, P.O. Box 2008, Oak Ridge, Tennessee 37831 (United States); Park, J.-K.; Lazerson, S.; Reiman, A. [Princeton Plasma Physics Laboratory, P.O. Box 451, Princeton, New Jersey 08543-0451 (United States); Cooper, W. A. [Association Euratom-Confederation Suisse, Centre de Recherches en Physique des Plasmas, Ecole Polytechnique Federale de Lausanne, Lausanne (Switzerland); Liu, Y. Q. [Culham Centre for Fusion Energy, Culham Science Centre, Abingdon, Oxfordshire, OX14 3DB (United Kingdom); Turco, F. [Columbia University, 116th St and Broadway, New York, New York 10027 (United States)

    2013-05-15

    With the installation of non-axisymmetric coil systems on major tokamaks for the purpose of studying the prospects of ELM-free operation, understanding the plasma response to the applied fields is a crucial issue. Application of different response models, using standard tools, to DIII-D discharges with applied non-axisymmetric fields from internal coils, is shown to yield qualitatively different results. The plasma response can be treated as an initial value problem, following the system dynamically from an initial unperturbed state, or from a nearby perturbed equilibrium approach, and using both linear and nonlinear models [A. D. Turnbull, Nucl. Fusion 52, 054016 (2012)]. Criteria are discussed under which each of the approaches can yield a valid response. In the DIII-D cases studied, these criteria show a breakdown in the linear theory despite the small 10{sup −3} relative magnitude of the applied magnetic field perturbations in this case. For nonlinear dynamical evolution simulations to reach a saturated nonlinear steady state, appropriate damping mechanisms need to be provided for each normal mode comprising the response. Other issues arise in the technical construction of perturbed flux surfaces from a displacement and from the presence of near nullspace normal modes. For the nearby equilibrium approach, in the absence of a full 3D equilibrium reconstruction with a controlled comparison, constraints relating the 2D system profiles to the final profiles in the 3D system also need to be imposed to assure accessibility. The magnetic helicity profile has been proposed as an appropriate input to a 3D equilibrium calculation and tests of this show the anticipated qualitative behavior.

  15. Collective behaviour of linear perturbation waves observed through the energy density spectrum

    Energy Technology Data Exchange (ETDEWEB)

    Scarsoglio, S [Department of Water Engineering, Politecnico di Torino (Italy); De Santi, F; Tordella, D, E-mail: stefania.scarsoglio@polito.it [Department of Aeronautics and Space Engineering, Politecnico di Torino (Italy)

    2011-12-22

    We consider the collective behaviour of small three-dimensional transient perturbations in sheared flows. In particular, we observe their varied life history through the temporal evolution of the amplification factor. The spectrum of wave vectors considered fills the range from the size of the external flow scale to the size of the very short dissipative waves. We observe that the amplification factor distribution is scale-invariant. In the condition we analyze, the system is subject to all the physical processes included in the linearized Navier-Stokes equations. With the exception of the nonlinear interaction, these features are the same as those characterizing the turbulent state. The linearized perturbative system offers a great variety of different transient behaviours associated to the parameter combination present in the initial conditions. For the energy spectrum computed by freezing each wave at the instant where its asymptotic condition is met, we ask whether this system is able to show a power-law scaling analogous to the Kolmogorov argument. At the moment, for at least two typical shear flows, the bluff-body wake and the plane Poiseuille flow, the answer is yes.

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

    Energy Technology Data Exchange (ETDEWEB)

    Dotti, Gustavo; Gleiser, Reinaldo J [Facultad de Matematica, AstronomIa y Fisica (FaMAF), Universidad Nacional de Cordoba, Ciudad Universitaria, 5000 Cordoba (Argentina)

    2009-11-07

    The coupled equations for the scalar modes of the linearized Einstein equations around Schwarzschild's spacetime were reduced by Zerilli to a (1+1) wave equation partial deriv{sup 2}PSI{sub z} /partial derivt{sup 2} +HPSI{sub z} =0, where H= -partial deriv{sup 2} /partial derivx{sup 2} + V(x) is the Zerilli 'Hamiltonian' and x is the tortoise radial coordinate. From its definition, for smooth metric perturbations the field PSI{sub z} is singular at r{sub s} = -6M/(l - 1)(l +2), with l being the mode harmonic number. The equation PSI{sub z} obeys is also singular, since V has a second-order pole at r{sub s}. This is irrelevant to the black hole exterior stability problem, where r > 2M > 0, and r{sub s} < 0, but it introduces a non-trivial problem in the naked singular case where M < 0, then r{sub s} > 0, and the singularity appears in the relevant range of r (0 < r < infinity). We solve this problem by developing a new approach to the evolution of the even mode, based on a new gauge invariant function, PSI-circumflex, that is a regular function of the metric perturbation for any value of M. The relation of PSI-circumflex to PSI{sub z} is provided by an intertwiner operator. The spatial pieces of the (1 + 1) wave equations that PSI-circumflex and PSI{sub z} obey are related as a supersymmetric pair of quantum Hamiltonians H and H-circumflex. For M < 0,H-circumflex has a regular potential and a unique self-adjoint extension in a domain D defined by a physically motivated boundary condition at r = 0. This allows us to address the issue of evolution of gravitational perturbations in this non-globally hyperbolic background. This formulation is used to complete the proof of the linear instability of the Schwarzschild naked singularity, by showing that a previously found unstable mode belongs to a complete basis of H-circumflex in D, and thus is excitable by generic initial data. This is further illustrated by numerically solving the linearized equations for

  17. 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)

  18. Nonrigid, Linear Plasma Response Model Based on Perturbed Equilibria for Axisymmetric Tokamak Control Design

    International Nuclear Information System (INIS)

    Welander, A.S.; Deranian, R.D.; Humphreys, D.A.; Leuer, J.A.; Walker, M.L.

    2005-01-01

    Tokamak control design relies on an accurate linear model of the plasma response, which can often dominate the local field variations in regions under active feedback control. For example, when fluxes at selected points on the plasma boundary are regulated in DIII-D, the plasma response to a change in a coil current gives rise to a flux change which can be larger than and opposite to the flux change caused by the coil alone.In the past, rigid plasma models have been used for linear stability and shape control design. In a rigid model, the plasma current profile is considered fixed and moves rigidly in response to control coils to maintain radial and vertical force balance. In a nonrigid model, however, changes in the plasma shape and current profile are taken into account. Such models are expected to be important for future advanced tokamak control design. The present work describes development of a nonrigid plasma response model for high-accuracy multivariable control design and provides comparisons of model predictions against DIII-D experimental data. The linear perturbed plasma response model is calculated rapidly from an existing equilibrium solution

  19. Correlation function for density perturbations in an expanding universe. I. Linear theory

    International Nuclear Information System (INIS)

    McClelland, J.; Silk, J.

    1977-01-01

    We derive analytic solutions for the evolution of linearized adiabatic spherically symmetric density perturbations and the two-point correlation function in two regimes of the early universe: the radiation-dominated regime prior to decoupling, and the matter-dominated regime after decoupling. The solutions are for an Einstein--de Sitter universe, and include pressure effects. In the radiation era, we find that individual spherically symmetric adiabatic density perturbations smaller than the Jeans length flow outward like water waves instead of oscillating as infinite plane waves. It seems likely that the only primordial structures on scales smaller than the maximum Jeans length which could survive are very regular waves such as infinite plane waves. However, structure does build up in the correlation function over distances comparable with the maximum Jeans length in the radiation regime, and could lead to the eventual formation of galaxy superclusters. This scale (approx.10 17 Ω -2 M/sub sun)/therefore provides a natural dimension for large-scale structure arising out of the early universe. A general technique is described for constructing solutions for the evolution of the two-point correlation function, and applied to study white noise and power-law initial conditions for primordial inhomogeneities

  20. Stabilization of Hypersonic Boundary Layers by Linear and Nonlinear Optimal Perturbations

    Science.gov (United States)

    Paredes, Pedro; Choudhari, Meelan M.; Li, Fei

    2017-01-01

    The effect of stationary, finite-amplitude, linear and nonlinear optimal perturbations on the modal disturbance growth in a Mach 6 axisymmetric flow over a 7 deg. half-angle cone with 0:126 mm nose radius and 0:305 m length is investigated. The freestream parameters (M = 6, Re(exp 1) = 18 x 10(exp. 6) /m) are selected to match the flow conditions of a previous experiment in the VKI H3 hypersonic tunnel. Plane-marching parabolized stability equations are used in conjunction with a partial-differential equation based planar eigenvalue analysis to characterize the boundary layer instability in the presence of azimuthally periodic streaks. The streaks are observed to stabilize nominally planar Mack mode instabilities, although oblique Mack mode and first-mode disturbances are destabilized. Experimentally measured transition onset in the absence of any streaks correlates with an amplification factor of N = 6 for the planar Mack modes. For high enough streak amplitudes, the transition threshold of N = 6 is not reached by the Mack mode instabilities within the length of the cone; however, subharmonic first-mode instabilities, which are destabilized by the presence of the streaks, do reach N = 6 near the end of the cone. The highest stabilization is observed at streak amplitudes of approximately 20 percent of the freestream velocity. Because the use of initial disturbance profiles based on linear optimal growth theory may yield suboptimal control in the context of nonlinear streaks, the computational predictions are extended to nonlinear optimal growth theory. Results show that by using nonlinearly optimal perturbation leads to slightly enhanced stabilization of plane Mack mode disturbances as well as reduced destabilization of subharmonic first-mode disturbances.

  1. New evidence and impact of electron transport non-linearities based on new perturbative inter-modulation analysis

    Science.gov (United States)

    van Berkel, M.; Kobayashi, T.; Igami, H.; Vandersteen, G.; Hogeweij, G. M. D.; Tanaka, K.; Tamura, N.; Zwart, H. J.; Kubo, S.; Ito, S.; Tsuchiya, H.; de Baar, M. R.; LHD Experiment Group

    2017-12-01

    A new methodology to analyze non-linear components in perturbative transport experiments is introduced. The methodology has been experimentally validated in the Large Helical Device for the electron heat transport channel. Electron cyclotron resonance heating with different modulation frequencies by two gyrotrons has been used to directly quantify the amplitude of the non-linear component at the inter-modulation frequencies. The measurements show significant quadratic non-linear contributions and also the absence of cubic and higher order components. The non-linear component is analyzed using the Volterra series, which is the non-linear generalization of transfer functions. This allows us to study the radial distribution of the non-linearity of the plasma and to reconstruct linear profiles where the measurements were not distorted by non-linearities. The reconstructed linear profiles are significantly different from the measured profiles, demonstrating the significant impact that non-linearity can have.

  2. Averaging and Linear Programming in Some Singularly Perturbed Problems of Optimal Control

    Energy Technology Data Exchange (ETDEWEB)

    Gaitsgory, Vladimir, E-mail: vladimir.gaitsgory@mq.edu.au [Macquarie University, Department of Mathematics (Australia); Rossomakhine, Sergey, E-mail: serguei.rossomakhine@flinders.edu.au [Flinders University, Flinders Mathematical Sciences Laboratory, School of Computer Science, Engineering and Mathematics (Australia)

    2015-04-15

    The paper aims at the development of an apparatus for analysis and construction of near optimal solutions of singularly perturbed (SP) optimal controls problems (that is, problems of optimal control of SP systems) considered on the infinite time horizon. We mostly focus on problems with time discounting criteria but a possibility of the extension of results to periodic optimization problems is discussed as well. Our consideration is based on earlier results on averaging of SP control systems and on linear programming formulations of optimal control problems. The idea that we exploit is to first asymptotically approximate a given problem of optimal control of the SP system by a certain averaged optimal control problem, then reformulate this averaged problem as an infinite-dimensional linear programming (LP) problem, and then approximate the latter by semi-infinite LP problems. We show that the optimal solution of these semi-infinite LP problems and their duals (that can be found with the help of a modification of an available LP software) allow one to construct near optimal controls of the SP system. We demonstrate the construction with two numerical examples.

  3. Non-linear magnetohydrodynamic modeling of plasma response to resonant magnetic perturbations

    Energy Technology Data Exchange (ETDEWEB)

    Orain, F.; Bécoulet, M.; Dif-Pradalier, G.; Nardon, E.; Passeron, C.; Latu, G.; Grandgirard, V.; Fil, A.; Ratnani, A. [CEA, IRFM, F-13108 Saint-Paul-Lez-Durance (France); Huijsmans, G. [ITER Organization, Route de Vinon, F-13115 Saint-Paul-Lez-Durance (France); Pamela, S. [IIFS-PIIM. Aix Marseille Université - CNRS, 13397 Marseille Cedex20 (France); Chapman, I.; Kirk, A.; Thornton, A. [EURATOM/CCFE Fusion Association, Culham Science Centre, Oxon OX14 3DB (United Kingdom); Hoelzl, M. [Max-Planck-Institut für Plasmaphysik, EURATOM Association, Garching (Germany); Cahyna, P. [Association EURATOM/IPP.CR, Prague (Czech Republic)

    2013-10-15

    The interaction of static Resonant Magnetic Perturbations (RMPs) with the plasma flows is modeled in toroidal geometry, using the non-linear resistive MHD code JOREK, which includes the X-point and the scrape-off-layer. Two-fluid diamagnetic effects, the neoclassical poloidal friction and a source of toroidal rotation are introduced in the model to describe realistic plasma flows. RMP penetration is studied taking self-consistently into account the effects of these flows and the radial electric field evolution. JET-like, MAST, and ITER parameters are used in modeling. For JET-like parameters, three regimes of plasma response are found depending on the plasma resistivity and the diamagnetic rotation: at high resistivity and slow rotation, the islands generated by the RMPs at the edge resonant surfaces rotate in the ion diamagnetic direction and their size oscillates. At faster rotation, the generated islands are static and are more screened by the plasma. An intermediate regime with static islands which slightly oscillate is found at lower resistivity. In ITER simulations, the RMPs generate static islands, which forms an ergodic layer at the very edge (ψ≥0.96) characterized by lobe structures near the X-point and results in a small strike point splitting on the divertor targets. In MAST Double Null Divertor geometry, lobes are also found near the X-point and the 3D-deformation of the density and temperature profiles is observed.

  4. Expectation propagation for large scale Bayesian inference of non-linear molecular networks from perturbation data.

    Science.gov (United States)

    Narimani, Zahra; Beigy, Hamid; Ahmad, Ashar; Masoudi-Nejad, Ali; Fröhlich, Holger

    2017-01-01

    Inferring the structure of molecular networks from time series protein or gene expression data provides valuable information about the complex biological processes of the cell. Causal network structure inference has been approached using different methods in the past. Most causal network inference techniques, such as Dynamic Bayesian Networks and ordinary differential equations, are limited by their computational complexity and thus make large scale inference infeasible. This is specifically true if a Bayesian framework is applied in order to deal with the unavoidable uncertainty about the correct model. We devise a novel Bayesian network reverse engineering approach using ordinary differential equations with the ability to include non-linearity. Besides modeling arbitrary, possibly combinatorial and time dependent perturbations with unknown targets, one of our main contributions is the use of Expectation Propagation, an algorithm for approximate Bayesian inference over large scale network structures in short computation time. We further explore the possibility of integrating prior knowledge into network inference. We evaluate the proposed model on DREAM4 and DREAM8 data and find it competitive against several state-of-the-art existing network inference methods.

  5. Reconstruction of cellular signal transduction networks using perturbation assays and linear programming.

    Science.gov (United States)

    Knapp, Bettina; Kaderali, Lars

    2013-01-01

    Perturbation experiments for example using RNA interference (RNAi) offer an attractive way to elucidate gene function in a high throughput fashion. The placement of hit genes in their functional context and the inference of underlying networks from such data, however, are challenging tasks. One of the problems in network inference is the exponential number of possible network topologies for a given number of genes. Here, we introduce a novel mathematical approach to address this question. We formulate network inference as a linear optimization problem, which can be solved efficiently even for large-scale systems. We use simulated data to evaluate our approach, and show improved performance in particular on larger networks over state-of-the art methods. We achieve increased sensitivity and specificity, as well as a significant reduction in computing time. Furthermore, we show superior performance on noisy data. We then apply our approach to study the intracellular signaling of human primary nave CD4(+) T-cells, as well as ErbB signaling in trastuzumab resistant breast cancer cells. In both cases, our approach recovers known interactions and points to additional relevant processes. In ErbB signaling, our results predict an important role of negative and positive feedback in controlling the cell cycle progression.

  6. An linear matrix inequality approach to global synchronisation of non-parameter perturbations of multi-delay Hopfield neural network

    International Nuclear Information System (INIS)

    Shao Hai-Jian; Cai Guo-Liang; Wang Hao-Xiang

    2010-01-01

    In this study, a successful linear matrix inequality approach is used to analyse a non-parameter perturbation of multi-delay Hopfield neural network by constructing an appropriate Lyapunov-Krasovskii functional. This paper presents the comprehensive discussion of the approach and also extensive applications

  7. New evidence and impact of electron transport non-linearities based on new perturbative inter-modulation analysis

    NARCIS (Netherlands)

    van Berkel, M.; Kobayashi, T.; Igami, H.; Vandersteen, Gerd; Hogeweij, G.M.D.; Tanaka, K.; Tamura, N.; Zwart, Hans; Kubo, S.; Ito, S.; Tsuchiya, H.; de Baar, M.R.

    2017-01-01

    A new methodology to analyze non-linear components in perturbative transport experiments is introduced. The methodology has been experimentally validated in the Large Helical Device for the electron heat transport channel. Electron cyclotron resonance heating with different modulation frequencies by

  8. 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.

  9. A perturbative approach to mass-generation - the non-linear sigma model

    International Nuclear Information System (INIS)

    Davis, A.C.; Nahm, W.

    1985-01-01

    A calculational scheme is presented to include non-perturbative effects into the perturbation expansion. As an example we use the O(N + 1) sigma model. The scheme uses a natural parametrisation such that the lagrangian can be written in a form normal-ordered with respect to the O(N + 1) symmetric vacuum plus vacuum expectation values, the latter calculated by symmetry alone. Including such expectation values automatically leads to the inclusion of a mass-gap in the perturbation series. (orig.)

  10. Perturbative calculations of flow patterns in free convection between coaxial cylinders. Non-linear temperature dependences of the fluid properties

    International Nuclear Information System (INIS)

    Navarro, J. A.; Madariaga, J. A.; Santamaria, C. M.; Saviron, J. M.

    1980-01-01

    10 refs. Flow pattern calculations in natural convection between two vertical coaxial cylinders are reported. It is assumed trough the paper. that fluid properties, viscosity, thermal conductivity and density, depend no-linearly on temperature and that the aspects (height/radius) ratio of the cylinders is high. Velocity profiles are calculated trough a perturbative scheme and analytic results for the three first perturbation orders are presented. We outline also an iterative method to estimate the perturbations on the flow patterns which arise when a radial composition gradient is established by external forces in a two-component fluid. This procedure, based on semiempirical basis, is applied to gaseous convection. The influence of the molecules gas properties on tho flow is also discussed. (Author) 10 refs

  11. Linear force and moment equations for an annular smooth shaft seal perturbed both angularly and laterally

    Science.gov (United States)

    Fenwick, J.; Dijulio, R.; Ek, M. C.; Ehrgott, R.

    1982-01-01

    Coefficients are derived for equations expressing the lateral force and pitching moments associated with both planar translation and angular perturbations from a nominally centered rotating shaft with respect to a stationary seal. The coefficients for the lowest order and first derivative terms emerge as being significant and are of approximately the same order of magnitude as the fundamental coefficients derived by means of Black's equations. Second derivative, shear perturbation, and entrance coefficient variation effects are adjudged to be small.

  12. Quantization of the linearized Einstein–Klein–Gordon system on arbitrary backgrounds and the special case of perturbations in inflation

    International Nuclear Information System (INIS)

    Hack, Thomas-Paul

    2014-01-01

    We quantize the linearized Einstein–Klein–Gordon system on arbitrary on-shell backgrounds in a manifestly covariant and gauge-invariant manner. For the special case of perturbations in inflation, i.e. on-shell backgrounds of Friedmann–Lemaître–Robertson–Walker type, we compare our general quantization construction with the standard approach to the quantum theory of perturbations in inflation. We find that not all local quantum observables of the linearized Einstein–Klein–Gordon system can be split into local observables of scalar and tensor type as in the standard approach. However, we argue that this subclass of observables is sufficient for measuring perturbations that vanish at spatial infinity, which is in line with standard assumptions. Finally, we comment on a recent observation that, upon standard quantization, the quantum Bardeen potentials display a non-local behaviour and argue that a similar phenomenon occurs in any local quantum field theory. It is the hope of the author that the present work may constitute a bridge between the generally applicable and thus powerful framework of algebraic quantum field theory in curved spacetimes and the standard treatment of perturbations in inflation. (paper)

  13. Response analysis of a laminar premixed M-flame to flow perturbations using a linearized compressible Navier-Stokes solver

    International Nuclear Information System (INIS)

    Blanchard, M.; Schuller, T.; Sipp, D.; Schmid, P. J.

    2015-01-01

    The response of a laminar premixed methane-air flame subjected to flow perturbations around a steady state is examined experimentally and using a linearized compressible Navier-Stokes solver with a one-step chemistry mechanism to describe combustion. The unperturbed flame takes an M-shape stabilized both by a central bluff body and by the external rim of a cylindrical nozzle. This base flow is computed by a nonlinear direct simulation of the steady reacting flow, and the flame topology is shown to qualitatively correspond to experiments conducted under comparable conditions. The flame is then subjected to acoustic disturbances produced at different locations in the numerical domain, and its response is examined using the linearized solver. This linear numerical model then allows the componentwise investigation of the effects of flow disturbances on unsteady combustion and the feedback from the flame on the unsteady flow field. It is shown that a wrinkled reaction layer produces hydrodynamic disturbances in the fresh reactant flow field that superimpose on the acoustic field. This phenomenon, observed in several experiments, is fully interpreted here. The additional perturbations convected by the mean flow stem from the feedback of the perturbed flame sheet dynamics onto the flow field by a mechanism similar to that of a perturbed vortex sheet. The different regimes where this mechanism prevails are investigated by examining the phase and group velocities of flow disturbances along an axis oriented along the main direction of the flow in the fresh reactant flow field. It is shown that this mechanism dominates the low-frequency response of the wrinkled shape taken by the flame and, in particular, that it fully determines the dynamics of the flame tip from where the bulk of noise is radiated

  14. Non linear interaction between a Langmuir wave and a ballistic perturbation

    International Nuclear Information System (INIS)

    Gervais, F.; Olivain, J.; Quemeneur, A.; Trocheris, M.

    1979-05-01

    The theoretical solutions of the Landau-Vlasov initial value problem giving mode-mode coupling usually neglect the free-streaming contribution. We solve theoretically this problem including the ballistic terms. We find that a new mode appears resulting from the nonlinear interaction between the Landau component and the ballistic perturbation. The amplitude of this mode is calculated as a function of distance and compared with experimental results in a plasma column

  15. Linear perturbation theory for tidal streams and the small-scale CDM power spectrum

    Science.gov (United States)

    Bovy, Jo; Erkal, Denis; Sanders, Jason L.

    2017-04-01

    Tidal streams in the Milky Way are sensitive probes of the population of low-mass dark matter subhaloes predicted in cold dark matter (CDM) simulations. We present a new calculus for computing the effect of subhalo fly-bys on cold streams based on the action-angle representation of streams. The heart of this calculus is a line-of-parallel-angle approach that calculates the perturbed distribution function of a stream segment by undoing the effect of all relevant impacts. This approach allows one to compute the perturbed stream density and track in any coordinate system in minutes for realizations of the subhalo distribution down to 105 M⊙, accounting for the stream's internal dispersion and overlapping impacts. We study the statistical properties of density and track fluctuations with large suites of simulations of the effect of subhalo fly-bys. The one-dimensional density and track power spectra along the stream trace the subhalo mass function, with higher mass subhaloes producing power only on large scales, while lower mass subhaloes cause structure on smaller scales. We also find significant density and track bispectra that are observationally accessible. We further demonstrate that different projections of the track all reflect the same pattern of perturbations, facilitating their observational measurement. We apply this formalism to data for the Pal 5 stream and make a first rigorous determination of 10^{+11}_{-6} dark matter subhaloes with masses between 106.5 and 109 M⊙ within 20 kpc from the Galactic centre [corresponding to 1.4^{+1.6}_{-0.9} times the number predicted by CDM-only simulations or to fsub(r matter is clumpy on the smallest scales relevant for galaxy formation.

  16. Upper and Lower Bounds of Frequency Interval Gramians for a Class of Perturbed Linear Systems

    DEFF Research Database (Denmark)

    Shaker, Hamid Reza

    2012-01-01

    if the system is controllable or observable, but also it is required to know the degree of controllability or observability of the system. Gramian matrices were introduced to address this issue by providing a quantitative measure for controllability and observability. In many applications, the information...... of uncertain systems. In this paper, we derive upper and lower bounds of frequency interval gramians under perturbations of an A-matrix in the state-space form. These bounds are obtained by solving algebraic Riccati equations. The results are further used to obtain upper and lower bounds of the frequency...

  17. The linear stability of the Schwarzschild solution to gravitational perturbations in the generalised wave gauge

    OpenAIRE

    Johnson, Thomas

    2018-01-01

    In a recent seminal paper \\cite{D--H--R} of Dafermos, Holzegel and Rodnianski the linear stability of the Schwarzschild family of black hole solutions to the Einstein vacuum equations was established by imposing a double null gauge. In this paper we shall prove that the Schwarzschild family is linearly stable as solutions to the Einstein vacuum equations by imposing instead a generalised wave gauge: all sufficiently regular solutions to the system of equations that result from linearising the...

  18. A general theory of linear cosmological perturbations: stability conditions, the quasistatic limit and dynamics

    Science.gov (United States)

    Lagos, Macarena; Bellini, Emilio; Noller, Johannes; Ferreira, Pedro G.; Baker, Tessa

    2018-03-01

    We analyse cosmological perturbations around a homogeneous and isotropic background for scalar-tensor, vector-tensor and bimetric theories of gravity. Building on previous results, we propose a unified view of the effective parameters of all these theories. Based on this structure, we explore the viable space of parameters for each family of models by imposing the absence of ghosts and gradient instabilities. We then focus on the quasistatic regime and confirm that all these theories can be approximated by the phenomenological two-parameter model described by an effective Newton's constant and the gravitational slip. Within the quasistatic regime we pinpoint signatures which can distinguish between the broad classes of models (scalar-tensor, vector-tensor or bimetric). Finally, we present the equations of motion for our unified approach in such a way that they can be implemented in Einstein-Boltzmann solvers.

  19. New Designs of Reduced-Order Observer-Based Controllers for Singularly Perturbed Linear Systems

    Directory of Open Access Journals (Sweden)

    Heonjong Yoo

    2017-01-01

    Full Text Available The slow and fast reduced-order observers and reduced-order observer-based controllers are designed by using the two-stage feedback design technique for slow and fast subsystems. The new designs produce an arbitrary order of accuracy, while the previously known designs produce the accuracy of O(ϵ only where ϵ is a small singular perturbation parameter. Several cases of reduced-order observer designs are considered depending on the measured state space variables: only all slow variables are measured, only all fast variables are measured, and some combinations of the slow and fast variables are measured. Since the two-stage methods have been used to overcome the numerical ill-conditioning problem for Cases (III–(V, they have similar procedures. The numerical ill-conditioning problem is avoided so that independent feedback controllers can be applied to each subsystem. The design allows complete time-scale separation for both the reduced-order observer and controller through the complete and exact decomposition into slow and fast time scales. This method reduces both offline and online computations.

  20. An optimally weighted estimator of the linear power spectrum disentangling the growth of density perturbations across galaxy surveys

    International Nuclear Information System (INIS)

    Sorini, D.

    2017-01-01

    Measuring the clustering of galaxies from surveys allows us to estimate the power spectrum of matter density fluctuations, thus constraining cosmological models. This requires careful modelling of observational effects to avoid misinterpretation of data. In particular, signals coming from different distances encode information from different epochs. This is known as ''light-cone effect'' and is going to have a higher impact as upcoming galaxy surveys probe larger redshift ranges. Generalising the method by Feldman, Kaiser and Peacock (1994) [1], I define a minimum-variance estimator of the linear power spectrum at a fixed time, properly taking into account the light-cone effect. An analytic expression for the estimator is provided, and that is consistent with the findings of previous works in the literature. I test the method within the context of the Halofit model, assuming Planck 2014 cosmological parameters [2]. I show that the estimator presented recovers the fiducial linear power spectrum at present time within 5% accuracy up to k ∼ 0.80 h Mpc −1 and within 10% up to k ∼ 0.94 h Mpc −1 , well into the non-linear regime of the growth of density perturbations. As such, the method could be useful in the analysis of the data from future large-scale surveys, like Euclid.

