Perturbational formulation of principal component analysis in molecular dynamics simulation

NASA Astrophysics Data System (ADS)

Koyama, Yohei M.; Kobayashi, Tetsuya J.; Tomoda, Shuji; Ueda, Hiroki R.

2008-10-01

Conformational fluctuations of a molecule are important to its function since such intrinsic fluctuations enable the molecule to respond to the external environmental perturbations. For extracting large conformational fluctuations, which predict the primary conformational change by the perturbation, principal component analysis (PCA) has been used in molecular dynamics simulations. However, several versions of PCA, such as Cartesian coordinate PCA and dihedral angle PCA (dPCA), are limited to use with molecules with a single dominant state or proteins where the dihedral angle represents an important internal coordinate. Other PCAs with general applicability, such as the PCA using pairwise atomic distances, do not represent the physical meaning clearly. Therefore, a formulation that provides general applicability and clearly represents the physical meaning is yet to be developed. For developing such a formulation, we consider the conformational distribution change by the perturbation with arbitrary linearly independent perturbation functions. Within the second order approximation of the Kullback-Leibler divergence by the perturbation, the PCA can be naturally interpreted as a method for (1) decomposing a given perturbation into perturbations that independently contribute to the conformational distribution change or (2) successively finding the perturbation that induces the largest conformational distribution change. In this perturbational formulation of PCA, (i) the eigenvalue measures the Kullback-Leibler divergence from the unperturbed to perturbed distributions, (ii) the eigenvector identifies the combination of the perturbation functions, and (iii) the principal component determines the probability change induced by the perturbation. Based on this formulation, we propose a PCA using potential energy terms, and we designate it as potential energy PCA (PEPCA). The PEPCA provides both general applicability and clear physical meaning. For demonstrating its power, we apply the PEPCA to an alanine dipeptide molecule in vacuum as a minimal model of a nonsingle dominant conformational biomolecule. The first and second principal components clearly characterize two stable states and the transition state between them. Positive and negative components with larger absolute values of the first and second eigenvectors identify the electrostatic interactions, which stabilize or destabilize each stable state and the transition state. Our result therefore indicates that PCA can be applied, by carefully selecting the perturbation functions, not only to identify the molecular conformational fluctuation but also to predict the conformational distribution change by the perturbation beyond the limitation of the previous methods.

Robust exponential stability of uncertain delayed neural networks with stochastic perturbation and impulse effects.

PubMed

Huang, Tingwen; Li, Chuandong; Duan, Shukai; Starzyk, Janusz A

2012-06-01

This paper focuses on the hybrid effects of parameter uncertainty, stochastic perturbation, and impulses on global stability of delayed neural networks. By using the Ito formula, Lyapunov function, and Halanay inequality, we established several mean-square stability criteria from which we can estimate the feasible bounds of impulses, provided that parameter uncertainty and stochastic perturbations are well-constrained. Moreover, the present method can also be applied to general differential systems with stochastic perturbation and impulses.

Modularity and the spread of perturbations in complex dynamical systems

NASA Astrophysics Data System (ADS)

Kolchinsky, Artemy; Gates, Alexander J.; Rocha, Luis M.

2015-12-01

We propose a method to decompose dynamical systems based on the idea that modules constrain the spread of perturbations. We find partitions of system variables that maximize "perturbation modularity," defined as the autocovariance of coarse-grained perturbed trajectories. The measure effectively separates the fast intramodular from the slow intermodular dynamics of perturbation spreading (in this respect, it is a generalization of the "Markov stability" method of network community detection). Our approach captures variation of modular organization across different system states, time scales, and in response to different kinds of perturbations: aspects of modularity which are all relevant to real-world dynamical systems. It offers a principled alternative to detecting communities in networks of statistical dependencies between system variables (e.g., "relevance networks" or "functional networks"). Using coupled logistic maps, we demonstrate that the method uncovers hierarchical modular organization planted in a system's coupling matrix. Additionally, in homogeneously coupled map lattices, it identifies the presence of self-organized modularity that depends on the initial state, dynamical parameters, and type of perturbations. Our approach offers a powerful tool for exploring the modular organization of complex dynamical systems.

Modularity and the spread of perturbations in complex dynamical systems.

PubMed

Kolchinsky, Artemy; Gates, Alexander J; Rocha, Luis M

2015-12-01

We propose a method to decompose dynamical systems based on the idea that modules constrain the spread of perturbations. We find partitions of system variables that maximize "perturbation modularity," defined as the autocovariance of coarse-grained perturbed trajectories. The measure effectively separates the fast intramodular from the slow intermodular dynamics of perturbation spreading (in this respect, it is a generalization of the "Markov stability" method of network community detection). Our approach captures variation of modular organization across different system states, time scales, and in response to different kinds of perturbations: aspects of modularity which are all relevant to real-world dynamical systems. It offers a principled alternative to detecting communities in networks of statistical dependencies between system variables (e.g., "relevance networks" or "functional networks"). Using coupled logistic maps, we demonstrate that the method uncovers hierarchical modular organization planted in a system's coupling matrix. Additionally, in homogeneously coupled map lattices, it identifies the presence of self-organized modularity that depends on the initial state, dynamical parameters, and type of perturbations. Our approach offers a powerful tool for exploring the modular organization of complex dynamical systems.

Solution of linear systems by a singular perturbation technique

NASA Technical Reports Server (NTRS)

Ardema, M. D.

1976-01-01

An approximate solution is obtained for a singularly perturbed system of initial valued, time invariant, linear differential equations with multiple boundary layers. Conditions are stated under which the approximate solution converges uniformly to the exact solution as the perturbation parameter tends to zero. The solution is obtained by the method of matched asymptotic expansions. Use of the results for obtaining approximate solutions of general linear systems is discussed. An example is considered to illustrate the method and it is shown that the formulas derived give a readily computed uniform approximation.

A collision history-based approach to Sensitivity/Perturbation calculations in the continuous energy Monte Carlo code SERPENT

DOE Office of Scientific and Technical Information (OSTI.GOV)

Giuseppe Palmiotti

In this work, the implementation of a collision history-based approach to sensitivity/perturbation calculations in the Monte Carlo code SERPENT is discussed. The proposed methods allow the calculation of the eects of nuclear data perturbation on several response functions: the eective multiplication factor, reaction rate ratios and bilinear ratios (e.g., eective kinetics parameters). SERPENT results are compared to ERANOS and TSUNAMI Generalized Perturbation Theory calculations for two fast metallic systems and for a PWR pin-cell benchmark. New methods for the calculation of sensitivities to angular scattering distributions are also presented, which adopts fully continuous (in energy and angle) Monte Carlo estimators.

Computing singularities of perturbation series

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kvaal, Simen; Jarlebring, Elias; Michiels, Wim

2011-03-15

Many properties of current ab initio approaches to the quantum many-body problem, both perturbational and otherwise, are related to the singularity structure of the Rayleigh-Schroedinger perturbation series. A numerical procedure is presented that in principle computes the complete set of singularities, including the dominant singularity which limits the radius of convergence. The method approximates the singularities as eigenvalues of a certain generalized eigenvalue equation which is solved using iterative techniques. It relies on computation of the action of the Hamiltonian matrix on a vector and does not rely on the terms in the perturbation series. The method can be usefulmore » for studying perturbation series of typical systems of moderate size, for fundamental development of resummation schemes, and for understanding the structure of singularities for typical systems. Some illustrative model problems are studied, including a helium-like model with {delta}-function interactions for which Moeller-Plesset perturbation theory is considered and the radius of convergence found.« less

Application of the generalized Euler series transformation for calculation of vibration-rotation energy levels of diatomic molecules

NASA Astrophysics Data System (ADS)

Kruglova, T. V.

2004-01-01

The detailed spectroscope information about highly excited molecules and radicals such us as H+3, H2, HI, H2O, CH2 is needed for a number of applications in the field of laser physics, astrophysics and chemistry. Studies of highly excited molecular vibration-rotation states face several problems connected with slowly convergence or even divergences of perturbation expansions. The physical reason for a perturbation expansion divergence is the large amplitude motion and strong vibration-rotation coupling. In this case one needs to use the special method of series summation. There were a number of papers devoted to this problem: papers 1-10 in the reference list are only example of studies on this topic. The present report is aimed at the application of GET method (Generalized Euler Transformation) to the diatomic molecule. Energy levels of a diatomic molecule is usually represented as Dunham series on rotational J(J+1) and vibrational (V+1/2) quantum numbers (within the perturbation approach). However, perturbation theory is not applicable for highly excited vibration-rotation states because the perturbation expansion in this case becomes divergent. As a consequence one need to use special method for the series summation. The Generalized Euler Transformation (GET) is known to be efficient method for summing of slowly convergent series, it was already used for solving of several quantum problems Refs.13 and 14. In this report the results of Euler transformation of diatomic molecule Dunham series are presented. It is shown that Dunham power series can be represented of functional series that is equivalent to its partial summation. It is also shown that transformed series has the butter convergent properties, than the initial series.

Curvature perturbations in the early universe: Theoretical models and observational tests

NASA Astrophysics Data System (ADS)

Vallinotto, Alberto

A very general prediction of inflation is that the power spectrum of density perturbations is characterized by a spectral index ns which is scale independent and approximately equal to unity. Drawing from the potential reconstruction method and adopting the slow-roll parameter expansion technique, we derive all possible single field inflationary potentials that would lead to a scale invariant density spectral index, consistent with current observations. In the process, a new method to determine the functional form of the inflationary potential in the slow roll approximation is devised, based on the reparametrization of the field dynamics with respect to the slow roll parameter epsilon which also allowed to show that under the assumptions made the investigation proved to be exhaustive and that no other solutions are available. Next, we focus on the fact that there exist a large class of inflationary models currently ruled out because the predicted production of curvature perturbations during the slow-roll stage results exponentially suppressed. We investigate whether an alternative mechanism for the generation of curvature perturbations can be devised for such a class of models. In the process, it is shown that it is sufficient for the inflationary potential to exhibit a broken symmetry to successfully convert isocurvature perturbations, which are excited during the slow-roll stage, into curvature perturbations thanks to an inhomogeneous decay stage. This conclusion is general, requiring as a sufficient condition only the fact that the inflation potential is characterized by a broken symmetry. Finally, we show that the perturbations thus produced are generally characterized by a non-negligible degree of non-gaussianity, which then provides a clear experimental signature for experimental detection or rejection.

Study of diatomic molecules. 2: Intensities. [optical emission spectroscopy of ScO

NASA Technical Reports Server (NTRS)

Femenias, J. L.

1978-01-01

The theory of perturbations, giving the diatomic effective Hamiltonian, is used for calculating actual molecular wave functions and intensity factors involved in transitions between states arising from Hund's coupling cases a,b, intermediate a-b, and c tendency. The Herman and Wallis corrections are derived, without any knowledge of the analytical expressions of the wave functions, and generalized to transitions between electronic states with whatever symmetry and multiplicity. A general method for studying perturbed intensities is presented using primarily modern spectroscopic numerical approaches. The method is used in the study of the ScO optical emission spectrum.

Robustness of Synchrony in Complex Networks and Generalized Kirchhoff Indices

NASA Astrophysics Data System (ADS)

Tyloo, M.; Coletta, T.; Jacquod, Ph.

2018-02-01

In network theory, a question of prime importance is how to assess network vulnerability in a fast and reliable manner. With this issue in mind, we investigate the response to external perturbations of coupled dynamical systems on complex networks. We find that for specific, nonaveraged perturbations, the response of synchronous states depends on the eigenvalues of the stability matrix of the unperturbed dynamics, as well as on its eigenmodes via their overlap with the perturbation vector. Once averaged over properly defined ensembles of perturbations, the response is given by new graph topological indices, which we introduce as generalized Kirchhoff indices. These findings allow for a fast and reliable method for assessing the specific or average vulnerability of a network against changing operational conditions, faults, or external attacks.

Source Distribution Method for Unsteady One-Dimensional Flows With Small Mass, Momentum, and Heat Addition and Small Area Variation

NASA Technical Reports Server (NTRS)

Mirels, Harold

1959-01-01

A source distribution method is presented for obtaining flow perturbations due to small unsteady area variations, mass, momentum, and heat additions in a basic uniform (or piecewise uniform) one-dimensional flow. First, the perturbations due to an elemental area variation, mass, momentum, and heat addition are found. The general solution is then represented by a spatial and temporal distribution of these elemental (source) solutions. Emphasis is placed on discussing the physical nature of the flow phenomena. The method is illustrated by several examples. These include the determination of perturbations in basic flows consisting of (1) a shock propagating through a nonuniform tube, (2) a constant-velocity piston driving a shock, (3) ideal shock-tube flows, and (4) deflagrations initiated at a closed end. The method is particularly applicable for finding the perturbations due to relatively thin wall boundary layers.

Development of New Methods for the Solution of Nonlinear Differential Equations by the Method of Lie Series and Extension to New Fields.

DTIC Science & Technology

perturbation formulas of Groebner (1960) and Alexseev (1961) for the solution of ordinary differential equations. These formulas are generalized and...iteration methods are given, which include the Methods of Picard, Groebner -Knapp, Poincare, Chen, as special cases. Chapter 3 generalizes an iterated

Ecological modeling from time-series inference: insight into dynamics and stability of intestinal microbiota.

PubMed

Stein, Richard R; Bucci, Vanni; Toussaint, Nora C; Buffie, Charlie G; Rätsch, Gunnar; Pamer, Eric G; Sander, Chris; Xavier, João B

2013-01-01

The intestinal microbiota is a microbial ecosystem of crucial importance to human health. Understanding how the microbiota confers resistance against enteric pathogens and how antibiotics disrupt that resistance is key to the prevention and cure of intestinal infections. We present a novel method to infer microbial community ecology directly from time-resolved metagenomics. This method extends generalized Lotka-Volterra dynamics to account for external perturbations. Data from recent experiments on antibiotic-mediated Clostridium difficile infection is analyzed to quantify microbial interactions, commensal-pathogen interactions, and the effect of the antibiotic on the community. Stability analysis reveals that the microbiota is intrinsically stable, explaining how antibiotic perturbations and C. difficile inoculation can produce catastrophic shifts that persist even after removal of the perturbations. Importantly, the analysis suggests a subnetwork of bacterial groups implicated in protection against C. difficile. Due to its generality, our method can be applied to any high-resolution ecological time-series data to infer community structure and response to external stimuli.

Ecological Modeling from Time-Series Inference: Insight into Dynamics and Stability of Intestinal Microbiota

PubMed Central

Toussaint, Nora C.; Buffie, Charlie G.; Rätsch, Gunnar; Pamer, Eric G.; Sander, Chris; Xavier, João B.

2013-01-01

The intestinal microbiota is a microbial ecosystem of crucial importance to human health. Understanding how the microbiota confers resistance against enteric pathogens and how antibiotics disrupt that resistance is key to the prevention and cure of intestinal infections. We present a novel method to infer microbial community ecology directly from time-resolved metagenomics. This method extends generalized Lotka–Volterra dynamics to account for external perturbations. Data from recent experiments on antibiotic-mediated Clostridium difficile infection is analyzed to quantify microbial interactions, commensal-pathogen interactions, and the effect of the antibiotic on the community. Stability analysis reveals that the microbiota is intrinsically stable, explaining how antibiotic perturbations and C. difficile inoculation can produce catastrophic shifts that persist even after removal of the perturbations. Importantly, the analysis suggests a subnetwork of bacterial groups implicated in protection against C. difficile. Due to its generality, our method can be applied to any high-resolution ecological time-series data to infer community structure and response to external stimuli. PMID:24348232

Perturbative description of the fermionic projector: Normalization, causality, and Furry's theorem

NASA Astrophysics Data System (ADS)

Finster, Felix; Tolksdorf, Jürgen

2014-05-01

The causal perturbation expansion of the fermionic projector is performed with a contour integral method. Different normalization conditions are analyzed. It is shown that the corresponding light-cone expansions are causal in the sense that they only involve bounded line integrals. For the resulting loop diagrams we prove a generalized Furry theorem.

Nonlinear Waves, Dynamical Systems and Other Applied Mathematics Programs

DTIC Science & Technology

1991-10-04

present a general scheme of perturbation method for perturbed soliton systems, based on the normal form theory and the method of multiple scales. By this...dimension, and discuss possible consequences of the interplay between wavefront- interactions and curvature in two dimensions. Thursday, October 19 All ... normal speed D parametrized by the local mean surface curvature x. Its solution provides a relation D = D(x) which determines the evolution of the front

Generalized perturbation (n, M)-fold Darboux transformations and multi-rogue-wave structures for the modified self-steepening nonlinear Schrödinger equation.

PubMed

Wen, Xiao-Yong; Yang, Yunqing; Yan, Zhenya

2015-07-01

In this paper, a simple and constructive method is presented to find the generalized perturbation (n,M)-fold Darboux transformations (DTs) of the modified nonlinear Schrödinger (MNLS) equation in terms of fractional forms of determinants. In particular, we apply the generalized perturbation (1,N-1)-fold DTs to find its explicit multi-rogue-wave solutions. The wave structures of these rogue-wave solutions of the MNLS equation are discussed in detail for different parameters, which display abundant interesting wave structures, including the triangle and pentagon, etc., and may be useful to study the physical mechanism of multirogue waves in optics. The dynamical behaviors of these multi-rogue-wave solutions are illustrated using numerical simulations. The same Darboux matrix can also be used to investigate the Gerjikov-Ivanov equation such that its multi-rogue-wave solutions and their wave structures are also found. The method can also be extended to find multi-rogue-wave solutions of other nonlinear integrable equations.

The Harmonic Oscillator with a Gaussian Perturbation: Evaluation of the Integrals and Example Applications

ERIC Educational Resources Information Center

Earl, Boyd L.

2008-01-01

A general result for the integrals of the Gaussian function over the harmonic oscillator wavefunctions is derived using generating functions. Using this result, an example problem of a harmonic oscillator with various Gaussian perturbations is explored in order to compare the results of precise numerical solution, the variational method, and…

Computation of diverging sums based on a finite number of terms

NASA Astrophysics Data System (ADS)

Lv, Q. Z.; Norris, S.; Pelphrey, R.; Su, Q.; Grobe, R.

2017-10-01

We propose a numerical method that permits us to compute the sum of a diverging series from only the first N terms by generalizing the traditional Borel technique. The method is rather robust and can be used to recover the ground state energy from the diverging perturbation theory for quantum field theoretical systems that are spatially constrained. Surprisingly, even the corresponding eigenvectors can be generated despite the intrinsic non-perturbative nature of bound state problems.

Convergence of high order perturbative expansions in open system quantum dynamics.

PubMed

Xu, Meng; Song, Linze; Song, Kai; Shi, Qiang

2017-02-14

We propose a new method to directly calculate high order perturbative expansion terms in open system quantum dynamics. They are first written explicitly in path integral expressions. A set of differential equations are then derived by extending the hierarchical equation of motion (HEOM) approach. As two typical examples for the bosonic and fermionic baths, specific forms of the extended HEOM are obtained for the spin-boson model and the Anderson impurity model. Numerical results are then presented for these two models. General trends of the high order perturbation terms as well as the necessary orders for the perturbative expansions to converge are analyzed.

A general formula for Rayleigh-Schroedinger perturbation energy utilizing a power series expansion of the quantum mechanical Hamiltonian

DOE Office of Scientific and Technical Information (OSTI.GOV)

Herbert, J.M.

1997-02-01

Perturbation theory has long been utilized by quantum chemists as a method for approximating solutions to the Schroedinger equation. Perturbation treatments represent a system`s energy as a power series in which each additional term further corrects the total energy; it is therefore convenient to have an explicit formula for the nth-order energy correction term. If all perturbations are collected into a single Hamiltonian operator, such a closed-form expression for the nth-order energy correction is well known; however, use of a single perturbed Hamiltonian often leads to divergent energy series, while superior convergence behavior is obtained by expanding the perturbed Hamiltonianmore » in a power series. This report presents a closed-form expression for the nth-order energy correction obtained using Rayleigh-Schroedinger perturbation theory and a power series expansion of the Hamiltonian.« less

Galilean invariant resummation schemes of cosmological perturbations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Peloso, Marco; Pietroni, Massimo, E-mail: peloso@physics.umn.edu, E-mail: massimo.pietroni@unipr.it

2017-01-01

Many of the methods proposed so far to go beyond Standard Perturbation Theory break invariance under time-dependent boosts (denoted here as extended Galilean Invariance, or GI). This gives rise to spurious large scale effects which spoil the small scale predictions of these approximation schemes. By using consistency relations we derive fully non-perturbative constraints that GI imposes on correlation functions. We then introduce a method to quantify the amount of GI breaking of a given scheme, and to correct it by properly tailored counterterms. Finally, we formulate resummation schemes which are manifestly GI, discuss their general features, and implement them inmore » the so called Time-Flow, or TRG, equations.« less

Structural-change localization and monitoring through a perturbation-based inverse problem.

PubMed

Roux, Philippe; Guéguen, Philippe; Baillet, Laurent; Hamze, Alaa

2014-11-01

Structural-change detection and characterization, or structural-health monitoring, is generally based on modal analysis, for detection, localization, and quantification of changes in structure. Classical methods combine both variations in frequencies and mode shapes, which require accurate and spatially distributed measurements. In this study, the detection and localization of a local perturbation are assessed by analysis of frequency changes (in the fundamental mode and overtones) that are combined with a perturbation-based linear inverse method and a deconvolution process. This perturbation method is applied first to a bending beam with the change considered as a local perturbation of the Young's modulus, using a one-dimensional finite-element model for modal analysis. Localization is successful, even for extended and multiple changes. In a second step, the method is numerically tested under ambient-noise vibration from the beam support with local changes that are shifted step by step along the beam. The frequency values are revealed using the random decrement technique that is applied to the time-evolving vibrations recorded by one sensor at the free extremity of the beam. Finally, the inversion method is experimentally demonstrated at the laboratory scale with data recorded at the free end of a Plexiglas beam attached to a metallic support.

Auxiliary principle technique and iterative algorithm for a perturbed system of generalized multi-valued mixed quasi-equilibrium-like problems.

PubMed

Rahaman, Mijanur; Pang, Chin-Tzong; Ishtyak, Mohd; Ahmad, Rais

2017-01-01

In this article, we introduce a perturbed system of generalized mixed quasi-equilibrium-like problems involving multi-valued mappings in Hilbert spaces. To calculate the approximate solutions of the perturbed system of generalized multi-valued mixed quasi-equilibrium-like problems, firstly we develop a perturbed system of auxiliary generalized multi-valued mixed quasi-equilibrium-like problems, and then by using the celebrated Fan-KKM technique, we establish the existence and uniqueness of solutions of the perturbed system of auxiliary generalized multi-valued mixed quasi-equilibrium-like problems. By deploying an auxiliary principle technique and an existence result, we formulate an iterative algorithm for solving the perturbed system of generalized multi-valued mixed quasi-equilibrium-like problems. Lastly, we study the strong convergence analysis of the proposed iterative sequences under monotonicity and some mild conditions. These results are new and generalize some known results in this field.

A hybrid Pade-Galerkin technique for differential equations

NASA Technical Reports Server (NTRS)

Geer, James F.; Andersen, Carl M.

1993-01-01

A three-step hybrid analysis technique, which successively uses the regular perturbation expansion method, the Pade expansion method, and then a Galerkin approximation, is presented and applied to some model boundary value problems. In the first step of the method, the regular perturbation method is used to construct an approximation to the solution in the form of a finite power series in a small parameter epsilon associated with the problem. In the second step of the method, the series approximation obtained in step one is used to construct a Pade approximation in the form of a rational function in the parameter epsilon. In the third step, the various powers of epsilon which appear in the Pade approximation are replaced by new (unknown) parameters (delta(sub j)). These new parameters are determined by requiring that the residual formed by substituting the new approximation into the governing differential equation is orthogonal to each of the perturbation coordinate functions used in step one. The technique is applied to model problems involving ordinary or partial differential equations. In general, the technique appears to provide good approximations to the solution even when the perturbation and Pade approximations fail to do so. The method is discussed and topics for future investigations are indicated.

A general theory of linear cosmological perturbations: scalar-tensor and vector-tensor theories

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lagos, Macarena; Baker, Tessa; Ferreira, Pedro G.

We present a method for parametrizing linear cosmological perturbations of theories of gravity, around homogeneous and isotropic backgrounds. The method is sufficiently general and systematic that it can be applied to theories with any degrees of freedom (DoFs) and arbitrary gauge symmetries. In this paper, we focus on scalar-tensor and vector-tensor theories, invariant under linear coordinate transformations. In the case of scalar-tensor theories, we use our framework to recover the simple parametrizations of linearized Horndeski and ''Beyond Horndeski'' theories, and also find higher-derivative corrections. In the case of vector-tensor theories, we first construct the most general quadratic action for perturbationsmore » that leads to second-order equations of motion, which propagates two scalar DoFs. Then we specialize to the case in which the vector field is time-like (à la Einstein-Aether gravity), where the theory only propagates one scalar DoF. As a result, we identify the complete forms of the quadratic actions for perturbations, and the number of free parameters that need to be defined, to cosmologically characterize these two broad classes of theories.« less

Celestial mechanics with geometric algebra

NASA Technical Reports Server (NTRS)

Hestenes, D.

1983-01-01

Geometric algebra is introduced as a general tool for Celestial Mechanics. A general method for handling finite rotations and rotational kinematics is presented. The constants of Kepler motion are derived and manipulated in a new way. A new spinor formulation of perturbation theory is developed.

Maintenance and suppression of chaos by weak harmonic perturbations: a unified view.

PubMed

Chacón, R

2001-02-26

General results concerning maintenance or enhancement of chaos are presented for dissipative systems subjected to two harmonic perturbations (one chaos inducing and the other chaos enhancing). The connection with previous results on chaos suppression is also discussed in a general setting. It is demonstrated that, in general, a second harmonic perturbation can reliably play an enhancer or inhibitor role by solely adjusting its initial phase. Numerical results indicate that general theoretical findings concerning periodic chaos-inducing perturbations also work for aperiodic chaos-inducing perturbations, and in arrays of identical chaotic coupled oscillators.

Application of perturbation theory to lattice calculations based on method of cyclic characteristics

NASA Astrophysics Data System (ADS)

Assawaroongruengchot, Monchai

Perturbation theory is a technique used for the estimation of changes in performance functionals, such as linear reaction rate ratio and eigenvalue affected by small variations in reactor core compositions. Here the algorithm of perturbation theory is developed for the multigroup integral neutron transport problems in 2D fuel assemblies with isotropic scattering. The integral transport equation is used in the perturbative formulation because it represents the interconnecting neutronic systems of the lattice assemblies via the tracking lines. When the integral neutron transport equation is used in the formulation, one needs to solve the resulting integral transport equations for the flux importance and generalized flux importance functions. The relationship between the generalized flux importance and generalized source importance functions is defined in order to transform the generalized flux importance transport equations into the integro-differential equations for the generalized adjoints. Next we develop the adjoint and generalized adjoint transport solution algorithms based on the method of cyclic characteristics (MOCC) in DRAGON code. In the MOCC method, the adjoint characteristics equations associated with a cyclic tracking line are formulated in such a way that a closed form for the adjoint angular function can be obtained. The MOCC method then requires only one cycle of scanning over the cyclic tracking lines in each spatial iteration. We also show that the source importance function by CP method is mathematically equivalent to the adjoint function by MOCC method. In order to speed up the MOCC solution algorithm, a group-reduction and group-splitting techniques based on the structure of the adjoint scattering matrix are implemented. A combined forward flux/adjoint function iteration scheme, based on the group-splitting technique and the common use of a large number of variables storing tracking-line data and exponential values, is proposed to reduce the computing time when both direct and adjoint solutions are required. A problem that arises for the generalized adjoint problem is that the direct use of the negative external generalized adjoint sources in the adjoint solution algorithm results in negative generalized adjoint functions. A coupled flux biasing/decontamination scheme is applied to make the generalized adjoint functions positive using the adjoint functions in such a way that it can be used for the multigroup rebalance technique. Next we consider the application of the perturbation theory to the reactor problems. Since the coolant void reactivity (CVR) is a important factor in reactor safety analysis, we have decided to select this parameter for optimization studies. We consider the optimization and adjoint sensitivity techniques for the adjustments of CVR at beginning of burnup cycle (BOC) and k eff at end of burnup cycle (EOC) for a 2D Advanced CANDU Reactor (ACR) lattice. The sensitivity coefficients are evaluated using the perturbation theory based on the integral transport equations. Three sets of parameters for CVR-BOC and keff-EOC adjustments are studied: (1) Dysprosium density in the central pin with Uranium enrichment in the outer fuel rings, (2) Dysprosium density and Uranium enrichment both in the central pin, and (3) the same parameters as in the first case but the objective is to obtain a negative checkerboard CVR at beginning of cycle (CBCVR-BOC). To approximate the sensitivity coefficient at EOC, we perform constant-power burnup/depletion calculations for 600 full power days (FPD) using a slightly perturbed nuclear library and the unperturbed neutron fluxes to estimate the variation of nuclide densities at EOC. Sensitivity analyses of CVR and eigenvalue are included in the study. In addition the optimization and adjoint sensitivity techniques are applied to the CBCVR-BOC and keff-EOC adjustment of the ACR lattices with Gadolinium in the central pin. Finally we apply these techniques to the CVR-BOC, CVR-EOC and keff-EOC adjustment of a CANDU lattice of which the burnup period is extended from 300 to 450 FPDs. The cases with the central pin containing either Dysprosium or Gadolinium in the natural Uranium are considered in our study. (Abstract shortened by UMI.)

The multi-reference retaining the excitation degree perturbation theory: A size-consistent, unitary invariant, and rapidly convergent wavefunction based ab initio approach

NASA Astrophysics Data System (ADS)

Fink, Reinhold F.

2009-02-01

The retaining the excitation degree (RE) partitioning [R.F. Fink, Chem. Phys. Lett. 428 (2006) 461(20 September)] is reformulated and applied to multi-reference cases with complete active space (CAS) reference wave functions. The generalised van Vleck perturbation theory is employed to set up the perturbation equations. It is demonstrated that this leads to a consistent and well defined theory which fulfils all important criteria of a generally applicable ab initio method: The theory is proven numerically and analytically to be size-consistent and invariant with respect to unitary orbital transformations within the inactive, active and virtual orbital spaces. In contrast to most previously proposed multi-reference perturbation theories the necessary condition for a proper perturbation theory to fulfil the zeroth order perturbation equation is exactly satisfied with the RE partitioning itself without additional projectors on configurational spaces. The theory is applied to several excited states of the benchmark systems CH2 , SiH2 , and NH2 , as well as to the lowest states of the carbon, nitrogen and oxygen atoms. In all cases comparisons are made with full configuration interaction results. The multi-reference (MR)-RE method is shown to provide very rapidly converging perturbation series. Energy differences between states of similar configurations converge even faster.

Block correlated second order perturbation theory with a generalized valence bond reference function.

PubMed

Xu, Enhua; Li, Shuhua

2013-11-07

The block correlated second-order perturbation theory with a generalized valence bond (GVB) reference (GVB-BCPT2) is proposed. In this approach, each geminal in the GVB reference is considered as a "multi-orbital" block (a subset of spin orbitals), and each occupied or virtual spin orbital is also taken as a single block. The zeroth-order Hamiltonian is set to be the summation of the individual Hamiltonians of all blocks (with explicit two-electron operators within each geminal) so that the GVB reference function and all excited configuration functions are its eigenfunctions. The GVB-BCPT2 energy can be directly obtained without iteration, just like the second order Mo̸ller-Plesset perturbation method (MP2), both of which are size consistent. We have applied this GVB-BCPT2 method to investigate the equilibrium distances and spectroscopic constants of 7 diatomic molecules, conformational energy differences of 8 small molecules, and bond-breaking potential energy profiles in 3 systems. GVB-BCPT2 is demonstrated to have noticeably better performance than MP2 for systems with significant multi-reference character, and provide reasonably accurate results for some systems with large active spaces, which are beyond the capability of all CASSCF-based methods.

Regularization of the Perturbed Spatial Restricted Three-Body Problem by L-Transformations

NASA Astrophysics Data System (ADS)

Poleshchikov, S. M.

2018-03-01

Equations of motion for the perturbed circular restricted three-body problem have been regularized in canonical variables in a moving coordinate system. Two different L-matrices of the fourth order are used in the regularization. Conditions for generalized symplecticity of the constructed transform have been checked. In the unperturbed case, the regular equations have a polynomial structure. The regular equations have been numerically integrated using the Runge-Kutta-Fehlberg method. The results of numerical experiments are given for the Earth-Moon system parameters taking into account the perturbation of the Sun for different L-matrices.

Second-Order Perturbation Theory for Generalized Active Space Self-Consistent-Field Wave Functions.

PubMed

Ma, Dongxia; Li Manni, Giovanni; Olsen, Jeppe; Gagliardi, Laura

2016-07-12

A multireference second-order perturbation theory approach based on the generalized active space self-consistent-field (GASSCF) wave function is presented. Compared with the complete active space (CAS) and restricted active space (RAS) wave functions, GAS wave functions are more flexible and can employ larger active spaces and/or different truncations of the configuration interaction expansion. With GASSCF, one can explore chemical systems that are not affordable with either CASSCF or RASSCF. Perturbation theory to second order on top of GAS wave functions (GASPT2) has been implemented to recover the remaining electron correlation. The method has been benchmarked by computing the chromium dimer ground-state potential energy curve. These calculations show that GASPT2 gives results similar to CASPT2 even with a configuration interaction expansion much smaller than the corresponding CAS expansion.

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

PubMed

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, temperature of addition, or time of reaction). The model also account for changes in chemical structure (connectivity structure and/or chirality paterns in substrate, product, electrophile agent, organolithium, and ligand of the asymmetric catalyst). The second model classifies more than 150,000 cases with 85-100% of Ac, Sn, and Sp. The data contains experimental shifts in up to 18 different pharmacological parameters determined in >3000 assays of ADMET (Absorption, Distribution, Metabolism, Elimination, and Toxicity) properties and/or interactions between 31723 drugs and 100 targets (metabolizing enzymes, drug transporters, or organisms). The third model classifies more than 260,000 cases of perturbations in the self-aggregation of drugs and surfactants to form micelles with Ac, Sn, and Sp of 94-95%. The model predicts changes in 8 physicochemical and/or thermodynamics output parameters (critic micelle concentration, aggregation number, degree of ionization, surface area, enthalpy, free energy, entropy, heat capacity) of self-aggregation due to perturbations. The perturbations refers to changes in initial temperature, solvent, salt, salt concentration, solvent, and/or structure of the anion or cation of more than 150 different drugs and surfactants. QSPR-Perturbation Theory models may be useful for multi-objective optimization of organic synthesis, physicochemical properties, biological activity, metabolism, and distribution profiles towards the design of new drugs, surfactants, asymmetric ligands for catalysts, and other materials.

Newton gauge cosmological perturbations for static spherically symmetric modifications of the de Sitter metric

NASA Astrophysics Data System (ADS)

Santa Vélez, Camilo; Enea Romano, Antonio

2018-05-01

Static coordinates can be convenient to solve the vacuum Einstein's equations in presence of spherical symmetry, but for cosmological applications comoving coordinates are more suitable to describe an expanding Universe, especially in the framework of cosmological perturbation theory (CPT). Using CPT we develop a method to transform static spherically symmetric (SSS) modifications of the de Sitter solution from static coordinates to the Newton gauge. We test the method with the Schwarzschild de Sitter (SDS) metric and then derive general expressions for the Bardeen's potentials for a class of SSS metrics obtained by adding to the de Sitter metric a term linear in the mass and proportional to a general function of the radius. Using the gauge invariance of the Bardeen's potentials we then obtain a gauge invariant definition of the turn around radius. We apply the method to an SSS solution of the Brans-Dicke theory, confirming the results obtained independently by solving the perturbation equations in the Newton gauge. The Bardeen's potentials are then derived for new SSS metrics involving logarithmic, power law and exponential modifications of the de Sitter metric. We also apply the method to SSS metrics which give flat rotation curves, computing the radial energy density profile in comoving coordinates in presence of a cosmological constant.

Gravitoelectromagnetic perturbations of Kerr-Newman black holes: stability and isospectrality in the slow-rotation limit.

PubMed

Pani, Paolo; Berti, Emanuele; Gualtieri, Leonardo

2013-06-14

The most general stationary black-hole solution of Einstein-Maxwell theory in vacuum is the Kerr-Newman metric, specified by three parameters: mass M, spin J, and charge Q. Within classical general relativity, one of the most important and challenging open problems in black-hole perturbation theory is the study of gravitational and electromagnetic fields in the Kerr-Newman geometry, because of the indissoluble coupling of the perturbation functions. Here we circumvent this long-standing problem by working in the slow-rotation limit. We compute the quasinormal modes up to linear order in J for any value of Q and provide the first, fully consistent stability analysis of the Kerr-Newman metric. For scalar perturbations the quasinormal modes can be computed exactly, and we demonstrate that the method is accurate within 3% for spins J/J(max) ≲ 0.5, where J(max) is the maximum allowed spin for any value of Q. Quite remarkably, we find numerical evidence that the axial and polar sectors of the gravitoelectromagnetic perturbations are isospectral to linear order in the spin. The extension of our results to nonasymptotically flat space-times could be useful in the context of gauge-gravity dualities and string theory.

Optimal projection method determination by Logdet Divergence and perturbed von-Neumann Divergence.

PubMed

Jiang, Hao; Ching, Wai-Ki; Qiu, Yushan; Cheng, Xiao-Qing

2017-12-14

Positive semi-definiteness is a critical property in kernel methods for Support Vector Machine (SVM) by which efficient solutions can be guaranteed through convex quadratic programming. However, a lot of similarity functions in applications do not produce positive semi-definite kernels. We propose projection method by constructing projection matrix on indefinite kernels. As a generalization of the spectrum method (denoising method and flipping method), the projection method shows better or comparable performance comparing to the corresponding indefinite kernel methods on a number of real world data sets. Under the Bregman matrix divergence theory, we can find suggested optimal λ in projection method using unconstrained optimization in kernel learning. In this paper we focus on optimal λ determination, in the pursuit of precise optimal λ determination method in unconstrained optimization framework. We developed a perturbed von-Neumann divergence to measure kernel relationships. We compared optimal λ determination with Logdet Divergence and perturbed von-Neumann Divergence, aiming at finding better λ in projection method. Results on a number of real world data sets show that projection method with optimal λ by Logdet divergence demonstrate near optimal performance. And the perturbed von-Neumann Divergence can help determine a relatively better optimal projection method. Projection method ia easy to use for dealing with indefinite kernels. And the parameter embedded in the method can be determined through unconstrained optimization under Bregman matrix divergence theory. This may provide a new way in kernel SVMs for varied objectives.

Photonic Crystals from Order to Disorder: Perturbative Methods in Nanophotonics

ScienceCinema

Johnson, Steven G. [MIT, Cambridge, Massachusetts, United States

2017-12-09

Photonic crystals are periodic dielectric structures in which light can behave much differently than in a homogeneous medium. This talk gives an overview of some of the interesting properties and applications of these media, from switching in subwavelength microcavities to slow-light devices, to guiding light in air. However, some of the most interesting and challenging problems occur when the periodicity is disturbed, either by design or by inevitable fabrication imperfections. The talk focuses especially on small perturbations that have important effects, from slow-light tapers to surface roughness disorder, and will show that many classic perturbative approaches must be rethought for high-contrast nanophotonics. The combination of strong periodicity with large field discontinuities at interfaces causes standard methods to fail, but succumbs to new generalizations, while some problems remain open.

Detection and Characterization of Exoplanets using Projections on Karhunen-Loeve Eigenimages: Forward Modeling

NASA Astrophysics Data System (ADS)

Pueyo, Laurent

2016-01-01

A new class of high-contrast image analysis algorithms, that empirically fit and subtract systematic noise has lead to recent discoveries of faint exoplanet /substellar companions and scattered light images of circumstellar disks. The consensus emerging in the community is that these methods are extremely efficient at enhancing the detectability of faint astrophysical signal, but do generally create systematic biases in their observed properties. This poster provides a solution this outstanding problem. We present an analytical derivation of a linear expansion that captures the impact of astrophysical over/self-subtraction in current image analysis techniques. We examine the general case for which the reference images of the astrophysical scene moves azimuthally and/or radially across the field of view as a result of the observation strategy. Our new method method is based on perturbing the covariance matrix underlying any least-squares speckles problem and propagating this perturbation through the data analysis algorithm. This work is presented in the framework of Karhunen-Loeve Image Processing (KLIP) but it can be easily generalized to methods relying on linear combination of images (instead of eigen-modes). Based on this linear expansion, obtained in the most general case, we then demonstrate practical applications of this new algorithm. We first consider the case of the spectral extraction of faint point sources in IFS data and illustrate, using public Gemini Planet Imager commissioning data, that our novel perturbation based Forward Modeling (which we named KLIP-FM) can indeed alleviate algorithmic biases. We then apply KLIP-FM to the detection of point sources and show how it decreases the rate of false negatives while keeping the rate of false positives unchanged when compared to classical KLIP. This can potentially have important consequences on the design of follow-up strategies of ongoing direct imaging surveys.

Internal wave energy flux from density perturbations in nonlinear stratifications

NASA Astrophysics Data System (ADS)

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.

Reanalysis information for eigenvalues derived from a differential equation analysis formulation. [for shell of revolution buckling

NASA Technical Reports Server (NTRS)

Thornton, W. A.; Majumder, D. K.

1974-01-01

The investigation reported demonstrates that in the case considered perturbation methods can be used in a straightforward manner to obtain reanalysis information. A perturbation formula for the buckling loads of a general shell of revolution is derived. The accuracy of the obtained relations and their range of application is studied with the aid of a specific example involving a particular stiffened shell of revolution.

Approximation for limit cycles and their isochrons.

PubMed

Demongeot, Jacques; Françoise, Jean-Pierre

2006-12-01

Local analysis of trajectories of dynamical systems near an attractive periodic orbit displays the notion of asymptotic phase and isochrons. These notions are quite useful in applications to biosciences. In this note, we give an expression for the first approximation of equations of isochrons in the setting of perturbations of polynomial Hamiltonian systems. This method can be generalized to perturbations of systems that have a polynomial integral factor (like the Lotka-Volterra equation).

Spin-component-scaled Møller-Plesset (SCS-MP) perturbation theory: a generalization of the MP approach with improved properties.

PubMed

Fink, Reinhold F

2010-11-07

A rigorous perturbation theory is proposed, which has the same second order energy as the spin-component-scaled Møller-Plesset second order (SCS-MP2) method of Grimme [J. Chem. Phys. 118, 9095 (2003)]. This upgrades SCS-MP2 to a systematically improvable, true wave-function-based method. The perturbation theory is defined by an unperturbed Hamiltonian, Ĥ(0), that contains the ordinary Fock operator and spin operators Ŝ(2) that act either on the occupied or the virtual orbital spaces. Two choices for Ĥ(0) are discussed and the importance of a spin-pure Ĥ((0)) is underlined. Like the SCS-MP2 approach, the theory contains two parameters (c(os) and c(ss)) that scale the opposite-spin and the same-spin contributions to the second order perturbation energy. It is shown that these parameters can be determined from theoretical considerations by a Feenberg scaling approach or a fit of the wave functions from the perturbation theory to the exact one from a full configuration interaction calculation. The parameters c(os)=1.15 and c(ss)=0.75 are found to be optimal for a reasonable test set of molecules. The meaning of these parameters and the consequences following from a well defined improved MP method are discussed.

Multireference second order perturbation theory with a simplified treatment of dynamical correlation.

PubMed

Xu, Enhua; Zhao, Dongbo; Li, Shuhua

2015-10-13

A multireference second order perturbation theory based on a complete active space configuration interaction (CASCI) function or density matrix renormalized group (DMRG) function has been proposed. This method may be considered as an approximation to the CAS/A approach with the same reference, in which the dynamical correlation is simplified with blocked correlated second order perturbation theory based on the generalized valence bond (GVB) reference (GVB-BCPT2). This method, denoted as CASCI-BCPT2/GVB or DMRG-BCPT2/GVB, is size consistent and has a similar computational cost as the conventional second order perturbation theory (MP2). We have applied it to investigate a number of problems of chemical interest. These problems include bond-breaking potential energy surfaces in four molecules, the spectroscopic constants of six diatomic molecules, the reaction barrier for the automerization of cyclobutadiene, and the energy difference between the monocyclic and bicyclic forms of 2,6-pyridyne. Our test applications demonstrate that CASCI-BCPT2/GVB can provide comparable results with CASPT2 (second order perturbation theory based on the complete active space self-consistent-field wave function) for systems under study. Furthermore, the DMRG-BCPT2/GVB method is applicable to treat strongly correlated systems with large active spaces, which are beyond the capability of CASPT2.

Complete Hamiltonian analysis of cosmological perturbations at all orders II: non-canonical scalar field

DOE Office of Scientific and Technical Information (OSTI.GOV)

Nandi, Debottam; Shankaranarayanan, S., E-mail: debottam@iisertvm.ac.in, E-mail: shanki@iisertvm.ac.in

2016-10-01

In this work, we present a consistent Hamiltonian analysis of cosmological perturbations for generalized non-canonical scalar fields. In order to do so, we introduce a new phase-space variable that is uniquely defined for different non-canonical scalar fields. We also show that this is the simplest and efficient way of expressing the Hamiltonian. We extend the Hamiltonian approach of [1] to non-canonical scalar field and obtain an unique expression of speed of sound in terms of phase-space variable. In order to invert generalized phase-space Hamilton's equations to Euler-Lagrange equations of motion, we prescribe a general inversion formulae and show that ourmore » approach for non-canonical scalar field is consistent. We also obtain the third and fourth order interaction Hamiltonian for generalized non-canonical scalar fields and briefly discuss the extension of our method to generalized Galilean scalar fields.« less

A new perturbative approach to nonlinear partial differential equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bender, C.M.; Boettcher, S.; Milton, K.A.

1991-11-01

This paper shows how to solve some nonlinear wave equations as perturbation expansions in powers of a parameter that expresses the degree of nonlinearity. For the case of the Burgers equation {ital u}{sub {ital t}}+{ital uu}{sub {ital x}}={ital u}{sub {ital xx}}, the general nonlinear equation {ital u}{sub {ital t}}+{ital u}{sup {delta}}{ital u}{sub {ital x}}={ital u}{sub {ital xx}} is considered and expanded in powers of {delta}. The coefficients of the {delta} series to sixth order in powers of {delta} is determined and Pade summation is used to evaluate the perturbation series for large values of {delta}. The numerical results are accuratemore » and the method is very general; it applies to other well-studied partial differential equations such as the Korteweg--de Vries equation, {ital u}{sub {ital t}}+{ital uu}{sub {ital x}} ={ital u}{sub {ital xxx}}.« less

Resonant-state expansion for open optical systems: generalization to magnetic, chiral, and bi-anisotropic materials

NASA Astrophysics Data System (ADS)

Muljarov, E. A.; Weiss, T.

2018-05-01

The resonant-state expansion, a recently developed powerful method in electrodynamics, is generalized here for open optical systems containing magnetic, chiral, or bi-anisotropic materials. It is shown that the key matrix eigenvalue equation of the method remains the same, but the matrix elements of the perturbation now contain variations of the permittivity, permeability, and bi-anisotropy tensors. A general normalization of resonant states in terms of the electric and magnetic fields is presented.

CONTINUOUS-ENERGY MONTE CARLO METHODS FOR CALCULATING GENERALIZED RESPONSE SENSITIVITIES USING TSUNAMI-3D

DOE Office of Scientific and Technical Information (OSTI.GOV)

Perfetti, Christopher M; Rearden, Bradley T

2014-01-01

This work introduces a new approach for calculating sensitivity coefficients for generalized neutronic responses to nuclear data uncertainties using continuous-energy Monte Carlo methods. The approach presented in this paper, known as the GEAR-MC method, allows for the calculation of generalized sensitivity coefficients for multiple responses in a single Monte Carlo calculation with no nuclear data perturbations or knowledge of nuclear covariance data. The theory behind the GEAR-MC method is presented here, and proof of principle is demonstrated by using the GEAR-MC method to calculate sensitivity coefficients for responses in several 3D, continuous-energy Monte Carlo applications.

Perturbations and 3R in carbon management.

PubMed

Pant, Deepak; Sharma, Virbala; Singh, Pooja; Kumar, Manoj; Giri, Anand; Singh, M P

2017-02-01

Perturbations in various carbon pools like biological, geological, oceanic, and missing carbon sink affect its global data, which are generally neglected or ignored in routine calculations. These natural and anthropogenic events need to be considered before projecting a sustainable carbon management plan. These plans have both general and experimental aspects. General plans should focus on (a) minimizing emission; (b) maximizing environmentally sound reuse, reduce, and recycling; (c) effective treatment; and (d) converting carbon into valuable products with atom economy. Experimental carbon management plans involving various biological and chemical techniques with limitation in terms of research level and economic feasibility. Chemical options have benefits of higher productivity and wider product range, but it suffers from its higher-energy requirements and environmental unfriendliness. In contrast to this, biological options are more selective and less energy intensive, but their productivity is very low. Hence, there is a requirement of hybrid process where the benefits of both the options, i.e., biological and chemical, can be reaped. In view of above, the proposed review targets to highlight the various perturbations in the global carbon cycle and their effects; study the currently practiced options of carbon management, specifically in light of 3R principle; and propose various new hybrid methods by compatible combinations of chemical and biological processes to develop better and safer carbon management. These methods are hypothetical so they may require further research and validations but may provide a comprehensive base for developing such management methods.

Optimal guidance law development for an advanced launch system

NASA Technical Reports Server (NTRS)

Calise, Anthony J.; Hodges, Dewey H.; Leung, Martin S.; Bless, Robert R.

1991-01-01

The proposed investigation on a Matched Asymptotic Expansion (MAE) method was carried out. It was concluded that the method of MAE is not applicable to launch vehicle ascent trajectory optimization due to a lack of a suitable stretched variable. More work was done on the earlier regular perturbation approach using a piecewise analytic zeroth order solution to generate a more accurate approximation. In the meantime, a singular perturbation approach using manifold theory is also under current investigation. Work on a general computational environment based on the use of MACSYMA and the weak Hamiltonian finite element method continued during this period. This methodology is capable of the solution of a large class of optimal control problems.

Covariant extension of the GPD overlap representation at low Fock states

DOE PAGES

Chouika, N.; Mezrag, C.; Moutarde, H.; ...

2017-12-26

Here, we present a novel approach to compute generalized parton distributions within the lightfront wave function overlap framework. We show how to systematically extend generalized parton distributions computed within the DGLAP region to the ERBL one, fulfilling at the same time both the polynomiality and positivity conditions. We exemplify our method using pion lightfront wave functions inspired by recent results of non-perturbative continuum techniques and algebraic nucleon lightfront wave functions. We also test the robustness of our algorithm on reggeized phenomenological parameterizations. This approach paves the way to a better understanding of the nucleon structure from non-perturbative techniques and tomore » a unification of generalized parton distributions and transverse momentum dependent parton distribution functions phenomenology through lightfront wave functions.« less

Unified Lambert Tool for Massively Parallel Applications in Space Situational Awareness

NASA Astrophysics Data System (ADS)

Woollands, Robyn M.; Read, Julie; Hernandez, Kevin; Probe, Austin; Junkins, John L.

2018-03-01

This paper introduces a parallel-compiled tool that combines several of our recently developed methods for solving the perturbed Lambert problem using modified Chebyshev-Picard iteration. This tool (unified Lambert tool) consists of four individual algorithms, each of which is unique and better suited for solving a particular type of orbit transfer. The first is a Keplerian Lambert solver, which is used to provide a good initial guess (warm start) for solving the perturbed problem. It is also used to determine the appropriate algorithm to call for solving the perturbed problem. The arc length or true anomaly angle spanned by the transfer trajectory is the parameter that governs the automated selection of the appropriate perturbed algorithm, and is based on the respective algorithm convergence characteristics. The second algorithm solves the perturbed Lambert problem using the modified Chebyshev-Picard iteration two-point boundary value solver. This algorithm does not require a Newton-like shooting method and is the most efficient of the perturbed solvers presented herein, however the domain of convergence is limited to about a third of an orbit and is dependent on eccentricity. The third algorithm extends the domain of convergence of the modified Chebyshev-Picard iteration two-point boundary value solver to about 90% of an orbit, through regularization with the Kustaanheimo-Stiefel transformation. This is the second most efficient of the perturbed set of algorithms. The fourth algorithm uses the method of particular solutions and the modified Chebyshev-Picard iteration initial value solver for solving multiple revolution perturbed transfers. This method does require "shooting" but differs from Newton-like shooting methods in that it does not require propagation of a state transition matrix. The unified Lambert tool makes use of the General Mission Analysis Tool and we use it to compute thousands of perturbed Lambert trajectories in parallel on the Space Situational Awareness computer cluster at the LASR Lab, Texas A&M University. We demonstrate the power of our tool by solving a highly parallel example problem, that is the generation of extremal field maps for optimal spacecraft rendezvous (and eventual orbit debris removal). In addition we demonstrate the need for including perturbative effects in simulations for satellite tracking or data association. The unified Lambert tool is ideal for but not limited to space situational awareness applications.

Comparison of initial perturbation methods for the mesoscale ensemble prediction system of the Meteorological Research Institute for the WWRP Beijing 2008 Olympics Research and Development Project (B08RDP)

NASA Astrophysics Data System (ADS)

Saito, Kazuo; Hara, Masahiro; Kunii, Masaru; Seko, Hiromu; Yamaguchi, Munehiko

2011-05-01

Different initial perturbation methods for the mesoscale ensemble prediction were compared by the Meteorological Research Institute (MRI) as a part of the intercomparison of mesoscale ensemble prediction systems (EPSs) of the World Weather Research Programme (WWRP) Beijing 2008 Olympics Research and Development Project (B08RDP). Five initial perturbation methods for mesoscale ensemble prediction were developed for B08RDP and compared at MRI: (1) a downscaling method of the Japan Meteorological Agency (JMA)'s operational one-week EPS (WEP), (2) a targeted global model singular vector (GSV) method, (3) a mesoscale model singular vector (MSV) method based on the adjoint model of the JMA non-hydrostatic model (NHM), (4) a mesoscale breeding growing mode (MBD) method based on the NHM forecast and (5) a local ensemble transform (LET) method based on the local ensemble transform Kalman filter (LETKF) using NHM. These perturbation methods were applied to the preliminary experiments of the B08RDP Tier-1 mesoscale ensemble prediction with a horizontal resolution of 15 km. To make the comparison easier, the same horizontal resolution (40 km) was employed for the three mesoscale model-based initial perturbation methods (MSV, MBD and LET). The GSV method completely outperformed the WEP method, confirming the advantage of targeting in mesoscale EPS. The GSV method generally performed well with regard to root mean square errors of the ensemble mean, large growth rates of ensemble spreads throughout the 36-h forecast period, and high detection rates and high Brier skill scores (BSSs) for weak rains. On the other hand, the mesoscale model-based initial perturbation methods showed good detection rates and BSSs for intense rains. The MSV method showed a rapid growth in the ensemble spread of precipitation up to a forecast time of 6 h, which suggests suitability of the mesoscale SV for short-range EPSs, but the initial large growth of the perturbation did not last long. The performance of the MBD method was good for ensemble prediction of intense rain with a relatively small computing cost. The LET method showed similar characteristics to the MBD method, but the spread and growth rate were slightly smaller and the relative operating characteristic area skill score and BSS did not surpass those of MBD. These characteristic features of the five methods were confirmed by checking the evolution of the total energy norms and their growth rates. Characteristics of the initial perturbations obtained by four methods (GSV, MSV, MBD and LET) were examined for the case of a synoptic low-pressure system passing over eastern China. With GSV and MSV, the regions of large spread were near the low-pressure system, but with MSV, the distribution was more concentrated on the mesoscale disturbance. On the other hand, large-spread areas were observed southwest of the disturbance in MBD and LET. The horizontal pattern of LET perturbation was similar to that of MBD, but the amplitude of the LET perturbation reflected the observation density.

Systematic Expansion of Active Spaces beyond the CASSCF Limit: A GASSCF/SplitGAS Benchmark Study.

PubMed

Vogiatzis, Konstantinos D; Li Manni, Giovanni; Stoneburner, Samuel J; Ma, Dongxia; Gagliardi, Laura

2015-07-14

The applicability and accuracy of the generalized active space self-consistent field, (GASSCF), and (SplitGAS) methods are presented. The GASSCF method enables the exploration of larger active spaces than with the conventional complete active space SCF, (CASSCF), by fragmentation of a large space into subspaces and by controlling the interspace excitations. In the SplitGAS method, the GAS configuration interaction, CI, expansion is further partitioned in two parts: the principal, which includes the most important configuration state functions, and an extended, containing less relevant but not negligible ones. An effective Hamiltonian is then generated, with the extended part acting as a perturbation to the principal space. Excitation energies of ozone, furan, pyrrole, nickel dioxide, and copper tetrachloride dianion are reported. Various partitioning schemes of the GASSCF and SplitGAS CI expansions are considered and compared with the complete active space followed by second-order perturbation theory, (CASPT2), and multireference CI method, (MRCI), or available experimental data. General guidelines for the optimum applicability of these methods are discussed together with their current limitations.

Perturbation Theory for Scattering from Multilayers with Randomly Rough Fractal Interfaces: Remote Sensing Applications.

PubMed

Imperatore, Pasquale; Iodice, Antonio; Riccio, Daniele

2017-12-27

A general, approximate perturbation method, able to provide closed-form expressions of scattering from a layered structure with an arbitrary number of rough interfaces, has been recently developed. Such a method provides a unique tool for the characterization of radar response patterns of natural rough multilayers. In order to show that, here, for the first time in a journal paper, we describe the application of the developed perturbation theory to fractal interfaces; we then employ the perturbative method solution to analyze the scattering from real-world layered structures of practical interest in remote sensing applications. We focus on the dependence of normalized radar cross section on geometrical and physical properties of the considered scenarios, and we choose two classes of natural stratifications: wet paleosoil covered by a low-loss dry sand layer and a sea-ice layer above water with dry snow cover. Results are in accordance with the experimental evidence available in the literature for the low-loss dry sand layer, and they may provide useful indications about the actual ability of remote sensing instruments to perform sub-surface sensing for different sensor and scene parameters.

Perturbation Theory for Scattering from Multilayers with Randomly Rough Fractal Interfaces: Remote Sensing Applications

PubMed Central

2017-01-01

A general, approximate perturbation method, able to provide closed-form expressions of scattering from a layered structure with an arbitrary number of rough interfaces, has been recently developed. Such a method provides a unique tool for the characterization of radar response patterns of natural rough multilayers. In order to show that, here, for the first time in a journal paper, we describe the application of the developed perturbation theory to fractal interfaces; we then employ the perturbative method solution to analyze the scattering from real-world layered structures of practical interest in remote sensing applications. We focus on the dependence of normalized radar cross section on geometrical and physical properties of the considered scenarios, and we choose two classes of natural stratifications: wet paleosoil covered by a low-loss dry sand layer and a sea-ice layer above water with dry snow cover. Results are in accordance with the experimental evidence available in the literature for the low-loss dry sand layer, and they may provide useful indications about the actual ability of remote sensing instruments to perform sub-surface sensing for different sensor and scene parameters. PMID:29280979

DOE Office of Scientific and Technical Information (OSTI.GOV)

Krasnov, Kirill; Shtanov, Yuri, E-mail: kirill.krasnov@nottingham.ac.uk, E-mail: shtanov@bitp.kiev.ua

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-energymore » 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.« less

Improvement and performance evaluation of the perturbation source method for an exact Monte Carlo perturbation calculation in fixed source problems

NASA Astrophysics Data System (ADS)

Sakamoto, Hiroki; Yamamoto, Toshihiro

2017-09-01

This paper presents improvement and performance evaluation of the "perturbation source method", which is one of the Monte Carlo perturbation techniques. The formerly proposed perturbation source method was first-order accurate, although it is known that the method can be easily extended to an exact perturbation method. A transport equation for calculating an exact flux difference caused by a perturbation is solved. A perturbation particle representing a flux difference is explicitly transported in the perturbed system, instead of in the unperturbed system. The source term of the transport equation is defined by the unperturbed flux and the cross section (or optical parameter) changes. The unperturbed flux is provided by an "on-the-fly" technique during the course of the ordinary fixed source calculation for the unperturbed system. A set of perturbation particle is started at the collision point in the perturbed region and tracked until death. For a perturbation in a smaller portion of the whole domain, the efficiency of the perturbation source method can be improved by using a virtual scattering coefficient or cross section in the perturbed region, forcing collisions. Performance is evaluated by comparing the proposed method to other Monte Carlo perturbation methods. Numerical tests performed for a particle transport in a two-dimensional geometry reveal that the perturbation source method is less effective than the correlated sampling method for a perturbation in a larger portion of the whole domain. However, for a perturbation in a smaller portion, the perturbation source method outperforms the correlated sampling method. The efficiency depends strongly on the adjustment of the new virtual scattering coefficient or cross section.

