initial perturbation methods: Topics by Science.gov

Sample records for initial perturbation methods

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.
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.
A new Method for the Estimation of Initial Condition Uncertainty Structures in Mesoscale Models

NASA Astrophysics Data System (ADS)

Keller, J. D.; Bach, L.; Hense, A.

2012-12-01

The estimation of fast growing error modes of a system is a key interest of ensemble data assimilation when assessing uncertainty in initial conditions. Over the last two decades three methods (and variations of these methods) have evolved for global numerical weather prediction models: ensemble Kalman filter, singular vectors and breeding of growing modes (or now ensemble transform). While the former incorporates a priori model error information and observation error estimates to determine ensemble initial conditions, the latter two techniques directly address the error structures associated with Lyapunov vectors. However, in global models these structures are mainly associated with transient global wave patterns. When assessing initial condition uncertainty in mesoscale limited area models, several problems regarding the aforementioned techniques arise: (a) additional sources of uncertainty on the smaller scales contribute to the error and (b) error structures from the global scale may quickly move through the model domain (depending on the size of the domain). To address the latter problem, perturbation structures from global models are often included in the mesoscale predictions as perturbed boundary conditions. However, the initial perturbations (when used) are often generated with a variant of an ensemble Kalman filter which does not necessarily focus on the large scale error patterns. In the framework of the European regional reanalysis project of the Hans-Ertel-Center for Weather Research we use a mesoscale model with an implemented nudging data assimilation scheme which does not support ensemble data assimilation at all. In preparation of an ensemble-based regional reanalysis and for the estimation of three-dimensional atmospheric covariance structures, we implemented a new method for the assessment of fast growing error modes for mesoscale limited area models. The so-called self-breeding is development based on the breeding of growing modes technique. Initial perturbations are integrated forward for a short time period and then rescaled and added to the initial state again. Iterating this rapid breeding cycle provides estimates for the initial uncertainty structure (or local Lyapunov vectors) given a specific norm. To avoid that all ensemble perturbations converge towards the leading local Lyapunov vector we apply an ensemble transform variant to orthogonalize the perturbations in the sub-space spanned by the ensemble. By choosing different kind of norms to measure perturbation growth, this technique allows for estimating uncertainty patterns targeted at specific sources of errors (e.g. convection, turbulence). With case study experiments we show applications of the self-breeding method for different sources of uncertainty and different horizontal scales.
A perturbative approach for enhancing the performance of time series forecasting.

PubMed

de Mattos Neto, Paulo S G; Ferreira, Tiago A E; Lima, Aranildo R; Vasconcelos, Germano C; Cavalcanti, George D C

2017-04-01

This paper proposes a method to perform time series prediction based on perturbation theory. The approach is based on continuously adjusting an initial forecasting model to asymptotically approximate a desired time series model. First, a predictive model generates an initial forecasting for a time series. Second, a residual time series is calculated as the difference between the original time series and the initial forecasting. If that residual series is not white noise, then it can be used to improve the accuracy of the initial model and a new predictive model is adjusted using residual series. The whole process is repeated until convergence or the residual series becomes white noise. The output of the method is then given by summing up the outputs of all trained predictive models in a perturbative sense. To test the method, an experimental investigation was conducted on six real world time series. A comparison was made with six other methods experimented and ten other results found in the literature. Results show that not only the performance of the initial model is significantly improved but also the proposed method outperforms the other results previously published. Copyright © 2017 Elsevier Ltd. All rights reserved.
The stability of freak waves with regard to external impact and perturbation of initial data

NASA Astrophysics Data System (ADS)

Smirnova, Anna; Shamin, Roman

2014-05-01

We investigate solutions of the equations, describing freak waves, in perspective of stability with regard to external impact and perturbation of initial data. The modeling of freak waves is based on numerical solution of equations describing a non-stationary potential flow of the ideal fluid with a free surface. We consider the two-dimensional infinitely deep flow. For waves modeling we use the equations in conformal variables. The variant of these equations is offered in [1]. Mathematical correctness of these equations was discussed in [2]. These works establish the uniqueness of solutions, offer the effective numerical solution calculation methods, prove the numerical convergence of these methods. The important aspect of numerical modeling of freak waves is the stability of solutions, describing these waves. In this work we study the questions of stability with regards to external impact and perturbation of initial data. We showed the stability of freak waves numerical model, corresponding to the external impact. We performed series of computational experiments with various freak wave initial data and random external impact. This impact means the power density on free surface. In each experiment examine two waves: the wave that was formed by external impact and without one. In all the experiments we see the stability of equation`s solutions. The random external impact practically does not change the time of freak wave formation and its form. Later our work progresses to the investigation of solution's stability under perturbations of initial data. We take the initial data that provide a freak wave and get the numerical solution. In common we take the numerical solution of equation with perturbation of initial data. The computing experiments showed that the freak waves equations solutions are stable under perturbations of initial data.So we can make a conclusion that freak waves are stable relatively external perturbation and perturbation of initial data both. 1. Zakharov V.E., Dyachenko A.I., Vasilyev O.A. New method for numerical simulation of a nonstationary potential flow of incompressible fluid with a free surface// Eur. J.~Mech. B Fluids. 2002. V. 21. P. 283-291. 2. R.V. Shamin. Dynamics of an Ideal Liquid with a Free Surface in Conformal Variables // Journal of Mathematical Sciences, Vol. 160, No. 5, 2009. P. 537-678. 3. R.V. Shamin, V.E. Zakharov, A.I. Dyachenko. How probability for freak wave formation can be found // THE EUROPEAN PHYSICAL JOURNAL - SPECIAL TOPICS Volume 185, Number 1, 113-124, DOI: 10.1140/epjst/e2010-01242-y
Predicting areas of sustainable error growth in quasigeostrophic flows using perturbation alignment properties

NASA Astrophysics Data System (ADS)

Rivière, G.; Hua, B. L.

2004-10-01

A new perturbation initialization method is used to quantify error growth due to inaccuracies of the forecast model initial conditions in a quasigeostrophic box ocean model describing a wind-driven double gyre circulation. This method is based on recent analytical results on Lagrangian alignment dynamics of the perturbation velocity vector in quasigeostrophic flows. More specifically, it consists in initializing a unique perturbation from the sole knowledge of the control flow properties at the initial time of the forecast and whose velocity vector orientation satisfies a Lagrangian equilibrium criterion. This Alignment-based Initialization method is hereafter denoted as the AI method.In terms of spatial distribution of the errors, we have compared favorably the AI error forecast with the mean error obtained with a Monte-Carlo ensemble prediction. It is shown that the AI forecast is on average as efficient as the error forecast initialized with the leading singular vector for the palenstrophy norm, and significantly more efficient than that for total energy and enstrophy norms. Furthermore, a more precise examination shows that the AI forecast is systematically relevant for all control flows whereas the palenstrophy singular vector forecast leads sometimes to very good scores and sometimes to very bad ones.A principal component analysis at the final time of the forecast shows that the AI mode spatial structure is comparable to that of the first eigenvector of the error covariance matrix for a "bred mode" ensemble. Furthermore, the kinetic energy of the AI mode grows at the same constant rate as that of the "bred modes" from the initial time to the final time of the forecast and is therefore characterized by a sustained phase of error growth. In this sense, the AI mode based on Lagrangian dynamics of the perturbation velocity orientation provides a rationale of the "bred mode" behavior.
A simple method to design non-collision relative orbits for close spacecraft formation flying

NASA Astrophysics Data System (ADS)

Jiang, Wei; Li, JunFeng; Jiang, FangHua; Bernelli-Zazzera, Franco

2018-05-01

A set of linearized relative motion equations of spacecraft flying on unperturbed elliptical orbits are specialized for particular cases, where the leader orbit is circular or equatorial. Based on these extended equations, we are able to analyze the relative motion regulation between a pair of spacecraft flying on arbitrary unperturbed orbits with the same semi-major axis in close formation. Given the initial orbital elements of the leader, this paper presents a simple way to design initial relative orbital elements of close spacecraft with the same semi-major axis, thus preventing collision under non-perturbed conditions. Considering the mean influence of J 2 perturbation, namely secular J 2 perturbation, we derive the mean derivatives of orbital element differences, and then expand them to first order. Thus the first order expansion of orbital element differences can be added to the relative motion equations for further analysis. For a pair of spacecraft that will never collide under non-perturbed situations, we present a simple method to determine whether a collision will occur when J 2 perturbation is considered. Examples are given to prove the validity of the extended relative motion equations and to illustrate how the methods presented can be used. The simple method for designing initial relative orbital elements proposed here could be helpful to the preliminary design of the relative orbital elements between spacecraft in a close formation, when collision avoidance is necessary.
Effect of small perturbations on the evolution of polycrystalline structure during plastic deformation

NASA Astrophysics Data System (ADS)

Korznikova, E. A.; Baimova, Yu. A.; Kistanov, A. A.; Dmitriev, S. V.; Korznikov, A. V.

2014-09-01

The method of molecular dynamics has been used to study the influence of initial perturbations on the evolution of grain boundaries during the shear plastic deformation of a two-dimensional polycrystalline material with nanoscale grains. It has been shown that short-term thermalization-induced small perturbations result in noticeable differences in grain boundaries configurations at the deformation of 0.05 and the polycrystal completely loses its initial grain boundary structure at the deformation of 0.4.
Experiments and simulations of Richtmyer-Meshkov Instability with measured,volumetric initial conditions

NASA Astrophysics Data System (ADS)

Sewell, Everest; Ferguson, Kevin; Jacobs, Jeffrey; Greenough, Jeff; Krivets, Vitaliy

2016-11-01

We describe experiments of single-shock Richtmyer-Meskhov Instability (RMI) performed on the shock tube apparatus at the University of Arizona in which the initial conditions are volumetrically imaged prior to shock wave arrival. Initial perturbations play a major role in the evolution of RMI, and previous experimental efforts only capture a single plane of the initial condition. The method presented uses a rastered laser sheet to capture additional images throughout the depth of the initial condition immediately before the shock arrival time. These images are then used to reconstruct a volumetric approximation of the experimental perturbation. Analysis of the initial perturbations is performed, and then used as initial conditions in simulations using the hydrodynamics code ARES, developed at Lawrence Livermore National Laboratory (LLNL). Experiments are presented and comparisons are made with simulation results.
Strength and viscosity effects on perturbed shock front stability in metals

DOE PAGES

Opie, Saul; Loomis, Eric Nicholas; Peralta, Pedro; ...

2017-05-09

Here, computational modeling and experimental measurements on metal samples subject to a laser-driven, ablative Richtmyer-Meshkov instability showed differences between viscosity and strength effects. In particular, numerical and analytical solutions, coupled with measurements of fed-through perturbations, generated by perturbed shock fronts onto initially flat surfaces, show promise as a validation method for models of deviatoric response in the post shocked material. Analysis shows that measurements of shock perturbation amplitudes at low sample thickness-to-wavelength ratios are not enough to differentiate between strength and viscosity effects, but that surface displacement data of the fed-through fed-thru perturbations appears to resolve the ambiguity. Additionally, analyticalmore » and numerical results show shock front perturbation evolution dependence on initial perturbation amplitude and wavelength is significantly different in viscous and materials with strength, suggesting simple experimental geometry changes should provide data supporting one model or the other.« less
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.
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.
Coupling between interface and velocity perturbations in the weakly nonlinear Rayleigh-Taylor instability

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

Wang, L. F.; Ye, W. H.; He, X. T.

2012-11-15

Weakly nonlinear (WN) Rayleigh-Taylor instability (RTI) initiated by single-mode cosinusoidal interface and velocity perturbations is investigated analytically up to the third order. Expressions of the temporal evolutions of the amplitudes of the first three harmonics are derived. It is shown that there are coupling between interface and velocity perturbations, which plays a prominent role in the WN growth. When the 'equivalent amplitude' of the initial velocity perturbation, which is normalized by its linear growth rate, is compared to the amplitude of the initial interface perturbation, the coupling between them dominates the WN growth of the RTI. Furthermore, the RTI wouldmore » be mitigated by initiating a velocity perturbation with a relative phase shift against the interface perturbation. More specifically, when the phase shift between the interface perturbation and the velocity perturbation is {pi} and their equivalent amplitudes are equal, the RTI could be completely quenched. If the equivalent amplitude of the initial velocity perturbation is equal to the initial interface perturbation, the difference between the WN growth of the RTI initiated by only an interface perturbation and by only a velocity perturbation is found to be asymptotically negligible. The dependence of the WN growth on the Atwood numbers and the initial perturbation amplitudes is discussed. In particular, we investigate the dependence of the saturation amplitude (time) of the fundamental mode on the Atwood numbers and the initial perturbation amplitudes. It is found that the Atwood numbers and the initial perturbation amplitudes play a crucial role in the WN growth of the RTI. Thus, it should be included in applications where the seeds of the RTI have velocity perturbations, such as inertial confinement fusion implosions and supernova explosions.« less
Numerical method for the solution of large systems of differential equations of the boundary layer type

NASA Technical Reports Server (NTRS)

Green, M. J.; Nachtsheim, P. R.

1972-01-01

A numerical method for the solution of large systems of nonlinear differential equations of the boundary-layer type is described. The method is a modification of the technique for satisfying asymptotic boundary conditions. The present method employs inverse interpolation instead of the Newton method to adjust the initial conditions of the related initial-value problem. This eliminates the so-called perturbation equations. The elimination of the perturbation equations not only reduces the user's preliminary work in the application of the method, but also reduces the number of time-consuming initial-value problems to be numerically solved at each iteration. For further ease of application, the solution of the overdetermined system for the unknown initial conditions is obtained automatically by applying Golub's linear least-squares algorithm. The relative ease of application of the proposed numerical method increases directly as the order of the differential-equation system increases. Hence, the method is especially attractive for the solution of large-order systems. After the method is described, it is applied to a fifth-order problem from boundary-layer theory.
Perturbing engine performance measurements to determine optimal engine control settings

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

Jiang, Li; Lee, Donghoon; Yilmaz, Hakan

Methods and systems for optimizing a performance of a vehicle engine are provided. The method includes determining an initial value for a first engine control parameter based on one or more detected operating conditions of the vehicle engine, determining a value of an engine performance variable, and artificially perturbing the determined value of the engine performance variable. The initial value for the first engine control parameter is then adjusted based on the perturbed engine performance variable causing the engine performance variable to approach a target engine performance variable. Operation of the vehicle engine is controlled based on the adjusted initialmore » value for the first engine control parameter. These acts are repeated until the engine performance variable approaches the target engine performance variable.« less
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.
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.
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.
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.
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.
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.
System design optimization for a Mars-roving vehicle and perturbed-optimal solutions in nonlinear programming

NASA Technical Reports Server (NTRS)

Pavarini, C.

1974-01-01

Work in two somewhat distinct areas is presented. First, the optimal system design problem for a Mars-roving vehicle is attacked by creating static system models and a system evaluation function and optimizing via nonlinear programming techniques. The second area concerns the problem of perturbed-optimal solutions. Given an initial perturbation in an element of the solution to a nonlinear programming problem, a linear method is determined to approximate the optimal readjustments of the other elements of the solution. Then, the sensitivity of the Mars rover designs is described by application of this method.
THE FIRST FERMI IN A HIGH ENERGY NUCLEAR COLLISION.

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

KRASNITZ,A.

1999-08-09

At very high energies, weak coupling, non-perturbative methods can be used to study classical gluon production in nuclear collisions. One observes in numerical simulations that after an initial formation time, the produced partons are on shell, and their subsequent evolution can be studied using transport theory. At the initial formation time, a simple non-perturbative relation exists between the energy and number densities of the produced partons, and a scale determined by the saturated parton density in the nucleus.
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 three different methods of perturbing the potential vorticity field in mesoscale forecasts of Mediterranean heavy precipitation events: PV-gradient, PV-adjoint and PV-satellite

NASA Astrophysics Data System (ADS)

Vich, M.; Romero, R.; Richard, E.; Arbogast, P.; Maynard, K.