  1. Application of perturbation theory to the non-linear vibration analysis of a string including the bending moment effects

    International Nuclear Information System (INIS)

    Esmaeilzadeh Khadem, S.; Rezaee, M.

    2001-01-01

    In this paper the large amplitude and non-linear vibration of a string is considered. The initial tension, lateral vibration amplitude, diameter and the modulus of elasticity of the string have main effects on its natural frequencies. Increasing the lateral vibration amplitude makes the assumption of constant initial tension invalid. In this case, therefore, it is impossible to use the classical equation of string with small amplitude transverse motion assumption. On the other hand, by increasing the string diameter, the bending moment effect will increase dramatically, and acts as an impressive restoring moment. Considering the effects of the bending moments, the nonlinear equation governing the large amplitude transverse vibration of a string is derived. The time dependent portion of the governing equation has the from of Duff ing equation is solved using the perturbation theory. The results of the analysis are shown in appropriate graphs, and the natural frequencies of the string due to the non-linear factors are compared with the natural frequencies of the linear vibration os a string without bending moment effects

  2. PWR in-core nuclear fuel management optimization utilizing nodal (non-linear NEM) generalized perturbation theory

    International Nuclear Information System (INIS)

    Maldonado, G.I.; Turinsky, P.J.; Kropaczek, D.J.

    1993-01-01

    The computational capability of efficiently and accurately evaluate reactor core attributes (i.e., k eff and power distributions as a function of cycle burnup) utilizing a second-order accurate advanced nodal Generalized Perturbation Theory (GPT) model has been developed. The GPT model is derived from the forward non-linear iterative Nodal Expansion Method (NEM) strategy, thereby extending its inherent savings in memory storage and high computational efficiency to also encompass GPT via the preservation of the finite-difference matrix structure. The above development was easily implemented into the existing coarse-mesh finite-difference GPT-based in-core fuel management optimization code FORMOSA-P, thus combining the proven robustness of its adaptive Simulated Annealing (SA) multiple-objective optimization algorithm with a high-fidelity NEM GPT neutronics model to produce a powerful computational tool used to generate families of near-optimum loading patterns for PWRs. (orig.)

  3. Perturbation-Based Regularization for Signal Estimation in Linear Discrete Ill-posed Problems

    KAUST Repository

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

    2016-01-01

    Estimating the values of unknown parameters from corrupted measured data faces a lot of challenges in ill-posed problems. In such problems, many fundamental estimation methods fail to provide a meaningful stabilized solution. In this work, we propose a new regularization approach and a new regularization parameter selection approach for linear least-squares discrete ill-posed problems. The proposed approach is based on enhancing the singular-value structure of the ill-posed model matrix to acquire a better solution. Unlike many other regularization algorithms that seek to minimize the estimated data error, the proposed approach is developed to minimize the mean-squared error of the estimator which is the objective in many typical estimation scenarios. The performance of the proposed approach is demonstrated by applying it to a large set of real-world discrete ill-posed problems. Simulation results demonstrate that the proposed approach outperforms a set of benchmark regularization methods in most cases. In addition, the approach also enjoys the lowest runtime and offers the highest level of robustness amongst all the tested benchmark regularization methods.

  4. Perturbation-Based Regularization for Signal Estimation in Linear Discrete Ill-posed Problems

    KAUST Repository

    Suliman, Mohamed Abdalla Elhag

    2016-11-29

    Estimating the values of unknown parameters from corrupted measured data faces a lot of challenges in ill-posed problems. In such problems, many fundamental estimation methods fail to provide a meaningful stabilized solution. In this work, we propose a new regularization approach and a new regularization parameter selection approach for linear least-squares discrete ill-posed problems. The proposed approach is based on enhancing the singular-value structure of the ill-posed model matrix to acquire a better solution. Unlike many other regularization algorithms that seek to minimize the estimated data error, the proposed approach is developed to minimize the mean-squared error of the estimator which is the objective in many typical estimation scenarios. The performance of the proposed approach is demonstrated by applying it to a large set of real-world discrete ill-posed problems. Simulation results demonstrate that the proposed approach outperforms a set of benchmark regularization methods in most cases. In addition, the approach also enjoys the lowest runtime and offers the highest level of robustness amongst all the tested benchmark regularization methods.

  5. Global Well-Posedness of the Incompressible Magnetohydrodynamics

    Science.gov (United States)

    Cai, Yuan; Lei, Zhen

    2018-06-01

    This paper studies the Cauchy problem of the incompressible magnetohydro dynamic systems with or without viscosity ν. Under the assumption that the initial velocity field and the displacement of the initialmagnetic field froma non-zero constant are sufficiently small in certain weighted Sobolev spaces, the Cauchy problem is shown to be globally well-posed for all ν ≧ 0 and all spaces with dimension n ≧ 2. Such a result holds true uniformly in nonnegative viscosity parameters. The proof is based on the inherent strong null structure of the systems introduced by Lei (Commun Pure Appl Math 69(11):2072-2106, 2016) and the ghost weight technique introduced by Alinhac (Invent Math 145(3):597-618, 2001).

  6. Variance analysis of the Monte Carlo perturbation source method in inhomogeneous linear particle transport problems. Derivation of formulae

    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

  7. Linear perturbation of spherically symmetric flows: a first-order upwind scheme for the gas dynamics equations in Lagrangian coordinates; Perturbation lineaire d'ecoulements a symetrie spherique: schema decentre d'ordre 1 pour les equations de la dynamique des gaz en variables de Lagrange

    Energy Technology Data Exchange (ETDEWEB)

    Clarisse, J.M

    2007-07-01

    A numerical scheme for computing linear Lagrangian perturbations of spherically symmetric flows of gas dynamics is proposed. This explicit first-order scheme uses the Roe method in Lagrangian coordinates, for computing the radial spherically symmetric mean flow, and its linearized version, for treating the three-dimensional linear perturbations. Fulfillment of the geometric conservation law discrete formulations for both the mean flow and its perturbation is ensured. This scheme capabilities are illustrated by the computation of free-surface mode evolutions at the boundaries of a spherical hollow shell undergoing an homogeneous cumulative compression, showing excellent agreement with reference results. (author)

  8. A high-order perturbation of surfaces method for scattering of linear waves by periodic multiply layered gratings in two and three dimensions

    Science.gov (United States)

    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.

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

    Directory of Open Access Journals (Sweden)

    Chi-Chang Wang

    2013-09-01

    Full Text Available This paper seeks to use the proposed residual correction method in coordination with the monotone iterative technique to obtain upper and lower approximate solutions of singularly perturbed non-linear boundary value problems. First, the monotonicity of a non-linear differential equation is reinforced using the monotone iterative technique, then the cubic-spline method is applied to discretize and convert the differential equation into the mathematical programming problems of an inequation, and finally based on the residual correction concept, complex constraint solution problems are transformed into simpler questions of equational iteration. As verified by the four examples given in this paper, the method proposed hereof can be utilized to fast obtain the upper and lower solutions of questions of this kind, and to easily identify the error range between mean approximate solutions and exact solutions.

  10. Quasi-minimal active disturbance rejection control of MIMO perturbed linear systems based on differential neural networks and the attractive ellipsoid method.

    Science.gov (United States)

    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.

  11. The effects of static quartic anharmonicity on the quantum dynamics of a linear oscillator with time-dependent harmonic frequency: Perturbative analysis and numerical calculations

    International Nuclear Information System (INIS)

    Sarkar, P.; Bhattacharyya, S.P.

    1995-01-01

    The effects of quartic anharmonicity on the quantum dynamics of a linear oscillator with time-dependent force constant (K) or harmonic frequency (ω) are studied both perturbatively and numerically by the time-dependent Fourier grid Hamiltonian method. In the absence of anharmonicity, the ground-state population decreases and the population of an accessible excited state (k = 2.4, 6 ... ) increases with time. However, when anharmonicity is introduced, both the ground- and excited-state populations show typical oscillations. For weak coupling, the population of an accessible excited state at a certain instant of time (short) turns out to be a parabolic function of the anharmonic coupling constant (λ), when all other parameters of the system are kept fixed. This parabolic nature of the excited-state population vs. the λ profile is independent of the specific form of the time dependence of the force constant, K t . However, it depends upon the rate at which K t relaxes. For small anharmonic coupling strength and short time scales, the numerical results corroborate expectations based on the first-order time-dependent perturbative analysis, using a suitably repartitioned Hamiltonian that makes H 0 time-independent. Some of the possible experimental implications of our observations are analyzed, especially in relation to intensity oscillations observed in some charge-transfer spectra in systems in which the dephasing rates are comparable with the time scale of the electron transfer. 21 refs., 7 figs., 1 tab

  12. Linear perturbation renormalization group for the two-dimensional Ising model with nearest- and next-nearest-neighbor interactions in a field

    Science.gov (United States)

    Sznajd, J.

    2016-12-01

    The linear perturbation renormalization group (LPRG) is used to study the phase transition of the weakly coupled Ising chains with intrachain (J ) and interchain nearest-neighbor (J1) and next-nearest-neighbor (J2) interactions forming the triangular and rectangular lattices in a field. The phase diagrams with the frustration point at J2=-J1/2 for a rectangular lattice and J2=-J1 for a triangular lattice have been found. The LPRG calculations support the idea that the phase transition is always continuous except for the frustration point and is accompanied by a divergence of the specific heat. For the antiferromagnetic chains, the external field does not change substantially the shape of the phase diagram. The critical temperature is suppressed to zero according to the power law when approaching the frustration point with an exponent dependent on the value of the field.

  13. Inverse problems in linear transport theory

    International Nuclear Information System (INIS)

    Dressler, K.

    1988-01-01

    Inverse problems for a class of linear kinetic equations are investigated. The aim is to identify the scattering kernel of a transport equation (corresponding to the structure of a background medium) by observing the 'albedo' part of the solution operator for the corresponding direct initial boundary value problem. This means to get information on some integral operator in an integrodifferential equation through on overdetermined boundary value problem. We first derive a constructive method for solving direct halfspace problems and prove a new factorization theorem for the solutions. Using this result we investigate stationary inverse problems with respect to well posedness (e.g. reduce them to classical ill-posed problems, such as integral equations of first kind). In the time-dependent case we show that a quite general inverse problem is well posed and solve it constructively. (orig.)

  14. Communication: An improved linear scaling perturbative triples correction for the domain based local pair-natural orbital based singles and doubles coupled cluster method [DLPNO-CCSD(T)

    KAUST Repository

    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).

  15. Communication: An improved linear scaling perturbative triples correction for the domain based local pair-natural orbital based singles and doubles coupled cluster method [DLPNO-CCSD(T)

    KAUST Repository

    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).

  16. General theory for multiple input-output perturbations in complex molecular systems. 1. Linear QSPR electronegativity models in physical, organic, and medicinal chemistry.

    Science.gov (United States)

    González-Díaz, Humberto; Arrasate, Sonia; Gómez-SanJuan, Asier; Sotomayor, Nuria; Lete, Esther; Besada-Porto, Lina; Ruso, Juan M

    2013-01-01

    In general perturbation methods starts with a known exact solution of a problem and add "small" variation terms in order to approach to a solution for a related problem without known exact solution. Perturbation theory has been widely used in almost all areas of science. Bhor's quantum model, Heisenberg's matrix mechanincs, Feyman diagrams, and Poincare's chaos model or "butterfly effect" in complex systems are examples of perturbation theories. On the other hand, the study of Quantitative Structure-Property Relationships (QSPR) in molecular complex systems is an ideal area for the application of perturbation theory. There are several problems with exact experimental solutions (new chemical reactions, physicochemical properties, drug activity and distribution, metabolic networks, etc.) in public databases like CHEMBL. However, in all these cases, we have an even larger list of related problems without known solutions. We need to know the change in all these properties after a perturbation of initial boundary conditions. It means, when we test large sets of similar, but different, compounds and/or chemical reactions under the slightly different conditions (temperature, time, solvents, enzymes, assays, protein targets, tissues, partition systems, organisms, etc.). However, to the best of our knowledge, there is no QSPR general-purpose perturbation theory to solve this problem. In this work, firstly we review general aspects and applications of both perturbation theory and QSPR models. Secondly, we formulate a general-purpose perturbation theory for multiple-boundary QSPR problems. Last, we develop three new QSPR-Perturbation theory models. The first model classify correctly >100,000 pairs of intra-molecular carbolithiations with 75-95% of Accuracy (Ac), Sensitivity (Sn), and Specificity (Sp). The model predicts probabilities of variations in the yield and enantiomeric excess of reactions due to at least one perturbation in boundary conditions (solvent, temperature

  17. Perturbation theory

    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

  18. PREFACE: International Conference on 'Quantum Control, Exact or Perturbative, Linear or Nonlinear' to celebrate 50 years of the scientific career of Professor Bogdan Mielnik (Mielnik50)

    Science.gov (United States)

    Bretón, N.; Fernández, D.; Kielanowski, P.

    2015-06-01

    The International Conference on 'Quantum Control, Exact or Perturbative, Linear or Nonlinear', took place in Mexico City on 22-24 October 2014. It was held with the aim of celebrating the first fifty years of scientific career of Bogdan Mielnik, an outstanding scientist whose professional trajectory spans over Poland and Mexico and who is currently Professor Emeritus in the Physics Department of Centro de Investigación y de Estudios Avanzados del IPN (Cinvestav) in Mexico. Bogdan Mielnik was born on May 6th, 1936 in Warsaw, Poland. He studied elementary and high school until 1953. In the autumn of 1953 he started the studies in the Faculty of Mathematics and Physics at the University of Warsaw, and at the end of 1957 he did his master work under the direction of Professor Jerzy Plebański. In 1962 he was invited to the newly opened Research Center of IPN (Cinvestav), in Mexico, as an assistant and PhD student of Jerzy Plebański. On October 22nd, 1964, he submitted to Cinvestav his PhD Thesis entitled ''Analytic functions of the displacement operator'', marking the offcial beginning of his scientific career. It is worth mentioning that Bogdan Mielnik is the first PhD graduate of the Physics Department of Cinvestav, so with this Conference our Department was also celebrating an important date on its calendar. A more detailed information can be found in the website http://www.fis.cinvestav.mx/mielnik50/. It was our great pleasure to see that many collaborators and former students of Bogdan Mielnik attended this Conference. The articles collected in this volume are the written contributions of the majority of talks presented at the conference. They have been organized according to the research subjects that Bogdan Mielnik has been involved in. Thus, the articles of JG Hirsch, L Hughston, G Morales-Luna, O Rosas-Ortiz and G Torres-Vega deal with Fundamental Problems in Quantum Mechanics. On the other hand, the papers by F Delgado, H Hernández-Coronado, G Herrera

  19. Solution to the Diffusion equation for multi groups in X Y geometry using Linear Perturbation theory; Solucion a la Ecuacion de Difusion para multigrupos en geometria XY utilizando teoria de perturbacion lineal

    Energy Technology Data Exchange (ETDEWEB)

    Mugica R, C.A. [IPN, ESFM, Depto. de Ingenieria Nuclear, 07738 Mexico D.F. (Mexico)

    2004-07-01

    Diverse methods exist to solve numerically the neutron diffusion equation for several energy groups in stationary state among those that highlight those of finite elements. In this work the numerical solution of this equation is presented using Raviart-Thomas nodal methods type finite element, the RT0 and RT1, in combination with iterative techniques that allow to obtain the approached solution in a quick form. Nevertheless the above mentioned, the precision of a method is intimately bound to the dimension of the approach space by cell, 5 for the case RT0 and 12 for the RT1, and/or to the mesh refinement, that makes the order of the problem of own value to solve to grow considerably. By this way if it wants to know an acceptable approach to the value of the effective multiplication factor of the system when this it has experimented a small perturbation it was appeal to the Linear perturbation theory with which is possible to determine it starting from the neutron flow and of the effective multiplication factor of the not perturbed case. Results are presented for a reference problem in which a perturbation is introduced in an assemble that simulates changes in the control bar. (Author)

  20. 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

  1. Exposures involving perturbations of the EM field have non-linear effects on radiation response and can alter the expression of radiation induced bystander effects

    Science.gov (United States)

    Mothersill, Carmel; Seymour, Colin

    2012-07-01

    Our recent data suggest there is a physical component to the bystander signal induced by radiation exposure and that alternative medicine techniques such as Reiki and acupuncture or exposures to weak EM fields alter the response of cells to direct irradiation and either altered bystander signal production or altered the response of cells receiving bystander signals. Our proposed mechanism to explain these findings is that perturbation of electromagnetic (EM) fields is central to the induction of low radiation dose responses especially non-targeted bystander effects. In this presentation we review the alternative medicine data and other data sets from our laboratory which test our hypothesis that perturbation of bio-fields will modulate radiation response in the low dose region. The other data sets include exposure to MRI, shielding using lead and or Faraday cages, the use of physical barriers to bystander signal transmission and the use of membrane channel blockers. The data taken together strongly suggest that EM field perturbation can modulate low dose response and that in fact the EM field rather than the targeted deposition of ionizing energy in the DNA may be the key determinant of dose response in a cell or organism The results also lead us to suspect that at least when chemical transmission is blocked, bystander signals can be transmitted by other means. Our recent experiments suggest light signals and volatiles are not likely. We conclude that alternative medicine and other techniques involving electromagnetic perturbations can modify the response of cells to low doses of ionizing radiation and can induce bystander effects similar to those seen in medium transfer experiments. In addition to the obvious implications for mechanistic studies of low dose effects, this could perhaps provide a novel target to exploit in space radiation protection and in optimizing therapeutic gain during radiotherapy.

  2. Chiral perturbation theory

    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)

  3. 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

  4. Traffic Perturbation

    CERN Multimedia

    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

  5. Well-posedness and stability characteristics of multi-phase models

    International Nuclear Information System (INIS)

    Ransom, V.H.; Trapp, J.A.

    1984-01-01

    The ill-posed characteristic associated with the basic two-fluid model for multi-phase flow is a natural consequence of the idealized physical model and the mean flow modeling approach. Two approaches are discussed whereby including added physics of the flow results in a well-posed system of partial differential equations. These models offer the possibility of improved accuracy and numerical efficiency compared to the numerical models used in the existing light water reactor safety analysis codes

  6. Well posedness and maximum entropy approximation for the dynamics of quantitative traits

    KAUST Repository

    Boďová , Katarí na; Haskovec, Jan; Markowich, Peter A.

    2017-01-01

    We study the Fokker–Planck equation derived in the large system limit of the Markovian process describing the dynamics of quantitative traits. The Fokker–Planck equation is posed on a bounded domain and its transport and diffusion coefficients vanish on the domain’s boundary. We first argue that, despite this degeneracy, the standard no-flux boundary condition is valid. We derive the weak formulation of the problem and prove the existence and uniqueness of its solutions by constructing the corresponding contraction semigroup on a suitable function space. Then, we prove that for the parameter regime with high enough mutation rate the problem exhibits a positive spectral gap, which implies exponential convergence to equilibrium.Next, we provide a simple derivation of the so-called Dynamic Maximum Entropy (DynMaxEnt) method for approximation of observables (moments) of the Fokker–Planck solution, which can be interpreted as a nonlinear Galerkin approximation. The limited applicability of the DynMaxEnt method inspires us to introduce its modified version that is valid for the whole range of admissible parameters. Finally, we present several numerical experiments to demonstrate the performance of both the original and modified DynMaxEnt methods. We observe that in the parameter regimes where both methods are valid, the modified one exhibits slightly better approximation properties compared to the original one.

  7. On the well-posedness of the Schrödinger-Korteweg-de Vries system

    Science.gov (United States)

    Guo, Zihua; Wang, Yuzhao

    We prove that the Cauchy problem for the Schrödinger-Korteweg-de Vries system is locally well-posed for the initial data belonging to the Sobolev spaces L(R)×H(R), and H(R)×H(R) ( s>-1/16) for the resonant case. The new ingredient is that we use the F-type space, introduced by the first author in Guo (2009) [10], to deal with the KdV part of the system and the coupling terms. In order to overcome the difficulty caused by the lack of scaling invariance, we prove uniform estimates for the multiplier. This result improves the previous one by Corcho and Linares (2007) [6].

  8. Well-posedness for one-dimensional anisotropic Cahn-Hilliard and Allen-Cahn systems

    Directory of Open Access Journals (Sweden)

    Ahmad Makki

    2015-01-01

    Full Text Available Our aim is to prove the existence and uniqueness of solutions for one-dimensional Cahn-Hilliard and Allen-Cahn type equations based on a modification of the Ginzburg-Landau free energy proposed in [8]. In particular, the free energy contains an additional term called Willmore regularization and takes into account strong anisotropy effects.

  9. Well-Posedness of Reset Control Systems as State-Dependent Impulsive Dynamical Systems

    Directory of Open Access Journals (Sweden)

    Alfonso Baños

    2012-01-01

    existence and uniqueness of solutions, and in particular to the resetting times to be well defined and distinct. A sufficient condition is developed for a reset system to have well-posed resetting times, which is also a sufficient condition for avoiding Zeno solutions and, thus, for a reset control system to be well-posed.

  10. Well-posedness for the compressible Navier–Stokes–Lamé system with a free interface

    International Nuclear Information System (INIS)

    Kukavica, Igor; Tuffaha, Amjad

    2012-01-01

    We address the system of fluid–structure interaction consisting of a compressible Navier–Stokes equation coupled with an elasticity equation, with the velocity and stress continuity requirements across the free moving interface. We prove the a priori estimates for existence of solutions when the initial velocity belongs to H 3 , the initial density is bounded from below and belongs to H 3/2+r , where r > 0, and the initial velocity of the displacement is in H 3/2+r . (paper)

  11. On the well posedness and further regularity of a diffusive three species aquatic model

    KAUST Repository

    Parshad, R.D.

    2012-01-01

    We consider Upadhay\\'s three species aquatic food chain model, with the inclusion of spatial spread. This is a well established food chain model for the interaction of three given aquatic species. It exhibits rich dynamical behavior, including chaos. We prove the existence of a global weak solution to the diffusive system, followed by existence of local mild and strong solution.

  12. Global well posedness of the relativistic Vlasov-Yukawa system with small data

    International Nuclear Information System (INIS)

    Ha, Seung-Yeal; Lee, Ho

    2007-01-01

    In this paper, we present an existence theory and uniform L 1 -stability estimate for classical solutions with small data to the Vlasov-Yukawa system. The Vlasov-Yukawa system corresponds to a short-range correction of the Vlasov-Poisson system appearing in plasma physics and astrophysics. For the existence and stability of classical solutions, we crucially use dispersion estimates due to the smallness of data

  13. Well-posedness of an extended model for water-ice phase transitions

    Czech Academy of Sciences Publication Activity Database

    Krejčí, Pavel; Rocca, E.

    2013-01-01

    Roč. 6, č. 2 (2013), s. 439-460 ISSN 1937-1632 R&D Projects: GA ČR GAP201/10/2315 Institutional support: RVO:67985840 Keywords : phase transitions * nonlocal problems * uniqueness Subject RIV: BA - General Mathematics http://www.aimsciences.org/journals/displayArticlesnew.jsp?paperID=7900

  14. On the well-posedness of the stochastic Allen–Cahn equation in two dimensions

    International Nuclear Information System (INIS)

    Ryser, Marc D.; Nigam, Nilima; Tupper, Paul F.

    2012-01-01

    White noise-driven nonlinear stochastic partial differential equations (SPDEs) of parabolic type are frequently used to model physical systems in space dimensions d = 1, 2, 3. Whereas existence and uniqueness of weak solutions to these equations are well established in one dimension, the situation is different for d ⩾ 2. Despite their popularity in the applied sciences, higher dimensional versions of these SPDE models are generally assumed to be ill-posed by the mathematics community. We study this discrepancy on the specific example of the two dimensional Allen–Cahn equation driven by additive white noise. Since it is unclear how to define the notion of a weak solution to this equation, we regularize the noise and introduce a family of approximations. Based on heuristic arguments and numerical experiments, we conjecture that these approximations exhibit divergent behavior in the continuum limit. The results strongly suggest that shrinking the mesh size in simulations of the two-dimensional white noise-driven Allen–Cahn equation does not lead to the recovery of a physically meaningful limit.

  15. A thermo-diffusion system with Smoluchowski interactions : well-posedness and homogenization

    NARCIS (Netherlands)

    Krehel, O.; Aiki, T.; Muntean, A.

    2014-01-01

    We study the solvability and homogenization of a thermal-diffusion reaction problem posed in a periodically perforated domain. The system describes the motion of populations of hot colloidal particles interacting together via Smoluchowski production terms. The upscaled system, obtained via two-scale

  16. Mathematical analysis of fluids in motion: from well-posedness to model reduction

    Czech Academy of Sciences Publication Activity Database

    Feireisl, Eduard

    2013-01-01

    Roč. 26, č. 2 (2013), s. 299-340 ISSN 1139-1138 Keywords : Navier-Stokes-Fourier system * compressible fluid * singular limits Subject RIV: BA - General Mathematics Impact factor: 0.585, year: 2013 http://link.springer.com/article/10.1007/s13163-013-0126-2

  17. Global well-posedness for nonlinear Schrodinger equations with energy-critical damping

    Directory of Open Access Journals (Sweden)

    Binhua Feng

    2015-01-01

    Full Text Available We consider the Cauchy problem for the nonlinear Schrodinger equations with energy-critical damping. We prove the existence of global in-time solutions for general initial data in the energy space. Our results extend some results from [1,2].

  18. Maximal dissipation and well-posedness for the compressible Euler system

    Czech Academy of Sciences Publication Activity Database

    Feireisl, Eduard

    2014-01-01

    Roč. 16, č. 3 (2014), s. 447-461 ISSN 1422-6928 EU Projects: European Commission(XE) 320078 - MATHEF Keywords : maximal dissipation * compressible Euler system * weak solution Subject RIV: BA - General Mathematics Impact factor: 1.186, year: 2014 http://link.springer.com/article/10.1007/s00021-014-0163-8

  19. Fermi-Dirac-Fokker-Planck equation : well-posedness & long-time asymptotics

    OpenAIRE

    Carrillo , José A.; Laurençot , Philippe; Rosado , Jesús

    2009-01-01

    International audience; A Fokker-Planck type equation for interacting particles with exclusion principle is analysed. The nonlinear drift gives rise to mathematical difficulties in controlling moments of the distribution function. Assuming enough initial moments are finite, we can show the global existence of weak solutions for this problem. The natural associated entropy of the equation is the main tool to derive uniform in time a priori estimates for the kinetic energy and entropy. As a con...

  20. Fermi-Dirac-Fokker-Planck equation: well-posedness and long-time asymptotics

    OpenAIRE

    Carrillo, José A.; Laurençot, Philippe; Rosado, Jesús

    2008-01-01

    A Fokker-Planck type equation for interacting particles with exclusion principle is analysed. The nonlinear drift gives rise to mathematical difficulties in controlling moments of the distribution function. Assuming enough initial moments are finite, we can show the global existence of weak solutions for this problem. The natural associated entropy of the equation is the main tool to derive uniform in time a priori estimates for the kinetic energy and entropy. As a consequence, long-time asym...

  1. Well-posedness of nonlocal parabolic differential problems with dependent operators.

    Science.gov (United States)

    Ashyralyev, Allaberen; Hanalyev, Asker

    2014-01-01

    The nonlocal boundary value problem for the parabolic differential equation v'(t) + A(t)v(t) = f(t) (0 ≤ t ≤ T), v(0) = v(λ) + φ, 0 exact estimates in Hölder norms for the solution of two nonlocal boundary value problems for parabolic equations with dependent coefficients are established.

  2. On the well posedness and further regularity of a diffusive three species aquatic model

    KAUST Repository

    Parshad, R.D.; Upadhyay, R.K.; Thakur, N.K.