A stochastic perturbation method to generate inflow turbulence in large-eddy simulation models: Application to neutrally stratified atmospheric boundary layers

DOE Office of Scientific and Technical Information (OSTI.GOV)

Muñoz-Esparza, D.; Kosović, B.; Beeck, J. van

2015-03-15

Despite the variety of existing methods, efficient generation of turbulent inflow conditions for large-eddy simulation (LES) models remains a challenging and active research area. Herein, we extend our previous research on the cell perturbation method, which uses a novel stochastic approach based upon finite amplitude perturbations of the potential temperature field applied within a region near the inflow boundaries of the LES domain [Muñoz-Esparza et al., “Bridging the transition from mesoscale to microscale turbulence in numerical weather prediction models,” Boundary-Layer Meteorol., 153, 409–440 (2014)]. The objective was twofold: (i) to identify the governing parameters of the method and their optimummore » values and (ii) to generalize the results over a broad range of atmospheric large-scale forcing conditions, U{sub g} = 5 − 25 m s{sup −1}, where U{sub g} is the geostrophic wind. We identified the perturbation Eckert number, Ec=U{sub g}{sup 2}/ρc{sub p}θ{sup ~}{sub pm}, to be the parameter governing the flow transition to turbulence in neutrally stratified boundary layers. Here, θ{sup ~}{sub pm} is the maximum perturbation amplitude applied, c{sub p} is the specific heat capacity at constant pressure, and ρ is the density. The optimal Eckert number was found for nonlinear perturbations allowed by Ec ≈ 0.16, which instigate formation of hairpin-like vortices that most rapidly transition to a developed turbulent state. Larger Ec numbers (linear small-amplitude perturbations) result in streaky structures requiring larger fetches to reach the quasi-equilibrium solution, while smaller Ec numbers lead to buoyancy dominated perturbations exhibiting difficulties for hairpin-like vortices to emerge. Cell perturbations with wavelengths within the inertial range of three-dimensional turbulence achieved identical quasi-equilibrium values of resolved turbulent kinetic energy, q, and Reynolds-shear stress, . In contrast, large-scale perturbations acting at the production range exhibited reduced levels of , due to the formation of coherent streamwise structures, while q was maintained, requiring larger fetches for the turbulent solution to stabilize. Additionally, the cell perturbation method was compared to a synthetic turbulence generator. The proposed stochastic approach provided at least the same efficiency in developing realistic turbulence, while accelerating the formation of large-scales associated with production of turbulent kinetic energy. Also, it is computationally inexpensive and does not require any turbulent information.« less

Método perturbativo aplicado a gravidade de quarta ordem e a relatividade geral corrigida pelo grupo de renormalização

NASA Astrophysics Data System (ADS)

Filho, Sebastião Mauro

2017-01-01

In this thesis we applied the perturbative method, on a classical level, to the fourth-order gravity and the Renormalization Group extended General Relativity (RGGR). We will consider auxiliary fields formulation for the general fourth-order gravity on an arbitrary curved back-ground to analyze the metric perturbations in this theory. The case of a Ricci-flat background was elaborated in detail. We noticed that the use of auxiliary fields helps to make the pertur-bative analysis easier and the results more clear. As an application we reconsider the stability problem of the Schwarzschild and Kerr black holes in the fourth-order gravity. We also used the perturbative method to develop the Newtonian and post-Newtonian limits of RGGR. In the Solar System, RGGR depends on a single dimensionless parameter 0, and this parameter is such that for 0 = 0 one fully recovers General Relativity in the Solar System. In order to study the Newtonian limit we used the conformal transformation technique and the dynamics of the Laplace-Runge-Lenz vector (LRL). In this way, we could estimate the upper bound for 0 within the Solar System in two case: the case where the external potential effect is considered and the another when it is not considered. Previously this parameter was constrained to be 0 < 10-21, without considering the external potential effect. However, as we showed, when such an effect is considered this bound increases by five orders of magnitude, O < 10-16. Moreover, we showed that under a certain approximation RGGR can be easily tested using the parametrized post-Newtonian (PPN) formalism.

Perturbed generalized multicritical one-matrix models

NASA Astrophysics Data System (ADS)

Ambjørn, J.; Chekhov, L.; Makeenko, Y.

2018-03-01

We study perturbations around the generalized Kazakov multicritical one-matrix model. The multicritical matrix model has a potential where the coefficients of zn only fall off as a power 1 /n s + 1. This implies that the potential and its derivatives have a cut along the real axis, leading to technical problems when one performs perturbations away from the generalized Kazakov model. Nevertheless it is possible to relate the perturbed partition function to the tau-function of a KdV hierarchy and solve the model by a genus expansion in the double scaling limit.

Nonlinear ideal magnetohydrodynamics instabilities

NASA Astrophysics Data System (ADS)

Pfirsch, D.; Sudan, R. N.

1993-07-01

Explosive phenomena such as internal disruptions in toroidal discharges and solar flares are difficult to explain in terms of linear instabilities. A plasma approaching a linear stability limit can, however, become nonlinearly and explosively unstable, with noninfinitesimal perturbations even before the marginal state is reached. For such investigations, a nonlinear extension of the usual MHD (magnetohydrodynamic) energy principle is helpful. (This was obtained by Merkel and Schlüter, Sitzungsberichted. Bayer. Akad. Wiss., Munich, 1976, No. 7, for Cartesian coordinate systems.) A coordinate system independent Eulerian formulation for the Lagrangian allowing for equilibria with flow and with built-in conservation laws for mass, magnetic flux, and entropy is developed in this paper which is similar to Newcomb's Lagrangian method of 1962 [Nucl. Fusion, Suppl., Pt. II, 452 (1962)]. For static equilibria nonlinear stability is completely determined by the potential energy. For a potential energy which contains second- and nth order or some more general contributions only, it is shown in full generality that linearly unstable and marginally stable systems are explosively unstable even for infinitesimal perturbations; linearly absolutely stable systems require finite initial perturbations. For equilibria with Abelian symmetries symmetry breaking initial perturbations are needed, which should be observed in numerical simulations. Nonlinear stability is proved for two simple examples, m=0 perturbations of a Bennet Z-pinch and z-independent perturbations of a θ pinch. The algebra for treating these cases reduces considerably if symmetries are taken into account from the outset, as suggested by M. N. Rosenbluth (private communication, 1992).

Predictive Sampling of Rare Conformational Events in Aqueous Solution: Designing a Generalized Orthogonal Space Tempering Method.

PubMed

Lu, Chao; Li, Xubin; Wu, Dongsheng; Zheng, Lianqing; Yang, Wei

2016-01-12

In aqueous solution, solute conformational transitions are governed by intimate interplays of the fluctuations of solute-solute, solute-water, and water-water interactions. To promote molecular fluctuations to enhance sampling of essential conformational changes, a common strategy is to construct an expanded Hamiltonian through a series of Hamiltonian perturbations and thereby broaden the distribution of certain interactions of focus. Due to a lack of active sampling of configuration response to Hamiltonian transitions, it is challenging for common expanded Hamiltonian methods to robustly explore solvent mediated rare conformational events. The orthogonal space sampling (OSS) scheme, as exemplified by the orthogonal space random walk and orthogonal space tempering methods, provides a general framework for synchronous acceleration of slow configuration responses. To more effectively sample conformational transitions in aqueous solution, in this work, we devised a generalized orthogonal space tempering (gOST) algorithm. Specifically, in the Hamiltonian perturbation part, a solvent-accessible-surface-area-dependent term is introduced to implicitly perturb near-solute water-water fluctuations; more importantly in the orthogonal space response part, the generalized force order parameter is generalized as a two-dimension order parameter set, in which essential solute-solvent and solute-solute components are separately treated. The gOST algorithm is evaluated through a molecular dynamics simulation study on the explicitly solvated deca-alanine (Ala10) peptide. On the basis of a fully automated sampling protocol, the gOST simulation enabled repetitive folding and unfolding of the solvated peptide within a single continuous trajectory and allowed for detailed constructions of Ala10 folding/unfolding free energy surfaces. The gOST result reveals that solvent cooperative fluctuations play a pivotal role in Ala10 folding/unfolding transitions. In addition, our assessment analysis suggests that because essential conformational events are mainly driven by the compensating fluctuations of essential solute-solvent and solute-solute interactions, commonly employed "predictive" sampling methods are unlikely to be effective on this seemingly "simple" system. The gOST development presented in this paper illustrates how to employ the OSS scheme for physics-based sampling method designs.

Magnetic Properties of Strongly Correlated Hubbard Model and Quantum Spin-One Ferromagnets with Arbitrary Crystal-Field Potential: Linked Cluster Series Expansion Approach

NASA Astrophysics Data System (ADS)

Pan, Kok-Kwei

We have generalized the linked cluster expansion method to solve more many-body quantum systems, such as quantum spin systems with crystal-field potentials and the Hubbard model. The technique sums up all connected diagrams to a certain order of the perturbative Hamiltonian. The modified multiple-site Wick reduction theorem and the simple tau dependence of the standard basis operators have been used to facilitate the evaluation of the integration procedures in the perturbation expansion. Computational methods are developed to calculate all terms in the series expansion. As a first example, the perturbation series expansion of thermodynamic quantities of the single-band Hubbard model has been obtained using a linked cluster series expansion technique. We have made corrections to all previous results of several papers (up to fourth order). The behaviors of the three dimensional simple cubic and body-centered cubic systems have been discussed from the qualitative analysis of the perturbation series up to fourth order. We have also calculated the sixth-order perturbation series of this model. As a second example, we present the magnetic properties of spin-one Heisenberg model with arbitrary crystal-field potential using a linked cluster series expansion. The calculation of the thermodynamic properties using this method covers the whole range of temperature, in both magnetically ordered and disordered phases. The series for the susceptibility and magnetization have been obtained up to fourth order for this model. The method sums up all perturbation terms to certain order and estimates the result using a well -developed and highly successful extrapolation method (the standard ratio method). The dependence of critical temperature on the crystal-field potential and the magnetization as a function of temperature and crystal-field potential are shown. The critical behaviors at zero temperature are also shown. The range of the crystal-field potential for Ni(2+) compounds is roughly estimated based on this model using known experimental results.

Fast determination of the spatially distributed photon fluence for light dose evaluation of PDT

NASA Astrophysics Data System (ADS)

Zhao, Kuanxin; Chen, Weiting; Li, Tongxin; Yan, Panpan; Qin, Zhuanping; Zhao, Huijuan

2018-02-01

Photodynamic therapy (PDT) has shown superiorities of noninvasiveness and high-efficiency in the treatment of early-stage skin cancer. Rapid and accurate determination of spatially distributed photon fluence in turbid tissue is essential for the dosimetry evaluation of PDT. It is generally known that photon fluence can be accurately obtained by Monte Carlo (MC) methods, while too much time would be consumed especially for complex light source mode or online real-time dosimetry evaluation of PDT. In this work, a method to rapidly calculate spatially distributed photon fluence in turbid medium is proposed implementing a classical perturbation and iteration theory on mesh Monte Carlo (MMC). In the proposed method, photon fluence can be obtained by superposing a perturbed and iterative solution caused by the defects in turbid medium to an unperturbed solution for the background medium and therefore repetitive MMC simulations can be avoided. To validate the method, a non-melanoma skin cancer model is carried out. The simulation results show the solution of photon fluence can be obtained quickly and correctly by perturbation algorithm.

Targets of drugs are generally, and targets of drugs having side effects are specifically good spreaders of human interactome perturbations.

PubMed

Perez-Lopez, Áron R; Szalay, Kristóf Z; Türei, Dénes; Módos, Dezső; Lenti, Katalin; Korcsmáros, Tamás; Csermely, Peter

2015-05-11

Network-based methods are playing an increasingly important role in drug design. Our main question in this paper was whether the efficiency of drug target proteins to spread perturbations in the human interactome is larger if the binding drugs have side effects, as compared to those which have no reported side effects. Our results showed that in general, drug targets were better spreaders of perturbations than non-target proteins, and in particular, targets of drugs with side effects were also better spreaders of perturbations than targets of drugs having no reported side effects in human protein-protein interaction networks. Colorectal cancer-related proteins were good spreaders and had a high centrality, while type 2 diabetes-related proteins showed an average spreading efficiency and had an average centrality in the human interactome. Moreover, the interactome-distance between drug targets and disease-related proteins was higher in diabetes than in colorectal cancer. Our results may help a better understanding of the network position and dynamics of drug targets and disease-related proteins, and may contribute to develop additional, network-based tests to increase the potential safety of drug candidates.

Targets of drugs are generally, and targets of drugs having side effects are specifically good spreaders of human interactome perturbations

NASA Astrophysics Data System (ADS)

Perez-Lopez, Áron R.; Szalay, Kristóf Z.; Türei, Dénes; Módos, Dezső; Lenti, Katalin; Korcsmáros, Tamás; Csermely, Peter

2015-05-01

Network-based methods are playing an increasingly important role in drug design. Our main question in this paper was whether the efficiency of drug target proteins to spread perturbations in the human interactome is larger if the binding drugs have side effects, as compared to those which have no reported side effects. Our results showed that in general, drug targets were better spreaders of perturbations than non-target proteins, and in particular, targets of drugs with side effects were also better spreaders of perturbations than targets of drugs having no reported side effects in human protein-protein interaction networks. Colorectal cancer-related proteins were good spreaders and had a high centrality, while type 2 diabetes-related proteins showed an average spreading efficiency and had an average centrality in the human interactome. Moreover, the interactome-distance between drug targets and disease-related proteins was higher in diabetes than in colorectal cancer. Our results may help a better understanding of the network position and dynamics of drug targets and disease-related proteins, and may contribute to develop additional, network-based tests to increase the potential safety of drug candidates.

Targets of drugs are generally, and targets of drugs having side effects are specifically good spreaders of human interactome perturbations

PubMed Central

Perez-Lopez, Áron R.; Szalay, Kristóf Z.; Türei, Dénes; Módos, Dezső; Lenti, Katalin; Korcsmáros, Tamás; Csermely, Peter

2015-01-01

Network-based methods are playing an increasingly important role in drug design. Our main question in this paper was whether the efficiency of drug target proteins to spread perturbations in the human interactome is larger if the binding drugs have side effects, as compared to those which have no reported side effects. Our results showed that in general, drug targets were better spreaders of perturbations than non-target proteins, and in particular, targets of drugs with side effects were also better spreaders of perturbations than targets of drugs having no reported side effects in human protein-protein interaction networks. Colorectal cancer-related proteins were good spreaders and had a high centrality, while type 2 diabetes-related proteins showed an average spreading efficiency and had an average centrality in the human interactome. Moreover, the interactome-distance between drug targets and disease-related proteins was higher in diabetes than in colorectal cancer. Our results may help a better understanding of the network position and dynamics of drug targets and disease-related proteins, and may contribute to develop additional, network-based tests to increase the potential safety of drug candidates. PMID:25960144

Covariant conserved currents for scalar-tensor Horndeski theory

NASA Astrophysics Data System (ADS)

Schmidt, J.; Bičák, J.

2018-04-01

The scalar-tensor theories have become popular recently in particular in connection with attempts to explain present accelerated expansion of the universe, but they have been considered as a natural extension of general relativity long time ago. The Horndeski scalar-tensor theory involving four invariantly defined Lagrangians is a natural choice since it implies field equations involving at most second derivatives. Following the formalisms of defining covariant global quantities and conservation laws for perturbations of spacetimes in standard general relativity, we extend these methods to the general Horndeski theory and find the covariant conserved currents for all four Lagrangians. The current is also constructed in the case of linear perturbations involving both metric and scalar fields. As a specific illustration, we derive a superpotential that leads to the covariantly conserved current in the Branse-Dicke theory.

A perturbation approach for assessing trends in precipitation extremes across Iran

NASA Astrophysics Data System (ADS)

Tabari, Hossein; AghaKouchak, Amir; Willems, Patrick

2014-11-01

Extreme precipitation events have attracted a great deal of attention among the scientific community because of their devastating consequences on human livelihood and socio-economic development. To assess changes in precipitation extremes in a given region, it is essential to analyze decadal oscillations in precipitation extremes. This study examines temporal oscillations in precipitation data in several sub-regions of Iran using a novel quantile perturbation method during 1980-2010. Precipitation data from NASA's Modern-Era Retrospective Analysis for Research and Applications-Land (MERRA-Land) are used in this study. The results indicate significant anomalies in precipitation extremes in the northwest and southeast regions of Iran. Analysis of extreme precipitation perturbations reveals that perturbations for the monthly aggregation level are generally lower than the annual perturbations. Furthermore, high-oscillation and low-oscillation periods are found in extreme precipitation quantiles across different seasons. In all selected regions, a significant anomaly (i.e., extreme wet/dry conditions) in precipitation extremes is observed during spring.

Perturbation biology nominates upstream-downstream drug combinations in RAF inhibitor resistant melanoma cells.

PubMed

Korkut, Anil; Wang, Weiqing; Demir, Emek; Aksoy, Bülent Arman; Jing, Xiaohong; Molinelli, Evan J; Babur, Özgün; Bemis, Debra L; Onur Sumer, Selcuk; Solit, David B; Pratilas, Christine A; Sander, Chris

2015-08-18

Resistance to targeted cancer therapies is an important clinical problem. The discovery of anti-resistance drug combinations is challenging as resistance can arise by diverse escape mechanisms. To address this challenge, we improved and applied the experimental-computational perturbation biology method. Using statistical inference, we build network models from high-throughput measurements of molecular and phenotypic responses to combinatorial targeted perturbations. The models are computationally executed to predict the effects of thousands of untested perturbations. In RAF-inhibitor resistant melanoma cells, we measured 143 proteomic/phenotypic entities under 89 perturbation conditions and predicted c-Myc as an effective therapeutic co-target with BRAF or MEK. Experiments using the BET bromodomain inhibitor JQ1 affecting the level of c-Myc protein and protein kinase inhibitors targeting the ERK pathway confirmed the prediction. In conclusion, we propose an anti-cancer strategy of co-targeting a specific upstream alteration and a general downstream point of vulnerability to prevent or overcome resistance to targeted drugs.

A purely Lagrangian method for computing linearly-perturbed flows in spherical geometry

NASA Astrophysics Data System (ADS)

Jaouen, Stéphane

2007-07-01

In many physical applications, one wishes to control the development of multi-dimensional instabilities around a one-dimensional (1D) complex flow. For predicting the growth rates of these perturbations, a general numerical approach is viable which consists in solving simultaneously the one-dimensional equations and their linearized form for three-dimensional perturbations. In Clarisse et al. [J.-M. Clarisse, S. Jaouen, P.-A. Raviart, A Godunov-type method in Lagrangian coordinates for computing linearly-perturbed planar-symmetric flows of gas dynamics, J. Comp. Phys. 198 (2004) 80-105], a class of Godunov-type schemes for planar-symmetric flows of gas dynamics has been proposed. Pursuing this effort, we extend these results to spherically symmetric flows. A new method to derive the Lagrangian perturbation equations, based on the canonical form of systems of conservation laws with zero entropy flux [B. Després, Lagrangian systems of conservation laws. Invariance properties of Lagrangian systems of conservation laws, approximate Riemann solvers and the entropy condition, Numer. Math. 89 (2001) 99-134; B. Després, C. Mazeran, Lagrangian gas dynamics in two dimensions and Lagrangian systems, Arch. Rational Mech. Anal. 178 (2005) 327-372] is also described. It leads to many advantages. First of all, many physical problems we are interested in enter this formalism (gas dynamics, two-temperature plasma equations, ideal magnetohydrodynamics, etc.) whatever is the geometry. Secondly, a class of numerical entropic schemes is available for the basic flow [11]. Last, linearizing and devising numerical schemes for the perturbed flow is straightforward. The numerical capabilities of these methods are illustrated on three test cases of increasing difficulties and we show that - due to its simplicity and its low computational cost - the Linear Perturbations Code (LPC) is a powerful tool to understand and predict the development of hydrodynamic instabilities in the linear regime.

Tensor renormalization group methods for spin and gauge models

NASA Astrophysics Data System (ADS)

Zou, Haiyuan

The analysis of the error of perturbative series by comparing it to the exact solution is an important tool to understand the non-perturbative physics of statistical models. For some toy models, a new method can be used to calculate higher order weak coupling expansion and modified perturbation theory can be constructed. However, it is nontrivial to generalize the new method to understand the critical behavior of high dimensional spin and gauge models. Actually, it is a big challenge in both high energy physics and condensed matter physics to develop accurate and efficient numerical algorithms to solve these problems. In this thesis, one systematic way named tensor renormalization group method is discussed. The applications of the method to several spin and gauge models on a lattice are investigated. theoretically, the new method allows one to write an exact representation of the partition function of models with local interactions. E.g. O(N) models, Z2 gauge models and U(1) gauge models. Practically, by using controllable approximations, results in both finite volume and the thermodynamic limit can be obtained. Another advantage of the new method is that it is insensitive to sign problems for models with complex coupling and chemical potential. Through the new approach, the Fisher's zeros of the 2D O(2) model in the complex coupling plane can be calculated and the finite size scaling of the results agrees well with the Kosterlitz-Thouless assumption. Applying the method to the O(2) model with a chemical potential, new phase diagram of the models can be obtained. The structure of the tensor language may provide a new tool to understand phase transition properties in general.

Perturbed invariant subspaces and approximate generalized functional variable separation solution for nonlinear diffusion-convection equations with weak source

NASA Astrophysics Data System (ADS)

Xia, Ya-Rong; Zhang, Shun-Li; Xin, Xiang-Peng

2018-03-01

In this paper, we propose the concept of the perturbed invariant subspaces (PISs), and study the approximate generalized functional variable separation solution for the nonlinear diffusion-convection equation with weak source by the approximate generalized conditional symmetries (AGCSs) related to the PISs. Complete classification of the perturbed equations which admit the approximate generalized functional separable solutions (AGFSSs) is obtained. As a consequence, some AGFSSs to the resulting equations are explicitly constructed by way of examples.

Lagrangian theory of structure formation in relativistic cosmology. IV. Lagrangian approach to gravitational waves

NASA Astrophysics Data System (ADS)

Al Roumi, Fosca; Buchert, Thomas; Wiegand, Alexander

2017-12-01

The relativistic generalization of the Newtonian Lagrangian perturbation theory is investigated. In previous works, the perturbation and solution schemes that are generated by the spatially projected gravitoelectric part of the Weyl tensor were given to any order of the perturbations, together with extensions and applications for accessing the nonperturbative regime. We here discuss more in detail the general first-order scheme within the Cartan formalism including and concentrating on the gravitational wave propagation in matter. We provide master equations for all parts of Lagrangian-linearized perturbations propagating in the perturbed spacetime, and we outline the solution procedure that allows one to find general solutions. Particular emphasis is given to global properties of the Lagrangian perturbation fields by employing results of Hodge-de Rham theory. We here discuss how the Hodge decomposition relates to the standard scalar-vector-tensor decomposition. Finally, we demonstrate that we obtain the known linear perturbation solutions of the standard relativistic perturbation scheme by performing two steps: first, by restricting our solutions to perturbations that propagate on a flat unperturbed background spacetime and, second, by transforming to Eulerian background coordinates with truncation of nonlinear terms.

A Scenario-Based Parametric Analysis of Stable Marriage Approaches to the Army Officer Assignment Problem

DTIC Science & Technology

2017-03-23

solutions obtained through their proposed method to comparative instances of a generalized assignment problem with either ordinal cost components or... method flag: Designates the method by which the changed/ new assignment problem instance is solved. methodFlag = 0:SMAWarmstart Returns a matching...of randomized perturbations. We examine the contrasts between these methods in the context of assigning Army Officers among a set of identified

Symbolic derivation of high-order Rayleigh-Schroedinger perturbation energies using computer algebra: Application to vibrational-rotational analysis of diatomic molecules

DOE Office of Scientific and Technical Information (OSTI.GOV)

Herbert, John M.

1997-01-01

Rayleigh-Schroedinger perturbation theory is an effective and popular tool for describing low-lying vibrational and rotational states of molecules. This method, in conjunction with ab initio techniques for computation of electronic potential energy surfaces, can be used to calculate first-principles molecular vibrational-rotational energies to successive orders of approximation. Because of mathematical complexities, however, such perturbation calculations are rarely extended beyond the second order of approximation, although recent work by Herbert has provided a formula for the nth-order energy correction. This report extends that work and furnishes the remaining theoretical details (including a general formula for the Rayleigh-Schroedinger expansion coefficients) necessary formore » calculation of energy corrections to arbitrary order. The commercial computer algebra software Mathematica is employed to perform the prohibitively tedious symbolic manipulations necessary for derivation of generalized energy formulae in terms of universal constants, molecular constants, and quantum numbers. As a pedagogical example, a Hamiltonian operator tailored specifically to diatomic molecules is derived, and the perturbation formulae obtained from this Hamiltonian are evaluated for a number of such molecules. This work provides a foundation for future analyses of polyatomic molecules, since it demonstrates that arbitrary-order perturbation theory can successfully be applied with the aid of commercially available computer algebra software.« less

Degree of Approximation by a General Cλ -Summability Method

NASA Astrophysics Data System (ADS)

Sonker, S.; Munjal, A.

2018-03-01

In the present study, two theorems explaining the degree of approximation of signals belonging to the class Lip(α, p, w) by a more general C λ -method (Summability method) have been formulated. Improved estimations have been observed in terms of λ(n) where (λ(n))‑α ≤ n ‑α for 0 < α ≤ 1 as compared to previous studies presented in terms of n. These estimations of infinite matrices are very much applicable in solid state physics which further motivates for an investigation of perturbations of matrix valued functions.

Primal-dual methods of shape sensitivity analysis for curvilinear cracks with nonpenetration

NASA Astrophysics Data System (ADS)

Kovtunenko, V. A.

2006-10-01

Based on a level-set description of a crack moving with a given velocity, the problem of shape perturb-ation of the crack is considered. Nonpenetration conditions are imposed between opposite crack surfaces which result in a constrained minimization problem describing equilibrium of a solid with the crack. We suggest a minimax formulation of the state problem thus allowing curvilinear (nonplanar) cracks for the consideration. Utilizing primal-dual methods of shape sensitivity analysis we obtain the general formula for a shape derivative of the potential energy, which describes an energy-release rate for the curvilinear cracks. The conditions sufficient to rewrite it in the form of a path-independent integral (J-integral) are derived.

Development and evaluation of a hybrid averaged orbit generator

NASA Technical Reports Server (NTRS)

Mcclain, W. D.; Long, A. C.; Early, L. W.

1978-01-01

A rapid orbit generator based on a first-order application of the Generalized Method of Averaging has been developed for the Research and Development (R&D) version of the Goddard Trajectory Determination System (GTDS). The evaluation of the averaged equations of motion can use both numerically averaged and recursively evaluated, analytically averaged perturbation models. These equations are numerically integrated to obtain the secular and long-period motion. Factors affecting efficient orbit prediction are discussed and guidelines are presented for treatment of each major perturbation. Guidelines for obtaining initial mean elements compatible with the theory are presented. An overview of the orbit generator is presented and comparisons with high precision methods are given.

Perturbation theory for cosmologies with nonlinear structure

NASA Astrophysics Data System (ADS)

Goldberg, Sophia R.; Gallagher, Christopher S.; Clifton, Timothy

2017-11-01

The next generation of cosmological surveys will operate over unprecedented scales, and will therefore provide exciting new opportunities for testing general relativity. The standard method for modelling the structures that these surveys will observe is to use cosmological perturbation theory for linear structures on horizon-sized scales, and Newtonian gravity for nonlinear structures on much smaller scales. We propose a two-parameter formalism that generalizes this approach, thereby allowing interactions between large and small scales to be studied in a self-consistent and well-defined way. This uses both post-Newtonian gravity and cosmological perturbation theory, and can be used to model realistic cosmological scenarios including matter, radiation and a cosmological constant. We find that the resulting field equations can be written as a hierarchical set of perturbation equations. At leading-order, these equations allow us to recover a standard set of Friedmann equations, as well as a Newton-Poisson equation for the inhomogeneous part of the Newtonian energy density in an expanding background. For the perturbations in the large-scale cosmology, however, we find that the field equations are sourced by both nonlinear and mode-mixing terms, due to the existence of small-scale structures. These extra terms should be expected to give rise to new gravitational effects, through the mixing of gravitational modes on small and large scales—effects that are beyond the scope of standard linear cosmological perturbation theory. We expect our formalism to be useful for accurately modeling gravitational physics in universes that contain nonlinear structures, and for investigating the effects of nonlinear gravity in the era of ultra-large-scale surveys.

Nonlinear ideal magnetohydrodynamics instabilities

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pfirsch, D.; Sudan, R.N.

1993-07-01

Explosive phenomena such as internal disruptions in toroidal discharges and solar flares are difficult to explain in terms of linear instabilities. A plasma approaching a linear stability limit can, however, become nonlinearly and explosively unstable, with noninfinitesimal perturbations even before the marginal state is reached. For such investigations, a nonlinear extension of the usual MHD (magnetohydrodynamic) energy principle is helpful. (This was obtained by Merkel and Schlueter, Sitzungsberichted. Bayer. Akad. Wiss., Munich, 1976, No. 7, for Cartesian coordinate systems.) A coordinate system independent Eulerian formulation for the Lagrangian allowing for equilibria with flow and with built-in conservation laws for mass,more » magnetic flux, and entropy is developed in this paper which is similar to Newcomb's Lagrangian method of 1962 [Nucl. Fusion, Suppl., Pt. II, 452 (1962)]. For static equilibria nonlinear stability is completely determined by the potential energy. For a potential energy which contains second- and [ital n]th order or some more general contributions only, it is shown in full generality that linearly unstable and marginally stable systems are explosively unstable even for infinitesimal perturbations; linearly absolutely stable systems require finite initial perturbations. For equilibria with Abelian symmetries symmetry breaking initial perturbations are needed, which should be observed in numerical simulations. Nonlinear stability is proved for two simple examples, [ital m]=0 perturbations of a Bennet Z-pinch and [ital z]-independent perturbations of a [theta] pinch. The algebra for treating these cases reduces considerably if symmetries are taken into account from the outset, as suggested by M. N. Rosenbluth (private communication, 1992).« less

On the initial conditions of scalar and tensor fluctuations in f(R,φ ) gravity

NASA Astrophysics Data System (ADS)

Cheraghchi, S.; Shojai, F.

2018-05-01

We have considered the perturbation equations governing the growth of fluctuations during inflation in generalized scalar tensor theory f(R,φ ). We have found that the scalar metric perturbations at very early times are negligible compared to the scalar field perturbation, just like general relativity. At sufficiently early times, when the physical momentum of perturbation mode, q / a is much larger than the Hubble parameter H, i.e. q/a≫ H, we have obtained the metric and scalar field perturbation in the form of WKB solutions up to an undetermined coefficient. Then we have quantized the scalar fluctuations and expanded the metric and the scalar field perturbations with the help of annihilation and creation operators of the scalar field perturbation. The standard commutation relations of annihilation and creation operators fix the unknown coefficient. Going over to the gauge invariant quantities which are conserved beyond the horizon, we have obtained the initial condition of the generalized Mukhanov-Sasaki equation. Then a similar procedure is performed for the case of tensor metric perturbation. As an example of the generalized Mukhanov-Sasaki equation and its initial condition, we have proposed a power-law functional form as f(R,φ )=f_0 R^m φ ^n and obtained an exact inflationary solution. In this background, then we have discussed how the scalar and tensor fluctuations grow.

Non-perturbative background field calculations

NASA Astrophysics Data System (ADS)

Stephens, C. R.

1988-01-01

New methods are developed for calculating one loop functional determinants in quantum field theory. Instead of relying on a calculation of all the eigenvalues of the small fluctuation equation, these techniques exploit the ability of the proper time formalism to reformulate an infinite dimensional field theoretic problem into a finite dimensional covariant quantum mechanical analog, thereby allowing powerful tools such as the method of Jacobi fields to be used advantageously in a field theory setting. More generally the methods developed herein should be extremely valuable when calculating quantum processes in non-constant background fields, offering a utilitarian alternative to the two standard methods of calculation—perturbation theory in the background field or taking the background field into account exactly. The formalism developed also allows for the approximate calculation of covariances of partial differential equations from a knowledge of the solutions of a homogeneous ordinary differential equation.

Engineering calculations for communications satellite systems planning

NASA Technical Reports Server (NTRS)

Walton, E.; Aebker, E.; Mata, F.; Reilly, C.

1991-01-01

The final phase of a satellite synthesis project is described. Several methods for generating satellite positionings with improved aggregate carrier to interference characteristics were studied. Two general methods for modifying required separation values are presented. Also, two methods for improving aggregate carrier to interference (C/I) performance of given satellite synthesis solutions are presented. A perturbation of the World Administrative Radio Conference (WARC) synthesis is presented.

A general mass term for bigravity

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cusin, Giulia; Durrer, Ruth; Guarato, Pietro

2016-04-01

We introduce a new formalism to study perturbations of Hassan-Rosen bigravity theory, around general backgrounds for the two dynamical metrics. In particular, we derive the general expression for the mass term of the perturbations and we explicitly compute it for cosmological settings. We study tensor perturbations in a specific branch of bigravity using this formalism. We show that the tensor sector is affected by a late-time instability, which sets in when the mass matrix is no longer positive definite.

Partitioning technique for open systems

NASA Astrophysics Data System (ADS)

Brändas, Erkki J.

2010-11-01

The focus of the present contribution is essentially confined to three research areas carried out during the author's turns as visiting (assistant, associate and full) professor at the University of Florida's Quantum Theory Project, QTP. The first two topics relate to perturbation theory and spectral theory for self-adjoint operators in Hilbert space. The third subject concerns analytic extensions to non-self-adjoint problems, where particular consequences of the occurrence of continuous energy spectra are measured. In these studies general partitioning methods serve as general cover for perturbation-, variational- and general matrix theory. In addition we follow up associated inferences for the time dependent problem as well as recent results and conclusions of a rather general yet surprising character. Although the author spent most of his times at QTP during visits in the 1970s and 1980s, collaborations with department members and shorter stays continued through later decades. Nevertheless the impact must be somewhat fragmentary, yet it is hoped that the present account is sufficiently self-contained to be realistic and constructive.

High-order perturbations of a spherical collapsing star

DOE Office of Scientific and Technical Information (OSTI.GOV)

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

2010-11-15

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.more » 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.« less

Approximate non-linear multiparameter inversion for multicomponent single and double P-wave scattering in isotropic elastic media

NASA Astrophysics Data System (ADS)

Ouyang, Wei; Mao, Weijian

2018-03-01

An asymptotic quadratic true-amplitude inversion method for isotropic elastic P waves is proposed to invert medium parameters. The multicomponent P-wave scattered wavefield is computed based on a forward relationship using second-order Born approximation and corresponding high-frequency ray theoretical methods. Within the local double scattering mechanism, the P-wave transmission factors are elaborately calculated, which results in the radiation pattern for P-waves scattering being a quadratic combination of the density and Lamé's moduli perturbation parameters. We further express the elastic P-wave scattered wavefield in a form of generalized Radon transform (GRT). After introducing classical backprojection operators, we obtain an approximate solution of the inverse problem by solving a quadratic non-linear system. Numerical tests with synthetic data computed by finite-differences scheme demonstrate that our quadratic inversion can accurately invert perturbation parameters for strong perturbations, compared with the P-wave single-scattering linear inversion method. Although our inversion strategy here is only syncretized with P-wave scattering, it can be extended to invert multicomponent elastic data containing both P-wave and S-wave information.

Approximate nonlinear multiparameter inversion for multicomponent single and double P-wave scattering in isotropic elastic media

NASA Astrophysics Data System (ADS)

Ouyang, Wei; Mao, Weijian

2018-07-01

An asymptotic quadratic true-amplitude inversion method for isotropic elastic P waves is proposed to invert medium parameters. The multicomponent P-wave scattered wavefield is computed based on a forward relationship using second-order Born approximation and corresponding high-frequency ray theoretical methods. Within the local double scattering mechanism, the P-wave transmission factors are elaborately calculated, which results in the radiation pattern for P-wave scattering being a quadratic combination of the density and Lamé's moduli perturbation parameters. We further express the elastic P-wave scattered wavefield in a form of generalized Radon transform. After introducing classical backprojection operators, we obtain an approximate solution of the inverse problem by solving a quadratic nonlinear system. Numerical tests with synthetic data computed by finite-differences scheme demonstrate that our quadratic inversion can accurately invert perturbation parameters for strong perturbations, compared with the P-wave single-scattering linear inversion method. Although our inversion strategy here is only syncretized with P-wave scattering, it can be extended to invert multicomponent elastic data containing both P- and S-wave information.

Extended multi-configuration quasi-degenerate perturbation theory: the new approach to multi-state multi-reference perturbation theory.

PubMed

Granovsky, Alexander A

2011-06-07

The distinctive desirable features, both mathematically and physically meaningful, for all partially contracted multi-state multi-reference perturbation theories (MS-MR-PT) are explicitly formulated. The original approach to MS-MR-PT theory, called extended multi-configuration quasi-degenerate perturbation theory (XMCQDPT), having most, if not all, of the desirable properties is introduced. The new method is applied at the second order of perturbation theory (XMCQDPT2) to the 1(1)A(')-2(1)A(') conical intersection in allene molecule, the avoided crossing in LiF molecule, and the 1(1)A(1) to 2(1)A(1) electronic transition in cis-1,3-butadiene. The new theory has several advantages compared to those of well-established approaches, such as second order multi-configuration quasi-degenerate perturbation theory and multi-state-second order complete active space perturbation theory. The analysis of the prevalent approaches to the MS-MR-PT theory performed within the framework of the XMCQDPT theory unveils the origin of their common inherent problems. We describe the efficient implementation strategy that makes XMCQDPT2 an especially useful general-purpose tool in the high-level modeling of small to large molecular systems. © 2011 American Institute of Physics

Perturbation biology nominates upstream–downstream drug combinations in RAF inhibitor resistant melanoma cells

PubMed Central

Korkut, Anil; Wang, Weiqing; Demir, Emek; Aksoy, Bülent Arman; Jing, Xiaohong; Molinelli, Evan J; Babur, Özgün; Bemis, Debra L; Onur Sumer, Selcuk; Solit, David B; Pratilas, Christine A; Sander, Chris

2015-01-01

Resistance to targeted cancer therapies is an important clinical problem. The discovery of anti-resistance drug combinations is challenging as resistance can arise by diverse escape mechanisms. To address this challenge, we improved and applied the experimental-computational perturbation biology method. Using statistical inference, we build network models from high-throughput measurements of molecular and phenotypic responses to combinatorial targeted perturbations. The models are computationally executed to predict the effects of thousands of untested perturbations. In RAF-inhibitor resistant melanoma cells, we measured 143 proteomic/phenotypic entities under 89 perturbation conditions and predicted c-Myc as an effective therapeutic co-target with BRAF or MEK. Experiments using the BET bromodomain inhibitor JQ1 affecting the level of c-Myc protein and protein kinase inhibitors targeting the ERK pathway confirmed the prediction. In conclusion, we propose an anti-cancer strategy of co-targeting a specific upstream alteration and a general downstream point of vulnerability to prevent or overcome resistance to targeted drugs. DOI: http://dx.doi.org/10.7554/eLife.04640.001 PMID:26284497

Quasi-degenerate perturbation theory using matrix product states

NASA Astrophysics Data System (ADS)

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.

Application of hard sphere perturbation theory for thermodynamics of model liquid metals

NASA Astrophysics Data System (ADS)

Mon, K. K.

2001-06-01

Hard sphere perturbation theory (HSPT) has contributed toward the fundamental understanding of dense fluids for over 30 years. In recent decades, other techniques have been more popular. In this paper, we argue for the revival of hard sphere perturbation theory for the study of thermodynamics of dense liquid in general, and in liquid metal in particular. The weakness of HSPT is now well understood, and can be easily overcome by using a simple convenient Monte Carlo method to calculate the intrinsic error of HSPT free energy density. To demonstrate this approach, we consider models of liquid aluminum and sodium. We obtain the intrinsic error of HSPT with the Monte Carlo method. HSPT is shown to provide a lower free energy upper bound than one-component plasma (OCP) for alkali metals and polyvalent metals. We are thus able to provide insight into the long standing observation that a OCP is a better reference system than a HS for alkali metals.

Bifurcation-based approach reveals synergism and optimal combinatorial perturbation.

PubMed

Liu, Yanwei; Li, Shanshan; Liu, Zengrong; Wang, Ruiqi

2016-06-01

Cells accomplish the process of fate decisions and form terminal lineages through a series of binary choices in which cells switch stable states from one branch to another as the interacting strengths of regulatory factors continuously vary. Various combinatorial effects may occur because almost all regulatory processes are managed in a combinatorial fashion. Combinatorial regulation is crucial for cell fate decisions because it may effectively integrate many different signaling pathways to meet the higher regulation demand during cell development. However, whether the contribution of combinatorial regulation to the state transition is better than that of a single one and if so, what the optimal combination strategy is, seem to be significant issue from the point of view of both biology and mathematics. Using the approaches of combinatorial perturbations and bifurcation analysis, we provide a general framework for the quantitative analysis of synergism in molecular networks. Different from the known methods, the bifurcation-based approach depends only on stable state responses to stimuli because the state transition induced by combinatorial perturbations occurs between stable states. More importantly, an optimal combinatorial perturbation strategy can be determined by investigating the relationship between the bifurcation curve of a synergistic perturbation pair and the level set of a specific objective function. The approach is applied to two models, i.e., a theoretical multistable decision model and a biologically realistic CREB model, to show its validity, although the approach holds for a general class of biological systems.

Comment on ``Alternative approach to the solution of the dispersion relation for a generalized lattice Boltzmann equation''

NASA Astrophysics Data System (ADS)

Lallemand, Pierre; Luo, Li-Shi

2008-12-01

Recently Reis and Phillips [Phys. Rev. E 77, 026702 (2008)] proposed a perturbative method to solve the dispersion equation derived from the linearized lattice Boltzmann equation. We will demonstrate that the method proposed by Reis and Phillips is a reinvention of an existing method. We would also like to refute a number of claims made by Reis and Phillips.

Performance and Self-Consistency of the Generalized Dielectric Dependent Hybrid Functional

DOE Office of Scientific and Technical Information (OSTI.GOV)

Brawand, Nicholas P.; Govoni, Marco; Vörös, Márton

Here, we analyze the performance of the recently proposed screened exchange constant functional (SX) on the GW100 test set, and we discuss results obtained at different levels of self-consistency. The SX functional is a generalization of dielectric dependent hybrid functionals to finite systems; it is nonempirical and depends on the average screening of the exchange interaction. We compare results for ionization potentials obtained with SX to those of CCSD(T) calculations and experiments, and we find excellent agreement, on par with recent state of the art methods based on many body perturbation theory. Applying SX perturbatively to correct PBE eigenvalues yieldsmore » improved results in most cases, except for ionic molecules, for which wave function self-consistency is instead crucial. Calculations where wave functions and the screened exchange constant (α SX) are determined self-consistently, and those where α SX is fixed to the value determined within PBE, yield results of comparable accuracy. Perturbative G 0W 0 corrections of eigenvalues obtained with self-consistent αSX are small on average, for all molecules in the GW100 test set.« less

Performance and Self-Consistency of the Generalized Dielectric Dependent Hybrid Functional

DOE PAGES

Brawand, Nicholas P.; Govoni, Marco; Vörös, Márton; ...

2017-05-24

Here, we analyze the performance of the recently proposed screened exchange constant functional (SX) on the GW100 test set, and we discuss results obtained at different levels of self-consistency. The SX functional is a generalization of dielectric dependent hybrid functionals to finite systems; it is nonempirical and depends on the average screening of the exchange interaction. We compare results for ionization potentials obtained with SX to those of CCSD(T) calculations and experiments, and we find excellent agreement, on par with recent state of the art methods based on many body perturbation theory. Applying SX perturbatively to correct PBE eigenvalues yieldsmore » improved results in most cases, except for ionic molecules, for which wave function self-consistency is instead crucial. Calculations where wave functions and the screened exchange constant (α SX) are determined self-consistently, and those where α SX is fixed to the value determined within PBE, yield results of comparable accuracy. Perturbative G 0W 0 corrections of eigenvalues obtained with self-consistent αSX are small on average, for all molecules in the GW100 test set.« less

Two-photon processes based on quantum commutators

NASA Astrophysics Data System (ADS)

Fratini, F.; Safari, L.; Amaro, P.; Santos, J. P.

2018-04-01

We developed a method to calculate two-photon processes in quantum mechanics that replaces the infinite summation over the intermediate states by a perturbation expansion. This latter consists of a series of commutators that involve position, momentum, and Hamiltonian quantum operators. We analyzed several single- and many-particle cases for which a closed-form solution to the perturbation expansion exists, as well as more complicated cases for which a solution is found by convergence. Throughout the article, Rayleigh and Raman scattering are taken as examples of two-photon processes. The present method provides a clear distinction between the Thomson scattering, regarded as classical scattering, and quantum contributions. Such a distinction lets us derive general results concerning light scattering. Finally, possible extensions to the developed formalism are discussed.

Performance prediction of electrohydrodynamic thrusters by the perturbation method

DOE Office of Scientific and Technical Information (OSTI.GOV)

Shibata, H., E-mail: shibata@daedalus.k.u-tokyo.ac.jp; Watanabe, Y.; Suzuki, K.

2016-05-15

In this paper, we present a novel method for analyzing electrohydrodynamic (EHD) thrusters. The method is based on a perturbation technique applied to a set of drift-diffusion equations, similar to the one introduced in our previous study on estimating breakdown voltage. The thrust-to-current ratio is generalized to represent the performance of EHD thrusters. We have compared the thrust-to-current ratio obtained theoretically with that obtained from the proposed method under atmospheric air conditions, and we have obtained good quantitative agreement. Also, we have conducted a numerical simulation in more complex thruster geometries, such as the dual-stage thruster developed by Masuyama andmore » Barrett [Proc. R. Soc. A 469, 20120623 (2013)]. We quantitatively clarify the fact that if the magnitude of a third electrode voltage is low, the effective gap distance shortens, whereas if the magnitude of the third electrode voltage is sufficiently high, the effective gap distance lengthens.« less

A hybrid-perturbation-Galerkin technique which combines multiple expansions

NASA Technical Reports Server (NTRS)

Geer, James F.; Andersen, Carl M.

1989-01-01

A two-step hybrid perturbation-Galerkin method for the solution of a variety of differential equations type problems is found to give better results when multiple perturbation expansions are employed. The method assumes that there is parameter in the problem formulation and that a perturbation method can be sued to construct one or more expansions in this perturbation coefficient functions multiplied by computed amplitudes. In step one, regular and/or singular perturbation methods are used to determine the perturbation coefficient functions. The results of step one are in the form of one or more expansions each expressed as a sum of perturbation coefficient functions multiplied by a priori known gauge functions. In step two the classical Bubnov-Galerkin method uses the perturbation coefficient functions computed in step one to determine a set of amplitudes which replace and improve upon the gauge functions. The hybrid method has the potential of overcoming some of the drawbacks of the perturbation and Galerkin methods as applied separately, while combining some of their better features. The proposed method is applied, with two perturbation expansions in each case, to a variety of model ordinary differential equations problems including: a family of linear two-boundary-value problems, a nonlinear two-point boundary-value problem, a quantum mechanical eigenvalue problem and a nonlinear free oscillation problem. The results obtained from the hybrid methods are compared with approximate solutions obtained by other methods, and the applicability of the hybrid method to broader problem areas is discussed.

Generalization and Parallelization of Messy Genetic Algorithms and Communication in Parallel Genetic Algorithms.

DTIC Science & Technology

1992-12-01

Dynamics and Free Energy Perturbation Methods." Reviews in Computational Chem- istry edited by Kenny B. Lipkowitz and Donald B. Boyd, chapter 8, 295-320...atomic motions during annealing, allows the search to probabilistically move in a locally non-optimal direction. The probability of doing so is...Network processors communicate via communication links. This type of communication is generally very slow relative to other processor activities

Interlaminar stresses in composite laminates: A perturbation analysis

NASA Technical Reports Server (NTRS)

Hsu, P. W.; Herakovich, C. T.

1976-01-01

A general method of solution for an elastic balanced symmetric composite laminate subject to a uniaxial extension was developed based upon a perturbation analysis of a limiting free body containing an interfacial plane. The solution satisfies more physical requirements and boundary conditions than previous investigations, and predicts smooth continuous interlaminar stresses with no instabilities. It determines the finite maximum intensity for the interlaminar normal stress in all laminates, provides mathematical evidences for the singular stresses in angle-ply laminates, suggests the need for the experimental determination of an important problem parameter, and introduces a viable means for solving related problems of practical interest.

Collapse of ultrashort spatiotemporal pulses described by the cubic generalized Kadomtsev-Petviashvili equation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Leblond, Herve; Kremer, David; Mihalache, Dumitru

2010-03-15

By using a reductive perturbation method, we derive from Maxwell-Bloch equations a cubic generalized Kadomtsev-Petviashvili equation for ultrashort spatiotemporal optical pulse propagation in cubic (Kerr-like) media without the use of the slowly varying envelope approximation. We calculate the collapse threshold for the propagation of few-cycle spatiotemporal pulses described by the generic cubic generalized Kadomtsev-Petviashvili equation by a direct numerical method and compare it to analytic results based on a rigorous virial theorem. Besides, typical evolution of the spectrum (integrated over the transverse spatial coordinate) is given and a strongly asymmetric spectral broadening of ultrashort spatiotemporal pulses during collapse is evidenced.

Hydrodynamic representation of the Klein-Gordon-Einstein equations in the weak field limit: General formalism and perturbations analysis

NASA Astrophysics Data System (ADS)

Suárez, Abril; Chavanis, Pierre-Henri

2015-07-01

Using a generalization of the Madelung transformation, we derive the hydrodynamic representation of the Klein-Gordon-Einstein equations in the weak field limit. We consider a complex self-interacting scalar field with a λ |φ |4 potential. We study the evolution of the spatially homogeneous background in the fluid representation and derive the linearized equations describing the evolution of small perturbations in a static and in an expanding Universe. We compare the results with simplified models in which the gravitational potential is introduced by hand in the Klein-Gordon equation, and assumed to satisfy a (generalized) Poisson equation. Nonrelativistic hydrodynamic equations based on the Schrödinger-Poisson equations or on the Gross-Pitaevskii-Poisson equations are recovered in the limit c →+∞. We study the evolution of the perturbations in the matter era using the nonrelativistic limit of our formalism. Perturbations whose wavelength is below the Jeans length oscillate in time while perturbations whose wavelength is above the Jeans length grow linearly with the scale factor as in the cold dark matter model. The growth of perturbations in the scalar field model is substantially faster than in the cold dark matter model. When the wavelength of the perturbations approaches the cosmological horizon (Hubble length), a relativistic treatment is mandatory. In that case, we find that relativistic effects attenuate or even prevent the growth of perturbations. This paper exposes the general formalism and provides illustrations in simple cases. Other applications of our formalism will be considered in companion papers.

Shape design sensitivity analysis and optimization of three dimensional elastic solids using geometric modeling and automatic regridding. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Yao, Tse-Min; Choi, Kyung K.

1987-01-01

An automatic regridding method and a three dimensional shape design parameterization technique were constructed and integrated into a unified theory of shape design sensitivity analysis. An algorithm was developed for general shape design sensitivity analysis of three dimensional eleastic solids. Numerical implementation of this shape design sensitivity analysis method was carried out using the finite element code ANSYS. The unified theory of shape design sensitivity analysis uses the material derivative of continuum mechanics with a design velocity field that represents shape change effects over the structural design. Automatic regridding methods were developed by generating a domain velocity field with boundary displacement method. Shape design parameterization for three dimensional surface design problems was illustrated using a Bezier surface with boundary perturbations that depend linearly on the perturbation of design parameters. A linearization method of optimization, LINRM, was used to obtain optimum shapes. Three examples from different engineering disciplines were investigated to demonstrate the accuracy and versatility of this shape design sensitivity analysis method.

Robust stability of linear systems: Some computational considerations

NASA Technical Reports Server (NTRS)

Laub, A. J.

1979-01-01

The cases of both additive and multiplicative perturbations were discussed and a number of relationships between the two cases were given. A number of computational aspects of the theory were also discussed, including a proposed new method for evaluating general transfer or frequency response matrices. The new method is numerically stable and efficient, requiring only operations to update for new values of the frequency parameter.

Adiabatic invariants in stellar dynamics. 1: Basic concepts

NASA Technical Reports Server (NTRS)

Weinberg, Martin D.

1994-01-01

The adiabatic criterion, widely used in astronomical dynamics, is based on the harmonic oscillator. It asserts that the change in action under a slowly varying perturbation is exponentially small. Recent mathematical results that precisely define the conditions for invariance show that this model does not apply in general. In particular, a slowly varying perturbation may cause significant evolution stellar dynamical systems even if its time scale is longer than any internal orbital time scale. This additional 'heating' may have serious implications for the evolution of star clusters and dwarf galaxies which are subject to long-term environmental forces. The mathematical developments leading to these results are reviewed, and the conditions for applicability to and further implications for stellar systems are discussed. Companion papers present a computational method for a general time-dependent disturbance and detailed example.

PP/PS anisotropic stereotomography

NASA Astrophysics Data System (ADS)

Nag, Steinar; Alerini, Mathias; Ursin, Bjørn

2010-04-01

Stereotomography is a slope tomographic method which gives good results for background velocity model estimation in 2-D isotropic media. We develop here the extension of the method to 3-D general anisotropic media for PP and PS events. We do not take into account the issue of shear wave degeneracy. As in isotropic media, the sensitivity matrix of the inversion can be computed by paraxial ray tracing. We introduce a `constant Z stereotomography' approach, which can reduce the size of the sensitivity matrix. Based on ray perturbation theory, we give all the derivatives of stereotomography data parameters with respect to model parameters in a 3-D general anisotropic medium. These general formulas for the derivatives can also be used in other applications that rely on anisotropic ray perturbation theory. In particular, we obtain derivatives of the phase velocity with respect to position, phase angle and elastic medium parameters, all for general anisotropic media. The derivatives are expressed using the Voigt notation for the elastic medium parameters. We include a Jacobian that allows to change the model parametrization from Voigt to Thomsen parameters. Explicit expressions for the derivatives of the data are given for the case of 2-D tilted transversely isotropic (TTI) media. We validate the method by single-parameter estimation of each Thomsen parameter field of a 2-D TTI synthetic model, where data are modelled by ray tracing. For each Thomsen parameter, the estimated velocity field fits well with the true velocity field.

Emergence and space-time structure of lump solution to the (2+1)-dimensional generalized KP equation

NASA Astrophysics Data System (ADS)

Tan, Wei; Dai, Houping; Dai, Zhengde; Zhong, Wenyong

2017-11-01

A periodic breather-wave solution is obtained using homoclinic test approach and Hirota's bilinear method with a small perturbation parameter u0 for the (2+1)-dimensional generalized Kadomtsev-Petviashvili equation. Based on the periodic breather-wave, a lump solution is emerged by limit behaviour. Finally, three different forms of the space-time structure of the lump solution are investigated and discussed using the extreme value theory.

A Navier-Stokes-Based Approach for Mean Flow Perturbation Analysis

NASA Astrophysics Data System (ADS)

Bhaumik, Swagata; Gaitonde, Datta; Waindim, Mbu; The Ohio State University Team

2014-11-01

The manner in which a basic state, obtained from a time-averaged unsteady flowfield, processes perturbations can provide significant insight into the cause and evolution of instabilities. A widely used approach is based on Parabolized Stability Equations (PSE), which limits streamwise mean flow variation and is often applied to 2-D base flows. To avoid some of these issues, we advance a Navier-Stokes-based method, which can address non-trivial three-dimensional fields. The method stems from that employed by Touber and Sandham (Theor. Comput. Fluid. Dyn., 23, 79, 2009) to analyze global modes in nominally 2-D shock-wave turbulent-boundary layer interactions (STBLI). We first develop its theoretical underpinnings by examining conditions under which it degenerates to traditional methods. We then illustrate the application by considering perturbations to an entropy layer at Mach 6, a turbulent supersonic jet at Mach 1.3 and STBLI at Mach 2.3. For the entropy layer and jet cases, known linear stability and PSE results are successfully reproduced, while global modes are obtained for STBLI. The results not only validate the proposed technique, but also demonstrate its suitability in analyzing instabilities for any general 3D basic state, including impulse response. Sponsored by AFOSR.

Non-perturbative calculation of orbital and spin effects in molecules subject to non-uniform magnetic fields

NASA Astrophysics Data System (ADS)

Sen, Sangita; Tellgren, Erik I.

2018-05-01

External non-uniform magnetic fields acting on molecules induce non-collinear spin densities and spin-symmetry breaking. This necessitates a general two-component Pauli spinor representation. In this paper, we report the implementation of a general Hartree-Fock method, without any spin constraints, for non-perturbative calculations with finite non-uniform fields. London atomic orbitals are used to ensure faster basis convergence as well as invariance under constant gauge shifts of the magnetic vector potential. The implementation has been applied to investigate the joint orbital and spin response to a field gradient—quantified through the anapole moments—of a set of small molecules. The relative contributions of orbital and spin-Zeeman interaction terms have been studied both theoretically and computationally. Spin effects are stronger and show a general paramagnetic behavior for closed shell molecules while orbital effects can have either direction. Basis set convergence and size effects of anapole susceptibility tensors have been reported. The relation of the mixed anapole susceptibility tensor to chirality is also demonstrated.

Statistical variation in progressive scrambling

NASA Astrophysics Data System (ADS)

Clark, Robert D.; Fox, Peter C.

2004-07-01

The two methods most often used to evaluate the robustness and predictivity of partial least squares (PLS) models are cross-validation and response randomization. Both methods may be overly optimistic for data sets that contain redundant observations, however. The kinds of perturbation analysis widely used for evaluating model stability in the context of ordinary least squares regression are only applicable when the descriptors are independent of each other and errors are independent and normally distributed; neither assumption holds for QSAR in general and for PLS in particular. Progressive scrambling is a novel, non-parametric approach to perturbing models in the response space in a way that does not disturb the underlying covariance structure of the data. Here, we introduce adjustments for two of the characteristic values produced by a progressive scrambling analysis - the deprecated predictivity (Q_s^{ast^2}) and standard error of prediction (SDEP s * ) - that correct for the effect of introduced perturbation. We also explore the statistical behavior of the adjusted values (Q_0^{ast^2} and SDEP 0 * ) and the sensitivity to perturbation (d q 2/d r yy ' 2). It is shown that the three statistics are all robust for stable PLS models, in terms of the stochastic component of their determination and of their variation due to sampling effects involved in training set selection.