2010-09-01

Heavy precipitation events occur regularly in the western Mediterranean region. These events often have a high impact on the society due to economic and personal losses. The improvement of the mesoscale numerical forecasts of these events can be used to prevent or minimize their impact on the society. In previous studies, two ensemble prediction systems (EPSs) based on perturbing the model initial and boundary conditions were developed and tested for a collection of high-impact MEDEX cyclonic episodes. These EPSs perturb the initial and boundary potential vorticity (PV) field through a PV inversion algorithm. This technique ensures modifications of all the meteorological fields without compromising the mass-wind balance. One EPS introduces the perturbations along the zones of the three-dimensional PV structure presenting the local most intense values and gradients of the field (a semi-objective choice, PV-gradient), while the other perturbs the PV field over the MM5 adjoint model calculated sensitivity zones (an objective method, PV-adjoint). The PV perturbations are set from a PV error climatology (PVEC) that characterizes typical PV errors in the ECMWF forecasts, both in intensity and displacement. This intensity and displacement perturbation of the PV field is chosen randomly, while its location is given by the perturbation zones defined in each ensemble generation method. Encouraged by the good results obtained by these two EPSs that perturb the PV field, a new approach based on a manual perturbation of the PV field has been tested and compared with the previous results. This technique uses the satellite water vapor (WV) observations to guide the correction of initial PV structures. The correction of the PV field intents to improve the match between the PV distribution and the WV image, taking advantage of the relation between dark and bright features of WV images and PV anomalies, under some assumptions. Afterwards, the PV inversion algorithm is applied to run a forecast with the corresponding perturbed initial state (PV-satellite). The non hydrostatic MM5 mesoscale model has been used to run all forecasts. The simulations are performed for a two-day period with a 22.5 km resolution domain (Domain 1 in http://mm5forecasts.uib.es) nested in the ECMWF large-scale forecast fields. The MEDEX cyclone of 10 June 2000, also known as the Montserrat Case, is a suitable testbed to compare the performance of each ensemble and the PV-satellite method. This case is characterized by an Atlantic upper-level trough and low-level cold front which generated a stationary mesoscale cyclone over the Spanish Mediterranean coast, advecting warm and moist air toward Catalonia from the Mediterranean Sea. The consequences of the resulting mesoscale convective system were 6-h accumulated rainfall amounts of 180 mm with estimated material losses to exceed 65 million euros by media. The performace of both ensemble forecasting systems and PV-satellite technique for our case study is evaluated through the verification of the rainfall field. Since the EPSs are probabilistic forecasts and the PV-satellite is deterministic, their comparison is done using the individual ensemble members. Therefore the verification procedure uses deterministic scores, like the ROC curve, the Taylor diagram or the Q-Q plot. These scores cover the different quality attributes of the forecast such as reliability, resolution, uncertainty and sharpness. The results show that the PV-satellite technique performance lies within the performance range obtained by both ensembles; it is even better than the non-perturbed ensemble member. Thus, perturbing randomly using the PV error climatology and introducing the perturbations in the zones given by each EPS captures the mismatch between PV and WV fields better than manual perturbations made by an expert forecaster, at least for this case study.
Automated startup of the MIT research reactor

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

Kwok, K.S.

1992-01-01

This summary describes the development, implementation, and testing of a generic method for performing automated startups of nuclear reactors described by space-independent kinetics under conditions of closed-loop digital control. The technique entails first obtaining a reliable estimate of the reactor's initial degree of subcriticality and then substituting that estimate into a model-based control law so as to permit a power increase from subcritical on a demanded trajectory. The estimation of subcriticality is accomplished by application of the perturbed reactivity method. The shutdown reactor is perturbed by the insertion of reactivity at a known rate. Observation of the resulting period permitsmore » determination of the initial degree of subcriticality. A major advantage to this method is that repeated estimates are obtained of the same quantity. Hence, statistical methods can be applied to improve the quality of the calculation.« less
An approach for finding long period elliptical orbits for precursor SEI missions

NASA Technical Reports Server (NTRS)

Fraietta, Michael F.; Bond, Victor R.

1993-01-01

Precursors for Solar System Exploration Initiative (SEI) missions may require long period elliptical orbits about a planet. These orbits will typically have periods on the order of tens to hundreds of days. Some potential uses for these orbits may include the following: studying the effects of galactic cosmic radiation, parking orbits for engineering and operational test of systems, and ferrying orbits between libration points and low altitude orbits. This report presents an approach that can be used to find these orbits. The approach consists of three major steps. First, it uses a restricted three-body targeting algorithm to determine the initial conditions which satisfy certain desired final conditions in a system of two massive primaries. Then the initial conditions are transformed to an inertial coordinate system for use by a special perturbation method. Finally, using the special perturbation method, other perturbations (e.g., sun third body and solar radiation pressure) can be easily incorporated to determine their effects on the nominal trajectory. An algorithm potentially suitable for on-board guidance will also be discussed. This algorithm uses an analytic method relying on Chebyshev polynomials to compute the desired position and velocity of the satellite as a function of time. Together with navigation updates, this algorithm can be implemented to predict the size and timing for AV corrections.
Manipulation of three-dimensional Richtmyer-Meshkov instability by initial interfacial principal curvatures

NASA Astrophysics Data System (ADS)

Guan, Ben; Zhai, Zhigang; Si, Ting; Lu, Xiyun; Luo, Xisheng

2017-03-01

The characteristics of three-dimensional (3D) Richtmyer-Meshkov instability (RMI) in the early stages are studied numerically. By designing 3D interfaces that initially possess various identical and opposite principal curvature combinations, the growth rate of perturbations can be effectively manipulated. The weighted essentially nonoscillatory scheme and the level set method combined with the real ghost fluid method are used to simulate the flow. The results indicate that the interface development and the shock propagation in 3D cases are much more complicated than those in 2D case, and the evolution of 3D interfaces is heavily dependent on the initial interfacial principal curvatures. The 3D structure of wave patterns induces high pressure zones in the flow field, and the pressure oscillations change the local instabilities of interfaces. In the linear stages, the perturbation growth rate follows regularity as the interfacial principal curvatures vary, which is further predicted by the stability theory of 2D and 3D interfaces. It is also found that hysteresis effects exist at the onset of the linear stages in the 3D case for the same initial perturbations as the 2D case, resulting in different evolutions of 3D RMI in the nonlinear stages.
Numerical analysis of soliton solutions of the modified Korteweg-de Vries-sine-Gordon equation

NASA Astrophysics Data System (ADS)

Popov, S. P.

2015-03-01

Multisoliton solutions of the modified Korteweg-de Vries-sine-Gordon equation (mKdV-SG) are found numerically by applying the quasi-spectral Fourier method and the fourth-order Runge-Kutta method. The accuracy and features of the approach are determined as applied to problems with initial data in the form of various combinations of perturbed soliton distributions. Three-soliton solutions are obtained, and the generation of kinks, breathers, wobblers, perturbed kinks, and nonlinear oscillatory waves is studied.
Three-dimensional simulation of the free shear layer using the vortex-in-cell method

NASA Technical Reports Server (NTRS)

Couet, B.; Buneman, O.; Leonard, A.

1979-01-01

We present numerical simulations of the evolution of a mixing layer from an initial state of uniform vorticity with simple two- and three-dimensional small perturbations. A new method for tracing a large number of three-dimensional vortex filaments is used in the simulations. Vortex tracing by Biot-Savart interaction originally implied ideal (non-viscous) flow, but we use a 3-d mesh, Fourier transforms and filtering for vortex tracing, which implies 'modeling' of subgrid scale motion and hence some viscosity. Streamwise perturbations lead to the usual roll-up of vortex patterns with spanwise uniformity maintained. Remarkably, spanwise perturbations generate streamwise distortions of the vortex filaments and the combination of both perturbations leads to patterns with interesting features discernable in the movies and in the records of enstrophy and energy for the three components of the flow.
Asymptotic behaviors of a cell-to-cell HIV-1 infection model perturbed by white noise

NASA Astrophysics Data System (ADS)

Liu, Qun

2017-02-01

In this paper, we analyze a mathematical model of cell-to-cell HIV-1 infection to CD4+ T cells perturbed by stochastic perturbations. First of all, we investigate that there exists a unique global positive solution of the system for any positive initial value. Then by using Lyapunov analysis methods, we study the asymptotic property of this solution. Moreover, we discuss whether there is a stationary distribution for this system and if it owns the ergodic property. Numerical simulations are presented to illustrate the theoretical results.
An initial investigation into methods of computing transonic aerodynamic sensitivity coefficients

NASA Technical Reports Server (NTRS)

Carlson, Leland A.

1988-01-01

The initial effort was concentrated on developing the quasi-analytical approach for two-dimensional transonic flow. To keep the problem computationally efficient and straightforward, only the two-dimensional flow was considered and the problem was modeled using the transonic small perturbation equation.
Initial conditions and degrees of freedom of non-local gravity

NASA Astrophysics Data System (ADS)

Calcagni, Gianluca; Modesto, Leonardo; Nardelli, Giuseppe

2018-05-01

We prove the equivalence between non-local gravity with an arbitrary form factor and a non-local gravitational system with an extra rank-2 symmetric tensor. Thanks to this reformulation, we use the diffusion-equation method to transform the dynamics of renormalizable non-local gravity with exponential operators into a higher-dimensional system local in spacetime coordinates. This method, first illustrated with a scalar field theory and then applied to gravity, allows one to solve the Cauchy problem and count the number of initial conditions and of non-perturbative degrees of freedom, which is finite. In particular, the non-local scalar and gravitational theories with exponential operators are both characterized by four initial conditions in any dimension and, respectively, by one and eight degrees of freedom in four dimensions. The fully covariant equations of motion are written in a form convenient to find analytic non-perturbative solutions.
Shock wave viscosity measurements

NASA Astrophysics Data System (ADS)

Celliers, Peter

2013-06-01

Several decades ago a method was proposed and demonstrated to measure the viscosity of fluids at high pressure by observing the oscillatory damping of sinusoidal perturbations on a shock front. A detailed mathematical analysis of the technique carried out subsequently by Miller and Ahrens revealed its potential, as well as a deep level of complexity in the analysis. We revisit the ideas behind this technique in the context of a recent experimental development: two-dimensional imaging velocimetry. The new technique allows one to capture a broad spectrum of perturbations down to few micron scale-lengths imposed on a shock front from an initial perturbation. The detailed evolution of the perturbation spectrum is sensitive to the viscosity in the fluid behind the shock front. Initial experiments are aimed at examining the viscosity of shock compressed SiO2 just above the shock melting transition. This work performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344.
Final state interactions and the transverse structure of the pion using non-perturbative eikonal methods

DOE PAGES

Gamberg, Leonard; Schlegel, Marc

2010-01-18

In the factorized picture of semi-inclusive hadronic processes the naive time reversal-odd parton distributions exist by virtue of the gauge link which renders it color gauge invariant. The link characterizes the dynamical effect of initial/final-state interactions of the active parton due soft gluon exchanges with the target remnant. Though these interactions are non-perturbative, studies of final-state interaction have been approximated by perturbative one-gluon approximation in Abelian models. We include higher-order contributions by applying non-perturbative eikonal methods incorporating color degrees of freedom in a calculation of the Boer-Mulders function of the pion. Lastly, using this framework we explore under what conditionsmore » the Boer Mulders function can be described in terms of factorization of final state interactions and a spatial distribution in impact parameter space.« less
Numerical simulations of the process of multiple shock-flame interactions

NASA Astrophysics Data System (ADS)

Jiang, Hua; Dong, Gang; chen, Xiao; Wu, Jin-Tao

2016-08-01

Based on a weighted essentially nonoscillatory scheme, the multiple interactions of a flame interface with an incident shock wave and its reshock waves are numerically simulated by solving the compressible reactive Navier-Stokes equations with a single-step Arrhenius chemical reaction. The two-dimensional sinusoidally perturbed premixed flames with different initial perturbed amplitudes are used to investigate the effect of the initial perturbation on the flame evolutions. The results show that the development of the flame interface is directly affected by the initial perturbed amplitudes before the passages of reshock waves, and the perturbation development is mainly controlled by the Richtmyer-Meshkov instability (RMI). After the successive impacts of multiple reshock waves, the chemical reaction accelerates the consumption of reactants and leads to a gradual disappearance of the initial perturbed information. The perturbation developments in frozen flows with the same initial interface as those in reactive flows are also demonstrated. Comparisons of results between the reactive and frozen flows show that a chemical reaction changes the perturbation pattern of the flame interface by decreasing the density gradient, thereby weakening the baroclinic torque in the flame mixing region, and therefore plays a dominant role after the passage of reshock waves.
Experiments and simulations of single shock Richtmeyer-Meshkov Instability with measured, volumetric initial conditions

NASA Astrophysics Data System (ADS)

Sewell, Everest; Ferguson, Kevin; Greenough, Jeffrey; Jacobs, Jeffrey

2014-11-01

We describe new experiments of single shock Richtmeyer-Meshkov Instability (RMI) performed on the shock tube apparatus at the University of Arizona in which the initial conditions are volumetrically imaged prior to shock wave arrival. Initial perturbation plays a major role in the evolution of RMI, and previous experimental efforts only capture a narrow slice of the initial condition. The method presented uses a rastered laser sheet to capture additional images in the depth of the initial condition shortly before the experimental start time. These images are then used to reconstruct a volumetric approximation of the experimental perturbation, which is simulated using the hydrodynamics code ARES, developed at Lawrence Livermore National Laboratory (LLNL). Comparison is made between the time evolution of the interface width and the mixedness ratio measured from the experiments against the predictions from the numerical simulations.
DROMO formulation for planar motions: solution to the Tsien problem

NASA Astrophysics Data System (ADS)

Urrutxua, Hodei; Morante, David; Sanjurjo-Rivo, Manuel; Peláez, Jesús

2015-06-01

The two-body problem subject to a constant radial thrust is analyzed as a planar motion. The description of the problem is performed in terms of three perturbation methods: DROMO and two others due to Deprit. All of them rely on Hansen's ideal frame concept. An explicit, analytic, closed-form solution is obtained for this problem when the initial orbit is circular (Tsien problem), based on the DROMO special perturbation method, and expressed in terms of elliptic integral functions. The analytical solution to the Tsien problem is later used as a reference to test the numerical performance of various orbit propagation methods, including DROMO and Deprit methods, as well as Cowell and Kustaanheimo-Stiefel methods.
The stability of the contact interface of cylindrical and spherical shock tubes

NASA Astrophysics Data System (ADS)

Crittenden, Paul E.; Balachandar, S.

2018-06-01

The stability of the contact interface for radial shock tubes is investigated as a model for explosive dispersal. The advection upstream splitting method with velocity and pressure diffusion (AUSM+-up) is used to solve for the radial base flow. To investigate the stability of the resulting contact interface, perturbed governing equations are derived assuming harmonic modes in the transverse directions. The perturbed harmonic flow is solved by assuming an initial disturbance and using a perturbed version of AUSM+-up derived in this paper. The intensity of the perturbation near the contact interface is computed and compared to theoretical results obtained by others. Despite the simplifying assumptions of the theoretical analysis, very good agreement is observed. Not only can the magnitude of the instability be predicted during the initial expansion, but also remarkably the agreement between the numerical and theoretical results can be maintained through the collision between the secondary shock and the contact interface. Since the theoretical results only depend upon the time evolution of the base flow, the stability of various modes could be quickly investigated without explicitly solving a system of partial differential equations for the perturbed flow.