    2012-01-01

    We consider Upadhay's three species aquatic food chain model, with the inclusion of spatial spread. This is a well established food chain model for the interaction of three given aquatic species. It exhibits rich dynamical behavior, including chaos

  3. Well-posedness of Prandtl equations with non-compatible data

    International Nuclear Information System (INIS)

    Cannone, M; Lombardo, M C; Sammartino, M

    2013-01-01

    In this paper we shall be concerned with Prandtl's equations with incompatible data, i.e. with initial data that, in general, do not fulfil the boundary conditions imposed on the solution. Under the hypothesis of analyticity in the streamwise variable, we shall prove that Prandtl's equations, on the half-plane or on the half-space, are well posed for a short time. (paper)

  4. Well posedness and maximum entropy approximation for the dynamics of quantitative traits

    KAUST Repository

    Boďová, Katarína

    2017-11-06

    We study the Fokker–Planck equation derived in the large system limit of the Markovian process describing the dynamics of quantitative traits. The Fokker–Planck equation is posed on a bounded domain and its transport and diffusion coefficients vanish on the domain’s boundary. We first argue that, despite this degeneracy, the standard no-flux boundary condition is valid. We derive the weak formulation of the problem and prove the existence and uniqueness of its solutions by constructing the corresponding contraction semigroup on a suitable function space. Then, we prove that for the parameter regime with high enough mutation rate the problem exhibits a positive spectral gap, which implies exponential convergence to equilibrium.Next, we provide a simple derivation of the so-called Dynamic Maximum Entropy (DynMaxEnt) method for approximation of observables (moments) of the Fokker–Planck solution, which can be interpreted as a nonlinear Galerkin approximation. The limited applicability of the DynMaxEnt method inspires us to introduce its modified version that is valid for the whole range of admissible parameters. Finally, we present several numerical experiments to demonstrate the performance of both the original and modified DynMaxEnt methods. We observe that in the parameter regimes where both methods are valid, the modified one exhibits slightly better approximation properties compared to the original one.

  5. 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 = ...

  6. 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 ) ¯ ...

  7. Analysis of two-phase flow instability in vertical boiling channels I: development of a linear model for the inlet velocity perturbation

    International Nuclear Information System (INIS)

    Hwang, D.H.; Yoo, Y.J.; Kim, K.K.

    1998-08-01

    A linear model, named ALFS, is developed for the analysis of two-phase flow instabilities caused by density wave oscillation and flow excursion in a vertical boiling channel with constant pressure drop conditions. The ALFS code can take into account the effect of the phase velocity difference and the thermally non-equilibrium phenomena, and the neutral boundary of the two-phase flow instability was analyzed by D-partition method. Three representative two-phase flow models ( i.e. HEM, DEM, and DNEM) were examined to investigate the effects on the stability analysis. As the results, it reveals that HEM shows the most conservative prediction of heat flux at the onset of flow instability. three linear models, Ishiis DEM, Sahas DNEM, and ALFS model, were applied to Sahas experimental data of density wave oscillation, and as the result, the mean and standard deviation of the predicted-to-measured heat flux at the onset of instability were calculated as 0.93/0.162, 0.79/0.112, and 0.95/0.143, respectively. For the long test section, however, ALFS model tends to predict the heat fluxes about 30 % lower than the measured values. (author). 14 refs

  8. 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)

  9. A non-perturbative study of matter field propagators in Euclidean Yang-Mills theory in linear covariant, Curci-Ferrari and maximal Abelian gauges

    Energy Technology Data Exchange (ETDEWEB)

    Capri, M.A.L.; Fiorentini, D.; Sorella, S.P. [UERJ - Universidade do Estado do Rio de Janeiro, Departamento de Fisica Teorica, Rio de Janeiro (Brazil); Pereira, A.D. [UERJ - Universidade do Estado do Rio de Janeiro, Departamento de Fisica Teorica, Rio de Janeiro (Brazil); UFF - Universidade Federal Fluminense, Instituto de Fisica, Niteroi, RJ (Brazil)

    2017-08-15

    In this work, we study the propagators of matter fields within the framework of the refined Gribov-Zwanziger theory, which takes into account the effects of the Gribov copies in the gauge-fixing quantization procedure of Yang-Mills theory. In full analogy with the pure gluon sector of the refined Gribov-Zwanziger action, a non-local long-range term in the inverse of the Faddeev-Popov operator is added in the matter sector. Making use of the recent BRST-invariant formulation of the Gribov-Zwanziger framework achieved in Capri et al. (Phys Rev D 92(4):045039, 2015), (Phys Rev D 94(2):025035, 2016), (Phys Rev D 93(6):065019, 2016), (arXiv:1611.10077 [hepth]), Pereira et al. (arXiv:1605.09747 [hep-th]), the propagators of scalar and quark fields in the adjoint and fundamental representations of the gauge group are worked out explicitly in the linear covariant, Curci-Ferrari and maximal Abelian gauges. Whenever lattice data are available, our results exhibit good qualitative agreement. (orig.)

  10. A non-perturbative study of matter field propagators in Euclidean Yang-Mills theory in linear covariant, Curci-Ferrari and maximal Abelian gauges

    Science.gov (United States)

    Capri, M. A. L.; Fiorentini, D.; Pereira, A. D.; Sorella, S. P.

    2017-08-01

    In this work, we study the propagators of matter fields within the framework of the refined Gribov-Zwanziger theory, which takes into account the effects of the Gribov copies in the gauge-fixing quantization procedure of Yang-Mills theory. In full analogy with the pure gluon sector of the refined Gribov-Zwanziger action, a non-local long-range term in the inverse of the Faddeev-Popov operator is added in the matter sector. Making use of the recent BRST-invariant formulation of the Gribov-Zwanziger framework achieved in Capri et al. (Phys Rev D 92(4):045039, 2015), (Phys Rev D 94(2):025035, 2016), (Phys Rev D 93(6):065019, 2016), (arXiv:1611.10077 [hep-th]), Pereira et al. (arXiv:1605.09747 [hep-th]),the propagators of scalar and quark fields in the adjoint and fundamental representations of the gauge group are worked out explicitly in the linear covariant, Curci-Ferrari and maximal Abelian gauges. Whenever lattice data are available, our results exhibit good qualitative agreement.

  11. Removing an intersubject variance component in a general linear model improves multiway factoring of event-related spectral perturbations in group EEG studies.

    Science.gov (United States)

    Spence, Jeffrey S; Brier, Matthew R; Hart, John; Ferree, Thomas C

    2013-03-01

    Linear statistical models are used very effectively to assess task-related differences in EEG power spectral analyses. Mixed models, in particular, accommodate more than one variance component in a multisubject study, where many trials of each condition of interest are measured on each subject. Generally, intra- and intersubject variances are both important to determine correct standard errors for inference on functions of model parameters, but it is often assumed that intersubject variance is the most important consideration in a group study. In this article, we show that, under common assumptions, estimates of some functions of model parameters, including estimates of task-related differences, are properly tested relative to the intrasubject variance component only. A substantial gain in statistical power can arise from the proper separation of variance components when there is more than one source of variability. We first develop this result analytically, then show how it benefits a multiway factoring of spectral, spatial, and temporal components from EEG data acquired in a group of healthy subjects performing a well-studied response inhibition task. Copyright © 2011 Wiley Periodicals, Inc.

  12. The theory of singular perturbations

    CERN Document Server

    De Jager, E M

    1996-01-01

    The subject of this textbook is the mathematical theory of singular perturbations, which despite its respectable history is still in a state of vigorous development. Singular perturbations of cumulative and of boundary layer type are presented. Attention has been given to composite expansions of solutions of initial and boundary value problems for ordinary and partial differential equations, linear as well as quasilinear; also turning points are discussed. The main emphasis lies on several methods of approximation for solutions of singularly perturbed differential equations and on the mathemat

  13. Perturbation methods

    CERN Document Server

    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

  14. SparseMaps—A systematic infrastructure for reduced-scaling electronic structure methods. III. Linear-scaling multireference domain-based pair natural orbital N-electron valence perturbation theory

    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

  15. 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

  16. 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

  17. 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

  18. Perturbative calculations of flow patterns in free convection between coaxial cylinders. Non-linear temperature dependences of the fluid properties; Un metodo de perturbaciones para la obtencion de perfiles de velocidad en conveccion natural entre cilindros coaxiales, dependencias de la temperatura no-lineales de las propiedades del fluido

    Energy Technology Data Exchange (ETDEWEB)

    Navarro, J A; Madariaga, J A; Santamaria, C M; Saviron, J M

    1980-07-01

    10 refs. Flow pattern calculations in natural convection between two vertical coaxial cylinders are reported. It is assumed trough the paper. that fluid properties, viscosity, thermal conductivity and density, depend no-linearly on temperature and that the aspects (height/radius) ratio of the cylinders is high. Velocity profiles are calculated trough a perturbative scheme and analytic results for the three first perturbation orders are presented. We outline also an iterative method to estimate the perturbations on the flow patterns which arise when a radial composition gradient is established by external forces in a two-component fluid. This procedure, based on semiempirical basis, is applied to gaseous convection. The influence of the molecules gas properties on tho flow is also discussed. (Author) 10 refs.

  19. Euclidean null controllability of perturbed infinite delay systems with ...

    African Journals Online (AJOL)

    Euclidean null controllability of perturbed infinite delay systems with limited control. ... Open Access DOWNLOAD FULL TEXT ... The results are established by placing conditions on the perturbation function which guarantee that, if the linear control base system is completely Euclidean controllable, then the perturbed system ...

  20. 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

  1. The triangulation in a perturbed Friedmann universe

    International Nuclear Information System (INIS)

    Kasai, Masumi.

    1987-12-01

    A formula for the parallax distance in a general space-time is shown and it is applied to the linearly perturbed Friedmann universe. Its invariance under any coordinate-gauge transformations and any infinitesimal affine transformations is also shown. Then it is applied to the Einstein-de Sitter background model, and it is found that the perturbed space-time behaves as a Friedmann-like universe with the direction-dependent H 0 and q 0 . (author)

  2. Well-posedness and decay for the dissipative system modeling electro-hydrodynamics in negative Besov spaces

    Science.gov (United States)

    Zhao, Jihong; Liu, Qiao

    2017-07-01

    In Guo and Wang (2012) [10], Y. Guo and Y. Wang developed a general new energy method for proving the optimal time decay rates of the solutions to dissipative equations. In this paper, we generalize this method in the framework of homogeneous Besov spaces. Moreover, we apply this method to a model arising from electro-hydrodynamics, which is a strongly coupled system of the Navier-Stokes equations and the Poisson-Nernst-Planck equations through charge transport and external forcing terms. We show that some weighted negative Besov norms of solutions are preserved along time evolution, and obtain the optimal time decay rates of the higher-order spatial derivatives of solutions by the Fourier splitting approach and the interpolation techniques.

  3. A moving boundary problem for the Stokes equations involving osmosis : Variational modelling and short-time well-posedness

    NARCIS (Netherlands)

    Lippoth, F.; Peletier, M.A.; Prokert, G.

    2016-01-01

    Within the framework of variational modelling we derive a one-phase moving boundary problem describing the motion of a semipermeable membrane enclosing a viscous liquid, driven by osmotic pressure and surface tension of the membrane. For this problem we prove the existence of classical solutions for

  4. Global well-posedness and asymptotic behavior of the solutions to non-classical thermo(visco)elastic models

    CERN Document Server

    Qin, Yuming

    2016-01-01

    This book presents recent findings on the global existence, the uniqueness and the large-time behavior of global solutions of thermo(vis)coelastic systems and related models arising in physics, mechanics and materials science such as thermoviscoelastic systems, thermoelastic systems of types II and III, as well as Timoshenko-type systems with past history. Part of the book is based on the research conducted by the authors and their collaborators in recent years. The book will benefit interested beginners in the field and experts alike.

  5. Local well-posedness for a higher order nonlinear Schrodinger equation in Sobolev spaces of negative indices

    Directory of Open Access Journals (Sweden)

    Xavier Carvajal

    2004-01-01

    Full Text Available We prove that the initial value problem associated with $$ partial_tu+ialpha partial^2_x u+Beta partial^3_x u +igamma|u|^2u = 0, quad x,t in mathbb{R}, $$ is locally well-posed in $H^s$ for $s>-1/4$.

  6. Some results on the well-posedness of Euler-Voigt and Navier-Stokes-Voigt models

    OpenAIRE

    Berselli, Luigi C.; Bisconti, Luca

    2010-01-01

    We consider the Euler-Voigt equations and the Navier-Stokes-Voigt equations, which are obtained by an inviscid alpha-regularization from the corresponding equations. The main result we show is the structural stability of the system in term of the variations of both viscosity of regularization parameters.

  7. Status of perturbative QCD

    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

  8. 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)

  9. Nonlinear spherical perturbations in quintessence models of dark energy

    Science.gov (United States)

    Pratap Rajvanshi, Manvendra; Bagla, J. S.

    2018-06-01

    Observations have confirmed the accelerated expansion of the universe. The accelerated expansion can be modelled by invoking a cosmological constant or a dynamical model of dark energy. A key difference between these models is that the equation of state parameter w for dark energy differs from ‑1 in dynamical dark energy (DDE) models. Further, the equation of state parameter is not constant for a general DDE model. Such differences can be probed using the variation of scale factor with time by measuring distances. Another significant difference between the cosmological constant and DDE models is that the latter must cluster. Linear perturbation analysis indicates that perturbations in quintessence models of dark energy do not grow to have a significant amplitude at small length scales. In this paper we study the response of quintessence dark energy to non-linear perturbations in dark matter. We use a fully relativistic model for spherically symmetric perturbations. In this study we focus on thawing models. We find that in response to non-linear perturbations in dark matter, dark energy perturbations grow at a faster rate than expected in linear perturbation theory. We find that dark energy perturbation remains localised and does not diffuse out to larger scales. The dominant drivers of the evolution of dark energy perturbations are the local Hubble flow and a supression of gradients of the scalar field. We also find that the equation of state parameter w changes in response to perturbations in dark matter such that it also becomes a function of position. The variation of w in space is correlated with density contrast for matter. Variation of w and perturbations in dark energy are more pronounced in response to large scale perturbations in matter while the dependence on the amplitude of matter perturbations is much weaker.

  10. Mode coupling of Schwarzschild perturbations: Ringdown frequencies

    International Nuclear Information System (INIS)

    Pazos, Enrique; Brizuela, David; Martin-Garcia, Jose M.; Tiglio, Manuel

    2010-01-01

    Within linearized perturbation theory, black holes decay to their final stationary state through the well-known spectrum of quasinormal modes. Here we numerically study whether nonlinearities change this picture. For that purpose we study the ringdown frequencies of gauge-invariant second-order gravitational perturbations induced by self-coupling of linearized perturbations of Schwarzschild black holes. We do so through high-accuracy simulations in the time domain of first and second-order Regge-Wheeler-Zerilli type equations, for a variety of initial data sets. We consider first-order even-parity (l=2, m=±2) perturbations and odd-parity (l=2, m=0) ones, and all the multipoles that they generate through self-coupling. For all of them and all the initial data sets considered we find that--in contrast to previous predictions in the literature--the numerical decay frequencies of second-order perturbations are the same ones of linearized theory, and we explain the observed behavior. This would indicate, in particular, that when modeling or searching for ringdown gravitational waves, appropriately including the standard quasinormal modes already takes into account nonlinear effects.

  11. Perturbations of higher-dimensional spacetimes

    Energy Technology Data Exchange (ETDEWEB)

    Durkee, Mark; Reall, Harvey S, E-mail: M.N.Durkee@damtp.cam.ac.uk, E-mail: H.S.Reall@damtp.cam.ac.uk [DAMTP, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge, CB3 0WA (United Kingdom)

    2011-02-07

    We discuss linearized gravitational perturbations of higher-dimensional spacetimes. For algebraically special spacetimes (e.g. Myers-Perry black holes), we show that there exist local gauge invariant quantities linear in the metric perturbation. These are the higher-dimensional generalizations of the 4D Newman-Penrose scalars that (in an algebraically special vacuum spacetime) satisfy decoupled equations of motion. We show that decoupling occurs in more than four dimensions if, and only if, the spacetime admits a null geodesic congruence with vanishing expansion, rotation and shear. Decoupling of electromagnetic perturbations occurs under the same conditions. Although these conditions are not satisfied in black hole spacetimes, they are satisfied in the near-horizon geometry of an extreme black hole.

  12. Redshift-space distortions from vector perturbations

    Science.gov (United States)

    Bonvin, Camille; Durrer, Ruth; Khosravi, Nima; Kunz, Martin; Sawicki, Ignacy

    2018-02-01

    We compute a general expression for the contribution of vector perturbations to the redshift space distortion of galaxy surveys. We show that they contribute to the same multipoles of the correlation function as scalar perturbations and should thus in principle be taken into account in data analysis. We derive constraints for next-generation surveys on the amplitude of two sources of vector perturbations, namely non-linear clustering and topological defects. While topological defects leave a very small imprint on redshift space distortions, we show that the multipoles of the correlation function are sensitive to vorticity induced by non-linear clustering. Therefore future redshift surveys such as DESI or the SKA should be capable of measuring such vector modes, especially with the hexadecapole which appears to be the most sensitive to the presence of vorticity.

  13. Perturbative QCD and jets

    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)

  14. 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

  15. Stationary axially symmetric perturbations of a rotating black hole. [Space-time perturbation, Newman-Penrose formalism

    Energy Technology Data Exchange (ETDEWEB)

    Demianski, M [California Inst. of Tech., Pasadena (USA)

    1976-07-01

    A stationary axially symmetric perturbation of a rotating black hole due to a distribution of test matter is investigated. The Newman-Penrose spin coefficient formalism is used to derive a general set of equations describing the perturbed space-time. In a linear approximation it is shown that the mass and angular momentum of a rotating black hole is not affected by the perturbation. The metric perturbations near the horizon are given. It is concluded that given a perturbing test fluid distribution, one can always find a corresponding metric perturbation such that the mass and angular momentum of the black hole are not changed. It was also noticed that when a tends to M, those perturbed spin coefficients and components of the Weyl tensor which determine the intrinsic properties of the incoming null cone near the horizon grow indefinitely.

  16. Finite field-dependent symmetries in perturbative quantum gravity

    International Nuclear Information System (INIS)

    Upadhyay, Sudhaker

    2014-01-01

    In this paper we discuss the absolutely anticommuting nilpotent symmetries for perturbative quantum gravity in general curved spacetime in linear and non-linear gauges. Further, we analyze the finite field-dependent BRST (FFBRST) transformation for perturbative quantum gravity in general curved spacetime. The FFBRST transformation changes the gauge-fixing and ghost parts of the perturbative quantum gravity within functional integration. However, the operation of such symmetry transformation on the generating functional of perturbative quantum gravity does not affect the theory on physical ground. The FFBRST transformation with appropriate choices of finite BRST parameter connects non-linear Curci–Ferrari and Landau gauges of perturbative quantum gravity. The validity of the results is also established at quantum level using Batalin–Vilkovisky (BV) formulation. -- Highlights: •The perturbative quantum gravity is treated as gauge theory. •BRST and anti-BRST transformations are developed in linear and non-linear gauges. •BRST transformation is generalized by making it finite and field dependent. •Connection between linear and non-linear gauges is established. •Using BV formulation the results are established at quantum level also

  17. Perturbative anyon gas

    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

  18. On the singular perturbations for fractional differential equation.

    Science.gov (United States)

    Atangana, Abdon

    2014-01-01

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

  19. 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.

  20. 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'.

  1. 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

  2. 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

  3. Divergent Perturbation Series

    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

  4. 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.

  5. Cosmological perturbations in antigravity

    Science.gov (United States)

    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.

  6. Perturbed Markov chains

    OpenAIRE

    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.

  7. 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

  8. Perturbed S3 neutrinos

    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....

  9. Perturbations of ultralight vector field dark matter

    Energy Technology Data Exchange (ETDEWEB)

    Cembranos, J.A.R.; Maroto, A.L.; Jareño, S.J. Núñez [Departamento de Física Teórica I, Universidad Complutense de Madrid, E-28040 Madrid (Spain)

    2017-02-13

    We study the dynamics of cosmological perturbations in models of dark matter based on ultralight coherent vector fields. Very much as for scalar field dark matter, we find two different regimes in the evolution: for modes with k{sup 2}≪Hma, we have a particle-like behaviour indistinguishable from cold dark matter, whereas for modes with k{sup 2}≫Hma, we get a wave-like behaviour in which the sound speed is non-vanishing and of order c{sub s}{sup 2}≃k{sup 2}/m{sup 2}a{sup 2}. This implies that, also in these models, structure formation could be suppressed on small scales. However, unlike the scalar case, the fact that the background evolution contains a non-vanishing homogeneous vector field implies that, in general, the evolution of the three kinds of perturbations (scalar, vector and tensor) can no longer be decoupled at the linear level. More specifically, in the particle regime, the three types of perturbations are actually decoupled, whereas in the wave regime, the three vector field perturbations generate one scalar-tensor and two vector-tensor perturbations in the metric. Also in the wave regime, we find that a non-vanishing anisotropic stress is present in the perturbed energy-momentum tensor giving rise to a gravitational slip of order (Φ−Ψ)/Φ∼c{sub s}{sup 2}. Moreover in this regime the amplitude of the tensor to scalar ratio of the scalar-tensor modes is also h/Φ∼c{sub s}{sup 2}. This implies that small-scale density perturbations are necessarily associated to the presence of gravity waves in this model. We compare their spectrum with the sensitivity of present and future gravity waves detectors.

  10. Symmetry-preserving perturbations of the Bateman Lagrangian and dissipative systems

    Science.gov (United States)

    Campoamor-Stursberg, Rutwig

    2017-03-01

    Perturbations of the classical Bateman Lagrangian preserving a certain subalgebra of Noether symmetries are studied, and conservative perturbations are characterized by the Lie algebra sl(2, ℝ) ⊕ so(2). Non-conservative albeit integrable perturbations are determined by the simple Lie algebra sl(2,ℝ), showing further the relation of the corresponding non-linear systems with the notion of generalized Ermakov systems.

  11. Application of a perturbation method for realistic dynamic simulation of industrial robots

    NARCIS (Netherlands)

    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

  12. Symmetry-preserving perturbations of the Bateman Lagrangian and dissipative systems

    International Nuclear Information System (INIS)

    Campoamor-Stursberg, Rutwig

    2017-01-01

    Perturbations of the classical Bateman Lagrangian preserving a certain subalgebra of Noether symmetries are studied, and conservative perturbations are characterized by the Lie algebra sl(2, ℝ) ⊕ so(2). Non-conservative albeit integrable perturbations are determined by the simple Lie algebra sl(2,ℝ), showing further the relation of the corresponding non-linear systems with the notion of generalized Ermakov systems.

  13. Symmetry-preserving perturbations of the Bateman Lagrangian and dissipative systems

    Energy Technology Data Exchange (ETDEWEB)

    Campoamor-Stursberg, Rutwig, E-mail: rutwig@ucm.es [Faculted de Ciencias Matematicas Universidad Complutense, Instituto de Matemática Interdisciplinar and Departamento Geometría y Topología (Spain)

    2017-03-15

    Perturbations of the classical Bateman Lagrangian preserving a certain subalgebra of Noether symmetries are studied, and conservative perturbations are characterized by the Lie algebra sl(2, ℝ) ⊕ so(2). Non-conservative albeit integrable perturbations are determined by the simple Lie algebra sl(2,ℝ), showing further the relation of the corresponding non-linear systems with the notion of generalized Ermakov systems.

  14. 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.)

  15. 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

  16. Linear waves and instabilities

    International Nuclear Information System (INIS)

    Bers, A.

    1975-01-01

    The electrodynamic equations for small-amplitude waves and their dispersion relation in a homogeneous plasma are outlined. For such waves, energy and momentum, and their flow and transformation, are described. Perturbation theory of waves is treated and applied to linear coupling of waves, and the resulting instabilities from such interactions between active and passive waves. Linear stability analysis in time and space is described where the time-asymptotic, time-space Green's function for an arbitrary dispersion relation is developed. The perturbation theory of waves is applied to nonlinear coupling, with particular emphasis on pump-driven interactions of waves. Details of the time--space evolution of instabilities due to coupling are given. (U.S.)

  17. Perturbative Gaussianizing transforms for cosmological fields

    Science.gov (United States)

    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.

  18. 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.)

  19. Modeling Small-Amplitude Perturbations in Inertial Confinement Fusion Pellets

    Science.gov (United States)

    Zalesak, Steven; Metzler, N.; Velikovich, A. L.; Gardner, J. H.; Manheimer, W.

    2005-10-01

    Recent advances in inertial confinement fusion (ICF) technology serve to ensure that imploding laser-driven ICF pellets will spend a significantly larger portion of their time in what is regarded as the ``linear'' portion of their perturbation evolution, i.e., in the presence of small-amplitude but nonetheless evolving perturbations. Since the evolution of these linear perturbations collectively form the initial conditions for the subsequent nonlinear evolution of the pellet, which in turn determines the energy yield of the pellet, the accurate numerical modeling of these small-amplitude perturbations has taken on an increased importance. This modeling is difficult despite the expected linear evolution of the perturbations themselves, because these perturbations are embedded in a highly nonlinear, strongly-shocked, and highly complex flow field which in and of itself stresses numerical computation capabilities, and whose simulation often employs numerical techniques which were not designed with the proper treatment of small-amplitude perturbations in mind. In this paper we will review some of the techniques that we have recently found to be of use toward this end.

  20. 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.

  1. 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

  2. Unique Fock quantization of scalar cosmological perturbations

    Science.gov (United States)

    Fernández-Méndez, Mikel; Mena Marugán, Guillermo A.; Olmedo, Javier; Velhinho, José M.

    2012-05-01

    We investigate the ambiguities in the Fock quantization of the scalar perturbations of a Friedmann-Lemaître-Robertson-Walker model with a massive scalar field as matter content. We consider the case of compact spatial sections (thus avoiding infrared divergences), with the topology of a three-sphere. After expanding the perturbations in series of eigenfunctions of the Laplace-Beltrami operator, the Hamiltonian of the system is written up to quadratic order in them. We fix the gauge of the local degrees of freedom in two different ways, reaching in both cases the same qualitative results. A canonical transformation, which includes the scaling of the matter-field perturbations by the scale factor of the geometry, is performed in order to arrive at a convenient formulation of the system. We then study the quantization of these perturbations in the classical background determined by the homogeneous variables. Based on previous work, we introduce a Fock representation for the perturbations in which: (a) the complex structure is invariant under the isometries of the spatial sections and (b) the field dynamics is implemented as a unitary operator. These two properties select not only a unique unitary equivalence class of representations, but also a preferred field description, picking up a canonical pair of field variables among all those that can be obtained by means of a time-dependent scaling of the matter field (completed into a linear canonical transformation). Finally, we present an equivalent quantization constructed in terms of gauge-invariant quantities. We prove that this quantization can be attained by a mode-by-mode time-dependent linear canonical transformation which admits a unitary implementation, so that it is also uniquely determined.

  3. Operator Decomposition Framework for Perturbation Theory

    Energy Technology Data Exchange (ETDEWEB)

    Abdel-Khalik, Hany S.; Wang, Congjian; Bang, Young Suk [North Carolina State University, Raleigh (United States)

    2012-05-15

    This summary describes a new framework for perturbation theory intended to improve its performance, in terms of the associated computational cost and the complexity of implementation, for routine reactor calculations in support of design, analysis, and regulation. Since its first introduction in reactor analysis by Winger, perturbation theory has assumed an aura of sophistication with regard to its implementation and its capabilities. Only few reactor physicists, typically mathematically proficient, have contributed to its development, with the general body of the nuclear engineering community remaining unaware of its current status, capabilities, and challenges. Given its perceived sophistication and the small body of community users, the application of perturbation theory has been limited to investigatory analyses only. It is safe to say that the nuclear community is split into two groups, a small one which understands the theory and, and a much bigger group with the perceived notion that perturbation theory is nothing but a fancy mathematical approach that has very little use in practice. Over the past three years, research has demonstrated two goals. First, reduce the computational cost of perturbation theory in order to enable its use for routine reactor calculations. Second, expose some of the myth about perturbation theory and present it in a form that is simple and relatable in order to stimulate the interest of nuclear practitioners, especially those who are currently working on the development of next generation reactor design and analysis tools. The operator decomposition approach has its roots in linear algebra and can be easily understood by code developers, especially those involved in the design of iterative numerical solution strategies

  4. Non-Perturbative Renormalization

    CERN Document Server

    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

  5. Perturbative quantum chromodynamics

    CERN Document Server

    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

  6. 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

  7. Scalar perturbations on Lemaitre-Tolman-Bondi spacetimes

    International Nuclear Information System (INIS)

    Zibin, J. P.

    2008-01-01

    In recent years there has been growing interest in verifying the horizon-scale homogeneity of the Universe that follows from applying the Copernican principle to the observed isotropy. This program has been stimulated by the discovery that a very large void, centered near us, can explain supernova luminosity distance measurements without dark energy. It is crucial to confront such models with as wide a variety of data as possible. With this application in mind, we develop the relativistic theory of linear scalar perturbations on spherically symmetric dust (Lemaitre-Tolman-Bondi) spacetimes, using the covariant 1+1+2 formalism. We show that the evolution of perturbations is determined by a small set of new linear transfer functions. If decaying modes are ignored (to be consistent with the standard inflationary paradigm), the standard techniques of perturbation theory on homogeneous backgrounds, such as harmonic expansion, can be applied, and results closely paralleling those of familiar cosmological perturbation theory can be obtained.