The linear stability of the post-Newtonian triangular equilibrium in the three-body problem

NASA Astrophysics Data System (ADS)

Yamada, Kei; Tsuchiya, Takuya

2017-12-01

Continuing a work initiated in an earlier publication (Yamada et al. in Phys Rev D 91:124016, 2015), we reexamine the linear stability of the triangular solution in the relativistic three-body problem for general masses by the standard linear algebraic analysis. In this paper, we start with the Einstein-Infeld-Hoffmann form of equations of motion for N-body systems in the uniformly rotating frame. As an extension of the previous work, we consider general perturbations to the equilibrium, i.e., we take account of perturbations orthogonal to the orbital plane, as well as perturbations lying on it. It is found that the orthogonal perturbations depend on each other by the first post-Newtonian (1PN) three-body interactions, though these are independent of the lying ones likewise the Newtonian case. We also show that the orthogonal perturbations do not affect the condition of stability. This is because these do not grow with time, but always precess with two frequency modes, namely, the same with the orbital frequency and the slightly different one due to the 1PN effect. The condition of stability, which is identical to that obtained by the previous work (Yamada et al. 2015) and is valid for the general perturbations, is obtained from the lying perturbations.

Perturbational treatment of spin-orbit coupling for generally applicable high-level multi-reference methods

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mai, Sebastian; Marquetand, Philipp; González, Leticia

2014-08-21

An efficient perturbational treatment of spin-orbit coupling within the framework of high-level multi-reference techniques has been implemented in the most recent version of the COLUMBUS quantum chemistry package, extending the existing fully variational two-component (2c) multi-reference configuration interaction singles and doubles (MRCISD) method. The proposed scheme follows related implementations of quasi-degenerate perturbation theory (QDPT) model space techniques. Our model space is built either from uncontracted, large-scale scalar relativistic MRCISD wavefunctions or based on the scalar-relativistic solutions of the linear-response-theory-based multi-configurational averaged quadratic coupled cluster method (LRT-MRAQCC). The latter approach allows for a consistent, approximatively size-consistent and size-extensive treatment of spin-orbitmore » coupling. The approach is described in detail and compared to a number of related techniques. The inherent accuracy of the QDPT approach is validated by comparing cuts of the potential energy surfaces of acrolein and its S, Se, and Te analoga with the corresponding data obtained from matching fully variational spin-orbit MRCISD calculations. The conceptual availability of approximate analytic gradients with respect to geometrical displacements is an attractive feature of the 2c-QDPT-MRCISD and 2c-QDPT-LRT-MRAQCC methods for structure optimization and ab inito molecular dynamics simulations.« less

ProteinAC: a frequency domain technique for analyzing protein dynamics

NASA Astrophysics Data System (ADS)

Bozkurt Varolgunes, Yasemin; Demir, Alper

2018-03-01

It is widely believed that the interactions of proteins with ligands and other proteins are determined by their dynamic characteristics as opposed to only static, time-invariant processes. We propose a novel computational technique, called ProteinAC (PAC), that can be used to analyze small scale functional protein motions as well as interactions with ligands directly in the frequency domain. PAC was inspired by a frequency domain analysis technique that is widely used in electronic circuit design, and can be applied to both coarse-grained and all-atom models. It can be considered as a generalization of previously proposed static perturbation-response methods, where the frequency of the perturbation becomes the key. We discuss the precise relationship of PAC to static perturbation-response schemes. We show that the frequency of the perturbation may be an important factor in protein dynamics. Perturbations at different frequencies may result in completely different response behavior while magnitude and direction are kept constant. Furthermore, we introduce several novel frequency dependent metrics that can be computed via PAC in order to characterize response behavior. We present results for the ferric binding protein that demonstrate the potential utility of the proposed techniques.

Disformal invariance of curvature perturbation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Motohashi, Hayato; White, Jonathan, E-mail: motohashi@kicp.uchicago.edu, E-mail: jwhite@post.kek.jp

2016-02-01

We show that under a general disformal transformation the linear comoving curvature perturbation is not identically invariant, but is invariant on superhorizon scales for any theory that is disformally related to Horndeski's theory. The difference between disformally related curvature perturbations is found to be given in terms of the comoving density perturbation associated with a single canonical scalar field. In General Relativity it is well-known that this quantity vanishes on superhorizon scales through the Poisson equation that is obtained on combining the Hamiltonian and momentum constraints, and we confirm that a similar result holds for any theory that is disformallymore » related to Horndeski's scalar-tensor theory so long as the invertibility condition for the disformal transformation is satisfied. We also consider the curvature perturbation at full nonlinear order in the unitary gauge, and find that it is invariant under a general disformal transformation if we assume that an attractor regime has been reached. Finally, we also discuss the counting of degrees of freedom in theories disformally related to Horndeski's.« less

Cosmological perturbation theory using the FFTLog: formalism and connection to QFT loop integrals

NASA Astrophysics Data System (ADS)

Simonović, Marko; Baldauf, Tobias; Zaldarriaga, Matias; Carrasco, John Joseph; Kollmeier, Juna A.

2018-04-01

We present a new method for calculating loops in cosmological perturbation theory. This method is based on approximating a ΛCDM-like cosmology as a finite sum of complex power-law universes. The decomposition is naturally achieved using an FFTLog algorithm. For power-law cosmologies, all loop integrals are formally equivalent to loop integrals of massless quantum field theory. These integrals have analytic solutions in terms of generalized hypergeometric functions. We provide explicit formulae for the one-loop and the two-loop power spectrum and the one-loop bispectrum. A chief advantage of our approach is that the difficult part of the calculation is cosmology independent, need be done only once, and can be recycled for any relevant predictions. Evaluation of standard loop diagrams then boils down to a simple matrix multiplication. We demonstrate the promise of this method for applications to higher multiplicity/loop correlation functions.

Conditional nonlinear optimal perturbations based on the particle swarm optimization and their applications to the predictability problems

NASA Astrophysics Data System (ADS)

Zheng, Qin; Yang, Zubin; Sha, Jianxin; Yan, Jun

2017-02-01

In predictability problem research, the conditional nonlinear optimal perturbation (CNOP) describes the initial perturbation that satisfies a certain constraint condition and causes the largest prediction error at the prediction time. The CNOP has been successfully applied in estimation of the lower bound of maximum predictable time (LBMPT). Generally, CNOPs are calculated by a gradient descent algorithm based on the adjoint model, which is called ADJ-CNOP. This study, through the two-dimensional Ikeda model, investigates the impacts of the nonlinearity on ADJ-CNOP and the corresponding precision problems when using ADJ-CNOP to estimate the LBMPT. Our conclusions are that (1) when the initial perturbation is large or the prediction time is long, the strong nonlinearity of the dynamical model in the prediction variable will lead to failure of the ADJ-CNOP method, and (2) when the objective function has multiple extreme values, ADJ-CNOP has a large probability of producing local CNOPs, hence making a false estimation of the LBMPT. Furthermore, the particle swarm optimization (PSO) algorithm, one kind of intelligent algorithm, is introduced to solve this problem. The method using PSO to compute CNOP is called PSO-CNOP. The results of numerical experiments show that even with a large initial perturbation and long prediction time, or when the objective function has multiple extreme values, PSO-CNOP can always obtain the global CNOP. Since the PSO algorithm is a heuristic search algorithm based on the population, it can overcome the impact of nonlinearity and the disturbance from multiple extremes of the objective function. In addition, to check the estimation accuracy of the LBMPT presented by PSO-CNOP and ADJ-CNOP, we partition the constraint domain of initial perturbations into sufficiently fine grid meshes and take the LBMPT obtained by the filtering method as a benchmark. The result shows that the estimation presented by PSO-CNOP is closer to the true value than the one by ADJ-CNOP with the forecast time increasing.

Incremental dynamical downscaling for probabilistic analysis based on multiple GCM projections

NASA Astrophysics Data System (ADS)

Wakazuki, Y.

2015-12-01

A dynamical downscaling method for probabilistic regional scale climate change projections was developed to cover an uncertainty of multiple general circulation model (GCM) climate simulations. The climatological increments (future minus present climate states) estimated by GCM simulation results were statistically analyzed using the singular vector decomposition. Both positive and negative perturbations from the ensemble mean with the magnitudes of their standard deviations were extracted and were added to the ensemble mean of the climatological increments. The analyzed multiple modal increments were utilized to create multiple modal lateral boundary conditions for the future climate regional climate model (RCM) simulations by adding to an objective analysis data. This data handling is regarded to be an advanced method of the pseudo-global-warming (PGW) method previously developed by Kimura and Kitoh (2007). The incremental handling for GCM simulations realized approximated probabilistic climate change projections with the smaller number of RCM simulations. Three values of a climatological variable simulated by RCMs for a mode were used to estimate the response to the perturbation of the mode. For the probabilistic analysis, climatological variables of RCMs were assumed to show linear response to the multiple modal perturbations, although the non-linearity was seen for local scale rainfall. Probability of temperature was able to be estimated within two modes perturbation simulations, where the number of RCM simulations for the future climate is five. On the other hand, local scale rainfalls needed four modes simulations, where the number of the RCM simulations is nine. The probabilistic method is expected to be used for regional scale climate change impact assessment in the future.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gonzalez, J.E.; Alcaniz, J.S.; Carvalho, J.C., E-mail: javierernesto@on.br, E-mail: alcaniz@on.br, E-mail: jcarvalho@on.br

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{submore » 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.« less

Effective gravitational couplings for cosmological perturbations in generalized Proca theories

NASA Astrophysics Data System (ADS)

De Felice, Antonio; Heisenberg, Lavinia; Kase, Ryotaro; Mukohyama, Shinji; Tsujikawa, Shinji; Zhang, Ying-li

2016-08-01

We consider the finite interactions of the generalized Proca theory including the sixth-order Lagrangian and derive the full linear perturbation equations of motion on the flat Friedmann-Lemaître-Robertson-Walker background in the presence of a matter perfect fluid. By construction, the propagating degrees of freedom (besides the matter perfect fluid) are two transverse vector perturbations, one longitudinal scalar, and two tensor polarizations. The Lagrangians associated with intrinsic vector modes neither affect the background equations of motion nor the second-order action of tensor perturbations, but they do give rise to nontrivial modifications to the no-ghost condition of vector perturbations and to the propagation speeds of vector and scalar perturbations. We derive the effective gravitational coupling Geff with matter density perturbations under a quasistatic approximation on scales deep inside the sound horizon. We find that the existence of intrinsic vector modes allows a possibility for reducing Geff. In fact, within the parameter space, Geff can be even smaller than the Newton gravitational constant G at the late cosmological epoch, with a peculiar phantom dark energy equation of state (without ghosts). The modifications to the slip parameter η and the evolution of the growth rate f σ8 are discussed as well. Thus, dark energy models in the framework of generalized Proca theories can be observationally distinguished from the Λ CDM model according to both cosmic growth and expansion history. Furthermore, we study the evolution of vector perturbations and show that outside the vector sound horizon the perturbations are nearly frozen and start to decay with oscillations after the horizon entry.

Stability analysis of nonlinear autonomous systems - General theory and application to flutter

NASA Technical Reports Server (NTRS)

Smith, L. L.; Morino, L.

1975-01-01

The analysis makes use of a singular perturbation method, the multiple time scaling. Concepts of stable and unstable limit cycles are introduced. The solution is obtained in the form of an asymptotic expansion. Numerical results are presented for the nonlinear flutter of panels and airfoils in supersonic flow. The approach used is an extension of a method for analyzing nonlinear panel flutter reported by Morino (1969).

A mean spherical model for soft potentials: The hard core revealed as a perturbation

NASA Technical Reports Server (NTRS)

Rosenfeld, Y.; Ashcroft, N. W.

1978-01-01

The mean spherical approximation for fluids is extended to treat the case of dense systems interacting via soft-potentials. The extension takes the form of a generalized statement concerning the behavior of the direct correlation function c(r) and radial distribution g(r). From a detailed analysis that views the hard core portion of a potential as a perturbation on the whole, a specific model is proposed which possesses analytic solutions for both Coulomb and Yukawa potentials, in addition to certain other remarkable properties. A variational principle for the model leads to a relatively simple method for obtaining numerical solutions.

New optical solitons of space-time conformable fractional perturbed Gerdjikov-Ivanov equation by sine-Gordon equation method

NASA Astrophysics Data System (ADS)

Yaşar, Elif; Yıldırım, Yakup; Yaşar, Emrullah

2018-06-01

This paper devotes to conformable fractional space-time perturbed Gerdjikov-Ivanov (GI) equation which appears in nonlinear fiber optics and photonic crystal fibers (PCF). We consider the model with full nonlinearity in order to give a generalized flavor. The sine-Gordon equation approach is carried out to model equation for retrieving the dark, bright, dark-bright, singular and combined singular optical solitons. The constraint conditions are also reported for guaranteeing the existence of these solitons. We also present some graphical simulations of the solutions for better understanding the physical phenomena of the behind the considered model.

Causality violations in Lovelock theories

NASA Astrophysics Data System (ADS)

Brustein, Ram; Sherf, Yotam

2018-04-01

Higher-derivative gravity theories, such as Lovelock theories, generalize Einstein's general relativity (GR). Modifications to GR are expected when curvatures are near Planckian and appear in string theory or supergravity. But can such theories describe gravity on length scales much larger than the Planck cutoff length scale? Here we find causality constraints on Lovelock theories that arise from the requirement that the equations of motion (EOM) of perturbations be hyperbolic. We find a general expression for the "effective metric" in field space when Lovelock theories are perturbed around some symmetric background solution. In particular, we calculate explicitly the effective metric for a general Lovelock theory perturbed around cosmological Friedman-Robertson-Walker backgrounds and for some specific cases when perturbed around Schwarzschild-like solutions. For the EOM to be hyperbolic, the effective metric needs to be Lorentzian. We find that, unlike for GR, the effective metric is generically not Lorentzian when the Lovelock modifications are significant. So, we conclude that Lovelock theories can only be considered as perturbative extensions of GR and not as truly modified theories of gravity. We compare our results to those in the literature and find that they agree with and reproduce the results of previous studies.

General conditions for scale-invariant perturbations in an expanding universe

DOE Office of Scientific and Technical Information (OSTI.GOV)

Geshnizjani, Ghazal; Kinney, William H.; Dizgah, Azadeh Moradinezhad, E-mail: ggeshnizjani@perimeterinstitute.ca, E-mail: whkinney@buffalo.edu, E-mail: am248@buffalo.edu

2011-11-01

We investigate the general properties of expanding cosmological models which generate scale-invariant curvature perturbations in the presence of a variable speed of sound. We show that in an expanding universe, generation of a super-Hubble, nearly scale-invariant spectrum of perturbations over a range of wavelengths consistent with observation requires at least one of three conditions: (1) accelerating expansion, (2) a speed of sound faster than the speed of light, or (3) super-Planckian energy density.

Stability of stationary-axisymmetric black holes in vacuum general relativity to axisymmetric electromagnetic perturbations

NASA Astrophysics Data System (ADS)

Prabhu, Kartik; Wald, Robert M.

2018-01-01

We consider arbitrary stationary and axisymmetric black holes in general relativity in (d +1) dimensions (with d ≥slant 3 ) that satisfy the vacuum Einstein equation and have a non-degenerate horizon. We prove that the canonical energy of axisymmetric electromagnetic perturbations is positive definite. This establishes that all vacuum black holes are stable to axisymmetric electromagnetic perturbations. Our results also hold for asymptotically de Sitter black holes that satisfy the vacuum Einstein equation with a positive cosmological constant. Our results also apply to extremal black holes provided that the initial perturbation vanishes in a neighborhood of the horizon.

Stability of the line preserving flows

NASA Astrophysics Data System (ADS)

Figura, Przemysław

2017-11-01

We examine the equations that are used to describe flows which preserve field lines. We study what happens if we introduce perturbations to the governing equations. The stability of the line preserving flows in the case of the magneto-fluids permeated by magnetic fields is strictly connected to the non-null magnetic reconnection processes. In most of our study we use the Euler potential representation of the external magnetic field. We provide general expressions for the perturbations of the Euler potentials that describe the magnetic field. Similarly, we provide expressions for the case of steady flow as well as we obtain certain conditions required for the stability of the flow. In addition, for steady flows we formulate conditions under which the perturbations of the external field are negligible and the field may be described by its initial unperturbed form. Then we consider the flow equation that transforms quantities from the laboratory coordinate system to the related external field coordinate system. We introduce perturbations to the equation and obtain its simplified versions for the case of a steady flow. For a given system, use of this method allows us to simplify the considerations provided that some part of the system may be described as a perturbation. Next, to study regions favourable for the magnetic reconnection to occur we introduce a deviation vector to the basic line preserving flows condition equation. We provide expressions of the vector for some simplifying cases. This method allows us to examine if given perturbations either stabilise the system or induce magnetic reconnection. To illustrate some of our results we study two examples, namely a simple laboratory plasma flow and a simple planetary magnetosphere model.

Consequences of using nonlinear particle trajectories to compute spatial diffusion coefficients. [for charged particles in interplanetary space

NASA Technical Reports Server (NTRS)

Goldstein, M. L.

1976-01-01

The propagation of charged particles through interstellar and interplanetary space has often been described as a random process in which the particles are scattered by ambient electromagnetic turbulence. In general, this changes both the magnitude and direction of the particles' momentum. Some situations for which scattering in direction (pitch angle) is of primary interest were studied. A perturbed orbit, resonant scattering theory for pitch-angle diffusion in magnetostatic turbulence was slightly generalized and then utilized to compute the diffusion coefficient for spatial propagation parallel to the mean magnetic field, Kappa. All divergences inherent in the quasilinear formalism when the power spectrum of the fluctuation field falls off as K to the minus Q power (Q less than 2) were removed. Various methods of computing Kappa were compared and limits on the validity of the theory discussed. For Q less than 1 or 2, the various methods give roughly comparable values of Kappa, but use of perturbed orbits systematically results in a somewhat smaller Kappa than can be obtained from quasilinear theory.

Statistical Mechanics of Node-perturbation Learning with Noisy Baseline

NASA Astrophysics Data System (ADS)

Hara, Kazuyuki; Katahira, Kentaro; Okada, Masato

2017-02-01

Node-perturbation learning is a type of statistical gradient descent algorithm that can be applied to problems where the objective function is not explicitly formulated, including reinforcement learning. It estimates the gradient of an objective function by using the change in the object function in response to the perturbation. The value of the objective function for an unperturbed output is called a baseline. Cho et al. proposed node-perturbation learning with a noisy baseline. In this paper, we report on building the statistical mechanics of Cho's model and on deriving coupled differential equations of order parameters that depict learning dynamics. We also show how to derive the generalization error by solving the differential equations of order parameters. On the basis of the results, we show that Cho's results are also apply in general cases and show some general performances of Cho's model.

On the singular perturbations for fractional differential equation.

PubMed

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.

A hybrid perturbation Galerkin technique with applications to slender body theory

NASA Technical Reports Server (NTRS)

Geer, James F.; Andersen, Carl M.

1989-01-01

A two-step hybrid perturbation-Galerkin method to solve a variety of applied mathematics problems which involve a small parameter is presented. The method consists of: (1) the use of a regular or singular perturbation method to determine the asymptotic expansion of the solution in terms of the small parameter; (2) construction of an approximate solution in the form of a sum of the perturbation coefficient functions multiplied by (unknown) amplitudes (gauge functions); and (3) the use of the classical Bubnov-Galerkin method to determine these amplitudes. This hybrid method has the potential of overcoming some of the drawbacks of the perturbation method and the Bubnov-Galerkin method when they are applied by themselves, while combining some of the good features of both. The proposed method is applied to some singular perturbation problems in slender body theory. The results obtained from the hybrid method are compared with approximate solutions obtained by other methods, and the degree of applicability of the hybrid method to broader problem areas is discussed.

A hybrid perturbation Galerkin technique with applications to slender body theory

NASA Technical Reports Server (NTRS)

Geer, James F.; Andersen, Carl M.

1987-01-01

A two step hybrid perturbation-Galerkin method to solve a variety of applied mathematics problems which involve a small parameter is presented. The method consists of: (1) the use of a regular or singular perturbation method to determine the asymptotic expansion of the solution in terms of the small parameter; (2) construction of an approximate solution in the form of a sum of the perturbation coefficient functions multiplied by (unknown) amplitudes (gauge functions); and (3) the use of the classical Bubnov-Galerkin method to determine these amplitudes. This hybrid method has the potential of overcoming some of the drawbacks of the perturbation method and the Bubnov-Galerkin method when they are applied by themselves, while combining some of the good features of both. The proposed method is applied to some singular perturbation problems in slender body theory. The results obtained from the hybrid method are compared with approximate solutions obtained by other methods, and the degree of applicability of the hybrid method to broader problem areas is discussed.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wright, Bill S.; Winther, Hans A.; Koyama, Kazuya, E-mail: bill.wright@port.ac.uk, E-mail: hans.winther@port.ac.uk, E-mail: kazuya.koyama@port.ac.uk

The effect of massive neutrinos on the growth of cold dark matter perturbations acts as a scale-dependent Newton's constant and leads to scale-dependent growth factors just as we often find in models of gravity beyond General Relativity. We show how to compute growth factors for ΛCDM and general modified gravity cosmologies combined with massive neutrinos in Lagrangian perturbation theory for use in COLA and extensions thereof. We implement this together with the grid-based massive neutrino method of Brandbyge and Hannestad in MG-PICOLA and compare COLA simulations to full N -body simulations of ΛCDM and f ( R ) gravity withmore » massive neutrinos. Our implementation is computationally cheap if the underlying cosmology already has scale-dependent growth factors and it is shown to be able to produce results that match N -body to percent level accuracy for both the total and CDM matter power-spectra up to k ∼< 1 h /Mpc.« less

Gravitational signature of Schwarzschild black holes in dynamical Chern-Simons gravity

NASA Astrophysics Data System (ADS)

Molina, C.; Pani, Paolo; Cardoso, Vitor; Gualtieri, Leonardo

2010-06-01

Dynamical Chern-Simons gravity is an extension of general relativity in which the gravitational field is coupled to a scalar field through a parity-violating Chern-Simons term. In this framework, we study perturbations of spherically symmetric black hole spacetimes, assuming that the background scalar field vanishes. Our results suggest that these spacetimes are stable, and small perturbations die away as a ringdown. However, in contrast to standard general relativity, the gravitational waveforms are also driven by the scalar field. Thus, the gravitational oscillation modes of black holes carry imprints of the coupling to the scalar field. This is a smoking gun for Chern-Simons theory and could be tested with gravitational-wave detectors, such as LIGO or LISA. For negative values of the coupling constant, ghosts are known to arise, and we explicitly verify their appearance numerically. Our results are validated using both time evolution and frequency domain methods.

COLA with massive neutrinos

NASA Astrophysics Data System (ADS)

Wright, Bill S.; Winther, Hans A.; Koyama, Kazuya

2017-10-01

The effect of massive neutrinos on the growth of cold dark matter perturbations acts as a scale-dependent Newton's constant and leads to scale-dependent growth factors just as we often find in models of gravity beyond General Relativity. We show how to compute growth factors for ΛCDM and general modified gravity cosmologies combined with massive neutrinos in Lagrangian perturbation theory for use in COLA and extensions thereof. We implement this together with the grid-based massive neutrino method of Brandbyge and Hannestad in MG-PICOLA and compare COLA simulations to full N-body simulations of ΛCDM and f(R) gravity with massive neutrinos. Our implementation is computationally cheap if the underlying cosmology already has scale-dependent growth factors and it is shown to be able to produce results that match N-body to percent level accuracy for both the total and CDM matter power-spectra up to klesssim 1 h/Mpc.

Gravitational signature of Schwarzschild black holes in dynamical Chern-Simons gravity

DOE Office of Scientific and Technical Information (OSTI.GOV)

Molina, C.; Pani, Paolo; Cardoso, Vitor

2010-06-15

Dynamical Chern-Simons gravity is an extension of general relativity in which the gravitational field is coupled to a scalar field through a parity-violating Chern-Simons term. In this framework, we study perturbations of spherically symmetric black hole spacetimes, assuming that the background scalar field vanishes. Our results suggest that these spacetimes are stable, and small perturbations die away as a ringdown. However, in contrast to standard general relativity, the gravitational waveforms are also driven by the scalar field. Thus, the gravitational oscillation modes of black holes carry imprints of the coupling to the scalar field. This is a smoking gun formore » Chern-Simons theory and could be tested with gravitational-wave detectors, such as LIGO or LISA. For negative values of the coupling constant, ghosts are known to arise, and we explicitly verify their appearance numerically. Our results are validated using both time evolution and frequency domain methods.« less

Regularization of the big bang singularity with random perturbations

NASA Astrophysics Data System (ADS)

Belbruno, Edward; Xue, BingKan

2018-03-01

We show how to regularize the big bang singularity in the presence of random perturbations modeled by Brownian motion using stochastic methods. We prove that the physical variables in a contracting universe dominated by a scalar field can be continuously and uniquely extended through the big bang as a function of time to an expanding universe only for a discrete set of values of the equation of state satisfying special co-prime number conditions. This result significantly generalizes a previous result (Xue and Belbruno 2014 Class. Quantum Grav. 31 165002) that did not model random perturbations. This result implies that the extension from a contracting to an expanding universe for the discrete set of co-prime equation of state is robust, which is a surprising result. Implications for a purely expanding universe are discussed, such as a non-smooth, randomly varying scale factor near the big bang.

Perturbative Quantum Gauge Theories on Manifolds with Boundary

NASA Astrophysics Data System (ADS)

Cattaneo, Alberto S.; Mnev, Pavel; Reshetikhin, Nicolai

2018-01-01

This paper introduces a general perturbative quantization scheme for gauge theories on manifolds with boundary, compatible with cutting and gluing, in the cohomological symplectic (BV-BFV) formalism. Explicit examples, like abelian BF theory and its perturbations, including nontopological ones, are presented.

Solution of Fifth-order Korteweg and de Vries Equation by Homotopy perturbation Transform Method using He's Polynomial

NASA Astrophysics Data System (ADS)

Sharma, Dinkar; Singh, Prince; Chauhan, Shubha

2017-06-01

In this paper, a combined form of the Laplace transform method with the homotopy perturbation method is applied to solve nonlinear fifth order Korteweg de Vries (KdV) equations. The method is known as homotopy perturbation transform method (HPTM). The nonlinear terms can be easily handled by the use of He's polynomials. Two test examples are considered to illustrate the present scheme. Further the results are compared with Homotopy perturbation method (HPM).

Do kinematic metrics of walking balance adapt to perturbed optical flow?

PubMed

Thompson, Jessica D; Franz, Jason R

2017-08-01

Visual (i.e., optical flow) perturbations can be used to study balance control and balance deficits. However, it remains unclear whether walking balance control adapts to such perturbations over time. Our purpose was to investigate the propensity for visuomotor adaptation in walking balance control using prolonged exposure to optical flow perturbations. Ten subjects (age: 25.4±3.8years) walked on a treadmill while watching a speed-matched virtual hallway with and without continuous mediolateral optical flow perturbations of three different amplitudes. Each of three perturbation trials consisted of 8min of prolonged exposure followed by 1min of unperturbed walking. Using 3D motion capture, we analyzed changes in foot placement kinematics and mediolateral sacrum motion. At their onset, perturbations elicited wider and shorter steps, alluding to a more cautious, general anticipatory balance control strategy. As perturbations continued, foot placement tended toward values seen during unperturbed walking while step width variability and mediolateral sacrum motion concurrently increased. Our findings suggest that subjects progressively shifted from a general anticipatory balance control strategy to a reactive, task-specific strategy using step-to-step adjustments. Prolonged exposure to optical flow perturbations may have clinical utility to reinforce reactive, task-specific balance control through training. Copyright © 2017 Elsevier B.V. All rights reserved.

Study of modal coupling procedures for the shuttle: A matrix method for damping synthesis

NASA Technical Reports Server (NTRS)

Hasselman, T. K.

1972-01-01

The damping method was applied successfully to real structures as well as analytical models. It depends on the ability to determine an appropriate modal damping matrix for each substructure. In the past, modal damping matrices were assumed diagonal for lack of being able to determine the coupling terms which are significant in the general case of nonproportional damping. This problem was overcome by formulating the damped equations of motion as a linear perturbation of the undamped equations for light structural damping. Damped modes are defined as complex vectors derived from the complex frequency response vectors of each substructure and are obtained directly from sinusoidal vibration tests. The damped modes are used to compute first order approximations to the modal damping matrices. The perturbation approach avoids ever having to solve a complex eigenvalue problem.

Microscopic Lagrangian description of warm plasmas. I - Linear wave propagation. II - Nonlinear wave interactions

NASA Technical Reports Server (NTRS)

Kim, H.; Crawford, F. W.

1977-01-01

It is pointed out that the conventional iterative analysis of nonlinear plasma wave phenomena, which involves a direct use of Maxwell's equations and the equations describing the particle dynamics, leads to formidable theoretical and algebraic complexities, especially for warm plasmas. As an effective alternative, the Lagrangian method may be applied. It is shown how this method may be used in the microscopic description of small-signal wave propagation and in the study of nonlinear wave interactions. The linear theory is developed for an infinite, homogeneous, collisionless, warm magnetoplasma. A summary is presented of a perturbation expansion scheme described by Galloway and Kim (1971), and Lagrangians to third order in perturbation are considered. Attention is given to the averaged-Lagrangian density, the action-transfer and coupled-mode equations, and the general solution of the coupled-mode equations.

On the Singular Perturbations for Fractional Differential Equation

PubMed Central

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. PMID:24683357

Instability of black strings in the third-order Lovelock theory

NASA Astrophysics Data System (ADS)

Giacomini, Alex; Henríquez-Báez, Carla; Lagos, Marcela; Oliva, Julio; Vera, Aldo

2016-05-01

We show that homogeneous black strings of third-order Lovelock theory are unstable under s-wave perturbations. This analysis is done in dimension D =9 , which is the lowest dimension that allows the existence of homogeneous black strings in a theory that contains only the third-order Lovelock term in the Lagrangian. As is the case in general relativity, the instability is produced by long wavelength perturbations and it stands for the perturbative counterpart of a thermal instability. We also provide a comparative analysis of the instabilities of black strings at a fixed radius in general relativity, Gauss-Bonnet, and third-order Lovelock theories. We show that the minimum critical wavelength that triggers the instability grows with the power of the curvature defined in the Lagrangian. The maximum exponential growth during the time of the perturbation is the largest in general relativity and it decreases with the number of curvatures involved in the Lagrangian.

General theories of linear gravitational perturbations to a Schwarzschild black hole

NASA Astrophysics Data System (ADS)

Tattersall, Oliver J.; Ferreira, Pedro G.; Lagos, Macarena

2018-02-01

We use the covariant formulation proposed by Tattersall, Lagos, and Ferreira [Phys. Rev. D 96, 064011 (2017), 10.1103/PhysRevD.96.064011] to analyze the structure of linear perturbations about a spherically symmetric background in different families of gravity theories, and hence study how quasinormal modes of perturbed black holes may be affected by modifications to general relativity. We restrict ourselves to single-tensor, scalar-tensor and vector-tensor diffeomorphism-invariant gravity models in a Schwarzschild black hole background. We show explicitly the full covariant form of the quadratic actions in such cases, which allow us to then analyze odd parity (axial) and even parity (polar) perturbations simultaneously in a straightforward manner.

Estimating Atomic Contributions to Hydration and Binding Using Free Energy Perturbation.

PubMed

Irwin, Benedict W J; Huggins, David J

2018-06-12

We present a general method called atom-wise free energy perturbation (AFEP), which extends a conventional molecular dynamics free energy perturbation (FEP) simulation to give the contribution to a free energy change from each atom. AFEP is derived from an expansion of the Zwanzig equation used in the exponential averaging method by defining that the system total energy can be partitioned into contributions from each atom. A partitioning method is assumed and used to group terms in the expansion to correspond to individual atoms. AFEP is applied to six example free energy changes to demonstrate the method. Firstly, the hydration free energies of methane, methanol, methylamine, methanethiol, and caffeine in water. AFEP highlights the atoms in the molecules that interact favorably or unfavorably with water. Finally AFEP is applied to the binding free energy of human immunodeficiency virus type 1 protease to lopinavir, and AFEP reveals the contribution of each atom to the binding free energy, indicating candidate areas of the molecule to improve to produce a more strongly binding inhibitor. FEP gives a single value for the free energy change and is already a very useful method. AFEP gives a free energy change for each "part" of the system being simulated, where part can mean individual atoms, chemical groups, amino acids, or larger partitions depending on what the user is trying to measure. This method should have various applications in molecular dynamics studies of physical, chemical, or biochemical phenomena, specifically in the field of computational drug discovery.

Resummed memory kernels in generalized system-bath master equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mavros, Michael G.; Van Voorhis, Troy, E-mail: tvan@mit.edu

2014-08-07

Generalized master equations provide a concise formalism for studying reduced population dynamics. Usually, these master equations require a perturbative expansion of the memory kernels governing the dynamics; in order to prevent divergences, these expansions must be resummed. Resummation techniques of perturbation series are ubiquitous in physics, but they have not been readily studied for the time-dependent memory kernels used in generalized master equations. In this paper, we present a comparison of different resummation techniques for such memory kernels up to fourth order. We study specifically the spin-boson Hamiltonian as a model system bath Hamiltonian, treating the diabatic coupling between themore » two states as a perturbation. A novel derivation of the fourth-order memory kernel for the spin-boson problem is presented; then, the second- and fourth-order kernels are evaluated numerically for a variety of spin-boson parameter regimes. We find that resumming the kernels through fourth order using a Padé approximant results in divergent populations in the strong electronic coupling regime due to a singularity introduced by the nature of the resummation, and thus recommend a non-divergent exponential resummation (the “Landau-Zener resummation” of previous work). The inclusion of fourth-order effects in a Landau-Zener-resummed kernel is shown to improve both the dephasing rate and the obedience of detailed balance over simpler prescriptions like the non-interacting blip approximation, showing a relatively quick convergence on the exact answer. The results suggest that including higher-order contributions to the memory kernel of a generalized master equation and performing an appropriate resummation can provide a numerically-exact solution to system-bath dynamics for a general spectral density, opening the way to a new class of methods for treating system-bath dynamics.« less

Symmetry-preserving perturbations of the Bateman Lagrangian and dissipative systems

NASA Astrophysics Data System (ADS)

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.

Symmetry-preserving perturbations of the Bateman Lagrangian and dissipative systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Campoamor-Stursberg, Rutwig, E-mail: rutwig@ucm.es

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.

Numerical solution to generalized Burgers'-Fisher equation using Exp-function method hybridized with heuristic computation.

PubMed

Malik, Suheel Abdullah; Qureshi, Ijaz Mansoor; Amir, Muhammad; Malik, Aqdas Naveed; Haq, Ihsanul

2015-01-01

In this paper, a new heuristic scheme for the approximate solution of the generalized Burgers'-Fisher equation is proposed. The scheme is based on the hybridization of Exp-function method with nature inspired algorithm. The given nonlinear partial differential equation (NPDE) through substitution is converted into a nonlinear ordinary differential equation (NODE). The travelling wave solution is approximated by the Exp-function method with unknown parameters. The unknown parameters are estimated by transforming the NODE into an equivalent global error minimization problem by using a fitness function. The popular genetic algorithm (GA) is used to solve the minimization problem, and to achieve the unknown parameters. The proposed scheme is successfully implemented to solve the generalized Burgers'-Fisher equation. The comparison of numerical results with the exact solutions, and the solutions obtained using some traditional methods, including adomian decomposition method (ADM), homotopy perturbation method (HPM), and optimal homotopy asymptotic method (OHAM), show that the suggested scheme is fairly accurate and viable for solving such problems.

Numerical Solution to Generalized Burgers'-Fisher Equation Using Exp-Function Method Hybridized with Heuristic Computation

PubMed Central

Malik, Suheel Abdullah; Qureshi, Ijaz Mansoor; Amir, Muhammad; Malik, Aqdas Naveed; Haq, Ihsanul

2015-01-01

In this paper, a new heuristic scheme for the approximate solution of the generalized Burgers'-Fisher equation is proposed. The scheme is based on the hybridization of Exp-function method with nature inspired algorithm. The given nonlinear partial differential equation (NPDE) through substitution is converted into a nonlinear ordinary differential equation (NODE). The travelling wave solution is approximated by the Exp-function method with unknown parameters. The unknown parameters are estimated by transforming the NODE into an equivalent global error minimization problem by using a fitness function. The popular genetic algorithm (GA) is used to solve the minimization problem, and to achieve the unknown parameters. The proposed scheme is successfully implemented to solve the generalized Burgers'-Fisher equation. The comparison of numerical results with the exact solutions, and the solutions obtained using some traditional methods, including adomian decomposition method (ADM), homotopy perturbation method (HPM), and optimal homotopy asymptotic method (OHAM), show that the suggested scheme is fairly accurate and viable for solving such problems. PMID:25811858

Linear stability and nonlinear analyses of traffic waves for the general nonlinear car-following model with multi-time delays

NASA Astrophysics Data System (ADS)

Sun, Dihua; Chen, Dong; Zhao, Min; Liu, Weining; Zheng, Linjiang

2018-07-01

In this paper, the general nonlinear car-following model with multi-time delays is investigated in order to describe the reactions of vehicle to driving behavior. Platoon stability and string stability criteria are obtained for the general nonlinear car-following model. Burgers equation and Korteweg de Vries (KdV) equation and their solitary wave solutions are derived adopting the reductive perturbation method. We investigate the properties of typical optimal velocity model using both analytic and numerical methods, which estimates the impact of delays about the evolution of traffic congestion. The numerical results show that time delays in sensing relative movement is more sensitive to the stability of traffic flow than time delays in sensing host motion.

Comparison of two perturbation methods to estimate the land surface modeling uncertainty

NASA Astrophysics Data System (ADS)

Su, H.; Houser, P.; Tian, Y.; Kumar, S.; Geiger, J.; Belvedere, D.

2007-12-01

In land surface modeling, it is almost impossible to simulate the land surface processes without any error because the earth system is highly complex and the physics of the land processes has not yet been understood sufficiently. In most cases, people want to know not only the model output but also the uncertainty in the modeling, to estimate how reliable the modeling is. Ensemble perturbation is an effective way to estimate the uncertainty in land surface modeling, since land surface models are highly nonlinear which makes the analytical approach not applicable in this estimation. The ideal perturbation noise is zero mean Gaussian distribution, however, this requirement can't be satisfied if the perturbed variables in land surface model have physical boundaries because part of the perturbation noises has to be removed to feed the land surface models properly. Two different perturbation methods are employed in our study to investigate their impact on quantifying land surface modeling uncertainty base on the Land Information System (LIS) framework developed by NASA/GSFC land team. One perturbation method is the built-in algorithm named "STATIC" in LIS version 5; the other is a new perturbation algorithm which was recently developed to minimize the overall bias in the perturbation by incorporating additional information from the whole time series for the perturbed variable. The statistical properties of the perturbation noise generated by the two different algorithms are investigated thoroughly by using a large ensemble size on a NASA supercomputer and then the corresponding uncertainty estimates based on the two perturbation methods are compared. Their further impacts on data assimilation are also discussed. Finally, an optimal perturbation method is suggested.

Generalizing genetical genomics: getting added value from environmental perturbation.

PubMed

Li, Yang; Breitling, Rainer; Jansen, Ritsert C

2008-10-01

Genetical genomics is a useful approach for studying the effect of genetic perturbations on biological systems at the molecular level. However, molecular networks depend on the environmental conditions and, thus, a comprehensive understanding of biological systems requires studying them across multiple environments. We propose a generalization of genetical genomics, which combines genetic and sensibly chosen environmental perturbations, to study the plasticity of molecular networks. This strategy forms a crucial step toward understanding why individuals respond differently to drugs, toxins, pathogens, nutrients and other environmental influences. Here we outline a strategy for selecting and allocating individuals to particular treatments, and we discuss the promises and pitfalls of the generalized genetical genomics approach.

Stability derivatives for bodies of revolution at subsonic speeds

NASA Technical Reports Server (NTRS)

Liu, D. D.; Platzer, M. F.; Ruo, S. Y.

1976-01-01

The paper considers a rigid pointed body of revolution in a steady uniform subsonic flow. The body performs harmonic small-amplitude pitching oscillations around its zero angle of attack position. The body is assumed to be smooth and sufficiently slender so that the small perturbation concept can be applied. The basis of the method used, following Revell (1960), is the relation of a body-fixed perturbation potential to the general velocity potential. Normal force distributions as well as total force and moment coefficients are calculated for parabolic spindles and the numerical results show good agreement between Revell's second-order slender body theory and the present theory for the static stability derivatives of the parabolic spindles.

The impacts of oceanic deep temperature perturbations in the North Atlantic on decadal climate variability and predictability

NASA Astrophysics Data System (ADS)

Germe, Agathe; Sévellec, Florian; Mignot, Juliette; Fedorov, Alexey; Nguyen, Sébastien; Swingedouw, Didier

2017-12-01

Decadal climate predictability in the North Atlantic is largely related to ocean low frequency variability, whose sensitivity to initial conditions is not very well understood. Recently, three-dimensional oceanic temperature anomalies optimally perturbing the North Atlantic Mean Temperature (NAMT) have been computed via an optimization procedure using a linear adjoint to a realistic ocean general circulation model. The spatial pattern of the identified perturbations, localized in the North Atlantic, has the largest magnitude between 1000 and 4000 m depth. In the present study, the impacts of these perturbations on NAMT, on the Atlantic meridional overturning circulation (AMOC), and on climate in general are investigated in a global coupled model that uses the same ocean model as was used to compute the three-dimensional optimal perturbations. In the coupled model, these perturbations induce AMOC and NAMT anomalies peaking after 5 and 10 years, respectively, generally consistent with the ocean-only linear predictions. To further understand their impact, their magnitude was varied in a broad range. For initial perturbations with a magnitude comparable to the internal variability of the coupled model, the model response exhibits a strong signature in sea surface temperature and precipitation over North America and the Sahel region. The existence and impacts of these ocean perturbations have important implications for decadal prediction: they can be seen either as a source of predictability or uncertainty, depending on whether the current observing system can detect them or not. In fact, comparing the magnitude of the imposed perturbations with the uncertainty of available ocean observations such as Argo data or ocean state estimates suggests that only the largest perturbations used in this study could be detectable. This highlights the importance for decadal climate prediction of accurate ocean density initialisation in the North Atlantic at intermediate and greater depths.

Stability and bifurcation analysis of oscillators with piecewise-linear characteristics - A general approach

NASA Technical Reports Server (NTRS)

Noah, S. T.; Kim, Y. B.

1991-01-01

A general approach is developed for determining the periodic solutions and their stability of nonlinear oscillators with piecewise-smooth characteristics. A modified harmonic balance/Fourier transform procedure is devised for the analysis. The procedure avoids certain numerical differentiation employed previously in determining the periodic solutions, therefore enhancing the reliability and efficiency of the method. Stability of the solutions is determined via perturbations of their state variables. The method is applied to a forced oscillator interacting with a stop of finite stiffness. Flip and fold bifurcations are found to occur. This led to the identification of parameter ranges in which chaotic response occurred.

Orbit Mechanics about Small Asteroids

NASA Technical Reports Server (NTRS)

Scheeres, D. J.

2007-01-01

Space missions to small solar system bodies must deal with multiple perturbations acting on the spacecraft. These include strong perturbations from the gravity field and solar tide, but for small bodies the most important perturbations may arise from solar radiation pressure (SRP) acting on the spacecraft. Previous research has generally investigated the effect of the gravity field, solar tide, and SRP acting on a spacecraft trajectory about an asteroid in isolation and has not considered their joint effect. In this paper a more general theoretical discussion of the joint effects of these forces is given.

Growth histories in bimetric massive gravity

DOE Office of Scientific and Technical Information (OSTI.GOV)

Berg, Marcus; Buchberger, Igor; Enander, Jonas

2012-12-01

We perform cosmological perturbation theory in Hassan-Rosen bimetric gravity for general homogeneous and isotropic backgrounds. In the de Sitter approximation, we obtain decoupled sets of massless and massive scalar gravitational fluctuations. Matter perturbations then evolve like in Einstein gravity. We perturb the future de Sitter regime by the ratio of matter to dark energy, producing quasi-de Sitter space. In this more general setting the massive and massless fluctuations mix. We argue that in the quasi-de Sitter regime, the growth of structure in bimetric gravity differs from that of Einstein gravity.

Development of a generalized perturbation theory method for sensitivity analysis using continuous-energy Monte Carlo methods

DOE PAGES

Perfetti, Christopher M.; Rearden, Bradley T.

2016-03-01

The sensitivity and uncertainty analysis tools of the ORNL SCALE nuclear modeling and simulation code system that have been developed over the last decade have proven indispensable for numerous application and design studies for nuclear criticality safety and reactor physics. SCALE contains tools for analyzing the uncertainty in the eigenvalue of critical systems, but cannot quantify uncertainty in important neutronic parameters such as multigroup cross sections, fuel fission rates, activation rates, and neutron fluence rates with realistic three-dimensional Monte Carlo simulations. A more complete understanding of the sources of uncertainty in these design-limiting parameters could lead to improvements in processmore » optimization, reactor safety, and help inform regulators when setting operational safety margins. A novel approach for calculating eigenvalue sensitivity coefficients, known as the CLUTCH method, was recently explored as academic research and has been found to accurately and rapidly calculate sensitivity coefficients in criticality safety applications. The work presented here describes a new method, known as the GEAR-MC method, which extends the CLUTCH theory for calculating eigenvalue sensitivity coefficients to enable sensitivity coefficient calculations and uncertainty analysis for a generalized set of neutronic responses using high-fidelity continuous-energy Monte Carlo calculations. Here, several criticality safety systems were examined to demonstrate proof of principle for the GEAR-MC method, and GEAR-MC was seen to produce response sensitivity coefficients that agreed well with reference direct perturbation sensitivity coefficients.« less

Large leptonic Dirac CP phase from broken democracy with random perturbations

NASA Astrophysics Data System (ADS)

Ge, Shao-Feng; Kusenko, Alexander; Yanagida, Tsutomu T.

2018-06-01

A large value of the leptonic Dirac CP phase can arise from broken democracy, where the mass matrices are democratic up to small random perturbations. Such perturbations are a natural consequence of broken residual S3 symmetries that dictate the democratic mass matrices at leading order. With random perturbations, the leptonic Dirac CP phase has a higher probability to attain a value around ± π / 2. Comparing with the anarchy model, broken democracy can benefit from residual S3 symmetries, and it can produce much better, realistic predictions for the mass hierarchy, mixing angles, and Dirac CP phase in both quark and lepton sectors. Our approach provides a general framework for a class of models in which a residual symmetry determines the general features at leading order, and where, in the absence of other fundamental principles, the symmetry breaking appears in the form of random perturbations.

Inhomogeneous Jacobi equation for minimal surfaces and perturbative change in holographic entanglement entropy

NASA Astrophysics Data System (ADS)

Ghosh, Avirup; Mishra, Rohit

2018-04-01

The change in holographic entanglement entropy (HEE) for small fluctuations about pure anti-de Sitter (AdS) is obtained by a perturbative expansion of the area functional in terms of the change in the bulk metric and the embedded extremal surface. However it is known that change in the embedding appears at second order or higher. It was shown that these changes in the embedding can be calculated in the 2 +1 dimensional case by solving a "generalized geodesic deviation equation." We generalize this result to arbitrary dimensions by deriving an inhomogeneous form of the Jacobi equation for minimal surfaces. The solutions of this equation map a minimal surface in a given space time to a minimal surface in a space time which is a perturbation over the initial space time. Using this we perturbatively calculate the changes in HEE up to second order for boosted black brane like perturbations over AdS4.

Operator Approach to the Master Equation for the One-Step Process

NASA Astrophysics Data System (ADS)

Hnatič, M.; Eferina, E. G.; Korolkova, A. V.; Kulyabov, D. S.; Sevastyanov, L. A.

2016-02-01

Background. Presentation of the probability as an intrinsic property of the nature leads researchers to switch from deterministic to stochastic description of the phenomena. The kinetics of the interaction has recently attracted attention because it often occurs in the physical, chemical, technical, biological, environmental, economic, and sociological systems. However, there are no general methods for the direct study of this equation. The expansion of the equation in a formal Taylor series (the so called Kramers-Moyal's expansion) is used in the procedure of stochastization of one-step processes. Purpose. However, this does not eliminate the need for the study of the master equation. Method. It is proposed to use quantum field perturbation theory for the statistical systems (the so-called Doi method). Results: This work is a methodological material that describes the principles of master equation solution based on quantum field perturbation theory methods. The characteristic property of the work is that it is intelligible for non-specialists in quantum field theory. Conclusions: We show the full equivalence of the operator and combinatorial methods of obtaining and study of the one-step process master equation.

Stationary axisymmetric exteriors for perturbations of isolated bodies in general relativity, to second order

DOE Office of Scientific and Technical Information (OSTI.GOV)

MacCallum, Malcolm A. H.; Mars, Marc; Vera, Rauel

Perturbed stationary axisymmetric isolated bodies, e.g. stars, represented by a matter-filled interior and an asymptotically flat vacuum exterior joined at a surface where the Darmois matching conditions are satisfied, are considered. The initial state is assumed to be static. The perturbations of the matching conditions are derived and used as boundary conditions for the perturbed Ernst equations in the exterior region. The perturbations are calculated to second order. The boundary conditions are overdetermined: necessary and sufficient conditions for their compatibility are derived. The special case of perturbations of spherical bodies is given in detail.

The spectrum of density perturbations in an expanding universe

NASA Technical Reports Server (NTRS)

Silk, J.

1974-01-01

The basic dynamic equations that govern the evolution of perturbations in a Friedmann-Lemaitre universe are derived. General solutions describing the evolution of adiabatic perturbations in the density of matter are obtained, and the choice of the appropriate initial conditions is examined. The various perturbation modes are compared, and the effects of decoupling on the perturbation spectrum are studied. The scheme used to follow the evolution of density perturbations through decoupling is based on an extension of the Eddington approximation to the radiative transfer equation, and is strictly valid in both optically thick and thin limits.

Double power series method for approximating cosmological perturbations

NASA Astrophysics Data System (ADS)

Wren, Andrew J.; Malik, Karim A.

2017-04-01

We introduce a double power series method for finding approximate analytical solutions for systems of differential equations commonly found in cosmological perturbation theory. The method was set out, in a noncosmological context, by Feshchenko, Shkil' and Nikolenko (FSN) in 1966, and is applicable to cases where perturbations are on subhorizon scales. The FSN method is essentially an extension of the well known Wentzel-Kramers-Brillouin (WKB) method for finding approximate analytical solutions for ordinary differential equations. The FSN method we use is applicable well beyond perturbation theory to solve systems of ordinary differential equations, linear in the derivatives, that also depend on a small parameter, which here we take to be related to the inverse wave-number. We use the FSN method to find new approximate oscillating solutions in linear order cosmological perturbation theory for a flat radiation-matter universe. Together with this model's well-known growing and decaying Mészáros solutions, these oscillating modes provide a complete set of subhorizon approximations for the metric potential, radiation and matter perturbations. Comparison with numerical solutions of the perturbation equations shows that our approximations can be made accurate to within a typical error of 1%, or better. We also set out a heuristic method for error estimation. A Mathematica notebook which implements the double power series method is made available online.

Second-order cosmological perturbations. I. Produced by scalar-scalar coupling in synchronous gauge

NASA Astrophysics Data System (ADS)

Wang, Bo; Zhang, Yang

2017-11-01

We present a systematic study of the 2nd-order scalar, vector, and tensor metric perturbations in the Einstein-de Sitter Universe in synchronous coordinates. For the scalar-scalar coupling between 1st-order perturbations, we decompose the 2nd-order perturbed Einstein equation into the respective field equations of 2nd-order scalar, vector, and tensor perturbations, and obtain their solutions with general initial conditions. In particular, the decaying modes of solution are included, the 2nd-order vector is generated even if the 1st-order vector is absent, and the solution of the 2nd-order tensor corrects that in literature. We perform general synchronous-to-synchronous gauge transformations up to 2nd order generated by a 1st-order vector field ξ(1 )μ and a 2nd-order ξ(2 )μ . All the residual gauge modes of 2nd-order metric perturbations and density contrast are found, and their number is substantially reduced when the transformed 3-velocity of dust is set to zero. Moreover, we show that only ξ(2 )μ is effective in carrying out 2nd-order transformations that we consider, because ξ(1 )μ has been used in obtaining the 1st-order perturbations. Holding the 1st-order perturbations fixed, the transformations by ξ(2 )μ on the 2nd-order perturbations have the same structure as those by ξ(1 )μ on the 1st-order perturbations.

Improved perturbation method for gadolinia worth calculation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chiang, R.T.; Congdon, S.P.

1986-01-01

Gadolinia is utilized in light water power reactors as burnable poison for reserving excess reactivity. Good gadolinia worth estimation is useful for evaluating fuel bundle designs, core operating strategies, and fuel cycle economics. The authors have developed an improved perturbation method based on exact perturbation theory for gadolinia worth calculations in fuel bundles. The method predicts much more accurate gadolinia worth than the first-order perturbation method (commonly used to estimate nuclide worths) for bundles containing fresh or partly burned gadolinia.

An Efficient Algorithm for Perturbed Orbit Integration Combining Analytical Continuation and Modified Chebyshev Picard Iteration

NASA Astrophysics Data System (ADS)

Elgohary, T.; Kim, D.; Turner, J.; Junkins, J.

2014-09-01

Several methods exist for integrating the motion in high order gravity fields. Some recent methods use an approximate starting orbit, and an efficient method is needed for generating warm starts that account for specific low order gravity approximations. By introducing two scalar Lagrange-like invariants and employing Leibniz product rule, the perturbed motion is integrated by a novel recursive formulation. The Lagrange-like invariants allow exact arbitrary order time derivatives. Restricting attention to the perturbations due to the zonal harmonics J2 through J6, we illustrate an idea. The recursively generated vector-valued time derivatives for the trajectory are used to develop a continuation series-based solution for propagating position and velocity. Numerical comparisons indicate performance improvements of ~ 70X over existing explicit Runge-Kutta methods while maintaining mm accuracy for the orbit predictions. The Modified Chebyshev Picard Iteration (MCPI) is an iterative path approximation method to solve nonlinear ordinary differential equations. The MCPI utilizes Picard iteration with orthogonal Chebyshev polynomial basis functions to recursively update the states. The key advantages of the MCPI are as follows: 1) Large segments of a trajectory can be approximated by evaluating the forcing function at multiple nodes along the current approximation during each iteration. 2) It can readily handle general gravity perturbations as well as non-conservative forces. 3) Parallel applications are possible. The Picard sequence converges to the solution over large time intervals when the forces are continuous and differentiable. According to the accuracy of the starting solutions, however, the MCPI may require significant number of iterations and function evaluations compared to other integrators. In this work, we provide an efficient methodology to establish good starting solutions from the continuation series method; this warm start improves the performance of the MCPI significantly and will likely be useful for other applications where efficiently computed approximate orbit solutions are needed.

Adaptive Modeling Procedure Selection by Data Perturbation.

PubMed

Zhang, Yongli; Shen, Xiaotong

2015-10-01

Many procedures have been developed to deal with the high-dimensional problem that is emerging in various business and economics areas. To evaluate and compare these procedures, modeling uncertainty caused by model selection and parameter estimation has to be assessed and integrated into a modeling process. To do this, a data perturbation method estimates the modeling uncertainty inherited in a selection process by perturbing the data. Critical to data perturbation is the size of perturbation, as the perturbed data should resemble the original dataset. To account for the modeling uncertainty, we derive the optimal size of perturbation, which adapts to the data, the model space, and other relevant factors in the context of linear regression. On this basis, we develop an adaptive data-perturbation method that, unlike its nonadaptive counterpart, performs well in different situations. This leads to a data-adaptive model selection method. Both theoretical and numerical analysis suggest that the data-adaptive model selection method adapts to distinct situations in that it yields consistent model selection and optimal prediction, without knowing which situation exists a priori. The proposed method is applied to real data from the commodity market and outperforms its competitors in terms of price forecasting accuracy.

An analysis of USSPACECOM's space surveillance network sensor tasking methodology

NASA Astrophysics Data System (ADS)

Berger, Jeff M.; Moles, Joseph B.; Wilsey, David G.

1992-12-01

This study provides the basis for the development of a cost/benefit assessment model to determine the effects of alterations to the Space Surveillance Network (SSN) on orbital element (OE) set accuracy. It provides a review of current methods used by NORAD and the SSN to gather and process observations, an alternative to the current Gabbard classification method, and the development of a model to determine the effects of observation rate and correction interval on OE set accuracy. The proposed classification scheme is based on satellite J2 perturbations. Specifically, classes were established based on mean motion, eccentricity, and inclination since J2 perturbation effects are functions of only these elements. Model development began by creating representative sensor observations using a highly accurate orbital propagation model. These observations were compared to predicted observations generated using the NORAD Simplified General Perturbation (SGP4) model and differentially corrected using a Bayes, sequential estimation, algorithm. A 10-run Monte Carlo analysis was performed using this model on 12 satellites using 16 different observation rate/correction interval combinations. An ANOVA and confidence interval analysis of the results show that this model does demonstrate the differences in steady state position error based on varying observation rate and correction interval.

Non-numeric computation for high eccentricity orbits. [Earth satellite orbit perturbation

NASA Technical Reports Server (NTRS)

Sridharan, R.; Renard, M. L.

1975-01-01

Geocentric orbits of large eccentricity (e = 0.9 to 0.95) are significantly perturbed in cislunar space by the sun and moon. The time-history of the height of perigee, subsequent to launch, is particularly critical. The determination of 'launch windows' is mostly concerned with preventing the height of perigee from falling below its low initial value before the mission lifetime has elapsed. Between the extremes of high accuracy digital integration of the equations of motion and of using an approximate, but very fast, stability criteria method, this paper is concerned with the developement of a method of intermediate complexity using non-numeric computation. The computer is used as the theory generator to generalize Lidov's theory using six osculating elements. Symbolic integration is completely automatized and the output is a set of condensed formulae well suited for repeated applications in launch window analysis. Examples of applications are given.

Second-order singular pertubative theory for gravitational lenses

NASA Astrophysics Data System (ADS)

Alard, C.

2018-03-01

The extension of the singular perturbative approach to the second order is presented in this paper. The general expansion to the second order is derived. The second-order expansion is considered as a small correction to the first-order expansion. Using this approach, it is demonstrated that in practice the second-order expansion is reducible to a first order expansion via a re-definition of the first-order pertubative fields. Even if in usual applications the second-order correction is small the reducibility of the second-order expansion to the first-order expansion indicates a potential degeneracy issue. In general, this degeneracy is hard to break. A useful and simple second-order approximation is the thin source approximation, which offers a direct estimation of the correction. The practical application of the corrections derived in this paper is illustrated by using an elliptical NFW lens model. The second-order pertubative expansion provides a noticeable improvement, even for the simplest case of thin source approximation. To conclude, it is clear that for accurate modelization of gravitational lenses using the perturbative method the second-order perturbative expansion should be considered. In particular, an evaluation of the degeneracy due to the second-order term should be performed, for which the thin source approximation is particularly useful.

Phases, periphases, and interphases equilibrium by molecular modeling. I. Mass equilibrium by the semianalytical stochastic perturbations method and application to a solution between (120) gypsum faces

NASA Astrophysics Data System (ADS)

Pedesseau, Laurent; Jouanna, Paul

2004-12-01

The SASP (semianalytical stochastic perturbations) method is an original mixed macro-nano-approach dedicated to the mass equilibrium of multispecies phases, periphases, and interphases. This general method, applied here to the reflexive relation Ck⇔μk between the concentrations Ck and the chemical potentials μk of k species within a fluid in equilibrium, leads to the distribution of the particles at the atomic scale. The macroaspects of the method, based on analytical Taylor's developments of chemical potentials, are intimately mixed with the nanoaspects of molecular mechanics computations on stochastically perturbed states. This numerical approach, directly linked to definitions, is universal by comparison with current approaches, DLVO Derjaguin-Landau-Verwey-Overbeek, grand canonical Monte Carlo, etc., without any restriction on the number of species, concentrations, or boundary conditions. The determination of the relation Ck⇔μk implies in fact two problems: a direct problem Ck⇒μk and an inverse problem μk⇒Ck. Validation of the method is demonstrated in case studies A and B which treat, respectively, a direct problem and an inverse problem within a free saturated gypsum solution. The flexibility of the method is illustrated in case study C dealing with an inverse problem within a solution interphase, confined between two (120) gypsum faces, remaining in connection with a reference solution. This last inverse problem leads to the mass equilibrium of ions and water molecules within a 3 Å thick gypsum interface. The major unexpected observation is the repulsion of SO42- ions towards the reference solution and the attraction of Ca2+ ions from the reference solution, the concentration being 50 times higher within the interphase as compared to the free solution. The SASP method is today the unique approach able to tackle the simulation of the number and distribution of ions plus water molecules in such extreme confined conditions. This result is of prime importance for all coupled chemical-mechanical problems dealing with interfaces, and more generally for a wide variety of applications such as phase changes, osmotic equilibrium, surface energy, etc., in complex chemical-physics situations.