Regularization and computational methods for precise solution of perturbed orbit transfer problems

NASA Astrophysics Data System (ADS)

Woollands, Robyn Michele

The author has developed a suite of algorithms for solving the perturbed Lambert's problem in celestial mechanics. These algorithms have been implemented as a parallel computation tool that has broad applicability. This tool is composed of four component algorithms and each provides unique benefits for solving a particular type of orbit transfer problem. The first one utilizes a Keplerian solver (a-iteration) for solving the unperturbed Lambert's problem. This algorithm not only provides a "warm start" for solving the perturbed problem but is also used to identify which of several perturbed solvers is best suited for the job. The second algorithm solves the perturbed Lambert's problem using a variant of the modified Chebyshev-Picard iteration initial value solver that solves two-point boundary value problems. This method converges over about one third of an orbit and does not require a Newton-type shooting method and thus no state transition matrix needs to be computed. The third algorithm makes use of regularization of the differential equations through the Kustaanheimo-Stiefel transformation and extends the domain of convergence over which the modified Chebyshev-Picard iteration two-point boundary value solver will converge, from about one third of an orbit to almost a full orbit. This algorithm also does not require a Newton-type shooting method. The fourth algorithm uses the method of particular solutions and the modified Chebyshev-Picard iteration initial value solver to solve the perturbed two-impulse Lambert problem over multiple revolutions. The method of particular solutions is a shooting method but differs from the Newton-type shooting methods in that it does not require integration of the state transition matrix. The mathematical developments that underlie these four algorithms are derived in the chapters of this dissertation. For each of the algorithms, some orbit transfer test cases are included to provide insight on accuracy and efficiency of these individual algorithms. Following this discussion, the combined parallel algorithm, known as the unified Lambert tool, is presented and an explanation is given as to how it automatically selects which of the three perturbed solvers to compute the perturbed solution for a particular orbit transfer. The unified Lambert tool may be used to determine a single orbit transfer or for generating of an extremal field map. A case study is presented for a mission that is required to rendezvous with two pieces of orbit debris (spent rocket boosters). The unified Lambert tool software developed in this dissertation is already being utilized by several industrial partners and we are confident that it will play a significant role in practical applications, including solution of Lambert problems that arise in the current applications focused on enhanced space situational awareness.
Initial-boundary layer associated with the nonlinear Darcy-Brinkman-Oberbeck-Boussinesq system

NASA Astrophysics Data System (ADS)

Fei, Mingwen; Han, Daozhi; Wang, Xiaoming

2017-01-01

In this paper, we study the vanishing Darcy number limit of the nonlinear Darcy-Brinkman-Oberbeck-Boussinesq system (DBOB). This singular perturbation problem involves singular structures both in time and in space giving rise to initial layers, boundary layers and initial-boundary layers. We construct an approximate solution to the DBOB system by the method of multiple scale expansions. The convergence with optimal convergence rates in certain Sobolev norms is established rigorously via the energy method.
A comparison of breeding and ensemble transform vectors for global ensemble generation

NASA Astrophysics Data System (ADS)

Deng, Guo; Tian, Hua; Li, Xiaoli; Chen, Jing; Gong, Jiandong; Jiao, Meiyan

2012-02-01

To compare the initial perturbation techniques using breeding vectors and ensemble transform vectors, three ensemble prediction systems using both initial perturbation methods but with different ensemble member sizes based on the spectral model T213/L31 are constructed at the National Meteorological Center, China Meteorological Administration (NMC/CMA). A series of ensemble verification scores such as forecast skill of the ensemble mean, ensemble resolution, and ensemble reliability are introduced to identify the most important attributes of ensemble forecast systems. The results indicate that the ensemble transform technique is superior to the breeding vector method in light of the evaluation of anomaly correlation coefficient (ACC), which is a deterministic character of the ensemble mean, the root-mean-square error (RMSE) and spread, which are of probabilistic attributes, and the continuous ranked probability score (CRPS) and its decomposition. The advantage of the ensemble transform approach is attributed to its orthogonality among ensemble perturbations as well as its consistence with the data assimilation system. Therefore, this study may serve as a reference for configuration of the best ensemble prediction system to be used in operation.
Robust, optimal subsonic airfoil shapes

NASA Technical Reports Server (NTRS)

Rai, Man Mohan (Inventor)

2008-01-01

Method system, and product from application of the method, for design of a subsonic airfoil shape, beginning with an arbitrary initial airfoil shape and incorporating one or more constraints on the airfoil geometric parameters and flow characteristics. The resulting design is robust against variations in airfoil dimensions and local airfoil shape introduced in the airfoil manufacturing process. A perturbation procedure provides a class of airfoil shapes, beginning with an initial airfoil shape.
Relativistic initial conditions for N-body simulations

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

Fidler, Christian; Tram, Thomas; Crittenden, Robert

2017-06-01

Initial conditions for (Newtonian) cosmological N-body simulations are usually set by re-scaling the present-day power spectrum obtained from linear (relativistic) Boltzmann codes to the desired initial redshift of the simulation. This back-scaling method can account for the effect of inhomogeneous residual thermal radiation at early times, which is absent in the Newtonian simulations. We analyse this procedure from a fully relativistic perspective, employing the recently-proposed Newtonian motion gauge framework. We find that N-body simulations for ΛCDM cosmology starting from back-scaled initial conditions can be self-consistently embedded in a relativistic space-time with first-order metric potentials calculated using a linear Boltzmann code.more » This space-time coincides with a simple ''N-body gauge'' for z < 50 for all observable modes. Care must be taken, however, when simulating non-standard cosmologies. As an example, we analyse the back-scaling method in a cosmology with decaying dark matter, and show that metric perturbations become large at early times in the back-scaling approach, indicating a breakdown of the perturbative description. We suggest a suitable ''forwards approach' for such cases.« less
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.
From star-disc encounters to numerical solutions for a subset of the restricted three-body problem

NASA Astrophysics Data System (ADS)

Breslau, Andreas; Vincke, Kirsten; Pfalzner, Susanne

2017-03-01

Various astrophysical processes exist, where the fly-by of a massive object affects matter that is initially supported against gravity by rotation. Examples are perturbations of galaxies, protoplanetary discs, or planetary systems. We approximate such events as a subset of the restricted three-body problem by considering only perturbations of non-interacting low-mass objects that are initially on circular Keplerian orbits. In this paper, we present a new parametrisation of the initial conditions of this problem. Under certain conditions, the initial positions of the low-mass objects can be specified as being largely independent of the initial position of the perturber. In addition, exploiting the known scalings of the problem reduces the parameter space of initial conditions for one specific perturbation to two dimensions. To this two-dimensional initial condition space, we have related the final properties of the perturbed trajectories of the low-mass objects from our numerical simulations. In this way, maps showing the effect of the perturbation on the low-mass objects were created, which provide a new view on the perturbation process. Comparing the maps for different mass-ratios reveals that the perturbations by low- and high-mass perturbers are dominated by different physical processes. The equal-mass case is a complicated mixture of the other two cases. Since the final properties of trajectories with similar initial conditions are also usually similar, the results of the limited number of integrated trajectories can be generalised to the full presented parameter space by interpolation. Since our results are also unique within the accuracy strived for, they constitute general numerical solutions for this subset of the restricted three-body problem. As such, they can be used to predict the evolution of real physical problems by simple transformations, such as scaling, without further simulations. Possible applications are the perturbation of protoplanetary discs or planetary systems by the fly-by of another star. Here, the maps enable us, for example, to quantify the portion of unbound material for any periastron distance without the need for further simulations.
''Cloud in Cell'' technique applied to the roll up of vortex sheets

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

Baker, G.R.

The problem of the roll up of a two dimensional vortex sheet generated by a wing in an ideal fluid is phrased in terms of the streamfunction and the vortex sheet strength. A numerical method is used to calculate the time evolution of the vortex sheet by adapting the ''Cloud In Cell'' technique introduced in solving many particle simulations in plasma physics (see J. P. Christiansen, J. Computational Physics 13 (1973)). Two cases are considered for the initial distribution of circulation, one corresponding to an elliptically loaded wing and the other simulating the wing with a flap deployed. Results indicatemore » that small scale behaviour plays an important part in the roll up. Typically, small scale perturbations result in small structures which evolve into ever increasing larger structures by vortex amalgamation. Conclusions are given from a number of tests exploring the validity of the method. Briefly, small scale perturbations are introduced artificially by the grid; but once the process of vortex amalgamation is well underway, the emerging large scale behaviour is relatively insensitive to the precise details of the initial perturbations. Since clearly defined structures result from the application of this method, it promises to aid considerably in understanding the behaviour of vortex wakes.« less
A flyer-impact technique for measuring viscosity of metal under shock compression

NASA Astrophysics Data System (ADS)

Li, Yilei; Liu, Fusheng; Ma, Xiaojuan; Li, Yinglei; Yu, Ming; Zhang, Jichun; Jing, Fuqian

2009-01-01

A flyer-impact technique, different from the explosive method of [Sakharov et al., Sov. Phys. Dokl. 9, 1091 (1965)], is developed to investigate the viscosity of shocked metals. The shock wave with a front of sinusoidal perturbation is induced by the sinusoidal profile of the impact surface of the sample by use of two-stage light-gas gun. The oscillatory damping process of the perturbation amplitude is monitored by electric pins. Two damping curves (perturbation amplitude relative to its initial value versus propagated distance relative to the wavelength of sinusoidal perturbation) of aluminum are determined at 78 and 101 GPa. The effective shear viscosity coefficients are deduced to be about 1300 and 800 Pa s based on the Miller and Ahrens analytic solution for viscous fluid.
Optimal Damping of Perturbations of Moving Thermoelastic Panel

NASA Astrophysics Data System (ADS)

Banichuk, N. V.; Ivanova, S. Yu.

2018-01-01

The translational motion of a thermoelastic web subject to transverse vibrations caused by initial perturbations is considered. It is assumed that a web moving with a constant translational velocity is described by the model of a thermoelastic panel simply supported at its ends. The problem of optimal damping of vibrations when applying active transverse actions is formulated. For solving the optimization problem, modern methods developed in control theory for systems with distributed parameters described by partial differential equations are used.
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.
Objective quantification of perturbations produced with a piecewise PV inversion technique

NASA Astrophysics Data System (ADS)

Fita, L.; Romero, R.; Ramis, C.

2007-11-01

PV inversion techniques have been widely used in numerical studies of severe weather cases. These techniques can be applied as a way to study the sensitivity of the responsible meteorological system to changes in the initial conditions of the simulations. Dynamical effects of a collection of atmospheric features involved in the evolution of the system can be isolated. However, aspects, such as the definition of the atmospheric features or the amount of change in the initial conditions, are largely case-dependent and/or subjectively defined. An objective way to calculate the modification of the initial fields is proposed to alleviate this problem. The perturbations are quantified as the mean absolute variations of the total energy between the original and modified fields, and an unique energy variation value is fixed for all the perturbations derived from different PV anomalies. Thus, PV features of different dimensions and characteristics introduce the same net modification of the initial conditions from an energetic point of view. The devised quantification method is applied to study the high impact weather case of 9-11 November 2001 in the Western Mediterranean basin, when a deep and strong cyclone was formed. On the Balearic Islands 4 people died, and sustained winds of 30 ms-1 and precipitation higher than 200 mm/24 h were recorded. Moreover, 700 people died in Algiers during the first phase of the event. The sensitivities to perturbations in the initial conditions of a deep upper level trough, the anticyclonic system related to the North Atlantic high and the surface thermal anomaly related to the baroclinicity of the environment are determined. Results reveal a high influence of the upper level trough and the surface thermal anomaly and a minor role of the North Atlantic high during the genesis of the cyclone.
Perturbation Effects on a Supercritical C7H16/N2 Mixing Layer

NASA Technical Reports Server (NTRS)

Okongo'o, Nora; Bellan, Josette

2008-01-01

A computational-simulation study has been presented of effects of perturbation wavelengths and initial Reynolds numbers on the transition to turbulence of a heptane/nitrogen mixing layer at supercritical pressure. The governing equations for the simulations were the same as those of related prior studies reported in NASA Tech Briefs. Two-dimensional (2D) simulations were performed with initially im posed span wise perturbations whereas three-dimensional (3D) simulations had both streamwise and spanwise initial perturbations. The 2D simulations were undertaken to ascertain whether perturbations having the shortest unstable wavelength obtained from a linear stability analysis for inviscid flow are unstable in viscous nonlinear flows. The goal of the 3D simulations was to ascertain whether perturbing the mixing layer at different wavelengths affects the transition to turbulence. It was found that transitions to turbulence can be obtained at different perturbation wavelengths, provided that they are longer than the shortest unstable wavelength as determined by 2D linear stability analysis for the inviscid case and that the initial Reynolds number is proportionally increased as the wavelength is decreased. The transitional states thus obtained display different dynamic and mixture characteristics, departing strongly from the behaviors of perfect gases and ideal mixtures.
Perturbation-Induced False Starts as a Test of the Jirsa–Kelso Excitator Model

PubMed Central

Fink, Philip W.; Kelso, J. A. Scott; Jirsa, Viktor K.

2009-01-01

One difference between the excitator model and other theoretical models of coordination is the mechanism of discrete movement initiation. In addition to an imperative signal common to all discrete movement initiation, the excitator model proposes that movements are initiated when a threshold element in state space, the so-called separatrix, is crossed as a consequence of stimulation or random fluctuations. The existence of a separatrix predicts that false starts will be caused by mechanical perturbations and that they depend on the perturbation's direction. The authors tested this prediction in a reaction-time task to an auditory stimulus. Participants applied perturbations in the direction of motion (i.e., index finger flexion) or opposed to the motion prior to the stimulus on 1/4 of the trials. The authors found false starts in 34% and 9% of trials following flexion perturbations and extension perturbations, respectively, as compared with only 2% of trials without perturbations, confirming a unique prediction of the excitator model. PMID:19201685
Spatio-temporal evolution of perturbations in ensembles initialized by bred, Lyapunov and singular vectors

NASA Astrophysics Data System (ADS)

Pazó, Diego; Rodríguez, Miguel A.; López, Juan M.

2010-05-01

We study the evolution of finite perturbations in the Lorenz ‘96 model, a meteorological toy model of the atmosphere. The initial perturbations are chosen to be aligned along different dynamic vectors: bred, Lyapunov, and singular vectors. Using a particular vector determines not only the amplification rate of the perturbation but also the spatial structure of the perturbation and its stability under the evolution of the flow. The evolution of perturbations is systematically studied by means of the so-called mean-variance of logarithms diagram that provides in a very compact way the basic information to analyse the spatial structure. We discuss the corresponding advantages of using those different vectors for preparing initial perturbations to be used in ensemble prediction systems, focusing on key properties: dynamic adaptation to the flow, robustness, equivalence between members of the ensemble, etc. Among all the vectors considered here, the so-called characteristic Lyapunov vectors are possibly optimal, in the sense that they are both perfectly adapted to the flow and extremely robust.
Spatio-temporal evolution of perturbations in ensembles initialized by bred, Lyapunov and singular vectors

NASA Astrophysics Data System (ADS)

Pazó, Diego; Rodríguez, Miguel A.; López, Juan M.