  8. The mass and angular momentum of reconstructed metric perturbations

    Science.gov (United States)

    van de Meent, Maarten

    2017-06-01

    We prove a key result regarding the mass and angular momentum content of linear vacuum perturbations of the Kerr metric obtained through the formalism developed by Chrzarnowski, Cohen, and Kegeles (CCK). More precisely, we prove that the Abbott-Deser mass and angular momentum integrals of any such perturbation vanish when that perturbation was obtained from a regular Fourier mode of the Hertz potential. As a corollary we obtain a generalization of previous results on the completion of the ‘no string’ radiation gauge metric perturbation generated by a point particle. We find that for any bound orbit around a Kerr black hole, the mass and angular momentum perturbations completing the CCK metric are simply the energy and angular momentum of the particle ‘outside’ the orbit and vanish ‘inside’ the orbit.

  9. Perturbed soliton excitations in inhomogeneous DNA

    International Nuclear Information System (INIS)

    Daniel, M.; Vasumathi, V.

    2005-05-01

    We study nonlinear dynamics of inhomogeneous DNA double helical chain under dynamic plane-base rotator model by considering angular rotation of bases in a plane normal to the helical axis. The DNA dynamics in this case is found to be governed by a perturbed sine-Gordon equation when taking into account the interstrand hydrogen bonding energy and intrastrand inhomogeneous stacking energy and making an analogy with the Heisenberg model of the Hamiltonian for an inhomogeneous anisotropic spin ladder with ferromagnetic legs and antiferromagentic rung coupling. In the homogeneous limit the dynamics is governed by the kink-antikink soliton of the sine-Gordon equation which represents the formation of open state configuration in DNA double helix. The effect of inhomogeneity in stacking energy in the form of localized and periodic variations on the formation of open states in DNA is studied under perturbation. The perturbed soliton is obtained using a multiple scale soliton perturbation theory by solving the associated linear eigen value problem and constructing the complete set of eigen functions. The inhomogeneity in stacking energy is found to modulate the width and speed of the soliton depending on the nature of inhomogeneity. Also it introduces fluctuations in the form of train of pulses or periodic oscillation in the open state configuration (author)

  10. 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)

  11. Perturbation on diffusion problems in domain with interfaces

    International Nuclear Information System (INIS)

    Watson, F.V.

    1985-01-01

    A perturbative type algorithm for the solution of linear diffusion equation at two dimensions, in domain with interfaces is presented. The perturbative scheme should be assembled in the weak formulation of diffusion equation, even if the strong solution exists, and when it is taken in terms superiors to first order, it should be calculated analytically, in one of the dimensions to avoid problems of slow convergence. (M.C.K.) [pt

  12. Perturbations from cosmic strings in cold dark matter

    Science.gov (United States)

    Albrecht, Andreas; Stebbins, Albert

    1991-01-01

    A systematic linear analysis of the perturbations induced by cosmic strings in cold dark matter is presented. The power spectrum is calculated and it is found that the strings produce a great deal of power on small scales. It is shown that the perturbations on interesting scales are the result of many uncorrelated string motions, which indicates a much more Gaussian distribution than was previously supposed.

  13. Current Density and Plasma Displacement Near Perturbed Rational Surface

    International Nuclear Information System (INIS)

    Boozer, A.H.; Pomphrey, N.

    2010-01-01

    The current density in the vicinity of a rational surface of a force-free magnetic field subjected to an ideal perturbation is shown to be the sum of both a smooth and a delta-function distribution, which give comparable currents. The maximum perturbation to the smooth current density is comparable to a typical equilibrium current density and the width of the layer in which the current flows is shown to be proportional to the perturbation amplitude. In the standard linearized theory, the plasma displacement has an unphysical jump across the rational surface, but the full theory gives a continuous displacement.

  14. 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

  15. Perturbative analysis of multiple-field cosmological inflation

    International Nuclear Information System (INIS)

    Lahiri, Joydev; Bhattacharya, Gautam

    2006-01-01

    We develop a general formalism for analyzing linear perturbations in multiple-field cosmological inflation based on the gauge-ready approach. Our inflationary model consists of an arbitrary number of scalar fields with non-minimal kinetic terms. We solve the equations for scalar- and tensor-type perturbations during inflation to the first order in slow roll, and then obtain the super-horizon solutions for adiabatic and isocurvature perturbations after inflation. Analytic expressions for power-spectra and spectral indices arising from multiple-field inflation are presented

  16. Linearized gravity in terms of differential forms

    Science.gov (United States)

    Baykal, Ahmet; Dereli, Tekin

    2017-01-01

    A technique to linearize gravitational field equations is developed in which the perturbation metric coefficients are treated as second rank, symmetric, 1-form fields belonging to the Minkowski background spacetime by using the exterior algebra of differential forms.

  17. 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.)

  18. Application of functional analysis to perturbation theory of differential equations. [nonlinear perturbation of the harmonic oscillator

    Science.gov (United States)

    Bogdan, V. M.; Bond, V. B.

    1980-01-01

    The deviation of the solution of the differential equation y' = f(t, y), y(O) = y sub O from the solution of the perturbed system z' = f(t, z) + g(t, z), z(O) = z sub O was investigated for the case where f and g are continuous functions on I x R sup n into R sup n, where I = (o, a) or I = (o, infinity). These functions are assumed to satisfy the Lipschitz condition in the variable z. The space Lip(I) of all such functions with suitable norms forms a Banach space. By introducing a suitable norm in the space of continuous functions C(I), introducing the problem can be reduced to an equivalent problem in terminology of operators in such spaces. A theorem on existence and uniqueness of the solution is presented by means of Banach space technique. Norm estimates on the rate of growth of such solutions are found. As a consequence, estimates of deviation of a solution due to perturbation are obtained. Continuity of the solution on the initial data and on the perturbation is established. A nonlinear perturbation of the harmonic oscillator is considered a perturbation of equations of the restricted three body problem linearized at libration point.

  19. Primordial black holes in linear and non-linear regimes

    Energy Technology Data Exchange (ETDEWEB)

    Allahyari, Alireza; Abolhasani, Ali Akbar [Department of Physics, Sharif University of Technology, Tehran (Iran, Islamic Republic of); Firouzjaee, Javad T., E-mail: allahyari@physics.sharif.edu, E-mail: j.taghizadeh.f@ipm.ir [School of Astronomy, Institute for Research in Fundamental Sciences (IPM), P.O. Box 19395-5531, Tehran (Iran, Islamic Republic of)

    2017-06-01

    We revisit the formation of primordial black holes (PBHs) in the radiation-dominated era for both linear and non-linear regimes, elaborating on the concept of an apparent horizon. Contrary to the expectation from vacuum models, we argue that in a cosmological setting a density fluctuation with a high density does not always collapse to a black hole. To this end, we first elaborate on the perturbation theory for spherically symmetric space times in the linear regime. Thereby, we introduce two gauges. This allows to introduce a well defined gauge-invariant quantity for the expansion of null geodesics. Using this quantity, we argue that PBHs do not form in the linear regime irrespective of the density of the background. Finally, we consider the formation of PBHs in non-linear regimes, adopting the spherical collapse picture. In this picture, over-densities are modeled by closed FRW models in the radiation-dominated era. The difference of our approach is that we start by finding an exact solution for a closed radiation-dominated universe. This yields exact results for turn-around time and radius. It is important that we take the initial conditions from the linear perturbation theory. Additionally, instead of using uniform Hubble gauge condition, both density and velocity perturbations are admitted in this approach. Thereby, the matching condition will impose an important constraint on the initial velocity perturbations δ {sup h} {sub 0} = −δ{sub 0}/2. This can be extended to higher orders. Using this constraint, we find that the apparent horizon of a PBH forms when δ > 3 at turn-around time. The corrections also appear from the third order. Moreover, a PBH forms when its apparent horizon is outside the sound horizon at the re-entry time. Applying this condition, we infer that the threshold value of the density perturbations at horizon re-entry should be larger than δ {sub th} > 0.7.

  20. 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

  1. A perturbative solution for gravitational waves in quadratic gravity

    International Nuclear Information System (INIS)

    Neto, Edgard C de Rey; Aguiar, Odylio D; Araujo, Jose C N de

    2003-01-01

    We find a gravitational wave solution to the linearized version of quadratic gravity by adding successive perturbations to Einstein's linearized field equations. We show that only the Ricci-squared quadratic invariant contributes to give a different solution to those found in Einstein's general relativity. The perturbative solution is written as a power series in the β parameter, the coefficient of the Ricci-squared term in the quadratic gravitational action. We also show that, for monochromatic waves of a given angular frequency ω, the perturbative solution can be summed out to give an exact solution to the linearized version of quadratic gravity, for 0 1/2 . This result may lead to implications for the predictions for gravitational wave backgrounds of cosmological origin

  2. 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.

  3. Introduction to perturbation methods

    CERN Document Server

    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.

  4. 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 +...

  5. Linear algebra

    CERN Document Server

    Shilov, Georgi E

    1977-01-01

    Covers determinants, linear spaces, systems of linear equations, linear functions of a vector argument, coordinate transformations, the canonical form of the matrix of a linear operator, bilinear and quadratic forms, Euclidean spaces, unitary spaces, quadratic forms in Euclidean and unitary spaces, finite-dimensional space. Problems with hints and answers.

  6. Cosmological perturbations in the projectable version of Hořava-Lifshitz gravity

    International Nuclear Information System (INIS)

    Cerioni, Alessandro; Brandenberger, Robert H.

    2011-01-01

    We consider linear perturbations about a homogeneous and isotropic cosmological background in the projectable version of Hořava-Lifshitz gravity. Starting from the action for cosmological perturbations, we identify the canonically normalized fluctuation variables. We find that - in contrast to what happens in the non-projectable version of the theory - the extra scalar cosmological perturbation mode is already dynamical at the level of linear perturbations and is either ghost-like or tachyonic depending on the value of a free parameter. This indicates a problem for the projectable version of Hořava-Lifshitz gravity

  7. Perturbations of spacetimes in general relativity

    International Nuclear Information System (INIS)

    Walker, M.

    1977-01-01

    In the case of gravitation, the differential equation of interest is Einstein's equation. Being a tensor equation, this is rather complicated. Moreover, gravitational theory throws up its own peculiar difficulty, the lack of a fixed background space on which to expand things. The plan of these lecture notes is therefore to discuss linear vs. nonlinear differential equations, perturbation theory for ordinary differential equations (ODE), partial differential equations (PDE), and finally, spacetimes. In this way, the basic ideas can be introduced without interference from non-essential complications. (orig.) [de

  8. Anomaly freedom in perturbative loop quantum gravity

    International Nuclear Information System (INIS)

    Bojowald, Martin; Hossain, Golam Mortuza; Kagan, Mikhail; Shankaranarayanan, S.

    2008-01-01

    A fully consistent linear perturbation theory for cosmology is derived in the presence of quantum corrections as they are suggested by properties of inverse volume operators in loop quantum gravity. The underlying constraints present a consistent deformation of the classical system, which shows that the discreteness in loop quantum gravity can be implemented in effective equations without spoiling space-time covariance. Nevertheless, nontrivial quantum corrections do arise in the constraint algebra. Since correction terms must appear in tightly controlled forms to avoid anomalies, detailed insights for the correct implementation of constraint operators can be gained. The procedures of this article thus provide a clear link between fundamental quantum gravity and phenomenology.

  9. Chiral perturbation theory

    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)

  10. Perturbed angular correlation

    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

  11. 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

  12. 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

  13. Perturbative QCD (1/3)

    CERN Multimedia

    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.

  14. 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....

  15. 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)

  16. 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)

  17. 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

  18. 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

  19. Inflationary perturbations in anisotropic, shear-free universes

    International Nuclear Information System (INIS)

    Pereira, Thiago S.; Carneiro, Saulo; Marugan, Guillermo A. Mena

    2012-01-01

    In this work, the linear and gauge-invariant theory of cosmological perturbations in a class of anisotropic and shear-free spacetimes is developed. After constructing an explicit set of complete eigenfunctions in terms of which perturbations can be expanded, we identify the effective degrees of freedom during a generic slow-roll inflationary phase. These correspond to the anisotropic equivalent of the standard Mukhanov-Sasaki variables. The associated equations of motion present a remarkable resemblance to those found in perturbed Friedmann-Robertson-Walker spacetimes with curvature, apart from the spectrum of the Laplacian, which exhibits the characteristic frequencies of the underlying geometry. In particular, it is found that the perturbations cannot develop arbitrarily large super-Hubble modes

  20. The energy of perturbations for Vlasov plasmas

    International Nuclear Information System (INIS)

    Morrison, P.J.

    1994-02-01

    The energy content of electrostatic perturbations about homogeneous equilibria is discussed. The calculation leading to the well-known dielectric (or as it is sometimes called the wave) energy is revisited and interpreted in light of Vlasov theory. It is argued that this quantity is deficient because resonant particles are not correctly handled. A linear integral transform is presented that solves the linear Vlasov-Poisson equation. This solution together with the Kruskal-Oberman energy [Phys. Fluids 1, 275 (1958)] is used to obtain an energy expression in terms of the electric field [Phys. Fluids B 4, 3038 (1992)]. It is described how the integral transform amounts to a change to normal coordinates in an infinite dimensional Hamiltonian system

  1. 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.

  2. 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

  3. Meromorphic functions and linear algebra

    CERN Document Server

    Nevanlinna, Olavi

    2003-01-01

    This volume describes for the first time in monograph form important applications in numerical methods of linear algebra. The author presents new material and extended results from recent papers in a very readable style. The main goal of the book is to study the behavior of the resolvent of a matrix under the perturbation by low rank matrices. Whereas the eigenvalues (the poles of the resolvent) and the pseudospectra (the sets where the resolvent takes large values) can move dramatically under such perturbations, the growth of the resolvent as a matrix-valued meromorphic function remains essen

  4. Solutions to nonlinear Schrodinger equations for special initial data

    Directory of Open Access Journals (Sweden)

    Takeshi Wada

    2015-11-01

    Full Text Available This article concerns the solvability of the nonlinear Schrodinger equation with gauge invariant power nonlinear term in one space dimension. The well-posedness of this equation is known only for $H^s$ with $s\\ge 0$. Under some assumptions on the nonlinearity, this paper shows that this equation is uniquely solvable for special but typical initial data, namely the linear combinations of $\\delta(x$ and p.v. (1/x, which belong to $H^{-1/2-0}$. The proof in this article allows $L^2$-perturbations on the initial data.

  5. 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.

  6. 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.)

  7. 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.

  8. Short-term memories with a stochastic perturbation

    International Nuclear Information System (INIS)

    Pontes, Jose C.A. de; Batista, Antonio M.; Viana, Ricardo L.; Lopes, Sergio R.

    2005-01-01

    We investigate short-term memories in linear and weakly nonlinear coupled map lattices with a periodic external input. We use locally coupled maps to present numerical results about short-term memory formation adding a stochastic perturbation in the maps and in the external input

  9. Pressure-driven amplification and penetration of resonant magnetic perturbations

    Energy Technology Data Exchange (ETDEWEB)

    Loizu, J. [Max-Planck-Institut für Plasmaphysik, D-17491 Greifswald (Germany); Princeton Plasma Physics Laboratory, P.O. Box 451, Princeton, New Jersey 08543 (United States); Hudson, S. R.; Lazerson, S. A.; Bhattacharjee, A. [Princeton Plasma Physics Laboratory, P.O. Box 451, Princeton, New Jersey 08543 (United States); Helander, P. [Max-Planck-Institut für Plasmaphysik, D-17491 Greifswald (Germany)

    2016-05-15

    We show that a resonant magnetic perturbation applied to the boundary of an ideal plasma screw-pinch equilibrium with nested surfaces can penetrate inside the resonant surface and into the core. The response is significantly amplified with increasing plasma pressure. We present a rigorous verification of nonlinear equilibrium codes against linear theory, showing excellent agreement.

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

    OpenAIRE

    García Planas, María Isabel; Tarragona Romero, Sonia

    2014-01-01

    The problem to study small perturbations of simple eigenvalues with a change of parameters is of general interest in applied mathematics. After to introduce a systematic way to know if an eigenvalue of a singular system is simple or not, the aim of this work is to study the behavior of a simple eigenvalue of singular linear system family

  11. The magnitude-redshift relation in a perturbed Friedmann universe

    International Nuclear Information System (INIS)

    Sasaki, Misao.

    1987-02-01

    A general formula for the magnitude-redshift relation in a linearly perturbed Friedmann universe is derived. The formula does not assume any specific gauge condition, but the gauge-invariance of it is explicitly shown. Then the application of the formula to the spatially flat background model is considered and the implications are discussed. (author)

  12. 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 ...

  13. 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 ...

  14. Demand and choice probability generating functions for perturbed consumers

    DEFF Research Database (Denmark)

    Fosgerau, Mogens; McFadden, Daniel; Bierlaire, Michel

    2011-01-01

    This paper considers demand systems for utility-maximizing consumers equipped with additive linearly perturbed utility of the form U(x)+m⋅x and faced with general budget constraints x 2 B. Given compact budget sets, the paper provides necessary as well as sufficient conditions for a demand genera...

  15. The mathematical structure of the approximate linear response relation

    International Nuclear Information System (INIS)

    Yasuda, Muneki; Tanaka, Kazuyuki

    2007-01-01

    In this paper, we study the mathematical structures of the linear response relation based on Plefka's expansion and the cluster variation method in terms of the perturbation expansion, and we show how this linear response relation approximates the correlation functions of the specified system. Moreover, by comparing the perturbation expansions of the correlation functions estimated by the linear response relation based on these approximation methods with exact perturbative forms of the correlation functions, we are able to explain why the approximate techniques using the linear response relation work well

  16. Cosmological perturbations in a family of deformations of general relativity

    International Nuclear Information System (INIS)

    Krasnov, Kirill; Shtanov, Yuri

    2010-01-01

    We study linear cosmological perturbations in a previously introduced family of deformations of general relativity characterized by the absence of new degrees of freedom. The homogeneous and isotropic background in this class of theories is unmodified and is described by the usual Friedmann equations. The theory of cosmological perturbations is modified and the relevant deformation parameter has the dimension of length. Gravitational perturbations of the scalar type can be described by a certain relativistic potential related to the matter perturbations just as in general relativity. A system of differential equations describing the evolution of this potential and of the stress-energy density perturbations is obtained. We find that the evolution of scalar perturbations proceeds with a modified effective time-dependent speed of sound, which, contrary to the case of general relativity, does not vanish even at the matter-dominated stage. In a broad range of values of the length parameter controlling the deformation, a specific transition from the regime of modified gravity to the regime of general relativity in the evolution of scalar perturbations takes place during the radiation domination. In this case, the resulting power spectrum of perturbations in radiation and dark matter is suppressed on the comoving spatial scales that enter the Hubble radius before this transition. We estimate the bounds on the deformation parameter for which this suppression does not lead to observable consequences. Evolution of scalar perturbations at the inflationary stage is modified but very slightly and the primordial spectrum generated during inflation is not noticeably different from the one obtained in general relativity

  17. An analysis of the expected eccentricity perturbations for the second Radio Astronomy Explorer (RAE B)

    Science.gov (United States)

    Murphy, J. P.

    1972-01-01

    Analytical prediction of expected eccentricity perturbations for the RAE 2 lunar orbit shows that the eccentricity will grow linearly in time. Parametric inclination studies and analysis of perturbation equations establish a critical retrograde inclination of 116.565 at which the positive perturbation slope vanishes for a circular orbit about 1100 m above the lunar surface with an eccentricity constraint of less than 0.005 during a period of about one year.

  18. Contribution of higher order terms in the reductive perturbation theory, 2

    International Nuclear Information System (INIS)

    Ichikawa, Y.H.; Mitsuhashi, Teruo; Konno, Kimiaki.

    1977-01-01

    Contribution of higher order terms in the reductive perturbation theory has been investigated for nonlinear propagation of strongly dispersive ion plasma wave. The basic set of fluid equation is reduced to a coupled set of the nonlinear Schroedinger equation for the first order perturbed potential and a linear inhomogeneous equation for the second order perturbed potential. A steady state solution of the coupled set of equations has been solved analytically in the asymptotic limit of small wave number. (auth.)

  19. Linear gate

    International Nuclear Information System (INIS)

    Suwono.

    1978-01-01

    A linear gate providing a variable gate duration from 0,40μsec to 4μsec was developed. The electronic circuity consists of a linear circuit and an enable circuit. The input signal can be either unipolar or bipolar. If the input signal is bipolar, the negative portion will be filtered. The operation of the linear gate is controlled by the application of a positive enable pulse. (author)

  20. Odd-parity perturbations of the self-similar LTB spacetime

    Energy Technology Data Exchange (ETDEWEB)

    Duffy, Emily M; Nolan, Brien C, E-mail: emilymargaret.duffy27@mail.dcu.ie, E-mail: brien.nolan@dcu.ie [School of Mathematical Sciences, Dublin City University, Glasnevin, Dublin 9 (Ireland)

    2011-05-21

    We consider the behaviour of odd-parity perturbations of those self-similar LemaItre-Tolman-Bondi spacetimes which admit a naked singularity. We find that a perturbation which evolves from initially regular data remains finite on the Cauchy horizon. Finiteness is demonstrated by considering the behaviour of suitable energy norms of the perturbation (and pointwise values of these quantities) on natural spacelike hypersurfaces. This result holds for a general choice of initial data and initial data surface. Finally, we examine the perturbed Weyl scalars in order to provide a physical interpretation of our results. Taken on its own, this result does not support cosmic censorship; however, a full perturbation of this spacetime would include even-parity perturbations, so we cannot conclude that this spacetime is stable to all linear perturbations.

  1. Linear Accelerators

    International Nuclear Information System (INIS)

    Vretenar, M

    2014-01-01

    The main features of radio-frequency linear accelerators are introduced, reviewing the different types of accelerating structures and presenting the main characteristics aspects of linac beam dynamics

  2. 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.

  3. 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

  4. 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...

  5. 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)

  6. 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

  7. 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.

  8. 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

  9. Linearization Method and Linear Complexity

    Science.gov (United States)

    Tanaka, Hidema

    We focus on the relationship between the linearization method and linear complexity and show that the linearization method is another effective technique for calculating linear complexity. We analyze its effectiveness by comparing with the logic circuit method. We compare the relevant conditions and necessary computational cost with those of the Berlekamp-Massey algorithm and the Games-Chan algorithm. The significant property of a linearization method is that it needs no output sequence from a pseudo-random number generator (PRNG) because it calculates linear complexity using the algebraic expression of its algorithm. When a PRNG has n [bit] stages (registers or internal states), the necessary computational cost is smaller than O(2n). On the other hand, the Berlekamp-Massey algorithm needs O(N2) where N(≅2n) denotes period. Since existing methods calculate using the output sequence, an initial value of PRNG influences a resultant value of linear complexity. Therefore, a linear complexity is generally given as an estimate value. On the other hand, a linearization method calculates from an algorithm of PRNG, it can determine the lower bound of linear complexity.

  10. 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.

  11. Perturbed solutions of fixed boundary MHD equilibria

    International Nuclear Information System (INIS)

    Portone, A.

    2004-01-01

    In this study, the fixed boundary plasma MHD equilibrium problem is solved by the finite element method; then, by perturbing the flux at the plasma boundary nodes, linear formulae are derived linking the variation of several plasma parameters of interest to the variation of the currents flowing in the external circuits. On the basis of these formulae it is shown how it is possible to efficiently solve two central problems in plasma engineering, namely (1) the optimization of the currents in a given set of coils necessary to maintain a specified equilibrium configuration and (2) the derivation of a linear dynamic model describing the plasma axisymmetric displacement (n = 0 mode) about a given magnetic configuration. A case study-based on the ITER reference equilibrium magnetic configuration at burn-is analysed both in terms of equilibrium currents optimality as well as axisymmetric stability features. The results obtained by these formulae are also compared with the predictions of a non-linear free boundary code and of a linear, dynamic model. As shown, the formulae derived here are in good agreement with such predictions, confirming the validity of the present approach. (author)

  12. Linear algebra

    CERN Document Server

    Said-Houari, Belkacem

    2017-01-01

    This self-contained, clearly written textbook on linear algebra is easily accessible for students. It begins with the simple linear equation and generalizes several notions from this equation for the system of linear equations and introduces the main ideas using matrices. It then offers a detailed chapter on determinants and introduces the main ideas with detailed proofs. The third chapter introduces the Euclidean spaces using very simple geometric ideas and discusses various major inequalities and identities. These ideas offer a solid basis for understanding general Hilbert spaces in functional analysis. The following two chapters address general vector spaces, including some rigorous proofs to all the main results, and linear transformation: areas that are ignored or are poorly explained in many textbooks. Chapter 6 introduces the idea of matrices using linear transformation, which is easier to understand than the usual theory of matrices approach. The final two chapters are more advanced, introducing t...

  13. High-order perturbations of a spherical collapsing star

    International Nuclear Information System (INIS)

    Brizuela, David; Martin-Garcia, Jose M.; Sperhake, Ulrich; Kokkotas, Kostas D.

    2010-01-01

    A formalism to deal with high-order perturbations of a general spherical background was developed in earlier work [D. Brizuela, J. M. Martin-Garcia, and G. A. Mena Marugan, Phys. Rev. D 74, 044039 (2006); D. Brizuela, J. M. Martin-Garcia, and G. A. Mena Marugan, Phys. Rev. D 76, 024004 (2007)]. In this paper, we apply it to the particular case of a perfect fluid background. We have expressed the perturbations of the energy-momentum tensor at any order in terms of the perturbed fluid's pressure, density, and velocity. In general, these expressions are not linear and have sources depending on lower-order perturbations. For the second-order case we make the explicit decomposition of these sources in tensor spherical harmonics. Then, a general procedure is given to evolve the perturbative equations of motions of the perfect fluid for any value of the harmonic label. Finally, with the problem of a spherical collapsing star in mind, we discuss the high-order perturbative matching conditions across a timelike surface, in particular, the surface separating the perfect fluid interior from the exterior vacuum.

  14. 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

  15. Non-Linear Dynamics and Fundamental Interactions

    CERN Document Server

    Khanna, Faqir

    2006-01-01

    The book is directed to researchers and graduate students pursuing an advanced degree. It provides details of techniques directed towards solving problems in non-linear dynamics and chos that are, in general, not amenable to a perturbative treatment. The consideration of fundamental interactions is a prime example where non-perturbative techniques are needed. Extension of these techniques to finite temperature problems is considered. At present these ideas are primarily used in a perturbative context. However, non-perturbative techniques have been considered in some specific cases. Experts in the field on non-linear dynamics and chaos and fundamental interactions elaborate the techniques and provide a critical look at the present status and explore future directions that may be fruitful. The text of the main talks will be very useful to young graduate students who are starting their studies in these areas.

  16. 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.)

  17. Linear algebra

    CERN Document Server

    Stoll, R R

    1968-01-01

    Linear Algebra is intended to be used as a text for a one-semester course in linear algebra at the undergraduate level. The treatment of the subject will be both useful to students of mathematics and those interested primarily in applications of the theory. The major prerequisite for mastering the material is the readiness of the student to reason abstractly. Specifically, this calls for an understanding of the fact that axioms are assumptions and that theorems are logical consequences of one or more axioms. Familiarity with calculus and linear differential equations is required for understand

  18. Cosmological perturbation theory at three-loop order

    Energy Technology Data Exchange (ETDEWEB)

    Blas, Diego [European Organization for Nuclear Research (CERN), Geneva (Switzerland); Garny, Mathias; Konstandin, Thomas [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)

    2013-09-15

    We analyze the dark matter power spectrum at three-loop order in standard perturbation theory of large scale structure. We observe that at late times the loop expansion does not converge even for large scales (small momenta) well within the linear regime, but exhibits properties compatible with an asymptotic series. We propose a technique to restore the convergence in the limit of small momentum, and use it to obtain a perturbative expansion with improved convergence for momenta in the range where baryonic acoustic oscillations are present. Our results are compared with data from N-body simulations at different redshifts, and we find good agreement within this range.