Extension of local-type inequality for the higher order correlation functions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Suyama, Teruaki; Yokoyama, Shuichiro, E-mail: suyama@resceu.s.u-tokyo.ac.jp, E-mail: shu@a.phys.nagoya-u.ac.jp

2011-07-01

For the local-type primordial perturbation, it is known that there is an inequality between the bispectrum and the trispectrum. By using the diagrammatic method, we develop a general formalism to systematically construct the similar inequalities up to any order correlation function. As an application, we explicitly derive all the inequalities up to six and eight-point functions.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Fujiwara, K., E-mail: ku.fujiwara@screen.co.jp; Department of Mechanical Engineering, Graduate School of Engineering, Osaka University, 2-1 Yamadaoka, Suita, Osaka 565-0871; Shibahara, M., E-mail: siba@mech.eng.osaka-u.ac.jp

A classical molecular dynamics simulation was conducted for a system composed of fluid molecules between two planar solid surfaces, and whose interactions are described by the 12-6 Lennard-Jones form. This paper presents a general description of the pressure components and interfacial tension at a fluid-solid interface obtained by the perturbative method on the basis of statistical thermodynamics, proposes a method to consider the pressure components tangential to an interface which are affected by interactions with solid atoms, and applies this method to the calculation system. The description of the perturbative method is extended to subsystems, and the local pressure componentsmore » and interfacial tension at a liquid-solid interface are obtained and examined in one- and two-dimensions. The results are compared with those obtained by two alternative methods: (a) an evaluation of the intermolecular force acting on a plane, and (b) the conventional method based on the virial expression. The accuracy of the numerical results is examined through the comparison of the results obtained by each method. The calculated local pressure components and interfacial tension of the fluid at a liquid-solid interface agreed well with the results of the two alternative methods at each local position in one dimension. In two dimensions, the results showed a characteristic profile of the tangential pressure component which depended on the direction tangential to the liquid-solid interface, which agreed with that obtained by the evaluation of the intermolecular force acting on a plane in the present study. Such good agreement suggests that the perturbative method on the basis of statistical thermodynamics used in this study is valid to obtain the local pressure components and interfacial tension at a liquid-solid interface.« less

Application of Classical and Lie Transform Methods to Zonal Perturbation in the Artificial Satellite

NASA Astrophysics Data System (ADS)

San-Juan, J. F.; San-Martin, M.; Perez, I.; Lopez-Ochoa, L. M.

2013-08-01

A scalable second-order analytical orbit propagator program is being carried out. This analytical orbit propagator combines modern perturbation methods, based on the canonical frame of the Lie transform, and classical perturbation methods in function of orbit types or the requirements needed for a space mission, such as catalog maintenance operations, long period evolution, and so on. As a first step on the validation of part of our orbit propagator, in this work we only consider the perturbation produced by zonal harmonic coefficients in the Earth's gravity potential, so that it is possible to analyze the behaviour of the perturbation methods involved in the corresponding analytical theories.

Effect of a Perturbation on the Chemical Equilibrium: Comparison with Le Chatelier's Principle

ERIC Educational Resources Information Center

Torres, Emilio Martinez

2007-01-01

This article develops a general thermodynamic treatment to predict the direction of shift in a chemical equilibrium when it is subjected to a stress. This treatment gives an inequality that relates the change in the perturbed variable and the change that the equilibrium shift produces in the conjugated variable. To illustrate the generality of…

On the Absolutely Continuous Spectrum of Stark Operators

NASA Astrophysics Data System (ADS)

Perelman, Galina

The stability of the absolutely continuous spectrum of the one-dimensional Stark operator under perturbations of the potential is discussed. The focus is on proving this stability under minimal assumptions on smoothness of the perturbation. A general criterion is presented together with some applications. These include the case of periodic perturbations where we show that any perturbation vL1()∩H-1/2() preserves the a.c. spectrum.

Signal location using generalized linear constraints

NASA Astrophysics Data System (ADS)

Griffiths, Lloyd J.; Feldman, D. D.

1992-01-01

This report has presented a two-part method for estimating the directions of arrival of uncorrelated narrowband sources when there are arbitrary phase errors and angle independent gain errors. The signal steering vectors are estimated in the first part of the method; in the second part, the arrival directions are estimated. It should be noted that the second part of the method can be tailored to incorporate additional information about the nature of the phase errors. For example, if the phase errors are known to be caused solely by element misplacement, the element locations can be estimated concurrently with the DOA's by trying to match the theoretical steering vectors to the estimated ones. Simulation results suggest that, for general perturbation, the method can resolve closely spaced sources under conditions for which a standard high-resolution DOA method such as MUSIC fails.

Time-sliced perturbation theory for large scale structure I: general formalism

DOE Office of Scientific and Technical Information (OSTI.GOV)

Blas, Diego; Garny, Mathias; Sibiryakov, Sergey

2016-07-01

We present a new analytic approach to describe large scale structure formation in the mildly non-linear regime. The central object of the method is the time-dependent probability distribution function generating correlators of the cosmological observables at a given moment of time. Expanding the distribution function around the Gaussian weight we formulate a perturbative technique to calculate non-linear corrections to cosmological correlators, similar to the diagrammatic expansion in a three-dimensional Euclidean quantum field theory, with time playing the role of an external parameter. For the physically relevant case of cold dark matter in an Einstein-de Sitter universe, the time evolution ofmore » the distribution function can be found exactly and is encapsulated by a time-dependent coupling constant controlling the perturbative expansion. We show that all building blocks of the expansion are free from spurious infrared enhanced contributions that plague the standard cosmological perturbation theory. This paves the way towards the systematic resummation of infrared effects in large scale structure formation. We also argue that the approach proposed here provides a natural framework to account for the influence of short-scale dynamics on larger scales along the lines of effective field theory.« less

Global adiabaticity and non-Gaussianity consistency condition

NASA Astrophysics Data System (ADS)

Romano, Antonio Enea; Mooij, Sander; Sasaki, Misao

2016-10-01

In the context of single-field inflation, the conservation of the curvature perturbation on comoving slices, Rc, on super-horizon scales is one of the assumptions necessary to derive the consistency condition between the squeezed limit of the bispectrum and the spectrum of the primordial curvature perturbation. However, the conservation of Rc holds only after the perturbation has reached the adiabatic limit where the constant mode of Rc dominates over the other (usually decaying) mode. In this case, the non-adiabatic pressure perturbation defined in the thermodynamic sense, δPnad ≡ δP - cw2 δρ where cw2 = P ˙ / ρ ˙ , usually becomes also negligible on superhorizon scales. Therefore one might think that the adiabatic limit is the same as thermodynamic adiabaticity. This is in fact not true. In other words, thermodynamic adiabaticity is not a sufficient condition for the conservation of Rc on super-horizon scales. In this paper, we consider models that satisfy δPnad = 0 on all scales, which we call global adiabaticity (GA), which is guaranteed if cw2 = cs2, where cs is the phase velocity of the propagation of the perturbation. A known example is the case of ultra-slow-roll (USR) inflation in which cw2 = cs2 = 1. In order to generalize USR we develop a method to find the Lagrangian of GA K-inflation models from the behavior of background quantities as functions of the scale factor. Applying this method we show that there indeed exists a wide class of GA models with cw2 = cs2, which allows Rc to grow on superhorizon scales, and hence violates the non-Gaussianity consistency condition.

A hierarchical generalization of the acoustic reciprocity theorem involving higher-order derivatives and interaction quantities.

PubMed

Lin, Ju; Li, Jie; Li, Xiaolei; Wang, Ning

2016-10-01

An acoustic reciprocity theorem is generalized, for a smoothly varying perturbed medium, to a hierarchy of reciprocity theorems including higher-order derivatives of acoustic fields. The standard reciprocity theorem is the first member of the hierarchy. It is shown that the conservation of higher-order interaction quantities is related closely to higher-order derivative distributions of perturbed media. Then integral reciprocity theorems are obtained by applying Gauss's divergence theorem, which give explicit integral representations connecting higher-order interactions and higher-order derivative distributions of perturbed media. Some possible applications to an inverse problem are also discussed.

Perturbative computation in a generalized quantum field theory

NASA Astrophysics Data System (ADS)

Bezerra, V. B.; Curado, E. M.; Rego-Monteiro, M. A.

2002-10-01

We consider a quantum field theory that creates at any point of the space-time particles described by a q-deformed Heisenberg algebra which is interpreted as a phenomenological quantum theory describing the scattering of spin-0 composed particles. We discuss the generalization of Wick's expansion for this case and we compute perturbatively the scattering 1+2-->1'+2' to second order in the coupling constant. The result we find shows that the structure of a composed particle, described here phenomenologically by the deformed algebraic structure, can modify in a simple but nontrivial way the perturbation expansion for the process under consideration.

Study of the impact of resonant magnetic perturbation fields on gross tungsten erosion using DiMES samples in DIII-D

NASA Astrophysics Data System (ADS)

Hinson, E. T.; Schmitz, O.; Frerichs, H.; Abrams, T.; Briesemeister, A.; Rudakov, D. L.; Unterberg, E. A.; Wampler, W. R.; Watkins, J. G.; Wang, H. Q.

2017-12-01

An experiment was conducted in DIII-D to compare gross tungsten (W) erosion on samples exposed to outer strike point (OSP) sweeps in L-mode plasmas for three conditions. These included two phases of resonant magnetic perturbations (RMPs), and a set with no perturbations. Upon RMP application, lobe structures indicative of strike point splitting of the OSP were evident in divertor camera data and on Langmuir probes. Gross W erosion flux, {{{Γ }}}{{W}}, inferred spectroscopically using the S/XB method applied to the 400.9 nm W-I line, was generally in the range {{{Γ }}}{{W}}/{{{Γ }}}{{D}+,\\perp }=2× {10}-4 referenced to incident deuterium ion flux {{{Γ }}}{{D}+,\\perp }, and was increased in the RMP cases by no more than 30% of the level observed in unperturbed discharges. A large reduction in gross erosion (50%) was observed in the private flux region at the W sample for one specific toroidal phase of the RMP field.

Palaeostress perturbations near the El Castillo de las Guardas fault (SW Iberian Massif)

NASA Astrophysics Data System (ADS)

García-Navarro, Encarnación; Fernández, Carlos

2010-05-01

Use of stress inversion methods on faults measured at 33 sites located at the northwestern part of the South Portuguese Zone (Variscan Iberian Massif), and analysis of the basic dyke attitude at this same region, has revealed a prominent perturbation of the stress trajectories around some large, crustal-scale faults, like the El Castillo de las Guardas fault. The results are compared with the predictions of theoretical models of palaeostress deviations near master faults. According to this comparison, the El Castillo de las Guardas fault, an old structure that probably reversed several times its slip sense, can be considered as a sinistral strike-slip fault during the Moscovian. These results also point out the main shortcomings that still hinder a rigorous quantitative use of the theoretical models of stress perturbations around major faults: the spatial variation in the parameters governing the brittle behaviour of the continental crust, and the possibility of oblique slip along outcrop-scale faults in regions subjected to general, non-plane strain.

Spectral methods in general relativity and large Randall-Sundrum II black holes

NASA Astrophysics Data System (ADS)

Abdolrahimi, Shohreh; Cattoën, Céline; Page, Don N.; \\\\; Yaghoobpour-Tari, Shima

2013-06-01

Using a novel numerical spectral method, we have found solutions for large static Randall-Sundrum II (RSII) black holes by perturbing a numerical AdS5-CFT4 solution to the Einstein equation with a negative cosmological constant Λ that is asymptotically conformal to the Schwarzschild metric. We used a numerical spectral method independent of the Ricci-DeTurck-flow method used by Figueras, Lucietti, and Wiseman for a similar numerical solution. We have compared our black-hole solution to the one Figueras and Wiseman have derived by perturbing their numerical AdS5-CFT4 solution, showing that our solution agrees closely with theirs. We have obtained a closed-form approximation to the metric of the black hole on the brane. We have also deduced the new results that to first order in 1/(-ΛM2), the Hawking temperature and entropy of an RSII static black hole have the same values as the Schwarzschild metric with the same mass, but the horizon area is increased by about 4.7/(-Λ).

The method of similar operators in the study of the spectra of the adjacency matrices of graphs

NASA Astrophysics Data System (ADS)

Kozlukov, Serge

2018-03-01

The method of similar operators [1, 2, 3] is used to investigate spectral properties of a certain class of matrices in the context of graphs [4, 5]. Specifically, we consider the adjacency matrix of an “almost-complete graph”. Then we generalize the result to allow the matrices obtained as combinations of the Kronecker products [6, 7] and the small-norm perturbations. We derive the estimates of the spectra and the eigenvectors of such matrices.

Method for image reconstruction of moving radionuclide source distribution

DOEpatents

Stolin, Alexander V.; McKisson, John E.; Lee, Seung Joon; Smith, Mark Frederick

2012-12-18

A method for image reconstruction of moving radionuclide distributions. Its particular embodiment is for single photon emission computed tomography (SPECT) imaging of awake animals, though its techniques are general enough to be applied to other moving radionuclide distributions as well. The invention eliminates motion and blurring artifacts for image reconstructions of moving source distributions. This opens new avenues in the area of small animal brain imaging with radiotracers, which can now be performed without the perturbing influences of anesthesia or physical restraint on the biological system.

Advanced reliability methods for structural evaluation

NASA Technical Reports Server (NTRS)

Wirsching, P. H.; Wu, Y.-T.

1985-01-01

Fast probability integration (FPI) methods, which can yield approximate solutions to such general structural reliability problems as the computation of the probabilities of complicated functions of random variables, are known to require one-tenth the computer time of Monte Carlo methods for a probability level of 0.001; lower probabilities yield even more dramatic differences. A strategy is presented in which a computer routine is run k times with selected perturbed values of the variables to obtain k solutions for a response variable Y. An approximating polynomial is fit to the k 'data' sets, and FPI methods are employed for this explicit form.

The algebraic-hyperbolic approach to the linearized gravitational constraints on a Minkowski background

NASA Astrophysics Data System (ADS)

Winicour, Jeffrey

2017-08-01

An algebraic-hyperbolic method for solving the Hamiltonian and momentum constraints has recently been shown to be well posed for general nonlinear perturbations of the initial data for a Schwarzschild black hole. This is a new approach to solving the constraints of Einstein’s equations which does not involve elliptic equations and has potential importance for the construction of binary black hole data. In order to shed light on the underpinnings of this approach, we consider its application to obtain solutions of the constraints for linearized perturbations of Minkowski space. In that case, we find the surprising result that there are no suitable Cauchy hypersurfaces in Minkowski space for which the linearized algebraic-hyperbolic constraint problem is well posed.

Singularity and stability in a periodic system of particle accelerators

NASA Astrophysics Data System (ADS)

Cai, Yunhai

2018-05-01

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

Supercomputer optimizations for stochastic optimal control applications

NASA Technical Reports Server (NTRS)

Chung, Siu-Leung; Hanson, Floyd B.; Xu, Huihuang

1991-01-01

Supercomputer optimizations for a computational method of solving stochastic, multibody, dynamic programming problems are presented. The computational method is valid for a general class of optimal control problems that are nonlinear, multibody dynamical systems, perturbed by general Markov noise in continuous time, i.e., nonsmooth Gaussian as well as jump Poisson random white noise. Optimization techniques for vector multiprocessors or vectorizing supercomputers include advanced data structures, loop restructuring, loop collapsing, blocking, and compiler directives. These advanced computing techniques and superconducting hardware help alleviate Bellman's curse of dimensionality in dynamic programming computations, by permitting the solution of large multibody problems. Possible applications include lumped flight dynamics models for uncertain environments, such as large scale and background random aerospace fluctuations.

A modified homotopy perturbation method and the axial secular frequencies of a non-linear ion trap.

PubMed

Doroudi, Alireza

2012-01-01

In this paper, a modified version of the homotopy perturbation method, which has been applied to non-linear oscillations by V. Marinca, is used for calculation of axial secular frequencies of a non-linear ion trap with hexapole and octopole superpositions. The axial equation of ion motion in a rapidly oscillating field of an ion trap can be transformed to a Duffing-like equation. With only octopole superposition the resulted non-linear equation is symmetric; however, in the presence of hexapole and octopole superpositions, it is asymmetric. This modified homotopy perturbation method is used for solving the resulting non-linear equations. As a result, the ion secular frequencies as a function of non-linear field parameters are obtained. The calculated secular frequencies are compared with the results of the homotopy perturbation method and the exact results. With only hexapole superposition, the results of this paper and the homotopy perturbation method are the same and with hexapole and octopole superpositions, the results of this paper are much more closer to the exact results compared with the results of the homotopy perturbation method.

An attempt to estimate isotropic and anisotropic lateral structure of the Earth by spectral inversion incorporating mixed coupling

NASA Astrophysics Data System (ADS)

Oda, Hitoshi

2005-02-01

We present a way to calculate free oscillation spectra for an aspherical earth model, which is constructed by adding isotropic and anisotropic velocity perturbations to the seismic velocity parameters of a reference earth model, and examine the effect of the velocity perturbations on the free oscillation spectrum. Lateral variations of the velocity perturbations are parametrized as an expansion in generalized spherical harmonics. We assume weak hexagonal anisotropy for the seismic wave anisotropy in the upper mantle, where the hexagonal symmetry axes are horizontally distributed. The synthetic spectra show that the velocity perturbations cause not only strong self-coupling among singlets of a multiplet but also mixed coupling between toroidal and spheroidal multiplets. Both the couplings give rise to an amplitude anomaly on the vertical component spectrum. In this study, we identify the amplitude anomaly resulting from the mixed coupling as quasi-toroidal mode. Excitation of the quasi-toroidal mode by a vertical strike-slip fault is largest on nodal lines of the Rayleigh wave, decreases with increasing azimuth angle and becomes smallest on loop lines. This azimuthal dependence of the spectral amplitude is quite similar to the Love wave radiation pattern. In addition, the amplitude spectrum of the quasi-toroidal mode is more sensitive to the anisotropic velocity perturbation than to the isotropic velocity perturbation. This means that the mode spectrum allowing for the mixed-coupling effect may provide constraints on the anisotropic lateral structure as well as the isotropic lateral structure. An inversion method, called mixed-coupling spectral inversion, is devised to retrieve the isotropic and anisotropic velocity perturbations from the free oscillation spectra incorporating the quasi-toroidal mode. We confirm that the spectral inversion method correctly recovers the isotropic and anisotropic lateral structure. Moreover introducing the mixed-coupling effect in the spectral inversion makes it possible to estimate the odd-order lateral structure, which cannot be determined by the conventional spectral inversion, which takes no account of the mixed coupling. Higher order structure is biased by the mixed coupling when the conventional spectral inversion is applied to the amplitude spectra incorporating the mixed coupling.

Generalization of treadmill perturbation to overground slip during gait: Effect of different perturbation distances on slip recovery.

PubMed

Lee, Anna; Bhatt, Tanvi; Pai, Yi-Chung

2016-01-25

Treadmill-perturbation training (TM-training) may improve a person׳s fall-resistance, whereby adjusting slip distance can be a simple way to manipulate training intensity. The purpose of this study was to determine the effects of different slip distances in TM-training (12-cm vs. 18-cm) on its generalization to the recovery from a novel "free" slip during overground walking. Generalization here means the ability to apply learned skill from TM-training to slip recovery during overground walking. Thirty-six young adults in the TM_12 or the TM_18 group underwent either a 12-cm or an 18-cm slip during the treadmill walking for seven times, or in the control group were not exposed to any perturbation. Their responses were also contrasted with previously reported results from overground-perturbation training (OG-training) in which participants received either a 12-cm or an 18-cm slip during level walking with the same number of repetitions. Everyone was then exposed to the same generalization test during a novel "free" slip in overground walking. Their proactive and reactive control of stability was measured and compared. TM-training displayed a significant training effect in comparison to the control group (p<0.05), while most of the improvements were found in the reactive control of stability and were much-limited in comparison to that of OG-training. Also unlike OG-training, no significant differences were found between the results obtained from the TM_12 and the TM_18 groups (p>0.05). These results underscore the further needs to investigate the potential of the treadmill as a convenient instrument that can effectively deliver perturbation training. Published by Elsevier Ltd.

Generalization of treadmill perturbation to overground slip during gait: Effect of different perturbation distances on slip recovery

PubMed Central

Lee, Anna; Bhatt, Tanvi; Pai, Yi-Chung

2016-01-01

Treadmill-perturbation training (TM-training) may improve a person’s fall-resistance, whereby adjusting slip distance can be a simple way to manipulate training intensity. The purpose of this study was to determine the effects of different slip distances in TM-training (12-cm vs. 18-cm) on its generalization to the recovery from a novel “free” slip during overground walking. Generalization here means the ability to apply learned skill from TM-training to slip recovery during overground walking. Thirty-six young adults in the TM_12 or the TM_18 group underwent either a 12-cm or an 18-cm slip during the treadmill walking for seven times, or in the control group were not exposed to any perturbation. Their responses were also contrasted with previously reported results from overground-perturbation training (OG-training) in which participants received either a 12-cm or an 18-cm slip during level walking with the same number of repetitions. Everyone was then exposed to the same generalization test during a novel “free” slip in overground walking. Their proactive and reactive control of stability was measured and compared. TM-training displayed a significant training effect in comparison to the control group (p<0.05), while most of the improvements were found in the reactive control of stability and were much-limited in comparison to that of OG-training. Also unlike OG-training, no significant differences were found between the results obtained from the TM_12 and the TM_18 groups (p>0.05). These results underscore the further needs to investigate the potential of the treadmill as a convenient instrument that can effectively deliver perturbation training. PMID:26653674

Global Melnikov Theory in Hamiltonian Systems with General Time-Dependent Perturbations

NASA Astrophysics Data System (ADS)

Gidea, Marian; de la Llave, Rafael

2018-04-01

We consider a mechanical system consisting of n-penduli and a d-degree-of-freedom rotator. The phase space of the rotator defines a normally hyperbolic invariant manifold Λ _0 . We apply a time-dependent perturbation, which is not assumed to be either Hamiltonian, or periodic, or quasi-periodic, as we allow for rather general time dependence. The strength of the perturbation is given by a parameter ɛ \\in R . For all |ɛ | sufficiently small, the augmented flow—obtained by making the time into a new variable—has a normally hyperbolic locally invariant manifold \\tilde{Λ }_ɛ . For ɛ =0 , \\tilde{Λ }_0=Λ _0× R . We define a Melnikov-type vector, which gives the first-order expansion of the displacement of the stable and unstable manifolds of \\tilde{Λ }_0 under the perturbation. We provide an explicit formula for the Melnikov vector in terms of convergent improper integrals of the perturbation along homoclinic orbits of the unperturbed system. We show that if the perturbation satisfies some explicit non-degeneracy conditions, then the stable and unstable manifolds of \\tilde{Λ }_ɛ , W^s(\\tilde{Λ }_ɛ ) and W^u(\\tilde{Λ }_ɛ ) , respectively, intersect along a transverse homoclinic manifold, and, moreover, the splitting of W^s(\\tilde{Λ }_ɛ ) and W^u(\\tilde{Λ }_ɛ ) can be explicitly computed, up to the first order, in terms of the Melnikov-type vector. This implies that the excursions along some homoclinic trajectories yield a non-trivial increase of order O(ɛ ) in the action variables of the rotator, for all sufficiently small perturbations. The formulas that we obtain are independent of the unperturbed motions in Λ _0 , and give, at the same time, the effects on periodic, quasi-periodic, or general-type orbits. When the perturbation is Hamiltonian, we express the effects of the perturbation, up to the first order, in terms of a Melnikov potential. In addition, if the perturbation is periodic, we obtain that the non-degeneracy conditions on the Melnikov potential are generic.

Least Squares Moving-Window Spectral Analysis.

PubMed

Lee, Young Jong

2017-08-01

Least squares regression is proposed as a moving-windows method for analysis of a series of spectra acquired as a function of external perturbation. The least squares moving-window (LSMW) method can be considered an extended form of the Savitzky-Golay differentiation for nonuniform perturbation spacing. LSMW is characterized in terms of moving-window size, perturbation spacing type, and intensity noise. Simulation results from LSMW are compared with results from other numerical differentiation methods, such as single-interval differentiation, autocorrelation moving-window, and perturbation correlation moving-window methods. It is demonstrated that this simple LSMW method can be useful for quantitative analysis of nonuniformly spaced spectral data with high frequency noise.

Gravitational perturbations and metric reconstruction: Method of extended homogeneous solutions applied to eccentric orbits on a Schwarzschild black hole

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hopper, Seth; Evans, Charles R.

2010-10-15

We calculate the gravitational perturbations produced by a small mass in eccentric orbit about a much more massive Schwarzschild black hole and use the numerically computed perturbations to solve for the metric. The calculations are initially made in the frequency domain and provide Fourier-harmonic modes for the gauge-invariant master functions that satisfy inhomogeneous versions of the Regge-Wheeler and Zerilli equations. These gravitational master equations have specific singular sources containing both delta function and derivative-of-delta function terms. We demonstrate in this paper successful application of the method of extended homogeneous solutions, developed recently by Barack, Ori, and Sago, to handle sourcemore » terms of this type. The method allows transformation back to the time domain, with exponential convergence of the partial mode sums that represent the field. This rapid convergence holds even in the region of r traversed by the point mass and includes the time-dependent location of the point mass itself. We present numerical results of mode calculations for certain orbital parameters, including highly accurate energy and angular momentum fluxes at infinity and at the black hole event horizon. We then address the issue of reconstructing the metric perturbation amplitudes from the master functions, the latter being weak solutions of a particular form to the wave equations. The spherical harmonic amplitudes that represent the metric in Regge-Wheeler gauge can themselves be viewed as weak solutions. They are in general a combination of (1) two differentiable solutions that adjoin at the instantaneous location of the point mass (a result that has order of continuity C{sup -1} typically) and (2) (in some cases) a delta function distribution term with a computable time-dependent amplitude.« less

Nonlinear phenomena in general relativity

NASA Astrophysics Data System (ADS)

Allahyari, Alireza; Firouzjaee, Javad T.; Mansouri, Reza

2018-04-01

The perturbation theory plays an important role in studying structure formation in cosmology and post-Newtonian physics, but not all phenomena can be described by the linear perturbation theory. Thus, it is necessary to study exact solutions or higher-order perturbations. Specifically, we study black hole (apparent) horizons and the cosmological event horizon formation in the perturbation theory. We emphasize that in the perturbative regime of the gravitational potential these horizons cannot form in the lower order. Studying the infinite plane metric, we show that, to capture the cosmological constant effect, we need at least a second-order expansion.

Effective fragment potential study of the interaction of DNA bases.

PubMed

Smith, Quentin A; Gordon, Mark S; Slipchenko, Lyudmila V

2011-10-20

Hydrogen-bonded and stacked structures of adenine-thymine and guanine-cytosine nucleotide base pairs, along with their methylated analogues, are examined with the ab inito based general effective fragment potential (EFP2) method. A comparison of coupled cluster with single, double, and perturbative triple (CCSD(T)) energies is presented, along with an EFP2 energy decomposition to illustrate the components of the interaction energy.

Making classical and quantum canonical general relativity computable through a power series expansion in the inverse cosmological constant.

PubMed

Gambini, R; Pullin, J

2000-12-18

We consider general relativity with a cosmological constant as a perturbative expansion around a completely solvable diffeomorphism invariant field theory. This theory is the lambda --> infinity limit of general relativity. This allows an explicit perturbative computational setup in which the quantum states of the theory and the classical observables can be explicitly computed. An unexpected relationship arises at a quantum level between the discrete spectrum of the volume operator and the allowed values of the cosmological constant.

A hybrid perturbation-Galerkin technique for partial differential equations

NASA Technical Reports Server (NTRS)

Geer, James F.; Anderson, Carl M.

1990-01-01

A two-step hybrid perturbation-Galerkin technique for improving the usefulness of perturbation solutions to partial differential equations which contain a parameter is presented and discussed. In the first step of the method, the leading terms in the asymptotic expansion(s) of the solution about one or more values of the perturbation parameter are obtained using standard perturbation methods. In the second step, the perturbation functions obtained in the first step are used as trial functions in a Bubnov-Galerkin approximation. This semi-analytical, semi-numerical hybrid technique appears to overcome some of the drawbacks of the perturbation and Galerkin methods when they are applied by themselves, while combining some of the good features of each. The technique is illustrated first by a simple example. It is then applied to the problem of determining the flow of a slightly compressible fluid past a circular cylinder and to the problem of determining the shape of a free surface due to a sink above the surface. Solutions obtained by the hybrid method are compared with other approximate solutions, and its possible application to certain problems associated with domain decomposition is discussed.

Validation and application of auxiliary density perturbation theory and non-iterative approximation to coupled-perturbed Kohn-Sham approach for calculation of dipole-quadrupole polarizability

NASA Astrophysics Data System (ADS)

Shedge, Sapana V.; Pal, Sourav; Köster, Andreas M.

2011-07-01

Recently, two non-iterative approaches have been proposed to calculate response properties within density functional theory (DFT). These approaches are auxiliary density perturbation theory (ADPT) and the non-iterative approach to the coupled-perturbed Kohn-Sham (NIA-CPKS) method. Though both methods are non-iterative, they use different techniques to obtain the perturbed Kohn-Sham matrix. In this Letter, for the first time, both of these two independent methods have been used for the calculation of dipole-quadrupole polarizabilities. To validate these methods, three tetrahedral molecules viz., P4,CH4 and adamantane (C10H16) have been used as examples. The comparison with MP2 and CCSD proves the reliability of the methodology.

Test-retest reliability of a balance testing protocol with external perturbations in young healthy adults.

PubMed

Robbins, Shawn M; Caplan, Ryan M; Aponte, Daniel I; St-Onge, Nancy

2017-10-01

External perturbations are utilized to challenge balance and mimic realistic balance threats in patient populations. The reliability of such protocols has not been established. The purpose was to examine test-retest reliability of balance testing with external perturbations. Healthy adults (n=34; mean age 23 years) underwent balance testing over two visits. Participants completed ten balance conditions in which the following parameters were combined: perturbation or non-perturbation, single or double leg, and eyes open or closed. Three trials were collected for each condition. Data were collected on a force plate and external perturbations were applied by translating the plate. Force plate center of pressure (CoP) data were summarized using 13 different CoP measures. Test-retest reliability was examined using intraclass correlation coefficients (ICC) and Bland-Altman plots. CoP measures of total speed and excursion in both anterior-posterior and medial-lateral directions generally had acceptable ICC values for perturbation conditions (ICC=0.46 to 0.87); however, many other CoP measures (e.g. range, area of ellipse) had unacceptable test-retest reliability (ICC<0.70). Improved CoP measures were present on the second visit indicating a potential learning effect. Non-perturbation conditions generally produced more reliable CoP measures than perturbation conditions during double leg standing, but not single leg standing. Therefore, changes to balance testing protocols that include external perturbations should be made to improve test-retest reliability and diminish learning including more extensive participant training and increasing the number of trials. CoP measures that consider all data points (e.g. total speed) are more reliable than those that only consider a few data points. Copyright © 2017 Elsevier B.V. All rights reserved.

Transition energy and potential energy curves for ionized inner-shell states of CO, O2 and N 2 calculated by several inner-shell multiconfigurational approaches.

PubMed

Moura, Carlos E V de; Oliveira, Ricardo R; Rocha, Alexandre B

2013-05-01

Potential energy curves and inner-shell ionization energies of carbon monoxide, oxygen and nitrogen molecules were calculated using several forms of the inner-shell multiconfigurational self-consistent field (IS-MCSCF) method-a recently proposed protocol to obtain specifically converged inner-shell states at this level. The particular forms of the IS-MCSCF method designated IS-GVB-PP, IS-FVBL and IS-CASSCF stand for perfect pairing generalized valence bond, full valence bond-like MCSCF and complete active space self consistent field, respectively. A comparison of these different versions of the IS-MCSCF method was carried out for the first time. The results indicate that inner-shell states are described accurately even for the simplest version of the method (IS-GVB-PP). Dynamic correlation was recovered by multireference configuration interaction or multireference perturbation theory. For molecules not having equivalent atoms, all methods led to comparable and accurate transition energies. For molecules with equivalent atoms, the most accurate results were obtained by multireference perturbation theory. Scalar relativistic effects were accounted for using the Douglas-Kroll-Hess Hamiltonian.

A new method to compute lunisolar perturbations in satellite motions

NASA Technical Reports Server (NTRS)

Kozai, Y.

1973-01-01

A new method to compute lunisolar perturbations in satellite motion is proposed. The disturbing function is expressed by the orbital elements of the satellite and the geocentric polar coordinates of the moon and the sun. The secular and long periodic perturbations are derived by numerical integrations, and the short periodic perturbations are derived analytically. The perturbations due to the tides can be included in the same way. In the Appendix, the motion of the orbital plane for a synchronous satellite is discussed; it is concluded that the inclination cannot stay below 7 deg.

Robust dynamic mitigation of instabilities

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kawata, S.; Karino, T.

2015-04-15

A dynamic mitigation mechanism for instability growth was proposed and discussed in the paper [S. Kawata, Phys. Plasmas 19, 024503 (2012)]. In the present paper, the robustness of the dynamic instability mitigation mechanism is discussed further. The results presented here show that the mechanism of the dynamic instability mitigation is rather robust against changes in the phase, the amplitude, and the wavelength of the wobbling perturbation applied. Generally, instability would emerge from the perturbation of the physical quantity. Normally, the perturbation phase is unknown so that the instability growth rate is discussed. However, if the perturbation phase is known, themore » instability growth can be controlled by a superposition of perturbations imposed actively: If the perturbation is induced by, for example, a driving beam axis oscillation or wobbling, the perturbation phase could be controlled, and the instability growth is mitigated by the superposition of the growing perturbations.« less

Exact Delaunay normalization of the perturbed Keplerian Hamiltonian with tesseral harmonics

NASA Astrophysics Data System (ADS)

Mahajan, Bharat; Vadali, Srinivas R.; Alfriend, Kyle T.

2018-03-01

A novel approach for the exact Delaunay normalization of the perturbed Keplerian Hamiltonian with tesseral and sectorial spherical harmonics is presented in this work. It is shown that the exact solution for the Delaunay normalization can be reduced to quadratures by the application of Deprit's Lie-transform-based perturbation method. Two different series representations of the quadratures, one in powers of the eccentricity and the other in powers of the ratio of the Earth's angular velocity to the satellite's mean motion, are derived. The latter series representation produces expressions for the short-period variations that are similar to those obtained from the conventional method of relegation. Alternatively, the quadratures can be evaluated numerically, resulting in more compact expressions for the short-period variations that are valid for an elliptic orbit with an arbitrary value of the eccentricity. Using the proposed methodology for the Delaunay normalization, generalized expressions for the short-period variations of the equinoctial orbital elements, valid for an arbitrary tesseral or sectorial harmonic, are derived. The result is a compact unified artificial satellite theory for the sub-synchronous and super-synchronous orbit regimes, which is nonsingular for the resonant orbits, and is closed-form in the eccentricity as well. The accuracy of the proposed theory is validated by comparison with numerical orbit propagations.

Harnessing molecular excited states with Lanczos chains.

PubMed

Baroni, Stefano; Gebauer, Ralph; Bariş Malcioğlu, O; Saad, Yousef; Umari, Paolo; Xian, Jiawei

2010-02-24

The recursion method of Haydock, Heine and Kelly is a powerful tool for calculating diagonal matrix elements of the resolvent of quantum-mechanical Hamiltonian operators by elegantly expressing them in terms of continued fractions. In this paper we extend the recursion method to off-diagonal matrix elements of general (possibly non-Hermitian) operators and apply it to the simulation of molecular optical absorption and photoemission spectra within time-dependent density-functional and many-body perturbation theories, respectively. This method is demonstrated with a couple of applications to the optical absorption and photoemission spectra of the caffeine molecule.

Harnessing molecular excited states with Lanczos chains

NASA Astrophysics Data System (ADS)

Baroni, Stefano; Gebauer, Ralph; Bariş Malcioğlu, O.; Saad, Yousef; Umari, Paolo; Xian, Jiawei

2010-02-01

The recursion method of Haydock, Heine and Kelly is a powerful tool for calculating diagonal matrix elements of the resolvent of quantum-mechanical Hamiltonian operators by elegantly expressing them in terms of continued fractions. In this paper we extend the recursion method to off-diagonal matrix elements of general (possibly non-Hermitian) operators and apply it to the simulation of molecular optical absorption and photoemission spectra within time-dependent density-functional and many-body perturbation theories, respectively. This method is demonstrated with a couple of applications to the optical absorption and photoemission spectra of the caffeine molecule.

Subtraction method of computing QCD jet cross sections at NNLO accuracy

NASA Astrophysics Data System (ADS)

Trócsányi, Zoltán; Somogyi, Gábor

2008-10-01

We present a general subtraction method for computing radiative corrections to QCD jet cross sections at next-to-next-to-leading order accuracy. The steps needed to set up this subtraction scheme are the same as those used in next-to-leading order computations. However, all steps need non-trivial modifications, which we implement such that that those can be defined at any order in perturbation theory. We give a status report of the implementation of the method to computing jet cross sections in electron-positron annihilation at the next-to-next-to-leading order accuracy.

Primordial perturbations in a rainbow universe with running Newton constant

NASA Astrophysics Data System (ADS)

Brighenti, Francesco; Gubitosi, Giulia; Magueijo, Joao

2017-03-01

We compute the spectral index of primordial perturbations in a rainbow universe. We allow the Newton constant G to run at (super-) Planckian energies and we consider both vacuum and thermal perturbations. If the rainbow metric is the one associated to a generalized Horava-Lifshitz dispersion relation, we find that only when G tends asymptotically to 0 can one match the observed value of the spectral index and solve the horizon problem, both for vacuum and thermal perturbations. For vacuum fluctuations the observational constraints imply that the primordial universe expansion can be both accelerating or decelerating, while in the case of thermal perturbations only decelerating expansion is allowed.

A double perturbation method of postbuckling analysis in 2D curved beams for assembly of 3D ribbon-shaped structures

NASA Astrophysics Data System (ADS)

Fan, Zhichao; Hwang, Keh-Chih; Rogers, John A.; Huang, Yonggang; Zhang, Yihui

2018-02-01

Mechanically-guided 3D assembly based on controlled, compressive buckling represents a promising, emerging approach for forming complex 3D mesostructures in advanced materials. Due to the versatile applicability to a broad set of material types (including device-grade single-crystal silicon) over length scales from nanometers to centimeters, a wide range of novel applications have been demonstrated in soft electronic systems, interactive bio-interfaces as well as tunable electromagnetic devices. Previously reported 3D designs relied mainly on finite element analyses (FEA) as a guide, but the massive numerical simulations and computational efforts necessary to obtain the assembly parameters for a targeted 3D geometry prevent rapid exploration of engineering options. A systematic understanding of the relationship between a 3D shape and the associated parameters for assembly requires the development of a general theory for the postbuckling process. In this paper, a double perturbation method is established for the postbuckling analyses of planar curved beams, of direct relevance to the assembly of ribbon-shaped 3D mesostructures. By introducing two perturbation parameters related to the initial configuration and the deformation, the highly nonlinear governing equations can be transformed into a series of solvable, linear equations that give analytic solutions to the displacements and curvatures during postbuckling. Systematic analyses of postbuckling in three representative ribbon shapes (sinusoidal, polynomial and arc configurations) illustrate the validity of theoretical method, through comparisons to the results of experiment and FEA. These results shed light on the relationship between the important deformation quantities (e.g., mode ratio and maximum strain) and the assembly parameters (e.g., initial configuration and the applied strain). This double perturbation method provides an attractive route to the inverse design of ribbon-shaped 3D geometries, as demonstrated in a class of helical mesostructures.

Short-ranged interaction effects on Z2 topological phase transitions: The perturbative mean-field method

NASA Astrophysics Data System (ADS)

Lai, Hsin-Hua; Hung, Hsiang-Hsuan

2015-02-01

Time-reversal symmetric topological insulator (TI) is a novel state of matter that a bulk-insulating state carries dissipationless spin transport along the surfaces, embedded by the Z2 topological invariant. In the noninteracting limit, this exotic state has been intensively studied and explored with realistic systems, such as HgTe/(Hg, Cd)Te quantum wells. On the other hand, electronic correlation plays a significant role in many solid-state systems, which further influences topological properties and triggers topological phase transitions. Yet an interacting TI is still an elusive subject and most related analyses rely on the mean-field approximation and numerical simulations. Among the approaches, the mean-field approximation fails to predict the topological phase transition, in particular at intermediate interaction strength without spontaneously breaking symmetry. In this paper, we develop an analytical approach based on a combined perturbative and self-consistent mean-field treatment of interactions that is capable of capturing topological phase transitions beyond either method when used independently. As an illustration of the method, we study the effects of short-ranged interactions on the Z2 TI phase, also known as the quantum spin Hall (QSH) phase, in three generalized versions of the Kane-Mele (KM) model at half-filling on the honeycomb lattice. The results are in excellent agreement with quantum Monte Carlo (QMC) calculations on the same model and cannot be reproduced by either a perturbative treatment or a self-consistent mean-field treatment of the interactions. Our analytical approach helps to clarify how the symmetries of the one-body terms of the Hamiltonian determine whether interactions tend to stabilize or destabilize a topological phase. Moreover, our method should be applicable to a wide class of models where topological transitions due to interactions are in principle possible, but are not correctly predicted by either perturbative or self-consistent treatments.

Electromagnetic perturbations of black holes in general relativity coupled to nonlinear electrodynamics

NASA Astrophysics Data System (ADS)

Toshmatov, Bobir; Stuchlík, Zdeněk; Schee, Jan; Ahmedov, Bobomurat

2018-04-01

The electromagnetic (EM) perturbations of the black hole solutions in general relativity coupled to nonlinear electrodynamics (NED) are studied for both electrically and magnetically charged black holes, assuming that the EM perturbations do not alter the spacetime geometry. It is shown that the effective potentials of the electrically and magnetically charged black holes related to test perturbative NED EM fields are related to the effective metric governing the photon motion, contrary to the effective potential of the linear electrodynamic (Maxwell) field that is related to the spacetime metric. Consequently, corresponding quasinormal (QN) frequencies differ as well. As a special case, we study new family of the NED black hole solutions which tend in the weak field limit to the Maxwell field, giving the Reissner-Nordström (RN) black hole solution. We compare the NED Maxwellian black hole QN spectra with the RN black hole QN spectra.

A generalized non-Gaussian consistency relation for single field inflation

NASA Astrophysics Data System (ADS)

Bravo, Rafael; Mooij, Sander; Palma, Gonzalo A.; Pradenas, Bastián

2018-05-01

We show that a perturbed inflationary spacetime, driven by a canonical single scalar field, is invariant under a special class of coordinate transformations together with a field reparametrization of the curvature perturbation in co-moving gauge. This transformation may be used to derive the squeezed limit of the 3-point correlation function of the co-moving curvature perturbations valid in the case that these do not freeze after horizon crossing. This leads to a generalized version of Maldacena's non-Gaussian consistency relation in the sense that the bispectrum squeezed limit is completely determined by spacetime diffeomorphisms. Just as in the case of the standard consistency relation, this result may be understood as the consequence of how long-wavelength modes modulate those of shorter wavelengths. This relation allows one to derive the well known violation to the consistency relation encountered in ultra slow-roll, where curvature perturbations grow exponentially after horizon crossing.

Multiple and exact soliton solutions of the perturbed Korteweg-de Vries equation of long surface waves in a convective fluid via Painlevé analysis, factorization, and simplest equation methods.

PubMed

Selima, Ehab S; Yao, Xiaohua; Wazwaz, Abdul-Majid

2017-06-01

In this research, the surface waves of a horizontal fluid layer open to air under gravity field and vertical temperature gradient effects are studied. The governing equations of this model are reformulated and converted to a nonlinear evolution equation, the perturbed Korteweg-de Vries (pKdV) equation. We investigate the latter equation, which includes dispersion, diffusion, and instability effects, in order to examine the evolution of long surface waves in a convective fluid. Dispersion relation of the pKdV equation and its properties are discussed. The Painlevé analysis is applied not only to check the integrability of the pKdV equation but also to establish the Bäcklund transformation form. In addition, traveling wave solutions and a general form of the multiple-soliton solutions of the pKdV equation are obtained via Bäcklund transformation, the simplest equation method using Bernoulli, Riccati, and Burgers' equations as simplest equations, and the factorization method.

Analytic Perturbation Method for Estimating Ground Flash Fraction from Satellite Lightning Observations

NASA Technical Reports Server (NTRS)

Koshak, William; Solakiewicz, Richard

2013-01-01

An analytic perturbation method is introduced for estimating the lightning ground flash fraction in a set of N lightning flashes observed by a satellite lightning mapper. The value of N is large, typically in the thousands, and the observations consist of the maximum optical group area produced by each flash. The method is tested using simulated observations that are based on Optical Transient Detector (OTD) and Lightning Imaging Sensor (LIS) data. National Lightning Detection NetworkTM (NLDN) data is used to determine the flash-type (ground or cloud) of the satellite-observed flashes, and provides the ground flash fraction truth for the simulation runs. It is found that the mean ground flash fraction retrieval errors are below 0.04 across the full range 0-1 under certain simulation conditions. In general, it is demonstrated that the retrieval errors depend on many factors (i.e., the number, N, of satellite observations, the magnitude of random and systematic measurement errors, and the number of samples used to form certain climate distributions employed in the model).

Minimum current principle and variational method in theory of space charge limited flow

NASA Astrophysics Data System (ADS)

Rokhlenko, A.

2015-10-01

In spirit of the principle of least action, which means that when a perturbation is applied to a physical system, its reaction is such that it modifies its state to "agree" with the perturbation by "minimal" change of its initial state. In particular, the electron field emission should produce the minimum current consistent with boundary conditions. It can be found theoretically by solving corresponding equations using different techniques. We apply here the variational method for the current calculation, which can be quite effective even when involving a short set of trial functions. The approach to a better result can be monitored by the total current that should decrease when we on the right track. Here, we present only an illustration for simple geometries of devices with the electron flow. The development of these methods can be useful when the emitter and/or anode shapes make difficult the use of standard approaches. Though direct numerical calculations including particle-in-cell technique are very effective, but theoretical calculations can provide an important insight for understanding general features of flow formation and even sometimes be realized by simpler routines.

Semiclassical Path Integral Calculation of Nonlinear Optical Spectroscopy.

PubMed

Provazza, Justin; Segatta, Francesco; Garavelli, Marco; Coker, David F

2018-02-13

Computation of nonlinear optical response functions allows for an in-depth connection between theory and experiment. Experimentally recorded spectra provide a high density of information, but to objectively disentangle overlapping signals and to reach a detailed and reliable understanding of the system dynamics, measurements must be integrated with theoretical approaches. Here, we present a new, highly accurate and efficient trajectory-based semiclassical path integral method for computing higher order nonlinear optical response functions for non-Markovian open quantum systems. The approach is, in principle, applicable to general Hamiltonians and does not require any restrictions on the form of the intrasystem or system-bath couplings. This method is systematically improvable and is shown to be valid in parameter regimes where perturbation theory-based methods qualitatively breakdown. As a test of the methodology presented here, we study a system-bath model for a coupled dimer for which we compare against numerically exact results and standard approximate perturbation theory-based calculations. Additionally, we study a monomer with discrete vibronic states that serves as the starting point for future investigation of vibronic signatures in nonlinear electronic spectroscopy.

Propagation of nonlinear shock waves for the generalised Oskolkov equation and its dynamic motions in the presence of an external periodic perturbation

NASA Astrophysics Data System (ADS)

Ak, Turgut; Aydemir, Tugba; Saha, Asit; Kara, Abdul Hamid

2018-06-01

Propagation of nonlinear shock waves for the generalised Oskolkov equation and dynamic motions of the perturbed Oskolkov equation are investigated. Employing the unified method, a collection of exact shock wave solutions for the generalised Oskolkov equations is presented. Collocation finite element method is applied to the generalised Oskolkov equation for checking the accuracy of the proposed method by two test problems including the motion of shock wave and evolution of waves with Gaussian and undular bore initial conditions. Considering an external periodic perturbation, the dynamic motions of the perturbed generalised Oskolkov equation are studied depending on the system parameters with the help of phase portrait and time series plot. The perturbed generalised Oskolkov equation exhibits period-3, quasiperiodic and chaotic motions for some special values of the system parameters, whereas the generalised Oskolkov equation presents shock waves in the absence of external periodic perturbation.

Structural stability and chaotic solutions of perturbed Benjamin-Ono equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Birnir, B.; Morrison, P.J.

1986-11-01

A method for proving chaos in partial differential equations is discussed and applied to the Benjamin-Ono equation subject to perturbations. The perturbations are of two types: one that corresponds to viscous dissipation, the so-called Burger's term, and one that involves the Hilbert transform and has been used to model Landau damping. The method proves chaos in the PDE by proving temporal chaos in its pole solutions. The spatial structure of the pole solutions remains intact, but their positions are chaotic in time. Melnikov's method is invoked to show this temporal chaos. It is discovered that the pole behavior is verymore » sensitive to the Burger's perturbation, but is quite insensitive to the perturbation involving the Hilbert transform.« less

Constructive methods for the ground-state energy of fully interacting fermion gases

DOE Office of Scientific and Technical Information (OSTI.GOV)

Aguilera Navarro, V.C.; Baker G.A. Jr.; Benofy, L.P.

1987-11-01

A perturbation scheme based not on the ideal gas but on a system of purely repulsive cores is applied to a typical fully interacting fermion gas. This is ''neutron matter'' interacting via (a) the repulsive ''Bethe homework-problem'' potential, (b) a hard-core--plus--square-well potential, and (c) the Baker-Hind-Kahane modification of the latter, suitable for describing a more accurate two-nucleon potential. Pade extrapolation techniques and generalizations thereof are employed to represent both the density dependence as well as the attractive coupling dependence of the perturbation expansion. Equations of state are constructed and compared with Jastrow--Monte Carlo calculations as well as expectations based onmore » semiempirical mass formulas. Excellent agreement is found with the latter.« less

A Korteweg-de Vries description of dark solitons in polariton superfluids

NASA Astrophysics Data System (ADS)

Carretero-González, R.; Cuevas-Maraver, J.; Frantzeskakis, D. J.; Horikis, T. P.; Kevrekidis, P. G.; Rodrigues, A. S.

2017-12-01

We study the dynamics of dark solitons in an incoherently pumped exciton-polariton condensate by means of a system composed of a generalized open-dissipative Gross-Pitaevskii equation for the polaritons' wavefunction and a rate equation for the exciton reservoir density. Considering a perturbative regime of sufficiently small reservoir excitations, we use the reductive perturbation method, to reduce the system to a Korteweg-de Vries (KdV) equation with linear loss. This model is used to describe the analytical form and the dynamics of dark solitons. We show that the polariton field supports decaying dark soliton solutions with a decay rate determined analytically in the weak pumping regime. We also find that the dark soliton evolution is accompanied by a shelf, whose dynamics follows qualitatively the effective KdV picture.

Understanding the large-distance behavior of transverse-momentum-dependent parton densities and the Collins-Soper evolution kernel

DOE PAGES

Collins, John; Rogers, Ted

2015-04-01

There is considerable controversy about the size and importance of non-perturbative contributions to the evolution of transverse momentum dependent (TMD) parton distribution functions. Standard fits to relatively high-energy Drell-Yan data give evolution that when taken to lower Q is too rapid to be consistent with recent data in semi-inclusive deeply inelastic scattering. Some authors provide very different forms for TMD evolution, even arguing that non-perturbative contributions at large transverse distance bT are not needed or are irrelevant. Here, we systematically analyze the issues, both perturbative and non-perturbative. We make a motivated proposal for the parameterization of the non-perturbative part ofmore » the TMD evolution kernel that could give consistency: with the variety of apparently conflicting data, with theoretical perturbative calculations where they are applicable, and with general theoretical non-perturbative constraints on correlation functions at large distances. We propose and use a scheme- and scale-independent function A(bT) that gives a tool to compare and diagnose different proposals for TMD evolution. We also advocate for phenomenological studies of A(bT) as a probe of TMD evolution. The results are important generally for applications of TMD factorization. In particular, they are important to making predictions for proposed polarized Drell- Yan experiments to measure the Sivers function.« less

Understanding the large-distance behavior of transverse-momentum-dependent parton densities and the Collins-Soper evolution kernel

DOE Office of Scientific and Technical Information (OSTI.GOV)

Collins, John; Rogers, Ted

There is considerable controversy about the size and importance of non-perturbative contributions to the evolution of transverse momentum dependent (TMD) parton distribution functions. Standard fits to relatively high-energy Drell-Yan data give evolution that when taken to lower Q is too rapid to be consistent with recent data in semi-inclusive deeply inelastic scattering. Some authors provide very different forms for TMD evolution, even arguing that non-perturbative contributions at large transverse distance bT are not needed or are irrelevant. Here, we systematically analyze the issues, both perturbative and non-perturbative. We make a motivated proposal for the parameterization of the non-perturbative part ofmore » the TMD evolution kernel that could give consistency: with the variety of apparently conflicting data, with theoretical perturbative calculations where they are applicable, and with general theoretical non-perturbative constraints on correlation functions at large distances. We propose and use a scheme- and scale-independent function A(bT) that gives a tool to compare and diagnose different proposals for TMD evolution. We also advocate for phenomenological studies of A(bT) as a probe of TMD evolution. The results are important generally for applications of TMD factorization. In particular, they are important to making predictions for proposed polarized Drell- Yan experiments to measure the Sivers function.« less

Computerized series solution of relativistic equations of motion.

NASA Technical Reports Server (NTRS)

Broucke, R.

1971-01-01

A method of solution of the equations of planetary motion is described. It consists of the use of numerical general perturbations in orbital elements and in rectangular coordinates. The solution is expanded in Fourier series in the mean anomaly with the aid of harmonic analysis and computerized series manipulation techniques. A detailed application to the relativistic motion of the planet Mercury is described both for Schwarzschild and isotropic coordinates.

Patient observers and non-perturbative infrared dynamics in inflation

NASA Astrophysics Data System (ADS)

Ferreira, Ricardo Z.; Sandora, McCullen; Sloth, Martin S.

2018-02-01

We have previously derived the effect of soft graviton modes on the quantum state of de Sitter using spontaneously broken asymptotic symmetries. In the present paper we prove that this effect can be reinterpreted in terms of Bogoliubov transformations acting on the quantum state. This also enables us to address the much discussed issues regarding the observability of infrared effects in de Sitter from a new perspective. While it is commonly agreed that infrared effects are not visible to a single sub-horizon observer at late times, we argue that the question is less trivial for a patient observer who has lived long enough to have a record of the state before the soft mode was created. Though classically there is no obstruction to measuring this effect locally, we give several indications that quantum mechanical uncertainties may censor the effect. We then apply our methods to find a non-perturbative description of the quantum state pertaining to the Page time of de Sitter, and derive with these new methods the probability distribution for the local quantum states of de Sitter and slow-roll inflation in the presence of long modes. Finally, we show that this formalism reproduces and generalizes the usual criterion for the presence of eternal inflation in general classes of slow-roll inflation.

Diagnosis of dynamic process over rainband of landfall typhoon

NASA Astrophysics Data System (ADS)

Ran, Ling-Kun; Yang, Wen-Xia; Chu, Yan-Li

2010-07-01

This paper introduces a new physical parameter — thermodynamic shear advection parameter combining the perturbation vertical component of convective vorticity vector with the coupling of horizontal divergence perturbation and vertical gradient of general potential temperature perturbation. For a heavy-rainfall event resulting from the landfall typhoon 'Wipha', the parameter is calculated by using National Centres for Enviromental Prediction/National Centre for Atmospheric Research global final analysis data. The results showed that the parameter corresponds to the observed 6 h accumulative rainband since it is capable of catching hold of the dynamic and thermodynamic disturbance in the lower troposphere over the observed rainband. Before the typhoon landed, the advection of the parameter by basic-state flow and the coupling of general potential temperature perturbation with curl of Coriolis force perturbation are the primary dynamic processes which are responsible for the local change of the parameter. After the typhoon landed, the disturbance is mainly driven by the combination of five primary dynamic processes. The advection of the parameter by basic-state flow was weakened after the typhoon landed.

Dynamics of a prey-predator system under Poisson white noise excitation

NASA Astrophysics Data System (ADS)

Pan, Shan-Shan; Zhu, Wei-Qiu

2014-10-01

The classical Lotka-Volterra (LV) model is a well-known mathematical model for prey-predator ecosystems. In the present paper, the pulse-type version of stochastic LV model, in which the effect of a random natural environment has been modeled as Poisson white noise, is investigated by using the stochastic averaging method. The averaged generalized Itô stochastic differential equation and Fokker-Planck-Kolmogorov (FPK) equation are derived for prey-predator ecosystem driven by Poisson white noise. Approximate stationary solution for the averaged generalized FPK equation is obtained by using the perturbation method. The effect of prey self-competition parameter ɛ2 s on ecosystem behavior is evaluated. The analytical result is confirmed by corresponding Monte Carlo (MC) simulation.

Signatures of extra dimensions in gravitational waves from black hole quasinormal modes

NASA Astrophysics Data System (ADS)

Chakraborty, Sumanta; Chakravarti, Kabir; Bose, Sukanta; SenGupta, Soumitra

2018-05-01

In this work, we have derived the evolution equation for gravitational perturbation in four-dimensional spacetime in the presence of a spatial extra dimension. The evolution equation is derived by perturbing the effective gravitational field equations on the four-dimensional spacetime, which inherits nontrivial higher-dimensional effects. Note that this is different from the perturbation of the five-dimensional gravitational field equations that exist in the literature and possess quantitatively new features. The gravitational perturbation has further been decomposed into a purely four-dimensional part and another piece that depends on extra dimensions. The four-dimensional gravitational perturbation now admits massive propagating degrees of freedom, owing to the existence of higher dimensions. We have also studied the influence of these massive propagating modes on the quasinormal mode frequencies, signaling the higher-dimensional nature of the spacetime, and have contrasted these massive modes with the massless modes in general relativity. Surprisingly, it turns out that the massive modes experience damping much smaller than that of the massless modes in general relativity and may even dominate over and above the general relativity contribution if one observes the ringdown phase of a black hole merger event at sufficiently late times. Furthermore, the whole analytical framework has been supplemented by the fully numerical Cauchy evolution problem, as well. In this context, we have shown that, except for minute details, the overall features of the gravitational perturbations are captured both in the Cauchy evolution as well as in the analysis of quasinormal modes. The implications on observations of black holes with LIGO and proposed space missions such as LISA are also discussed.

Application of multivariable search techniques to the optimization of airfoils in a low speed nonlinear inviscid flow field

NASA Technical Reports Server (NTRS)

Hague, D. S.; Merz, A. W.

1975-01-01

Multivariable search techniques are applied to a particular class of airfoil optimization problems. These are the maximization of lift and the minimization of disturbance pressure magnitude in an inviscid nonlinear flow field. A variety of multivariable search techniques contained in an existing nonlinear optimization code, AESOP, are applied to this design problem. These techniques include elementary single parameter perturbation methods, organized search such as steepest-descent, quadratic, and Davidon methods, randomized procedures, and a generalized search acceleration technique. Airfoil design variables are seven in number and define perturbations to the profile of an existing NACA airfoil. The relative efficiency of the techniques are compared. It is shown that elementary one parameter at a time and random techniques compare favorably with organized searches in the class of problems considered. It is also shown that significant reductions in disturbance pressure magnitude can be made while retaining reasonable lift coefficient values at low free stream Mach numbers.

Celestial mechanics - Methods of the theory of motion of 'artificial' celestial bodies

NASA Astrophysics Data System (ADS)

Duboshin, G. N.