2010-01-01

We study the evolution of finite perturbations in the Lorenz `96 model, a meteorological toy model of the atmosphere. The initial perturbations are chosen to be aligned along different dynamic vectors: bred, Lyapunov, and singular vectors. Using a particular vector determines not only the amplification rate of the perturbation but also the spatial structure of the perturbation and its stability under the evolution of the flow. The evolution of perturbations is systematically studied by means of the so-called mean-variance of logarithms diagram that provides in a very compact way the basic information to analyse the spatial structure. We discuss the corresponding advantages of using those different vectors for preparing initial perturbations to be used in ensemble prediction systems, focusing on key properties: dynamic adaptation to the flow, robustness, equivalence between members of the ensemble, etc. Among all the vectors considered here, the so-called characteristic Lyapunov vectors are possibly optimal, in the sense that they are both perfectly adapted to the flow and extremely robust.
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).
Creation and perturbation of planar networks of chemical oscillators

PubMed Central

Tompkins, Nathan; Cambria, Matthew Carl; Wang, Adam L.; Heymann, Michael; Fraden, Seth

2015-01-01

Methods for creating custom planar networks of diffusively coupled chemical oscillators and perturbing individual oscillators within the network are presented. The oscillators consist of the Belousov-Zhabotinsky (BZ) reaction contained in an emulsion. Networks of drops of the BZ reaction are created with either Dirichlet (constant-concentration) or Neumann (no-flux) boundary conditions in a custom planar configuration using programmable illumination for the perturbations. The differences between the observed network dynamics for each boundary condition are described. Using light, we demonstrate the ability to control the initial conditions of the network and to cause individual oscillators within the network to undergo sustained period elongation or a one-time phase delay. PMID:26117136
Parallel methodology to capture cyclic variability in motored engines

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

Ameen, Muhsin M.; Yang, Xiaofeng; Kuo, Tang-Wei

2016-07-28

Numerical prediction of of cycle-to-cycle variability (CCV) in SI engines is extremely challenging for two key reasons: (i) high-fidelity methods such as large eddy simulation (LES) are require to accurately capture the in-cylinder turbulent flowfield, and (ii) CCV is experienced over long timescales and hence the simulations need to be performed for hundreds of consecutive cycles. In this study, a new methodology is proposed to dissociate this long time-scale problem into several shorter time-scale problems, which can considerably reduce the computational time without sacrificing the fidelity of the simulations. The strategy is to perform multiple single-cycle simulations in parallel bymore » effectively perturbing the simulation parameters such as the initial and boundary conditions. It is shown that by perturbing the initial velocity field effectively based on the intensity of the in-cylinder turbulence, the mean and variance of the in-cylinder flowfield is captured reasonably well. Adding perturbations in the initial pressure field and the boundary pressure improves the predictions. It is shown that this new approach is able to give accurate predictions of the flowfield statistics in less than one-tenth of time required for the conventional approach of simulating consecutive engine cycles.« less
Over/Undervoltage and undervoltage shift of hybrid islanding detection method of distributed generation.

PubMed

Yingram, Manop; Premrudeepreechacharn, Suttichai

2015-01-01

The mainly used local islanding detection methods may be classified as active and passive methods. Passive methods do not perturb the system but they have larger nondetection zones, whereas active methods have smaller nondetection zones but they perturb the system. In this paper, a new hybrid method is proposed to solve this problem. An over/undervoltage (passive method) has been used to initiate an undervoltage shift (active method), which changes the undervoltage shift of inverter, when the passive method cannot have a clear discrimination between islanding and other events in the system. Simulation results on MATLAB/SIMULINK show that over/undervoltage and undervoltage shifts of hybrid islanding detection method are very effective because they can determine anti-islanding condition very fast. ΔP/P > 38.41% could determine anti-islanding condition within 0.04 s; ΔP/P < -24.39% could determine anti-islanding condition within 0.04 s; -24.39% ≤ ΔP/P ≤ 38.41% could determine anti-islanding condition within 0.08 s. This method perturbed the system, only in the case of -24.39% ≤ ΔP/P ≤ 38.41% at which the control system of inverter injected a signal of undervoltage shift as necessary to check if the occurrence condition was an islanding condition or not.

The effects of magnetic fields on the growth of thermal instabilities in cooling flows

NASA Technical Reports Server (NTRS)

David, Laurence P.; Bregman, Joel N.

1989-01-01

The effects of heat conduction and magnetic fields on the growth of thermal instabilities in cooling flows are examined using a time-dependent hydrodynamics code. It is found that, for magnetic field strengths of roughly 1 micro-Gauss, magnetic pressure forces can completely suppress shocks from forming in thermally unstable entropy perturbations with initial length scales as large as 20 kpc, even for initial amplitudes as great as 60 percent. Perturbations with initial amplitudes of 50 percent and initial magnetic field strengths of 1 micro-Gauss cool to 10,000 K on a time scale which is only 22 percent of the initial instantaneous cooling time. Nonlinear perturbations can thus condense out of cooling flows on a time scale substantially less than the time required for linear perturbations and produce significant mass deposition of cold gas while the accreting intracluster gas is still at large radii.
Perturbative Gaussianizing transforms for cosmological fields

NASA Astrophysics Data System (ADS)

Hall, Alex; Mead, Alexander

2018-01-01

Constraints on cosmological parameters from large-scale structure have traditionally been obtained from two-point statistics. However, non-linear structure formation renders these statistics insufficient in capturing the full information content available, necessitating the measurement of higher order moments to recover information which would otherwise be lost. We construct quantities based on non-linear and non-local transformations of weakly non-Gaussian fields that Gaussianize the full multivariate distribution at a given order in perturbation theory. Our approach does not require a model of the fields themselves and takes as input only the first few polyspectra, which could be modelled or measured from simulations or data, making our method particularly suited to observables lacking a robust perturbative description such as the weak-lensing shear. We apply our method to simulated density fields, finding a significantly reduced bispectrum and an enhanced correlation with the initial field. We demonstrate that our method reconstructs a large proportion of the linear baryon acoustic oscillations, improving the information content over the raw field by 35 per cent. We apply the transform to toy 21 cm intensity maps, showing that our method still performs well in the presence of complications such as redshift-space distortions, beam smoothing, pixel noise and foreground subtraction. We discuss how this method might provide a route to constructing a perturbative model of the fully non-Gaussian multivariate likelihood function.
Anomaly transform methods based on total energy and ocean heat content norms for generating ocean dynamic disturbances for ensemble climate forecasts

NASA Astrophysics Data System (ADS)

Romanova, Vanya; Hense, Andreas

2017-08-01

In our study we use the anomaly transform, a special case of ensemble transform method, in which a selected set of initial oceanic anomalies in space, time and variables are defined and orthogonalized. The resulting orthogonal perturbation patterns are designed such that they pick up typical balanced anomaly structures in space and time and between variables. The metric used to set up the eigen problem is taken either as the weighted total energy with its zonal, meridional kinetic and available potential energy terms having equal contributions, or the weighted ocean heat content in which a disturbance is applied only to the initial temperature fields. The choices of a reference state for defining the initial anomalies are such that either perturbations on seasonal timescales and or on interannual timescales are constructed. These project a-priori only the slow modes of the ocean physical processes, such that the disturbances grow mainly in the Western Boundary Currents, in the Antarctic Circumpolar Current and the El Nino Southern Oscillation regions. An additional set of initial conditions is designed to fit in a least square sense data from global ocean reanalysis. Applying the AT produced sets of disturbances to oceanic initial conditions initialized by observations of the MPIOM-ESM coupled model on T63L47/GR15 resolution, four ensemble and one hind-cast experiments were performed. The weighted total energy norm is used to monitor the amplitudes and rates of the fastest growing error modes. The results showed minor dependence of the instabilities or error growth on the selected metric but considerable change due to the magnitude of the scaling amplitudes of the perturbation patterns. In contrast to similar atmospheric applications, we find an energy conversion from kinetic to available potential energy, which suggests a different source of uncertainty generation in the ocean than in the atmosphere mainly associated with changes in the density field.
Adverse outcome pathways (AOPs): A framework to support predictive toxicology

EPA Science Inventory

High throughput and in silico methods are providing the regulatory toxicology community with capacity to rapidly and cost effectively generate data concerning a chemical’s ability to initiate one or more biological perturbations that may culminate in an adverse ecological o...
Isocurvature constraints and anharmonic effects on QCD axion dark matter

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

Kobayashi, Takeshi; Kurematsu, Ryosuke; Takahashi, Fuminobu, E-mail: takeshi@cita.utoronto.ca, E-mail: rkurematsu@tuhep.phys.tohoku.ac.jp, E-mail: fumi@tuhep.phys.tohoku.ac.jp

2013-09-01

We revisit the isocurvature density perturbations induced by quantum fluctuations of the axion field by extending a recently developed analytic method and approximations to a time-dependent scalar potential, which enables us to follow the evolution of the axion until it starts to oscillate. We find that, as the initial misalignment angle approaches the hilltop of the potential, the isocurvature perturbations become significantly enhanced, while the non-Gaussianity parameter increases slowly but surely. As a result, the isocurvature constraint on the inflation scale is tightened as H{sub inf}∼
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
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.
Size-guided multi-seed heuristic method for geometry optimization of clusters: Application to benzene clusters.

PubMed

Takeuchi, Hiroshi

2018-05-08

Since searching for the global minimum on the potential energy surface of a cluster is very difficult, many geometry optimization methods have been proposed, in which initial geometries are randomly generated and subsequently improved with different algorithms. In this study, a size-guided multi-seed heuristic method is developed and applied to benzene clusters. It produces initial configurations of the cluster with n molecules from the lowest-energy configurations of the cluster with n - 1 molecules (seeds). The initial geometries are further optimized with the geometrical perturbations previously used for molecular clusters. These steps are repeated until the size n satisfies a predefined one. The method locates putative global minima of benzene clusters with up to 65 molecules. The performance of the method is discussed using the computational cost, rates to locate the global minima, and energies of initial geometries. © 2018 Wiley Periodicals, Inc. © 2018 Wiley Periodicals, Inc.
Solving regularly and singularly perturbed reaction-diffusion equations in three space dimensions

NASA Astrophysics Data System (ADS)

Moore, Peter K.

2007-06-01

In [P.K. Moore, Effects of basis selection and h-refinement on error estimator reliability and solution efficiency for higher-order methods in three space dimensions, Int. J. Numer. Anal. Mod. 3 (2006) 21-51] a fixed, high-order h-refinement finite element algorithm, Href, was introduced for solving reaction-diffusion equations in three space dimensions. In this paper Href is coupled with continuation creating an automatic method for solving regularly and singularly perturbed reaction-diffusion equations. The simple quasilinear Newton solver of Moore, (2006) is replaced by the nonlinear solver NITSOL [M. Pernice, H.F. Walker, NITSOL: a Newton iterative solver for nonlinear systems, SIAM J. Sci. Comput. 19 (1998) 302-318]. Good initial guesses for the nonlinear solver are obtained using continuation in the small parameter ɛ. Two strategies allow adaptive selection of ɛ. The first depends on the rate of convergence of the nonlinear solver and the second implements backtracking in ɛ. Finally a simple method is used to select the initial ɛ. Several examples illustrate the effectiveness of the algorithm.
Adverse outcome pathways (AOPs): A framework to support predictive toxicology (presentation)

EPA Science Inventory

High throughput and in silico methods are providing the regulatory toxicology community with capacity to rapidly and cost effectively generate data concerning a chemical’s ability to initiate one or more biological perturbations that may culminate in an adverse ecological o...
The effect of cane use on the compensatory step following posterior perturbations.

PubMed

Hall, Courtney D; Jensen, Jody L

2004-08-01

The compensatory step is a critical component of the balance response and is impaired in older fallers. The purpose of this research was to examine whether utilization of a cane modified the compensatory step response following external posterior perturbations. Single subject withdrawal design was employed. Single subject statistical analysis--the standard deviation bandwidth-method--supplemented visual analysis of the data. Four older adults (range: 73-83 years) with balance impairment who habitually use a cane completed this study. Subjects received a series of sudden backward pulls that were large enough to elicit compensatory stepping. We examined the following variables both with and without cane use: timing of cane loading relative to step initiation and center of mass acceleration, stability margin, center of mass excursion and velocity, step length and width. No participant loaded the cane prior to initiation of the first compensatory step. There was no effect of cane use on the stability margin, nor was there an effect of cane use on center of mass excursion or velocity, or step length or width. These data suggest that cane use does not necessarily improve balance recovery following an external posterior perturbation when the individual is forced to rely on compensatory stepping. Instead these data suggest that the strongest factor in modifying step characteristics is experience with the perturbation.
Resonances and vibrations in an elevator cable system due to boundary sway

NASA Astrophysics Data System (ADS)

Gaiko, Nick V.; van Horssen, Wim T.

2018-06-01

In this paper, an analytical method is presented to study an initial-boundary value problem describing the transverse displacements of a vertically moving beam under boundary excitation. The length of the beam is linearly varying in time, i.e., the axial, vertical velocity of the beam is assumed to be constant. The bending stiffness of the beam is assumed to be small. This problem may be regarded as a model describing the lateral vibrations of an elevator cable excited at its boundaries by the wind-induced building sway. Slow variation of the cable length leads to a singular perturbation problem which is expressed in slowly changing, time-dependent coefficients in the governing differential equation. By providing an interior layer analysis, infinitely many resonance manifolds are detected. Further, the initial-boundary value problem is studied in detail using a three-timescales perturbation method. The constructed formal approximations of the solutions are in agreement with the numerical results.
The exact solutions and approximate analytic solutions of the (2 + 1)-dimensional KP equation based on symmetry method.

PubMed

Gai, Litao; Bilige, Sudao; Jie, Yingmo

2016-01-01

In this paper, we successfully obtained the exact solutions and the approximate analytic solutions of the (2 + 1)-dimensional KP equation based on the Lie symmetry, the extended tanh method and the homotopy perturbation method. In first part, we obtained the symmetries of the (2 + 1)-dimensional KP equation based on the Wu-differential characteristic set algorithm and reduced it. In the second part, we constructed the abundant exact travelling wave solutions by using the extended tanh method. These solutions are expressed by the hyperbolic functions, the trigonometric functions and the rational functions respectively. It should be noted that when the parameters are taken as special values, some solitary wave solutions are derived from the hyperbolic function solutions. Finally, we apply the homotopy perturbation method to obtain the approximate analytic solutions based on four kinds of initial conditions.
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.
Maximum initial growth-rate of strong-shock-driven Richtmyer-Meshkov instability

NASA Astrophysics Data System (ADS)

Abarzhi, Snezhana I.; Bhowmich, Aklant K.; Dell, Zachary R.; Pandian, Arun; Stanic, Milos; Stellingwerf, Robert F.; Swisher, Nora C.

2017-10-01

We focus on classical problem of dependence on the initial conditions of the initial growth-rate of strong shocks driven Richtmyer-Meshkov instability (RMI) by developing a novel empirical model and by employing rigorous theories and Smoothed Particle Hydrodynamics (SPH) simulations to describe the simulations data with statistical confidence in a broad parameter regime. For given values of the shock strength, fluids' density ratio, and wavelength of the initial perturbation of the fluid interface, we find the maximum value of RMI initial growth-rate, the corresponding amplitude scale of the initial perturbation, and the maximum fraction of interfacial energy. This amplitude scale is independent of the shock strength and density ratio, and is characteristic quantity of RMI dynamics. We discover the exponential decay of the ratio of the initial and linear growth-rates of RMI with the initial perturbation amplitude that excellently agrees with available data. National Science Foundation, USA.
Maximum initial growth-rate of strong-shock-driven Richtmyer-Meshkov instability

NASA Astrophysics Data System (ADS)

Abarzhi, Snezhana I.; Bhowmich, Aklant K.; Dell, Zachary R.; Pandian, Arun; Stanic, Milos; Stellingwerf, Robert F.; Swisher, Nora C.