  19. Cosmological perturbation theory at three-loop order

    International Nuclear Information System (INIS)

    Blas, Diego; Garny, Mathias; Konstandin, Thomas

    2013-09-01

    We analyze the dark matter power spectrum at three-loop order in standard perturbation theory of large scale structure. We observe that at late times the loop expansion does not converge even for large scales (small momenta) well within the linear regime, but exhibits properties compatible with an asymptotic series. We propose a technique to restore the convergence in the limit of small momentum, and use it to obtain a perturbative expansion with improved convergence for momenta in the range where baryonic acoustic oscillations are present. Our results are compared with data from N-body simulations at different redshifts, and we find good agreement within this range.

  20. Performance of Power Systems under Sustained Random Perturbations

    Directory of Open Access Journals (Sweden)

    Humberto Verdejo

    2014-01-01

    Full Text Available This paper studies linear systems under sustained additive random perturbations. The stable operating point of an electric power system is replaced by an attracting stationary solution if the system is subjected to (small random additive perturbations. The invariant distribution of this stationary solution gives rise to several performance indices that measure how well the system copes with the randomness. These indices are introduced, showing how they can be used for the optimal tuning of system parameters in the presence of noise. Results on a four-generator two-area system are presented and discussed.

  1. 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

  2. Gauge-invariant perturbations in hybrid quantum cosmology

    Energy Technology Data Exchange (ETDEWEB)

    Gomar, Laura Castelló; Marugán, Guillermo A. Mena [Instituto de Estructura de la Materia, CSIC, Serrano 121, 28006 Madrid (Spain); Martín-Benito, Mercedes, E-mail: laura.castello@iem.cfmac.csic.es, E-mail: m.martin@hef.ru.nl, E-mail: mena@iem.cfmac.csic.es [Institute for Mathematics, Astrophysics and Particle Physics, Radboud University Nijmegen, Heyendaalseweg 135, NL-6525 AJ Nijmegen (Netherlands)

    2015-06-01

    We consider cosmological perturbations around homogeneous and isotropic spacetimes minimally coupled to a scalar field and present a formulation which is designed to preserve covariance. We truncate the action at quadratic perturbative order and particularize our analysis to flat compact spatial sections and a field potential given by a mass term, although the formalism can be extended to other topologies and potentials. The perturbations are described in terms of Mukhanov-Sasaki gauge invariants, linear perturbative constraints, and variables canonically conjugate to them. This set is completed into a canonical one for the entire system, including the homogeneous degrees of freedom. We find the global Hamiltonian constraint of the model, in which the contribution of the homogeneous sector is corrected with a term quadratic in the perturbations, that can be identified as the Mukhanov-Sasaki Hamiltonian in our formulation. We then adopt a hybrid approach to quantize the model, combining a quantum representation of the homogeneous sector with a more standard field quantization of the perturbations. Covariance is guaranteed in this approach inasmuch as no gauge fixing is adopted. Next, we adopt a Born-Oppenheimer ansatz for physical states and show how to obtain a Schrödinger-like equation for the quantum evolution of the perturbations. This evolution is governed by the Mukhanov-Sasaki Hamiltonian, with the dependence on the homogeneous geometry evaluated at quantum expectation values, and with a time parameter defined also in terms of suitable expectation values on that geometry. Finally, we derive effective equations for the dynamics of the Mukhanov-Sasaki gauge invariants, that include quantum contributions, but have the same ultraviolet limit as the classical equations. They provide the master equation to extract predictions about the power spectrum of primordial scalar perturbations.

  3. Gauge-invariant perturbations in hybrid quantum cosmology

    International Nuclear Information System (INIS)

    Gomar, Laura Castelló; Marugán, Guillermo A. Mena; Martín-Benito, Mercedes

    2015-01-01

    We consider cosmological perturbations around homogeneous and isotropic spacetimes minimally coupled to a scalar field and present a formulation which is designed to preserve covariance. We truncate the action at quadratic perturbative order and particularize our analysis to flat compact spatial sections and a field potential given by a mass term, although the formalism can be extended to other topologies and potentials. The perturbations are described in terms of Mukhanov-Sasaki gauge invariants, linear perturbative constraints, and variables canonically conjugate to them. This set is completed into a canonical one for the entire system, including the homogeneous degrees of freedom. We find the global Hamiltonian constraint of the model, in which the contribution of the homogeneous sector is corrected with a term quadratic in the perturbations, that can be identified as the Mukhanov-Sasaki Hamiltonian in our formulation. We then adopt a hybrid approach to quantize the model, combining a quantum representation of the homogeneous sector with a more standard field quantization of the perturbations. Covariance is guaranteed in this approach inasmuch as no gauge fixing is adopted. Next, we adopt a Born-Oppenheimer ansatz for physical states and show how to obtain a Schrödinger-like equation for the quantum evolution of the perturbations. This evolution is governed by the Mukhanov-Sasaki Hamiltonian, with the dependence on the homogeneous geometry evaluated at quantum expectation values, and with a time parameter defined also in terms of suitable expectation values on that geometry. Finally, we derive effective equations for the dynamics of the Mukhanov-Sasaki gauge invariants, that include quantum contributions, but have the same ultraviolet limit as the classical equations. They provide the master equation to extract predictions about the power spectrum of primordial scalar perturbations

  4. Tikhonov theorem for linear hyperbolic systems

    OpenAIRE

    Tang , Ying; Prieur , Christophe; Girard , Antoine

    2015-01-01

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

  5. 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

  6. Spatial growth of fundamental solutions for certain perturbations of the harmonic oscillator

    DEFF Research Database (Denmark)

    Jensen, Arne; Yajima, Kenji

    We consider the fundamental solution for the Cauchy problem for perturbations of the harmonic oscillator by time dependent potentials, which grow at spatial infinity slower than quadratic, but faster than linear functions, and whose Hessian matrices have a fixed sign. We prove that the fundamental...... solution at resonant times grows indefinitely at spatial infinity with the algebraic growth rate, which increases indefinitely, when the growth rate of perturbations at infinity decrease from the near quadratic to the near linear ones....

  7. Spatial growth of fundamental solutions for certain perturbations of the harmonic oscillator

    DEFF Research Database (Denmark)

    Jensen, Arne; Yajima, Kenji

    2010-01-01

    We consider the fundamental solution for the Cauchy problem for perturbations of the harmonic oscillator by time dependent potentials which grow at spatial infinity slower than quadratic but faster than linear functions and whose Hessian matrices have a fixed sign. We prove that the fundamental...... solution at resonant times grows indefinitely at spatial infinity with an algebraic growth rate, which increases indefinitely when the growth rate of perturbations at infinity decreases from the near quadratic to the near linear ones....

  8. 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

  9. Linear programming

    CERN Document Server

    Solow, Daniel

    2014-01-01

    This text covers the basic theory and computation for a first course in linear programming, including substantial material on mathematical proof techniques and sophisticated computation methods. Includes Appendix on using Excel. 1984 edition.

  10. Linear algebra

    CERN Document Server

    Liesen, Jörg

    2015-01-01

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

  11. Linear algebra

    CERN Document Server

    Berberian, Sterling K

    2014-01-01

    Introductory treatment covers basic theory of vector spaces and linear maps - dimension, determinants, eigenvalues, and eigenvectors - plus more advanced topics such as the study of canonical forms for matrices. 1992 edition.

  12. Linear Models

    CERN Document Server

    Searle, Shayle R

    2012-01-01

    This 1971 classic on linear models is once again available--as a Wiley Classics Library Edition. It features material that can be understood by any statistician who understands matrix algebra and basic statistical methods.

  13. LINEAR ACCELERATOR

    Science.gov (United States)

    Christofilos, N.C.; Polk, I.J.

    1959-02-17

    Improvements in linear particle accelerators are described. A drift tube system for a linear ion accelerator reduces gap capacity between adjacent drift tube ends. This is accomplished by reducing the ratio of the diameter of the drift tube to the diameter of the resonant cavity. Concentration of magnetic field intensity at the longitudinal midpoint of the external sunface of each drift tube is reduced by increasing the external drift tube diameter at the longitudinal center region.

  14. Covariant perturbations of Schwarzschild black holes

    International Nuclear Information System (INIS)

    Clarkson, Chris A; Barrett, Richard K

    2003-01-01

    We present a new covariant and gauge-invariant perturbation formalism for dealing with spacetimes having spherical symmetry (or some preferred spatial direction) in the background, and apply it to the case of gravitational wave propagation in a Schwarzschild black-hole spacetime. The 1 + 3 covariant approach is extended to a '1 + 1 + 2 covariant sheet' formalism by introducing a radial unit vector in addition to the timelike congruence, and decomposing all covariant quantities with respect to this. The background Schwarzschild solution is discussed and a covariant characterization is given. We give the full first-order system of linearized 1 + 1 + 2 covariant equations, and we show how, by introducing (time and spherical) harmonic functions, these may be reduced to a system of first-order ordinary differential equations and algebraic constraints for the 1 + 1 + 2 variables which may be solved straightforwardly. We show how both odd- and even-parity perturbations may be unified by the discovery of a covariant, frame- and gauge-invariant, transverse-traceless tensor describing gravitational waves, which satisfies a covariant wave equation equivalent to the Regge-Wheeler equation for both even- and odd-parity perturbations. We show how the Zerilli equation may be derived from this tensor, and derive a similar transverse-traceless tensor equation equivalent to this equation. The so-called special quasinormal modes with purely imaginary frequency emerge naturally. The significance of the degrees of freedom in the choice of the two frame vectors is discussed, and we demonstrate that, for a certain frame choice, the underlying dynamics is governed purely by the Regge-Wheeler tensor. The two transverse-traceless Weyl tensors which carry the curvature of gravitational waves are discussed, and we give the closed system of four first-order ordinary differential equations describing their propagation. Finally, we consider the extension of this work to the study of

  15. 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)

  16. 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

  17. 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

  18. Numerical Integration of a Class of Singularly Perturbed Delay Differential Equations with Small Shift

    Directory of Open Access Journals (Sweden)

    Gemechis File

    2012-01-01

    Full Text Available We have presented a numerical integration method to solve a class of singularly perturbed delay differential equations with small shift. First, we have replaced the second-order singularly perturbed delay differential equation by an asymptotically equivalent first-order delay differential equation. Then, Simpson’s rule and linear interpolation are employed to get the three-term recurrence relation which is solved easily by discrete invariant imbedding algorithm. The method is demonstrated by implementing it on several linear and nonlinear model examples by taking various values for the delay parameter and the perturbation parameter .

  19. Perturbation analysis of nonlinear matrix population models

    Directory of Open Access Journals (Sweden)

    Hal Caswell

    2008-03-01

    Full Text Available Perturbation analysis examines the response of a model to changes in its parameters. It is commonly applied to population growth rates calculated from linear models, but there has been no general approach to the analysis of nonlinear models. Nonlinearities in demographic models may arise due to density-dependence, frequency-dependence (in 2-sex models, feedback through the environment or the economy, and recruitment subsidy due to immigration, or from the scaling inherent in calculations of proportional population structure. This paper uses matrix calculus to derive the sensitivity and elasticity of equilibria, cycles, ratios (e.g. dependency ratios, age averages and variances, temporal averages and variances, life expectancies, and population growth rates, for both age-classified and stage-classified models. Examples are presented, applying the results to both human and non-human populations.

  20. Noise-induced perturbations of dispersion-managed solitons

    International Nuclear Information System (INIS)

    Li, Jinglai; Spiller, Elaine; Biondini, Gino

    2007-01-01

    We study noise-induced perturbations of dispersion-managed solitons. We do so by first developing soliton perturbation theory for the dispersion-managed nonlinear Schroedinger (DMNLS) equation, which governs the long-term behavior of optical fiber transmission systems and certain kinds of femtosecond lasers. We show that the eigenmodes and generalized eigenmodes of the linearized DMNLS equation around traveling-wave solutions can be generated from the invariances of the DMNLS equations, we quantify the perturbation-induced parameter changes of the solution in terms of the eigenmodes and the adjoint eigenmodes, and we obtain evolution equations for the solution parameters. We then apply these results to guide importance-sampled Monte Carlo (MC) simulations and reconstruct the probability density functions of the solution parameters under the effect of noise, and we compare with standard MC simulations of the unaveraged system. The comparison further validates the use of the DMNLS equation as a model for dispersion-managed systems

  1. A Theory of the Perturbed Consumer with General Budgets

    DEFF Research Database (Denmark)

    McFadden, Daniel L; Fosgerau, Mogens

    We consider demand systems for utility-maximizing consumers facing general budget constraints whose utilities are perturbed by additive linear shifts in marginal utilities. Budgets are required to be compact but are not required to be convex. We define demand generating functions (DGF) whose...... subgradients with respect to these perturbations are convex hulls of the utility-maximizing demands. We give necessary as well as sufficient conditions for DGF to be consistent with utility maximization, and establish under quite general conditions that utility-maximizing demands are almost everywhere single......-valued and smooth in their arguments. We also give sufficient conditions for integrability of perturbed demand. Our analysis provides a foundation for applications of consumer theory to problems with nonlinear budget constraints....

  2. Two-scale approach to oscillatory singularly perturbed transport equations

    CERN Document Server

    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.

  3. 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.

  4. 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.)

  5. Quantum linear Boltzmann equation

    International Nuclear Information System (INIS)

    Vacchini, Bassano; Hornberger, Klaus

    2009-01-01

    We review the quantum version of the linear Boltzmann equation, which describes in a non-perturbative fashion, by means of scattering theory, how the quantum motion of a single test particle is affected by collisions with an ideal background gas. A heuristic derivation of this Lindblad master equation is presented, based on the requirement of translation-covariance and on the relation to the classical linear Boltzmann equation. After analyzing its general symmetry properties and the associated relaxation dynamics, we discuss a quantum Monte Carlo method for its numerical solution. We then review important limiting forms of the quantum linear Boltzmann equation, such as the case of quantum Brownian motion and pure collisional decoherence, as well as the application to matter wave optics. Finally, we point to the incorporation of quantum degeneracies and self-interactions in the gas by relating the equation to the dynamic structure factor of the ambient medium, and we provide an extension of the equation to include internal degrees of freedom.

  6. Linear regression

    CERN Document Server

    Olive, David J

    2017-01-01

    This text covers both multiple linear regression and some experimental design models. The text uses the response plot to visualize the model and to detect outliers, does not assume that the error distribution has a known parametric distribution, develops prediction intervals that work when the error distribution is unknown, suggests bootstrap hypothesis tests that may be useful for inference after variable selection, and develops prediction regions and large sample theory for the multivariate linear regression model that has m response variables. A relationship between multivariate prediction regions and confidence regions provides a simple way to bootstrap confidence regions. These confidence regions often provide a practical method for testing hypotheses. There is also a chapter on generalized linear models and generalized additive models. There are many R functions to produce response and residual plots, to simulate prediction intervals and hypothesis tests, to detect outliers, and to choose response trans...

  7. Linear Colliders

    International Nuclear Information System (INIS)

    Alcaraz, J.

    2001-01-01

    After several years of study e''+ e''- linear colliders in the TeV range have emerged as the major and optimal high-energy physics projects for the post-LHC era. These notes summarize the present status form the main accelerator and detector features to their physics potential. The LHC era. These notes summarize the present status, from the main accelerator and detector features to their physics potential. The LHC is expected to provide first discoveries in the new energy domain, whereas an e''+ e''- linear collider in the 500 GeV-1 TeV will be able to complement it to an unprecedented level of precision in any possible areas: Higgs, signals beyond the SM and electroweak measurements. It is evident that the Linear Collider program will constitute a major step in the understanding of the nature of the new physics beyond the Standard Model. (Author) 22 refs

  8. Linear algebra

    CERN Document Server

    Edwards, Harold M

    1995-01-01

    In his new undergraduate textbook, Harold M Edwards proposes a radically new and thoroughly algorithmic approach to linear algebra Originally inspired by the constructive philosophy of mathematics championed in the 19th century by Leopold Kronecker, the approach is well suited to students in the computer-dominated late 20th century Each proof is an algorithm described in English that can be translated into the computer language the class is using and put to work solving problems and generating new examples, making the study of linear algebra a truly interactive experience Designed for a one-semester course, this text adopts an algorithmic approach to linear algebra giving the student many examples to work through and copious exercises to test their skills and extend their knowledge of the subject Students at all levels will find much interactive instruction in this text while teachers will find stimulating examples and methods of approach to the subject

  9. Nonlinear 2D arm dynamics in response to continuous and pulse-shaped force perturbations.

    Science.gov (United States)

    Happee, Riender; de Vlugt, Erwin; van Vliet, Bart

    2015-01-01

    Ample evidence exists regarding the nonlinearity of the neuromuscular system but linear models are widely applied to capture postural dynamics. This study quantifies the nonlinearity of human arm postural dynamics applying 2D continuous force perturbations (0.2-40 Hz) inducing three levels of hand displacement (5, 15, 45 mm RMS) followed by force-pulse perturbations inducing large hand displacements (up to 250 mm) in a position task (PT) and a relax task (RT) recording activity of eight shoulder and elbow muscles. The continuous perturbation data were used to analyze the 2D endpoint dynamics in the frequency domain and to identify reflexive and intrinsic parameters of a linear neuromuscular shoulder-elbow model. Subsequently, it was assessed to what extent the large displacements in response to force pulses could be predicted from the 'small amplitude' linear neuromuscular model. Continuous and pulse perturbation responses with varying amplitudes disclosed highly nonlinear effects. In PT, a larger continuous perturbation induced stiffening with a factor of 1.5 attributed to task adaptation evidenced by increased co-contraction and reflexive activity. This task adaptation was even more profound in the pulse responses where reflexes and displacements were strongly affected by the presence and amplitude of preceding continuous perturbations. In RT, a larger continuous perturbation resulted in yielding with a factor of 3.8 attributed to nonlinear mechanical properties as no significant reflexive activity was found. Pulse perturbations always resulted in yielding where a model fitted to the preceding 5-mm continuous perturbations predicted only 37% of the recorded peak displacements in RT and 79% in PT. This demonstrates that linear neuromuscular models, identified using continuous perturbations with small amplitudes, strongly underestimate displacements in pulse-shaped (e.g., impact) loading conditions. The data will be used to validate neuromuscular models including

  10. 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

  11. 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

  12. 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

  13. 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)

  14. 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

  15. 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.)

  16. 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.

  17. 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)

  18. 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)

  19. 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

  20. 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

  1. 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

  2. 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

  3. Solving the Linear 1D Thermoelasticity Equations with Pure Delay

    Directory of Open Access Journals (Sweden)

    Denys Ya. Khusainov

    2015-01-01

    Full Text Available We propose a system of partial differential equations with a single constant delay τ>0 describing the behavior of a one-dimensional thermoelastic solid occupying a bounded interval of R1. For an initial-boundary value problem associated with this system, we prove a well-posedness result in a certain topology under appropriate regularity conditions on the data. Further, we show the solution of our delayed model to converge to the solution of the classical equations of thermoelasticity as τ→0. Finally, we deduce an explicit solution representation for the delay problem.

  4. Step Prediction During Perturbed Standing Using Center Of Pressure Measurements

    Directory of Open Access Journals (Sweden)

    Milos R. Popovic

    2007-04-01

    Full Text Available The development of a sensor that can measure balance during quiet standing and predict stepping response in the event of perturbation has many clinically relevant applica- tions, including closed-loop control of a neuroprothesis for standing. This study investigated the feasibility of an algorithm that can predict in real-time when an able-bodied individual who is quietly standing will have to make a step to compensate for an external perturbation. Anterior and posterior perturbations were performed on 16 able-bodied subjects using a pul- ley system with a dropped weight. A linear relationship was found between the peak center of pressure (COP velocity and the peak COP displacement caused by the perturbation. This result suggests that one can predict when a person will have to make a step based on COP velocity measurements alone. Another important feature of this finding is that the peak COP velocity occurs considerably before the peak COP displacement. As a result, one can predict if a subject will have to make a step in response to a perturbation sufficiently ahead of the time when the subject is actually forced to make the step. The proposed instability detection algorithm will be implemented in a sensor system using insole sheets in shoes with minitur- ized pressure sensors by which the COPv can be continuously measured. The sensor system will be integrated in a closed-loop feedback system with a neuroprosthesis for standing in the near future.

  5. Perturbation Biology: Inferring Signaling Networks in Cellular Systems

    Science.gov (United States)

    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

  6. Uniqueness of the gauge invariant action for cosmological perturbations

    International Nuclear Information System (INIS)

    Prokopec, Tomislav; Weenink, Jan

    2012-01-01

    In second order perturbation theory different definitions are known of gauge invariant perturbations in single field inflationary models. Consequently the corresponding gauge invariant cubic actions do not have the same form. Here we show that the cubic action for one choice of gauge invariant variables is unique in the following sense: the action for any other, non-linearly related variable can be brought to the same bulk action, plus additional boundary terms. These boundary terms correspond to the choice of hypersurface and generate extra, disconnected contributions to the bispectrum. We also discuss uniqueness of the action with respect to conformal frames. When expressed in terms of the gauge invariant curvature perturbation on uniform field hypersurfaces the action for cosmological perturbations has a unique form, independent of the original Einstein or Jordan frame. Crucial is that the gauge invariant comoving curvature perturbation is frame independent, which makes it extremely helpful in showing the quantum equivalence of the two frames, and therefore in calculating quantum effects in nonminimally coupled theories such as Higgs inflation

  7. BRST and Anti-BRST Symmetries in Perturbative Quantum Gravity

    Science.gov (United States)

    Faizal, Mir

    2011-02-01

    In perturbative quantum gravity, the sum of the classical Lagrangian density, a gauge fixing term and a ghost term is invariant under two sets of supersymmetric transformations called the BRST and the anti-BRST transformations. In this paper we will analyse the BRST and the anti-BRST symmetries of perturbative quantum gravity in curved spacetime, in linear as well as non-linear gauges. We will show that even though the sum of ghost term and the gauge fixing term can always be expressed as a total BRST or a total anti-BRST variation, we can express it as a combination of both of them only in certain special gauges. We will also analyse the violation of nilpotency of the BRST and the anti-BRST transformations by introduction of a bare mass term, in the massive Curci-Ferrari gauge.

  8. Non-Perturbative Formulation of Time-Dependent String Solutions

    CERN Document Server

    Alexandre, J; Mavromatos, Nikolaos E; Alexandre, Jean; Ellis, John; Mavromatos, Nikolaos E.

    2006-01-01

    We formulate here a new world-sheet renormalization-group technique for the bosonic string, which is non-perturbative in the Regge slope alpha' and based on a functional method for controlling the quantum fluctuations, whose magnitudes are scaled by the value of alpha'. Using this technique we exhibit, in addition to the well-known linear-dilaton cosmology, a new, non-perturbative time-dependent background solution. Using the reparametrization invariance of the string S-matrix, we demonstrate that this solution is conformally invariant to alpha', and we give a heuristic inductive argument that conformal invariance can be maintained to all orders in alpha'. This new time-dependent string solution may be applicable to primordial cosmology or to the exit from linear-dilaton cosmology at large times.

  9. Nonlinear damped Schrodinger equation in two space dimensions

    Directory of Open Access Journals (Sweden)

    Tarek Saanouni

    2015-04-01

    Full Text Available In this article, we study the initial value problem for a semi-linear damped Schrodinger equation with exponential growth nonlinearity in two space dimensions. We show global well-posedness and exponential decay.

  10. The Schroedinger equation as a singular perturbation problem

    International Nuclear Information System (INIS)

    Jager, E.M. de; Kuepper, T.

    1978-01-01

    Comparisons are made of the eigenvalues and the corresponding eigenfunctions of the eigenvalue problem connected with the one dimensional Schroedinger equation in Hilbert space. The difference of the eigenvalues is estimated by applying Weyl's monotonicity principle and the minimum maximum principle. The difference of the eigenfunctions is estimated in L 2 norm and in maximum norm obtained by using simple tools from operator theory in Hilbert spaces. An application concerning perturbations of the Planck ideal linear oscillator is given. (author)

  11. 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

  12. The computation of stationary distributions of Markov chains through perturbations

    Directory of Open Access Journals (Sweden)

    Jeffery J. Hunter

    1991-01-01

    Full Text Available An algorithmic procedure for the determination of the stationary distribution of a finite, m-state, irreducible Markov chain, that does not require the use of methods for solving systems of linear equations, is presented. The technique is based upon a succession of m, rank one, perturbations of the trivial doubly stochastic matrix whose known steady state vector is updated at each stage to yield the required stationary probability vector.

  13. Nonlinear singular perturbation problems of arbitrary real orders

    International Nuclear Information System (INIS)

    Bijura, Angelina M.

    2003-10-01

    Higher order asymptotic solutions of singularly perturbed nonlinear fractional integral and derivatives of order 1/2 are investigated. It is particularly shown that whilst certain asymptotic expansions are applied successfully to linear equations and particular nonlinear problems, the standard formal asymptotic expansion is appropriate for the general class of nonlinear equations. This theory is then generalised to the general equation (of order β, 0 < β < 1). (author)

  14. Linear programming

    CERN Document Server

    Karloff, Howard

    1991-01-01

    To this reviewer’s knowledge, this is the first book accessible to the upper division undergraduate or beginning graduate student that surveys linear programming from the Simplex Method…via the Ellipsoid algorithm to Karmarkar’s algorithm. Moreover, its point of view is algorithmic and thus it provides both a history and a case history of work in complexity theory. The presentation is admirable; Karloff's style is informal (even humorous at times) without sacrificing anything necessary for understanding. Diagrams (including horizontal brackets that group terms) aid in providing clarity. The end-of-chapter notes are helpful...Recommended highly for acquisition, since it is not only a textbook, but can also be used for independent reading and study. —Choice Reviews The reader will be well served by reading the monograph from cover to cover. The author succeeds in providing a concise, readable, understandable introduction to modern linear programming. —Mathematics of Computing This is a textbook intend...

  15. Strong-stability-preserving additive linear multistep methods

    KAUST Repository

    Hadjimichael, Yiannis; Ketcheson, David I.

    2018-01-01

    The analysis of strong-stability-preserving (SSP) linear multistep methods is extended to semi-discretized problems for which different terms on the right-hand side satisfy different forward Euler (or circle) conditions. Optimal perturbed

  16. 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

  17. 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.

  18. 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

  19. 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

  20. 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

  1. Application of homotopy perturbation method for systems of Volterra integral equations of the first kind

    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.

  2. He's homotopy perturbation method for solving systems of Volterra integral equations of the second kind

    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.

  3. SAMPO: a code system giving different orders of approximation for sensitivity and perturbation analysis

    International Nuclear Information System (INIS)

    Estiot, J.C.; Salvatores, M.; Palmiotti, G.

    1981-01-01

    We present the characteristics of SAMPO, a one dimension transport theory code system, which is used for the following types of calculation: sensitivity analysis for functional linear or bi-linear on the direct or adjoint flux and their ratios; classic perturbation analysis. First order calculations, as well higher order, can be presented

  4. 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)

  5. 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)

  6. Gauge invariant perturbations of self-similar Lemaitre-Tolman-Bondi spacetime: Even parity modes with l≥2

    International Nuclear Information System (INIS)

    Waters, Thomas J.; Nolan, Brien C.

    2009-01-01

    In this paper we consider gauge invariant linear perturbations of the metric and matter tensors describing the self-similar Lemaitre-Tolman-Bondi (timelike dust) spacetime containing a naked singularity. We decompose the angular part of the perturbation in terms of spherical harmonics and perform a Mellin transform to reduce the perturbation equations to a set of ordinary differential equations with singular points. We fix initial data so the perturbation is finite on the axis and the past null cone of the singularity, and follow the perturbation modes up to the Cauchy horizon. There we argue that certain scalars formed from the modes of the perturbation remain finite, indicating linear stability of the Cauchy horizon.

  7. Efficient perturbation theory to improve the density matrix renormalization group

    Science.gov (United States)

    Tirrito, Emanuele; Ran, Shi-Ju; Ferris, Andrew J.; McCulloch, Ian P.; Lewenstein, Maciej

    2017-02-01

    The density matrix renormalization group (DMRG) is one of the most powerful numerical methods available for many-body systems. It has been applied to solve many physical problems, including the calculation of ground states and dynamical properties. In this work, we develop a perturbation theory of the DMRG (PT-DMRG) to greatly increase its accuracy in an extremely simple and efficient way. Using the canonical matrix product state (MPS) representation for the ground state of the considered system, a set of orthogonal basis functions {| ψi> } is introduced to describe the perturbations to the ground state obtained by the conventional DMRG. The Schmidt numbers of the MPS that are beyond the bond dimension cutoff are used to define these perturbation terms. The perturbed Hamiltonian is then defined as H˜i j= ; its ground state permits us to calculate physical observables with a considerably improved accuracy compared to the original DMRG results. We benchmark the second-order perturbation theory with the help of a one-dimensional Ising chain in a transverse field and the Heisenberg chain, where the precision of the DMRG is shown to be improved O (10 ) times. Furthermore, for moderate L the errors of the DMRG and PT-DMRG both scale linearly with L-1 (with L being the length of the chain). The linear relation between the dimension cutoff of the DMRG and that of the PT-DMRG at the same precision shows a considerable improvement in efficiency, especially for large dimension cutoffs. In the thermodynamic limit we show that the errors of the PT-DMRG scale with √{L-1}. Our work suggests an effective way to define the tangent space of the ground-state MPS, which may shed light on the properties beyond the ground state. This second-order PT-DMRG can be readily generalized to higher orders, as well as applied to models in higher dimensions.