This book is concerned with the translational motion of 'artificial' celestial bodies. The difference between natural celestial bodies, which are ordinarily considered by celestial mechanics, and 'artificial' celestial bodies is discussed, taking into account hypothetical celestial bodies introduced in connection with mathematical developments and problems, invisible celestial bodies whose existence can be assumed on the basis of some plausible hypothesis, and man-made satellites of the earth. The book consists of two parts. The first part presents introductory material, and examines a number of general mathematical questions to provide a basis for the studies conducted in the second part. Subjects considered in the first part are related to basic problems, integration methods, and perturbation theory. In the second part, attention is given to the motion of artificial celestial bodies in the gravitational field of the basic planet, external perturbations regarding the motion of these bodies, the motion of the bodies in the earth-moon system, and periodic solutions.

NMR shieldings from density functional perturbation theory: GIPAW versus all-electron calculations

NASA Astrophysics Data System (ADS)

de Wijs, G. A.; Laskowski, R.; Blaha, P.; Havenith, R. W. A.; Kresse, G.; Marsman, M.

2017-02-01

We present a benchmark of the density functional linear response calculation of NMR shieldings within the gauge-including projector-augmented-wave method against all-electron augmented-plane-wave+local-orbital and uncontracted Gaussian basis set results for NMR shieldings in molecular and solid state systems. In general, excellent agreement between the aforementioned methods is obtained. Scalar relativistic effects are shown to be quite large for nuclei in molecules in the deshielded limit. The small component makes up a substantial part of the relativistic corrections.

NMR shieldings from density functional perturbation theory: GIPAW versus all-electron calculations.

PubMed

de Wijs, G A; Laskowski, R; Blaha, P; Havenith, R W A; Kresse, G; Marsman, M

2017-02-14

We present a benchmark of the density functional linear response calculation of NMR shieldings within the gauge-including projector-augmented-wave method against all-electron augmented-plane-wave+local-orbital and uncontracted Gaussian basis set results for NMR shieldings in molecular and solid state systems. In general, excellent agreement between the aforementioned methods is obtained. Scalar relativistic effects are shown to be quite large for nuclei in molecules in the deshielded limit. The small component makes up a substantial part of the relativistic corrections.

On the perturbation and subproper splittings for the generalized inverse AT,S(2) of rectangular matrix A

NASA Astrophysics Data System (ADS)

Wei, Yimin; Wu, Hebing

2001-12-01

In this paper, the perturbation and subproper splittings for the generalized inverse AT,S(2), the unique matrix X such that XAX=X, R(X)=T and N(X)=S, are considered. We present lower and upper bounds for the perturbation of AT,S(2). Convergence of subproper splittings for computing the special solution AT,S(2)b of restricted rectangular linear system Ax=b, x[set membership, variant]T, are studied. For the solution AT,S(2)b we develop a characterization. Therefore, we give a unified treatment of the related problems considered in literature by Ben-Israel, Berman, Hanke, Neumann, Plemmons, etc.

Grid sensitivity capability for large scale structures

NASA Technical Reports Server (NTRS)

Nagendra, Gopal K.; Wallerstein, David V.

1989-01-01

The considerations and the resultant approach used to implement design sensitivity capability for grids into a large scale, general purpose finite element system (MSC/NASTRAN) are presented. The design variables are grid perturbations with a rather general linking capability. Moreover, shape and sizing variables may be linked together. The design is general enough to facilitate geometric modeling techniques for generating design variable linking schemes in an easy and straightforward manner. Test cases have been run and validated by comparison with the overall finite difference method. The linking of a design sensitivity capability for shape variables in MSC/NASTRAN with an optimizer would give designers a powerful, automated tool to carry out practical optimization design of real life, complicated structures.

Steady and Oscillatory, Subsonic and Supersonic, Aerodynamic Pressure and Generalized Forces for Complex Aircraft Configurations and Applications to Flutter. M.S. Thesis

NASA Technical Reports Server (NTRS)

Chen, L. T.

1975-01-01

A general method for analyzing aerodynamic flows around complex configurations is presented. By applying the Green function method, a linear integral equation relating the unknown, small perturbation potential on the surface of the body, to the known downwash is obtained. The surfaces of the aircraft, wake and diaphragm (if necessary) are divided into small quadrilateral elements which are approximated with hyperboloidal surfaces. The potential and its normal derivative are assumed to be constant within each element. This yields a set of linear algebraic equations and the coefficients are evaluated analytically. By using Gaussian elimination method, equations are solved for the potentials at the centroids of elements. The pressure coefficient is evaluated by the finite different method; the lift and moment coefficients are evaluated by numerical integration. Numerical results are presented, and applications to flutter are also included.

Tracking perturbations in Boolean networks with spectral methods

NASA Astrophysics Data System (ADS)

Kesseli, Juha; Rämö, Pauli; Yli-Harja, Olli

2005-08-01

In this paper we present a method for predicting the spread of perturbations in Boolean networks. The method is applicable to networks that have no regular topology. The prediction of perturbations can be performed easily by using a presented result which enables the efficient computation of the required iterative formulas. This result is based on abstract Fourier transform of the functions in the network. In this paper the method is applied to show the spread of perturbations in networks containing a distribution of functions found from biological data. The advances in the study of the spread of perturbations can directly be applied to enable ways of quantifying chaos in Boolean networks. Derrida plots over an arbitrary number of time steps can be computed and thus distributions of functions compared with each other with respect to the amount of order they create in random networks.

The mass and angular momentum of reconstructed metric perturbations

NASA Astrophysics Data System (ADS)

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.

Perception of socket alignment perturbations in amputees with transtibial prostheses.

PubMed

Boone, David A; Kobayashi, Toshiki; Chou, Teri G; Arabian, Adam K; Coleman, Kim L; Orendurff, Michael S; Zhang, Ming

2012-01-01

A person with amputation's subjective perception is the only tool available to describe fit and comfort to a prosthetist. However, few studies have investigated the effect of alignment on this perception. The aim of this article is to determine whether people with amputation could perceive the alignment perturbations of their prostheses and effectively communicate them. A randomized controlled perturbation of angular (3 and 6 degrees) and translational (5 and 10 mm) alignments in the sagittal (flexion, extension, and anterior and posterior translations) and coronal (abduction, adduction, and medial and lateral translations) planes were induced from an aligned condition in 11 subjects with transtibial prostheses. The perception was evaluated when standing (static) and immediately after walking (dynamic) using software that used a visual analog scale under each alignment condition. In the coronal plane, Friedman test demonstrated general statistical differences in static (p < 0.001) and dynamic (p < 0.001) measures of perceptions with angular perturbations. In the sagittal plane, it also demonstrated general statistical differences in late-stance dynamic measures of perceptions (p < 0.001) with angular perturbations, as well as in early-stance dynamic measures of perceptions (p < 0.05) with translational perturbations. Fisher exact test suggested that people with amputation's perceptions were good indicators for coronal angle malalignments but less reliable when defining other alignment conditions.

The causal perturbation expansion revisited: Rescaling the interacting Dirac sea

NASA Astrophysics Data System (ADS)

Finster, Felix; Grotz, Andreas

2010-07-01

The causal perturbation expansion defines the Dirac sea in the presence of a time-dependent external field. It yields an operator whose image generalizes the vacuum solutions of negative energy and thus gives a canonical splitting of the solution space into two subspaces. After giving a self-contained introduction to the ideas and techniques, we show that this operator is, in general, not idempotent. We modify the standard construction by a rescaling procedure giving a projector on the generalized negative-energy subspace. The resulting rescaled causal perturbation expansion uniquely defines the fermionic projector in terms of a series of distributional solutions of the Dirac equation. The technical core of the paper is to work out the combinatorics of the expansion in detail. It is also shown that the fermionic projector with interaction can be obtained from the free projector by a unitary transformation. We finally analyze the consequences of the rescaling procedure on the light-cone expansion.

Experience in estimating neutron poison worths

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chiang, R.T.; Congdon, S.P.

1989-01-01

Gadolinia, {sup 135}Xe, {sup 149}Sm, control rod, and soluble boron are five neutron poisons that may appear in light water reactor assemblies. Reliable neutron poison worth estimation is useful for evaluating core operating strategies, fuel cycle economics, and reactor safety design. Based on physical presence, neutron poisons can be divided into two categories: local poisons and global poisons. Gadolinia and control rod are local poisons, and {sup 135}Xe, {sup 149}Sm, and soluble boron are global poisons. The first-order perturbation method is commonly used to estimate nuclide worths in fuel assemblies. It is well known, however, that the first-order perturbation methodmore » was developed for small perturbations, such as the perturbation due to weak absorbers, and that neutron poisons are not weak absorbers. The authors have developed an improved method to replace the first-order perturbation method, which yields very poor results, for estimating local poison worths. It has also been shown that the first-order perturbation method seems adequate to estimate worths for global poisons caused by flux compensation.« less

Divergence of perturbation theory in large scale structures

NASA Astrophysics Data System (ADS)

Pajer, Enrico; van der Woude, Drian

2018-05-01

We make progress towards an analytical understanding of the regime of validity of perturbation theory for large scale structures and the nature of some non-perturbative corrections. We restrict ourselves to 1D gravitational collapse, for which exact solutions before shell crossing are known. We review the convergence of perturbation theory for the power spectrum, recently proven by McQuinn and White [1], and extend it to non-Gaussian initial conditions and the bispectrum. In contrast, we prove that perturbation theory diverges for the real space two-point correlation function and for the probability density function (PDF) of the density averaged in cells and all the cumulants derived from it. We attribute these divergences to the statistical averaging intrinsic to cosmological observables, which, even on very large and "perturbative" scales, gives non-vanishing weight to all extreme fluctuations. Finally, we discuss some general properties of non-perturbative effects in real space and Fourier space.

Application of adenosine triphosphate affinity probe and scheduled multiple-reaction monitoring analysis for profiling global kinome in human cells in response to arsenite treatment.

PubMed

Guo, Lei; Xiao, Yongsheng; Wang, Yinsheng

2014-11-04

Phosphorylation of cellular components catalyzed by kinases plays important roles in cell signaling and proliferation. Quantitative assessment of perturbation in global kinome may provide crucial knowledge for elucidating the mechanisms underlying the cytotoxic effects of environmental toxicants. Here, we utilized an adenosine triphosphate (ATP) affinity probe coupled with stable isotope labeling by amino acids in cell culture (SILAC) to assess quantitatively the arsenite-induced alteration of global kinome in human cells. We constructed a SILAC-compatible kinome library for scheduled multiple-reaction monitoring (MRM) analysis and adopted on-the-fly recalibration of retention time shift, which provided better throughput of the analytical method and enabled the simultaneous quantification of the expression of ∼300 kinases in two LC-MRM runs. With this improved analytical method, we conducted an in-depth quantitative analysis of the perturbation of kinome of GM00637 human skin fibroblast cells induced by arsenite exposure. Several kinases involved in cell cycle progression, including cyclin-dependent kinases (CDK1 and CDK4) and Aurora kinases A, B, and C, were found to be hyperactivated, and the altered expression of CDK1 was further validated by Western analysis. In addition, treatment with a CDK inhibitor, flavopiridol, partially restored the arsenite-induced growth inhibition of human skin fibroblast cells. Thus, sodium arsenite may confer its cytotoxic effect partly through the aberrant activation of CDKs and the resultant perturbation of cell cycle progression. Together, we developed a high-throughput, SILAC-compatible, and MRM-based kinome profiling method and demonstrated that the method is powerful in deciphering the molecular modes of action of a widespread environmental toxicant. The method should be generally applicable for uncovering the cellular pathways triggered by other extracellular stimuli.

Application of Adenosine Triphosphate Affinity Probe and Scheduled Multiple-Reaction Monitoring Analysis for Profiling Global Kinome in Human Cells in Response to Arsenite Treatment

PubMed Central

2015-01-01

Phosphorylation of cellular components catalyzed by kinases plays important roles in cell signaling and proliferation. Quantitative assessment of perturbation in global kinome may provide crucial knowledge for elucidating the mechanisms underlying the cytotoxic effects of environmental toxicants. Here, we utilized an adenosine triphosphate (ATP) affinity probe coupled with stable isotope labeling by amino acids in cell culture (SILAC) to assess quantitatively the arsenite-induced alteration of global kinome in human cells. We constructed a SILAC-compatible kinome library for scheduled multiple-reaction monitoring (MRM) analysis and adopted on-the-fly recalibration of retention time shift, which provided better throughput of the analytical method and enabled the simultaneous quantification of the expression of ∼300 kinases in two LC-MRM runs. With this improved analytical method, we conducted an in-depth quantitative analysis of the perturbation of kinome of GM00637 human skin fibroblast cells induced by arsenite exposure. Several kinases involved in cell cycle progression, including cyclin-dependent kinases (CDK1 and CDK4) and Aurora kinases A, B, and C, were found to be hyperactivated, and the altered expression of CDK1 was further validated by Western analysis. In addition, treatment with a CDK inhibitor, flavopiridol, partially restored the arsenite-induced growth inhibition of human skin fibroblast cells. Thus, sodium arsenite may confer its cytotoxic effect partly through the aberrant activation of CDKs and the resultant perturbation of cell cycle progression. Together, we developed a high-throughput, SILAC-compatible, and MRM-based kinome profiling method and demonstrated that the method is powerful in deciphering the molecular modes of action of a widespread environmental toxicant. The method should be generally applicable for uncovering the cellular pathways triggered by other extracellular stimuli. PMID:25301106

The influence of Stochastic perturbation of Geotechnical media On Electromagnetic tomography

NASA Astrophysics Data System (ADS)

Song, Lei; Yang, Weihao; Huangsonglei, Jiahui; Li, HaiPeng

2015-04-01

Electromagnetic tomography (CT) are commonly utilized in Civil engineering to detect the structure defects or geological anomalies. CT are generally recognized as a high precision geophysical method and the accuracy of CT are expected to be several centimeters and even to be several millimeters. Then, high frequency antenna with short wavelength are utilized commonly in Civil Engineering. As to the geotechnical media, stochastic perturbation of the EM parameters are inevitably exist in geological scales, in structure scales and in local scales, et al. In those cases, the geometric dimensionings of the target body, the EM wavelength and the accuracy expected might be of the same order. When the high frequency EM wave propagated in the stochastic geotechnical media, the GPR signal would be reflected not only from the target bodies but also from the stochastic perturbation of the background media. To detect the karst caves in dissolution fracture rock, one need to assess the influence of the stochastic distributed dissolution holes and fractures; to detect the void in a concrete structure, one should master the influence of the stochastic distributed stones, et al. In this paper, on the base of stochastic media discrete realizations, the authors try to evaluate quantificationally the influence of the stochastic perturbation of Geotechnical media by Radon/Iradon Transfer through full-combined Monte Carlo numerical simulation. It is found the stochastic noise is related with transfer angle, perturbing strength, angle interval, autocorrelation length, et al. And the quantitative formula of the accuracy of the electromagnetic tomography is also established, which could help on the precision estimation of GPR tomography in stochastic perturbation Geotechnical media. Key words: Stochastic Geotechnical Media; Electromagnetic Tomography; Radon/Iradon Transfer.

Role of the Euclidean signature in lattice calculations of quasidistributions and other nonlocal matrix elements

NASA Astrophysics Data System (ADS)

Briceño, Raúl A.; Hansen, Maxwell T.; Monahan, Christopher J.

2017-07-01

Lattice quantum chromodynamics (QCD) provides the only known systematic, nonperturbative method for first-principles calculations of nucleon structure. However, for quantities such as light-front parton distribution functions (PDFs) and generalized parton distributions (GPDs), the restriction to Euclidean time prevents direct calculation of the desired observable. Recently, progress has been made in relating these quantities to matrix elements of spatially nonlocal, zero-time operators, referred to as quasidistributions. Still, even for these time-independent matrix elements, potential subtleties have been identified in the role of the Euclidean signature. In this work, we investigate the analytic behavior of spatially nonlocal correlation functions and demonstrate that the matrix elements obtained from Euclidean lattice QCD are identical to those obtained using the Lehmann-Symanzik-Zimmermann reduction formula in Minkowski space. After arguing the equivalence on general grounds, we also show that it holds in a perturbative calculation, where special care is needed to identify the lattice prediction. Finally we present a proof of the uniqueness of the matrix elements obtained from Minkowski and Euclidean correlation functions to all order in perturbation theory.

Role of the Euclidean signature in lattice calculations of quasidistributions and other nonlocal matrix elements

DOE PAGES

Briceno, Raul A.; Hansen, Maxwell T.; Monahan, Christopher J.

2017-07-11

Lattice quantum chromodynamics (QCD) provides the only known systematic, nonperturbative method for first-principles calculations of nucleon structure. However, for quantities such as light-front parton distribution functions (PDFs) and generalized parton distributions (GPDs), the restriction to Euclidean time prevents direct calculation of the desired observable. Recently, progress has been made in relating these quantities to matrix elements of spatially nonlocal, zero-time operators, referred to as quasidistributions. Still, even for these time-independent matrix elements, potential subtleties have been identified in the role of the Euclidean signature. In this work, we investigate the analytic behavior of spatially nonlocal correlation functions and demonstrate thatmore » the matrix elements obtained from Euclidean lattice QCD are identical to those obtained using the Lehmann-Symanzik-Zimmermann reduction formula in Minkowski space. After arguing the equivalence on general grounds, we also show that it holds in a perturbative calculation, where special care is needed to identify the lattice prediction. Lastly, we present a proof of the uniqueness of the matrix elements obtained from Minkowski and Euclidean correlation functions to all order in perturbation theory.« less

DOE Office of Scientific and Technical Information (OSTI.GOV)

Briceno, Raul A.; Hansen, Maxwell T.; Monahan, Christopher J.

Lattice quantum chromodynamics (QCD) provides the only known systematic, nonperturbative method for first-principles calculations of nucleon structure. However, for quantities such as light-front parton distribution functions (PDFs) and generalized parton distributions (GPDs), the restriction to Euclidean time prevents direct calculation of the desired observable. Recently, progress has been made in relating these quantities to matrix elements of spatially nonlocal, zero-time operators, referred to as quasidistributions. Still, even for these time-independent matrix elements, potential subtleties have been identified in the role of the Euclidean signature. In this work, we investigate the analytic behavior of spatially nonlocal correlation functions and demonstrate thatmore » the matrix elements obtained from Euclidean lattice QCD are identical to those obtained using the Lehmann-Symanzik-Zimmermann reduction formula in Minkowski space. After arguing the equivalence on general grounds, we also show that it holds in a perturbative calculation, where special care is needed to identify the lattice prediction. Lastly, we present a proof of the uniqueness of the matrix elements obtained from Minkowski and Euclidean correlation functions to all order in perturbation theory.« less

On gauge invariant cosmological perturbations in UV-modified Hořava gravity

NASA Astrophysics Data System (ADS)

Shin, Sunyoung; Park, Mu-In

2017-12-01

We consider gauge invariant cosmological perturbations in UV-modified, z = 3 (non-projectable) Hořava gravity with one scalar matter field, which has been proposed as a renormalizable gravity theory without the ghost problem in four dimensions. In order to exhibit its dynamical degrees of freedom, we consider the Hamiltonian reduction method and find that, by solving all the constraint equations, the degrees of freedom are the same as those of Einstein gravity: one scalar and two tensor (graviton) modes when a scalar matter field presents. However, we confirm that there is no extra graviton modes and general relativity is recovered in IR, which achieves the consistency of the model. From the UV-modification terms which break the detailed balance condition in UV, we obtain scale-invariant power spectrums for non-inflationary backgrounds, like the power-law expansions, without knowing the details of early expansion history of Universe. This could provide a new framework for the Big Bang cosmology. Moreover, we find that tensor and scalar fluctuations travel differently in UV, generally. We present also some clarifying remarks about confusing points in the literatures.

Computer analysis of flow perturbations generated by placement of choke bumps in a wind tunnel

NASA Technical Reports Server (NTRS)

Campbell, R. L.

1981-01-01

An inviscid analytical study was conducted to determine the upstream flow perturbations caused by placing choke bumps in a wind tunnel. A computer program based on the stream-tube curvature method was used to calculate the resulting flow fields for a nominal free-stream Mach number range of 0.6 to 0.9. The choke bump geometry was also varied to investigate the effect of bump shape on the disturbance produced. Results from the study indicate that a region of significant variation from the free-stream conditions exists upstream of the throat of the tunnel. The extent of the disturbance region was, as a rule, dependent on Mach number and the geometry of the choke bump. In general, the upstream disturbance distance decreased for increasing nominal free-stream Mach number and for decreasing length-to-height ratio of the bump. A polynomial-curve choke bump usually produced less of a disturbance than did a circular-arc bump and going to an axisymmetric configuration (modeling choke bumps on all the tunnel walls) generally resulted in a lower disturbance than with the corresponding two dimensional case.

Influence maximization in time bounded network identifies transcription factors regulating perturbed pathways

PubMed Central

Jo, Kyuri; Jung, Inuk; Moon, Ji Hwan; Kim, Sun

2016-01-01

Motivation: To understand the dynamic nature of the biological process, it is crucial to identify perturbed pathways in an altered environment and also to infer regulators that trigger the response. Current time-series analysis methods, however, are not powerful enough to identify perturbed pathways and regulators simultaneously. Widely used methods include methods to determine gene sets such as differentially expressed genes or gene clusters and these genes sets need to be further interpreted in terms of biological pathways using other tools. Most pathway analysis methods are not designed for time series data and they do not consider gene-gene influence on the time dimension. Results: In this article, we propose a novel time-series analysis method TimeTP for determining transcription factors (TFs) regulating pathway perturbation, which narrows the focus to perturbed sub-pathways and utilizes the gene regulatory network and protein–protein interaction network to locate TFs triggering the perturbation. TimeTP first identifies perturbed sub-pathways that propagate the expression changes along the time. Starting points of the perturbed sub-pathways are mapped into the network and the most influential TFs are determined by influence maximization technique. The analysis result is visually summarized in TF-Pathway map in time clock. TimeTP was applied to PIK3CA knock-in dataset and found significant sub-pathways and their regulators relevant to the PIP3 signaling pathway. Availability and Implementation: TimeTP is implemented in Python and available at http://biohealth.snu.ac.kr/software/TimeTP/. Supplementary information: Supplementary data are available at Bioinformatics online. Contact: sunkim.bioinfo@snu.ac.kr PMID:27307609

Cosmology in beyond-generalized Proca theories

NASA Astrophysics Data System (ADS)

Nakamura, Shintaro; Kase, Ryotaro; Tsujikawa, Shinji

2017-05-01

The beyond-generalized Proca theories are the extension of second-order massive vector-tensor theories (dubbed generalized Proca theories) with two transverse vector modes and one longitudinal scalar besides two tensor polarizations. Even with this extension, the propagating degrees of freedom remain unchanged on the isotropic cosmological background without an Ostrogradski instability. We study the cosmology in beyond-generalized Proca theories by paying particular attention to the dynamics of late-time cosmic acceleration and resulting observational consequences. We derive conditions for avoiding ghosts and instabilities of tensor, vector, and scalar perturbations and discuss viable parameter spaces in concrete models allowing the dark energy equation of state smaller than -1 . The propagation speeds of those perturbations are subject to modifications beyond the domain of generalized Proca theories. There is a mixing between scalar and matter sound speeds, but such a mixing is suppressed during most of the cosmic expansion history without causing a new instability. On the other hand, we find that derivative interactions arising in beyond-generalized Proca theories give rise to important modifications to the cosmic growth history. The growth rate of matter perturbations can be compatible with the redshift-space distortion data due to the realization of gravitational interaction weaker than that in generalized Proca theories. Thus, it is possible to distinguish the dark energy model in beyond-generalized Proca theories from the counterpart in generalized Proca theories as well as from the Λ CDM model.

Detecting and correcting the bias of unmeasured factors using perturbation analysis: a data-mining approach.

PubMed

Lee, Wen-Chung

2014-02-05

The randomized controlled study is the gold-standard research method in biomedicine. In contrast, the validity of a (nonrandomized) observational study is often questioned because of unknown/unmeasured factors, which may have confounding and/or effect-modifying potential. In this paper, the author proposes a perturbation test to detect the bias of unmeasured factors and a perturbation adjustment to correct for such bias. The proposed method circumvents the problem of measuring unknowns by collecting the perturbations of unmeasured factors instead. Specifically, a perturbation is a variable that is readily available (or can be measured easily) and is potentially associated, though perhaps only very weakly, with unmeasured factors. The author conducted extensive computer simulations to provide a proof of concept. Computer simulations show that, as the number of perturbation variables increases from data mining, the power of the perturbation test increased progressively, up to nearly 100%. In addition, after the perturbation adjustment, the bias decreased progressively, down to nearly 0%. The data-mining perturbation analysis described here is recommended for use in detecting and correcting the bias of unmeasured factors in observational studies.

One-step leapfrog ADI-FDTD method for simulating electromagnetic wave propagation in general dispersive media.

PubMed

Wang, Xiang-Hua; Yin, Wen-Yan; Chen, Zhi Zhang David

2013-09-09

The one-step leapfrog alternating-direction-implicit finite-difference time-domain (ADI-FDTD) method is reformulated for simulating general electrically dispersive media. It models material dispersive properties with equivalent polarization currents. These currents are then solved with the auxiliary differential equation (ADE) and then incorporated into the one-step leapfrog ADI-FDTD method. The final equations are presented in the form similar to that of the conventional FDTD method but with second-order perturbation. The adapted method is then applied to characterize (a) electromagnetic wave propagation in a rectangular waveguide loaded with a magnetized plasma slab, (b) transmission coefficient of a plane wave normally incident on a monolayer graphene sheet biased by a magnetostatic field, and (c) surface plasmon polaritons (SPPs) propagation along a monolayer graphene sheet biased by an electrostatic field. The numerical results verify the stability, accuracy and computational efficiency of the proposed one-step leapfrog ADI-FDTD algorithm in comparison with analytical results and the results obtained with the other methods.

Classification and Evaluation of Coherent Synchronous Sampled-Data Telemetry Systems

NASA Technical Reports Server (NTRS)

Viterbi, Andrew

1961-01-01

This paper analyzes the various types of continuous wave and pulse modulation for the transmission of sampled data over channels perturbed by white gaussian noise. Optimal coherent synchronous detection schemes for all the different modulation methods are shown to belong to one of two general classes: linear synchronous detection and correlation detection. The figures of merit, mean-square signal-to-error ratio and bandwidth occupancy, are determined for each system and compared.

Perturbations of non-resonant satellite orbits due to a rotating earth. [tesseral harmonics and the Von Ziepel method

NASA Technical Reports Server (NTRS)

Mueller, A.

1978-01-01

The dominant perturbations of the motion of a satellite near the earth are due to atmospheric drag and the non-symmetrical gravitational field. Atmospheric drag perturbation continually pulls the satellite in and out of the different long period resonant frequencies. The result is that the resonances never become apparent and may be neglected. The tesseral harmonics have no true secular perturbation but the periodicities in the mean motion induce a secular perturbation in the mean anomaly. This secular perturbation may be determined by simply using the average mean motion instead of the osculating mean motion. The Von Ziepel method is used to determine tesseral perturbations. The solution is found first in the singular DS phi elements and then rewritten in the PS phi elements to remove singularities. The notation used in the development is described in the appendix.

Shielding application of perturbation theory to determine changes in neutron and gamma doses due to changes in shield layers

NASA Technical Reports Server (NTRS)

Fieno, D.

1972-01-01

Perturbation theory formulas were derived and applied to determine changes in neutron and gamma-ray doses due to changes in various radiation shield layers for fixed sources. For a given source and detector position, the perturbation method enables dose derivatives with respect to density, or equivalently thickness, for every layer to be determined from one forward and one inhomogeneous adjoint calculation. A direct determination without the perturbation approach would require two forward calculations to evaluate the dose derivative due to a change in a single layer. Hence, the perturbation method for obtaining dose derivatives requires fewer computations for design studies of multilayer shields. For an illustrative problem, a comparison was made of the fractional change in the dose per unit change in the thickness of each shield layer in a two-layer spherical configuration as calculated by perturbation theory and by successive direct calculations; excellent agreement was obtained between the two methods.

Yield strength measurement of shock-loaded metal by flyer-impact perturbation method

NASA Astrophysics Data System (ADS)

Ma, Xiaojuan; Shi, Zhan

2018-06-01

Yield strength is one of the most important physical properties of a solid material, especially far from its melting line. The flyer-impact perturbation method measures material yield strength on the basis of correlation between the yield strength under shock compression and the damping of oscillatory perturbations in the shape of a shock front passing through the material. We used flyer-impact experiments on targets with machined grooves on the impact surface of shock 6061-T6 aluminum to between 32 and 61 GPa and recorded the evolution of the shock front perturbation amplitude in the sample with electric pins. Simulations using the elastic-plastic model can be matched to the experiments, explaining well the form of the perturbation decay and constraining the yield strength of 6061-T6 aluminum to be 1.31-1.75 GPa. These results are in agreement with values obtained from reshock and release wave profiles. We conclude that the flyer-impact perturbation method is indeed a new means to measure material strength.

Instabilities in mimetic matter perturbations

NASA Astrophysics Data System (ADS)

Firouzjahi, Hassan; Gorji, Mohammad Ali; Mansoori, Seyed Ali Hosseini

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.

Perturbative Out of Equilibrium Quantum Field Theory beyond the Gradient Approximation and Generalized Boltzmann Equation

NASA Astrophysics Data System (ADS)

Ozaki, H.

2004-01-01

Using the closed-time-path formalism, we construct perturbative frameworks, in terms of quasiparticle picture, for studying quasiuniform relativistic quantum field systems near equilibrium and non-equilibrium quasistationary systems. We employ the derivative expansion and take in up to the second-order term, i.e., one-order higher than the gradient approximation. After constructing self-energy resummed propagator, we formulated two kinds of mutually equivalent perturbative frameworks: The first one is formulated on the basis of the ``bare'' number density function, and the second one is formulated on the basis of ``physical'' number density function. In the course of construction of the second framework, the generalized Boltzmann equations directly come out, which describe the evolution of the system.

General Relativistic MHD Simulations of Jet Formation

NASA Technical Reports Server (NTRS)

Mizuno, Y.; Nishikawa, K.-I.; Hardee, P.; Koide, S.; Fishman, G. J.

2005-01-01

We have performed 3-dimensional general relativistic magnetohydrodynamic (GRMHD) simulations of jet formation from an accretion disk with/without initial perturbation around a rotating black hole. We input a sinusoidal perturbation (m = 5 mode) in the rotation velocity of the accretion disk. The simulation results show the formation of a relativistic jet from the accretion disk. Although the initial perturbation becomes weakened by the coupling among different modes, it survives and triggers lower modes. As a result, complex non-axisymmetric density structure develops in the disk and the jet. Newtonian MHD simulations of jet formation with a non-axisymmetric mode show the growth of the m = 2 mode but GRMHD simulations cannot see the clear growth of the m = 2 mode.

Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review

NASA Technical Reports Server (NTRS)

Kennedy, Christopher A.; Carpenter, Mark H.

2016-01-01

A review of diagonally implicit Runge-Kutta (DIRK) methods applied to rst-order ordinary di erential equations (ODEs) is undertaken. The goal of this review is to summarize the characteristics, assess the potential, and then design several nearly optimal, general purpose, DIRK-type methods. Over 20 important aspects of DIRKtype methods are reviewed. A design study is then conducted on DIRK-type methods having from two to seven implicit stages. From this, 15 schemes are selected for general purpose application. Testing of the 15 chosen methods is done on three singular perturbation problems. Based on the review of method characteristics, these methods focus on having a stage order of two, sti accuracy, L-stability, high quality embedded and dense-output methods, small magnitudes of the algebraic stability matrix eigenvalues, small values of aii, and small or vanishing values of the internal stability function for large eigenvalues of the Jacobian. Among the 15 new methods, ESDIRK4(3)6L[2]SA is recommended as a good default method for solving sti problems at moderate error tolerances.

Perturbational blowup solutions to the compressible Euler equations with damping.

PubMed

Cheung, Ka Luen

2016-01-01

The N-dimensional isentropic compressible Euler system with a damping term is one of the most fundamental equations in fluid dynamics. Since it does not have a general solution in a closed form for arbitrary well-posed initial value problems. Constructing exact solutions to the system is a useful way to obtain important information on the properties of its solutions. In this article, we construct two families of exact solutions for the one-dimensional isentropic compressible Euler equations with damping by the perturbational method. The two families of exact solutions found include the cases [Formula: see text] and [Formula: see text], where [Formula: see text] is the adiabatic constant. With analysis of the key ordinary differential equation, we show that the classes of solutions include both blowup type and global existence type when the parameters are suitably chosen. Moreover, in the blowup cases, we show that the singularities are of essential type in the sense that they cannot be smoothed by redefining values at the odd points. The two families of exact solutions obtained in this paper can be useful to study of related numerical methods and algorithms such as the finite difference method, the finite element method and the finite volume method that are applied by scientists to simulate the fluids for applications.

Molecular-dynamics evaluation of fluid-phase equilibrium properties by a novel free-energy perturbation approach: Application to gas solubility and vapor pressure of liquid hexane

NASA Astrophysics Data System (ADS)

Kuwajima, Satoru; Kikuchi, Hiroaki; Fukuda, Mitsuhiro

2006-03-01

A novel free-energy perturbation method is developed for the computation of the free energy of transferring a molecule between fluid phases. The methodology consists in drawing a free-energy profile of the target molecule moving across a binary-phase structure built in the computer. The novelty of the method lies in the difference of the definition of the free-energy profile from the common definition. As an important element of the method, the process of making a correction to the transfer free energy with respect to the cutoff of intermolecular forces is elucidated. In order to examine the performance of the method in the application to fluid-phase equilibrium properties, molecular-dynamics computations are carried out for the evaluation of gas solubility and vapor pressure of liquid n-hexane at 298.15K. The gas species treated are methane, ethane, propane, and n-butane, with the gas solubility expressed as Henry's constant. It is shown that the method works fine and calculated results are generally in good agreement with experiments. It is found that the cutoff correction is strikingly large, constituting a dominant part of the calculated transfer free energy at the cutoff of 8Å.

Special cases of friction and applications

NASA Technical Reports Server (NTRS)

Litvin, F. L.; Coy, J. J.

1983-01-01

Two techniques for reducing friction forces are presented. The techniques are applied to the generalized problem of reducing the friction between kinematic pairs which connect a moveable link to a frame. The basic principles are: (1) Let the moveable link be supported by two bearings where the relative velocities of the link with respect to each bearing are of opposite directions. Thus the resultant force (torque) of friction acting on the link due to the bearings is approximately zero. Then, additional perturbation of motion parallel to the main motion of the moveable link will require only a very small force; (2) Let the perturbation in motion be perpendicular to the main motion. Equations are developed which explain these two methods. The results are discussed in relation to friction in geared couplings, gyroscope gimbal bearings and a rotary conveyor system. Design examples are presented.

Counting the number of Feynman graphs in QCD

NASA Astrophysics Data System (ADS)

Kaneko, T.

2018-05-01

Information about the number of Feynman graphs for a given physical process in a given field theory is especially useful for confirming the result of a Feynman graph generator used in an automatic system of perturbative calculations. A method of counting the number of Feynman graphs with weight of symmetry factor was established based on zero-dimensional field theory, and was used in scalar theories and QED. In this article this method is generalized to more complicated models by direct calculation of generating functions on a computer algebra system. This method is applied to QCD with and without counter terms, where many higher order are being calculated automatically.

Reconstruction of local perturbations in periodic surfaces

NASA Astrophysics Data System (ADS)

Lechleiter, Armin; Zhang, Ruming

2018-03-01

This paper concerns the inverse scattering problem to reconstruct a local perturbation in a periodic structure. Unlike the periodic problems, the periodicity for the scattered field no longer holds, thus classical methods, which reduce quasi-periodic fields in one periodic cell, are no longer available. Based on the Floquet-Bloch transform, a numerical method has been developed to solve the direct problem, that leads to a possibility to design an algorithm for the inverse problem. The numerical method introduced in this paper contains two steps. The first step is initialization, that is to locate the support of the perturbation by a simple method. This step reduces the inverse problem in an infinite domain into one periodic cell. The second step is to apply the Newton-CG method to solve the associated optimization problem. The perturbation is then approximated by a finite spline basis. Numerical examples are given at the end of this paper, showing the efficiency of the numerical method.

Generalization of improved step length symmetry from treadmill to overground walking in persons with stroke and hemiparesis†

PubMed Central

Savin, Douglas N.; Morton, Susanne M.; Whitall, Jill

2013-01-01

Objectives Determine whether adaptation to a swing phase perturbation during gait transferred from treadmill to overground walking, the rate of overground deadaptation, and whether overground aftereffects improved step length asymmetry in persons with hemiparetic stroke and gait asymmetry. Methods Ten participants with stroke and hemiparesis and 10 controls walked overground on an instrumented gait mat, adapted gait to a swing phase perturbation on a treadmill, then walked overground on the gait mat again. Outcome measures, primary: overground step length symmetry, rates of treadmill step length symmetry adaptation and overground step length symmetry deadaptation; secondary: overground gait velocity, stride length, and stride cycle duration. Results Step length symmetry aftereffects generalized to overground walking and adapted at a similar rate on the treadmill in both groups. Aftereffects decayed at a slower rate overground in participants with stroke and temporarily improved overground step length asymmetry. Both groups’ overground gait velocity increased post adaptation due to increased stride length and decreased stride duration. Conclusions Stroke and hemiparesis do not impair generalization of step length symmetry changes from adapted treadmill to overground walking, but prolong overground aftereffects. Significance Motor adaptation during treadmill walking may be an effective treatment for improving overground gait asymmetries post-stroke. PMID:24286858

Black hole formation in a contracting universe

DOE Office of Scientific and Technical Information (OSTI.GOV)

Quintin, Jerome; Brandenberger, Robert H., E-mail: jquintin@physics.mcgill.ca, E-mail: rhb@hep.physics.mcgill.ca

We study the evolution of cosmological perturbations in a contracting universe. We aim to determine under which conditions density perturbations grow to form large inhomogeneities and collapse into black holes. Our method consists in solving the cosmological perturbation equations in complete generality for a hydrodynamical fluid. We then describe the evolution of the fluctuations over the different length scales of interest and as a function of the equation of state for the fluid, and we explore two different types of initial conditions: quantum vacuum and thermal fluctuations. We also derive a general requirement for black hole collapse on sub-Hubble scales,more » and we use the Press-Schechter formalism to describe the black hole formation probability. For a fluid with a small sound speed (e.g., dust), we find that both quantum and thermal initial fluctuations grow in a contracting universe, and the largest inhomogeneities that first collapse into black holes are of Hubble size and the collapse occurs well before reaching the Planck scale. For a radiation-dominated fluid, we find that no black hole can form before reaching the Planck scale. In the context of matter bounce cosmology, it thus appears that only models in which a radiation-dominated era begins early in the cosmological evolution are robust against the formation of black holes. Yet, the formation of black holes might be an interesting feature for other models. We comment on a number of possible alternative early universe scenarios that could take advantage of this feature.« less

Optimal guidance law development for an advanced launch system

NASA Technical Reports Server (NTRS)

Calise, Anthony J.; Leung, Martin S. K.

1995-01-01

The objective of this research effort was to develop a real-time guidance approach for launch vehicles ascent to orbit injection. Various analytical approaches combined with a variety of model order and model complexity reduction have been investigated. Singular perturbation methods were first attempted and found to be unsatisfactory. The second approach based on regular perturbation analysis was subsequently investigated. It also fails because the aerodynamic effects (ignored in the zero order solution) are too large to be treated as perturbations. Therefore, the study demonstrates that perturbation methods alone (both regular and singular perturbations) are inadequate for use in developing a guidance algorithm for the atmospheric flight phase of a launch vehicle. During a second phase of the research effort, a hybrid analytic/numerical approach was developed and evaluated. The approach combines the numerical methods of collocation and the analytical method of regular perturbations. The concept of choosing intelligent interpolating functions is also introduced. Regular perturbation analysis allows the use of a crude representation for the collocation solution, and intelligent interpolating functions further reduce the number of elements without sacrificing the approximation accuracy. As a result, the combined method forms a powerful tool for solving real-time optimal control problems. Details of the approach are illustrated in a fourth order nonlinear example. The hybrid approach is then applied to the launch vehicle problem. The collocation solution is derived from a bilinear tangent steering law, and results in a guidance solution for the entire flight regime that includes both atmospheric and exoatmospheric flight phases.

Hamiltonian formalism for Perturbed Black Hole Spacetimes

NASA Astrophysics Data System (ADS)

Mihaylov, Deyan; Gair, Jonathan

2017-01-01

Present and future gravitational wave observations provide a new mechanism to probe the predictions of general relativity. Observations of extreme mass ratio inspirals with millihertz gravitational wave detectors such as LISA will provide exquisite constraints on the spacetime structure outside astrophysical black holes, enabling tests of the no-hair property that all general relativistic black holes are described by the Kerr metric. Previous work to understand what constraints LISA observations will be able to place has focussed on specific alternative theories of gravity, or generic deviations that preserve geodesic separability. We describe an alternative approach to this problem--a technique that employs canonical perturbations of the Hamiltonian function describing motion in the Kerr metric. We derive this new approach and demonstrate its application to the cases of a slowly rotating Kerr black hole which is viewed as a perturbation of a Schwarzschild black hole, of coupled perturbations of black holes in the second-order Chern-Simons modified gravity theory, and several more indicative scenarios. Deyan Mihaylov is funded by STFC.

How to resum perturbative series in 3d N =2 Chern-Simons matter theories

NASA Astrophysics Data System (ADS)

Honda, Masazumi

2016-07-01

Continuing the work of Honda [Phys. Rev. Lett. 116, 211601 (2016)], we study the perturbative series in general 3d N =2 supersymmetric Chern-Simons matter theory with U (1 )R symmetry, which is given by a power series expansion of inverse Chern-Simons levels. We find that the perturbative series is usually non-Borel summable along a positive real axis for various observables. Alternatively, we prove that the perturbative series is always Borel summable along a negative (positive) imaginary axis for positive (negative) Chern-Simons levels. It turns out that the Borel resummations along this direction are the same as the exact results and, therefore, are correct ways of resumming the perturbative series.

Development of a multiple-parameter nonlinear perturbation procedure for transonic turbomachinery flows: Preliminary application to design/optimization problems

NASA Technical Reports Server (NTRS)

Stahara, S. S.; Elliott, J. P.; Spreiter, J. R.

1983-01-01

An investigation was conducted to continue the development of perturbation procedures and associated computational codes for rapidly determining approximations to nonlinear flow solutions, with the purpose of establishing a method for minimizing computational requirements associated with parametric design studies of transonic flows in turbomachines. The results reported here concern the extension of the previously developed successful method for single parameter perturbations to simultaneous multiple-parameter perturbations, and the preliminary application of the multiple-parameter procedure in combination with an optimization method to blade design/optimization problem. In order to provide as severe a test as possible of the method, attention is focused in particular on transonic flows which are highly supercritical. Flows past both isolated blades and compressor cascades, involving simultaneous changes in both flow and geometric parameters, are considered. Comparisons with the corresponding exact nonlinear solutions display remarkable accuracy and range of validity, in direct correspondence with previous results for single-parameter perturbations.

Perturbative and Ab-Initio Calculations of Electrical Susceptibilities of Atoms

NASA Astrophysics Data System (ADS)

Spott, Andrew

Perturbative nonlinear optics consists of many powerful predictive theoretical methods, including the perturbative series of observables related to the interaction of light with matter. The light intensity limits of such series have been studied in the past for highly nonlinear processes such as above threshold ionization and high harmonic generation. A more recent debate focuses on the limits of applicability of perturbation theory for the nonlinear electrical susceptibility and the nonlinear index of refraction of atoms, which are important parameters to study, for example, for filamentation of laser pulses in nonlinear media. In this thesis we analyze theoretical predictions for the electrical susceptibility of atoms for the transition from the perturbative to the nonperturbative intensity regime. To this end, we apply a numerical basis state method that allows us to perform respective calculations in the framework of perturbation theory as well as using ab-initio methods. The results let us identify the intensity at which the application of perturbation theory breaks down. Furthermore, we provide an analysis of the nonlinear susceptibility as a function of time during the interaction with the laser pulse and find that theoretical predictions are in good agreement with recent experimental data.

Quasinormal modes as a distinguisher between general relativity and f (R ) gravity

NASA Astrophysics Data System (ADS)

Bhattacharyya, Soham; Shankaranarayanan, S.

2017-09-01

Quasinormal modes (QNMs) or the ringdown phase of gravitational waves provide critical information about the structure of compact objects like black holes. Thus, QNMs can be a tool to test general relativity (GR) and possible deviations from it. In the case of GR, it has been known for a long time that a relation between two types of black hole perturbations—scalar (Zerilli) and vector (Regge-Wheeler)—leads to an equal share of emitted gravitational energy. With the direct detection of gravitational waves, it is now natural to ask whether the same relation (between scalar and vector perturbations) holds for modified gravity theories, and if not, whether one can use this as a way to probe deviations from general relativity. As a first step, we show explicitly that the above relation between Regge-Wheeler and Zerilli perturbations breaks down for a general f (R ) model and hence the two perturbations do not share equal amounts of emitted gravitational energy. We discuss the implication of this imbalance for observations and the no-hair conjecture.

Response formulae for n-point correlations in statistical mechanical systems and application to a problem of coarse graining

NASA Astrophysics Data System (ADS)

Lucarini, Valerio; Wouters, Jeroen

2017-09-01

Predicting the response of a system to perturbations is a key challenge in mathematical and natural sciences. Under suitable conditions on the nature of the system, of the perturbation, and of the observables of interest, response theories allow to construct operators describing the smooth change of the invariant measure of the system of interest as a function of the small parameter controlling the intensity of the perturbation. In particular, response theories can be developed both for stochastic and chaotic deterministic dynamical systems, where in the latter case stricter conditions imposing some degree of structural stability are required. In this paper we extend previous findings and derive general response formulae describing how n- point correlations are affected by perturbations to the vector flow. We also show how to compute the response of the spectral properties of the system to perturbations. We then apply our results to the seemingly unrelated problem of coarse graining in multiscale systems: we find explicit formulae describing the change in the terms describing the parameterisation of the neglected degrees of freedom resulting from applying perturbations to the full system. All the terms envisioned by the Mori-Zwanzig theory—the deterministic, stochastic, and non-Markovian terms—are affected at first order in the perturbation. The obtained results provide a more comprehensive understanding of the response of statistical mechanical systems to perturbations. They also contribute to the goal of constructing accurate and robust parameterisations and are of potential relevance for fields like molecular dynamics, condensed matter, and geophysical fluid dynamics. We envision possible applications of our general results to the study of the response of climate variability to anthropogenic and natural forcing and to the study of the equivalence of thermostatted statistical mechanical systems.

Derivation of general analytic gradient expressions for density-fitted post-Hartree-Fock methods: An efficient implementation for the density-fitted second-order Møller–Plesset perturbation theory

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bozkaya, Uğur, E-mail: ugur.bozkaya@atauni.edu.tr

General analytic gradient expressions (with the frozen-core approximation) are presented for density-fitted post-HF methods. An efficient implementation of frozen-core analytic gradients for the second-order Møller–Plesset perturbation theory (MP2) with the density-fitting (DF) approximation (applying to both reference and correlation energies), which is denoted as DF-MP2, is reported. The DF-MP2 method is applied to a set of alkanes, conjugated dienes, and noncovalent interaction complexes to compare the computational cost of single point analytic gradients with MP2 with the resolution of the identity approach (RI-MP2) [F. Weigend and M. Häser, Theor. Chem. Acc. 97, 331 (1997); R. A. Distasio, R. P. Steele,more » Y. M. Rhee, Y. Shao, and M. Head-Gordon, J. Comput. Chem. 28, 839 (2007)]. In the RI-MP2 method, the DF approach is used only for the correlation energy. Our results demonstrate that the DF-MP2 method substantially accelerate the RI-MP2 method for analytic gradient computations due to the reduced input/output (I/O) time. Because in the DF-MP2 method the DF approach is used for both reference and correlation energies, the storage of 4-index electron repulsion integrals (ERIs) are avoided, 3-index ERI tensors are employed instead. Further, as in case of integrals, our gradient equation is completely avoid construction or storage of the 4-index two-particle density matrix (TPDM), instead we use 2- and 3-index TPDMs. Hence, the I/O bottleneck of a gradient computation is significantly overcome. Therefore, the cost of the generalized-Fock matrix (GFM), TPDM, solution of Z-vector equations, the back transformation of TPDM, and integral derivatives are substantially reduced when the DF approach is used for the entire energy expression. Further application results show that the DF approach introduce negligible errors for closed-shell reaction energies and equilibrium bond lengths.« less

Development of a turbomachinery design optimization procedure using a multiple-parameter nonlinear perturbation method

NASA Technical Reports Server (NTRS)

Stahara, S. S.

1984-01-01

An investigation was carried out to complete the preliminary development of a combined perturbation/optimization procedure and associated computational code for designing optimized blade-to-blade profiles of turbomachinery blades. The overall purpose of the procedures developed is to provide demonstration of a rapid nonlinear perturbation method for minimizing the computational requirements associated with parametric design studies of turbomachinery flows. The method combines the multiple parameter nonlinear perturbation method, successfully developed in previous phases of this study, with the NASA TSONIC blade-to-blade turbomachinery flow solver, and the COPES-CONMIN optimization procedure into a user's code for designing optimized blade-to-blade surface profiles of turbomachinery blades. Results of several design applications and a documented version of the code together with a user's manual are provided.

Control optimization of a lifting body entry problem by an improved and a modified method of perturbation function. Ph.D. Thesis - Houston Univ.

NASA Technical Reports Server (NTRS)

Garcia, F., Jr.

1974-01-01

A study of the solution problem of a complex entry optimization was studied. The problem was transformed into a two-point boundary value problem by using classical calculus of variation methods. Two perturbation methods were devised. These methods attempted to desensitize the contingency of the solution of this type of problem on the required initial co-state estimates. Also numerical results are presented for the optimal solution resulting from a number of different initial co-states estimates. The perturbation methods were compared. It is found that they are an improvement over existing methods.

The Effects of Predator Evolution and Genetic Variation on Predator-Prey Population-Level Dynamics.

PubMed

Cortez, Michael H; Patel, Swati

2017-07-01

This paper explores how predator evolution and the magnitude of predator genetic variation alter the population-level dynamics of predator-prey systems. We do this by analyzing a general eco-evolutionary predator-prey model using four methods: Method 1 identifies how eco-evolutionary feedbacks alter system stability in the fast and slow evolution limits; Method 2 identifies how the amount of standing predator genetic variation alters system stability; Method 3 identifies how the phase lags in predator-prey cycles depend on the amount of genetic variation; and Method 4 determines conditions for different cycle shapes in the fast and slow evolution limits using geometric singular perturbation theory. With these four methods, we identify the conditions under which predator evolution alters system stability and shapes of predator-prey cycles, and how those effect depend on the amount of genetic variation in the predator population. We discuss the advantages and disadvantages of each method and the relations between the four methods. This work shows how the four methods can be used in tandem to make general predictions about eco-evolutionary dynamics and feedbacks.

Local well-posedness for dispersion generalized Benjamin-Ono equations in Sobolev spaces

NASA Astrophysics Data System (ADS)

Guo, Zihua

We prove that the Cauchy problem for the dispersion generalized Benjamin-Ono equation ∂u+|∂u+uu=0, u(x,0)=u(x), is locally well-posed in the Sobolev spaces H for s>1-α if 0⩽α⩽1. The new ingredient is that we generalize the methods of Ionescu, Kenig and Tataru (2008) [13] to approach the problem in a less perturbative way, in spite of the ill-posedness results of Molinet, Saut and Tzvetkov (2001) [21]. Moreover, as a bi-product we prove that if 0<α⩽1 the corresponding modified equation (with the nonlinearity ±uuu) is locally well-posed in H for s⩾1/2-α/4.

Perturbative dynamics of thin-shell wormholes beyond general relativity: An alternative approach

NASA Astrophysics Data System (ADS)

Rubín de Celis, Emilio; Tomasini, Cecilia; Simeone, Claudio

Recent studies relating the approximations for the equations-of-state for thin shells and their consequent perturbative evolution are extended to thin-shell wormholes in theories beyond general relativity and more than four spacetime dimensions. The assumption of equations-of-state of the same form for static and slowly evolving shells appears as a strong restriction excluding the possibility of oscillatory evolutions. Then the new results considerably differ from previous ones obtained within the usual linearized approach.

Influence diagnostics in meta-regression model.

PubMed

Shi, Lei; Zuo, ShanShan; Yu, Dalei; Zhou, Xiaohua

2017-09-01

This paper studies the influence diagnostics in meta-regression model including case deletion diagnostic and local influence analysis. We derive the subset deletion formulae for the estimation of regression coefficient and heterogeneity variance and obtain the corresponding influence measures. The DerSimonian and Laird estimation and maximum likelihood estimation methods in meta-regression are considered, respectively, to derive the results. Internal and external residual and leverage measure are defined. The local influence analysis based on case-weights perturbation scheme, responses perturbation scheme, covariate perturbation scheme, and within-variance perturbation scheme are explored. We introduce a method by simultaneous perturbing responses, covariate, and within-variance to obtain the local influence measure, which has an advantage of capable to compare the influence magnitude of influential studies from different perturbations. An example is used to illustrate the proposed methodology. Copyright © 2017 John Wiley & Sons, Ltd.

A pseudo energy-invariant method for relativistic wave equations with Riesz space-fractional derivatives

NASA Astrophysics Data System (ADS)

Macías-Díaz, J. E.; Hendy, A. S.; De Staelen, R. H.

2018-03-01

In this work, we investigate a general nonlinear wave equation with Riesz space-fractional derivatives that generalizes various classical hyperbolic models, including the sine-Gordon and the Klein-Gordon equations from relativistic quantum mechanics. A finite-difference discretization of the model is provided using fractional centered differences. The method is a technique that is capable of preserving an energy-like quantity at each iteration. Some computational comparisons against solutions available in the literature are performed in order to assess the capability of the method to preserve the invariant. Our experiments confirm that the technique yields good approximations to the solutions considered. As an application of our scheme, we provide simulations that confirm, for the first time in the literature, the presence of the phenomenon of nonlinear supratransmission in Riesz space-fractional Klein-Gordon equations driven by a harmonic perturbation at the boundary.

Control theory based airfoil design using the Euler equations

NASA Technical Reports Server (NTRS)

Jameson, Antony; Reuther, James

1994-01-01

This paper describes the implementation of optimization techniques based on control theory for airfoil design. In our previous work it was shown that control theory could be employed to devise effective optimization procedures for two-dimensional profiles by using the potential flow equation with either a conformal mapping or a general coordinate system. The goal of our present work is to extend the development to treat the Euler equations in two-dimensions by procedures that can readily be generalized to treat complex shapes in three-dimensions. Therefore, we have developed methods which can address airfoil design through either an analytic mapping or an arbitrary grid perturbation method applied to a finite volume discretization of the Euler equations. Here the control law serves to provide computationally inexpensive gradient information to a standard numerical optimization method. Results are presented for both the inverse problem and drag minimization problem.

Global stability of plane Couette flow beyond the energy stability limit

NASA Astrophysics Data System (ADS)

Fuentes, Federico; Goluskin, David

2017-11-01

This talk will present computations verifying that the laminar state of plane Couette flow is nonlinearly stable to all perturbations. The Reynolds numbers up to which this globally stability is verified are larger than those at which stability can be proven by the energy method, which is the typical method for demonstrating nonlinear stability of a fluid flow. This improvement is achieved by constructing Lyapunov functions that are more general than the energy. These functions are not restricted to being quadratic, and they are allowed to depend explicitly on the spectrum of the velocity field in the eigenbasis of the energy stability operator. The optimal choice of such a Lyapunov function is a convex optimization problem, and it can be constructed with computer assistance by solving a semidefinite program. This general method will be described in a companion talk by David Goluskin; the present talk focuses on its application to plane Couette flow.

Measuring Memory and Attention to Preview in Motion.

PubMed

Jagacinski, Richard J; Hammond, Gordon M; Rizzi, Emanuele

2017-08-01

Objective Use perceptual-motor responses to perturbations to reveal the spatio-temporal detail of memory for the recent past and attention to preview when participants track a winding roadway. Background Memory of the recently passed roadway can be inferred from feedback control models of the participants' manual movement patterns. Similarly, attention to preview of the upcoming roadway can be inferred from feedforward control models of manual movement patterns. Method Perturbation techniques were used to measure these memory and attention functions. Results In a laboratory tracking task, the bandwidth of lateral roadway deviations was found to primarily influence memory for the past roadway rather than attention to preview. A secondary auditory/verbal/vocal memory task resulted in higher velocity error and acceleration error in the tracking task but did not affect attention to preview. Attention to preview was affected by the frequency pattern of sinusoidal perturbations of the roadway. Conclusion Perturbation techniques permit measurement of the spatio-temporal span of memory and attention to preview that affect tracking a winding roadway. They also provide new ways to explore goal-directed forgetting and spatially distributed attention in the context of movement. More generally, these techniques provide sensitive measures of individual differences in cognitive aspects of action. Application Models of driving behavior and assessment of driving skill may benefit from more detailed spatio-temporal measurement of attention to preview.

The Effect of Global-Scale, Steady-State Convection and Elastic-Gravitational Asphericities on Helioseismic Oscillations

NASA Astrophysics Data System (ADS)

Lavely, Eugene M.; Ritzwoller, Michael H.

1992-06-01

In this paper we derive a theory, based on quasi-degenerate perturbation theory, that governs the effect of global-scale, steady-state convection and associated static asphericities in the elastic-gravitational variables (adiabatic bulk modulus kappa , density ρ , and gravitational potential φ ) on helioseismic eigenfrequencies and eigenfunctions and present a formalism with which this theory can be applied computationally. The theory rests on three formal assumptions: (1) that convection is temporally steady in a frame corotating with the Sun, (2) that accurate eigenfrequencies and eigenfunctions can be determined by retaining terms in the seismically perturbed equations of motion only to first order in p-mode displacement, and (3) that we are justified in retaining terms only to first order in convective velocity (this is tantamount to assuming that the convective flow is anelastic). The most physically unrealistic assumption is (1), and we view the results of this paper as the first step toward a more general theory governing the seismic effects of time-varying fields. Although the theory does not govern the seismic effects of non-stationary flows, it can be used to approximate the effects of unsteady flows on the acoustic wavefield if the flow is varying smoothly in time. The theory does not attempt to model seismic modal amplitudes since these are governed, in part, by the exchange of energy between convection and acoustic motions which is not a part of this theory. However, we show how theoretical wavefields can be computed given a description of the stress field produced by a source process such as turbulent convection. The basic reference model that will be perturbed by rotation, convection, structural asphericities, and acoustic oscillations is a spherically symmetric, non-rotating, non-magnetic, isotropic, static solar model that, when subject to acoustic oscillations, oscillates adiabatically. We call this the SNRNMAIS model. An acoustic mode of the SNRNMAIS model is denoted by k = (n,l,m), where n is the radial order, l is the harmonic degree, and m is the azimuthal order of the mode. The main result of the paper is the general matrix element Hn'n,l'lm'm for steady-state convection satisfying the anelastic condition with static structural asphericities. It is written in terms of the radial, scalar eigenfunctions of the SNRNMAIS model, resulting in equations (90)-(110). We prove Rayleigh's principle in our derivation of quasi-degenerate perturbation theory which, as a by-product, yields the general matrix element. Within this perturbative method, modes need not be exactly degenerate in the SNRNMAIS solar model to couple, only nearly so. General matrix elements compose the hermitian supermatrix Z. The eigenvalues of the supermatrix are the eigenfrequency perturbations of the convecting, aspherical model and the eigenvector components of Z are the expansion coefficients in the linear combination forming the eigenfunctions in which the eigenfunctions of the SNRNMAIS solar model act as basis functions. The properties of the Wigner 3j symbols and the reduced matrix elements composing Hn'n,l'lm' produce selection rules governing the coupling of SNRNMAIS modes that hold even for time-varying flows. We state selection rules for both quasi-degenerate and degenerate perturbation theories. For example, within degenerate perturbation theory, only odd-degree s toroidal flows and even degree structural asphericities, both with s <= 2l, will couple and/or split acoustic modes with harmonic degree l. In addition, the frequency perturbations caused by a toroidal flow display odd symmetry with respect to the degenerate frequency when ordered from the minimum to the maximum frequency perturbation. We consider the special case of differential rotation, the odd-degree, axisymmetric, toroidal component of general convection, and present the general matrix element and selection rules under quasi-degenerate perturbation theory. We argue that due to the spacing of modes that satisfy the selection rules, quasi-degenerate coupling can, for all practical purposes, be neglected in modelling the effect of low-degree differential rotation on helioseismic data. In effect, modes that can couple through low-degree differential rotation are too far separated in frequency to couple strongly. This is not the case for non-axisymmetric flows and asphericities where near degeneracies will regularly occur, and couplings can be relatively strong especially among SNRNMAIS modes within the same multiplet. All derivations are performed and all solutions are presented in a frame corotating with the mean solar angular rotation rate. Equation (18) shows how to transform the eigenfrequencies and eigenfunctions in the corotating frame into an inertial frame. The transformation has the effect that each eigenfunction in the inertial frame is itself time varying. That is, a mode of oscillation, which is defined to have a single frequency in the corotating frame, becomes multiply periodic in the inertial frame.