2017-11-01

We focus on classical problem of dependence on the initial conditions of the initial growth-rate of strong shocks driven Richtmyer-Meshkov instability (RMI) by developing a novel empirical model and by employing rigorous theories and Smoothed Particle Hydrodynamics (SPH) simulations to describe the simulations data with statistical confidence in a broad parameter regime. For given values of the shock strength, fluids' density ratio, and wavelength of the initial perturbation of the fluid interface, we find the maximum value of RMI initial growth-rate, the corresponding amplitude scale of the initial perturbation, and the maximum fraction of interfacial energy. This amplitude scale is independent of the shock strength and density ratio, and is characteristic quantity of RMI dynamics. We discover the exponential decay of the ratio of the initial and linear growth-rates of RMI with the initial perturbation amplitude that excellently agrees with available data. National Science Foundation, USA.
Secure steganographic communication algorithm based on self-organizing patterns.

PubMed

Saunoriene, Loreta; Ragulskis, Minvydas

2011-11-01

A secure steganographic communication algorithm based on patterns evolving in a Beddington-de Angelis-type predator-prey model with self- and cross-diffusion is proposed in this paper. Small perturbations of initial states of the system around the state of equilibrium result in the evolution of self-organizing patterns. Small differences between initial perturbations result in slight differences also in the evolving patterns. It is shown that the generation of interpretable target patterns cannot be considered as a secure mean of communication because contours of the secret image can be retrieved from the cover image using statistical techniques if only it represents small perturbations of the initial states of the system. An alternative approach when the cover image represents the self-organizing pattern that has evolved from initial states perturbed using the dot-skeleton representation of the secret image can be considered as a safe visual communication technique protecting both the secret image and communicating parties.
Over/Undervoltage and Undervoltage Shift of Hybrid Islanding Detection Method of Distributed Generation

PubMed Central

Premrudeepreechacharn, Suttichai

2015-01-01

The mainly used local islanding detection methods may be classified as active and passive methods. Passive methods do not perturb the system but they have larger nondetection zones, whereas active methods have smaller nondetection zones but they perturb the system. In this paper, a new hybrid method is proposed to solve this problem. An over/undervoltage (passive method) has been used to initiate an undervoltage shift (active method), which changes the undervoltage shift of inverter, when the passive method cannot have a clear discrimination between islanding and other events in the system. Simulation results on MATLAB/SIMULINK show that over/undervoltage and undervoltage shifts of hybrid islanding detection method are very effective because they can determine anti-islanding condition very fast. ΔP/P > 38.41% could determine anti-islanding condition within 0.04 s; ΔP/P < −24.39% could determine anti-islanding condition within 0.04 s; −24.39% ≤ ΔP/P ≤ 38.41% could determine anti-islanding condition within 0.08 s. This method perturbed the system, only in the case of −24.39% ≤ ΔP/P ≤ 38.41% at which the control system of inverter injected a signal of undervoltage shift as necessary to check if the occurrence condition was an islanding condition or not. PMID:25879064
Initiating Molecular Growth in the Interstellar Medium via Dimeric Complexes of Observed Ions and Molecules

NASA Technical Reports Server (NTRS)

Bera, Partha P.; Head-Gordon, Martin; Lee, Timothy J.

2011-01-01

A feasible initiation step for particle growth in the interstellar medium (ISM) is simulated by means of ab quantum chemistry methods. The systems studied are dimer ions formed by pairing nitrogen containing small molecules known to exist in the ISM with ions of unsaturated hydrocarbons or vice versa. Complexation energies, structures of ensuing complexes and electronic excitation spectra of the encounter complexes are estimated using various quantum chemistry methods. Moller-Plesset perturbation theory (MP2, Z-averaged perturbation theory (ZAP2), coupled cluster singles and doubles with perturbative triples corrections (CCSD(T)), and density functional theory (DFT) methods (B3LYP) were employed along with the correlation consistent cc-pVTZ and aug-cc-pVTZ basis sets. Two types of complexes are predicted. One type of complex has electrostatic binding with moderate (7-20 kcal per mol) binding energies, that are nonetheless significantly stronger than typical van der Waals interactions between molecules of this size. The other type of complex develops strong covalent bonds between the fragments. Cyclic isomers of the nitrogen containing complexes are produced very easily by ion-molecule reactions. Some of these complexes show intense ultraviolet visible spectra for electronic transitions with large oscillator strengths at the B3LYP, omegaB97, and equations of motion coupled cluster (EOM-CCSD) levels. The open shell nitrogen containing carbonaceous complexes especially exhibit a large oscillator strength electronic transition in the visible region of the electromagnetic spectrum.
Research in navigation and optimization for space trajectories

NASA Technical Reports Server (NTRS)

Pines, S.; Kelley, H. J.

1979-01-01

Topics covered include: (1) initial Cartesian coordinates for rapid precision orbit prediction; (2) accelerating convergence in optimization methods using search routines by applying curvilinear projection ideas; (3) perturbation-magnitude control for difference-quotient estimation of derivatives; and (4) determining the accelerometer bias for in-orbit shuttle trajectories.

Dynamic range in the C. elegans brain network

NASA Astrophysics Data System (ADS)

Antonopoulos, Chris G.

2016-01-01

We study external electrical perturbations and their responses in the brain dynamic network of the Caenorhabditis elegans soil worm, given by the connectome of its large somatic nervous system. Our analysis is inspired by a realistic experiment where one stimulates externally specific parts of the brain and studies the persistent neural activity triggered in other cortical regions. In this work, we perturb groups of neurons that form communities, identified by the walktrap community detection method, by trains of stereotypical electrical Poissonian impulses and study the propagation of neural activity to other communities by measuring the corresponding dynamic ranges and Steven law exponents. We show that when one perturbs specific communities, keeping the rest unperturbed, the external stimulations are able to propagate to some of them but not to all. There are also perturbations that do not trigger any response. We found that this depends on the initially perturbed community. Finally, we relate our findings for the former cases with low neural synchronization, self-criticality, and large information flow capacity, and interpret them as the ability of the brain network to respond to external perturbations when it works at criticality and its information flow capacity becomes maximal.
Effects of Nonlinear Inhomogeneity on the Cosmic Expansion with Numerical Relativity.

PubMed

Bentivegna, Eloisa; Bruni, Marco

2016-06-24

We construct a three-dimensional, fully relativistic numerical model of a universe filled with an inhomogeneous pressureless fluid, starting from initial data that represent a perturbation of the Einstein-de Sitter model. We then measure the departure of the average expansion rate with respect to this homogeneous and isotropic reference model, comparing local quantities to the predictions of linear perturbation theory. We find that collapsing perturbations reach the turnaround point much earlier than expected from the reference spherical top-hat collapse model and that the local deviation of the expansion rate from the homogeneous one can be as high as 28% at an underdensity, for an initial density contrast of 10^{-2}. We then study, for the first time, the exact behavior of the backreaction term Q_{D}. We find that, for small values of the initial perturbations, this term exhibits a 1/a scaling, and that it is negative with a linearly growing absolute value for larger perturbation amplitudes, thereby contributing to an overall deceleration of the expansion. Its magnitude, on the other hand, remains very small even for relatively large perturbations.
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.
Robustness of controllability and observability of linear time-varying systems with application to the emergency control of power systems

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

Sastry, S. S.; Desoer, C. A.

1980-01-01

Fixed point methods from nonlinear anaysis are used to establish conditions under which the uniform complete controllability of linear time-varying systems is preserved under non-linear perturbations in the state dynamics and the zero-input uniform complete observability of linear time-varying systems is preserved under non-linear perturbation in the state dynamics and output read out map. Algorithms for computing the specific input to steer the perturbed systems from a given initial state to a given final state are also presented. As an application, a very specific emergency control of an interconnected power system is formulated as a steering problem and it ismore » shown that this emergency control is indeed possible in finite time.« less
Discovering causal pathways linking genomic events to transcriptional states using Tied Diffusion Through Interacting Events (TieDIE).

PubMed

Paull, Evan O; Carlin, Daniel E; Niepel, Mario; Sorger, Peter K; Haussler, David; Stuart, Joshua M

2013-11-01

Identifying the cellular wiring that connects genomic perturbations to transcriptional changes in cancer is essential to gain a mechanistic understanding of disease initiation, progression and ultimately to predict drug response. We have developed a method called Tied Diffusion Through Interacting Events (TieDIE) that uses a network diffusion approach to connect genomic perturbations to gene expression changes characteristic of cancer subtypes. The method computes a subnetwork of protein-protein interactions, predicted transcription factor-to-target connections and curated interactions from literature that connects genomic and transcriptomic perturbations. Application of TieDIE to The Cancer Genome Atlas and a breast cancer cell line dataset identified key signaling pathways, with examples impinging on MYC activity. Interlinking genes are predicted to correspond to essential components of cancer signaling and may provide a mechanistic explanation of tumor character and suggest subtype-specific drug targets. Software is available from the Stuart lab's wiki: https://sysbiowiki.soe.ucsc.edu/tiedie. jstuart@ucsc.edu. Supplementary data are available at Bioinformatics online.
Effects of repeated walking in a perturbing environment: a 4-day locomotor learning study.

PubMed

Blanchette, Andreanne; Moffet, Helene; Roy, Jean-Sébastien; Bouyer, Laurent J

2012-07-01

Previous studies have shown that when subjects repeatedly walk in a perturbing environment, initial movement error becomes smaller, suggesting that retention of the adapted locomotor program occurred (learning). It has been proposed that the newly learned locomotor program may be stored separately from the baseline program. However, how locomotor performance evolves with repeated sessions of walking with the perturbation is not yet known. To address this question, 10 healthy subjects walked on a treadmill on 4 consecutive days. Each day, locomotor performance was measured using kinematics and surface electromyography (EMGs), before, during, and after exposure to a perturbation, produced by an elastic tubing that pulled the foot forward and up during swing, inducing a foot velocity error in the first strides. Initial movement error decreased significantly between days 1 and 2 and then remained stable. Associated changes in medial hamstring EMG activity stabilized only on day 3, however. Aftereffects were present after perturbation removal, suggesting that daily adaptation involved central command recalibration of the baseline program. Aftereffects gradually decreased across days but were still visible on day 4. Separation between the newly learned and baseline programs may take longer than suggested by the daily improvement in initial performance in the perturbing environment or may never be complete. These results therefore suggest that reaching optimal performance in a perturbing environment should not be used as the main indicator of a completed learning process, as central reorganization of the motor commands continues days after initial performance has stabilized.
Global Solutions for the zero-energy Novikov–Veselov equation by inverse scattering

NASA Astrophysics Data System (ADS)

Music, Michael; Perry, Peter

2018-07-01

Using the inverse scattering method, we construct global solutions to the Novikov–Veselov equation for real-valued decaying initial data q 0 with the property that the associated Schrödinger operator is nonnegative. Such initial data are either critical (an arbitrarily small perturbation of the potential makes the operator nonpositive) or subcritical (sufficiently small perturbations of the potential preserve non-negativity of the operator). Previously, Lassas, Mueller, Siltanen and Stahel proved global existence for critical potentials, also called potentials of conductivity type. We extend their results to include the much larger class of subcritical potentials. We show that the subcritical potentials form an open set and that the critical potentials form the nowhere dense boundary of this open set. Our analysis draws on previous work of the first author and on ideas of Grinevich and Manakov.
The effects of obesity on balance recovery using an ankle strategy.

PubMed

Matrangola, Sara L; Madigan, Michael L

2011-06-01

Obesity is associated with an increased risk of falls. The purpose of this study was to investigate the effects of obesity on balance recovery using an ankle strategy. In addition, computer simulations to understand how increased inertia and weight associated with obesity independently influence balance recovery. Ten normal weight (BMI: 22.7±0.6 kg/m(2)) and ten obese (BMI: 32.2±2.2 kg/m(2)) adult male subjects participated in the study. Subjects recovered balance using an ankle strategy after three types of postural perturbations: an initial angular displacement, an initial angular velocity from the natural stance, and an initial angular velocity from a prescribed position. Balance recovery was quantified by the largest initial angular displacement or angular velocity from which balance could be recovered. Obesity impaired balance recovery from perturbations involving an initial angular velocity, but not from an initial angular displacement. Similarly, computer simulations determined that increased inertia is beneficial to balance recovery when there is little to no initial angular velocity. These findings indicate that the effects of obesity on balance recovery are dependent on the type of perturbation, and that increased inertia associated with obesity can be beneficial for perturbations that involve little to no initial angular velocity. Copyright © 2011 Elsevier B.V. All rights reserved.
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.
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.
Effect of a relative phase of waves constituting the initial perturbation and the wave interference on the dynamics of strong-shock-driven Richtmyer-Meshkov flows

NASA Astrophysics Data System (ADS)

Pandian, Arun; Stellingwerf, Robert F.; Abarzhi, Snezhana I.

2017-07-01

While it is a common wisdom that initial conditions influence the evolution of the Richtmyer-Meshkov instability (RMI), the research in this area is focused primarily on the effects of the wavelength and amplitude of the interface perturbation. The information has hitherto largely ignored the influences on RMI dynamics of the relative phase of waves constituting a multiwave initial perturbation and the interference of the perturbation waves. In this work we systematically study the influence of the relative phase and the interference of waves constituting a multiwave initial perturbation on a strong-shock-driven Richtmyer-Meshkov unstable interface separating ideal fluids with contrast densities. We apply group theory analysis and smoothed particle hydrodynamics numerical simulations. For verification and validation of the simulations, qualitative and quantitative comparisons are performed with rigorous zeroth-order, linear, and nonlinear theories as well as with gas dynamics experiments achieving good agreement. For a sample case of a two-wave (two-mode) initial perturbation we select the first-wave amplitude enabling the maximum initial growth rate of the RMI and we vary the second-wave amplitude from 1% to 100% of the first-wave amplitude. We also vary the relative phase of the first and second waves and consider the in-phase, the antiphase and the random-phase cases. We find that the relative phase and the interference of waves are important factors of RMI dynamics influencing qualitatively and quantitatively the symmetry, morphology, and growth rate of the Richtmyer-Meshkov unstable interface, as well as the order and disorder in strong-shock-driven RMI.
A new approach to the stability analysis of transient natural convection in porous media

NASA Astrophysics Data System (ADS)

Tilton, Nils

2016-11-01

Onset of natural convection due to transient diffusion in porous media has attracted considerable attention for its applications to CO2 sequestration. Stability analyses typically investigate onset of convection using an initial value problem approach in which a perturbation is introduced to the concentration field at an initial time t =tp . This leads to debate concerning physically appropriate perturbations, the critical time tc for linear instability, and to the counter-intuitive notion of an optimal initial time tp that maximizes perturbation growth. We propose a new approach in which transient diffusion is continuously perturbed by small variations in the porosity. With this approach, instability occurs immediately (tc = 0) without violating any physical constraints, such that the concepts of initial time tp and critical time tc have less relevance. We argue that the onset time for nonlinear convection is a more physically relevant parameter, and show that it can be predicted using a simple asymptotic expansion. Using the expansion, we consider porosity perturbations that vary sinusoidally in the horizontal and vertical directions, and show there are optimal combinations of wavelengths that minimize the onset time of nonlinear convection.
Depletion Calculations Based on Perturbations. Application to the Study of a Rep-Like Assembly at Beginning of Cycle with TRIPOLI-4®.

NASA Astrophysics Data System (ADS)

Dieudonne, Cyril; Dumonteil, Eric; Malvagi, Fausto; M'Backé Diop, Cheikh

2014-06-01

For several years, Monte Carlo burnup/depletion codes have appeared, which couple Monte Carlo codes to simulate the neutron transport to deterministic methods, which handle the medium depletion due to the neutron flux. Solving Boltzmann and Bateman equations in such a way allows to track fine 3-dimensional effects and to get rid of multi-group hypotheses done by deterministic solvers. The counterpart is the prohibitive calculation time due to the Monte Carlo solver called at each time step. In this paper we present a methodology to avoid the repetitive and time-expensive Monte Carlo simulations, and to replace them by perturbation calculations: indeed the different burnup steps may be seen as perturbations of the isotopic concentration of an initial Monte Carlo simulation. In a first time we will present this method, and provide details on the perturbative technique used, namely the correlated sampling. In a second time the implementation of this method in the TRIPOLI-4® code will be discussed, as well as the precise calculation scheme a meme to bring important speed-up of the depletion calculation. Finally, this technique will be used to calculate the depletion of a REP-like assembly, studied at beginning of its cycle. After having validated the method with a reference calculation we will show that it can speed-up by nearly an order of magnitude standard Monte-Carlo depletion codes.
Numerical solutions of nonlinear STIFF initial value problems by perturbed functional iterations

NASA Technical Reports Server (NTRS)

Dey, S. K.