  8. 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

  9. FRW Cosmological Perturbations in Massive Bigravity

    CERN Document Server

    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.

  10. Quasi-linear evolution of tearing modes

    International Nuclear Information System (INIS)

    Pellat, R.; Frey, M.; Tagger, M.

    1983-07-01

    The growth of a Tearing instability in Rutherford's nonlinear regime is investigated. Using a singular perturbation technique, lowest order Rutherford's result is recovered. To the following order it is shown that the mode generates a quasi-linear deformation of the equilibrium flux profile, whose resistive diffusion slows down the growth and shows the possibility of a saturation of the instability

  11. Reduction of Linear Programming to Linear Approximation

    OpenAIRE

    Vaserstein, Leonid N.

    2006-01-01

    It is well known that every Chebyshev linear approximation problem can be reduced to a linear program. In this paper we show that conversely every linear program can be reduced to a Chebyshev linear approximation problem.

  12. 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.

  13. 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

  14. 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

  15. Mobile ankle and knee perturbator.

    Science.gov (United States)

    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.

  16. Effects of resonant magnetic perturbation on the triggering and the evolution of double-tearing mode

    Science.gov (United States)

    Wang, L.; Lin, W. B.; Wang, X. Q.

    2018-02-01

    The effects of resonant magnetic perturbation on the triggering and the evolution of the double-tearing mode are investigated by using nonlinear magnetohydrodynamics simulations in a slab geometry. It is found that the double-tearing mode can be destabilized by boundary magnetic perturbation. Moreover, the mode has three typical development stages before it reaches saturation: the linear stable stage, the linear-growth stage, and the exponential-growth stage. The onset and growth of the double-tearing mode significantly depend on the boundary magnetic perturbations, particularly in the early development stage of the mode. The influences of the magnetic perturbation amplitude on the mode for different separations of the two rational surfaces are also discussed.

  17. Optimal Monotonicity-Preserving Perturbations of a Given Runge–Kutta Method

    KAUST Repository

    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.

  18. Optimal Monotonicity-Preserving Perturbations of a Given Runge–Kutta Method

    KAUST Repository

    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.

  19. Quasi-degenerate perturbation theory using matrix product states

    International Nuclear Information System (INIS)

    Sharma, Sandeep; Jeanmairet, Guillaume; Alavi, Ali

    2016-01-01

    In this work, we generalize the recently proposed matrix product state perturbation theory (MPSPT) for calculating energies of excited states using quasi-degenerate (QD) perturbation theory. Our formulation uses the Kirtman-Certain-Hirschfelder canonical Van Vleck perturbation theory, which gives Hermitian effective Hamiltonians at each order, and also allows one to make use of Wigner’s 2n + 1 rule. Further, our formulation satisfies Granovsky’s requirement of model space invariance which is important for obtaining smooth potential energy curves. Thus, when we use MPSPT with the Dyall Hamiltonian, we obtain a model space invariant version of quasi-degenerate n-electron valence state perturbation theory (NEVPT), a property that the usual formulation of QD-NEVPT2 based on a multipartitioning technique lacked. We use our method on the benchmark problems of bond breaking of LiF which shows ionic to covalent curve crossing and the twist around the double bond of ethylene where significant valence-Rydberg mixing occurs in the excited states. In accordance with our previous work, we find that multi-reference linearized coupled cluster theory is more accurate than other multi-reference theories of similar cost

  20. Quasi-degenerate perturbation theory using matrix product states

    Energy Technology Data Exchange (ETDEWEB)

    Sharma, Sandeep, E-mail: sanshar@gmail.com; Jeanmairet, Guillaume [Max Planck Institute for Solid State Research, Heisenbergstraße 1, 70569 Stuttgart (Germany); Alavi, Ali, E-mail: a.alavi@fkf.mpg.de [Max Planck Institute for Solid State Research, Heisenbergstraße 1, 70569 Stuttgart (Germany); Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW (United Kingdom)

    2016-01-21

    In this work, we generalize the recently proposed matrix product state perturbation theory (MPSPT) for calculating energies of excited states using quasi-degenerate (QD) perturbation theory. Our formulation uses the Kirtman-Certain-Hirschfelder canonical Van Vleck perturbation theory, which gives Hermitian effective Hamiltonians at each order, and also allows one to make use of Wigner’s 2n + 1 rule. Further, our formulation satisfies Granovsky’s requirement of model space invariance which is important for obtaining smooth potential energy curves. Thus, when we use MPSPT with the Dyall Hamiltonian, we obtain a model space invariant version of quasi-degenerate n-electron valence state perturbation theory (NEVPT), a property that the usual formulation of QD-NEVPT2 based on a multipartitioning technique lacked. We use our method on the benchmark problems of bond breaking of LiF which shows ionic to covalent curve crossing and the twist around the double bond of ethylene where significant valence-Rydberg mixing occurs in the excited states. In accordance with our previous work, we find that multi-reference linearized coupled cluster theory is more accurate than other multi-reference theories of similar cost.

  1. Quasi-degenerate perturbation theory using matrix product states

    Science.gov (United States)

    Sharma, Sandeep; Jeanmairet, Guillaume; Alavi, Ali

    2016-01-01

    In this work, we generalize the recently proposed matrix product state perturbation theory (MPSPT) for calculating energies of excited states using quasi-degenerate (QD) perturbation theory. Our formulation uses the Kirtman-Certain-Hirschfelder canonical Van Vleck perturbation theory, which gives Hermitian effective Hamiltonians at each order, and also allows one to make use of Wigner's 2n + 1 rule. Further, our formulation satisfies Granovsky's requirement of model space invariance which is important for obtaining smooth potential energy curves. Thus, when we use MPSPT with the Dyall Hamiltonian, we obtain a model space invariant version of quasi-degenerate n-electron valence state perturbation theory (NEVPT), a property that the usual formulation of QD-NEVPT2 based on a multipartitioning technique lacked. We use our method on the benchmark problems of bond breaking of LiF which shows ionic to covalent curve crossing and the twist around the double bond of ethylene where significant valence-Rydberg mixing occurs in the excited states. In accordance with our previous work, we find that multi-reference linearized coupled cluster theory is more accurate than other multi-reference theories of similar cost.

  2. Level density approach to perturbation theory and inverse-energy-weighted sum-rules

    International Nuclear Information System (INIS)

    Halemane, T.R.

    1983-01-01

    The terms in the familiar Rayleigh-Schroedinger perturbation series involve eigenvalues and eigenfunctions of the unperturbed operator. A level density formalism, that does not involve computation of eigenvalues and eigenfunctions, is given here for the perturbation series. In the CLT (central limit theorem) limit the expressions take very simple linear forms. The evaluation is in terms of moments and traces of operators and operator products. 3 references

  3. "Phonon" scattering beyond perturbation theory

    Science.gov (United States)

    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.

  4. 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

  5. Fully nonlinear and exact perturbations of the Friedmann world model: non-flat background

    Energy Technology Data Exchange (ETDEWEB)

    Noh, Hyerim, E-mail: hr@kasi.ac.kr [Korea Astronomy and Space Science Institute, Daejeon, 305-348 (Korea, Republic of)

    2014-07-01

    We extend the fully non-linear and exact cosmological perturbation equations in a Friedmann background universe to include the background curvature. The perturbation equations are presented in a gauge ready form, so any temporal gauge condition can be adopted freely depending on the problem to be solved. We consider the scalar, and vector perturbations without anisotropic stress. As an application, we analyze the equations in the special case of irrotational zero-pressure fluid in the comoving gauge condition. We also present the fully nonlinear formulation for a minimally coupled scalar field.

  6. Generalized perturbation theory using two-dimensional, discrete ordinates transport theory

    International Nuclear Information System (INIS)

    Childs, R.L.

    1979-01-01

    Perturbation theory for changes in linear and bilinear functionals of the forward and adjoint fluxes in a critical reactor has been implemented using two-dimensional discrete ordinates transport theory. The computer program DOT IV was modified to calculate the generalized functions Λ and Λ*. Demonstration calculations were performed for changes in a reaction-rate ratio and a reactivity worth caused by system perturbations. The perturbation theory predictions agreed with direct calculations to within about 2%. A method has been developed for calculating higher lambda eigenvalues and eigenfunctions using techniques similar to those developed for generalized functions. Demonstration calculations have been performed to obtain these eigenfunctions

  7. linear-quadratic-linear model

    Directory of Open Access Journals (Sweden)

    Tanwiwat Jaikuna

    2017-02-01

    Full Text Available Purpose: To develop an in-house software program that is able to calculate and generate the biological dose distribution and biological dose volume histogram by physical dose conversion using the linear-quadratic-linear (LQL model. Material and methods : The Isobio software was developed using MATLAB version 2014b to calculate and generate the biological dose distribution and biological dose volume histograms. The physical dose from each voxel in treatment planning was extracted through Computational Environment for Radiotherapy Research (CERR, and the accuracy was verified by the differentiation between the dose volume histogram from CERR and the treatment planning system. An equivalent dose in 2 Gy fraction (EQD2 was calculated using biological effective dose (BED based on the LQL model. The software calculation and the manual calculation were compared for EQD2 verification with pair t-test statistical analysis using IBM SPSS Statistics version 22 (64-bit. Results: Two and three-dimensional biological dose distribution and biological dose volume histogram were displayed correctly by the Isobio software. Different physical doses were found between CERR and treatment planning system (TPS in Oncentra, with 3.33% in high-risk clinical target volume (HR-CTV determined by D90%, 0.56% in the bladder, 1.74% in the rectum when determined by D2cc, and less than 1% in Pinnacle. The difference in the EQD2 between the software calculation and the manual calculation was not significantly different with 0.00% at p-values 0.820, 0.095, and 0.593 for external beam radiation therapy (EBRT and 0.240, 0.320, and 0.849 for brachytherapy (BT in HR-CTV, bladder, and rectum, respectively. Conclusions : The Isobio software is a feasible tool to generate the biological dose distribution and biological dose volume histogram for treatment plan evaluation in both EBRT and BT.

  8. Perturbations i have Known and Loved

    Science.gov (United States)

    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

  9. 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.

  10. Second-order perturbations of cosmological fluids: Relativistic effects of pressure, multicomponent, curvature, and rotation

    International Nuclear Information System (INIS)

    Hwang, Jai-chan; Noh, Hyerim

    2007-01-01

    We present general relativistic correction terms appearing in Newton's gravity to the second-order perturbations of cosmological fluids. In our previous work we have shown that to the second-order perturbations, the density and velocity perturbation equations of general relativistic zero-pressure, irrotational, single-component fluid in a spatially flat background coincide exactly with the ones known in Newton's theory without using the gravitational potential. We also have shown the effect of gravitational waves to the second order, and pure general relativistic correction terms appearing in the third-order perturbations. Here, we present results of second-order perturbations relaxing all the assumptions made in our previous works. We derive the general relativistic correction terms arising due to (i) pressure, (ii) multicomponent, (iii) background spatial curvature, and (iv) rotation. In the case of multicomponent zero-pressure, irrotational fluids under the flat background, we effectively do not have relativistic correction terms, thus the relativistic equations expressed in terms of density and velocity perturbations again coincide with the Newtonian ones. In the other three cases we generally have pure general relativistic correction terms. In the case of pressure, the relativistic corrections appear even in the level of background and linear perturbation equations. In the presence of background spatial curvature, or rotation, pure relativistic correction terms directly appear in the Newtonian equations of motion of density and velocity perturbations to the second order; to the linear order, without using the gravitational potential (or metric perturbations), we have relativistic/Newtonian correspondences for density and velocity perturbations of a single-component fluid including the rotation even in the presence of background spatial curvature. In the small-scale limit (far inside the horizon), to the second-order, relativistic equations of density and

  11. Numerical solution of Euler's equation by perturbed functionals

    Science.gov (United States)

    Dey, S. K.

    1985-01-01

    A perturbed functional iteration has been developed to solve nonlinear systems. It adds at each iteration level, unique perturbation parameters to nonlinear Gauss-Seidel iterates which enhances its convergence properties. As convergence is approached these parameters are damped out. Local linearization along the diagonal has been used to compute these parameters. The method requires no computation of Jacobian or factorization of matrices. Analysis of convergence depends on properties of certain contraction-type mappings, known as D-mappings. In this article, application of this method to solve an implicit finite difference approximation of Euler's equation is studied. Some representative results for the well known shock tube problem and compressible flows in a nozzle are given.

  12. Nonlinear dynamics analysis of the human balance control subjected to physical and sensory perturbations.

    Science.gov (United States)

    Ashtiani, Mohammed N; Mahmood-Reza, Azghani

    2017-01-01

    Postural control after applying perturbation involves neural and muscular efforts to limit the center of mass (CoM) motion. Linear dynamical approaches may not unveil all complexities of body efforts. This study was aimed at determining two nonlinear dynamics parameters (fractal dimension (FD) and largest Lyapunov exponent (LLE)) in addition to the linear standing metrics of balance in perturbed stance. Sixteen healthy young males were subjected to sudden rotations of the standing platform. The vision and cognition during the standing were also interfered. Motion capturing was used to measure the lower limb joints and the CoM displacements. The CoM path length as a linear parameter was increased by elimination of vision (pnonlinear metric FD was decreased due to the cognitive loads (pnonlinear metrics of the perturbed stance showed that a combination of them may properly represent the body behavior.

  13. 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.

  14. Initial conditions for cosmological perturbations

    Science.gov (United States)

    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.

  15. 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)

  16. Curvature perturbations from dimensional decoupling

    CERN Document Server

    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.

  17. 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.

  18. Applicability of refined Born approximation to non-linear equations

    International Nuclear Information System (INIS)

    Rayski, J.

    1990-01-01

    A computational method called ''Refined Born Approximation'', formerly applied exclusively to linear problems, is shown to be successfully applicable also to non-linear problems enabling me to compute bifurcations and other irregular solutions which cannot be obtained by the standard perturbation procedures. (author)

  19. Analytic central path, sensitivity analysis and parametric linear programming

    NARCIS (Netherlands)

    A.G. Holder; J.F. Sturm; S. Zhang (Shuzhong)

    1998-01-01

    textabstractIn this paper we consider properties of the central path and the analytic center of the optimal face in the context of parametric linear programming. We first show that if the right-hand side vector of a standard linear program is perturbed, then the analytic center of the optimal face

  20. Linear Parametric Sensitivity Analysis of the Constraint Coefficient Matrix in Linear Programs

    OpenAIRE

    Zuidwijk, Rob

    2005-01-01

    textabstractSensitivity analysis is used to quantify the impact of changes in the initial data of linear programs on the optimal value. In particular, parametric sensitivity analysis involves a perturbation analysis in which the effects of small changes of some or all of the initial data on an optimal solution are investigated, and the optimal solution is studied on a so-called critical range of the initial data, in which certain properties such as the optimal basis in linear programming are ...

  1. 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.

  2. 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.

  3. 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.

  4. 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

  5. Strong-stability-preserving additive linear multistep methods

    KAUST Repository

    Hadjimichael, Yiannis

    2018-02-20

    The analysis of strong-stability-preserving (SSP) linear multistep methods is extended to semi-discretized problems for which different terms on the right-hand side 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 larger 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 nonadditive SSP linear multistep methods.

  6. Linear Parametric Sensitivity Analysis of the Constraint Coefficient Matrix in Linear Programs

    NARCIS (Netherlands)

    R.A. Zuidwijk (Rob)

    2005-01-01

    textabstractSensitivity analysis is used to quantify the impact of changes in the initial data of linear programs on the optimal value. In particular, parametric sensitivity analysis involves a perturbation analysis in which the effects of small changes of some or all of the initial data on an

  7. The linear-non-linear frontier for the Goldstone Higgs

    International Nuclear Information System (INIS)

    Gavela, M.B.; Saa, S.; Kanshin, K.; Machado, P.A.N.

    2016-01-01

    The minimal SO(5)/SO(4) σ-model is used as a template for the ultraviolet completion of scenarios in which the Higgs particle is a low-energy remnant of some high-energy dynamics, enjoying a (pseudo) Nambu-Goldstone-boson ancestry. Varying the σ mass allows one to sweep from the perturbative regime to the customary non-linear implementations. The low-energy benchmark effective non-linear Lagrangian for bosons and fermions is obtained, determining as well the operator coefficients including linear corrections. At first order in the latter, three effective bosonic operators emerge which are independent of the explicit soft breaking assumed. The Higgs couplings to vector bosons and fermions turn out to be quite universal: the linear corrections are proportional to the explicit symmetry-breaking parameters. Furthermore, we define an effective Yukawa operator which allows a simple parametrization and comparison of different heavy-fermion ultraviolet completions. In addition, one particular fermionic completion is explored in detail, obtaining the corresponding leading low-energy fermionic operators. (orig.)

  8. The linear-non-linear frontier for the Goldstone Higgs

    Energy Technology Data Exchange (ETDEWEB)

    Gavela, M.B.; Saa, S. [IFT-UAM/CSIC, Universidad Autonoma de Madrid, Departamento de Fisica Teorica y Instituto de Fisica Teorica, Madrid (Spain); Kanshin, K. [Universita di Padova, Dipartimento di Fisica e Astronomia ' G. Galilei' , Padua (Italy); INFN, Padova (Italy); Machado, P.A.N. [IFT-UAM/CSIC, Universidad Autonoma de Madrid, Departamento de Fisica Teorica y Instituto de Fisica Teorica, Madrid (Spain); Fermi National Accelerator Laboratory, Theoretical Physics Department, Batavia, IL (United States)

    2016-12-15

    The minimal SO(5)/SO(4) σ-model is used as a template for the ultraviolet completion of scenarios in which the Higgs particle is a low-energy remnant of some high-energy dynamics, enjoying a (pseudo) Nambu-Goldstone-boson ancestry. Varying the σ mass allows one to sweep from the perturbative regime to the customary non-linear implementations. The low-energy benchmark effective non-linear Lagrangian for bosons and fermions is obtained, determining as well the operator coefficients including linear corrections. At first order in the latter, three effective bosonic operators emerge which are independent of the explicit soft breaking assumed. The Higgs couplings to vector bosons and fermions turn out to be quite universal: the linear corrections are proportional to the explicit symmetry-breaking parameters. Furthermore, we define an effective Yukawa operator which allows a simple parametrization and comparison of different heavy-fermion ultraviolet completions. In addition, one particular fermionic completion is explored in detail, obtaining the corresponding leading low-energy fermionic operators. (orig.)

  9. In-core fuel management via perturbation theory

    International Nuclear Information System (INIS)

    Mingle, J.O.

    1975-01-01

    A two-step procedure is developed for the optimization of in-core nuclear fuel management using perturbation theory to predict the effects of various core configurations. The first procedure is a cycle cost minimization using linear programming with a zoned core and discrete burnup groups. The second program utilizes an individual fuel assembly shuffling sequence to minimize the maldistribution of power generation. This latter quantity is represented by a figure of merit or by an assembly power peaking factor. A pressurized water reactor example calculation is utilized. 24 references

  10. Unmatched Projector/Backprojector Pairs: Perturbation and Convergence Analysis

    DEFF Research Database (Denmark)

    Elfving, Tommy; Hansen, Per Christian

    2018-01-01

    are not each other's transpose. Surprisingly, the influence of such errors in algebraic iterative reconstruction methods has received little attention in the literature. The goal of this paper is to perform a rigorous first-order perturbation analysis of the minimization problems underlying the algebraic...... methods in order to understand the role played by the nonmatch of the matrices. We also study the convergence properties of linear stationary iterations based on unmatched matrix pairs, leading to insight into the behavior of some important row-and column-oriented algebraic iterative methods. We conclude...

  11. Geometric scaling in ultrahigh energy neutrinos and nonlinear perturbative QCD

    International Nuclear Information System (INIS)

    Machado, Magno V.T.

    2011-01-01

    The ultrahigh energy neutrino cross section is a crucial ingredient in the calculation of the event rate in high energy neutrino telescopes. Currently there are several approaches which predict different behaviors for its magnitude for ultrahigh energies. In this contribution is presented a summary of current predictions based on the non-linear QCD evolution equations, the so-called perturbative saturation physics. In particular, predictions are shown based on the parton saturation approaches and the consequences of geometric scaling property at high energies are discussed. The scaling property allows an analytical computation of the neutrino scattering on nucleon/nucleus at high energies, providing a theoretical parameterization. (author)

  12. 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

  13. 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

  14. 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.)

  15. 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)

  16. 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

  17. Gravitational Wave in Linear General Relativity

    Science.gov (United States)

    Cubillos, D. J.

    2017-07-01

    General relativity is the best theory currently available to describe the interaction due to gravity. Within Albert Einstein's field equations this interaction is described by means of the spatiotemporal curvature generated by the matter-energy content in the universe. Weyl worked on the existence of perturbations of the curvature of space-time that propagate at the speed of light, which are known as Gravitational Waves, obtained to a first approximation through the linearization of the field equations of Einstein. Weyl's solution consists of taking the field equations in a vacuum and disturbing the metric, using the Minkowski metric slightly perturbed by a factor ɛ greater than zero but much smaller than one. If the feedback effect of the field is neglected, it can be considered as a weak field solution. After introducing the disturbed metric and ignoring ɛ terms of order greater than one, we can find the linearized field equations in terms of the perturbation, which can then be expressed in terms of the Dalambertian operator of the perturbation equalized to zero. This is analogous to the linear wave equation in classical mechanics, which can be interpreted by saying that gravitational effects propagate as waves at the speed of light. In addition to this, by studying the motion of a particle affected by this perturbation through the geodesic equation can show the transversal character of the gravitational wave and its two possible states of polarization. It can be shown that the energy carried by the wave is of the order of 1/c5 where c is the speed of light, which explains that its effects on matter are very small and very difficult to detect.

  18. Linear Algebra and Smarandache Linear Algebra

    OpenAIRE

    Vasantha, Kandasamy

    2003-01-01

    The present book, on Smarandache linear algebra, not only studies the Smarandache analogues of linear algebra and its applications, it also aims to bridge the need for new research topics pertaining to linear algebra, purely in the algebraic sense. We have introduced Smarandache semilinear algebra, Smarandache bilinear algebra and Smarandache anti-linear algebra and their fuzzy equivalents. Moreover, in this book, we have brought out the study of linear algebra and vector spaces over finite p...

  19. Analytical Investigation of Beam Deformation Equation using Perturbation, Homotopy Perturbation, Variational Iteration and Optimal Homotopy Asymptotic Methods

    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...

  20. Smoothing expansion rate data to reconstruct cosmological matter perturbations

    Energy Technology Data Exchange (ETDEWEB)

    Gonzalez, J.E.; Alcaniz, J.S.; Carvalho, J.C., E-mail: javierernesto@on.br, E-mail: alcaniz@on.br, E-mail: jcarvalho@on.br [Departamento de Astronomia, Observatório Nacional, Rua Gal. José Cristino, 77, Rio de Janeiro, RJ 20921-400 (Brazil)

    2017-08-01

    The existing degeneracy between different dark energy and modified gravity cosmologies at the background level may be broken by analyzing quantities at the perturbative level. In this work, we apply a non-parametric smoothing (NPS) method to reconstruct the expansion history of the Universe ( H ( z )) from model-independent cosmic chronometers and high- z quasar data. Assuming a homogeneous and isotropic flat universe and general relativity (GR) as the gravity theory, we calculate the non-relativistic matter perturbations in the linear regime using the H ( z ) reconstruction and realistic values of Ω {sub m} {sub 0} and σ{sub 8} from Planck and WMAP-9 collaborations. We find a good agreement between the measurements of the growth rate and f σ{sub 8}( z ) from current large-scale structure observations and the estimates obtained from the reconstruction of the cosmic expansion history. Considering a recently proposed null test for GR using matter perturbations, we also apply the NPS method to reconstruct f σ{sub 8}( z ). For this case, we find a ∼ 3σ tension (good agreement) with the standard relativistic cosmology when the Planck (WMAP-9) priors are used.

  1. A nonlinear inversion for the velocity background and perturbation models

    KAUST Repository

    Wu, Zedong

    2015-08-19

    Reflected waveform inversion (RWI) provides a method to reduce the nonlinearity of the standard full waveform inversion (FWI) by inverting for the single scattered wavefield obtained using an image. However, current RWI methods usually neglect diving waves, which is an important source of information for extracting the long wavelength components of the velocity model. Thus, we propose a new optimization problem through breaking the velocity model into the background and the perturbation in the wave equation directly. In this case, the perturbed model is no longer the single scattering model, but includes all scattering. We optimize both components simultaneously, and thus, the objective function is nonlinear with respect to both the background and perturbation. The new introduced w can absorb the non-smooth update of background naturally. Application to the Marmousi model with frequencies that start at 5 Hz shows that this method can converge to the accurate velocity starting from a linearly increasing initial velocity. Application to the SEG2014 demonstrates the versatility of the approach.

  2. Some electromagnetic and gravitational perturbations of black holes

    International Nuclear Information System (INIS)

    Pollock, M.D.

    1978-08-01

    The dissertation is concerned with the changes which take place in a Kerr black hole which is subjected to electromagnetic or gravitational perturbations, in particular idealized configurations. A calculation is made of the interaction between a slowly rotating black hole and a uniform, weak magnetic field. The method used is to solve the tensorial Maxwell equations in the background geometry of the hole and then calculate the torque on the sources of the field, hence deducing the spin-down law of the hole. The calculation is extended to include black holes rotating with arbitrary angular velocity by a different method, which is based on Newman-Penrose spinor formalism and applies some work of Chandrasekhar. The analogous gravitational problem, in which the centrally located hole is perturbed by a spinning shell of matter is solved by drawing on the results of Chrzanowski on factorized Green functions and horizon multipole moments. Formulae are presented for the spin-down behaviour of a black hole under these two kinds of perturbation. In addition to these effects produced by the fields, there are also linear precessional effects in the gravitational case, but not in the electromagnetic case. (author)

  3. Stability and chaotic dynamics of a perturbed rate gyro

    International Nuclear Information System (INIS)

    Chen, H.-H.

    2006-01-01

    An analysis of stability and chaotic dynamics is presented by a single-axis rate gyro subjected to linear feedback control loops. This rate gyro is supposed to be mounted on a space vehicle which undergoes an uncertain angular velocity ω Z (t) around its spin axis and simultaneously acceleration ω-bar X (t) occurs with respect to the output axis. The necessary and sufficient conditions of stability and degeneracy conditions for the autonomous case, whose vehicle undergoes a steady rotation, were provided by Routh-Hurwitz theory. The stability of the nonlinear nonautonomous system was investigated by Liapunov stability and instability theorems. As the electrical time constant is much smaller than the mechanical time constant, the singularly perturbed system can be obtained by the singular perturbation theory. The Liapunov stability of this system by studying the reduced and boundary-layer systems was also analyzed. Using the Melinikov technique, we can give criteria for the existence of chaos in the gyro motion when the vehicle undergoes perturbed harmonic rotation about its spin and output axes

  4. Smoothing expansion rate data to reconstruct cosmological matter perturbations

    International Nuclear Information System (INIS)

    Gonzalez, J.E.; Alcaniz, J.S.; Carvalho, J.C.

    2017-01-01

    The existing degeneracy between different dark energy and modified gravity cosmologies at the background level may be broken by analyzing quantities at the perturbative level. In this work, we apply a non-parametric smoothing (NPS) method to reconstruct the expansion history of the Universe ( H ( z )) from model-independent cosmic chronometers and high- z quasar data. Assuming a homogeneous and isotropic flat universe and general relativity (GR) as the gravity theory, we calculate the non-relativistic matter perturbations in the linear regime using the H ( z ) reconstruction and realistic values of Ω m 0 and σ 8 from Planck and WMAP-9 collaborations. We find a good agreement between the measurements of the growth rate and f σ 8 ( z ) from current large-scale structure observations and the estimates obtained from the reconstruction of the cosmic expansion history. Considering a recently proposed null test for GR using matter perturbations, we also apply the NPS method to reconstruct f σ 8 ( z ). For this case, we find a ∼ 3σ tension (good agreement) with the standard relativistic cosmology when the Planck (WMAP-9) priors are used.