A shielding application of perturbation theory to determine changes in neutron and gamma doses due to changes in shield layers

NASA Technical Reports Server (NTRS)

Fieno, D.

1972-01-01

The perturbation theory for fixed sources was applied to radiation shielding problems to determine changes in neutron and gamma ray doses due to changes in various shield layers. For a given source and detector position the perturbation method enables dose derivatives due to all layer changes to be determined from one forward and one inhomogeneous adjoint calculation. The direct approach requires two forward calculations for the derivative due to a single layer change. Hence, the perturbation method for obtaining dose derivatives permits an appreciable savings in computation for a multilayered shield. For an illustrative problem, a comparison was made of the fractional change in the dose per unit change in the thickness of each shield layer as calculated by perturbation theory and by successive direct calculations; excellent agreement was obtained between the two methods.

Effect of fine dust particles and finite electron inertia of rotating magnetized plasma

NASA Astrophysics Data System (ADS)

Kumar, V.; Sutar, D. L.; Pensia, R. K.; Sharma, S.

2018-05-01

A theoretical investigation has been made of the effect of fine dust particles, viscosity and electron inertia on Jeans instability in a self-gravitating magnetized rotating plasma. The MHD model is used to formulate the problem in which a general dispersion relation. A general dispersion relation is obtained from the linearized perturbation equations using the normal mode analysis method. The analytical expressions of the growth rate of Jeans instability are obtained for the longitudinal and transverse mode of propagation. The present result shows that the Jeans criterion of instability is modified due to the presence of viscosity, rotation, and magnetic field.

Fully unsteady subsonic and supersonic potential aerodynamics for complex aircraft configurations for flutter applications

NASA Technical Reports Server (NTRS)

Tseng, K.; Morino, L.

1975-01-01

A general theory for study, oscillatory or fully unsteady potential compressible aerodynamics around complex configurations is presented. Using the finite-element method to discretize the space problem, one obtains a set of differential-delay equations in time relating the potential to its normal derivative which is expressed in terms of the generalized coordinates of the structure. For oscillatory flow, the motion consists of sinusoidal oscillations around a steady, subsonic or supersonic flow. For fully unsteady flow, the motion is assumed to consist of constant subsonic or supersonic speed for time t or = 0 and of small perturbations around the steady state for time t 0.

Stability analysis of a liquid fuel annular combustion chamber. M.S. Thesis

NASA Technical Reports Server (NTRS)

Mcdonald, G. H.

1978-01-01

High frequency combustion instability problems in a liquid fuel annular combustion chamber are examined. A modified Galerkin method was used to produce a set of modal amplitude equations from the general nonlinear partial differential acoustic wave equation in order to analyze the problem of instability. From these modal amplitude equations, the two variable perturbation method was used to develop a set of approximate equations of a given order of magnitude. These equations were modeled to show the effects of velocity sensitive combustion instabilities by evaluating the effects of certain parameters in the given set of equations.

Doi-Peliti path integral methods for stochastic systems with partial exclusion

NASA Astrophysics Data System (ADS)

Greenman, Chris D.

2018-09-01

Doi-Peliti methods are developed for stochastic models with finite maximum occupation numbers per site. We provide a generalized framework for the different Fock spaces reported in the literature. Paragrassmannian techniques are then utilized to construct path integral formulations of factorial moments. We show that for many models of interest, a Magnus expansion is required to construct a suitable action, meaning actions containing a finite number of terms are not always feasible. However, for such systems, perturbative techniques are still viable, and for some examples, including carrying capacity population dynamics, and diffusion with partial exclusion, the expansions are exactly summable.

Frequency-domain algorithm for the Lorenz-gauge gravitational self-force

NASA Astrophysics Data System (ADS)

Akcay, Sarp; Warburton, Niels; Barack, Leor

2013-11-01

State-of-the-art computations of the gravitational self-force (GSF) on massive particles in black hole spacetimes involve numerical evolution of the metric perturbation equations in the time domain, which is computationally very costly. We present here a new strategy based on a frequency-domain treatment of the perturbation equations, which offers considerable computational saving. The essential ingredients of our method are (i) a Fourier-harmonic decomposition of the Lorenz-gauge metric perturbation equations and a numerical solution of the resulting coupled set of ordinary equations with suitable boundary conditions; (ii) a generalized version of the method of extended homogeneous solutions [L. Barack, A. Ori, and N. Sago, Phys. Rev. D 78, 084021 (2008)] used to circumvent the Gibbs phenomenon that would otherwise hamper the convergence of the Fourier mode sum at the particle’s location; (iii) standard mode-sum regularization, which finally yields the physical GSF as a sum over regularized modal contributions. We present a working code that implements this strategy to calculate the Lorenz-gauge GSF along eccentric geodesic orbits around a Schwarzschild black hole. The code is far more efficient than existing time-domain methods; the gain in computation speed (at a given precision) is about an order of magnitude at an eccentricity of 0.2, and up to 3 orders of magnitude for circular or nearly circular orbits. This increased efficiency was crucial in enabling the recently reported calculation of the long-term orbital evolution of an extreme mass ratio inspiral [N. Warburton, S. Akcay, L. Barack, J. R. Gair, and N. Sago, Phys. Rev. D 85, 061501(R) (2012)]. Here we provide full technical details of our method to complement the above report.

On the solution of the complex eikonal equation in acoustic VTI media: A perturbation plus optimization scheme

NASA Astrophysics Data System (ADS)

Huang, Xingguo; Sun, Jianguo; Greenhalgh, Stewart

2018-04-01

We present methods for obtaining numerical and analytic solutions of the complex eikonal equation in inhomogeneous acoustic VTI media (transversely isotropic media with a vertical symmetry axis). The key and novel point of the method for obtaining numerical solutions is to transform the problem of solving the highly nonlinear acoustic VTI eikonal equation into one of solving the relatively simple eikonal equation for the background (isotropic) medium and a system of linear partial differential equations. Specifically, to obtain the real and imaginary parts of the complex traveltime in inhomogeneous acoustic VTI media, we generalize a perturbation theory, which was developed earlier for solving the conventional real eikonal equation in inhomogeneous anisotropic media, to the complex eikonal equation in such media. After the perturbation analysis, we obtain two types of equations. One is the complex eikonal equation for the background medium and the other is a system of linearized partial differential equations for the coefficients of the corresponding complex traveltime formulas. To solve the complex eikonal equation for the background medium, we employ an optimization scheme that we developed for solving the complex eikonal equation in isotropic media. Then, to solve the system of linearized partial differential equations for the coefficients of the complex traveltime formulas, we use the finite difference method based on the fast marching strategy. Furthermore, by applying the complex source point method and the paraxial approximation, we develop the analytic solutions of the complex eikonal equation in acoustic VTI media, both for the isotropic and elliptical anisotropic background medium. Our numerical results demonstrate the effectiveness of our derivations and illustrate the influence of the beam widths and the anisotropic parameters on the complex traveltimes.

Non-perturbative effects and wall-crossing from topological strings

NASA Astrophysics Data System (ADS)

Collinucci, Andrés; Soler, Pablo; Uranga, Angel M.

2009-11-01

We argue that the Gopakumar-Vafa interpretation of the topological string partition function can be used to compute and resum certain non-perturbative brane instanton effects of type II CY compactifications. In particular the topological string A-model encodes the non-perturbative corrections to the hypermultiplet moduli space metric from general D1/D(-1)-brane instantons in 4d Script N = 2 IIB models. We also discuss the reduction to 4d Script N = 1 by fluxes and/or orientifolds and/or D-branes, and the prospects to resum brane instanton contributions to non-perturbative superpotentials. We argue that the connection between non-perturbative effects and the topological string underlies the continuity of non-perturbative effects across lines of BPS stability. We also confirm this statement in mirror B-model matrix model examples, relating matrix model instantons to non-perturbative D-brane instantons. The computation of non-perturbative effects from the topological string requires a 3d circle compactification and T-duality, relating effects from particles and instantons, reminiscent of that involved in the physical derivation of the Kontsevich-Soibelmann wall-crossing formula.

Subsonic panel method for designing wing surfaces from pressure distribution

NASA Technical Reports Server (NTRS)

Bristow, D. R.; Hawk, J. D.

1983-01-01

An iterative method has been developed for designing wing section contours corresponding to a prescribed subcritical distribution of pressure. The calculations are initialized by using a surface panel method to analyze a baseline wing or wing-fuselage configuration. A first-order expansion to the baseline panel method equations is then used to calculate a matrix containing the partial derivative of potential at each control point with respect to each unknown geometry parameter. In every iteration cycle, the matrix is used both to calculate the geometry perturbation and to analyze the perturbed geometry. The distribution of potential on the perturbed geometry is established by simple linear extrapolation from the baseline solution. The extrapolated potential is converted to pressure by Bernoulli's equation. Not only is the accuracy of the approach good for very large perturbations, but the computing cost of each complete iteration cycle is substantially less than one analysis solution by a conventional panel method.

Optimization of Empirical Force Fields by Parameter Space Mapping: A Single-Step Perturbation Approach.

PubMed

Stroet, Martin; Koziara, Katarzyna B; Malde, Alpeshkumar K; Mark, Alan E

2017-12-12

A general method for parametrizing atomic interaction functions is presented. The method is based on an analysis of surfaces corresponding to the difference between calculated and target data as a function of alternative combinations of parameters (parameter space mapping). The consideration of surfaces in parameter space as opposed to local values or gradients leads to a better understanding of the relationships between the parameters being optimized and a given set of target data. This in turn enables for a range of target data from multiple molecules to be combined in a robust manner and for the optimal region of parameter space to be trivially identified. The effectiveness of the approach is illustrated by using the method to refine the chlorine 6-12 Lennard-Jones parameters against experimental solvation free enthalpies in water and hexane as well as the density and heat of vaporization of the liquid at atmospheric pressure for a set of 10 aromatic-chloro compounds simultaneously. Single-step perturbation is used to efficiently calculate solvation free enthalpies for a wide range of parameter combinations. The capacity of this approach to parametrize accurate and transferrable force fields is discussed.

Large-scale image-based profiling of single-cell phenotypes in arrayed CRISPR-Cas9 gene perturbation screens.

PubMed

de Groot, Reinoud; Lüthi, Joel; Lindsay, Helen; Holtackers, René; Pelkmans, Lucas

2018-01-23

High-content imaging using automated microscopy and computer vision allows multivariate profiling of single-cell phenotypes. Here, we present methods for the application of the CISPR-Cas9 system in large-scale, image-based, gene perturbation experiments. We show that CRISPR-Cas9-mediated gene perturbation can be achieved in human tissue culture cells in a timeframe that is compatible with image-based phenotyping. We developed a pipeline to construct a large-scale arrayed library of 2,281 sequence-verified CRISPR-Cas9 targeting plasmids and profiled this library for genes affecting cellular morphology and the subcellular localization of components of the nuclear pore complex (NPC). We conceived a machine-learning method that harnesses genetic heterogeneity to score gene perturbations and identify phenotypically perturbed cells for in-depth characterization of gene perturbation effects. This approach enables genome-scale image-based multivariate gene perturbation profiling using CRISPR-Cas9. © 2018 The Authors. Published under the terms of the CC BY 4.0 license.

Rows of optical vortices from elliptically perturbing a high-order beam

NASA Astrophysics Data System (ADS)

Dennis, Mark R.

2006-05-01

An optical vortex (phase singularity) with a high topological strength resides on the axis of a high-order light beam. The breakup of this vortex under elliptic perturbation into a straight row of unit-strength vortices is described. This behavior is studied in helical Ince-Gauss beams and astigmatic, generalized Hermite-Laguerre-Gauss beams, which are perturbations of Laguerre-Gauss beams. Approximations of these beams are derived for small perturbations, in which a neighborhood of the axis can be approximated by a polynomial in the complex plane: a Chebyshev polynomial for Ince-Gauss beams, and a Hermite polynomial for astigmatic beams.

Instabilities in mimetic matter perturbations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Firouzjahi, Hassan; Gorji, Mohammad Ali; 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

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 instabilitiesmore » such as the Ostrogradsky ghost.« less

Vertical Propagation and Temporal Growth of Perturbations in the Winter Atmosphere

NASA Astrophysics Data System (ADS)

Christiansen, B.

2001-12-01

We present a general circulation model study of the temporal growth and vertically propagation of perturbations following vertical confined forcings. Both transient and sustained forcings are considered. The motivation for the study is the recent recognition of downward propagation of anomalies from the stratosphere to the troposphere and its implications both for medium range forecasts and for a possible physical mechanism for stratospheric impacts on weather and climate. The dynamical link might also offer a mechanism for changes in the upper atmosphere to affect the tropospheric climate. Here we are thinking of changes in trace gases such as ozone, but also of modulations of the upper atmospheric structure related to the 11-year solar cycle. The model atmosphere is chaotic and shows growth of perturbations no matter which level is forced. The perturbations grow to a size comparable to the variability of the unperturbed atmosphere on a time-scale of 20 - 25 days in the troposphere and 30 - 40 days in the stratosphere. After the initial period of growth the perturbations have the same structure as the unperturbed atmosphere. Although the forcing is restricted to the northern hemisphere the perturbations encompass the whole atmosphere and develop on the same time scale on both hemispheres. Perturbations grow with time squared both when zonal mean and single cell values are considered. Such a power law growth suggest the existence of a finite predictability time which is independent of the initial perturbation as long as it is small. In the unperturbed atmosphere the stratospheric variability has the form of downward propagating stratospheric vacillations. However, in the initial period of growth the perturbations do not propagate downward and seem in general uncoupled to the background vacillations. This suggests that the downward propagation is a robust feature determined more by the processes in the troposphere than the state of the stratosphere. We note that downward propagation may still be a source for enhanced predictability of near-surface weather.

More is still not better: testing the perturbation model of temporal reference memory across different modalities and tasks.

PubMed

Ogden, Ruth S; Jones, Luke A

2009-05-01

The ability of the perturbation model (Jones & Wearden, 2003) to account for reference memory function in a visual temporal generalization task and auditory and visual reproduction tasks was examined. In all tasks the number of presentations of the standard was manipulated (1, 3, or 5), and its effect on performance was compared. In visual temporal generalization the number of presentations of the standard did not affect the number of times the standard was correctly identified, nor did it affect the overall temporal generalization gradient. In auditory reproduction there was no effect of the number of times the standard was presented on mean reproductions. In visual reproduction mean reproductions were shorter when the standard was only presented once; however, this effect was reduced when a visual cue was provided before the first presentation of the standard. Whilst the results of all experiments are best accounted for by the perturbation model there appears to be some attentional benefit to multiple presentations of the standard in visual reproduction.

Investigating a hybrid perturbation-Galerkin technique using computer algebra

NASA Technical Reports Server (NTRS)

Andersen, Carl M.; Geer, James F.

1988-01-01

A two-step hybrid perturbation-Galerkin method is presented for the solution of a variety of differential equations type problems which involve a scalar parameter. The resulting (approximate) solution has the form of a sum where each term consists of the product of two functions. The first function is a function of the independent field variable(s) x, and the second is a function of the parameter lambda. In step one the functions of x are determined by forming a perturbation expansion in lambda. In step two the functions of lambda are determined through the use of the classical Bubnov-Gelerkin method. The resulting hybrid method has the potential of overcoming some of the drawbacks of the perturbation and Bubnov-Galerkin methods applied separately, while combining some of the good features of each. In particular, the results can be useful well beyond the radius of convergence associated with the perturbation expansion. The hybrid method is applied with the aid of computer algebra to a simple two-point boundary value problem where the radius of convergence is finite and to a quantum eigenvalue problem where the radius of convergence is zero. For both problems the hybrid method apparently converges for an infinite range of the parameter lambda. The results obtained from the hybrid method are compared with approximate solutions obtained by other methods, and the applicability of the hybrid method to broader problem areas is discussed.

Casimir-Lifshitz interaction between dielectrics of arbitrary geometry: A dielectric contrast perturbation theory

DOE Office of Scientific and Technical Information (OSTI.GOV)

Golestanian, Ramin

2009-07-15

The general theory of electromagnetic-fluctuation-induced interactions in dielectric bodies as formulated by Dzyaloshinskii, Lifshitz, and Pitaevskii is rewritten as a perturbation theory in terms of the spatial contrast in (imaginary) frequency dependent dielectric function. The formulation can be used to calculate the Casimir-Lifshitz forces for dielectric objects of arbitrary geometry, as a perturbative expansion in the dielectric contrast, and could thus complement the existing theories that use perturbation in geometrical features. We find that expansion in dielectric contrast recasts the resulting Lifshitz energy into a sum of the different many-body contributions. The limit of validity and convergence properties of themore » perturbation theory is discussed using the example of parallel semi-infinite objects for which the exact result is known.« less

Multiconfigurational short-range density-functional theory for open-shell systems

NASA Astrophysics Data System (ADS)

Hedegârd, Erik Donovan; Toulouse, Julien; Jensen, Hans Jørgen Aagaard

2018-06-01

Many chemical systems cannot be described by quantum chemistry methods based on a single-reference wave function. Accurate predictions of energetic and spectroscopic properties require a delicate balance between describing the most important configurations (static correlation) and obtaining dynamical correlation efficiently. The former is most naturally done through a multiconfigurational (MC) wave function, whereas the latter can be done by, e.g., perturbation theory. We have employed a different strategy, namely, a hybrid between multiconfigurational wave functions and density-functional theory (DFT) based on range separation. The method is denoted by MC short-range DFT (MC-srDFT) and is more efficient than perturbative approaches as it capitalizes on the efficient treatment of the (short-range) dynamical correlation by DFT approximations. In turn, the method also improves DFT with standard approximations through the ability of multiconfigurational wave functions to recover large parts of the static correlation. Until now, our implementation was restricted to closed-shell systems, and to lift this restriction, we present here the generalization of MC-srDFT to open-shell cases. The additional terms required to treat open-shell systems are derived and implemented in the DALTON program. This new method for open-shell systems is illustrated on dioxygen and [Fe(H2O)6]3+.

A nonlinear approach to transition in subcritical plasmas with sheared flow

NASA Astrophysics Data System (ADS)

Pringle, Chris C. T.; McMillan, Ben F.; Teaca, Bogdan

2017-12-01

In many plasma systems, introducing a small background shear flow is enough to stabilize the system linearly. The nonlinear dynamics are much less sensitive to sheared flows than the average linear growth rates, and very small amplitude perturbations can lead to sustained turbulence. We explore the general problem of characterizing how and when the transition from near-laminar states to sustained turbulence occurs, with a model of the interchange instability being used as a concrete example. These questions are fundamentally nonlinear, and the answers must go beyond the linear transient amplification of small perturbations. Two methods that account for nonlinear interactions are therefore explored here. The first method explored is edge tracking, which identifies the boundary between the basins of attraction of the laminar and turbulent states. Here, the edge is found to be structured around an exact, localized, traveling wave solution that is qualitatively similar to avalanche-like bursts seen in the turbulent regime. The second method is an application of nonlinear, non-modal stability theory which allows us to identify the smallest disturbances which can trigger turbulence (the minimal seed for the problem) and hence to quantify how stable the laminar regime is. The results obtained from these fully nonlinear methods provide confidence in the derivation of a semi-analytic approximation for the minimal seed.

A second-order multi-reference perturbation method for molecular vibrations

NASA Astrophysics Data System (ADS)

Mizukami, Wataru; Tew, David P.

2013-11-01

We present a general multi-reference framework for treating strong correlation in vibrational structure theory, which we denote the vibrational active space self-consistent field (VASSCF) approach. Active configurations can be selected according to excitation level or the degrees of freedom involved, or both. We introduce a novel state-specific second-order multi-configurational perturbation correction that accounts for the remaining weak correlation between the vibrational modes. The resulting VASPT2 method is capable of accurately and efficiently treating strong correlation in the form of large anharmonic couplings, at the same time as correctly resolving resonances between states. These methods have been implemented in our new dynamics package DYNAMOL, which can currently treat up to four-body Hamiltonian coupling terms. We present a pilot application of the VASPT2 method to the trans isomer of formic acid. We have constructed a new analytic potential that reproduces frozen core CCSD(T)(F12*)/cc-pVDZ-F12 energies to within 0.25% RMSD over the energy range 0-15 000 cm-1. The computed VASPT2 fundamental transition energies are accurate to within 9 cm-1 RMSD from experimental values, which is close to the accuracy one can expect from a CCSD(T) potential energy surface.

Identification of spatially-localized initial conditions via sparse PCA

NASA Astrophysics Data System (ADS)

Dwivedi, Anubhav; Jovanovic, Mihailo

2017-11-01

Principal Component Analysis involves maximization of a quadratic form subject to a quadratic constraint on the initial flow perturbations and it is routinely used to identify the most energetic flow structures. For general flow configurations, principal components can be efficiently computed via power iteration of the forward and adjoint governing equations. However, the resulting flow structures typically have a large spatial support leading to a question of physical realizability. To obtain spatially-localized structures, we modify the quadratic constraint on the initial condition to include a convex combination with an additional regularization term which promotes sparsity in the physical domain. We formulate this constrained optimization problem as a nonlinear eigenvalue problem and employ an inverse power-iteration-based method to solve it. The resulting solution is guaranteed to converge to a nonlinear eigenvector which becomes increasingly localized as our emphasis on sparsity increases. We use several fluids examples to demonstrate that our method indeed identifies the most energetic initial perturbations that are spatially compact. This work was supported by Office of Naval Research through Grant Number N00014-15-1-2522.

Induction of Maternal Immune Activation in Mice at Mid-gestation Stage with Viral Mimic Poly(I:C)

PubMed Central

Wu, Wei-Li

2016-01-01

Maternal immune activation (MIA) model is increasingly well appreciated as a rodent model for the environmental risk factor of various psychiatric disorders. Numerous studies have demonstrated that MIA model is able to show face, construct, and predictive validity that are relevant to autism and schizophrenia. To model MIA, investigators often use viral mimic polyinosinic:polycytidylic acid (poly(I:C)) to activate the immune system in pregnant rodents. Generally, the offspring from immune activated dam exhibit behavioral abnormalities and physiological alterations that are associated with autism and schizophrenia. However, poly(I:C) injection with different dosages and at different time points could lead to different outcomes by perturbing brain development at different stages. Here we provide a detailed method of inducing MIA by intraperitoneal (i.p.) injection of 20 mg/kg poly(I:C) at mid-gestational embryonic 12.5 days (E12.5). This method has been shown to induce acute inflammatory response in the maternal-placental-fetal axis, which ultimately results in the brain perturbations and behavioral phenotypes that are associated with autism and schizophrenia. PMID:27078638

Prospects for an Improved Measurement of Experimental Limit on G-dot

NASA Technical Reports Server (NTRS)

Sanders, Alvin J.

2003-01-01

The orbital motion of an ultra-drag-free satellite, such as the large test body of the SEE (Satellite Energy Exchange) satellite, known as the "Shepherd," may possibly provide the best test for time variation of the gravitational constant G at the level of parts in 10(exp 14). Scarcely anything could be more significant scientifically than the incontestable discovery that a fundamental "constant" of Nature is not constant. A finding of non-zero (G-dot)/G would clearly mark the boundaries where general relativity is valid, and specify the onset of new physics. The requirements for measuring G-dot at the level proposed by SEE will require great care in treating perturbation forces. In the present paper we concentrate on the methods for dealing with the gravitational field due to possible large manufacturing defects in the SEE observatory. We find that, with adequate modeling of the perturbation forces and cancellation methods, the effective time-averaged acceleration on the SEE Shepherd will be approx. 10(exp -18) g (10(exp -17) m/sq s).

Why does MP2 work?

PubMed

Fink, Reinhold F

2016-11-14

We show analytically and numerically that the performance of second order Møller-Plesset (MP) perturbation theory (PT), coupled-cluster (CC) theory, and other perturbation theory approaches can be rationalized by analyzing the wavefunctions of these methods. While rather large deviations for the individual contributions of configurations to the electron correlation energy are found for MP wavefunctions, they profit from an advantageous and robust error cancellation: The absolute contribution to the correlation energy is generally underestimated for the critical excitations with small energy denominators and all other doubly excited configurations where the two excited electrons are coupled to a singlet. This is balanced by an overestimation of the contribution of triplet-coupled double excitations to the correlation energy. The even better performance of spin-component-scaled-MP2 theory is explained by a similar error compensation effect. The wavefunction analysis for the lowest singlet states of H 2 O, CH 2 , CO, and Cu + shows the predicted trends for MP methods, rapid but biased convergence of CC theory as well as the substantial potential of linearized CC, or retaining the excitation-degree (RE)-PT.

Induction of Maternal Immune Activation in Mice at Mid-gestation Stage with Viral Mimic Poly(I:C).

PubMed

Chow, Ke-Huan; Yan, Zihao; Wu, Wei-Li

2016-03-25

Maternal immune activation (MIA) model is increasingly well appreciated as a rodent model for the environmental risk factor of various psychiatric disorders. Numerous studies have demonstrated that MIA model is able to show face, construct, and predictive validity that are relevant to autism and schizophrenia. To model MIA, investigators often use viral mimic polyinosinic:polycytidylic acid (poly(I:C)) to activate the immune system in pregnant rodents. Generally, the offspring from immune activated dam exhibit behavioral abnormalities and physiological alterations that are associated with autism and schizophrenia. However, poly(I:C) injection with different dosages and at different time points could lead to different outcomes by perturbing brain development at different stages. Here we provide a detailed method of inducing MIA by intraperitoneal (i.p.) injection of 20 mg/kg poly(I:C) at mid-gestational embryonic 12.5 days (E12.5). This method has been shown to induce acute inflammatory response in the maternal-placental-fetal axis, which ultimately results in the brain perturbations and behavioral phenotypes that are associated with autism and schizophrenia.

Non-linear hydrodynamical evolution of rotating relativistic stars: numerical methods and code tests

NASA Astrophysics Data System (ADS)

Font, José A.; Stergioulas, Nikolaos; Kokkotas, Kostas D.

2000-04-01

We present numerical hydrodynamical evolutions of rapidly rotating relativistic stars, using an axisymmetric, non-linear relativistic hydrodynamics code. We use four different high-resolution shock-capturing (HRSC) finite-difference schemes (based on approximate Riemann solvers) and compare their accuracy in preserving uniformly rotating stationary initial configurations in long-term evolutions. Among these four schemes, we find that the third-order piecewise parabolic method scheme is superior in maintaining the initial rotation law in long-term evolutions, especially near the surface of the star. It is further shown that HRSC schemes are suitable for the evolution of perturbed neutron stars and for the accurate identification (via Fourier transforms) of normal modes of oscillation. This is demonstrated for radial and quadrupolar pulsations in the non-rotating limit, where we find good agreement with frequencies obtained with a linear perturbation code. The code can be used for studying small-amplitude or non-linear pulsations of differentially rotating neutron stars, while our present results serve as testbed computations for three-dimensional general-relativistic evolution codes.

Detection of symmetric homoclinic orbits to saddle-centres in reversible systems

NASA Astrophysics Data System (ADS)

Yagasaki, Kazuyuki; Wagenknecht, Thomas

2006-02-01

We present a perturbation technique for the detection of symmetric homoclinic orbits to saddle-centre equilibria in reversible systems of ordinary differential equations. We assume that the unperturbed system has primary, symmetric homoclinic orbits, which may be either isolated or appear in a family, and use an idea similar to that of Melnikov’s method to detect homoclinic orbits in their neighbourhood. This technique also allows us to identify bifurcations of unperturbed or perturbed, symmetric homoclinic orbits. Our technique is of importance in applications such as nonlinear optics and water waves since homoclinic orbits to saddle-centre equilibria describe embedded solitons (ESs) in systems of partial differential equations representing physical models, and except for special cases their existence has been previously studied only numerically using shooting methods and continuation techniques. We apply the general theory to two examples, a four-dimensional system describing ESs in nonlinear optical media and a six-dimensional system which can possess a one-parameter family of symmetric homoclinic orbits in the unperturbed case. For these examples, the analysis is compared with numerical computations and an excellent agreement between both results is found.

Broadband complex permeability characterization of magnetic thin films using shorted microstrip transmission-line perturbation

NASA Astrophysics Data System (ADS)

Liu, Yan; Chen, Linfeng; Tan, C. Y.; Liu, H. J.; Ong, C. K.

2005-06-01

A brief review of the methods used for broadband complex permeability measurement of magnetic thin films up to microwave frequencies is given. In particular, the working principles of the transmission-line perturbation methods for the characterization of magnetic thin films are discussed, with emphasis on short-circuited planar transmission-line perturbation methods. The algorithms for calculating the complex permeability of magnetic thin films for short-circuited planar transmission-line perturbation methods are analyzed. A shorted microstrip line is designed and fabricated as a prototype measurement fixture. The structure of the microstrip fixture and the corresponding measurement procedure are discussed in detail. A piece of 340 nm thick FeTaN thin film deposited on Si substrate using sputtering method is characterized using the microstrip fixture. An improved technique for obtaining permeability by using a saturation magnetization field is demonstrated here, and the results fit well with the Landau-Lifchitz-Gilbert theory. Approaches to extending this method to other aspects in the investigation of magnetic thin film are also discussed.

Perturbational and nonperturbational inversion of Rayleigh-wave velocities

USGS Publications Warehouse

Haney, Matt; Tsai, Victor C.

2017-01-01

The inversion of Rayleigh-wave dispersion curves is a classic geophysical inverse problem. We have developed a set of MATLAB codes that performs forward modeling and inversion of Rayleigh-wave phase or group velocity measurements. We describe two different methods of inversion: a perturbational method based on finite elements and a nonperturbational method based on the recently developed Dix-type relation for Rayleigh waves. In practice, the nonperturbational method can be used to provide a good starting model that can be iteratively improved with the perturbational method. Although the perturbational method is well-known, we solve the forward problem using an eigenvalue/eigenvector solver instead of the conventional approach of root finding. Features of the codes include the ability to handle any mix of phase or group velocity measurements, combinations of modes of any order, the presence of a surface water layer, computation of partial derivatives due to changes in material properties and layer boundaries, and the implementation of an automatic grid of layers that is optimally suited for the depth sensitivity of Rayleigh waves.

The AdS3 propagator and the fate of locality

NASA Astrophysics Data System (ADS)

Chen, Hongbin; Fitzpatrick, A. Liam; Kaplan, Jared; Li, Daliang

2018-04-01

We recently used Virasoro symmetry considerations to propose an exact formula for a bulk proto-field ϕ in AdS3. In this paper we study the propagator < ϕϕ>. We show that many techniques from the study of conformal blocks can be generalized to compute it, including the semiclassical monodromy method and both forms of the Zamolodchikov recursion relations. When the results from recursion are expanded at large central charge, they match gravitational perturbation theory for a free scalar field coupled to gravity in our chosen gauge. We find that although the propagator is finite and well-defined at long distances, its perturbative expansion in {G}_N=3/2c exhibits UV/IR mixing effects. If we nevertheless interpret < ϕϕ> as a probe of bulk locality, then when {G}_{N{m}_{φ }}≪ 1 locality breaks down at the new short-distance scale {σ}_{\\ast}˜ √[4]{G_N{R}_{AdS}^3} . For ϕ with very large bulk mass, or at small central charge, bulk locality fails at the AdS length scale. In all cases, locality `breakdown' manifests as singularities or branch cuts at spacelike separation arising from non-perturbative quantum gravitational effects.

Conformal expansions and renormalons

DOE Office of Scientific and Technical Information (OSTI.GOV)

Rathsman, J.

2000-02-07

The coefficients in perturbative expansions in gauge theories are factorially increasing, predominantly due to renormalons. This type of factorial increase is not expected in conformal theories. In QCD conformal relations between observables can be defined in the presence of a perturbative infrared fixed-point. Using the Banks-Zaks expansion the authors study the effect of the large-order behavior of the perturbative series on the conformal coefficients. The authors find that in general these coefficients become factorially increasing. However, when the factorial behavior genuinely originates in a renormalon integral, as implied by a postulated skeleton expansion, it does not affect the conformal coefficients.more » As a consequence, the conformal coefficients will indeed be free of renormalon divergence, in accordance with previous observations concerning the smallness of these coefficients for specific observables. The authors further show that the correspondence of the BLM method with the skeleton expansion implies a unique scale-setting procedure. The BLM coefficients can be interpreted as the conformal coefficients in the series relating the fixed-point value of the observable with that of the skeleton effective charge. Through the skeleton expansion the relevance of renormalon-free conformal coefficients extends to real-world QCD.« less

Stabilization of dynamics of oscillatory systems by nonautonomous perturbation.

PubMed

Lucas, Maxime; Newman, Julian; Stefanovska, Aneta

2018-04-01

Synchronization and stability under periodic oscillatory driving are well understood, but little is known about the effects of aperiodic driving, despite its abundance in nature. Here, we consider oscillators subject to driving with slowly varying frequency, and investigate both short-term and long-term stability properties. For a phase oscillator, we find that, counterintuitively, such variation is guaranteed to enlarge the Arnold tongue in parameter space. Using analytical and numerical methods that provide information on time-variable dynamical properties, we find that the growth of the Arnold tongue is specifically due to the growth of a region of intermittent synchronization where trajectories alternate between short-term stability and short-term neutral stability, giving rise to stability on average. We also present examples of higher-dimensional nonlinear oscillators where a similar stabilization phenomenon is numerically observed. Our findings help support the case that in general, deterministic nonautonomous perturbation is a very good candidate for stabilizing complex dynamics.

Stabilization of dynamics of oscillatory systems by nonautonomous perturbation

NASA Astrophysics Data System (ADS)

Lucas, Maxime; Newman, Julian; Stefanovska, Aneta

2018-04-01

Synchronization and stability under periodic oscillatory driving are well understood, but little is known about the effects of aperiodic driving, despite its abundance in nature. Here, we consider oscillators subject to driving with slowly varying frequency, and investigate both short-term and long-term stability properties. For a phase oscillator, we find that, counterintuitively, such variation is guaranteed to enlarge the Arnold tongue in parameter space. Using analytical and numerical methods that provide information on time-variable dynamical properties, we find that the growth of the Arnold tongue is specifically due to the growth of a region of intermittent synchronization where trajectories alternate between short-term stability and short-term neutral stability, giving rise to stability on average. We also present examples of higher-dimensional nonlinear oscillators where a similar stabilization phenomenon is numerically observed. Our findings help support the case that in general, deterministic nonautonomous perturbation is a very good candidate for stabilizing complex dynamics.

Analytical and regression models of glass rod drawing process

NASA Astrophysics Data System (ADS)

Alekseeva, L. B.

2018-03-01

The process of drawing glass rods (light guides) is being studied. The parameters of the process affecting the quality of the light guide have been determined. To solve the problem, mathematical models based on general equations of continuum mechanics are used. The conditions for the stable flow of the drawing process have been found, which are determined by the stability of the motion of the glass mass in the formation zone to small uncontrolled perturbations. The sensitivity of the formation zone to perturbations of the drawing speed and viscosity is estimated. Experimental models of the drawing process, based on the regression analysis methods, have been obtained. These models make it possible to customize a specific production process to obtain light guides of the required quality. They allow one to find the optimum combination of process parameters in the chosen area and to determine the required accuracy of maintaining them at a specified level.

The True- and Eccentric-Anomaly Parameterizations of the Perturbed Kepler Motion

NASA Astrophysics Data System (ADS)

Gergely, László Á.; Perjés, Zoltán I.; Vasúth, Mátyás

2000-01-01

The true- and eccentric-anomaly parameterizations of the Kepler motion are generalized to quasi-periodic orbits, by considering perturbations of the radial part of the kinetic energy in the form of a series of negative powers of the orbital radius. A toolbox of methods for averaging observables as functions of the energy E and angular momentum L is developed. A broad range of systems governed by the generic Brumberg force, as well as recent applications in the theory of gravitational radiation, involve integrals of these functions over a period of motion. These integrals are evaluated by using the residue theorem. In the course of this work, two important questions emerge: (1) When do the true- and eccentric-anomaly parameters exist? (2) Under what circumstances, and why, are the poles in the origin? The purpose of this paper is to find the answer to these queries.

Quantum tunneling and quasinormal modes in the spacetime of the Alcubierre warp drive

NASA Astrophysics Data System (ADS)

Jusufi, Kimet; Sakallı, İzzet; Övgün, Ali

2018-01-01

In a seminal paper, Alcubierre showed that Einstein's theory of general relativity appears to allow a super-luminal motion. In the present study, we use a recent eternal-warp-drive solution found by Alcubierre to study the effect of Hawking radiation upon an observer located within the warp drive in the framework of the quantum tunneling method. We find the same expression for the Hawking temperatures associated with the tunneling of both massive vector and scalar particles, and show this expression to be proportional to the velocity of the warp drive. On the other hand, since the discovery of gravitational waves, the quasinormal modes (QNMs) of black holes have also been extensively studied. With this purpose in mind, we perform a QNM analysis of massive scalar field perturbations in the background of the eternal-Alcubierre-warp-drive spacetime. Our analytical analysis shows that massive scalar perturbations lead to stable QNMs.

Background history and cosmic perturbations for a general system of self-conserved dynamical dark energy and matter

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gómez-Valent, Adrià; Karimkhani, Elahe; Solà, Joan, E-mail: adriagova@ecm.ub.edu, E-mail: e.karimkhani91@basu.ac.ir, E-mail: sola@ecm.ub.edu

We determine the Hubble expansion and the general cosmic perturbation equations for a general system consisting of self-conserved matter, ρ{sub m}, and self-conserved dark energy (DE), ρ{sub D}. While at the background level the two components are non-interacting, they do interact at the perturbations level. We show that the coupled system of matter and DE perturbations can be transformed into a single, third order, matter perturbation equation, which reduces to the (derivative of the) standard one in the case that the DE is just a cosmological constant. As a nontrivial application we analyze a class of dynamical models whose DEmore » density ρ{sub D}(H) consists of a constant term, C{sub 0}, and a series of powers of the Hubble rate. These models were previously analyzed from the point of view of dynamical vacuum models, but here we treat them as self-conserved DE models with a dynamical equation of state. We fit them to the wealth of expansion history and linear structure formation data and compare their fit quality with that of the concordance ΛCDM model. Those with C{sub 0}=0 include the so-called ''entropic-force'' and ''QCD-ghost'' DE models, as well as the pure linear model ρ{sub D}∼H, all of which appear strongly disfavored. The models with C{sub 0}≠0 , in contrast, emerge as promising dynamical DE candidates whose phenomenological performance is highly competitive with the rigid Λ-term inherent to the ΛCDM.« less

Nonperturbative calculations in the framework of variational perturbation theory in QCD

NASA Astrophysics Data System (ADS)

Solovtsova, O. P.

2017-07-01

We discuss applications of the method based on the variational perturbation theory to perform calculations down to the lowest energy scale. The variational series is different from the conventional perturbative expansion and can be used to go beyond the weak-coupling regime. We apply this method to investigate the Borel representation of the light Adler function constructed from the τ data and to determine the residual condensates. It is shown that within the method suggested the optimal values of these lower dimension condensates are close to zero.

Predicting Bond Dissociation Energies of Transition-Metal Compounds by Multiconfiguration Pair-Density Functional Theory and Second-Order Perturbation Theory Based on Correlated Participating Orbitals and Separated Pairs.

PubMed

Bao, Junwei Lucas; Odoh, Samuel O; Gagliardi, Laura; Truhlar, Donald G

2017-02-14

We study the performance of multiconfiguration pair-density functional theory (MC-PDFT) and multireference perturbation theory for the computation of the bond dissociation energies in 12 transition-metal-containing diatomic molecules and three small transition-metal-containing polyatomic molecules and in two transition-metal dimers. The first step is a multiconfiguration self-consistent-field calculation, for which two choices must be made: (i) the active space and (ii) its partition into subspaces, if the generalized active space formulation is used. In the present work, the active space is chosen systematically by using three correlated-participating-orbitals (CPO) schemes, and the partition is chosen by using the separated-pair (SP) approximation. Our calculations show that MC-PDFT generally has similar accuracy to CASPT2, and the active-space dependence of MC-PDFT is not very great for transition-metal-ligand bond dissociation energies. We also find that the SP approximation works very well, and in particular SP with the fully translated BLYP functional SP-ftBLYP is more accurate than CASPT2. SP greatly reduces the number of configuration state functions relative to CASSCF. For the cases of FeO and NiO with extended-CPO active space, for which complete active space calculations are unaffordable, SP calculations are not only affordable but also of satisfactory accuracy. All of the MC-PDFT results are significantly better than the corresponding results with broken-symmetry spin-unrestricted Kohn-Sham density functional theory. Finally we test a perturbation theory method based on the SP reference and find that it performs slightly worse than CASPT2 calculations, and for most cases of the nominal-CPO active space, the approximate SP perturbation theory calculations are less accurate than the much less expensive SP-PDFT calculations.

Generalization of the Mulliken-Hush treatment for the calculation of electron transfer matrix elements

NASA Astrophysics Data System (ADS)

Cave, Robert J.; Newton, Marshall D.

1996-01-01

A new method for the calculation of the electronic coupling matrix element for electron transfer processes is introduced and results for several systems are presented. The method can be applied to ground and excited state systems and can be used in cases where several states interact strongly. Within the set of states chosen it is a non-perturbative treatment, and can be implemented using quantities obtained solely in terms of the adiabatic states. Several applications based on quantum chemical calculations are briefly presented. Finally, since quantities for adiabatic states are the only input to the method, it can also be used with purely experimental data to estimate electron transfer matrix elements.

Wave propagation in a random medium

NASA Technical Reports Server (NTRS)

Lee, R. W.; Harp, J. C.

1969-01-01

A simple technique is used to derive statistical characterizations of the perturbations imposed upon a wave (plane, spherical or beamed) propagating through a random medium. The method is essentially physical rather than mathematical, and is probably equivalent to the Rytov method. The limitations of the method are discussed in some detail; in general they are restrictive only for optical paths longer than a few hundred meters, and for paths at the lower microwave frequencies. Situations treated include arbitrary path geometries, finite transmitting and receiving apertures, and anisotropic media. Results include, in addition to the usual statistical quantities, time-lagged functions, mixed functions involving amplitude and phase fluctuations, angle-of-arrival covariances, frequency covariances, and other higher-order quantities.

ENSO Bred Vectors in Coupled Ocean-Atmosphere General Circulation Models

NASA Technical Reports Server (NTRS)

Yang, S. C.; Cai, Ming; Kalnay, E.; Rienecker, M.; Yuan, G.; Toth, ZA.

2004-01-01

The breeding method has been implemented in the NASA Seasonal-to-Interannual Prediction Project (NSIPP) Coupled General Circulation Model (CGCM) with the goal of improving operational seasonal to interannual climate predictions through ensemble forecasting and data assimilation. The coupled instability as cap'tured by the breeding method is the first attempt to isolate the evolving ENSO instability and its corresponding global atmospheric response in a fully coupled ocean-atmosphere GCM. Our results show that the growth rate of the coupled bred vectors (BV) peaks at about 3 months before a background ENSO event. The dominant growing BV modes are reminiscent of the background ENSO anomalies and show a strong tropical response with wind/SST/thermocline interrelated in a manner similar to the background ENSO mode. They exhibit larger amplitudes in the eastern tropical Pacific, reflecting the natural dynamical sensitivity associated with the presence of the shallow thermocline. Moreover, the extratropical perturbations associated with these coupled BV modes reveal the variations related to the atmospheric teleconnection patterns associated with background ENSO variability, e.g. over the North Pacific and North America. A similar experiment was carried out with the NCEP/CFS03 CGCM. Comparisons between bred vectors from the NSIPP CGCM and NCEP/CFS03 CGCM demonstrate the robustness of the results. Our results strongly suggest that the breeding method can serve as a natural filter to identify the slowly varying, coupled instabilities in a coupled GCM, which can be used to construct ensemble perturbations for ensemble forecasts and to estimate the coupled background error covariance for coupled data assimilation.

Maximum a posteriori decoder for digital communications

NASA Technical Reports Server (NTRS)

Altes, Richard A. (Inventor)

1997-01-01

A system and method for decoding by identification of the most likely phase coded signal corresponding to received data. The present invention has particular application to communication with signals that experience spurious random phase perturbations. The generalized estimator-correlator uses a maximum a posteriori (MAP) estimator to generate phase estimates for correlation with incoming data samples and for correlation with mean phases indicative of unique hypothesized signals. The result is a MAP likelihood statistic for each hypothesized transmission, wherein the highest value statistic identifies the transmitted signal.

Modulational instability and dynamics of implicit higher-order rogue wave solutions for the Kundu equation

NASA Astrophysics Data System (ADS)

Wen, Xiao-Yong; Zhang, Guoqiang

2018-01-01

Under investigation in this paper is the Kundu equation, which may be used to describe the propagation process of ultrashort optical pulses in nonlinear optics. The modulational instability of the plane-wave for the possible reason of the formation of the rogue wave (RW) is studied for the system. Based on our proposed generalized perturbation (n,N - n)-fold Darboux transformation (DT), some new higher-order implicit RW solutions in terms of determinants are obtained by means of the generalized perturbation (1,N - 1)-fold DT, when choosing different special parameters, these results will reduce to the RW solutions of the Kaup-Newell (KN) equation, Chen-Lee-Liu (CLL) equation and Gerjikov-Ivanov (GI) equation, respectively. The relevant wave structures are shown graphically, which display abundant interesting wave structures. The dynamical behaviors and propagation stability of the first-order and second-order RW solutions are discussed by using numerical simulations, the higher-order nonlinear terms for the Kundu equation have an impact on the propagation instability of the RW. The method can also be extended to find the higher-order RW or rational solutions of other integrable nonlinear equations.

TH-C-19A-01: Analytic Design Method to Make a 2D Planar, Segmented Ion Chamber Water-Equivalent for Proton Dose Measurements

DOE Office of Scientific and Technical Information (OSTI.GOV)

Harris, W; Hollebeek, R; Teo, B

2014-06-15

Purpose: Quality Assurance (QA) measurements of proton therapy fields must accurately measure steep longitudinal dose gradients as well as characterize the dose distribution laterally. Currently, available devices for two-dimensional field measurements perturb the dose distribution such that routine QA measurements performed at multiple depths require multiple field deliveries and are time consuming. Methods: A design procedure for a two-dimensional detector array is introduced whereby the proton energy loss and scatter are adjusted so that the downstream dose distribution is maintained to be equivalent to that which would occur in uniform water. Starting with the design for an existing, functional two-dimensionalmore » segmented ion chamber prototype, a compensating material is introduced downstream of the detector to simultaneously equate the energy loss and lateral scatter in the detector assembly to the values in water. An analytic formalism and procedure is demonstrated to calculate the properties of the compensating material in the general case of multiple layers of arbitrary material. The resulting design is validated with Monte Carlo simulations. Results: With respect to the specific prototype design considered, the results indicate that a graphite compensating layer of the proper dimensions can yield proton beam range perturbation less than 0.1mm and beam sigma perturbation less than 2% across the energy range of therapeutic proton beams. Conclusion: We have shown that, for a 2D gas-filled detector array, a graphite-compensating layer can balance the energy loss and multiple Coulomb scattering relative to uniform water. We have demonstrated an analytic formalism and procedure to determine a compensating material in the general case of multiple layers of arbitrary material. This work was supported by the US Army Medical Research and Materiel Command under Contract Agreement No. DAMD17-W81XWH-04-2-0022. Opinions, interpretations, conclusions and recommendations are those of the author and are not necessarily endorsed by the US Army.« less

On choosing the start time of binary black hole ringdowns

NASA Astrophysics Data System (ADS)

Bhagwat, Swetha; Okounkova, Maria; Ballmer, Stefan W.; Brown, Duncan A.; Giesler, Matthew; Scheel, Mark A.; Teukolsky, Saul A.

2018-05-01

The final stage of a binary black hole merger is ringdown, in which the system is described by a Kerr black hole with quasinormal mode perturbations. It is far from straightforward to identify the time at which the ringdown begins. Yet determining this time is important for precision tests of the general theory of relativity that compare an observed signal with quasinormal mode descriptions of the ringdown, such as tests of the no-hair theorem. We present an algorithmic method to analyze the choice of ringdown start time in the observed waveform. This method is based on determining how close the strong field is to a Kerr black hole (Kerrness). Using numerical relativity simulations, we characterize the Kerrness of the strong-field region close to the black hole using a set of local, gauge-invariant geometric and algebraic conditions that measure local isometry to Kerr. We produce a map that associates each time in the gravitational waveform with a value of each of these Kerrness measures; this map is produced by following outgoing null characteristics from the strong and near-field regions to the wave zone. We perform this analysis on a numerical relativity simulation with parameters consistent with GW150914—the first gravitational-wave detection. We find that the choice of ringdown start time of 3 ms after merger used in the GW150914 study [B. P. Abbott et al. (Virgo Collaboration and LIGO Scientific Collaboration), Phys. Rev. Lett. 116, 221101 (2016)., 10.1103/PhysRevLett.116.221101] to test general relativity corresponds to a high dimensionless perturbation amplitude of ˜7.5 ×10-3 in the strong-field region. This suggests that in higher signal-to-noise detections, one would need to start analyzing the signal at a later time for studies that depend on the validity of black hole perturbation theory.

A finsler perturbation of the Poincaré metric

NASA Astrophysics Data System (ADS)

Rutz, Solange F.; McCarthy, Patrick J.

1993-02-01

One method of gaining some insight into Finsler geomety is that of studying small Finsler perturbations of Riemannian metrics. We consider here the the standard two-dimensional upper half plane Poincaré metric, for which the geodesics are semi-circles and vertical lines. The effect of a simple Finsler perturbation on these geodesics is given by an explicit computation of the perturbed geodesics.

Robust root clustering for linear uncertain systems using generalized Lyapunov theory

NASA Technical Reports Server (NTRS)

Yedavalli, R. K.

1993-01-01

Consideration is given to the problem of matrix root clustering in subregions of a complex plane for linear state space models with real parameter uncertainty. The nominal matrix root clustering theory of Gutman & Jury (1981) using the generalized Liapunov equation is extended to the perturbed matrix case, and bounds are derived on the perturbation to maintain root clustering inside a given region. The theory makes it possible to obtain an explicit relationship between the parameters of the root clustering region and the uncertainty range of the parameter space.

Coupling-parameter expansion in thermodynamic perturbation theory.

PubMed

Ramana, A Sai Venkata; Menon, S V G

2013-02-01

An approach to the coupling-parameter expansion in the liquid state theory of simple fluids is presented by combining the ideas of thermodynamic perturbation theory and integral equation theories. This hybrid scheme avoids the problems of the latter in the two phase region. A method to compute the perturbation series to any arbitrary order is developed and applied to square well fluids. Apart from the Helmholtz free energy, the method also gives the radial distribution function and the direct correlation function of the perturbed system. The theory is applied for square well fluids of variable ranges and compared with simulation data. While the convergence of perturbation series and the overall performance of the theory is good, improvements are needed for potentials with shorter ranges. Possible directions for further developments in the coupling-parameter expansion are indicated.

Analytic short period lunar and solar perturbations of artificial satellites.

NASA Technical Reports Server (NTRS)

Fisher, D.

1972-01-01

The short period luni-solar theory of Kozai is generalized for arbitrary obliquity of the ecliptic and inclination of the moon's orbit to the ecliptic. Analytic first order lunar perturbations to the elements are derived. The theory is illustrated by an application to the communication satellite Intelsat 3F3.

Analytic short period lunar and solar perturbations of artificial satellites

NASA Technical Reports Server (NTRS)

Fisher, D.

1972-01-01

A short period luni-solar theory was generalized for application to arbitrary obliquity of the ecliptic and inclination of the moon's orbit to the ecliptic. Analytic first order lunar perturbations to the elements were derived. The theory is illustrated by an application to the communication satellite Intelsat 3F3.

The Perturbational MO Method for Saturated Systems.

ERIC Educational Resources Information Center

Herndon, William C.

1979-01-01

Summarizes a theoretical approach using nonbonding MO's and perturbation theory to correlate properties of saturated hydrocarbons. Discussion is limited to correctly predicted using this method. Suggests calculations can be carried out quickly in organic chemistry. (Author/SA)

Theory of the control of structures by low authority controllers

NASA Technical Reports Server (NTRS)

Aubrun, J. N.

1978-01-01

The novel idea presented is based on the observation that if a structure is controlled by distributed systems of sensors and actuators with limited authority, i.e., if the controller is allowed to modify only moderately the natural modes and frequencies of the structure, then it should be possible to apply root perturbation techniques to predict analytically the behavior of the total system. Attention is given to the root perturbation formula first derived by Jacobi for infinitesimal perturbations which neglect the induced eigenvector perturbation, a more general form of Jacobi's formula, first-order structural equations and modal state vectors, state-space equations for damper-augmented structures, and modal damping prediction formulas.

Robust design optimization using the price of robustness, robust least squares and regularization methods

NASA Astrophysics Data System (ADS)

Bukhari, Hassan J.

2017-12-01

In this paper a framework for robust optimization of mechanical design problems and process systems that have parametric uncertainty is presented using three different approaches. Robust optimization problems are formulated so that the optimal solution is robust which means it is minimally sensitive to any perturbations in parameters. The first method uses the price of robustness approach which assumes the uncertain parameters to be symmetric and bounded. The robustness for the design can be controlled by limiting the parameters that can perturb.The second method uses the robust least squares method to determine the optimal parameters when data itself is subjected to perturbations instead of the parameters. The last method manages uncertainty by restricting the perturbation on parameters to improve sensitivity similar to Tikhonov regularization. The methods are implemented on two sets of problems; one linear and the other non-linear. This methodology will be compared with a prior method using multiple Monte Carlo simulation runs which shows that the approach being presented in this paper results in better performance.

A view on coupled cluster perturbation theory using a bivariational Lagrangian formulation.

PubMed

Kristensen, Kasper; Eriksen, Janus J; Matthews, Devin A; Olsen, Jeppe; Jørgensen, Poul

2016-02-14

We consider two distinct coupled cluster (CC) perturbation series that both expand the difference between the energies of the CCSD (CC with single and double excitations) and CCSDT (CC with single, double, and triple excitations) models in orders of the Møller-Plesset fluctuation potential. We initially introduce the E-CCSD(T-n) series, in which the CCSD amplitude equations are satisfied at the expansion point, and compare it to the recently developed CCSD(T-n) series [J. J. Eriksen et al., J. Chem. Phys. 140, 064108 (2014)], in which not only the CCSD amplitude, but also the CCSD multiplier equations are satisfied at the expansion point. The computational scaling is similar for the two series, and both are term-wise size extensive with a formal convergence towards the CCSDT target energy. However, the two series are different, and the CCSD(T-n) series is found to exhibit a more rapid convergence up through the series, which we trace back to the fact that more information at the expansion point is utilized than for the E-CCSD(T-n) series. The present analysis can be generalized to any perturbation expansion representing the difference between a parent CC model and a higher-level target CC model. In general, we demonstrate that, whenever the parent parameters depend upon the perturbation operator, a perturbation expansion of the CC energy (where only parent amplitudes are used) differs from a perturbation expansion of the CC Lagrangian (where both parent amplitudes and parent multipliers are used). For the latter case, the bivariational Lagrangian formulation becomes more than a convenient mathematical tool, since it facilitates a different and faster convergent perturbation series than the simpler energy-based expansion.

Towards the blackbox computation of magnetic exchange coupling parameters in polynuclear transition-metal complexes: theory, implementation, and application.

PubMed

Phillips, Jordan J; Peralta, Juan E

2013-05-07

We present a method for calculating magnetic coupling parameters from a single spin-configuration via analytic derivatives of the electronic energy with respect to the local spin direction. This method does not introduce new approximations beyond those found in the Heisenberg-Dirac Hamiltonian and a standard Kohn-Sham Density Functional Theory calculation, and in the limit of an ideal Heisenberg system it reproduces the coupling as determined from spin-projected energy-differences. Our method employs a generalized perturbative approach to constrained density functional theory, where exact expressions for the energy to second order in the constraints are obtained by analytic derivatives from coupled-perturbed theory. When the relative angle between magnetization vectors of metal atoms enters as a constraint, this allows us to calculate all the magnetic exchange couplings of a system from derivatives with respect to local spin directions from the high-spin configuration. Because of the favorable computational scaling of our method with respect to the number of spin-centers, as compared to the broken-symmetry energy-differences approach, this opens the possibility for the blackbox exploration of magnetic properties in large polynuclear transition-metal complexes. In this work we outline the motivation, theory, and implementation of this method, and present results for several model systems and transition-metal complexes with a variety of density functional approximations and Hartree-Fock.

Hard sphere perturbation theory of dense fluids with singular perturbation

NASA Astrophysics Data System (ADS)

Mon, K. K.

2000-02-01

Hard sphere perturbation theories (HSPT) played a significant role in the fundamental understanding of fluids and continues to be a popular method in a wide range of applications. The possibility of difficulty with singular perturbation for some classical soft core model fluids appears to have been overlooked or ignored in the literature. We address this issue in this short note and show by analysis that a region of phase space has been neglected in the standard application of HSPT involving singular perturbation.

An energy-based perturbation and a taboo strategy for improving the searching ability of stochastic structural optimization methods

NASA Astrophysics Data System (ADS)

Cheng, Longjiu; Cai, Wensheng; Shao, Xueguang

2005-03-01

An energy-based perturbation and a new idea of taboo strategy are proposed for structural optimization and applied in a benchmark problem, i.e., the optimization of Lennard-Jones (LJ) clusters. It is proved that the energy-based perturbation is much better than the traditional random perturbation both in convergence speed and searching ability when it is combined with a simple greedy method. By tabooing the most wide-spread funnel instead of the visited solutions, the hit rate of other funnels can be significantly improved. Global minima of (LJ) clusters up to 200 atoms are found with high efficiency.

Material strength measured by flyer-impact perturbation method

NASA Astrophysics Data System (ADS)

Ma, Xiaojuan; Asimow, Paul; Fatyanov, Oleg; Liu, Fusheng

2017-06-01

Yield strength is one of the most important physical properties of a solid material, especially far from its melting line. The flyer-impact perturbation method measures material yield strength on the basis of correlation between the yield strength under shock compression and the damping of oscillatory perturbations in the shape of a shock front passing through the material. We used flyer-plate impacts experiments on targets with machined grooves on the impact surface to shock aluminum to between 32 and 71 GPa and recorded the evolution of the shock front perturbation amplitude in the sample with electric pins and fibers. Simulations using the elastic-plastic model can be matched to the experiments, explaining well the form of the perturbation decay and constraining the yield strength of aluminum to be 1.3-3.1 GPa. These results are in agreement with values obtained from reshock and release wave profiles as well as the result deduced from the SCG model. We conclude that the flyer-impact perturbation method is indeed a reliable means to measure material strength. This work was supported by the National Natural Science Foundation of China (Grant No. 41674088) and the State Scholarship Fund of China Scholarship Council.

After total knee replacement younger patients demonstrate superior balance control compared to older patients when recovering from a forward fall.