1982-01-01

Numerical solution of nonlinear stiff initial value problems by a perturbed functional iterative scheme is discussed. The algorithm does not fully linearize the system and requires only the diagonal terms of the Jacobian. Some examples related to chemical kinetics are presented.
Measurement of inflight shell areal density near peak velocity using a self backlighting technique

NASA Astrophysics Data System (ADS)

Pickworth, L. A.; Hammel, B. A.; Smalyuk, V. A.; MacPhee, A. G.; Scott, H. A.; Robey, H. F.; Landen, O. L.; Barrios, M. A.; Regan, S. P.; Schneider, M. B.; Hoppe, M., Jr.; Kohut, T.; Holunga, D.; Walters, C.; Haid, B.; Dayton, M.

2016-05-01

The growth of perturbations in inertial confinement fusion (ICF) capsules can lead to significant variation of inflight shell areal density (ρR), ultimately resulting in poor compression and ablator material mixing into the hotspot. As the capsule is accelerated inward, the perturbation growth results from the initial shock-transit through the shell and then amplification by Rayleigh-Taylor as the shell accelerates inwards. Measurements of ρR perturbations near peak implosion velocity (PV) are essential to our understanding of ICF implosions because they reflect the integrity of the capsule, after the inward acceleration growth is complete, of the actual shell perturbations including native capsule surface roughness and “isolated defects”. Quantitative measurements of shell-ρR perturbations in capsules near PV are challenging, requiring a new method with which to radiograph the shell. An innovative method, utilized in this paper, is to use the self-emission from the hotspot to “self- backlight” the shell inflight. However, with nominal capsule fills there is insufficient self-emission for this method until the capsule nears peak compression (PC). We produce a sufficiently bright continuum self-emission backlighter through the addition of a high-Z gas (∼ 1% Ar) to the capsule fill. This provides a significant (∼10x) increase in emission at hυ∼8 keV over nominal fills. “Self backlit” radiographs are obtained for times when the shock is rebounding from the capsule center, expanding out to meet the incoming shell, providing a means to sample the capsule optical density though only one side, as it converges through PV.
Role of Perturbing Ocean Initial Condition in Simulated Regional Sea Level Change

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

Hu, Aixue; Meehl, Gerald; Stammer, Detlef

Multiple lines of observational evidence indicate that the global climate has been getting warmer since the early 20th century. This warmer climate has led to a global mean sea level rise of about 18 cm during the 20th century, and over 6 cm for the first 15 years of the 21st century. Regionally the sea level rise is not uniform due in large part to internal climate variability. To better serve the community, the uncertainties of predicting/projecting regional sea level changes associated with internal climate variability need to be quantified. Previous research on this topic has used single-model large ensemblesmore » with perturbed atmospheric initial conditions (ICs). Here we compare uncertainties associated with perturbing ICs in just the atmosphere and just the ocean using a state-of-the-art coupled climate model. We find that by perturbing the oceanic ICs, the uncertainties in regional sea level changes increase compared to those with perturbed atmospheric ICs. In order for us to better assess the full spectrum of the impacts of such internal climate variability on regional and global sea level rise, approaches that involve perturbing both atmospheric and oceanic initial conditions are thus necessary.« less
Role of Perturbing Ocean Initial Condition in Simulated Regional Sea Level Change

DOE PAGES

Hu, Aixue; Meehl, Gerald; Stammer, Detlef; ...

2017-06-05

Multiple lines of observational evidence indicate that the global climate has been getting warmer since the early 20th century. This warmer climate has led to a global mean sea level rise of about 18 cm during the 20th century, and over 6 cm for the first 15 years of the 21st century. Regionally the sea level rise is not uniform due in large part to internal climate variability. To better serve the community, the uncertainties of predicting/projecting regional sea level changes associated with internal climate variability need to be quantified. Previous research on this topic has used single-model large ensemblesmore » with perturbed atmospheric initial conditions (ICs). Here we compare uncertainties associated with perturbing ICs in just the atmosphere and just the ocean using a state-of-the-art coupled climate model. We find that by perturbing the oceanic ICs, the uncertainties in regional sea level changes increase compared to those with perturbed atmospheric ICs. In order for us to better assess the full spectrum of the impacts of such internal climate variability on regional and global sea level rise, approaches that involve perturbing both atmospheric and oceanic initial conditions are thus necessary.« less
Evolution of solar magnetic fields - A new approach to MHD initial-boundary value problems by the method of nearcharacteristics

NASA Technical Reports Server (NTRS)

Nakagawa, Y.

1980-01-01

A method of analysis for the MHD initial-boundary problem is presented in which the model's formulation is based on the method of nearcharacteristics developed by Werner (1968) and modified by Shin and Kot (1978). With this method, the physical causality relationship can be traced from the perturbation to the response as in the method of characteristics, while achieving the advantage of a considerable reduction in mathematical procedures. The method offers the advantage of examining not only the evolution of nonforce free fields, but also the changes of physical conditions in the atmosphere accompanying the evolution of magnetic fields. The physical validity of the method is demonstrated with examples, and their significance in interpreting observations is discussed.
Confinement with Perturbation Theory, After All?

NASA Astrophysics Data System (ADS)

Hoyer, Paul

2015-09-01

I call attention to the possibility that QCD bound states (hadrons) could be derived using rigorous Hamiltonian, perturbative methods. Solving Gauss' law for A 0 with a non-vanishing boundary condition at spatial infinity gives an linear potential for color singlet and qqq states. These states are Poincaré and gauge covariant and thus can serve as initial states of a perturbative expansion, replacing the conventional free in and out states. The coupling freezes at , allowing reasonable convergence. The bound states have a sea of pairs, while transverse gluons contribute only at . Pair creation in the linear A 0 potential leads to string breaking and hadron loop corrections. These corrections give finite widths to excited states, as required by unitarity. Several of these features have been verified analytically in D = 1 + 1 dimensions, and some in D = 3 + 1.
DOE Office of Scientific and Technical Information (OSTI.GOV)

Liu, W. H.; HEDPS and CAPT, Peking University, Beijing 100871; Wang, L. F.

In this research, the temporal evolution of the bubble tip velocity in Rayleigh-Taylor instability (RTI) at arbitrary Atwood numbers and different initial perturbation velocities with a discontinuous profile in irrotational, incompressible, and inviscid fluids (i.e., classical RTI) is investigated. Potential models from Layzer [Astrophys. J. 122, 1 (1955)] and perturbation velocity potentials from Goncharov [Phys. Rev. Lett. 88, 134502 (2002)] are introduced. It is found that the temporal evolution of bubble tip velocity [u(t)] depends essentially on the initial perturbation velocity [u(0)]. First, when the u(0)

W -Boson Production in Association with a Jet at Next-to-Next-to-Leading Order in Perturbative QCD

NASA Astrophysics Data System (ADS)

Boughezal, Radja; Focke, Christfried; Liu, Xiaohui; Petriello, Frank

2015-08-01

We present the complete calculation of W -boson production in association with a jet in hadronic collisions through next-to-next-to-leading order (NNLO) in perturbative QCD. To cancel infrared divergences, we discuss a new subtraction method that exploits the fact that the N -jettiness event-shape variable fully captures the singularity structure of QCD amplitudes with final-state partons. This method holds for processes with an arbitrary number of jets and is easily implemented into existing frameworks for higher-order calculations. We present initial phenomenological results for W +jet production at the LHC. The NNLO corrections are small and lead to a significantly reduced theoretical error, opening the door to precision measurements in the W +jet channel at the LHC.
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.
Linear perturbations in spherically symmetric dust cosmologies including a cosmological constant

NASA Astrophysics Data System (ADS)

Meyer, Sven; Bartelmann, Matthias

2017-12-01

We study the dynamical behaviour of gauge-invariant linear perturbations in spherically symmetric dust cosmologies including a cosmological constant. In contrast to spatially homogeneous FLRW models, the reduced degree of spatial symmetry causes a non-trivial dynamical coupling of gauge-invariant quantities already at first order perturbation theory and the strength and influence of this coupling on the spacetime evolution is investigated here. We present results on the underlying dynamical equations augmented by a cosmological constant and integrate them numerically. We also present a method to derive cosmologically relevant initial variables for this setup. Estimates of angular power spectra for each metric variable are computed and evaluated on the central observer's past null cone. By comparing the full evolution to the freely evolved initial profiles, the coupling strength will be determined for a best fit radially inhomogeneous patch obtained in previous works (see [1]). We find that coupling effects are not noticeable within the cosmic variance limit and can therefore safely be neglected for a relevant cosmological scenario. On the contrary, we find very strong coupling effects in a best fit spherical void model matching the distance redshift relation of SNe which is in accordance with previous findings using parametric void models.
Onset of natural convection in a continuously perturbed system

NASA Astrophysics Data System (ADS)

Ghorbani, Zohreh; Riaz, Amir

2017-11-01

The convective mixing triggered by gravitational instability plays an important role in CO2 sequestration in saline aquifers. The linear stability analysis and the numerical simulation concerning convective mixing in porous media requires perturbations of small amplitude to be imposed on the concentration field in the form of an initial shape function. In aquifers, however, the instability is triggered by local porosity and permeability. In this work, we consider a canonical 2D homogeneous system where perturbations arise due to spatial variation of porosity in the system. The advantage of this approach is not only the elimination of the required initial shape function, but it also serves as a more realistic approach. Using a reduced nonlinear method, we first explore the effect of harmonic variations of porosity in the transverse and streamwise direction on the onset time of convection and late time behavior. We then obtain the optimal porosity structure that minimizes the convection onset. We further examine the effect of a random porosity distribution, that is independent of the spatial mode of porosity structure, on the convection onset. Using high-order pseudospectral DNS, we explore how the random distribution differs from the modal approach in predicting the onset time.
High speed flow past wings

NASA Technical Reports Server (NTRS)

Norstrud, H.

1973-01-01

The analytical solution to the transonic small perturbation equation which describes steady compressible flow past finite wings at subsonic speeds can be expressed as a nonlinear integral equation with the perturbation velocity potential as the unknown function. This known formulation is substituted by a system of nonlinear algebraic equations to which various methods are applicable for its solution. Due to the presence of mathematical discontinuities in the flow solutions, however, a main computational difficulty was to ensure uniqueness of the solutions when local velocities on the wing exceeded the speed of sound. For continuous solutions this was achieved by embedding the algebraic system in an one-parameter operator homotopy in order to apply the method of parametric differentiation. The solution to the initial system of equations appears then as a solution to a Cauchy problem where the initial condition is related to the accompanying incompressible flow solution. In using this technique, however, a continuous dependence of the solution development on the initial data is lost when the solution reaches the minimum bifurcation point. A steepest descent iteration technique was therefore, added to the computational scheme for the calculation of discontinuous flow solutions. Results for purely subsonic flows and supersonic flows with and without compression shocks are given and compared with other available theoretical solutions.
A comparative study of the single-mode Richtmyer-Meshkov instability

NASA Astrophysics Data System (ADS)

Bai, X.; Deng, X.-L.; Jiang, L.

2018-07-01

In this work, the single-mode Richtmyer-Meshkov instability is studied numerically to find a reasonable nonlinear theoretical model which can be applied to predict the interface evolution from the linear stage to the early nonlinear stage. The cut-cell-based sharp-interface methods MuSiC+ (Chang et al. in J Comput Phys 242:946-990, 2013) and CCGF (Bai and Deng in Adv Appl Math Mech 9(5):1052-1075, 2017) are applied to generate numerical results for comparisons. Classical Air-SF6 and Air-Helium conditions are applied in this study, and initial amplitude and Atwood number are varied for comparison. Comparisons to the simulation results from the literature show the applicability of MuSiC+ and CCGF. Comparisons to the nonlinear theoretical models show that ZS (Zhang and Sohn in Phys Lett A 212:149-155, 1996; Phys Fluids 9:1106-1124, 1997), SEA (Sadot et al. in Phys Rev Lett 80:1654-1657, 1998), and DR (Dimonte and Ramaprabhu in Phys Fluids 22:014104, 2010) models are valid for both spike and bubble growth rates, and MIK (Mikaelian in Phys Rev E 67:026319, 2003) and ZG (Zhang and Guo in J Fluid Mech 786:47-61, 2016) models are valid for bubble growth rate, when the initial perturbation is small and the Atwood number is low, but only the DR model is applicable for both spike and bubble growth rates when the initial perturbation amplitude and the Atwood number are large. A new term of non-dimensional initial perturbation amplitude is presented and multiplied to the DR model to get a unified fitted DR model, which gives consistent results to the simulation ones for small and large initial amplitudes.
A comparative study of the single-mode Richtmyer-Meshkov instability

NASA Astrophysics Data System (ADS)

Bai, X.; Deng, X.-L.; Jiang, L.

2017-11-01

In this work, the single-mode Richtmyer-Meshkov instability is studied numerically to find a reasonable nonlinear theoretical model which can be applied to predict the interface evolution from the linear stage to the early nonlinear stage. The cut-cell-based sharp-interface methods MuSiC+ (Chang et al. in J Comput Phys 242:946-990, 2013) and CCGF (Bai and Deng in Adv Appl Math Mech 9(5):1052-1075, 2017) are applied to generate numerical results for comparisons. Classical Air-SF6 and Air-Helium conditions are applied in this study, and initial amplitude and Atwood number are varied for comparison. Comparisons to the simulation results from the literature show the applicability of MuSiC+ and CCGF. Comparisons to the nonlinear theoretical models show that ZS (Zhang and Sohn in Phys Lett A 212:149-155, 1996; Phys Fluids 9:1106-1124, 1997), SEA (Sadot et al. in Phys Rev Lett 80:1654-1657, 1998), and DR (Dimonte and Ramaprabhu in Phys Fluids 22:014104, 2010) models are valid for both spike and bubble growth rates, and MIK (Mikaelian in Phys Rev E 67:026319, 2003) and ZG (Zhang and Guo in J Fluid Mech 786:47-61, 2016) models are valid for bubble growth rate, when the initial perturbation is small and the Atwood number is low, but only the DR model is applicable for both spike and bubble growth rates when the initial perturbation amplitude and the Atwood number are large. A new term of non-dimensional initial perturbation amplitude is presented and multiplied to the DR model to get a unified fitted DR model, which gives consistent results to the simulation ones for small and large initial amplitudes.
L(2) stability for weak solutions of the Navier-Stokes equations in R(3)

NASA Astrophysics Data System (ADS)

Secchi, P.