  5. Internal wave energy flux from density perturbations in nonlinear stratifications

    Science.gov (United States)

    Lee, Frank M.; Allshouse, Michael R.; Swinney, Harry L.; Morrison, P. J.

    2017-11-01

    Tidal flow over the topography at the bottom of the ocean, whose density varies with depth, generates internal gravity waves that have a significant impact on the energy budget of the ocean. Thus, understanding the energy flux (J = p v) is important, but it is difficult to measure simultaneously the pressure and velocity perturbation fields, p and v . In a previous work, a Green's-function-based method was developed to calculate the instantaneous p, v , and thus J , given a density perturbation field for a constant buoyancy frequency N. Here we extend the previous analytic Green's function work to include nonuniform N profiles, namely the tanh-shaped and linear cases, because background density stratifications that occur in the ocean and some experiments are nonlinear. In addition, we present a finite-difference method for the general case where N has an arbitrary profile. Each method is validated against numerical simulations. The methods we present can be applied to measured density perturbation data by using our MATLAB graphical user interface EnergyFlux. PJM was supported by the U.S. Department of Energy Contract DE-FG05-80ET-53088. HLS and MRA were supported by ONR Grant No. N000141110701.

  6. From landscape to inflationary perturbations

    International Nuclear Information System (INIS)

    Hector, Cecelie

    2012-07-01

    We discuss a quantum tunneling event in a piecewise potential where the false vacuum part is either linear or quartic and the true vacuum is described by a quartic potential. We find exact solutions for these tunneling processes and explain how exact tunneling solutions can give information about the local shape of the string theory landscape. We investigate the existence of bounce solutions for effective potentials with sharp minima and maxima. We also partly derive the two-point correlation function for a λφ 4 -theory on a de Sitter background for a massless minimally coupled scalar field φ. (orig.)

  7. From landscape to inflationary perturbations

    Energy Technology Data Exchange (ETDEWEB)

    Hector, Cecelie

    2012-07-15

    We discuss a quantum tunneling event in a piecewise potential where the false vacuum part is either linear or quartic and the true vacuum is described by a quartic potential. We find exact solutions for these tunneling processes and explain how exact tunneling solutions can give information about the local shape of the string theory landscape. We investigate the existence of bounce solutions for effective potentials with sharp minima and maxima. We also partly derive the two-point correlation function for a {lambda}{phi}{sup 4}-theory on a de Sitter background for a massless minimally coupled scalar field {phi}. (orig.)

  8. Effects of collisions on linear and non-linear spectroscopic line shapes

    International Nuclear Information System (INIS)

    Berman, P.R.

    1978-01-01

    A fundamental physical problem is the determination of atom-atom, atom-molecule and molecule-molecule differential and total scattering cross sections. In this work, a technique for studying atomic and molecular collisions using spectroscopic line shape analysis is discussed. Collisions occurring within an atomic or molecular sample influence the sample's absorptive or emissive properties. Consequently the line shapes associated with the linear or non-linear absorption of external fields by an atomic system reflect the collisional processes occurring in the gas. Explicit line shape expressions are derived characterizing linear or saturated absorption by two-or three-level 'active' atoms which are undergoing collisions with perturber atoms. The line shapes may be broadened, shifted, narrowed, or distorted as a result of collisions which may be 'phase-interrupting' or 'velocity-changing' in nature. Systematic line shape studies can be used to obtain information on both the differential and total active atom-perturber scattering cross sections. (Auth.)

  9. Difference scheme for a singularly perturbed parabolic convection-diffusion equation in the presence of perturbations

    Science.gov (United States)

    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.

  10. Perturbation of eigenvalues of preconditioned Navier-Stokes operators

    Energy Technology Data Exchange (ETDEWEB)

    Elman, H.C. [Univ. of Maryland, College Park, MD (United States)

    1996-12-31

    We study the sensitivity of algebraic eigenvalue problems associated with matrices arising from linearization and discretization of the steady-state Navier-Stokes equations. In particular, for several choices of preconditioners applied to the system of discrete equations, we derive upper bounds on perturbations of eigenvalues as functions of the viscosity and discretization mesh size. The bounds suggest that the sensitivity of the eigenvalues is at worst linear in the inverse of the viscosity and quadratic in the inverse of the mesh size, and that scaling can be used to decrease the sensitivity in some cases. Experimental results supplement these results and confirm the relatively mild dependence on viscosity. They also indicate a dependence on the mesh size of magnitude smaller than the analysis suggests.

  11. Statistics of Smoothed Cosmic Fields in Perturbation Theory. I. Formulation and Useful Formulae in Second-Order Perturbation Theory

    Science.gov (United States)

    Matsubara, Takahiko

    2003-02-01

    We formulate a general method for perturbative evaluations of statistics of smoothed cosmic fields and provide useful formulae for application of the perturbation theory to various statistics. This formalism is an extensive generalization of the method used by Matsubara, who derived a weakly nonlinear formula of the genus statistic in a three-dimensional density field. After describing the general method, we apply the formalism to a series of statistics, including genus statistics, level-crossing statistics, Minkowski functionals, and a density extrema statistic, regardless of the dimensions in which each statistic is defined. The relation between the Minkowski functionals and other geometrical statistics is clarified. These statistics can be applied to several cosmic fields, including three-dimensional density field, three-dimensional velocity field, two-dimensional projected density field, and so forth. The results are detailed for second-order theory of the formalism. The effect of the bias is discussed. The statistics of smoothed cosmic fields as functions of rescaled threshold by volume fraction are discussed in the framework of second-order perturbation theory. In CDM-like models, their functional deviations from linear predictions plotted against the rescaled threshold are generally much smaller than that plotted against the direct threshold. There is still a slight meatball shift against rescaled threshold, which is characterized by asymmetry in depths of troughs in the genus curve. A theory-motivated asymmetry factor in the genus curve is proposed.

  12. Time-Sliced Perturbation Theory for Large Scale Structure I: General Formalism

    CERN Document Server

    Blas, Diego; Ivanov, Mikhail M.; Sibiryakov, Sergey

    2016-01-01

    We present a new analytic approach to describe large scale structure formation in the mildly non-linear regime. The central object of the method is the time-dependent probability distribution function generating correlators of the cosmological observables at a given moment of time. Expanding the distribution function around the Gaussian weight we formulate a perturbative technique to calculate non-linear corrections to cosmological correlators, similar to the diagrammatic expansion in a three-dimensional Euclidean quantum field theory, with time playing the role of an external parameter. For the physically relevant case of cold dark matter in an Einstein--de Sitter universe, the time evolution of the distribution function can be found exactly and is encapsulated by a time-dependent coupling constant controlling the perturbative expansion. We show that all building blocks of the expansion are free from spurious infrared enhanced contributions that plague the standard cosmological perturbation theory. This pave...

  13. Evolution of weak perturbations in gas-solid suspension with chemical reaction

    Energy Technology Data Exchange (ETDEWEB)

    Sharypov, O.V. [Russian Academy of Sciences, Novosibirsk (Russian Federation). Inst. of Thermophysics; Novosibirsk State Univ. (Russian Federation); Anufriev, I.S. [Novosibirsk State Univ. (Russian Federation)

    2013-07-01

    Dynamics of weak finite-amplitude perturbations in two-phase homogeneous medium (gas + solid particles) with non-equilibrium chemical reaction in gas is studied theoretically. Non-linear model of plane perturbation evolution is substantiated. The model takes into account wave-kinetic interaction and dissipation effects, including inter-phase heat and momentum transfer. Conditions for uniform state of the system are analyzed. Non-linear equation describing evolution of plane perturbation is derived under weak dispersion and dissipation effects. The obtained results demonstrate self-organization in the homogeneous system: steady-state periodic structure arises, its period, amplitude and velocity depends on the features of the medium. The dependencies of these parameters on dissipation and chemical kinetics are analyzed.

  14. Dynamics of bound vector solitons induced by stochastic perturbations: Soliton breakup and soliton switching

    International Nuclear Information System (INIS)

    Sun, Zhi-Yuan; Gao, Yi-Tian; Yu, Xin; Liu, Ying

    2013-01-01

    We respectively investigate breakup and switching of the Manakov-typed bound vector solitons (BVSs) induced by two types of stochastic perturbations: the homogenous and nonhomogenous. Symmetry-recovering is discovered for the asymmetrical homogenous case, while soliton switching is found to relate with the perturbation amplitude and soliton coherence. Simulations show that soliton switching in the circularly-polarized light system is much weaker than that in the Manakov and linearly-polarized systems. In addition, the homogenous perturbations can enhance the soliton switching in both of the Manakov and non-integrable (linearly- and circularly-polarized) systems. Our results might be helpful in interpreting dynamics of the BVSs with stochastic noises in nonlinear optics or with stochastic quantum fluctuations in Bose–Einstein condensates.

  15. Strings as perturbations of evolving spin networks

    International Nuclear Information System (INIS)

    Smolin, Lee

    2000-01-01

    One step in the construction of a background independent formulation of string theory is detailed, in which it is shown how perturbative strings may arise as small fluctuations around histories in a formulation of non-perturbative dynamics of spin networks due to Markopoulou. In this formulation the dynamics of spin network states and their generalizations is described in terms of histories which have discrete analogues of the causal structure and many fingered time of Lorentzian spacetimes. Perturbations of these histories turn out to be described in terms of spin systems defined on 2-dimensional timelike surfaces embedded in the discrete spacetime. When the history has a classical limit which is Minkowski spacetime, the action of the perturbation theory is given to leading order by the spacetime area of the surface, as in bosonic string theory. This map between a non-perturbative formulation of quantum gravity and a 1+1 dimensional theory generalizes to a large class of theories in which the group SU(2) i s extended to any quantum group or supergroup. It is argued that a necessary condition for the non-perturbative theory to have a good classical limit is that the resulting 1+1 dimensional theory defines a consistent and stable perturbative string theory

  16. Application of the perturbation theory for sensitivity calculations in thermalhydraulics reactor calculations

    International Nuclear Information System (INIS)

    Andrade Lima, F.R. de

    1986-01-01

    The sensitivity of non linear responses associated with physical quantities governed by non linear differential systems can be studied using perturbation theory. The equivalence and formal differences between the differential and GPT formalisms are shown and both are used for sensitivity calculations of transient problems in a typical PWR coolant channel. The results obtained are encouraging with respect to the potential of the method for thermalhydraulics calculations normally performed for reactor design and safety analysis. (Author) [pt

  17. Comparison between the Variational Iteration Method and the Homotopy Perturbation Method for the Sturm-Liouville Differential Equation

    Directory of Open Access Journals (Sweden)

    R. Darzi

    2010-01-01

    Full Text Available We applied the variational iteration method and the homotopy perturbation method to solve Sturm-Liouville eigenvalue and boundary value problems. The main advantage of these methods is the flexibility to give approximate and exact solutions to both linear and nonlinear problems without linearization or discretization. The results show that both methods are simple and effective.

  18. Comparison between the Variational Iteration Method and the Homotopy Perturbation Method for the Sturm-Liouville Differential Equation

    OpenAIRE

    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.

  19. Enforcing conservation laws in nonequilibrium cluster perturbation theory

    Science.gov (United States)

    Gramsch, Christian; Potthoff, Michael

    2017-05-01

    Using the recently introduced time-local formulation of the nonequilibrium cluster perturbation theory (CPT), we construct a generalization of the approach such that macroscopic conservation laws are respected. This is achieved by exploiting the freedom for the choice of the starting point of the all-order perturbation theory in the intercluster hopping. The proposed conserving CPT is a self-consistent propagation scheme which respects the conservation of energy, particle number, and spin, which treats short-range correlations exactly up to the linear scale of the cluster, and which represents a mean-field-like approach on length scales beyond the cluster size. Using Green's functions, conservation laws are formulated as local constraints on the local spin-dependent particle and the doublon density. We consider them as conditional equations to self-consistently fix the time-dependent intracluster one-particle parameters. Thanks to the intrinsic causality of the CPT, this can be set up as a step-by-step time propagation scheme with a computational effort scaling linearly with the maximum propagation time and exponentially in the cluster size. As a proof of concept, we consider the dynamics of the two-dimensional, particle-hole-symmetric Hubbard model following a weak interaction quench by simply employing two-site clusters only. Conservation laws are satisfied by construction. We demonstrate that enforcing them has strong impact on the dynamics. While the doublon density is strongly oscillating within plain CPT, a monotonic relaxation is observed within the conserving CPT.

  20. Kerr-CFT and gravitational perturbations

    International Nuclear Information System (INIS)

    Dias, Oscar J.C.; Reall, Harvey S.; Santos, Jorge E.

    2009-01-01

    Motivated by the Kerr-CFT conjecture, we investigate perturbations of the near-horizon extreme Kerr spacetime. The Teukolsky equation for a massless field of arbitrary spin is solved. Solutions fall into two classes: normal modes and traveling waves. Imposing suitable (outgoing) boundary conditions, we find that there are no unstable modes. The explicit form of metric perturbations is obtained using the Hertz potential formalism, and compared with the Kerr-CFT boundary conditions. The energy and angular momentum associated with scalar field and gravitational normal modes are calculated. The energy is positive in all cases. The behaviour of second order perturbations is discussed.

  1. Resolution of ambiguities in perturbative QCD

    International Nuclear Information System (INIS)

    Nakkagawa, Hisao; Niegawa, Akira.

    1984-01-01

    In the perturbative QCD analyses of the deeply inelastic processes, the coupling constant depends on at least two mass-scales, the renormalization scale and the factorization scale. By integrating the coupled renormalization group equations with respect to these two mass-scales, the running coupling constant is defined. A perturbative approximation then introduces a new ambiguity, the integration-path dependence, into the theory. We show that the problem of this new ambiguity is resolved by imposing Stevenson's principle of minimal sensitivity. Together with the analogous analysis of the operator matrix element or the cut vertex, we can completely solve the problem of getting an unambiguous perturbative QCD prediction. (author)

  2. Mass generation in perturbed massless integrable models

    International Nuclear Information System (INIS)

    Controzzi, D.; Mussardo, G.

    2005-01-01

    We extend form-factor perturbation theory to non-integrable deformations of massless integrable models, in order to address the problem of mass generation in such systems. With respect to the standard renormalisation group analysis this approach is more suitable for studying the particle content of the perturbed theory. Analogously to the massive case, interesting information can be obtained already at first order, such as the identification of the operators which create a mass gap and those which induce the confinement of the massless particles in the perturbed theory

  3. Non-perturbative effects in supersymmetry

    International Nuclear Information System (INIS)

    Veneziano, G.

    1987-01-01

    Some non perturbative aspects of globally supersymmetric (SUSY) gauge theories are discussed. These share with their non-supersymmetric analogues interesting non perturbative features, such as the spontaneous breaking of chiral symmetries via condensates. What is peculiar about supersymmetric theories, however, is that one is able to say a lot about non-perturbative effects even without resorting to elaborate numerical calculations: general arguments, supersymmetric and chiral Ward identities and analytic, dynamical calculations will turn out to effectively determine most of the supersymmetric vacuum properties. 28 references, 5 figures

  4. On perturbation theory for distance dependent statistics.

    Energy Technology Data Exchange (ETDEWEB)

    Mashkevich, S V

    1994-12-31

    It is known that perturbation theory for anyons has to be modified near Bose statistics in order to get correct finite results. For ``distance dependent statistics`` or anyons with smeared flux tubes, perturbation theory is in principle applicable directly but gives results which hold for too small values of the statistical parameter and, in particular, are not valid as the flux tube radius tends to zero. In this paper we discuss the way to modify perturbation theory for this situation, which allows to obtain the appropriate results. (author). 6 refs.

  5. Solitonic Integrable Perturbations of Parafermionic Theories

    CERN Document Server

    Fernández-Pousa, C R; Hollowood, Timothy J; Miramontes, J L

    1997-01-01

    The quantum integrability of a class of massive perturbations of the parafermionic conformal field theories associated to compact Lie groups is established by showing that they have quantum conserved densities of scale dimension 2 and 3. These theories are integrable for any value of a continuous vector coupling constant, and they generalize the perturbation of the minimal parafermionic models by their first thermal operator. The classical equations-of-motion of these perturbed theories are the non-abelian affine Toda equations which admit (charged) soliton solutions whose semi-classical quantization is expected to permit the identification of the exact S-matrix of the theory.

  6. Critical behaviors of gravity under quantum perturbations

    Directory of Open Access Journals (Sweden)

    ZHANG Hongsheng

    2014-02-01

    Full Text Available Phase transition and critical phenomenon is a very interesting topic in thermodynamics and statistical mechanics. Gravity is believed to have deep and inherent relation to thermodynamics. Near the critical point,the perturbation becomes significant. Thus for ordinary matter (governed by interactions besides gravity the critical behavior will become very different if we ignore the perturbations around the critical point,such as mean field theory. We find that the critical exponents for RN-AdS spacetime keep the same values even when we consider the full quantum perturbations. This indicates a key difference between gravity and ordinary thermodynamic system.

  7. B-spline solution of a singularly perturbed boundary value problem arising in biology

    International Nuclear Information System (INIS)

    Lin Bin; Li Kaitai; Cheng Zhengxing

    2009-01-01

    We use B-spline functions to develop a numerical method for solving a singularly perturbed boundary value problem associated with biology science. We use B-spline collocation method, which leads to a tridiagonal linear system. The accuracy of the proposed method is demonstrated by test problems. The numerical result is found in good agreement with exact solution.

  8. Determination of low-energy constants of Wilson chiral perturbation theory

    International Nuclear Information System (INIS)

    Herdoiza, Gregorio; Univ. Autonoma de Madrid, Contoblanco; Univ. Autonoma de Madrid; Jansen, Karl; Univ. Cyprus, Nicosia; Michael, Chris; Ottnad, Konstantin; Urbach, Carsten; Univ. Bonn

    2013-03-01

    By matching Wilson twisted mass lattice QCD determinations of pseudoscalar meson masses to Wilson Chiral Perturbation Theory we determine the low-energy constants W 6 ' , W 8 ' and their linear combination c 2 . We explore the dependence of these low-energy constants on the choice of the lattice action and on the number of dynamical flavours.

  9. Introduction to linear systems of differential equations

    CERN Document Server

    Adrianova, L Ya

    1995-01-01

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

  10. 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

  11. Inflation and the theory of cosmological perturbations

    International Nuclear Information System (INIS)

    Riotto, A.

    2003-01-01

    These lectures provide a pedagogical introduction to inflation and the theory of cosmological perturbations generated during inflation which are thought to be the origin of structure in the universe. (author)

  12. 't Hooft loops and perturbation theory

    CERN Document Server

    De Forcrand, Philippe; Noth, D; Forcrand, Philippe de; Lucini, Biagio; Noth, David

    2005-01-01

    We show that high-temperature perturbation theory describes extremely well the area law of SU(N) spatial 't Hooft loops, or equivalently the tension of the interface between different Z_N vacua in the deconfined phase. For SU(2), the disagreement between Monte Carlo data and lattice perturbation theory for sigma(T)/T^2 is less than 2%, down to temperatures O(10) T_c. For SU(N), N>3, the ratios of interface tensions, (sigma_k/sigma_1)(T), agree with perturbation theory, which predicts tiny deviations from the ratio of Casimirs, down to nearly T_c. In contrast, individual tensions differ markedly from the perturbative expression. In all cases, the required precision Monte Carlo measurements are made possible by a simple but powerful modification of the 'snake' algorithm.

  13. Isocurvature perturbations in the Ekpyrotic Universe

    International Nuclear Information System (INIS)

    Notari, A.; Riotto, A.

    2002-01-01

    The Ekpyrotic scenario assumes that our visible Universe is a boundary brane in a five-dimensional bulk and that the hot Big Bang occurs when a nearly supersymmetric five-brane travelling along the fifth dimension collides with our visible brane. We show that the generation of isocurvature perturbations is a generic prediction of the Ekpyrotic Universe. This is due to the interactions in the kinetic terms between the brane modulus parameterizing the position of the five-brane in the bulk and the dilaton and volume moduli. We show how to separate explicitly the adiabatic and isocurvature modes by performing a rotation in field space. Our results indicate that adiabatic and isocurvature perturbations might be cross-correlated and that curvature perturbations might be entirely seeded by isocurvature perturbations

  14. Simple Perturbation Example for Quantum Chemistry.

    Science.gov (United States)

    Goodfriend, P. L.

    1985-01-01

    Presents a simple example that illustrates various aspects of the Rayleigh-Schrodinger perturbation theory. The example is a particularly good one because it is straightforward and can be compared with both the exact solution and with experimental data. (JN)

  15. SHARP ENTRYWISE PERTURBATION BOUNDS FOR MARKOV CHAINS.

    Science.gov (United States)

    Thiede, Erik; VAN Koten, Brian; Weare, Jonathan

    For many Markov chains of practical interest, the invariant distribution is extremely sensitive to perturbations of some entries of the transition matrix, but insensitive to others; we give an example of such a chain, motivated by a problem in computational statistical physics. We have derived perturbation bounds on the relative error of the invariant distribution that reveal these variations in sensitivity. Our bounds are sharp, we do not impose any structural assumptions on the transition matrix or on the perturbation, and computing the bounds has the same complexity as computing the invariant distribution or computing other bounds in the literature. Moreover, our bounds have a simple interpretation in terms of hitting times, which can be used to draw intuitive but rigorous conclusions about the sensitivity of a chain to various types of perturbations.

  16. Renormalization scheme-invariant perturbation theory

    International Nuclear Information System (INIS)

    Dhar, A.

    1983-01-01

    A complete solution to the problem of the renormalization scheme dependence of perturbative approximants to physical quantities is presented. An equation is derived which determines any physical quantity implicitly as a function of only scheme independent variables. (orig.)

  17. Cosmological perturbations in the new Higgs inflation

    Energy Technology Data Exchange (ETDEWEB)

    Germani, Cristiano [Arnold Sommerfeld Center, Ludwig-Maximilians-University, Theresienstr, 37 80333 Muenchen (Germany); Kehagias, Alex, E-mail: cristiano.germani@lmu.de, E-mail: kehagias@central.ntua.gr [Physics Division, National Technical University of Athens, 15780 Zografou Campus, Athens (Greece)

    2010-05-01

    We study the cosmological perturbations created during the New Higgs inflationary phase. In the New Higgs Inflation, the Higgs boson is kinetically coupled to the Einstein tensor and only three perturbative degrees of freedom, a scalar and two tensorial (gravitational waves), propagate during Inflation. Scalar perturbations are found to match the latest WMAP-7yrs data within Standard Model Higgs parameters. Primordial gravitational waves also, although propagating with superluminal speed, are consistent with present data. Finally, we estimate the values of the parameter of the New Higgs Inflation in relation to the Higgs mass, the spectral index and amplitude of the primordial scalar perturbations showing that the unitarity bound of the theory is not violated.

  18. Prospects of inflation with perturbed throat geometry

    International Nuclear Information System (INIS)

    Ali, Amna; Chingangbam, R.; Panda, Sudhakar; Sami, M.

    2009-01-01

    We study brane inflation in a warped deformed conifold background that includes general possible corrections to the throat geometry sourced by coupling to the bulk of a compact Calabi-Yau space. We focus specifically, on the perturbation by chiral operator of dimension 3/2 in the CFT. We find that the effective potential in this case can give rise to required number of e-foldings and the spectral index n S consistent with observation. The tensor to scalar ratio of perturbations is generally very low in this scenario. The COBE normalization, however, poses certain difficulties which can be circumvented provided model parameters are properly fine tuned. We find the numerical values of parameters which can give rise to enough inflation, observationally consistent values of density perturbations, scalar to tensor ratio of perturbations and the spectral index n S .

  19. Linearization instability for generic gravity in AdS spacetime

    Science.gov (United States)

    Altas, Emel; Tekin, Bayram

    2018-01-01

    In general relativity, perturbation theory about a background solution fails if the background spacetime has a Killing symmetry and a compact spacelike Cauchy surface. This failure, dubbed as linearization instability, shows itself as non-integrability of the perturbative infinitesimal deformation to a finite deformation of the background. Namely, the linearized field equations have spurious solutions which cannot be obtained from the linearization of exact solutions. In practice, one can show the failure of the linear perturbation theory by showing that a certain quadratic (integral) constraint on the linearized solutions is not satisfied. For non-compact Cauchy surfaces, the situation is different and for example, Minkowski space having a non-compact Cauchy surface, is linearization stable. Here we study, the linearization instability in generic metric theories of gravity where Einstein's theory is modified with additional curvature terms. We show that, unlike the case of general relativity, for modified theories even in the non-compact Cauchy surface cases, there are some theories which show linearization instability about their anti-de Sitter backgrounds. Recent D dimensional critical and three dimensional chiral gravity theories are two such examples. This observation sheds light on the paradoxical behavior of vanishing conserved charges (mass, angular momenta) for non-vacuum solutions, such as black holes, in these theories.

  20. 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

  1. 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)

  2. A new perturbative approach to QCD

    International Nuclear Information System (INIS)

    Pervushin, V.N.; Kallies, W.; Sarikov, N.A.

    1988-01-01

    For the description of bound states in QED and QCD the physical perturbation theory on the spatial components of the vector over the exact solution, defined by the time one, is proposed. It is shown this perturbation theory in QCD can be redefined so that it reproduces the main elements of hadron physics: confinement, spectroscopy of light and heavy quarkonia, dual-resonance amplitudes, chiral Lagrangians and the parton model

  3. 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

  4. 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

  5. Double soft theorem for perturbative gravity

    OpenAIRE

    Saha, Arnab

    2016-01-01

    Following up on the recent work of Cachazo, He and Yuan \\cite{arXiv:1503.04816 [hep-th]}, we derive the double soft graviton theorem in perturbative gravity. We show that the double soft theorem derived using CHY formula precisely matches with the perturbative computation involving Feynman diagrams. In particular, we find how certain delicate limits of Feynman diagrams play an important role in obtaining this equivalence.

  6. On perturbations of a quintom bounce

    International Nuclear Information System (INIS)

    Cai Yifu; Qiu Taotao; Zhang Xinmin; Brandenberger, Robert; Piao Yunsong

    2008-01-01

    A quintom universe with an equation of state crossing the cosmological constant boundary can provide a bouncing solution dubbed the quintom bounce and thus resolve the big bang singularity. In this paper, we investigate the cosmological perturbations of the quintom bounce both analytically and numerically. We find that the fluctuations in the dominant mode in the post-bounce expanding phase couple to the growing mode of the perturbations in the pre-bounce contracting phase

  7. Computer fan performance enhancement via acoustic perturbations

    Energy Technology Data Exchange (ETDEWEB)

    Greenblatt, David, E-mail: davidg@technion.ac.il [Faculty of Mechanical Engineering, Technion - Israel Institute of Technology, Haifa (Israel); Avraham, Tzahi; Golan, Maayan [Faculty of Mechanical Engineering, Technion - Israel Institute of Technology, Haifa (Israel)

    2012-04-15

    Highlights: Black-Right-Pointing-Pointer Computer fan effectiveness was increased by introducing acoustic perturbations. Black-Right-Pointing-Pointer Acoustic perturbations controlled blade boundary layer separation. Black-Right-Pointing-Pointer Optimum frequencies corresponded with airfoils studies. Black-Right-Pointing-Pointer Exploitation of flow instabilities was responsible for performance improvements. Black-Right-Pointing-Pointer Peak pressure and peak flowrate were increased by 40% and 15% respectively. - Abstract: A novel technique for increasing computer fan effectiveness, based on introducing acoustic perturbations onto the fan blades to control boundary layer separation, was assessed. Experiments were conducted in a specially designed facility that simultaneously allowed characterization of fan performance and introduction of the perturbations. A parametric study was conducted to determine the optimum control parameters, namely those that deliver the largest increase in fan pressure for a given flowrate. The optimum reduced frequencies corresponded with those identified on stationary airfoils and it was thus concluded that the exploitation of Kelvin-Helmholtz instabilities, commonly observed on airfoils, was responsible for the fan blade performance improvements. The optimum control inputs, such as acoustic frequency and sound pressure level, showed some variation with different fan flowrates. With the near-optimum control conditions identified, the full operational envelope of the fan, when subjected to acoustic perturbations, was assessed. The peak pressure and peak flowrate were increased by up to 40% and 15% respectively. The peak fan efficiency increased with acoustic perturbations but the overall system efficiency was reduced when the speaker input power was accounted for.