PubMed

Street, Brian D; Gage, William

2017-05-01

National joint replacement registries have reported a substantial growth in younger knee osteoarthritic patients (<55years old) undergoing total knee replacement, however this younger population is generally understudied. Importantly, studies examining experimentally controlled perturbation have shown age-related differences between younger and older healthy adults, whether similar age-related differences exist among total knee replacement patients is unknown. A total of 59 participants, including 29 unilateral total knee replacement patients (six-months post-surgery) made up the four experimental groups: 1) younger patient (54.3 (SD 7.9) years), 2) younger control (55.2 (SD 4.0) years), 3) older patient (76.9 (SD 4.7) years), and 4) older control (77.7 (SD 4.1) years). Using a tether-release method to perturb balance and simulate a forward fall, center of mass and stepping characteristics were analyzed. Younger patients recovered following the perturbation with a significantly smaller center of mass displacement compared to the older patients (14.85 (SD 0.01) v. 18.13 (SD 0.02) %ht, p=0.02); utilizing a longer (0.43 (SD 0.02) v. 0.39 (SD 0.03) m, p<0.001) and higher velocity (2.01 (SD 0.2) v. 1.59 (SD 0.2) m/s, p=0.001) recovery step. Importantly, younger patients did not differ significantly from the younger controls in center of mass displacement or recovery step characteristics (p>0.05). The younger patients demonstrated superior center of mass control in response to a forward perturbation, suggesting that younger patients would be at a reduced risk of falling when recovering from a forward-directed postural perturbation compared to older patients. Copyright © 2017 Elsevier Ltd. All rights reserved.

Freezing-Induced Perturbation of Tertiary Structure of a Monoclonal Antibody

PubMed Central

LIU, LU; BRAUN, LATOYA JONES; WANG, WEI; RANDOLPH, THEODORE W.; CARPENTER, JOHN F.

2014-01-01

We studied the effects of pH and solution additives on freezing-induced perturbations in the tertiary structure of a monoclonal antibody (mAb) by intrinsic tryptophan fluorescence spectroscopy. In general, freezing caused perturbations in the tertiary structure of the mAb, which were reversible or irreversible depending on the pH or excipients present in the formulation. Protein aggregation occurred in freeze–thawed samples in which perturbations of the tertiary structure were observed, but the levels of protein aggregates formed were not proportional to the degree of structural perturbation. Protein aggregation also occurred in freeze–thawed samples without obvious structural perturbations, most likely because of freeze concentration of protein and salts, and thus reduced protein colloidal stability. Therefore, freezing-induced protein aggregation may or may not first involve the perturbation of its native structure, followed by the assembly processes to form aggregates. Depending on the solution conditions, either step can be rate limiting. Finally, this study demonstrates the potential of fluorescence spectroscopy as a valuable tool for screening therapeutic protein formulations subjected to freeze–thaw stress. PMID:24832730

Second order perturbations of a macroscopic string: Covariant approach

NASA Astrophysics Data System (ADS)

Larsen, A. L.; Nicolaidis, A.

2001-06-01

Using a world-sheet covariant formalism, we derive the equations of motion for second order perturbations of a generic macroscopic string, thus generalizing previous results for first order perturbations. We give the explicit results for the first and second order perturbations of a contracting near-circular string; these results are relevant for the understanding of the possible outcome when a cosmic string contracts under its own tension, as discussed in a series of papers by Vilenkin and Garriga. In particular, second order perturbations are necessary for a consistent computation of the energy. We also quantize the perturbations and derive the mass formula up to second order in perturbations for an observer using world-sheet time τ. The high frequency modes give the standard Minkowski result while, interestingly enough, the Hamiltonian turns out to be nondiagonal in oscillators for low-frequency modes. Using an alternative definition of the vacuum, it is possible to diagonalize the Hamiltonian, and the standard string mass spectrum appears for all frequencies. We finally discuss how our results are also relevant for the problems concerning string-spreading near a black hole horizon, as originally discussed by Susskind.

Spatially cascading effect of perturbations in experimental meta-ecosystems.

PubMed

Harvey, Eric; Gounand, Isabelle; Ganesanandamoorthy, Pravin; Altermatt, Florian

2016-09-14

Ecosystems are linked to neighbouring ecosystems not only by dispersal, but also by the movement of subsidy. Such subsidy couplings between ecosystems have important landscape-scale implications because perturbations in one ecosystem may affect community structure and functioning in neighbouring ecosystems via increased/decreased subsidies. Here, we combine a general theoretical approach based on harvesting theory and a two-patch protist meta-ecosystem experiment to test the effect of regional perturbations on local community dynamics. We first characterized the relationship between the perturbation regime and local population demography on detritus production using a mathematical model. We then experimentally simulated a perturbation gradient affecting connected ecosystems simultaneously, thus altering cross-ecosystem subsidy exchanges. We demonstrate that the perturbation regime can interact with local population dynamics to trigger unexpected temporal variations in subsidy pulses from one ecosystem to another. High perturbation intensity initially led to the highest level of subsidy flows; however, the level of perturbation interacted with population dynamics to generate a crash in subsidy exchange over time. Both theoretical and experimental results show that a perturbation regime interacting with local community dynamics can induce a collapse in population levels for recipient ecosystems. These results call for integrative management of human-altered landscapes that takes into account regional dynamics of both species and resource flows. © 2016 The Author(s).

Reconstruction of cosmological matter perturbations in modified gravity

NASA Astrophysics Data System (ADS)

Gonzalez, J. E.

2017-12-01

The analysis of perturbative quantities is a powerful tool to distinguish between different dark energy models and gravity theories degenerated at the background level. In this work, we generalize the integral solution of the matter density contrast for general relativity gravity [V. Sahni and A. Starobinsky, Int. J. Mod. Phys. D 15, 2105 (2006)., 10.1142/S0218271806009704, U. Alam, V. Sahni, and A. A. Starobinsky, Astrophys. J. 704, 1086 (2009)., 10.1088/0004-637X/704/2/1086] to a wide class of modified gravity (MG) theories. To calculate this solution, it is necessary to have prior knowledge of the Hubble rate, the density parameter at the present epoch (Ωm 0), and the functional form of the effective Newton's constant that characterizes the gravity theory. We estimate in a model-independent way the Hubble expansion rate by applying a nonparametric reconstruction method to model-independent cosmic chronometer data and high-z quasar data. In order to compare our generalized solution of the matter density contrast, using the nonparametric reconstruction of H (z ) from observational data, with a purely theoretical one, we choose a parametrization of the screened modified gravity and the Ωm 0 from WMAP-9 Collaborations. Finally, we calculate the growth index for the analyzed cases, finding very good agreement between theoretical values and the obtained ones using the approach presented in this work.

Nonlinear spherical perturbations in quintessence models of dark energy

NASA Astrophysics Data System (ADS)

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.

Parameterised post-Newtonian expansion in screened regions

NASA Astrophysics Data System (ADS)

McManus, Ryan; Lombriser, Lucas; Peñarrubia, Jorge

2017-12-01

The parameterised post-Newtonian (PPN) formalism has enabled stringent tests of static weak-field gravity in a theory-independent manner. Here we incorporate screening mechanisms of modified gravity theories into the framework by introducing an effective gravitational coupling and defining the PPN parameters as functions of position. To determine these functions we develop a general method for efficiently performing the post-Newtonian expansion in screened regimes. For illustration, we derive all the PPN functions for a cubic galileon and a chameleon model. We also analyse the Shapiro time delay effect for these two models and find no deviations from General Relativity insofar as the signal path and the perturbing mass reside in a screened region of space.

Classical stability of sudden and big rip singularities

DOE Office of Scientific and Technical Information (OSTI.GOV)

Barrow, John D.; Lip, Sean Z. W.

2009-08-15

We introduce a general characterization of sudden cosmological singularities and investigate the classical stability of homogeneous and isotropic cosmological solutions of all curvatures containing these singularities to small scalar, vector, and tensor perturbations using gauge-invariant perturbation theory. We establish that sudden singularities at which the scale factor, expansion rate, and density are finite are stable except for a set of special parameter values. We also apply our analysis to the stability of Big Rip singularities and find the conditions for their stability against small scalar, vector, and tensor perturbations.

Ionospheric vertical plasma drift perturbations due to the quasi 2 day wave

NASA Astrophysics Data System (ADS)

Gu, Sheng-Yang; Liu, Han-Li; Li, Tao; Dou, Xiankang

2015-05-01

The thermosphere-ionosphere-mesosphere-electrodynamics-general circulation model is utilized to study the vertical E × B drift perturbations due to the westward quasi 2 day wave with zonal wave numbers 2 and 3 (W2 and W3). The simulations show that both wind components contribute directly and significantly to the vertical drift, which is not merely confined to low latitudes. The vertical drifts at the equator induced by the total wind perturbations of W2 are comparable with that at middle latitudes, while the vertical drifts from W3 are much stronger at middle latitudes than at the equator. The ion drift perturbations induced by the zonal and meridional wind perturbations of W2 are nearly in-phase with each other, whereas the phase discrepancies of the ion drift induced by the individual wind component of W3 are much larger. This is because the wind perturbations of W2 and W3 have different latitudinal structures and phases, which result in different ionospheric responses through wind dynamo.

Magnetic imager and method

DOEpatents

Powell, J.; Reich, M.; Danby, G.

1997-07-22

A magnetic imager includes a generator for practicing a method of applying a background magnetic field over a concealed object, with the object being effective to locally perturb the background field. The imager also includes a sensor for measuring perturbations of the background field to detect the object. In one embodiment, the background field is applied quasi-statically. And, the magnitude or rate of change of the perturbations may be measured for determining location, size, and/or condition of the object. 25 figs.

Development of a Perfectly Matched Layer Technique for a Discontinuous-Galerkin Spectral-Element Method

NASA Technical Reports Server (NTRS)

Garai, Anirban; Diosady, Laslo T.; Murman, Scott M.; Madavan, Nateri K.

2016-01-01

The perfectly matched layer (PML) technique is developed in the context of a high- order spectral-element Discontinuous-Galerkin (DG) method. The technique is applied to a range of test cases and is shown to be superior compared to other approaches, such as those based on using characteristic boundary conditions and sponge layers, for treating the inflow and outflow boundaries of computational domains. In general, the PML technique improves the quality of the numerical results for simulations of practical flow configurations, but it also exhibits some instabilities for large perturbations. A preliminary analysis that attempts to understand the source of these instabilities is discussed.

Microscopic Lagrangian description of warm plasmas. IV - Macroscopic approximation

NASA Technical Reports Server (NTRS)

Kim, H.; Crawford, F. W.

1983-01-01

The averaged-Lagrangian method is applied to linear wave propagation and nonlinear three-wave interaction in a warm magnetoplasma, in the macroscopic approximation. The microscopic Lagrangian treated by Kim and Crawford (1977) and by Galloway and Crawford (1977) is first expanded to third order in perturbation. Velocity integration is then carried out, before applying Hamilton's principle to obtain a general description of wave propagation and coupling. The results are specialized to the case of interaction between two electron plasma waves and an Alfven wave. The method is shown to be more powerful than the alternative possibility of working from the beginning with a macroscopic Lagrangian density.

A critical evaluation of perturbation theories by Monte Carlo simulation of the first four perturbation terms in a Helmholtz energy expansion for the Lennard-Jones fluid

NASA Astrophysics Data System (ADS)

van Westen, Thijs; Gross, Joachim

2017-07-01

The Helmholtz energy of a fluid interacting by a Lennard-Jones pair potential is expanded in a perturbation series. Both the methods of Barker-Henderson (BH) and of Weeks-Chandler-Andersen (WCA) are evaluated for the division of the intermolecular potential into reference and perturbation parts. The first four perturbation terms are evaluated for various densities and temperatures (in the ranges ρ*=0 -1.5 and T*=0.5 -12 ) using Monte Carlo simulations in the canonical ensemble. The simulation results are used to test several approximate theoretical methods for describing perturbation terms or for developing an approximate infinite order perturbation series. Additionally, the simulations serve as a basis for developing fully analytical third order BH and WCA perturbation theories. The development of analytical theories allows (1) a careful comparison between the BH and WCA formalisms, and (2) a systematic examination of the effect of higher-order perturbation terms on calculated thermodynamic properties of fluids. Properties included in the comparison are supercritical thermodynamic properties (pressure, internal energy, and chemical potential), vapor-liquid phase equilibria, second virial coefficients, and heat capacities. For all properties studied, we find a systematically improved description upon using a higher-order perturbation theory. A result of particular relevance is that a third order perturbation theory is capable of providing a quantitative description of second virial coefficients to temperatures as low as the triple-point of the Lennard-Jones fluid. We find no reason to prefer the WCA formalism over the BH formalism.

Perturbation theory in light-cone quantization

DOE Office of Scientific and Technical Information (OSTI.GOV)

Langnau, A.

1992-01-01

A thorough investigation of light-cone properties which are characteristic for higher dimensions is very important. The easiest way of addressing these issues is by analyzing the perturbative structure of light-cone field theories first. Perturbative studies cannot be substituted for an analysis of problems related to a nonperturbative approach. However, in order to lay down groundwork for upcoming nonperturbative studies, it is indispensable to validate the renormalization methods at the perturbative level, i.e., to gain control over the perturbative treatment first. A clear understanding of divergences in perturbation theory, as well as their numerical treatment, is a necessary first step towardsmore » formulating such a program. The first objective of this dissertation is to clarify this issue, at least in second and fourth-order in perturbation theory. The work in this dissertation can provide guidance for the choice of counterterms in Discrete Light-Cone Quantization or the Tamm-Dancoff approach. A second objective of this work is the study of light-cone perturbation theory as a competitive tool for conducting perturbative Feynman diagram calculations. Feynman perturbation theory has become the most practical tool for computing cross sections in high energy physics and other physical properties of field theory. Although this standard covariant method has been applied to a great range of problems, computations beyond one-loop corrections are very difficult. Because of the algebraic complexity of the Feynman calculations in higher-order perturbation theory, it is desirable to automatize Feynman diagram calculations so that algebraic manipulation programs can carry out almost the entire calculation. This thesis presents a step in this direction. The technique we are elaborating on here is known as light-cone perturbation theory.« less

Resonant frequency calculations using a hybrid perturbation-Galerkin technique

NASA Technical Reports Server (NTRS)

Geer, James F.; Andersen, Carl M.

1991-01-01

A two-step hybrid perturbation Galerkin technique is applied to the problem of determining the resonant frequencies of one or several degree of freedom nonlinear systems involving a parameter. In one step, the Lindstedt-Poincare method is used to determine perturbation solutions which are formally valid about one or more special values of the parameter (e.g., for large or small values of the parameter). In step two, a subset of the perturbation coordinate functions determined in step one is used in Galerkin type approximation. The technique is illustrated for several one degree of freedom systems, including the Duffing and van der Pol oscillators, as well as for the compound pendulum. For all of the examples considered, it is shown that the frequencies obtained by the hybrid technique using only a few terms from the perturbation solutions are significantly more accurate than the perturbation results on which they are based, and they compare very well with frequencies obtained by purely numerical methods.

The Library of Integrated Network-Based Cellular Signatures NIH Program: System-Level Cataloging of Human Cells Response to Perturbations.

PubMed

Keenan, Alexandra B; Jenkins, Sherry L; Jagodnik, Kathleen M; Koplev, Simon; He, Edward; Torre, Denis; Wang, Zichen; Dohlman, Anders B; Silverstein, Moshe C; Lachmann, Alexander; Kuleshov, Maxim V; Ma'ayan, Avi; Stathias, Vasileios; Terryn, Raymond; Cooper, Daniel; Forlin, Michele; Koleti, Amar; Vidovic, Dusica; Chung, Caty; Schürer, Stephan C; Vasiliauskas, Jouzas; Pilarczyk, Marcin; Shamsaei, Behrouz; Fazel, Mehdi; Ren, Yan; Niu, Wen; Clark, Nicholas A; White, Shana; Mahi, Naim; Zhang, Lixia; Kouril, Michal; Reichard, John F; Sivaganesan, Siva; Medvedovic, Mario; Meller, Jaroslaw; Koch, Rick J; Birtwistle, Marc R; Iyengar, Ravi; Sobie, Eric A; Azeloglu, Evren U; Kaye, Julia; Osterloh, Jeannette; Haston, Kelly; Kalra, Jaslin; Finkbiener, Steve; Li, Jonathan; Milani, Pamela; Adam, Miriam; Escalante-Chong, Renan; Sachs, Karen; Lenail, Alex; Ramamoorthy, Divya; Fraenkel, Ernest; Daigle, Gavin; Hussain, Uzma; Coye, Alyssa; Rothstein, Jeffrey; Sareen, Dhruv; Ornelas, Loren; Banuelos, Maria; Mandefro, Berhan; Ho, Ritchie; Svendsen, Clive N; Lim, Ryan G; Stocksdale, Jennifer; Casale, Malcolm S; Thompson, Terri G; Wu, Jie; Thompson, Leslie M; Dardov, Victoria; Venkatraman, Vidya; Matlock, Andrea; Van Eyk, Jennifer E; Jaffe, Jacob D; Papanastasiou, Malvina; Subramanian, Aravind; Golub, Todd R; Erickson, Sean D; Fallahi-Sichani, Mohammad; Hafner, Marc; Gray, Nathanael S; Lin, Jia-Ren; Mills, Caitlin E; Muhlich, Jeremy L; Niepel, Mario; Shamu, Caroline E; Williams, Elizabeth H; Wrobel, David; Sorger, Peter K; Heiser, Laura M; Gray, Joe W; Korkola, James E; Mills, Gordon B; LaBarge, Mark; Feiler, Heidi S; Dane, Mark A; Bucher, Elmar; Nederlof, Michel; Sudar, Damir; Gross, Sean; Kilburn, David F; Smith, Rebecca; Devlin, Kaylyn; Margolis, Ron; Derr, Leslie; Lee, Albert; Pillai, Ajay

2018-01-24

The Library of Integrated Network-Based Cellular Signatures (LINCS) is an NIH Common Fund program that catalogs how human cells globally respond to chemical, genetic, and disease perturbations. Resources generated by LINCS include experimental and computational methods, visualization tools, molecular and imaging data, and signatures. By assembling an integrated picture of the range of responses of human cells exposed to many perturbations, the LINCS program aims to better understand human disease and to advance the development of new therapies. Perturbations under study include drugs, genetic perturbations, tissue micro-environments, antibodies, and disease-causing mutations. Responses to perturbations are measured by transcript profiling, mass spectrometry, cell imaging, and biochemical methods, among other assays. The LINCS program focuses on cellular physiology shared among tissues and cell types relevant to an array of diseases, including cancer, heart disease, and neurodegenerative disorders. This Perspective describes LINCS technologies, datasets, tools, and approaches to data accessibility and reusability. Copyright © 2017 Elsevier Inc. All rights reserved.

Development of an efficient procedure for calculating the aerodynamic effects of planform variation

NASA Technical Reports Server (NTRS)

Mercer, J. E.; Geller, E. W.

1981-01-01

Numerical procedures to compute gradients in aerodynamic loading due to planform shape changes using panel method codes were studied. Two procedures were investigated: one computed the aerodynamic perturbation directly; the other computed the aerodynamic loading on the perturbed planform and on the base planform and then differenced these values to obtain the perturbation in loading. It is indicated that computing the perturbed values directly can not be done satisfactorily without proper aerodynamic representation of the pressure singularity at the leading edge of a thin wing. For the alternative procedure, a technique was developed which saves most of the time-consuming computations from a panel method calculation for the base planform. Using this procedure the perturbed loading can be calculated in about one-tenth the time of that for the base solution.

Determination of Spatio-Temporal Characteristics of D-region Electron Density during Annular Solar Eclipse from VLF Network Observations

NASA Astrophysics Data System (ADS)

Basak, T.; Hobara, Y.

2015-12-01

A major part of the path of the annular solar eclipse of May 20, 2012 (magnitude 0.9439) was over southern Japan. The D-region ionospheric changes associated with that eclipse, led to several degree of observable perturbations of sub-ionospheric very low frequency (VLF) radio signal. The University of Electro-Communications (UEC) operates VLF observation network over Japan. The solar eclipse associated signal changes were recorded in several receiving stations (Rx) simultaneously for the VLF signals coming from NWC/19.8kHz, JJI/22.2kHz, JJY/40.0kHz, NLK/24.8kHz and other VLF transmitters (Tx). These temporal dependences of VLF signal perturbation have been analyzed and the spatio-temporal characteristics of respective sub-ionospheric perturbations has already been studied by earlier workers using 2D-Finite Difference Time Domain method of simulation. In this work, we determine the spatial scale, depth and temporal dependence of lower ionospheric perturbation in consistence with umbral and penumbral motion. We considered the 2-parameter D-region ionospheric model with exponential electron density profile. To model the solar obscuration effect over it, we assumed a generalized space-time dependent 2-dimensional elliptical Gaussian distribution for ionospheric parameters, such as, effective reflection height (h') and sharpness factor (β). The depth (△hmax, △βmax), center of shadow (lato(t), lono(t)) and spatial scale (σlat,lon) of that Gaussian distribution are used as model parameters. In the vicinity of the eclipse zone, we compute the VLF signal perturbations using Long Wave Propagation Capability (LWPC) code for several signal propagation paths. The propagation path characteristics, such as, ground and water conductivity and geomagnetic effect on ionosphere are considered from standard LWPC prescriptions. The model parameters are tuned to set an optimum agreement between our computation and observed positive and negative type of VLF perturbations. Thus, appropriate set of parameters lead us to the possible determination of spatial scale, depth and temporal dependence of eclipse associated D-region electron density perturbation solely from the VLF-network observations coupled with theoretical modeling.

Explicit Analytical Solution of a Pendulum with Periodically Varying Length

ERIC Educational Resources Information Center

Yang, Tianzhi; Fang, Bo; Li, Song; Huang, Wenhu

2010-01-01

A pendulum with periodically varying length is an interesting physical system. It has been studied by some researchers using traditional perturbation methods (for example, the averaging method). But due to the limitation of the conventional perturbation methods, the solutions are not valid for long-term prediction of the pendulum. In this paper,…

Periodic perturbations with rotational symmetry of planar systems driven by a central force

NASA Astrophysics Data System (ADS)

Fonda, Alessandro; Gallo, Anna Chiara

2018-06-01

We consider periodic perturbations of a central force field having a rotational symmetry, and prove the existence of nearly circular periodic orbits. We thus generalize, in the planar case, some previous bifurcation results obtained by Ambrosetti and Coti Zelati in [1]. Our results apply, in particular, to the classical Kepler problem.

A novel method to optimize the mode spectrum of the dynamic resonant magnetic perturbation on the J-TEXT tokamak.

PubMed

Yi, B; Rao, B; Ding, Y H; Li, M; Xu, H Y; Zhang, M; Zhuang, G; Pan, Y

2014-11-01

The dynamic resonant magnetic perturbation (DRMP) system has been developed for the J-TEXT tokamak to study the interaction between the rotating perturbation magnetic field and the plasma. When the DRMP coils are energized by two phase sinusoidal currents with the same frequency, a 2/1 rotating resonant magnetic perturbation component will be generated. But at the same time, a small perturbation component rotating in the opposite direction is also produced because of the control error of the currents. This small component has bad influence on the experiment investigations. Actually, the mode spectrum of the generated DRMP can be optimized with an accurate control of phase difference between the two currents. In this paper, a new phase control method based on a novel all-digital phase-locked loop (ADPLL) is proposed. The proposed method features accurate phase control and flexible phase adjustment. Modeling and analysis of the proposed ADPLL is presented to guide the design of the parameters of the phase controller in order to obtain a better performance. Testing results verify the effectiveness of the ADPLL and validity of the method applying to the DRMP system.

A novel method to optimize the mode spectrum of the dynamic resonant magnetic perturbation on the J-TEXT tokamak

NASA Astrophysics Data System (ADS)

Yi, B.; Rao, B.; Ding, Y. H.; Li, M.; Xu, H. Y.; Zhang, M.; Zhuang, G.; Pan, Y.

2014-11-01

The dynamic resonant magnetic perturbation (DRMP) system has been developed for the J-TEXT tokamak to study the interaction between the rotating perturbation magnetic field and the plasma. When the DRMP coils are energized by two phase sinusoidal currents with the same frequency, a 2/1 rotating resonant magnetic perturbation component will be generated. But at the same time, a small perturbation component rotating in the opposite direction is also produced because of the control error of the currents. This small component has bad influence on the experiment investigations. Actually, the mode spectrum of the generated DRMP can be optimized with an accurate control of phase difference between the two currents. In this paper, a new phase control method based on a novel all-digital phase-locked loop (ADPLL) is proposed. The proposed method features accurate phase control and flexible phase adjustment. Modeling and analysis of the proposed ADPLL is presented to guide the design of the parameters of the phase controller in order to obtain a better performance. Testing results verify the effectiveness of the ADPLL and validity of the method applying to the DRMP system.

A Generalized Perturbation Theory Solver In Rattlesnake Based On PETSc With Application To TREAT Steady State Uncertainty Quantification

DOE Office of Scientific and Technical Information (OSTI.GOV)

Schunert, Sebastian; Wang, Congjian; Wang, Yaqi

Rattlesnake and MAMMOTH are the designated TREAT analysis tools currently being developed at the Idaho National Laboratory. Concurrent with development of the multi-physics, multi-scale capabilities, sensitivity analysis and uncertainty quantification (SA/UQ) capabilities are required for predicitive modeling of the TREAT reactor. For steady-state SA/UQ, that is essential for setting initial conditions for the transients, generalized perturbation theory (GPT) will be used. This work describes the implementation of a PETSc based solver for the generalized adjoint equations that constitute a inhomogeneous, rank deficient problem. The standard approach is to use an outer iteration strategy with repeated removal of the fundamental modemore » contamination. The described GPT algorithm directly solves the GPT equations without the need of an outer iteration procedure by using Krylov subspaces that are orthogonal to the operator’s nullspace. Three test problems are solved and provide sufficient verification for the Rattlesnake’s GPT capability. We conclude with a preliminary example evaluating the impact of the Boron distribution in the TREAT reactor using perturbation theory.« less

Two-strain competition in quasineutral stochastic disease dynamics.

PubMed

Kogan, Oleg; Khasin, Michael; Meerson, Baruch; Schneider, David; Myers, Christopher R

2014-10-01

We develop a perturbation method for studying quasineutral competition in a broad class of stochastic competition models and apply it to the analysis of fixation of competing strains in two epidemic models. The first model is a two-strain generalization of the stochastic susceptible-infected-susceptible (SIS) model. Here we extend previous results due to Parsons and Quince [Theor. Popul. Biol. 72, 468 (2007)], Parsons et al. [Theor. Popul. Biol. 74, 302 (2008)], and Lin, Kim, and Doering [J. Stat. Phys. 148, 646 (2012)]. The second model, a two-strain generalization of the stochastic susceptible-infected-recovered (SIR) model with population turnover, has not been studied previously. In each of the two models, when the basic reproduction numbers of the two strains are identical, a system with an infinite population size approaches a point on the deterministic coexistence line (CL): a straight line of fixed points in the phase space of subpopulation sizes. Shot noise drives one of the strain populations to fixation, and the other to extinction, on a time scale proportional to the total population size. Our perturbation method explicitly tracks the dynamics of the probability distribution of the subpopulations in the vicinity of the CL. We argue that, whereas the slow strain has a competitive advantage for mathematically "typical" initial conditions, it is the fast strain that is more likely to win in the important situation when a few infectives of both strains are introduced into a susceptible population.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kuzmina, M.G.

The polarized radiation transfer problems for slabs of weakly anisotropic optically active media are considered as the perturbations of the corresponding problems for isotropic ones. The perturbation method is developed for the integral transport equation and the estimate for the total perturbation of the solution due to the anisotropy of the medium is obtained.

A generalized weight-based particle-in-cell simulation scheme

NASA Astrophysics Data System (ADS)

Lee, W. W.; Jenkins, T. G.; Ethier, S.

2011-03-01

A generalized weight-based particle simulation scheme suitable for simulating magnetized plasmas, where the zeroth-order inhomogeneity is important, is presented. The scheme is an extension of the perturbative simulation schemes developed earlier for particle-in-cell (PIC) simulations. The new scheme is designed to simulate both the perturbed distribution ( δf) and the full distribution (full- F) within the same code. The development is based on the concept of multiscale expansion, which separates the scale lengths of the background inhomogeneity from those associated with the perturbed distributions. The potential advantage for such an arrangement is to minimize the particle noise by using δf in the linear stage of the simulation, while retaining the flexibility of a full- F capability in the fully nonlinear stage of the development when signals associated with plasma turbulence are at a much higher level than those from the intrinsic particle noise.

Cosmic-string-induced hot dark matter perturbations

NASA Technical Reports Server (NTRS)

Van Dalen, Anthony

1990-01-01

This paper investigates the evolution of initially relativistic matter, radiation, and baryons around cosmic string seed perturbations. A detailed analysis of the linear evolution of spherical perturbations in a universe is carried out, and this formalism is used to study the evolution of perturbations around a sphere of uniform density and fixed radius, approximating a loop of cosmic string. It was found that, on scales less than a few megaparsec, the results agree with the nonrelativistic calculation of previous authors. On greater scales, there is a deviation approaching a factor of 2-3 in the perturbation mass. It is shown that a scenario with cosmic strings, hot dark matter, and a Hubble constant greater than 75 km/sec per Mpc can generally produce structure on the observed mass scales and at the appropriate time: 1 + z = about 4 for galaxies and 1 + z = about 1.5 for Abell clusters.

Relativistic magnetised perturbations: magnetic pressure versus magnetic tension

NASA Astrophysics Data System (ADS)

Tseneklidou, Dimitra; Tsagas, Christos G.; Barrow, John D.

2018-06-01

We study the linear evolution of magnetised cosmological perturbations in the post-recombination epoch. Using full general relativity and adopting the ideal magnetohydrodynamic approximation, we refine and extend the previous treatments. More specifically, this is the first relativistic study that accounts for the effects of the magnetic tension, in addition to those of the field’s pressure. Our solutions show that on sufficiently large scales, larger than the (purely magnetic) Jeans length, the perturbations evolve essentially unaffected by the magnetic presence. The magnetic pressure dominates on small scales, where it forces the perturbations to oscillate and decay. Close to the Jeans length, however, the field’s tension takes over and leads to a weak growth of the inhomogeneities. These solutions clearly demonstrate the opposing action of the aforementioned two magnetic agents, namely of the field’s pressure and tension, on the linear evolution of cosmological density perturbations.

Magnetic imager and method

DOEpatents

Powell, James; Reich, Morris; Danby, Gordon

1997-07-22

A magnetic imager 10 includes a generator 18 for practicing a method of applying a background magnetic field over a concealed object, with the object being effective to locally perturb the background field. The imager 10 also includes a sensor 20 for measuring perturbations of the background field to detect the object. In one embodiment, the background field is applied quasi-statically. And, the magnitude or rate of change of the perturbations may be measured for determining location, size, and/or condition of the object.

Cosmological perturbations in the DGP braneworld: Numeric solution

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cardoso, Antonio; Koyama, Kazuya; Silva, Fabio P.

2008-04-15

We solve for the behavior of cosmological perturbations in the Dvali-Gabadadze-Porrati (DGP) braneworld model using a new numerical method. Unlike some other approaches in the literature, our method uses no approximations other than linear theory and is valid on large scales. We examine the behavior of late-universe density perturbations for both the self-accelerating and normal branches of DGP cosmology. Our numerical results can form the basis of a detailed comparison between the DGP model and cosmological observations.

Kato expansion in quantum canonical perturbation theory

DOE Office of Scientific and Technical Information (OSTI.GOV)

Nikolaev, Andrey, E-mail: Andrey.Nikolaev@rdtex.ru

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.

Black branes and black strings in the astrophysical and cosmological context

NASA Astrophysics Data System (ADS)

Akarsu, Özgür; Chopovsky, Alexey; Zhuk, Alexander

2018-03-01

We consider Kaluza-Klein models where internal spaces are compact flat or curved Einstein spaces. This background is perturbed by a compact gravitating body with the dust-like equation of state (EoS) in the external/our space and an arbitrary EoS parameter Ω in the internal space. Without imposing any restrictions on the form of the perturbed metric and the distribution of the perturbed energy densities, we perform the general analysis of the Einstein and conservation equations in the weak-field limit. All conclusions follow from this analysis. For example, we demonstrate that the perturbed model is static and perturbed metric preserves the block-diagonal form. In a particular case Ω = - 1 / 2, the found solution corresponds to the weak-field limit of the black strings/branes. The black strings/branes are compact gravitating objects which have the topology (four-dimensional Schwarzschild spacetime) × (d-dimensional internal space) with d ≥ 1. We present the arguments in favour of these objects. First, they satisfy the gravitational tests for the parameterized post-Newtonian parameter γ at the same level of accuracy as General Relativity. Second, they are preferable from the thermodynamical point of view. Third, averaging over the Universe, they do not destroy the stabilization of the internal space. These are the astrophysical and cosmological aspects of the black strings/branes.

Breathing pulses in singularly perturbed reaction-diffusion systems

NASA Astrophysics Data System (ADS)

Veerman, Frits

2015-07-01

The weakly nonlinear stability of pulses in general singularly perturbed reaction-diffusion systems near a Hopf bifurcation is determined using a centre manifold expansion. A general framework to obtain leading order expressions for the (Hopf) centre manifold expansion for scale separated, localised structures is presented. Using the scale separated structure of the underlying pulse, directly calculable expressions for the Hopf normal form coefficients are obtained in terms of solutions to classical Sturm-Liouville problems. The developed theory is used to establish the existence of breathing pulses in a slowly nonlinear Gierer-Meinhardt system, and is confirmed by direct numerical simulation.

First moments of nucleon generalized parton distributions

DOE PAGES

Wang, P.; Thomas, A. W.

2010-06-01

We extrapolate the first moments of the generalized parton distributions using heavy baryon chiral perturbation theory. The calculation is based on the one loop level with the finite range regularization. The description of the lattice data is satisfactory, and the extrapolated moments at physical pion mass are consistent with the results obtained with dimensional regularization, although the extrapolation in the momentum transfer to t=0 does show sensitivity to form factor effects, which lie outside the realm of chiral perturbation theory. We discuss the significance of the results in the light of modern experiments as well as QCD inspired models.

Multi-Level Adaptive Techniques (MLAT) for singular-perturbation problems

NASA Technical Reports Server (NTRS)

Brandt, A.

1978-01-01

The multilevel (multigrid) adaptive technique, a general strategy of solving continuous problems by cycling between coarser and finer levels of discretization is described. It provides very fast general solvers, together with adaptive, nearly optimal discretization schemes. In the process, boundary layers are automatically either resolved or skipped, depending on a control function which expresses the computational goal. The global error decreases exponentially as a function of the overall computational work, in a uniform rate independent of the magnitude of the singular-perturbation terms. The key is high-order uniformly stable difference equations, and uniformly smoothing relaxation schemes.

A Unified Approach for Solving Nonlinear Regular Perturbation Problems

ERIC Educational Resources Information Center

Khuri, S. A.

2008-01-01

This article describes a simple alternative unified method of solving nonlinear regular perturbation problems. The procedure is based upon the manipulation of Taylor's approximation for the expansion of the nonlinear term in the perturbed equation. An essential feature of this technique is the relative simplicity used and the associated unified…

Stark effect on an excited hydrogen atom

DOE Office of Scientific and Technical Information (OSTI.GOV)

Barratt, C.

1983-07-01

The method of degenerate perturbation theory is used to study the dipolar nature of an excited hydrogen atom in an external electric field. The dependence of the atoms perturbed energy levels on the principal and magnetic quantum numbers, n and m, is investigated, along with the perturbed wave functions.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Rivasseau, Vincent, E-mail: vincent.rivasseau@th.u-psud.fr, E-mail: adrian.tanasa@ens-lyon.org; Tanasa, Adrian, E-mail: vincent.rivasseau@th.u-psud.fr, E-mail: adrian.tanasa@ens-lyon.org

The Loop Vertex Expansion (LVE) is a quantum field theory (QFT) method which explicitly computes the Borel sum of Feynman perturbation series. This LVE relies in a crucial way on symmetric tree weights which define a measure on the set of spanning trees of any connected graph. In this paper we generalize this method by defining new tree weights. They depend on the choice of a partition of a set of vertices of the graph, and when the partition is non-trivial, they are no longer symmetric under permutation of vertices. Nevertheless we prove they have the required positivity property tomore » lead to a convergent LVE; in fact we formulate this positivity property precisely for the first time. Our generalized tree weights are inspired by the Brydges-Battle-Federbush work on cluster expansions and could be particularly suited to the computation of connected functions in QFT. Several concrete examples are explicitly given.« less

Elastic Green’s Function in Anisotropic Bimaterials Considering Interfacial Elasticity

DOE Office of Scientific and Technical Information (OSTI.GOV)

Juan, Pierre -Alexandre; Dingreville, Remi

Here, the two-dimensional elastic Green’s function is calculated for a general anisotropic elastic bimaterial containing a line dislocation and a concentrated force while accounting for the interfacial structure by means of a generalized interfacial elasticity paradigm. The introduction of the interface elasticity model gives rise to boundary conditions that are effectively equivalent to those of a weakly bounded interface. The equations of elastic equilibrium are solved by complex variable techniques and the method of analytical continuation. The solution is decomposed into the sum of the Green’s function corresponding to the perfectly bonded interface and a perturbation term corresponding to themore » complex coupling nature between the interface structure and a line dislocation/concentrated force. Such construct can be implemented into the boundary integral equations and the boundary element method for analysis of nano-layered structures and epitaxial systems where the interface structure plays an important role.« less

Elastic Green’s Function in Anisotropic Bimaterials Considering Interfacial Elasticity

DOE PAGES

Juan, Pierre -Alexandre; Dingreville, Remi

2017-09-13

Here, the two-dimensional elastic Green’s function is calculated for a general anisotropic elastic bimaterial containing a line dislocation and a concentrated force while accounting for the interfacial structure by means of a generalized interfacial elasticity paradigm. The introduction of the interface elasticity model gives rise to boundary conditions that are effectively equivalent to those of a weakly bounded interface. The equations of elastic equilibrium are solved by complex variable techniques and the method of analytical continuation. The solution is decomposed into the sum of the Green’s function corresponding to the perfectly bonded interface and a perturbation term corresponding to themore » complex coupling nature between the interface structure and a line dislocation/concentrated force. Such construct can be implemented into the boundary integral equations and the boundary element method for analysis of nano-layered structures and epitaxial systems where the interface structure plays an important role.« less

Perturbation theory from automorphic forms

NASA Astrophysics Data System (ADS)

Lambert, Neil; West, Peter

2010-05-01

Using our previous construction of Eisenstein-like automorphic forms we derive formulae for the perturbative and non-perturbative parts for any group and representation. The result is written in terms of the weights of the representation and the derivation is largely group theoretical. Specialising to the E n+1 groups relevant to type II string theory and the representation associated with node n + 1 of the E n+1 Dynkin diagram we explicitly find the perturbative part in terms of String Theory variables, such as the string coupling g d and volume V n . For dimensions seven and higher we find that the perturbation theory involves only two terms. In six dimensions we construct the SO(5, 5) automorphic form using the vector representation. Although these automorphic forms are generally compatible with String Theory, the one relevant to R 4 involves terms with g d -6 and so is problematic. We then study a constrained SO(5, 5) automorphic form, obtained by summing over null vectors, and compute its perturbative part. We find that it is consistent with String Theory and makes precise predictions for the perturbative results. We also study the unconstrained automorphic forms for E 6 in the 27 representation and E 7 in the 133 representation, giving their perturbative part and commenting on their role in String Theory.

Ground-state energies of simple metals

NASA Technical Reports Server (NTRS)

Hammerberg, J.; Ashcroft, N. W.

1974-01-01

A structural expansion for the static ground-state energy of a simple metal is derived. Two methods are presented, one an approach based on single-particle band structure which treats the electron gas as a nonlinear dielectric, the other a more general many-particle analysis using finite-temperature perturbation theory. The two methods are compared, and it is shown in detail how band-structure effects, Fermi-surface distortions, and chemical-potential shifts affect the total energy. These are of special interest in corrections to the total energy beyond third order in the electron-ion interaction and hence to systems where differences in energies for various crystal structures are exceptionally small. Preliminary calculations using these methods for the zero-temperature thermodynamic functions of atomic hydrogen are reported.

A Tutorial Review on Fractal Spacetime and Fractional Calculus

NASA Astrophysics Data System (ADS)

He, Ji-Huan

2014-11-01

This tutorial review of fractal-Cantorian spacetime and fractional calculus begins with Leibniz's notation for derivative without limits which can be generalized to discontinuous media like fractal derivative and q-derivative of quantum calculus. Fractal spacetime is used to elucidate some basic properties of fractal which is the foundation of fractional calculus, and El Naschie's mass-energy equation for the dark energy. The variational iteration method is used to introduce the definition of fractional derivatives. Fractal derivative is explained geometrically and q-derivative is motivated by quantum mechanics. Some effective analytical approaches to fractional differential equations, e.g., the variational iteration method, the homotopy perturbation method, the exp-function method, the fractional complex transform, and Yang-Laplace transform, are outlined and the main solution processes are given.

Cylindrical dust acoustic solitary waves with transverse perturbations in quantum dusty plasmas

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mushtaq, A.

2007-11-15

The nonlinear quantum dust acoustic waves with effects of nonplanar cylindrical geometry, quantum corrections, and transverse perturbations are studied. By using the perturbation method, a cylindrical Kadomtsev-Petviashvili equation for dust acoustic waves is derived by incorporating quantum-mechanical effects. The quantum-mechanical effects via quantum diffraction and quantum statistics, and the role of transverse perturbations in cylindrical geometry on the dynamics of this wave, are studied both analytically and numerically.

Hamiltonian General Relativity in Finite Space and Cosmological Potential Perturbations

NASA Astrophysics Data System (ADS)

Barbashov, B. M.; Pervushin, V. N.; Zakharov, A. F.; Zinchuk, V. A.

The Hamiltonian formulation of general relativity is considered in finite space-time and a specific reference frame given by the diffeo-invariant components of the Fock simplex in terms of the Dirac-ADM variables. The evolution parameter and energy invariant with respect to the time-coordinate transformations are constructed by the separation of the cosmological scale factor a(x0) and its identification with the spatial averaging of the metric determinant, so that the dimension of the kinemetric group of diffeomorphisms coincides with the dimension of a set of variables whose velocities are removed by the Gauss-type constraints in accordance with the second Nöther theorem. This coincidence allows us to solve the energy constraint, fulfil Dirac's Hamiltonian reduction, and to describe the potential perturbations in terms of the Lichnerowicz scale-invariant variables distinguished by the absence of the time derivatives of the spatial metric determinant. It was shown that the Hamiltonian version of the cosmological perturbation theory acquires attributes of the theory of superfluid liquid, and it leads to a generalization of the Schwarzschild solution. The astrophysical application of this approach to general relativity is considered under supposition that the Dirac-ADM Hamiltonian frame is identified with that of the Cosmic Microwave Background radiation distinguished by its dipole component in the frame of an Earth observer.

Practical Considerations When Using Perturbed Forest Inventory Plot Locations To Develop Spatial Models: A Case Study

Treesearch

John W. Coulston; Gregory A. Reams; Ronald E. McRoberts; William D. Smith

2006-01-01

U.S. Department of Agriculture Forest Service Forest Inventory and Analysis plot information is used in many capacities including timber inventories, forest health assessments, and environmental risk analyses. With few exceptions, actual plot locations cannot be revealed to the general public. The public does, however, have access to perturbed plot coordinates. The...

Large-scale microwave anisotropy from gravitating seeds

NASA Technical Reports Server (NTRS)

Veeraraghavan, Shoba; Stebbins, Albert

1992-01-01

Topological defects could have seeded primordial inhomogeneities in cosmological matter. We examine the horizon-scale matter and geometry perturbations generated by such seeds in an expanding homogeneous and isotropic universe. Evolving particle horizons generally lead to perturbations around motionless seeds, even when there are compensating initial underdensities in the matter. We describe the pattern of the resulting large angular scale microwave anisotropy.

Size consistent formulations of the perturb-then-diagonalize Møller-Plesset perturbation theory correction to non-orthogonal configuration interaction

DOE Office of Scientific and Technical Information (OSTI.GOV)

Yost, Shane R.; Head-Gordon, Martin, E-mail: mhg@cchem.berkeley.edu; Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720

2016-08-07

In this paper we introduce two size consistent forms of the non-orthogonal configuration interaction with second-order Møller-Plesset perturbation theory method, NOCI-MP2. We show that the original NOCI-MP2 formulation [S. R. Yost, T. Kowalczyk, and T. VanVoorh, J. Chem. Phys. 193, 174104 (2013)], which is a perturb-then-diagonalize multi-reference method, is not size consistent. We also show that this causes significant errors in large systems like the linear acenes. By contrast, the size consistent versions of the method give satisfactory results for singlet and triplet excited states when compared to other multi-reference methods that include dynamic correlation. For NOCI-MP2 however, the numbermore » of required determinants to yield similar levels of accuracy is significantly smaller. These results show the promise of the NOCI-MP2 method, though work still needs to be done in creating a more consistent black-box approach to computing the determinants that comprise the many-electron NOCI basis.« less

Accelerated perturbation-resilient block-iterative projection methods with application to image reconstruction

PubMed Central

Nikazad, T; Davidi, R; Herman, G. T.

2013-01-01

We study the convergence of a class of accelerated perturbation-resilient block-iterative projection methods for solving systems of linear equations. We prove convergence to a fixed point of an operator even in the presence of summable perturbations of the iterates, irrespective of the consistency of the linear system. For a consistent system, the limit point is a solution of the system. In the inconsistent case, the symmetric version of our method converges to a weighted least squares solution. Perturbation resilience is utilized to approximate the minimum of a convex functional subject to the equations. A main contribution, as compared to previously published approaches to achieving similar aims, is a more than an order of magnitude speed-up, as demonstrated by applying the methods to problems of image reconstruction from projections. In addition, the accelerated algorithms are illustrated to be better, in a strict sense provided by the method of statistical hypothesis testing, than their unaccelerated versions for the task of detecting small tumors in the brain from X-ray CT projection data. PMID:23440911

Accelerated perturbation-resilient block-iterative projection methods with application to image reconstruction.

PubMed

Nikazad, T; Davidi, R; Herman, G T

2012-03-01

We study the convergence of a class of accelerated perturbation-resilient block-iterative projection methods for solving systems of linear equations. We prove convergence to a fixed point of an operator even in the presence of summable perturbations of the iterates, irrespective of the consistency of the linear system. For a consistent system, the limit point is a solution of the system. In the inconsistent case, the symmetric version of our method converges to a weighted least squares solution. Perturbation resilience is utilized to approximate the minimum of a convex functional subject to the equations. A main contribution, as compared to previously published approaches to achieving similar aims, is a more than an order of magnitude speed-up, as demonstrated by applying the methods to problems of image reconstruction from projections. In addition, the accelerated algorithms are illustrated to be better, in a strict sense provided by the method of statistical hypothesis testing, than their unaccelerated versions for the task of detecting small tumors in the brain from X-ray CT projection data.

Characterization of a Laser-Generated Perturbation in High-Speed Flow for Receptivity Studies

NASA Technical Reports Server (NTRS)

Chou, Amanda; Schneider, Steven P.; Kegerise, Michael A.

2014-01-01

A better understanding of receptivity can contribute to the development of an amplitude-based method of transition prediction. This type of prediction model would incorporate more physics than the semi-empirical methods, which are widely used. The experimental study of receptivity requires a characterization of the external disturbances and a study of their effect on the boundary layer instabilities. Characterization measurements for a laser-generated perturbation were made in two different wind tunnels. These measurements were made with hot-wire probes, optical techniques, and pressure transducer probes. Existing methods all have their limitations, so better measurements will require the development of new instrumentation. Nevertheless, the freestream laser-generated perturbation has been shown to be about 6 mm in diameter at a static density of about 0.045 kg/cubic m. The amplitude of the perturbation is large, which may be unsuitable for the study of linear growth.

Generalized nonlinear Schrödinger equation and ultraslow optical solitons in a cold four-state atomic system.

PubMed

Hang, Chao; Huang, Guoxiang; Deng, L

2006-03-01

We investigate the influence of high-order dispersion and nonlinearity on the propagation of ultraslow optical solitons in a lifetime broadened four-state atomic system under a Raman excitation. Using a standard method of multiple-scales we derive a generalized nonlinear Schrödinger equation and show that for realistic physical parameters and at the pulse duration of 10(-6)s, the effects of third-order linear dispersion, nonlinear dispersion, and delay in nonlinear refractive index can be significant and may not be considered as perturbations. We provide exact soliton solutions for the generalized nonlinear Schrödinger equation and demonstrate that optical solitons obtained may still have ultraslow propagating velocity. Numerical simulations on the stability and interaction of these ultraslow optical solitons in the presence of linear and differential absorptions are also presented.

Asymptotic Behaviour of the Ground State of Singularly Perturbed Elliptic Equations

NASA Astrophysics Data System (ADS)

Piatnitski, Andrey L.

The ground state of a singularly perturbed nonselfadjoint elliptic operator defined on a smooth compact Riemannian manifold with metric aij(x)=(aij(x))-1, is studied. We investigate the limiting behaviour of the first eigenvalue of this operator as μ goes to zero, and find the logarithmic asymptotics of the first eigenfunction everywhere on the manifold. The results are formulated in terms of auxiliary variational problems on the manifold. This approach also allows to study the general singularly perturbed second order elliptic operator on a bounded domain in Rn.

Hybrid normed ideal perturbations of n-tuples of operators I

NASA Astrophysics Data System (ADS)

Voiculescu, Dan-Virgil

2018-06-01

In hybrid normed ideal perturbations of n-tuples of operators, the normed ideal is allowed to vary with the component operators. We begin extending to this setting the machinery we developed for normed ideal perturbations based on the modulus of quasicentral approximation and an adaptation of our non-commutative generalization of the Weyl-von Neumann theorem. For commuting n-tuples of hermitian operators, the modulus of quasicentral approximation remains essentially the same when Cn- is replaced by a hybrid n-tuple Cp1,…- , … , Cpn- , p1-1 + ⋯ + pn-1 = 1. The proof involves singular integrals of mixed homogeneity.

Description of a computer program and numerical techniques for developing linear perturbation models from nonlinear systems simulations

NASA Technical Reports Server (NTRS)

Dieudonne, J. E.

1978-01-01

A numerical technique was developed which generates linear perturbation models from nonlinear aircraft vehicle simulations. The technique is very general and can be applied to simulations of any system that is described by nonlinear differential equations. The computer program used to generate these models is discussed, with emphasis placed on generation of the Jacobian matrices, calculation of the coefficients needed for solving the perturbation model, and generation of the solution of the linear differential equations. An example application of the technique to a nonlinear model of the NASA terminal configured vehicle is included.

Perturbed effects at radiation physics

NASA Astrophysics Data System (ADS)

Külahcı, Fatih; Şen, Zekâi

2013-09-01

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.

The molecular gradient using the divide-expand-consolidate resolution of the identity second-order Møller-Plesset perturbation theory: The DEC-RI-MP2 gradient

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bykov, Dmytro; Kristensen, Kasper; Kjærgaard, Thomas

We report an implementation of the molecular gradient using the divide-expand-consolidate resolution of the identity second-order Møller-Plesset perturbation theory (DEC-RI-MP2). The new DEC-RI-MP2 gradient method combines the precision control as well as the linear-scaling and massively parallel features of the DEC scheme with efficient evaluations of the gradient contributions using the RI approximation. We further demonstrate that the DEC-RI-MP2 gradient method is capable of calculating molecular gradients for very large molecular systems. A test set of supramolecular complexes containing up to 158 atoms and 1960 contracted basis functions has been employed to demonstrate the general applicability of the DEC-RI-MP2 methodmore » and to analyze the errors of the DEC approximation. Moreover, the test set contains molecules of complicated electronic structures and is thus deliberately chosen to stress test the DEC-RI-MP2 gradient implementation. Additionally, as a showcase example the full molecular gradient for insulin (787 atoms and 7604 contracted basis functions) has been evaluated.« less

Differential rotation in Jupiter: A comparison of methods

NASA Astrophysics Data System (ADS)

Wisdom, J.; Hubbard, W. B.

2016-03-01

Whether Jupiter rotates as a solid body or has some element of differential rotation along concentric cylinders is unknown. But Jupiter's zonal wind is not north/south symmetric so at most some average of the north/south zonal winds could be an expression of cylinders. Here we explore the signature in the gravitational moments of such a smooth differential rotation. We carry out this investigation with two general methods for solving for the interior structure of a differentially rotating planet: the CMS method of Hubbard (Hubbard, W.B. [2013]. Astrophys. J. 768, 1-8) and the CLC method of Wisdom (Wisdom, J. [1996]. Non-Perturbative Hydrostatic Equilibrium. http://web.mit.edu/wisdom/www/interior.pdf). The two methods are in remarkable agreement. We find that for smooth differential rotation the moments do not level off as they do for strong differential rotation.

A novel robot for imposing perturbations during overground walking: mechanism, control and normative stepping responses.

PubMed

Olenšek, Andrej; Zadravec, Matjaž; Matjačić, Zlatko

2016-06-11

The most common approach to studying dynamic balance during walking is by applying perturbations. Previous studies that investigated dynamic balance responses predominantly focused on applying perturbations in frontal plane while walking on treadmill. The goal of our work was to develop balance assessment robot (BAR) that can be used during overground walking and to assess normative balance responses to perturbations in transversal plane in a group of neurologically healthy individuals. BAR provides three passive degrees of freedom (DoF) and three actuated DoF in pelvis that are admittance-controlled in such a way that the natural movement of pelvis is not significantly affected. In this study BAR was used to assess normative balance responses in neurologically healthy individuals by applying linear perturbations in frontal and sagittal planes and angular perturbations in transversal plane of pelvis. One way repeated measure ANOVA was used to statistically evaluate the effect of selected perturbations on stepping responses. Standard deviations of assessed responses were similar in unperturbed and perturbed walking. Perturbations in frontal direction evoked substantial pelvis displacement and caused statistically significant effect on step length, step width and step time. Likewise, perturbations in sagittal plane also caused statistically significant effect on step length, step width and step time but with less explicit impact on pelvis movement in frontal plane. On the other hand, except from substantial pelvis rotation angular perturbations did not have substantial effect on pelvis movement in frontal and sagittal planes while statistically significant effect was noted only in step length and step width after perturbation in clockwise direction. Results indicate that the proposed device can repeatedly reproduce similar experimental conditions. Results also suggest that "stepping strategy" is the dominant strategy for coping with perturbations in frontal plane, perturbations in sagittal plane are to greater extent handled by "ankle strategy" while angular perturbations in transversal plane do not pose substantial challenge for balance. Results also show that specific perturbation in general elicits responses that extend also to other planes of movement that are not directly associated with plane of perturbation as well as to spatio temporal parameters of gait.

Thermophysical properties of simple liquid metals: A brief review of theory

NASA Technical Reports Server (NTRS)

Stroud, David

1993-01-01

In this paper, we review the current theory of the thermophysical properties of simple liquid metals. The emphasis is on thermodynamic properties, but we also briefly discuss the nonequilibrium properties of liquid metals. We begin by defining a 'simple liquid metal' as one in which the valence electrons interact only weakly with the ionic cores, so that the interaction can be treated by perturbation theory. We then write down the equilibrium Hamiltonian of a liquid metal as a sum of five terms: the bare ion-ion interaction, the electron-electron interaction, the bare electron-ion interaction, and the kinetic energies of electrons and ions. Since the electron-ion interaction can be treated by perturbation, the electronic part contributes in two ways to the Helmholtz free energy: it gives a density-dependent term which is independent of the arrangement of ions, and it acts to screen the ion-ion interaction, giving rise to effective ion-ion pair potentials which are density-dependent, in general. After sketching the form of a typical pair potential, we briefly enumerate some methods for calculating the ionic distribution function and hence the Helmholtz free energy of the liquid: monte Carlo simulations, molecular dynamics simulations, and thermodynamic perturbation theory. The final result is a general expression for the Helmholtz free energy of the liquid metal. It can be used to calculate a wide range of thermodynamic properties of simple metal liquids, which we enumerate. They include not only a range of thermodynamic coefficients of both metals and alloys, but also many aspects of the phase diagram, including freezing curves of pure elements and phase diagrams of liquid alloys (including liquidus and solidus curves). We briefly mention some key discoveries resulting from previous applications of this method, and point out that the same methods work for other materials not normally considered to be liquid metals (such as colloidal suspensions, in which the suspended microspheres behave like ions screened by the salt solution in which they are suspended). We conclude with a brief discussion of some non-equilibrium (i.e., transport) properties which can be treated by an extension of these methods. These include electrical resistivity, thermal conductivity, viscosity, atomic self-diffusion coefficients, concentration diffusion coefficients in alloys, surface tension and thermal emissivity. Finally, we briefly mention two methods by which the theory might be extended to non-simple liquid metals: these are empirical techniques (i.e., empirical two- and three-body potentials), and numerical many-body approaches. Both may be potentially applicable to extremely complex systems, such as nonstoichiometric liquid semiconductor alloys.

A study of the application of singular perturbation theory. [development of a real time algorithm for optimal three dimensional aircraft maneuvers

NASA Technical Reports Server (NTRS)

Mehra, R. K.; Washburn, R. B.; Sajan, S.; Carroll, J. V.

1979-01-01

A hierarchical real time algorithm for optimal three dimensional control of aircraft is described. Systematic methods are developed for real time computation of nonlinear feedback controls by means of singular perturbation theory. The results are applied to a six state, three control variable, point mass model of an F-4 aircraft. Nonlinear feedback laws are presented for computing the optimal control of throttle, bank angle, and angle of attack. Real Time capability is assessed on a TI 9900 microcomputer. The breakdown of the singular perturbation approximation near the terminal point is examined Continuation methods are examined to obtain exact optimal trajectories starting from the singular perturbation solutions.

Towards an exact relativistic theory of Earth's geoid undulation

NASA Astrophysics Data System (ADS)

Kopeikin, Sergei M.; Mazurova, Elena M.; Karpik, Alexander P.

2015-08-01

The present paper extends the Newtonian concept of the geoid in classic geodesy towards the realm of general relativity by utilizing the covariant geometric methods of the perturbation theory of curved manifolds. It yields a covariant definition of the anomalous (disturbing) gravity potential and formulates differential equation for it in the form of a covariant Laplace equation. The paper also derives the Bruns equation for calculation of geoid's height with full account for relativistic effects beyond the Newtonian approximation. A brief discussion of the relativistic Bruns formula is provided.

A limiting analysis for edge effects in angle-ply laminates

NASA Technical Reports Server (NTRS)

Hsu, P. W.; Herakovich, C. T.

1976-01-01

A zeroth order solution for edge effects in angle ply composite laminates using perturbation techniques and a limiting free body approach was developed. The general method of solution for laminates is developed and then applied to the special case of a graphite/epoxy laminate. Interlaminar stress distributions are obtained as a function of the laminate thickness to width ratio h/b and compared to existing numerical results. The solution predicts stable, continuous stress distributions, determines finite maximum tensile interlaminar normal stress for two laminates, and provides mathematical evidence for singular interlaminar shear stresses.

The Linear Perturbation Theory of Axially Symmetric Compressible Flow with Application to the Effect of Compressibility on the Pressure Coefficient at the Surface of a Body of Revolution

DTIC Science & Technology

1947-07-18

which + la constant constitute a surface vhlch say he called a streaa surface. The stream surface Is In torn Bode up of streaallnee. If a...potential and stream function would be, reapeetHely, VpX and ia ^r8. The stream awfaeoa would he right circular cylinders with axes along the x...there is a double infinity of methods. In general, !n transforming frem the compreeslhlo-flov field to the IncrwpreSBlble-flow field, streaa

Drag Minimization for Wings and Bodies in Supersonic Flow

NASA Technical Reports Server (NTRS)

Heaslet, Max A; Fuller, Franklyn B

1958-01-01

The minimization of inviscid fluid drag is studied for aerodynamic shapes satisfying the conditions of linearized theory, and subject to imposed constraints on lift, pitching moment, base area, or volume. The problem is transformed to one of determining two-dimensional potential flows satisfying either Laplace's or Poisson's equations with boundary values fixed by the imposed conditions. A general method for determining integral relations between perturbation velocity components is developed. This analysis is not restricted in application to optimum cases; it may be used for any supersonic wing problem.