1985-11-01

We consider the motion of a viscous fluid filling the whole space R3, governed by the classical Navier-Stokes equations (1). Existence of global (in time) regular solutions for that system of non-linear partial differential equations is still an open problem. Up to now, the only available global existence theorem (other than for sufficiently small initial data) is that of weak (turbulent) solutions. From both the mathematical and the physical point of view, an interesting property is the stability of such weak solutions. We assume that v(t,x) is a solution, with initial datum vO(x). We suppose that the initial datum is perturbed and consider one weak solution u corresponding to the new initial velocity. Then we prove that, due to viscosity, the perturbed weak solution u approaches in a suitable norm the unperturbed one, as time goes to + infinity, without smallness assumptions on the initial perturbation.
On the initial regime of pre-big bang cosmology

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

Gasperini, M., E-mail: gasperini@ba.infn.it

The production of a background of super-horizon curvature perturbations with the appropriate (red) spectrum needed to trigger the cosmic anisotropies observed on large scales is associated, in the context of pre-big bang inflation, with a phase of growing string coupling. The extension towards the past of such a phase is not limited in time by the dynamical backreaction of the quantum perturbations of the cosmological geometry and of its sources. A viable, slightly red spectrum of scalar perturbations can thus be the output of an asymptotic, perturbative regime which is well compatible with an initial string-vacuum state satisfying the postulatemore » of 'Asymptotic Past Triviality'.« less
Randomly correcting model errors in the ARPEGE-Climate v6.1 component of CNRM-CM: applications for seasonal forecasts

NASA Astrophysics Data System (ADS)

Batté, Lauriane; Déqué, Michel

2016-06-01

Stochastic methods are increasingly used in global coupled model climate forecasting systems to account for model uncertainties. In this paper, we describe in more detail the stochastic dynamics technique introduced by Batté and Déqué (2012) in the ARPEGE-Climate atmospheric model. We present new results with an updated version of CNRM-CM using ARPEGE-Climate v6.1, and show that the technique can be used both as a means of analyzing model error statistics and accounting for model inadequacies in a seasonal forecasting framework.The perturbations are designed as corrections of model drift errors estimated from a preliminary weakly nudged re-forecast run over an extended reference period of 34 boreal winter seasons. A detailed statistical analysis of these corrections is provided, and shows that they are mainly made of intra-month variance, thereby justifying their use as in-run perturbations of the model in seasonal forecasts. However, the interannual and systematic error correction terms cannot be neglected. Time correlation of the errors is limited, but some consistency is found between the errors of up to 3 consecutive days.These findings encourage us to test several settings of the random draws of perturbations in seasonal forecast mode. Perturbations are drawn randomly but consistently for all three prognostic variables perturbed. We explore the impact of using monthly mean perturbations throughout a given forecast month in a first ensemble re-forecast (SMM, for stochastic monthly means), and test the use of 5-day sequences of perturbations in a second ensemble re-forecast (S5D, for stochastic 5-day sequences). Both experiments are compared in the light of a REF reference ensemble with initial perturbations only. Results in terms of forecast quality are contrasted depending on the region and variable of interest, but very few areas exhibit a clear degradation of forecasting skill with the introduction of stochastic dynamics. We highlight some positive impacts of the method, mainly on Northern Hemisphere extra-tropics. The 500 hPa geopotential height bias is reduced, and improvements project onto the representation of North Atlantic weather regimes. A modest impact on ensemble spread is found over most regions, which suggests that this method could be complemented by other stochastic perturbation techniques in seasonal forecasting mode.
Initial contact guidance during cell spreading is contractility-independent.

PubMed

Sales, Adrià; Holle, Andrew W; Kemkemer, Ralf

2017-08-02

A wide variety of cell types exhibit substrate topography-based behavior, also known as contact guidance. However, the precise cellular mechanisms underlying this process are still unknown. In this study, we investigated contact guidance by studying the reaction of human endothelial cells (ECs) to well-defined microgroove topographies, both during and after initial cell spreading. As the cytoskeleton plays a major role in cellular adaptation to topographical features, two methods were used to perturb cytoskeletal structures. Inhibition of actomyosin contractility with the chemical inhibitor blebbistatatin demonstrated that initial contact guidance events are independent of traction force generation. However, cell alignment to the grooved substrate was altered at later time points, suggesting an initial 'passive' phase of contact guidance, followed by a contractility-dependent 'active' phase that relies on mechanosensitive feedback. The actin cytoskeleton was also perturbed in an indirect manner by culturing cells upside down, resulting in decreased levels of contact guidance and suggesting that a possible loss of contact between the actin cytoskeleton and the substrate could lead to cytoskeleton impairment. The process of contact guidance at the microscale was found to be primarily lamellipodia driven, as no bias in filopodia extension was observed on micron-scale grooves.
The effects of forced small-wavelength, finite-bandwidth initial perturbations and miscibility on the turbulent Rayleigh–Taylor instability

DOE PAGES

Roberts, M. S.; Jacobs, J. W.

2015-12-07

Rayleigh–Taylor instability experiments are performed using both immiscible and miscible incompressible liquid combinations having a relatively large Atwood number ofmore » $$A\\equiv ({\\it\\rho}_{2}-{\\it\\rho}_{1})/({\\it\\rho}_{2}+{\\it\\rho}_{1})=0.48$$. The liquid-filled tank is attached to a test sled that is accelerated downwards along a vertical rail system using a system of weights and pulleys producing approximately$1g$$net acceleration. The tank is backlit and images are digitally recorded using a high-speed video camera. The experiments are either initiated with forced initial perturbations or are left unforced. The forced experiments have an initial perturbation imposed by vertically oscillating the liquid-filled tank to produce Faraday waves at the interface. The unforced experiments rely on random interfacial fluctuations, resulting from background noise, to seed the instability. The main focus of this study is to determine the effects of forced initial perturbations and the effects of miscibility on the growth parameter,$${\\it\\alpha}$$. Measurements of the mixing-layer width,$$h$$, are acquired, from which$${\\it\\alpha}$$is determined. It is found that initial perturbations of the form used in this study do not affect measured$${\\it\\alpha}$$values. However, miscibility is observed to strongly affect$${\\it\\alpha}$$, resulting in a factor of two reduction in its value, a finding not previously observed in past experiments. In addition, all measured$${\\it\\alpha}$values are found to be smaller than those obtained in previous experimental studies.« less
Interrogating the Escherichia coli cell cycle by cell dimension perturbations

PubMed Central

Zheng, Hai; Ho, Po-Yi; Jiang, Meiling; Tang, Bin; Liu, Weirong; Li, Dengjin; Yu, Xuefeng; Kleckner, Nancy E.; Amir, Ariel; Liu, Chenli

2016-01-01

Bacteria tightly regulate and coordinate the various events in their cell cycles to duplicate themselves accurately and to control their cell sizes. Growth of Escherichia coli, in particular, follows a relation known as Schaechter’s growth law. This law says that the average cell volume scales exponentially with growth rate, with a scaling exponent equal to the time from initiation of a round of DNA replication to the cell division at which the corresponding sister chromosomes segregate. Here, we sought to test the robustness of the growth law to systematic perturbations in cell dimensions achieved by varying the expression levels of mreB and ftsZ. We found that decreasing the mreB level resulted in increased cell width, with little change in cell length, whereas decreasing the ftsZ level resulted in increased cell length. Furthermore, the time from replication termination to cell division increased with the perturbed dimension in both cases. Moreover, the growth law remained valid over a range of growth conditions and dimension perturbations. The growth law can be quantitatively interpreted as a consequence of a tight coupling of cell division to replication initiation. Thus, its robustness to perturbations in cell dimensions strongly supports models in which the timing of replication initiation governs that of cell division, and cell volume is the key phenomenological variable governing the timing of replication initiation. These conclusions are discussed in the context of our recently proposed “adder-per-origin” model, in which cells add a constant volume per origin between initiations and divide a constant time after initiation. PMID:27956612
Interrogating the Escherichia coli cell cycle by cell dimension perturbations.

PubMed

Zheng, Hai; Ho, Po-Yi; Jiang, Meiling; Tang, Bin; Liu, Weirong; Li, Dengjin; Yu, Xuefeng; Kleckner, Nancy E; Amir, Ariel; Liu, Chenli

2016-12-27

Bacteria tightly regulate and coordinate the various events in their cell cycles to duplicate themselves accurately and to control their cell sizes. Growth of Escherichia coli, in particular, follows a relation known as Schaechter's growth law. This law says that the average cell volume scales exponentially with growth rate, with a scaling exponent equal to the time from initiation of a round of DNA replication to the cell division at which the corresponding sister chromosomes segregate. Here, we sought to test the robustness of the growth law to systematic perturbations in cell dimensions achieved by varying the expression levels of mreB and ftsZ We found that decreasing the mreB level resulted in increased cell width, with little change in cell length, whereas decreasing the ftsZ level resulted in increased cell length. Furthermore, the time from replication termination to cell division increased with the perturbed dimension in both cases. Moreover, the growth law remained valid over a range of growth conditions and dimension perturbations. The growth law can be quantitatively interpreted as a consequence of a tight coupling of cell division to replication initiation. Thus, its robustness to perturbations in cell dimensions strongly supports models in which the timing of replication initiation governs that of cell division, and cell volume is the key phenomenological variable governing the timing of replication initiation. These conclusions are discussed in the context of our recently proposed "adder-per-origin" model, in which cells add a constant volume per origin between initiations and divide a constant time after initiation.
The ZH ratio method for long-period seismic data: inversion for S-wave velocity structure

NASA Astrophysics Data System (ADS)

Yano, Tomoko; Tanimoto, T.; Rivera, L.

2009-10-01

The particle motion of surface waves, in addition to phase and group velocities, can provide useful information for S-wave velocity structure in the crust and upper mantle. In this study, we applied a new method to retrieve velocity structure using the ZH ratio, the ratio between vertical and horizontal surface amplitudes of Rayleigh waves. Analysing data from the GEOSCOPE network, we measured the ZH ratios for frequencies between 0.004 and 0.05 Hz (period between 20 and 250s) and inverted them for S-wave velocity structure beneath each station. Our analysis showed that the resolving power of the ZH ratio is limited and final solutions display dependence on starting models; in particular, the depth of the Moho in the starting model is important in order to get reliable results. Thus, initial models for the inversion need to be carefully constructed. We chose PREM and CRUST2.0 in this study as a starting model for all but one station (ECH). The eigenvalue analysis of the least-squares problem that arises for each step of the iterative process shows a few dominant eigenvalues which explains the cause of the inversion's initial-model dependence. However, the ZH ratio is unique in having high sensitivity to near-surface structure and thus provides complementary information to phase and group velocities. Application of this method to GEOSCOPE data suggest that low velocity zones may exist beneath some stations near hotspots. Our tests with different starting models show that the models with low-velocity anomalies fit better to the ZH ratio data. Such low velocity zones are seen near Hawaii (station KIP), Crozet Island (CRZF) and Djibuti (ATD) but not near Reunion Island (RER). It is also found near Echery (ECH) which is in a geothermal area. However, this method has a tendency to produce spurious low velocity zones and resolution of the low velocity zones requires further careful study. We also performed simultaneous inversions for volumetric perturbation and discontinuity-depth perturbation. While its formulation and inversion were straightforward, there seemed to be a difficult trade-off problem between volumetric perturbation and discontinuity-depth perturbation.
Turbulence and mixing from optimal perturbations to a stratified shear layer

NASA Astrophysics Data System (ADS)

Kaminski, Alexis; Caulfield, C. P.; Taylor, John

2014-11-01

The stability and mixing of stratified shear layers is a canonical problem in fluid dynamics with relevance to flows in the ocean and atmosphere. The Miles-Howard theorem states that a necessary condition for normal-mode instability in parallel, inviscid, steady stratified shear flows is that the gradient Richardson number, Rig is less than 1/4 somewhere in the flow. However, substantial transient growth of non-normal modes may be possible at finite times even when Rig > 1 / 4 everywhere in the flow. We have calculated the ``optimal perturbations'' associated with maximum perturbation energy gain for a stably-stratified shear layer. These optimal perturbations are then used to initialize direct numerical simulations. For small but finite perturbation amplitudes, the optimal perturbations grow at the predicted linear rate initially, but then experience sufficient transient growth to become nonlinear and susceptible to secondary instabilities, which then break down into turbulence. Remarkably, this occurs even in flows for which Rig > 1 / 4 everywhere. We will describe the nonlinear evolution of the optimal perturbations and characterize the resulting turbulence and mixing.
Reliability of functional and predictive methods to estimate the hip joint centre in human motion analysis in healthy adults.

PubMed

Kainz, Hans; Hajek, Martin; Modenese, Luca; Saxby, David J; Lloyd, David G; Carty, Christopher P

2017-03-01

In human motion analysis predictive or functional methods are used to estimate the location of the hip joint centre (HJC). It has been shown that the Harrington regression equations (HRE) and geometric sphere fit (GSF) method are the most accurate predictive and functional methods, respectively. To date, the comparative reliability of both approaches has not been assessed. The aims of this study were to (1) compare the reliability of the HRE and the GSF methods, (2) analyse the impact of the number of thigh markers used in the GSF method on the reliability, (3) evaluate how alterations to the movements that comprise the functional trials impact HJC estimations using the GSF method, and (4) assess the influence of the initial guess in the GSF method on the HJC estimation. Fourteen healthy adults were tested on two occasions using a three-dimensional motion capturing system. Skin surface marker positions were acquired while participants performed quite stance, perturbed and non-perturbed functional trials, and walking trials. Results showed that the HRE were more reliable in locating the HJC than the GSF method. However, comparison of inter-session hip kinematics during gait did not show any significant difference between the approaches. Different initial guesses in the GSF method did not result in significant differences in the final HJC location. The GSF method was sensitive to the functional trial performance and therefore it is important to standardize the functional trial performance to ensure a repeatable estimate of the HJC when using the GSF method. Copyright © 2017 Elsevier B.V. All rights reserved.
Subcritical transition scenarios via linear and nonlinear localized optimal perturbations in plane Poiseuille flow

NASA Astrophysics Data System (ADS)

Farano, Mirko; Cherubini, Stefania; Robinet, Jean-Christophe; De Palma, Pietro

2016-12-01

Subcritical transition in plane Poiseuille flow is investigated by means of a Lagrange-multiplier direct-adjoint optimization procedure with the aim of finding localized three-dimensional perturbations optimally growing in a given time interval (target time). Space localization of these optimal perturbations (OPs) is achieved by choosing as objective function either a p-norm (with p\\gg 1) of the perturbation energy density in a linear framework; or the classical (1-norm) perturbation energy, including nonlinear effects. This work aims at analyzing the structure of linear and nonlinear localized OPs for Poiseuille flow, and comparing their transition thresholds and scenarios. The nonlinear optimization approach provides three types of solutions: a weakly nonlinear, a hairpin-like and a highly nonlinear optimal perturbation, depending on the value of the initial energy and the target time. The former shows localization only in the wall-normal direction, whereas the latter appears much more localized and breaks the spanwise symmetry found at lower target times. Both solutions show spanwise inclined vortices and large values of the streamwise component of velocity already at the initial time. On the other hand, p-norm optimal perturbations, although being strongly localized in space, keep a shape similar to linear 1-norm optimal perturbations, showing streamwise-aligned vortices characterized by low values of the streamwise velocity component. When used for initializing direct numerical simulations, in most of the cases nonlinear OPs provide the most efficient route to transition in terms of time to transition and initial energy, even when they are less localized in space than the p-norm OP. The p-norm OP follows a transition path similar to the oblique transition scenario, with slightly oscillating streaks which saturate and eventually experience secondary instability. On the other hand, the nonlinear OP rapidly forms large-amplitude bent streaks and skips the phases of streak saturation, providing a contemporary growth of all of the velocity components due to strong nonlinear coupling.
Stepping responses to treadmill perturbations vary with severity of motor deficits in human SCI.