  8. Secondary isocurvature perturbations from acoustic reheating

    Science.gov (United States)

    Ota, Atsuhisa; Yamaguchi, Masahide

    2018-06-01

    The superhorizon (iso)curvature perturbations are conserved if the following conditions are satisfied: (i) (each) non adiabatic pressure perturbation is zero, (ii) the gradient terms are ignored, that is, at the leading order of the gradient expansion (iii) (each) total energy momentum tensor is conserved. We consider the case with the violation of the last two requirements and discuss the generation of secondary isocurvature perturbations during the late time universe. Second order gradient terms are not necessarily ignored even if we are interested in the long wavelength modes because of the convolutions which may pick products of short wavelength perturbations up. We then introduce second order conserved quantities on superhorizon scales under the conditions (i) and (iii) even in the presence of the gradient terms by employing the full second order cosmological perturbation theory. We also discuss the violation of the condition (iii), that is, the energy momentum tensor is conserved for the total system but not for each component fluid. As an example, we explicitly evaluate second order heat conduction between baryons and photons due to the weak Compton scattering, which dominates during the period just before recombination. We show that such secondary effects can be recast into the isocurvature perturbations on superhorizon scales if the local type primordial non Gaussianity exists a priori.

  9. Computer fan performance enhancement via acoustic perturbations

    International Nuclear Information System (INIS)

    Greenblatt, David; Avraham, Tzahi; Golan, Maayan

    2012-01-01

    Highlights: ► Computer fan effectiveness was increased by introducing acoustic perturbations. ► Acoustic perturbations controlled blade boundary layer separation. ► Optimum frequencies corresponded with airfoils studies. ► Exploitation of flow instabilities was responsible for performance improvements. ► Peak pressure and peak flowrate were increased by 40% and 15% respectively. - Abstract: A novel technique for increasing computer fan effectiveness, based on introducing acoustic perturbations onto the fan blades to control boundary layer separation, was assessed. Experiments were conducted in a specially designed facility that simultaneously allowed characterization of fan performance and introduction of the perturbations. A parametric study was conducted to determine the optimum control parameters, namely those that deliver the largest increase in fan pressure for a given flowrate. The optimum reduced frequencies corresponded with those identified on stationary airfoils and it was thus concluded that the exploitation of Kelvin–Helmholtz instabilities, commonly observed on airfoils, was responsible for the fan blade performance improvements. The optimum control inputs, such as acoustic frequency and sound pressure level, showed some variation with different fan flowrates. With the near-optimum control conditions identified, the full operational envelope of the fan, when subjected to acoustic perturbations, was assessed. The peak pressure and peak flowrate were increased by up to 40% and 15% respectively. The peak fan efficiency increased with acoustic perturbations but the overall system efficiency was reduced when the speaker input power was accounted for.

  10. 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

  11. Influence of asymmetric magnetic perturbation on the nonlinear evolution of double tearing modes

    Science.gov (United States)

    Xiong, G. Z.; Wang, L.; Li, X. Q.; Liu, H. F.; Tang, C. J.; Huang, J.; Zhang, X.; Wang, X. Q.

    2017-06-01

    The effects of asymmetric magnetic perturbation on the triggering and evolution of double tearing modes (DTMs) are investigated using nonlinear magnetohydrodynamics simulations in a slab geometry. We find that for reversed magnetic shear plasmas the resistive reconnection process induced by the initial perturbation at one rational surface can drive a new island at the other rational surface with the same mode number. The four typical states of the mode for the time evolution are found, and include: (i) a linear growth stage; (ii) a linear/nonlinear stable stage; (iii) an interactively driving stage; and (iv) a symmetric DTM stage. These differ from previous simulation results. Moreover, nonlinear DTM growth is found to strongly depend on the asymmetric magnetic perturbation, particularly in the early nonlinear phase. The initial perturbation strength scale of island width suggests that the left island enters into a Sweet-Parker growth process when the right island is sufficiently large to effectively drive the other. These results predict that although externally applied magnetic perturbations can suppress the neoclassical tearing mode they can also trigger new instabilities such as asymmetric DTMs.

  12. Influence of asymmetric magnetic perturbation on the nonlinear evolution of double tearing modes

    International Nuclear Information System (INIS)

    Xiong, G Z; Liu, H F; Huang, J; Wang, X Q; Wang, L; Li, X Q; Tang, C J; Zhang, X

    2017-01-01

    The effects of asymmetric magnetic perturbation on the triggering and evolution of double tearing modes (DTMs) are investigated using nonlinear magnetohydrodynamics simulations in a slab geometry. We find that for reversed magnetic shear plasmas the resistive reconnection process induced by the initial perturbation at one rational surface can drive a new island at the other rational surface with the same mode number. The four typical states of the mode for the time evolution are found, and include: (i) a linear growth stage; (ii) a linear/nonlinear stable stage; (iii) an interactively driving stage; and (iv) a symmetric DTM stage. These differ from previous simulation results. Moreover, nonlinear DTM growth is found to strongly depend on the asymmetric magnetic perturbation, particularly in the early nonlinear phase. The initial perturbation strength scale of island width suggests that the left island enters into a Sweet–Parker growth process when the right island is sufficiently large to effectively drive the other. These results predict that although externally applied magnetic perturbations can suppress the neoclassical tearing mode they can also trigger new instabilities such as asymmetric DTMs. (paper)

  13. Application of linearized model to the stability analysis of the pressurized water reactor

    International Nuclear Information System (INIS)

    Li Haipeng; Huang Xiaojin; Zhang Liangju

    2008-01-01

    A Linear Time-Invariant model of the Pressurized Water Reactor is formulated through the linearization of the nonlinear model. The model simulation results show that the linearized model agrees well with the nonlinear model under small perturbation. Based upon the Lyapunov's First Method, the linearized model is applied to the stability analysis of the Pressurized Water Reactor. The calculation results show that the methodology of linearization to stability analysis is conveniently feasible. (authors)

  14. PerturbationAnalyzer: a tool for investigating the effects of concentration perturbation on protein interaction networks.

    Science.gov (United States)

    Li, Fei; Li, Peng; Xu, Wenjian; Peng, Yuxing; Bo, Xiaochen; Wang, Shengqi

    2010-01-15

    The propagation of perturbations in protein concentration through a protein interaction network (PIN) can shed light on network dynamics and function. In order to facilitate this type of study, PerturbationAnalyzer, which is an open source plugin for Cytoscape, has been developed. PerturbationAnalyzer can be used in manual mode for simulating user-defined perturbations, as well as in batch mode for evaluating network robustness and identifying significant proteins that cause large propagation effects in the PINs when their concentrations are perturbed. Results from PerturbationAnalyzer can be represented in an intuitive and customizable way and can also be exported for further exploration. PerturbationAnalyzer has great potential in mining the design principles of protein networks, and may be a useful tool for identifying drug targets. PerturbationAnalyzer can be accessed from the Cytoscape web site http://www.cytoscape.org/plugins/index.php or http://biotech.bmi.ac.cn/PerturbationAnalyzer. Supplementary data are available at Bioinformatics online.

  15. Linearly constrained minimax optimization

    DEFF Research Database (Denmark)

    Madsen, Kaj; Schjær-Jacobsen, Hans

    1978-01-01

    We present an algorithm for nonlinear minimax optimization subject to linear equality and inequality constraints which requires first order partial derivatives. The algorithm is based on successive linear approximations to the functions defining the problem. The resulting linear subproblems...

  16. Understanding the unsteady aerodynamics of a revolving wing with pitching-flapping perturbations

    Science.gov (United States)

    Chen, Long; Wu, Jianghao; Zhou, Chao; Hsu, Shih-Jung; Eslam Panah, Azar; Cheng, Bo

    2017-11-01

    Revolving wings become less efficient for lift generation at low Reynolds numbers. Unlike flying insects using reciprocating revolving wings to exploit unsteady mechanisms for lift enhancement, an alternative that introduces unsteadiness through vertical flapping perturbation, is studied via experiments and simulations. Substantial drag reduction, linearly dependent on Strouhal number, is observed for a flapping-perturbed revolving wing at zero angle of attack (AoA), which can be explained by changes in the effective angle of attack and formation of reverse Karman vortex streets. When the AoA increases, flapping perturbations improve the maximum lift coefficient attainable by the revolving wing, with minor increases of drag or even minor drag reductions depending on Strouhal number and normalized flapping amplitude. When the pitching perturbations are further introduced, more substantial drag reduction and lift enhancement can be achieved in zero and positive AoAs, respectively. As the flapping-perturbed wings are less efficient compared with revolving wings in terms of power loading, the pitching-flapping perturbations can achieve a higher power loading at 20°AoA and thus have potential applications in micro air vehicle designs. This research was supported by NSF, DURIP, NSFC and Penn State Multi-Campus SEED Grant.

  17. 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.

  18. Acoustic anisotropic wavefields through perturbation theory

    KAUST Repository

    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.

  19. Foundations of linear and generalized linear models

    CERN Document Server

    Agresti, Alan

    2015-01-01

    A valuable overview of the most important ideas and results in statistical analysis Written by a highly-experienced author, Foundations of Linear and Generalized Linear Models is a clear and comprehensive guide to the key concepts and results of linear statistical models. The book presents a broad, in-depth overview of the most commonly used statistical models by discussing the theory underlying the models, R software applications, and examples with crafted models to elucidate key ideas and promote practical model building. The book begins by illustrating the fundamentals of linear models,

  20. Parametric perturbations and suppression of chaos in n-dimensional maps

    International Nuclear Information System (INIS)

    Loskutov, A.Y.; Rybalko, S.D.

    1994-11-01

    The problem of a qualitative change in dynamics of n-dimensional chaotic maps under the influence of parametric perturbations is considered. We prove that for certain maps, - the quadratic maps family, a piece wise linear maps family, and a two-dimensional map having a hyberbolic attractor, - there are perturbations which lead to suppression of chaos. Arguments that for such maps the set of parameter values corresponding to the ordered behaviour has the positive Lebesgue measure, are given. (author). 36 refs, 12 figs

  1. Evolution of perturbed dynamical systems: analytical computation with time independent accuracy

    Energy Technology Data Exchange (ETDEWEB)

    Gurzadyan, A.V. [Russian-Armenian (Slavonic) University, Department of Mathematics and Mathematical Modelling, Yerevan (Armenia); Kocharyan, A.A. [Monash University, School of Physics and Astronomy, Clayton (Australia)

    2016-12-15

    An analytical method for investigation of the evolution of dynamical systems with independent on time accuracy is developed for perturbed Hamiltonian systems. The error-free estimation using of computer algebra enables the application of the method to complex multi-dimensional Hamiltonian and dissipative systems. It also opens principal opportunities for the qualitative study of chaotic trajectories. The performance of the method is demonstrated on perturbed two-oscillator systems. It can be applied to various non-linear physical and astrophysical systems, e.g. to long-term planetary dynamics. (orig.)

  2. Application of the perturbation iteration method to boundary layer type problems.

    Science.gov (United States)

    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.

  3. The non-linear evolution of edge localized modes

    International Nuclear Information System (INIS)

    Wenninger, Ronald

    2013-01-01

    Edge localized modes (ELMs) are instabilities in the edge of tokamak plasmas in the high confinement regime (H-mode). Without them the edge transport in ordinary H-mode plasmas is too low to establish a stationary situation. However in a future device large unmitigated ELMs are believed to cause divertor power flux densities far in excess of tolerable material limits. Hence the size of energy loss per ELM and the resulting ELM frequency must be controlled. To proceed in understanding how the ELM size is determined and how ELM mitigation methods work it is necessary to characterize the non-linear evolution of pedestal erosion. In order to achieve this experimental data is compared to the results of ELM simulations with the code JOREK (reduced MHD, non-linear) applying a specially developed synthetic magnetic diagnostic. The experimental data are acquired by several fast sampling diagnostics at the experiments ASDEX Upgrade and TCV at a large number of toroidal/poloidal positions. A central element of the presented work is the detailed characterization of dominant magnetic perturbations during ELMs. These footprints of the instability can be observed most intensely in close temporal vicinity to the onset of pedestal erosion. Dominant magnetic perturbations are caused by current perturbations located at or inside the last closed flux surface. In ASDEX Upgrade under certain conditions dominant magnetic perturbations like other H-mode edge instabilities display a similarity to solitons. Furthermore - as expected - they are often observed to be correlated to a perturbation of electron temperature. In TCV it is possible to characterize the evolution of the toroidal structure of dominant magnetic perturbations. Between growing above the level of background fluctuations and the maximum perturbation level for all time instance a similar toroidal structure is observed. This rigid mode-structure is an indication for non-linear coupling. Most frequently the dominant toroidal

  4. The non-linear evolution of edge localized modes

    Energy Technology Data Exchange (ETDEWEB)

    Wenninger, Ronald

    2013-01-09

    Edge localized modes (ELMs) are instabilities in the edge of tokamak plasmas in the high confinement regime (H-mode). Without them the edge transport in ordinary H-mode plasmas is too low to establish a stationary situation. However in a future device large unmitigated ELMs are believed to cause divertor power flux densities far in excess of tolerable material limits. Hence the size of energy loss per ELM and the resulting ELM frequency must be controlled. To proceed in understanding how the ELM size is determined and how ELM mitigation methods work it is necessary to characterize the non-linear evolution of pedestal erosion. In order to achieve this experimental data is compared to the results of ELM simulations with the code JOREK (reduced MHD, non-linear) applying a specially developed synthetic magnetic diagnostic. The experimental data are acquired by several fast sampling diagnostics at the experiments ASDEX Upgrade and TCV at a large number of toroidal/poloidal positions. A central element of the presented work is the detailed characterization of dominant magnetic perturbations during ELMs. These footprints of the instability can be observed most intensely in close temporal vicinity to the onset of pedestal erosion. Dominant magnetic perturbations are caused by current perturbations located at or inside the last closed flux surface. In ASDEX Upgrade under certain conditions dominant magnetic perturbations like other H-mode edge instabilities display a similarity to solitons. Furthermore - as expected - they are often observed to be correlated to a perturbation of electron temperature. In TCV it is possible to characterize the evolution of the toroidal structure of dominant magnetic perturbations. Between growing above the level of background fluctuations and the maximum perturbation level for all time instance a similar toroidal structure is observed. This rigid mode-structure is an indication for non-linear coupling. Most frequently the dominant toroidal

  5. Local perturbations perturb—exponentially–locally

    International Nuclear Information System (INIS)

    De Roeck, W.; Schütz, M.

    2015-01-01

    We elaborate on the principle that for gapped quantum spin systems with local interaction, “local perturbations [in the Hamiltonian] perturb locally [the groundstate].” This principle was established by Bachmann et al. [Commun. Math. Phys. 309, 835–871 (2012)], relying on the “spectral flow technique” or “quasi-adiabatic continuation” [M. B. Hastings, Phys. Rev. B 69, 104431 (2004)] to obtain locality estimates with sub-exponential decay in the distance to the spatial support of the perturbation. We use ideas of Hamza et al. [J. Math. Phys. 50, 095213 (2009)] to obtain similarly a transformation between gapped eigenvectors and their perturbations that is local with exponential decay. This allows to improve locality bounds on the effect of perturbations on the low lying states in certain gapped models with a unique “bulk ground state” or “topological quantum order.” We also give some estimate on the exponential decay of correlations in models with impurities where some relevant correlations decay faster than one would naively infer from the global gap of the system, as one also expects in disordered systems with a localized groundstate

  6. Supersymmetry restoration in superstring perturbation theory

    International Nuclear Information System (INIS)

    Sen, Ashoke

    2015-01-01

    Superstring perturbation theory based on the 1PI effective theory approach has been useful for addressing the problem of mass renormalization and vacuum shift. We derive Ward identities associated with space-time supersymmetry transformation in this approach. This leads to a proof of the equality of renormalized masses of bosons and fermions and identities relating fermionic amplitudes to bosonic amplitudes after taking into account the effect of mass renormalization. This also relates unbroken supersymmetry to a given order in perturbation theory to absence of tadpoles of massless scalars to higher order. The results are valid at the perturbative vacuum as well as in the shifted vacuum when the latter describes the correct ground state of the theory. We apply this to SO(32) heterotic string theory on Calabi-Yau 3-folds where a one loop Fayet-Iliopoulos term apparently breaks supersymmetry at one loop, but analysis of the low energy effective field theory indicates that there is a nearby vacuum where supersymmetry is restored. We explicitly prove that the perturbative amplitudes of this theory around the shifted vacuum indeed satisfy the Ward identities associated with unbroken supersymmetry. We also test the general arguments by explicitly verifying the equality of bosonic and fermionic masses at one loop order in the shifted vacuum, and the appearance of two loop dilaton tadpole in the perturbative vacuum where supersymmetry is expected to be broken.

  7. Supersymmetry restoration in superstring perturbation theory

    Energy Technology Data Exchange (ETDEWEB)

    Sen, Ashoke [Harish-Chandra Research Institute,Chhatnag Road, Jhusi, Allahabad 211019 (India)

    2015-12-14

    Superstring perturbation theory based on the 1PI effective theory approach has been useful for addressing the problem of mass renormalization and vacuum shift. We derive Ward identities associated with space-time supersymmetry transformation in this approach. This leads to a proof of the equality of renormalized masses of bosons and fermions and identities relating fermionic amplitudes to bosonic amplitudes after taking into account the effect of mass renormalization. This also relates unbroken supersymmetry to a given order in perturbation theory to absence of tadpoles of massless scalars to higher order. The results are valid at the perturbative vacuum as well as in the shifted vacuum when the latter describes the correct ground state of the theory. We apply this to SO(32) heterotic string theory on Calabi-Yau 3-folds where a one loop Fayet-Iliopoulos term apparently breaks supersymmetry at one loop, but analysis of the low energy effective field theory indicates that there is a nearby vacuum where supersymmetry is restored. We explicitly prove that the perturbative amplitudes of this theory around the shifted vacuum indeed satisfy the Ward identities associated with unbroken supersymmetry. We also test the general arguments by explicitly verifying the equality of bosonic and fermionic masses at one loop order in the shifted vacuum, and the appearance of two loop dilaton tadpole in the perturbative vacuum where supersymmetry is expected to be broken.

  8. Optimal random perturbations for stochastic approximation using a simultaneous perturbation gradient approximation

    DEFF Research Database (Denmark)

    Sadegh, Payman; Spall, J. C.

    1998-01-01

    simultaneous perturbation approximation to the gradient based on loss function measurements. SPSA is based on picking a simultaneous perturbation (random) vector in a Monte Carlo fashion as part of generating the approximation to the gradient. This paper derives the optimal distribution for the Monte Carlo...

  9. Edge localized modes control by resonant magnetic perturbations

    International Nuclear Information System (INIS)

    Nardon, E.

    2007-10-01

    The present work is dedicated to one of the most promising methods of control of the ELMs (Edge Localized Modes), based on a system of coils producing Resonant Magnetic Perturbations (RMPs). Our main objectives are, on the one hand, to improve the physical understanding of the mechanisms at play, and on the other hand to propose a concrete design of ELMs control coils for ITER. In order to calculate and analyze the magnetic perturbations produced by a given set of coils, we have developed the ERGOS code. The first ERGOS calculation was for the DIII-D ELMs control coils, the I-coils. It showed that they produce magnetic islands chains which overlap at the edge of the plasma, resulting in the ergodization of the magnetic field. We have then used ERGOS for the modelling of the experiments on ELMs control using the error field correction coils at JET and MAST. In the case of JET, we have shown the existence of a correlation between the mitigation of the ELMs and the ergodization of the magnetic field at the edge, in agreement with the DIII-D result. In order to design the ELMs control coils for ITER we have used ERGOS intensively, taking the case of the DIII-D I-coils as a reference. Three candidate designs came out, which we presented at the ITER Design Review, in 2007. Recently, the ITER management decided to provide a budget for building ELMs control coils, the design of which remains to be chosen between two of the three options that we proposed. Finally, in order to understand better the non-linear magnetohydrodynamics phenomena taking place in ELMs control by RMPs, we performed numerical simulations, in particular with the JOREK code for a DIII-D case. The simulations reveal the existence of convection cells induced at the edge by the magnetic perturbations, and the possible screening of the RMPs in presence of rotation

  10. Tension perturbations of black brane spacetimes

    International Nuclear Information System (INIS)

    Traschen, Jennie; Fox, Daniel

    2004-01-01

    We consider black brane spacetimes that have at least one spatial translation Killing field that is tangent to the brane. A new parameter, the tension of a spacetime, is defined. The tension parameter is associated with spatial translations in much the same way that the ADM mass is associated with the time translation Killing field. In this work, we explore the implications of the spatial translation symmetry for small perturbations around a background black brane. For static-charged black branes we derive a law which relates the tension perturbation to the surface gravity times the change in the horizon area, plus terms that involve variations in the charges and currents. We find that as a black brane evaporates the tension decreases. We also give a simple derivation of a first law for black brane spacetimes. These constructions hold when the background stress-energy is governed by a Hamiltonian, and the results include arbitrary perturbative stress-energy sources

  11. Perturbation measurement of waveguides for acoustic thermometry

    Science.gov (United States)

    Lin, H.; Feng, X. J.; Zhang, J. T.

    2013-09-01

    Acoustic thermometers normally embed small acoustic transducers in the wall bounding a gas-filled cavity resonator. At high temperature, insulators of transducers loss electrical insulation and degrade the signal-to-noise ratio. One essential solution to this technical trouble is to couple sound by acoustic waveguides between resonator and transducers. But waveguide will break the ideal acoustic surface and bring perturbations(Δf+ig) to the ideal resonance frequency. The perturbation model for waveguides was developed based on the first-order acoustic theory in this paper. The frequency shift Δf and half-width change g caused by the position, length and radius of waveguides were analyzed using this model. Six different length of waveguides (52˜1763 mm) were settled on the cylinder resonator and the perturbation (Δf+ig) were measured at T=332 K and p=250˜500 kPa. The experiment results agreed with the theoretical prediction very well.

  12. Microfluidic mixing through oscillatory transverse perturbations

    Science.gov (United States)

    Wu, J. W.; Xia, H. M.; Zhang, Y. Y.; Zhu, P.

    2018-05-01

    Fluid mixing in miniaturized fluidic devices is a challenging task. In this work, the mixing enhancement through oscillatory transverse perturbations coupling with divergent circular chambers is studied. To simplify the design, an autonomous microfluidic oscillator is used to produce the oscillatory flow. It is then applied to four side-channels that intersect with a central channel of constant flow. The mixing performance is tested at high fluid viscosities of up to 16 cP. Results show that the oscillatory flow can cause strong transverse perturbations which effectively enhance the mixing. The influence of a fluidic capacitor in the central channel is also examined, which at low viscosities can intensify the perturbations and further improve the mixing.

  13. One dimensional systems with singular perturbations

    International Nuclear Information System (INIS)

    Alvarez, J J; Gadella, M; Nieto, L M; Glasser, L M; Lara, L P

    2011-01-01

    This paper discusses some one dimensional quantum models with singular perturbations. Eventually, a mass discontinuity is added at the points that support the singular perturbations. The simplest model includes an attractive singular potential with a mass jump both located at the origin. We study the form of the only bound state. Another model exhibits a hard core at the origin plus one or more repulsive deltas with mass jumps at the points supporting these deltas. We study the location and the multiplicity of these resonances for the case of one or two deltas and settle the basis for a generalization. Finally, we consider the harmonic oscillator and the infinite square well plus a singular potential at the origin. We see how the energy of bound states is affected by the singular perturbation.

  14. On the domain of string perturbation theory

    International Nuclear Information System (INIS)

    Davis, S.

    1989-06-01

    For a large class of effectively closed surfaces, it is shown that the only divergences in string scattering amplitudes at each order in perturbation theory are those associated with the coincidence of vertex operators and the boundary of moduli space. This class includes all closed surfaces of finite genus, and infinite-genus surfaces which can be uniformized by a group of Schottky type. While the computation is done explicitly for bosonic strings in their ground states, it can also be extended to excited states and to superstrings. The properties of these amplitudes lead to a definition of the domain of perturbation theory as the set of effectively closed surfaces. The implications of the restriction to effectively closed surfaces on the behavior of the perturbation series are discussed. (author). 20 refs, 6 figs

  15. Perturbation theory for continuous stochastic equations

    International Nuclear Information System (INIS)

    Chechetkin, V.R.; Lutovinov, V.S.

    1987-01-01

    The various general perturbational schemes for continuous stochastic equations are considered. These schemes have many analogous features with the iterational solution of Schwinger equation for S-matrix. The following problems are discussed: continuous stochastic evolution equations for probability distribution functionals, evolution equations for equal time correlators, perturbation theory for Gaussian and Poissonian additive noise, perturbation theory for birth and death processes, stochastic properties of systems with multiplicative noise. The general results are illustrated by diffusion-controlled reactions, fluctuations in closed systems with chemical processes, propagation of waves in random media in parabolic equation approximation, and non-equilibrium phase transitions in systems with Poissonian breeding centers. The rate of irreversible reaction X + X → A (Smoluchowski process) is calculated with the use of general theory based on continuous stochastic equations for birth and death processes. The threshold criterion and range of fluctuational region for synergetic phase transition in system with Poissonian breeding centers are also considered. (author)

  16. 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

  17. 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

  18. Non-Perturbative Quantum Geometry III

    CERN Document Server

    Krefl, Daniel

    2016-08-02

    The Nekrasov-Shatashvili limit of the refined topological string on toric Calabi-Yau manifolds and the resulting quantum geometry is studied from a non-perturbative perspective. The quantum differential and thus the quantum periods exhibit Stockes phenomena over the combined string coupling and quantized Kaehler moduli space. We outline that the underlying formalism of exact quantization is generally applicable to points in moduli space featuring massless hypermultiplets, leading to non-perturbative band splitting. Our prime example is local P1xP1 near a conifold point in moduli space. In particular, we will present numerical evidence that in a Stockes chamber of interest the string based quantum geometry reproduces the non-perturbative corrections for the Nekrasov-Shatashvili limit of 4d supersymmetric SU(2) gauge theory at strong coupling found in the previous part of this series. A preliminary discussion of local P2 near the conifold point in moduli space is also provided.

  19. Schroedinger operators with singular perturbation potentials

    International Nuclear Information System (INIS)

    Harrell, E.M. II.

    1976-01-01

    This is a perturbative analysis of the eigenvalues and eigenfunctions of Schroedinger operators of the form -Δ + A + lambda V, defined on the Hilbert space L 2 (R/sup n/). A is a potential function (a smooth, real multiplication operator), and V is a ''spikelike'' perturbation, i.e., a perturbative potential function which diverges at some finite point. Lambda is a small real or complex parameter. The emphasis is on one-dimensional problems, and in particular the typical example is the ''spiked harmonic oscillator'' Hamiltonian, -d 2 /dx 2 + x 2 + lambda x/sup -α/, where α is a positive constant. An earlier study by L. Detwiler and J. R. Klauder [Phys. Rev. D 11 (1975) 1436] indicated that the lowest-order corrections to the ground-state eigenvalue of the spiked harmonic oscillator with lambda greater than 0 were proportional to lambda ln lambda when α = 3, and to lambda/sup 1/(α-2) when α is greater than 3. These and analogous results for a large class of operators and arbitrary eigenvalues are proved. Explicit constants in a modified perturbation series with a complicated dependence on lambda are determined and exhibited. Higher-order corrections for real lambda and lowest-order corrections for complex lambda are also discussed. While the substance of the dissertation is mathematical, its main applications are to quantum physics. The immediate cause of interest in such problems was the use of their peculiar convergence properties by J. R. Klauder as models for the behavior of nonrenormalizable quantum field theories. However, the results of this study are likely to be of greater importance in chemical or nuclear physics, as positive spikelike perturbations represent repulsive core interactions for quantum mechanical particles. The modified perturbation series are a new calculation technique for this situation

  20. Conservation laws and geometry of perturbed coset models

    CERN Document Server

    Bakas, Ioannis

    1994-01-01

    We present a Lagrangian description of the $SU(2)/U(1)$ coset model perturbed by its first thermal operator. This is the simplest perturbation that changes sign under Krammers--Wannier duality. The resulting theory, which is a 2--component generalization of the sine--Gordon model, is then taken in Minkowski space. For negative values of the coupling constant $g$, it is classically equivalent to the $O(4)$ non--linear $\\s$--model reduced in a certain frame. For $g > 0$, it describes the relativistic motion of vortices in a constant external field. Viewing the classical equations of motion as a zero curvature condition, we obtain recursive relations for the infinitely many conservation laws by the abelianization method of gauge connections. The higher spin currents are constructed entirely using an off--critical generalization of the $W_{\\infty}$ generators. We give a geometric interpretation to the corresponding charges in terms of embeddings. Applications to the chirally invariant $U(2)$ Gross--Neveu model ar...