Renormalized asymptotic enumeration of Feynman diagrams

NASA Astrophysics Data System (ADS)

Borinsky, Michael

2017-10-01

A method to obtain all-order asymptotic results for the coefficients of perturbative expansions in zero-dimensional quantum field is described. The focus is on the enumeration of the number of skeleton or primitive diagrams of a certain QFT and its asymptotics. The procedure heavily applies techniques from singularity analysis. To utilize singularity analysis, a representation of the zero-dimensional path integral as a generalized hyperelliptic curve is deduced. As applications the full asymptotic expansions of the number of disconnected, connected, 1PI and skeleton Feynman diagrams in various theories are given.

A new multi-step technique with differential transform method for analytical solution of some nonlinear variable delay differential equations.

PubMed

Benhammouda, Brahim; Vazquez-Leal, Hector

2016-01-01

This work presents an analytical solution of some nonlinear delay differential equations (DDEs) with variable delays. Such DDEs are difficult to treat numerically and cannot be solved by existing general purpose codes. A new method of steps combined with the differential transform method (DTM) is proposed as a powerful tool to solve these DDEs. This method reduces the DDEs to ordinary differential equations that are then solved by the DTM. Furthermore, we show that the solutions can be improved by Laplace-Padé resummation method. Two examples are presented to show the efficiency of the proposed technique. The main advantage of this technique is that it possesses a simple procedure based on a few straight forward steps and can be combined with any analytical method, other than the DTM, like the homotopy perturbation method.

Generalized Autobalanced Ramsey Spectroscopy of Clock Transitions

NASA Astrophysics Data System (ADS)

Yudin, V. I.; Taichenachev, A. V.; Basalaev, M. Yu.; Zanon-Willette, T.; Pollock, J. W.; Shuker, M.; Donley, E. A.; Kitching, J.

2018-05-01

When performing precision measurements, the quantity being measured is often perturbed by the measurement process itself. Such measurements include precision frequency measurements for atomic clock applications carried out with Ramsey spectroscopy. With the aim of eliminating probe-induced perturbations, a method of generalized autobalanced Ramsey spectroscopy (GABRS) is presented and rigorously substantiated. The usual local-oscillator frequency control loop is augmented with a second control loop derived from secondary Ramsey sequences interspersed with the primary sequences and with a different Ramsey period. This second loop feeds back to a secondary clock variable and ultimately compensates for the perturbation of the clock frequency caused by the measurements in the first loop. We show that such a two-loop scheme can lead to perfect compensation for measurement-induced light shifts and does not suffer from the effects of relaxation, time-dependent pulse fluctuations and phase-jump modulation errors that are typical of other hyper-Ramsey schemes. Several variants of GABRS are explored based on different secondary variables including added relative phase shifts between Ramsey pulses, external frequency-step compensation, and variable second-pulse duration. We demonstrate that a universal antisymmetric error signal, and hence perfect compensation at a finite modulation amplitude, is generated only if an additional frequency step applied during both Ramsey pulses is used as the concomitant variable parameter. This universal technique can be applied to the fields of atomic clocks, high-resolution molecular spectroscopy, magnetically induced and two-photon probing schemes, Ramsey-type mass spectrometry, and the field of precision measurements. Some variants of GABRS can also be applied for rf atomic clocks using coherent-population-trapping-based Ramsey spectroscopy of the two-photon dark resonance.

ADAPTATION AND GENERALIZATION TO OPPOSING PERTURBATIONS IN WALKING

PubMed Central

Bhatt, T.; Wang, T.-Y.; Yang, F.; Pai, Y.-C.

2013-01-01

Little is known on how the CNS would select its movement options when a person faces a novel or recurring perturbation of two opposing types (slip or trip) while walking. The purposes of this study were (1) to determine whether young adults’ adaptation to repeated slips would interfere with their recovery from a novel trip, and (2) to investigate the generalized strategies after they were exposed to a mixed training with both types of perturbation. Thirty-two young adults were assigned to either the training group, which first underwent repeated-slip training before encountering a novel, unannounced trip while walking, or to the control group, which only experienced the same novel, unannounced trip. The former group would then experience a mix of repeated trips and slips. The results indicated that prior adaptation to slips had only limited interference during the initial phase of trip recovery. In fact, the prior repeated-slip exposure had primed their reaction, which mitigated any error resulting from early interference. As a result, they did not have to take a longer compensatory step for trip recovery than did the controls. After the mixed training, subjects were able to converge effectively the motion state of their center of mass (in its position and velocity space) to a stable and generalized “middle ground” steady-state. Such movement strategies not only further strengthened their robust reactive control of stability, but also reduced the CNS’ overall reliance on accurate context prediction and on feedback correction of perturbation-induced movement error. PMID:23603517

Improvement of Microtremor Data Filtering and Processing Methods Used in Determining the Fundamental Frequency of Urban Areas

NASA Astrophysics Data System (ADS)

Mousavi Anzehaee, Mohammad; Adib, Ahmad; Heydarzadeh, Kobra

2015-10-01

The manner of microtremor data collection and filtering operation and also the method used for processing have a considerable effect on the accuracy of estimation of dynamic soil parameters. In this paper, running variance method was used to improve the automatic detection of data sections infected by local perturbations. In this method, the microtremor data running variance is computed using a sliding window. Then the obtained signal is used to remove the ranges of data affected by perturbations from the original data. Additionally, to determinate the fundamental frequency of a site, this study has proposed a statistical characteristics-based method. Actually, statistical characteristics, such as the probability density graph and the average and the standard deviation of all the frequencies corresponding to the maximum peaks in the H/ V spectra of all data windows, are used to differentiate the real peaks from the false peaks resulting from perturbations. The methods have been applied to the data recorded for the City of Meybod in central Iran. Experimental results show that the applied methods are able to successfully reduce the effects of extensive local perturbations on microtremor data and eventually to estimate the fundamental frequency more accurately compared to other common methods.

Quasinormal modes of gravitational perturbation around regular Bardeen black hole surrounded by quintessence

NASA Astrophysics Data System (ADS)

Saleh, Mahamat; Thomas, Bouetou Bouetou; Kofane, Timoleon Crepin

2018-04-01

In this paper, Quasinormal modes of gravitational perturbation are investigated for the regular Bardeen black hole surrounded by quintessence. Considering the metric of the Bardeen spacetime surrounded by quintessence, we derived the perturbation equation for gravitational perturbation using Regge-Wheeler gauge. The third order Wentzel-Kramers-Brillouin (WKB) approximation method is used to evaluate quasinormal frequencies. Explicitly, the behaviors of the black hole potential and quasinormal modes were plotted. The results show that, due to the presence of quintessence, the gravitational perturbation around the black hole damps more slowly and oscillates more slowly.

Determination of linear optics functions from turn-by-turn data

NASA Astrophysics Data System (ADS)

Alexahin, Y.; Gianfelice-Wendt, E.

2011-10-01

A method for evaluation of coupled optics functions, detection of strong perturbing elements, determination of BPM calibration errors and tilts using turn-by-turn (TBT) data is presented as well as the new version of the Hamiltonian perturbation theory of betatron oscillations the method is based upon. An example of application of the considered method to the Tevatron is given.

Nonspherically symmetric black string perturbations in the large dimension limit

NASA Astrophysics Data System (ADS)

Sadhu, Amruta; Suneeta, Vardarajan

2016-06-01

We consider nonspherically symmetric perturbations of the uncharged black string/flat black brane in the large dimension (D) limit of general relativity. We express the perturbations in a simplified form using variables introduced by Ishibashi and Kodama. We apply the large D limit to the equations and show that this leads to decoupling of the equations in the near-horizon and asymptotic regions. It also enables use of matched asymptotic expansions to obtain approximate analytical solutions and to analyze stability of the black string/brane. For a large class of nonspherically symmetric perturbations, we prove that there are no instabilities in the large D limit. For the rest, we provide additional matching arguments that indicate that the black string/brane is stable. In the static limit, we show that for all nonspherically symmetric perturbations, there is no instability. This is proof that the Gross-Perry-Yaffe mode for semiclassical black hole perturbations is the unique unstable mode even in the large D limit. This work is also a direct analytical indication that the only instability of the black string is the Gregory-Laflamme instability.

Monte Carlo Perturbation Theory Estimates of Sensitivities to System Dimensions

DOE PAGES

Burke, Timothy P.; Kiedrowski, Brian C.

2017-12-11

Here, Monte Carlo methods are developed using adjoint-based perturbation theory and the differential operator method to compute the sensitivities of the k-eigenvalue, linear functions of the flux (reaction rates), and bilinear functions of the forward and adjoint flux (kinetics parameters) to system dimensions for uniform expansions or contractions. The calculation of sensitivities to system dimensions requires computing scattering and fission sources at material interfaces using collisions occurring at the interface—which is a set of events with infinitesimal probability. Kernel density estimators are used to estimate the source at interfaces using collisions occurring near the interface. The methods for computing sensitivitiesmore » of linear and bilinear ratios are derived using the differential operator method and adjoint-based perturbation theory and are shown to be equivalent to methods previously developed using a collision history–based approach. The methods for determining sensitivities to system dimensions are tested on a series of fast, intermediate, and thermal critical benchmarks as well as a pressurized water reactor benchmark problem with iterated fission probability used for adjoint-weighting. The estimators are shown to agree within 5% and 3σ of reference solutions obtained using direct perturbations with central differences for the majority of test problems.« less

Effect of an ac Perturbation on the Electroosmotic Behavior of a Cation-Exchange Membrane. Influence of the Cation Nature.

PubMed

Barragán, V. M.; Bauzá, C. Ruíz

2001-08-01

The effect of an ac sinusoidal perturbation of known amplitude and frequency superimposed on the usual dc applied electric voltage difference on the electroosmotic flow through a typical cation-exchange membrane has been studied using different monovalent electrolytes. As a general trend, the presence of the ac perturbation increases the value of the electroosmotic flow with respect to the value in the absence of ac perturbation. A dispersion of the electroosmotic permeability on the frequency of the applied ac signal has been found for the three studied electrolytes, observing that the electroosmotic permeability reaches maximum values for some characteristic values of the frequency. This behavior may be related to the different relaxation processes in heterogeneous mediums. Copyright 2001 Academic Press.

The 1/ N Expansion of Tensor Models Beyond Perturbation Theory

NASA Astrophysics Data System (ADS)

Gurau, Razvan

2014-09-01

We analyze in full mathematical rigor the most general quartically perturbed invariant probability measure for a random tensor. Using a version of the Loop Vertex Expansion (which we call the mixed expansion) we show that the cumulants write as explicit series in 1/ N plus bounded rest terms. The mixed expansion recasts the problem of determining the subleading corrections in 1/ N into a simple combinatorial problem of counting trees decorated by a finite number of loop edges. As an aside, we use the mixed expansion to show that the (divergent) perturbative expansion of the tensor models is Borel summable and to prove that the cumulants respect an uniform scaling bound. In particular the quartically perturbed measures fall, in the N→ ∞ limit, in the universality class of Gaussian tensor models.

Thermal effects and sudden decay approximation in the curvaton scenario

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kitajima, Naoya; Takesako, Tomohiro; Yokoyama, Shuichiro

2014-10-01

We study the impact of a temperature-dependent curvaton decay rate on the primordial curvature perturbation generated in the curvaton scenario. Using the familiar sudden decay approximation, we obtain an analytical expression for the curvature perturbation after the decay of the curvaton. We then investigate numerically the evolution of the background and of the perturbations during the decay. We first show that the instantaneous transfer coefficient, related to the curvaton energy fraction at the decay, can be extended into a more general parameter, which depends on the net transfer of the curvaton energy into radiation energy or, equivalently, on the totalmore » entropy ratio after the complete curvaton decay. We then compute the curvature perturbation and compare this result with the sudden decay approximation prediction.« less

Dynamical inference: where phase synchronization and generalized synchronization meet.

PubMed

Stankovski, Tomislav; McClintock, Peter V E; Stefanovska, Aneta

2014-06-01

Synchronization is a widespread phenomenon that occurs among interacting oscillatory systems. It facilitates their temporal coordination and can lead to the emergence of spontaneous order. The detection of synchronization from the time series of such systems is of great importance for the understanding and prediction of their dynamics, and several methods for doing so have been introduced. However, the common case where the interacting systems have time-variable characteristic frequencies and coupling parameters, and may also be subject to continuous external perturbation and noise, still presents a major challenge. Here we apply recent developments in dynamical Bayesian inference to tackle these problems. In particular, we discuss how to detect phase slips and the existence of deterministic coupling from measured data, and we unify the concepts of phase synchronization and general synchronization. Starting from phase or state observables, we present methods for the detection of both phase and generalized synchronization. The consistency and equivalence of phase and generalized synchronization are further demonstrated, by the analysis of time series from analog electronic simulations of coupled nonautonomous van der Pol oscillators. We demonstrate that the detection methods work equally well on numerically simulated chaotic systems. In all the cases considered, we show that dynamical Bayesian inference can clearly identify noise-induced phase slips and distinguish coherence from intrinsic coupling-induced synchronization.

Perturbation-iteration theory for analyzing microwave striplines

NASA Technical Reports Server (NTRS)

Kretch, B. E.

1985-01-01

A perturbation-iteration technique is presented for determining the propagation constant and characteristic impedance of an unshielded microstrip transmission line. The method converges to the correct solution with a few iterations at each frequency and is equivalent to a full wave analysis. The perturbation-iteration method gives a direct solution for the propagation constant without having to find the roots of a transcendental dispersion equation. The theory is presented in detail along with numerical results for the effective dielectric constant and characteristic impedance for a wide range of substrate dielectric constants, stripline dimensions, and frequencies.

Flow and Heat Transfer Analysis of an Eyring-Powell Fluid in a Pipe

NASA Astrophysics Data System (ADS)

Ali, N.; Nazeer, F.; Nazeer, Mubbashar

2018-02-01

The steady non-isothermal flow of an Eyring-Powell fluid in a pipe is investigated using both perturbation and numerical methods. The results are presented for two viscosity models, namely the Reynolds model and the Vogel model. The shooting method is employed to compute the numerical solution. Criteria for validity of perturbation solution are developed. When these criteria are met, it is shown that the perturbation solution is in good agreement with the numerical solution. The influence of various emerging parameters on the velocity and temperature field is also shown.

Induced Ellipticity for Inspiraling Binary Systems

NASA Astrophysics Data System (ADS)

Randall, Lisa; Xianyu, Zhong-Zhi

2018-01-01

Although gravitational waves tend to erase eccentricity of an inspiraling binary system, ellipticity can be generated in the presence of surrounding matter. We present a semianalytical method for understanding the eccentricity distribution of binary black holes (BHs) in the presence of a supermassive BH in a galactic center. Given a matter distribution, we show how to determine the resultant eccentricity analytically in the presence of both tidal forces and evaporation up to one cutoff and one matter-distribution-independent function, paving the way for understanding the environment of detected inspiraling BHs. We furthermore generalize Kozai–Lidov dynamics to situations where perturbation theory breaks down for short time intervals, allowing more general angular momentum exchange, such that eccentricity is generated even when all bodies orbit in the same plane.

Free energy from molecular dynamics with multiple constraints

NASA Astrophysics Data System (ADS)

den Otter, W. K.; Briels, W. J.

In molecular dynamics simulations of reacting systems, the key step to determining the equilibrium constant and the reaction rate is the calculation of the free energy as a function of the reaction coordinate. Intuitively the derivative of the free energy is equal to the average force needed to constrain the reaction coordinate to a constant value, but the metric tensor effect of the constraint on the sampled phase space distribution complicates this relation. The appropriately corrected expression for the potential of mean constraint force method (PMCF) for systems in which only the reaction coordinate is constrained was published recently. Here we will consider the general case of a system with multiple constraints. This situation arises when both the reaction coordinate and the 'hard' coordinates are constrained, and also in systems with several reaction coordinates. The obvious advantage of this method over the established thermodynamic integration and free energy perturbation methods is that it avoids the cumbersome introduction of a full set of generalized coordinates complementing the constrained coordinates. Simulations of n -butane and n -pentane in vacuum illustrate the method.

Generalized Stability Analysis of Capillary Flow in Slender V-Grooves

NASA Astrophysics Data System (ADS)

White, Nicholas; Troian, Sandra

2017-11-01

Spontaneous capillary flow, an especially rapid process in slender open microchannels resembling V-grooves, is of significant importance to many applications requiring passive robust flow control. Many types of biomedical devices for point-of-care use in developing countries are being designed around this principle. Important fundamental work by Romero and Yost (1996) and Weislogel (1996) elucidated the behavior of Newtonian films in slender V-grooves driven to flow by the streamwise change in capillary pressure due to the change in radius of curvature of the circular arc describing the interface of wetting or non-wetting fluids. Self-similar solutions describing Washburn type dynamics were found but other solutions are possible. Here we extend the Romero and Yost model to include a variety of inlet and outlet boundary conditions and examine the transient growth and generalized stability of perturbations to steady state and self-similar flows. Although most cases examined for wetting fluids exhibit robust stability against small perturbations, some exceptions reveal unstable flow. In total, these results support decades of experimental work which has found this method of flow control to be especially reliable, robust and self-healing. The authors gratefully acknowledge financial support from the 2016 NASA/Jet Propulsion Laboratory President's and Director's Fund as well as a 2017 NASA Space Technology Research Fellowship.

Inter-species pathway perturbation prediction via data-driven detection of functional homology.

PubMed

Hafemeister, Christoph; Romero, Roberto; Bilal, Erhan; Meyer, Pablo; Norel, Raquel; Rhrissorrakrai, Kahn; Bonneau, Richard; Tarca, Adi L

2015-02-15

Experiments in animal models are often conducted to infer how humans will respond to stimuli by assuming that the same biological pathways will be affected in both organisms. The limitations of this assumption were tested in the IMPROVER Species Translation Challenge, where 52 stimuli were applied to both human and rat cells and perturbed pathways were identified. In the Inter-species Pathway Perturbation Prediction sub-challenge, multiple teams proposed methods to use rat transcription data from 26 stimuli to predict human gene set and pathway activity under the same perturbations. Submissions were evaluated using three performance metrics on data from the remaining 26 stimuli. We present two approaches, ranked second in this challenge, that do not rely on sequence-based orthology between rat and human genes to translate pathway perturbation state but instead identify transcriptional response orthologs across a set of training conditions. The translation from rat to human accomplished by these so-called direct methods is not dependent on the particular analysis method used to identify perturbed gene sets. In contrast, machine learning-based methods require performing a pathway analysis initially and then mapping the pathway activity between organisms. Unlike most machine learning approaches, direct methods can be used to predict the activation of a human pathway for a new (test) stimuli, even when that pathway was never activated by a training stimuli. Gene expression data are available from ArrayExpress (accession E-MTAB-2091), while software implementations are available from http://bioinformaticsprb.med.wayne.edu?p=50 and http://goo.gl/hJny3h. christoph.hafemeister@nyu.edu or atarca@med.wayne.edu. Supplementary data are available at Bioinformatics online. Published by Oxford University Press 2014. This work is written by US Government employees and is in the public domain in the US.

Extremal black holes in dynamical Chern-Simons gravity

NASA Astrophysics Data System (ADS)

McNees, Robert; Stein, Leo C.; Yunes, Nicolás

2016-12-01

Rapidly rotating black hole (BH) solutions in theories beyond general relativity (GR) play a key role in experimental gravity, as they allow us to compute observables in extreme spacetimes that deviate from the predictions of GR. Such solutions are often difficult to find in beyond-general-relativity theories due to the inclusion of additional fields that couple to the metric nonlinearly and non-minimally. In this paper, we consider rotating BH solutions in one such theory, dynamical Chern-Simons (dCS) gravity, where the Einstein-Hilbert action is modified by the introduction of a dynamical scalar field that couples to the metric through the Pontryagin density. We treat dCS gravity as an effective field theory and work in the decoupling limit, where corrections are treated as small perturbations from GR. We perturb about the maximally rotating Kerr solution, the so-called extremal limit, and develop mathematical insight into the analysis techniques needed to construct solutions for generic spin. First we find closed-form, analytic expressions for the extremal scalar field, and then determine the trace of the metric perturbation, giving both in terms of Legendre decompositions. Retaining only the first three and four modes in the Legendre representation of the scalar field and the trace, respectively, suffices to ensure a fidelity of over 99% relative to full numerical solutions. The leading-order mode in the Legendre expansion of the trace of the metric perturbation contains a logarithmic divergence at the extremal Kerr horizon, which is likely to be unimportant as it occurs inside the perturbed dCS horizon. The techniques employed here should enable the construction of analytic, closed-form expressions for the scalar field and metric perturbations on a background with arbitrary rotation.

- XSUMMER- Transcendental functions and symbolic summation in FORM

NASA Astrophysics Data System (ADS)

Moch, S.; Uwer, P.

2006-05-01

Harmonic sums and their generalizations are extremely useful in the evaluation of higher-order perturbative corrections in quantum field theory. Of particular interest have been the so-called nested sums, where the harmonic sums and their generalizations appear as building blocks, originating for example, from the expansion of generalized hypergeometric functions around integer values of the parameters. In this paper we discuss the implementation of several algorithms to solve these sums by algebraic means, using the computer algebra system FORM. Program summaryTitle of program:XSUMMER Catalogue identifier:ADXQ_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADXQ_v1_0 Program obtainable from:CPC Program Library, Queen's University of Belfast, N. Ireland License:GNU Public License and FORM License Computers:all Operating system:all Program language:FORM Memory required to execute:Depending on the complexity of the problem, recommended at least 64 MB RAM No. of lines in distributed program, including test data, etc.:9854 No. of bytes in distributed program, including test data, etc.:126 551 Distribution format:tar.gz Other programs called:none External files needed:none Nature of the physical problem:Systematic expansion of higher transcendental functions in a small parameter. The expansions arise in the calculation of loop integrals in perturbative quantum field theory. Method of solution:Algebraic manipulations of nested sums. Restrictions on complexity of the problem:Usually limited only by the available disk space. Typical running time:Dependent on the complexity of the problem.

Driven similarity renormalization group for excited states: A state-averaged perturbation theory

NASA Astrophysics Data System (ADS)

Li, Chenyang; Evangelista, Francesco A.

2018-03-01

The multireference driven similarity renormalization group (MRDSRG) approach [C. Li and F. A. Evangelista, J. Chem. Theory Comput. 11, 2097 (2015)] is generalized to treat quasi-degenerate electronic excited states. The new scheme, termed state-averaged (SA) MRDSRG, is a state-universal approach that considers an ensemble of quasi-degenerate states on an equal footing. Using the SA-MRDSRG framework, we implement second- (SA-DSRG-PT2) and third-order (SA-DSRG-PT3) perturbation theories. These perturbation theories can treat a manifold of near-degenerate states at the cost of a single state-specific computation. At the same time, they have several desirable properties: (1) they are intruder-free and size-extensive, (2) their energy expressions can be evaluated non-iteratively and require at most the three-body density cumulant of the reference states, and (3) the reference states are allowed to relax in the presence of dynamical correlation effects. Numerical benchmarks on the potential energy surfaces of lithium fluoride, ammonia, and the penta-2,4-dieniminium cation reveal that the SA-DSRG-PT2 method yields results with accuracy similar to that of other second-order quasi-degenerate perturbation theories. The SA-DSRG-PT3 results are instead consistent with those from multireference configuration interaction with singles and doubles (MRCISD). Finally, we compute the vertical excitation energies of (E,E)-1,3,5,7-octatetraene. The ordering of the lowest three states is predicted to be 2 1Ag-<1 1Bu+<1 1Bu- by both SA-DSRG-PT2 and SA-DSRG-PT3, in accordance with MRCISD plus Davidson correction.

Age-related differences in trunk muscle reflexive behaviors.

PubMed

Shojaei, Iman; Nussbaum, Maury A; Bazrgari, Babak

2016-10-03

Reports of larger passive and similar intrinsic trunk stiffness in older vs. younger populations suggest a diminishing demand for reflexive contributions of trunk muscles to spinal stability with aging. It remains unclear, though, whether such diminishing demands result in deterioration of trunk muscle reflexive behaviors. A cross-sectional study was completed to assess age-related differences in the latency and likelihood of trunk muscle reflexive responses to sudden perturbations. Sixty healthy individuals, aged 20-70 years, were recruited to form five equal-sized and gender-balanced age groups. Using a displacement-control, sudden perturbation paradigm, the latency and likelihood of trunk muscle reflexive responses to sudden perturbations were estimated, and the influences of age, gender, and level of effort (20% versus 30% of maximum voluntary exertion-MVE) were evaluated. There were no consistent age-related differences found in any of the measures of trunk muscle reflexive behavior. However, the latency of muscle response to perturbation was generally higher among older individuals, and this difference was significant in the condition involving 30% MVE effort. With an increase in level of effort (from 20% to 30% of MVE), there was a ~7% increase in the latency of trunk muscle responses to anteriorly-directed perturbations as well as ~ 15% (21%) decrease (increase) in response likelihood during anteriorly (posteriorly) directed perturbations. Furthermore, the reflexive response likelihood of trunk muscles was 28% (58%) larger (smaller) in female vs. male participants during anteriorly (posteriorly) directed perturbations. Our results did not, in general, support the hypothesis of an age-related decay in reflexive trunk muscle behaviors. Larger reflexive responses were associated with lower trunk intrinsic stiffness among females and during a lower level of effort, suggesting a secondary role for reflexive responses in spinal stability. Such secondary compensatory responses appear, however, to be consistent over a wide age range. Copyright © 2016 Elsevier Ltd. All rights reserved.

A New Approach on the Long Term Dynamics of NEO's Under Yarkovsky Effect.

NASA Astrophysics Data System (ADS)

Peláez, Jesús; Urrutxua, Hodei; Bombardelli, Claudio; Perez-Grande, Isabel

2011-12-01

A classical approach to the many-body problem is that of using special perturbation methods. Nowadays and due to the availability of high-speed computers is an essential tool in Space Dynamics which exhibits a great advantage: it is applicable to any orbit involving any number of bodies and all sorts of astrodynamical problems, especially when these problems fall into regions in which general perturbation theories are absent. One such case is, for example, that Near Earth Objects (NEO's) dynamics. In this field, the Group of Tether Dynamics of UPM (GDT) has developed a new regularisation scheme - called DROMO - which is characterised by only 8 ODE. This new regularisation scheme allows a new approach to the dynamics of NEO's in the long term, specially appropriated to consider the influence of the anisotropic thermal emission (Yarkovsky and YORP effects) on the dynamics. A new project, called NEODROMO, has been started in GDT that aims to provide a reliable tool for the long term dynamics of NEO's.

MAPPING GROWTH AND GRAVITY WITH ROBUST REDSHIFT SPACE DISTORTIONS

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kwan, Juliana; Lewis, Geraint F.; Linder, Eric V.

2012-04-01

Redshift space distortions (RSDs) caused by galaxy peculiar velocities provide a window onto the growth rate of large-scale structure and a method for testing general relativity. We investigate through a comparison of N-body simulations to various extensions of perturbation theory beyond the linear regime, the robustness of cosmological parameter extraction, including the gravitational growth index {gamma}. We find that the Kaiser formula and some perturbation theory approaches bias the growth rate by 1{sigma} or more relative to the fiducial at scales as large as k > 0.07 h Mpc{sup -1}. This bias propagates to estimates of the gravitational growth indexmore » as well as {Omega}{sub m} and the equation-of-state parameter and presents a significant challenge to modeling RSDs. We also determine an accurate fitting function for a combination of line-of-sight damping and higher order angular dependence that allows robust modeling of the redshift space power spectrum to substantially higher k.« less

Linear, multivariable robust control with a mu perspective

NASA Technical Reports Server (NTRS)

Packard, Andy; Doyle, John; Balas, Gary

1993-01-01

The structured singular value is a linear algebra tool developed to study a particular class of matrix perturbation problems arising in robust feedback control of multivariable systems. These perturbations are called linear fractional, and are a natural way to model many types of uncertainty in linear systems, including state-space parameter uncertainty, multiplicative and additive unmodeled dynamics uncertainty, and coprime factor and gap metric uncertainty. The structured singular value theory provides a natural extension of classical SISO robustness measures and concepts to MIMO systems. The structured singular value analysis, coupled with approximate synthesis methods, make it possible to study the tradeoff between performance and uncertainty that occurs in all feedback systems. In MIMO systems, the complexity of the spatial interactions in the loop gains make it difficult to heuristically quantify the tradeoffs that must occur. This paper examines the role played by the structured singular value (and its computable bounds) in answering these questions, as well as its role in the general robust, multivariable control analysis and design problem.

On analyticity of linear waves scattered by a layered medium

NASA Astrophysics Data System (ADS)

Nicholls, David P.

2017-10-01

The scattering of linear waves by periodic structures is a crucial phenomena in many branches of applied physics and engineering. In this paper we establish rigorous analytic results necessary for the proper numerical analysis of a class of High-Order Perturbation of Surfaces methods for simulating such waves. More specifically, we prove a theorem on existence and uniqueness of solutions to a system of partial differential equations which model the interaction of linear waves with a multiply layered periodic structure in three dimensions. This result provides hypotheses under which a rigorous numerical analysis could be conducted for recent generalizations to the methods of Operator Expansions, Field Expansions, and Transformed Field Expansions.

Perturbative Quantum Gravity from Gauge Theory

NASA Astrophysics Data System (ADS)

Carrasco, John Joseph

In this dissertation we present the graphical techniques recently developed in the construction of multi-loop scattering amplitudes using the method of generalized unitarity. We construct the three-loop and four-loop four-point amplitudes of N = 8 supergravity using these methods and the Kawaii, Lewellen and Tye tree-level relations which map tree-level gauge theory amplitudes to tree-level gravity theory amplitudes. We conclude by extending a tree-level duality between color and kinematics, generic to gauge theories, to a loop level conjecture, allowing the easy relation between loop-level gauge and gravity kinematics. We provide non-trivial evidence for this conjecture at three-loops in the particular case of maximal supersymmetry.

COLA with scale-dependent growth: applications to screened modified gravity models

NASA Astrophysics Data System (ADS)

Winther, Hans A.; Koyama, Kazuya; Manera, Marc; Wright, Bill S.; Zhao, Gong-Bo

2017-08-01

We present a general parallelized and easy-to-use code to perform numerical simulations of structure formation using the COLA (COmoving Lagrangian Acceleration) method for cosmological models that exhibit scale-dependent growth at the level of first and second order Lagrangian perturbation theory. For modified gravity theories we also include screening using a fast approximate method that covers all the main examples of screening mechanisms in the literature. We test the code by comparing it to full simulations of two popular modified gravity models, namely f(R) gravity and nDGP, and find good agreement in the modified gravity boost-factors relative to ΛCDM even when using a fairly small number of COLA time steps.

Vortex loops and Majoranas

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chesi, Stefano; CEMS, RIKEN, Wako, Saitama 351-0198; Jaffe, Arthur

2013-11-15

We investigate the role that vortex loops play in characterizing eigenstates of interacting Majoranas. We give some general results and then focus on ladder Hamiltonian examples as a test of further ideas. Two methods yield exact results: (i) A mapping of certain spin Hamiltonians to quartic interactions of Majoranas shows that the spectra of these two examples coincide. (ii) In cases with reflection-symmetric Hamiltonians, we use reflection positivity for Majoranas to characterize vortices in the ground states. Two additional methods suggest wider applicability of these results: (iii) Numerical evidence suggests similar behavior for certain systems without reflection symmetry. (iv) Amore » perturbative analysis also suggests similar behavior without the assumption of reflection symmetry.« less

DOE Office of Scientific and Technical Information (OSTI.GOV)

Winther, Hans A.; Koyama, Kazuya; Wright, Bill S.

We present a general parallelized and easy-to-use code to perform numerical simulations of structure formation using the COLA (COmoving Lagrangian Acceleration) method for cosmological models that exhibit scale-dependent growth at the level of first and second order Lagrangian perturbation theory. For modified gravity theories we also include screening using a fast approximate method that covers all the main examples of screening mechanisms in the literature. We test the code by comparing it to full simulations of two popular modified gravity models, namely f ( R ) gravity and nDGP, and find good agreement in the modified gravity boost-factors relative tomore » ΛCDM even when using a fairly small number of COLA time steps.« less

Time-dependent generalized Gibbs ensembles in open quantum systems

NASA Astrophysics Data System (ADS)

Lange, Florian; Lenarčič, Zala; Rosch, Achim

2018-04-01

Generalized Gibbs ensembles have been used as powerful tools to describe the steady state of integrable many-particle quantum systems after a sudden change of the Hamiltonian. Here, we demonstrate numerically that they can be used for a much broader class of problems. We consider integrable systems in the presence of weak perturbations which break both integrability and drive the system to a state far from equilibrium. Under these conditions, we show that the steady state and the time evolution on long timescales can be accurately described by a (truncated) generalized Gibbs ensemble with time-dependent Lagrange parameters, determined from simple rate equations. We compare the numerically exact time evolutions of density matrices for small systems with a theory based on block-diagonal density matrices (diagonal ensemble) and a time-dependent generalized Gibbs ensemble containing only a small number of approximately conserved quantities, using the one-dimensional Heisenberg model with perturbations described by Lindblad operators as an example.

On the account of gravitational perturbations in computer simulation technology of meteoroid complex formation and evolution

NASA Astrophysics Data System (ADS)

Kulikova, N. V.; Chepurova, V. M.

2009-10-01

So far we investigated the nonperturbation dynamics of meteoroid complexes. The numerical integration of the differential equations of motion in the N-body problem by the Everhart algorithm (N=2-6) and introduction of the intermediate hyperbolic orbits build on the base of the generalized problem of two fixed centers permit to take into account some gravitational perturbations.

Relative motion of orbiting particles under the influence of perturbing forces. Volume 1: Summary

NASA Technical Reports Server (NTRS)

Eades, J. B., Jr.

1974-01-01

The relative motion for orbiting vehicles, under the influence of various perturbing forces, has been studied to determine what influence these inputs, and others, can have. The analytical tasks are discribed in general terms; the force types considered, are outlined modelled and simulated, and the capabilities of the computer programs which have evolved in support of this work are denoted.

A conservative scheme for electromagnetic simulation of magnetized plasmas with kinetic electrons

NASA Astrophysics Data System (ADS)

Bao, J.; Lin, Z.; Lu, Z. X.

2018-02-01

A conservative scheme has been formulated and verified for gyrokinetic particle simulations of electromagnetic waves and instabilities in magnetized plasmas. An electron continuity equation derived from the drift kinetic equation is used to time advance the electron density perturbation by using the perturbed mechanical flow calculated from the parallel vector potential, and the parallel vector potential is solved by using the perturbed canonical flow from the perturbed distribution function. In gyrokinetic particle simulations using this new scheme, the shear Alfvén wave dispersion relation in the shearless slab and continuum damping in the sheared cylinder have been recovered. The new scheme overcomes the stringent requirement in the conventional perturbative simulation method that perpendicular grid size needs to be as small as electron collisionless skin depth even for the long wavelength Alfvén waves. The new scheme also avoids the problem in the conventional method that an unphysically large parallel electric field arises due to the inconsistency between electrostatic potential calculated from the perturbed density and vector potential calculated from the perturbed canonical flow. Finally, the gyrokinetic particle simulations of the Alfvén waves in sheared cylinder have superior numerical properties compared with the fluid simulations, which suffer from numerical difficulties associated with singular mode structures.

Comparing the structure of an emerging market with a mature one under global perturbation

NASA Astrophysics Data System (ADS)

Namaki, A.; Jafari, G. R.; Raei, R.

2011-09-01

In this paper we investigate the Tehran stock exchange (TSE) and Dow Jones Industrial Average (DJIA) in terms of perturbed correlation matrices. To perturb a stock market, there are two methods, namely local and global perturbation. In the local method, we replace a correlation coefficient of the cross-correlation matrix with one calculated from two Gaussian-distributed time series, whereas in the global method, we reconstruct the correlation matrix after replacing the original return series with Gaussian-distributed time series. The local perturbation is just a technical study. We analyze these markets through two statistical approaches, random matrix theory (RMT) and the correlation coefficient distribution. By using RMT, we find that the largest eigenvalue is an influence that is common to all stocks and this eigenvalue has a peak during financial shocks. We find there are a few correlated stocks that make the essential robustness of the stock market but we see that by replacing these return time series with Gaussian-distributed time series, the mean values of correlation coefficients, the largest eigenvalues of the stock markets and the fraction of eigenvalues that deviate from the RMT prediction fall sharply in both markets. By comparing these two markets, we can see that the DJIA is more sensitive to global perturbations. These findings are crucial for risk management and portfolio selection.

Classical evolution and quantum generation in generalized gravity theories including string corrections and tachyons: Unified analyses

NASA Astrophysics Data System (ADS)

Hwang, Jai-Chan; Noh, Hyerim

2005-03-01

We present cosmological perturbation theory based on generalized gravity theories including string theory correction terms and a tachyonic complication. The classical evolution as well as the quantum generation processes in these varieties of gravity theories are presented in unified forms. These apply both to the scalar- and tensor-type perturbations. Analyses are made based on the curvature variable in two different gauge conditions often used in the literature in Einstein’s gravity; these are the curvature variables in the comoving (or uniform-field) gauge and the zero-shear gauge. Applications to generalized slow-roll inflation and its consequent power spectra are derived in unified forms which include a wide range of inflationary scenarios based on Einstein’s gravity and others.

Renormalization of a tensorial field theory on the homogeneous space SU(2)/U(1)

NASA Astrophysics Data System (ADS)

Lahoche, Vincent; Oriti, Daniele

2017-01-01

We study the renormalization of a general field theory on the homogeneous space (SU(2)/ ≤ft. U(1)\\right){{}× d} with tensorial interaction and gauge invariance under the diagonal action of SU(2). We derive the power counting for arbitrary d. For the case d  =  4, we prove perturbative renormalizability to all orders via multi-scale analysis, study both the renormalized and effective perturbation series, and establish the asymptotic freedom of the model. We also outline a general power counting for the homogeneous space {{≤ft(SO(D)/SO(D-1)\\right)}× d} , of direct interest for quantum gravity models in arbitrary dimension, and point out the obstructions to the direct generalization of our results to these cases.

Variational Solutions and Random Dynamical Systems to SPDEs Perturbed by Fractional Gaussian Noise

PubMed Central

Zeng, Caibin; Yang, Qigui; Cao, Junfei

2014-01-01

This paper deals with the following type of stochastic partial differential equations (SPDEs) perturbed by an infinite dimensional fractional Brownian motion with a suitable volatility coefficient Φ: dX(t) = A(X(t))dt+Φ(t)dB H(t), where A is a nonlinear operator satisfying some monotonicity conditions. Using the variational approach, we prove the existence and uniqueness of variational solutions to such system. Moreover, we prove that this variational solution generates a random dynamical system. The main results are applied to a general type of nonlinear SPDEs and the stochastic generalized p-Laplacian equation. PMID:24574903

Applicability of transfer tensor method for open quantum system dynamics.

PubMed

Gelzinis, Andrius; Rybakovas, Edvardas; Valkunas, Leonas

2017-12-21

Accurate simulations of open quantum system dynamics is a long standing issue in the field of chemical physics. Exact methods exist, but are costly, while perturbative methods are limited in their applicability. Recently a new black-box type method, called transfer tensor method (TTM), was proposed [J. Cerrillo and J. Cao, Phys. Rev. Lett. 112, 110401 (2014)]. It allows one to accurately simulate long time dynamics with a numerical cost of solving a time-convolution master equation, provided many initial system evolution trajectories are obtained from some exact method beforehand. The possible time-savings thus strongly depend on the ratio of total versus initial evolution lengths. In this work, we investigate the parameter regimes where an application of TTM would be most beneficial in terms of computational time. We identify several promising parameter regimes. Although some of them correspond to cases when perturbative theories could be expected to perform well, we find that the accuracy of such approaches depends on system parameters in a more complex way than it is commonly thought. We propose that the TTM should be applied whenever system evolution is expected to be long and accuracy of perturbative methods cannot be ensured or in cases when the system under consideration does not correspond to any single perturbative regime.

Black hole perturbation under a 2 +2 decomposition in the action

NASA Astrophysics Data System (ADS)

Ripley, Justin L.; Yagi, Kent

2018-01-01

Black hole perturbation theory is useful for studying the stability of black holes and calculating ringdown gravitational waves after the collision of two black holes. Most previous calculations were carried out at the level of the field equations instead of the action. In this work, we compute the Einstein-Hilbert action to quadratic order in linear metric perturbations about a spherically symmetric vacuum background in Regge-Wheeler gauge. Using a 2 +2 splitting of spacetime, we expand the metric perturbations into a sum over scalar, vector, and tensor spherical harmonics, and dimensionally reduce the action to two dimensions by integrating over the two sphere. We find that the axial perturbation degree of freedom is described by a two-dimensional massive vector action, and that the polar perturbation degree of freedom is described by a two-dimensional dilaton massive gravity action. Varying the dimensionally reduced actions, we rederive covariant and gauge-invariant master equations for the axial and polar degrees of freedom. Thus, the two-dimensional massive vector and massive gravity actions we derive by dimensionally reducing the perturbed Einstein-Hilbert action describe the dynamics of a well-studied physical system: the metric perturbations of a static black hole. The 2 +2 formalism we present can be generalized to m +n -dimensional spacetime splittings, which may be useful in more generic situations, such as expanding metric perturbations in higher dimensional gravity. We provide a self-contained presentation of m +n formalism for vacuum spacetime splittings.

On optimizing the treatment of exchange perturbations

NASA Technical Reports Server (NTRS)

Hirschfelder, J. O.; Chipman, D. M.

1972-01-01

A method using the zeroth plus first order wave functions, obtained by optimizing the basic equation used in exchange perturbation treatments, is utilized in an attempt to determine the exact energy and wave function in the exchange process. Attempts to determine the first order perturbation solution by optimizing the sum of the first and second order energies were unsuccessful.

Expectation of an upcoming large postural perturbation influences the recovery stepping response and outcome.

PubMed

Pater, Mackenzie L; Rosenblatt, Noah J; Grabiner, Mark D

2015-01-01

Tripping during locomotion, the leading cause of falls in older adults, generally occurs without prior warning and often while performing a secondary task. Prior warning can alter the state of physiological preparedness and beneficially influence the response to the perturbation. Previous studies have examined how altering the initial "preparedness" for an upcoming perturbation can affect kinematic responses following small disturbances that did not require a stepping response to restore dynamic stability. The purpose of this study was to examine how expectation affected fall outcome and recovery response kinematics following a large, treadmill-delivered perturbation simulating a trip and requiring at least one recovery step to avoid a fall. Following the perturbation, 47% of subjects fell when they were not expecting the perturbation whereas 12% fell when they were aware that the perturbation would occur "sometime in the next minute". The between-group differences were accompanied by slower reaction times in the non-expecting group (p < 0.01). Slower reaction times were associated with kinematics that have previously been shown to increase the likelihood of falling following a laboratory-induced trip. The results demonstrate the importance of considering the context under which recovery responses are assessed, and further, gives insight to the context during which task-specific perturbation training is administered. Copyright © 2014 Elsevier B.V. All rights reserved.

Rotation of the cosmic microwave background polarization from weak gravitational lensing.

PubMed

Dai, Liang

2014-01-31

When a cosmic microwave background (CMB) photon travels from the surface of last scatter through spacetime metric perturbations, the polarization vector may rotate about its direction of propagation. This gravitational rotation is distinct from, and occurs in addition to, the lensing deflection of the photon trajectory. This rotation can be sourced by linear vector or tensor metric perturbations and is fully coherent with the curl deflection field. Therefore, lensing corrections to the CMB polarization power spectra as well as the temperature-polarization cross correlations due to nonscalar perturbations are modified. The rotation does not affect lensing by linear scalar perturbations, but needs to be included when calculations go to higher orders. We present complete results for weak lensing of the full-sky CMB power spectra by general linear metric perturbations, taking into account both deflection of the photon trajectory and rotation of the polarization. For the case of lensing by gravitational waves, we show that the B modes induced by the rotation largely cancel those induced by the curl component of deflection.

A Double Perturbation Method for Reducing Dynamical Degradation of the Digital Baker Map

NASA Astrophysics Data System (ADS)

Liu, Lingfeng; Lin, Jun; Miao, Suoxia; Liu, Bocheng

2017-06-01

The digital Baker map is widely used in different kinds of cryptosystems, especially for image encryption. However, any chaotic map which is realized on the finite precision device (e.g. computer) will suffer from dynamical degradation, which refers to short cycle lengths, low complexity and strong correlations. In this paper, a novel double perturbation method is proposed for reducing the dynamical degradation of the digital Baker map. Both state variables and system parameters are perturbed by the digital logistic map. Numerical experiments show that the perturbed Baker map can achieve good statistical and cryptographic properties. Furthermore, a new image encryption algorithm is provided as a simple application. With a rather simple algorithm, the encrypted image can achieve high security, which is competitive to the recently proposed image encryption algorithms.

The Laplace transformed divide-expand-consolidate resolution of the identity second-order Møller-Plesset perturbation (DEC-LT-RIMP2) theory method

NASA Astrophysics Data System (ADS)

Kjærgaard, Thomas

2017-01-01

The divide-expand-consolidate resolution of the identity second-order Møller-Plesset perturbation (DEC-RI-MP2) theory method introduced in Baudin et al. [J. Chem. Phys. 144, 054102 (2016)] is significantly improved by introducing the Laplace transform of the orbital energy denominator in order to construct the double amplitudes directly in the local basis. Furthermore, this paper introduces the auxiliary reduction procedure, which reduces the set of the auxiliary functions employed in the individual fragments. The resulting Laplace transformed divide-expand-consolidate resolution of the identity second-order Møller-Plesset perturbation method is applied to the insulin molecule where we obtain a factor 9.5 speedup compared to the DEC-RI-MP2 method.

Theoretical investigation of cyromazine tautomerism using density functional theory and Møller–Plesset perturbation theory methods

USDA-ARS?s Scientific Manuscript database

A computational chemistry analysis of six unique tautomers of cyromazine, a pesticide used for fly control, was performed with density functional theory (DFT) and canonical second order Møller–Plesset perturbation theory (MP2) methods to gain insight into the contributions of molecular structure to ...

Application of the enhanced homotopy perturbation method to solve the fractional-order Bagley-Torvik differential equation

NASA Astrophysics Data System (ADS)

Zolfaghari, M.; Ghaderi, R.; Sheikhol Eslami, A.; Ranjbar, A.; Hosseinnia, S. H.; Momani, S.; Sadati, J.

2009-10-01

The enhanced homotopy perturbation method (EHPM) is applied for finding improved approximate solutions of the well-known Bagley-Torvik equation for three different cases. The main characteristic of the EHPM is using a stabilized linear part, which guarantees the stability and convergence of the overall solution. The results are finally compared with the Adams-Bashforth-Moulton numerical method, the Adomian decomposition method (ADM) and the fractional differential transform method (FDTM) to verify the performance of the EHPM.

Dynamical Chaos in the Wisdom-Holman Integrator: Origins and Solutions

NASA Technical Reports Server (NTRS)

Rauch, Kevin P.; Holman, Matthew

1999-01-01

We examine the nonlinear stability of the Wisdom-Holman (WH) symplectic mapping applied to the integration of perturbed, highly eccentric (e-0.9) two-body orbits. We find that the method is unstable and introduces artificial chaos into the computed trajectories for this class of problems, unless the step size chosen 1s small enough that PeriaPse is always resolved, in which case the method is generically stable. This 'radial orbit instability' persists even for weakly perturbed systems. Using the Stark problem as a fiducial test case, we investigate the dynamical origin of this instability and argue that the numerical chaos results from the overlap of step-size resonances; interestingly, for the Stark-problem many of these resonances appear to be absolutely stable. We similarly examine the robustness of several alternative integration methods: a time-regularized version of the WH mapping suggested by Mikkola; the potential-splitting (PS) method of Duncan, Levison, Lee; and two original methods incorporating approximations based on Stark motion instead of Keplerian motion. The two fixed point problem and a related, more general problem are used to conduct a comparative test of the various methods for several types of motion. Among the algorithms tested, the time-transformed WH mapping is clearly the most efficient and stable method of integrating eccentric, nearly Keplerian orbits in the absence of close encounters. For test particles subject to both high eccentricities and very close encounters, we find an enhanced version of the PS method-incorporating time regularization, force-center switching, and an improved kernel function-to be both economical and highly versatile. We conclude that Stark-based methods are of marginal utility in N-body type integrations. Additional implications for the symplectic integration of N-body systems are discussed.

Density perturbations in general modified gravitational theories

DOE Office of Scientific and Technical Information (OSTI.GOV)

De Felice, Antonio; Tsujikawa, Shinji; Mukohyama, Shinji

2010-07-15

We derive the equations of linear cosmological perturbations for the general Lagrangian density f(R,{phi},X)/2+L{sub c}, where R is a Ricci scalar, {phi} is a scalar field, and X=-{partial_derivative}{sup {mu}{phi}{partial_derivative}}{sub {mu}{phi}/}2 is a field kinetic energy. We take into account a nonlinear self-interaction term L{sub c}={xi}({phi}) {open_square}{phi}({partial_derivative}{sup {mu}{phi}{partial_derivative}}{sub {mu}{phi}}) recently studied in the context of ''Galileon'' cosmology, which keeps the field equations at second order. Taking into account a scalar-field mass explicitly, the equations of matter density perturbations and gravitational potentials are obtained under a quasistatic approximation on subhorizon scales. We also derive conditions for the avoidance of ghosts and Laplacianmore » instabilities associated with propagation speeds. Our analysis includes most of modified gravity models of dark energy proposed in literature; and thus it is convenient to test the viability of such models from both theoretical and observational points of view.« less

Non-Abelian integrable hierarchies: matrix biorthogonal polynomials and perturbations

NASA Astrophysics Data System (ADS)

Ariznabarreta, Gerardo; García-Ardila, Juan C.; Mañas, Manuel; Marcellán, Francisco

2018-05-01

In this paper, Geronimus–Uvarov perturbations for matrix orthogonal polynomials on the real line are studied and then applied to the analysis of non-Abelian integrable hierarchies. The orthogonality is understood in full generality, i.e. in terms of a nondegenerate continuous sesquilinear form, determined by a quasidefinite matrix of bivariate generalized functions with a well-defined support. We derive Christoffel-type formulas that give the perturbed matrix biorthogonal polynomials and their norms in terms of the original ones. The keystone for this finding is the Gauss–Borel factorization of the Gram matrix. Geronimus–Uvarov transformations are considered in the context of the 2D non-Abelian Toda lattice and noncommutative KP hierarchies. The interplay between transformations and integrable flows is discussed. Miwa shifts, τ-ratio matrix functions and Sato formulas are given. Bilinear identities, involving Geronimus–Uvarov transformations, first for the Baker functions, then secondly for the biorthogonal polynomials and its second kind functions, and finally for the τ-ratio matrix functions, are found.

Extended mimetic gravity: Hamiltonian analysis and gradient instabilities

NASA Astrophysics Data System (ADS)

Takahashi, Kazufumi; Kobayashi, Tsutomu

2017-11-01

We propose a novel class of degenerate higher-order scalar-tensor theories as an extension of mimetic gravity. By performing a noninvertible conformal transformation on "seed" scalar-tensor theories which may be nondegenerate, we can generate a large class of theories with at most three physical degrees of freedom. We identify a general seed theory for which this is possible. Cosmological perturbations in these extended mimetic theories are also studied. It is shown that either of tensor or scalar perturbations is plagued with gradient instabilities, except for a special case where the scalar perturbations are presumably strongly coupled, or otherwise there appear ghost instabilities.

Superluminality in dilatationally invariant generalized Galileon theories

NASA Astrophysics Data System (ADS)

Kolevatov, R. S.

2015-12-01

We consider small perturbations about homogeneous backgrounds in dilatationally invariant Galileon models. The issues we address are stability (absence of ghosts and gradient instabilities) and superluminality. We show that in the Minkowski background, it is possible to construct the Lagrangian in such a way that any homogeneous Galileon background solution is stable and small perturbations about it are subluminal. On the other hand, in the case of Friedmann-Lemaitre-Robertson-Walker (FLRW) backgrounds, for any Lagrangian functions there exist homogeneous background solutions to the Galileon equation of motion and time dependence of the scale factor, such that the stability conditions are satisfied, but the Galileon perturbations propagate with superluminal speed.

Algebraic perturbation theory for dense liquids with discrete potentials

NASA Astrophysics Data System (ADS)

Adib, Artur B.

2007-06-01

A simple theory for the leading-order correction g1(r) to the structure of a hard-sphere liquid with discrete (e.g., square-well) potential perturbations is proposed. The theory makes use of a general approximation that effectively eliminates four-particle correlations from g1(r) with good accuracy at high densities. For the particular case of discrete perturbations, the remaining three-particle correlations can be modeled with a simple volume-exclusion argument, resulting in an algebraic and surprisingly accurate expression for g1(r) . The structure of a discrete “core-softened” model for liquids with anomalous thermodynamic properties is reproduced as an application.

A higher order panel method for linearized supersonic flow

NASA Technical Reports Server (NTRS)

Ehlers, F. E.; Epton, M. A.; Johnson, F. T.; Magnus, A. E.; Rubbert, P. E.

1979-01-01

The basic integral equations of linearized supersonic theory for an advanced supersonic panel method are derived. Methods using only linear varying source strength over each panel or only quadratic doublet strength over each panel gave good agreement with analytic solutions over cones and zero thickness cambered wings. For three dimensional bodies and wings of general shape, combined source and doublet panels with interior boundary conditions to eliminate the internal perturbations lead to a stable method providing good agreement experiment. A panel system with all edges contiguous resulted from dividing the basic four point non-planar panel into eight triangular subpanels, and the doublet strength was made continuous at all edges by a quadratic distribution over each subpanel. Superinclined panels were developed and tested on s simple nacelle and on an airplane model having engine inlets, with excellent results.

Prophetic Granger Causality to infer gene regulatory networks.

PubMed

Carlin, Daniel E; Paull, Evan O; Graim, Kiley; Wong, Christopher K; Bivol, Adrian; Ryabinin, Peter; Ellrott, Kyle; Sokolov, Artem; Stuart, Joshua M

2017-01-01

We introduce a novel method called Prophetic Granger Causality (PGC) for inferring gene regulatory networks (GRNs) from protein-level time series data. The method uses an L1-penalized regression adaptation of Granger Causality to model protein levels as a function of time, stimuli, and other perturbations. When combined with a data-independent network prior, the framework outperformed all other methods submitted to the HPN-DREAM 8 breast cancer network inference challenge. Our investigations reveal that PGC provides complementary information to other approaches, raising the performance of ensemble learners, while on its own achieves moderate performance. Thus, PGC serves as a valuable new tool in the bioinformatics toolkit for analyzing temporal datasets. We investigate the general and cell-specific interactions predicted by our method and find several novel interactions, demonstrating the utility of the approach in charting new tumor wiring.

Prophetic Granger Causality to infer gene regulatory networks

PubMed Central

Carlin, Daniel E.; Paull, Evan O.; Graim, Kiley; Wong, Christopher K.; Bivol, Adrian; Ryabinin, Peter; Ellrott, Kyle; Sokolov, Artem

2017-01-01

We introduce a novel method called Prophetic Granger Causality (PGC) for inferring gene regulatory networks (GRNs) from protein-level time series data. The method uses an L1-penalized regression adaptation of Granger Causality to model protein levels as a function of time, stimuli, and other perturbations. When combined with a data-independent network prior, the framework outperformed all other methods submitted to the HPN-DREAM 8 breast cancer network inference challenge. Our investigations reveal that PGC provides complementary information to other approaches, raising the performance of ensemble learners, while on its own achieves moderate performance. Thus, PGC serves as a valuable new tool in the bioinformatics toolkit for analyzing temporal datasets. We investigate the general and cell-specific interactions predicted by our method and find several novel interactions, demonstrating the utility of the approach in charting new tumor wiring. PMID:29211761

Lagrangian methods in the analysis of nonlinear wave interactions in plasma

NASA Technical Reports Server (NTRS)

Galloway, J. J.

1972-01-01

An averaged-Lagrangian method is developed for obtaining the equations which describe the nonlinear interactions of the wave (oscillatory) and background (nonoscillatory) components which comprise a continuous medium. The method applies to monochromatic waves in any continuous medium that can be described by a Lagrangian density, but is demonstrated in the context of plasma physics. The theory is presented in a more general and unified form by way of a new averaged-Lagrangian formalism which simplifies the perturbation ordering procedure. Earlier theory is extended to deal with a medium distributed in velocity space and to account for the interaction of the background with the waves. The analytic steps are systematized, so as to maximize calculational efficiency. An assessment of the applicability and limitations of the method shows that it has some definite advantages over other approaches in efficiency and versatility.

Induced matter brane gravity and Einstein static universe

DOE Office of Scientific and Technical Information (OSTI.GOV)

Heydarzade, Y.; Darabi, F., E-mail: heydarzade@azaruniv.edu, E-mail: f.darabi@azaruniv.edu

We investigate stability of the Einstein static universe against the scalar, vector and tensor perturbations in the context of induced matter brane gravity. It is shown that in the framework of this model, the Einstein static universe has a positive spatial curvature. In contrast to the classical general relativity, it is found that a stable Einstein static universe against the scalar perturbations does exist provided that the variation of time dependent geometrical equation of state parameter is proportional to the minus of the variation of the scale factor, δ ω{sub g}(t) = −Cδ a(t). We obtain neutral stability against the vector perturbations, and themore » stability against the tensor perturbations is guaranteed due to the positivity of the spatial curvature of the Einstein static universe in induced matter brane gravity.« less

Generalized banana-drift transport

NASA Astrophysics Data System (ADS)

Mynick, H. E.

1985-10-01

The theory of tokamak ripple transport in the banana-drift and ripple-plateau is extended in a number of directions. The theory is valid for small values of the toroidal periodicity number n of the perturbation, as well as for the moderate values (n approx. 10 - 20) previously assumed. It is shown that low-n perturbations can produce much greater transport than the larger-n perturbations usually studied. In addition, the ripple perturbation is allowed arbitrary values of poloidal mode number m and frequency omega, making it applicable to the transport induced by MHD modes. Bounce averaging is avoided, so the theory includes the contributions to transport from all harmonics of the bounce frequency, providing a continuous description of the transition from the banana drift to the ripple-plateau regime. The implications of the theory for toroidal rotation in tokamaks are considered.

A new method to study he effective shear modulus of shocked material

NASA Astrophysics Data System (ADS)

Xiaojuan, Ma; Fusheng, Liu

2013-06-01

Shear modulus is a crucial material parameter for description of mechanical behavior. However, at strong shock compression, it is generally deduced from the longitudinal and bulk sound velocity evaluated by unloading wave profile measurement. Here, a new method called the disturbed amplitude damping method of shock wave is presented, that can directly measure the shear modulus of material. This method relies on the correlation between the shear modulus of shock compressed state and amplitude damping and oscillation of an initial sinusoidal disturbance on shock front in concerned substance. Two important steps are required to determine the shear modulus of material. The first is to measure the damping and oscillation feature of disturbance by the flyer impacted method. The second is to find the quantitative relationship between the disturbed amplitude damping and shear modulus by the finite difference method which is applied to obtain the numerical solutions for disturbance amplitude damping behavior of sinusoidal shock front in flyer impacted flow field. When aluminum shocked to 80 GPa is taken as an example, the shape of perturbed shock front and its disturbed amplitude development with propagation distance, are approximately mapped out. The figure shows an oscillatory damping characteristic. At the early stage the perturbation amplitude on the shock front experiences a decaying process until to zero point, then it rises to a maximum but in reverse phase, and then it decays again. Comparing these data with those simulated using the SCG constitutive model, the effective shear modulus for aluminum shocked to 80 GPa is determined to be about 90 GPa, which is higher than the result given by Yu.