PubMed

Chu, Virginia Way Tong; Hornby, T George; Schmit, Brian D

2018-04-18

In this study, we investigated the responses to tread perturbations during human stepping on a treadmill. Our approach was to test the effects of perturbations to a single leg using a split-belt treadmill in healthy participants and in participants with varying severity of spinal cord injury (SCI). We recruited 11 people with incomplete SCI and 5 noninjured participants. As participants walked on an instrumented treadmill, the belt on one side was stopped or accelerated briefly during mid to late stance. A majority of participants initiated an unnecessary swing when the treadmill was stopped in mid stance, although the likelihood of initiating a step was decreased in participants with more severe SCI. Accelerating or decelerating one belt of the treadmill during stance altered the characteristics of swing. We observed delayed swing initiation when the belt was decelerated (i.e. the hip was in a more flexed position at time of swing) and advanced swing initiation with acceleration (i.e. hip extended at swing initiation). Further, the timing and leg posture of heel strike appeared to remain constant, reflected by a sagittal plane hip angle at heel strike that remained the same regardless of the perturbation. In summary, our results supported the current understanding of the role of sensory feedback and central drive in the control of stepping in participants with incomplete SCI and noninjured participants. In particular, the observation of unnecessary swing during a stop perturbation highlights the interdependence of central and sensory drive in walking control.
A study of numerical methods for computing reentry trajectories for shuttle-type space vehicles

NASA Technical Reports Server (NTRS)

1972-01-01

The reuseable exterior insulation system (REI) is studied to determine the optimal reentry trajectory for a space shuttle, which minimizes the heat input to the fuselage. The REI is composed of titanium, covered by a surface insulation material. The method of perturbation functions was used to generate the trajectories, and proved to be an effective technique for generating families of solutions, once an initial trajectory has been obtained.

Climateprediction.com: Public Involvement, Multi-Million Member Ensembles and Systematic Uncertainty Analysis

NASA Astrophysics Data System (ADS)

Stainforth, D. A.; Allen, M.; Kettleborough, J.; Collins, M.; Heaps, A.; Stott, P.; Wehner, M.

2001-12-01

The climateprediction.com project is preparing to carry out the first systematic uncertainty analysis of climate forecasts using large ensembles of GCM climate simulations. This will be done by involving schools, businesses and members of the public, and utilizing the novel technology of distributed computing. Each participant will be asked to run one member of the ensemble on their PC. The model used will initially be the UK Met Office's Unified Model (UM). It will be run under Windows and software will be provided to enable those involved to view their model output as it develops. The project will use this method to carry out large perturbed physics GCM ensembles and thereby analyse the uncertainty in the forecasts from such models. Each participant/ensemble member will therefore have a version of the UM in which certain aspects of the model physics have been perturbed from their default values. Of course the non-linear nature of the system means that it will be necessary to look not just at perturbations to individual parameters in specific schemes, such as the cloud parameterization, but also to the many combinations of perturbations. This rapidly leads to the need for very large, perhaps multi-million member ensembles, which could only be undertaken using the distributed computing methodology. The status of the project will be presented and the Windows client will be demonstrated. In addition, initial results will be presented from beta test runs using a demo release for Linux PCs and Alpha workstations. Although small by comparison to the whole project, these pilot results constitute a 20-50 member perturbed physics climate ensemble with results indicating how climate sensitivity can be substantially affected by individual parameter values in the cloud scheme.
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.
A method to simulate motor control strategies to recover from perturbations: application to a stumble recovery during gait.

PubMed

Forner-Cordero, Arturo; Ackermann, Marko; de Lima Freitas, Mateus

2011-01-01

Perturbations during human gait such as a trip or a slip can result in a fall, especially among frail populations such as the elderly. In order to recover from a trip or a stumble during gait, humans perform different types of recovery strategies. It is very useful to uncover the mechanisms of the recovery to improve training methods for populations at risk of falling. Moreover, human recovery strategies could be applied to implement controllers for bipedal robot walker, as an application of biomimetic design. A biomechanical model of the response to a trip during gait might uncover the control mechanisms underlying the different recovery strategies and the adaptation of the responses found during the execution of successive perturbation trials. This paper introduces a model of stumble in the multibody system framework. This model is used to assess different feedforward strategies to recover from a trip. First of all, normal gait patterns for the musculoskeletal system model are obtained by solving an optimal control problem. Secondly, the reference gait is perturbed by the application of forces on the swinging foot in different ways: as an instantaneous inelastic collision of the foot with an obstacle, as an impulsive horizontal force or using a force curve measured experimentally during gait perturbation experiments. The influence of the type of perturbation, the timing of the collision with respect to the gait cycle, as well as of the coefficient of restitution was investigated previously. Finally, in order to test the effects of different muscle excitation levels on the initial phases of the recovery response, several muscle excitations were added to selected muscles of the legs, thus providing a simulation of the recovery reactions. These results pave the way for future analysis and modeling of the control mechanisms of gait.
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.
Concept of Tone in Mandarin Revisited: A Perceptual Study on Tonal Coarticulation.

ERIC Educational Resources Information Center

Shen, Xiaonan Susan; Lin, Maocan

1991-01-01

Examination of the perceptibility of carryover coarticulatory perturbations occurring at syllabic vowels in Mandarin Chinese suggests that, in connected speech, a portion of fundamental frequency at intertonemic onset is perturbed, including initial voiced consonants and vowels, and that the perturbations result from preservative as well as…
Study of the Motion of an Anharmonic Oscillator Under the Action of a Sinusoidal Force, of Variable Frequency, near the Principal Resonance; ETUDE DU MOVEMENT D'UN OSCILLATEUR ANHARMONIQUE SOUS L'ACTION D'UNE FORCE SINUSOIDALE, DE FREQUENCE VARIABLE, AU VOISINAGE DE LA RESONANCE PRINCIPALE

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

Barbier, M.; Robouch, B.V.

1959-11-01

A study of non-linear oscillators is described which made possible the establishment of the space distribution of phases at the resonance of points corresronding to a given amplitude remote from this resonance and for a deviation direction of given frequency. An atlas of curves dyfining these; distributions for different initial amplitudes and perturbations was obtained. An evaluation was made dyviation direction of given frequency. An atlas of curves dyfining these distributions for different initial amplitudes and perturbations was obtained. An evaluation was made of the beam fraction whose oscillation amplitude does not exceed the initial amplitude after undergoing perturbation inmore » the course of a given passage. It was supposed that in all the calculations there was a uniform particle distribution in the phase-space before application of the perturbation and that the first approximation o; the Liouville theorem was valid ior the area of the contours which in fact do not correspond to a movement of the arrangement itself the results are presented graphically. The beam fraction susceptible to entrainment beginning with the resonance was studied as a function of the perturbation for different dimensions of the initial beam. (T.R.H.)« less
Harmonic growth of spherical Rayleigh-Taylor instability in weakly nonlinear regime

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

Liu, Wanhai; LHD, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190; Chen, Yulian

Harmonic growth in classical Rayleigh-Taylor instability (RTI) on a spherical interface is analytically investigated using the method of the parameter expansion up to the third order. Our results show that the amplitudes of the first four harmonics will recover those in planar RTI as the interface radius tends to infinity compared against the initial perturbation wavelength. The initial radius dramatically influences the harmonic development. The appearance of the second-order feedback to the initial unperturbed interface (i.e., the zeroth harmonic) makes the interface move towards the spherical center. For these four harmonics, the smaller the initial radius is, the faster theymore » grow.« less
Anomaly-free cosmological perturbations in effective canonical quantum gravity

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

Barrau, Aurelien; Bojowald, Martin; Kagan, Mikhail

2015-05-01

This article lays out a complete framework for an effective theory of cosmological perturbations with corrections from canonical quantum gravity. Since several examples exist for quantum-gravity effects that change the structure of space-time, the classical perturbative treatment must be rethought carefully. The present discussion provides a unified picture of several previous works, together with new treatments of higher-order perturbations and the specification of initial states.
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.
The growth of aspherical structure in the universe - Is the Local Supercluster an unusual system

NASA Technical Reports Server (NTRS)

White, S. D. M.; Silk, J.

1979-01-01

The growth and subsequent collapse of homogeneous ellipsoidal perturbations in a uniform expanding background is considered as a simple model for the formation of large-scale aspherical structures in the observed universe. Numerical calculations of the evolution of such perturbations turn out to be well described by an approximate analytic solution of the equations of motion, and simple relationships are found between the initial shape of a perturbation and its shape and kinematic properties at the time of collapse. Perturbations do not change their shape significantly until they reach a density contrast of order unity. As a result, structures with the kinematic properties of the Local Supercluster should form much more commonly in a low-density universe than in a flat universe. The homogeneity of the local Hubble flow, the motion of the Milky Way with respect to the microwave background, and the flattening of the Local Supercluster can be successfully accounted for by these models, provided that the initial perturbation is sufficiently flattened. Viable models are obtained only if the ratio of the lengths of the two smaller axes of the initial perturbation is at least 3:1 in an Einstein-de Sitter universe or at least 1.8:1 in a universe for which the density parameter (Omega) is of order 0.1, when the protocluster pancakes.
Sensory and motoric influences on attention dynamics during standing balance recovery in young and older adults.

PubMed

Redfern, Mark S; Chambers, April J; Jennings, J Richard; Furman, Joseph M

2017-08-01

This study investigated the impact of attention on the sensory and motor actions during postural recovery from underfoot perturbations in young and older adults. A dual-task paradigm was used involving disjunctive and choice reaction time (RT) tasks to auditory and visual stimuli at different delays from the onset of two types of platform perturbations (rotations and translations). The RTs were increased prior to the perturbation (preparation phase) and during the immediate recovery response (response initiation) in young and older adults, but this interference dissipated rapidly after the perturbation response was initiated (<220 ms). The sensory modality of the RT task impacted the results with interference being greater for the auditory task compared to the visual task. As motor complexity of the RT task increased (disjunctive versus choice) there was greater interference from the perturbation. Finally, increasing the complexity of the postural perturbation by mixing the rotational and translational perturbations together increased interference for the auditory RT tasks, but did not affect the visual RT responses. These results suggest that sensory and motoric components of postural control are under the influence of different dynamic attentional processes.
Towards the prediction of multiple necking during dynamic extension of round bar : linear stability approach versus finite element calculations

NASA Astrophysics Data System (ADS)

El Maï, S.; Mercier, S.; Petit, J.; Molinari, A.

2014-05-01

The fragmentation of structures subject to dynamic conditions is a matter of interest for civil industries as well as for Defence institutions. Dynamic expansions of structures, such as cylinders or rings, have been performed to obtain crucial information on fragment distributions. Many authors have proposed to capture by FEA the experimental distribution of fragment size by introducing in the FE model a perturbation. Stability and bifurcation analyses have also been proposed to describe the evolution of the perturbation growth rate. In the proposed contribution, the multiple necking of a round bar in dynamic tensile loading is analysed by the FE method. A perturbation on the initial flow stress is introduced in the numerical model to trigger instabilities. The onset time and the dominant mode of necking have been characterized precisely and showed power law evolutions, with the loading velocities and moderately with the amplitudes and the cell sizes of the perturbations. In the second part of the paper, the development of linear stability analysis and the use of salient criteria in terms of the growth rate of perturbations enabled comparisons with the numerical results. A good correlation in terms of onset time of instabilities and of number of necks is shown.
Testing higher-order Lagrangian perturbation theory against numerical simulation. 1: Pancake models

NASA Technical Reports Server (NTRS)

Buchert, T.; Melott, A. L.; Weiss, A. G.

1993-01-01

We present results showing an improvement of the accuracy of perturbation theory as applied to cosmological structure formation for a useful range of quasi-linear scales. The Lagrangian theory of gravitational instability of an Einstein-de Sitter dust cosmogony investigated and solved up to the third order is compared with numerical simulations. In this paper we study the dynamics of pancake models as a first step. In previous work the accuracy of several analytical approximations for the modeling of large-scale structure in the mildly non-linear regime was analyzed in the same way, allowing for direct comparison of the accuracy of various approximations. In particular, the Zel'dovich approximation (hereafter ZA) as a subclass of the first-order Lagrangian perturbation solutions was found to provide an excellent approximation to the density field in the mildly non-linear regime (i.e. up to a linear r.m.s. density contrast of sigma is approximately 2). The performance of ZA in hierarchical clustering models can be greatly improved by truncating the initial power spectrum (smoothing the initial data). We here explore whether this approximation can be further improved with higher-order corrections in the displacement mapping from homogeneity. We study a single pancake model (truncated power-spectrum with power-spectrum with power-index n = -1) using cross-correlation statistics employed in previous work. We found that for all statistical methods used the higher-order corrections improve the results obtained for the first-order solution up to the stage when sigma (linear theory) is approximately 1. While this improvement can be seen for all spatial scales, later stages retain this feature only above a certain scale which is increasing with time. However, third-order is not much improvement over second-order at any stage. The total breakdown of the perturbation approach is observed at the stage, where sigma (linear theory) is approximately 2, which corresponds to the onset of hierarchical clustering. This success is found at a considerable higher non-linearity than is usual for perturbation theory. Whether a truncation of the initial power-spectrum in hierarchical models retains this improvement will be analyzed in a forthcoming work.
A Study of the Unstable Modes in High Mach Number Gaseous Jets and Shear Layers

NASA Astrophysics Data System (ADS)

Bassett, Gene Marcel

1993-01-01

Instabilities affecting the propagation of supersonic gaseous jets have been studied using high resolution computer simulations with the Piecewise-Parabolic-Method (PPM). These results are discussed in relation to jets from galactic nuclei. These studies involve a detailed treatment of a single section of a very long jet, approximating the dynamics by using periodic boundary conditions. Shear layer simulations have explored the effects of shear layers on the growth of nonlinear instabilities. Convergence of the numerical approximations has been tested by comparing jet simulations with different grid resolutions. The effects of initial conditions and geometry on the dominant disruptive instabilities have also been explored. Simulations of shear layers with a variety of thicknesses, Mach numbers and densities perturbed by incident sound waves imply that the time for the excited kink modes to grow large in amplitude and disrupt the shear layer is taug = (546 +/- 24) (M/4)^{1.7 } (Apert/0.02) ^{-0.4} delta/c, where M is the jet Mach number, delta is the half-width of the shear layer, and A_ {pert} is the perturbation amplitude. For simulations of periodic jets, the initial velocity perturbations set up zig-zag shock patterns inside the jet. In each case a single zig-zag shock pattern (an odd mode) or a double zig-zag shock pattern (an even mode) grows to dominate the flow. The dominant kink instability responsible for these shock patterns moves approximately at the linear resonance velocity, nu_ {mode} = cextnu_ {relative}/(cjet + c_ {ext}). For high resolution simulations (those with 150 or more computational zones across the jet width), the even mode dominates if the even penetration is higher in amplitude initially than the odd perturbation. For low resolution simulations, the odd mode dominates even for a stronger even mode perturbation. In high resolution simulations the jet boundary rolls up and large amounts of external gas are entrained into the jet. In low resolution simulations this entrainment process is impeded by numerical viscosity. The three-dimensional jet simulations behave similarly to two-dimensional jet runs with the same grid resolutions.
Spherical collapse and virialization in f ( T ) gravities

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

Lin, Rui-Hui; Zhai, Xiang-Hua; Li, Xin-Zhou, E-mail: 1000379711@smail.shnu.edu.cn, E-mail: zhaixh@shnu.edu.cn, E-mail: kychz@shnu.edu.cn

2017-03-01

Using the classical top-hat profile, we study the non-linear growth of spherically symmetric density perturbation and structure formation in f ( T ) gravities. In particular, three concrete models, which have been tested against the observation of large-scale evolution and linear perturbation of the universe in the cosmological scenario, are investigated in this framework, covering both minimal and nonminimal coupling cases of f ( T ) gravities. Moreover, we consider the virialization of the overdense region in the models after they detach from the background expanding universe and turn around to collapse. We find that there are constraints in themore » magnitude and occurring epoch of the initial perturbation. The existence of these constraints indicates that a perturbation that is too weak or occurs too late will not be able to stop the expanding of the overdense region. The illustration of the evolution of the perturbation shows that in f ( T ) gravities, the initial perturbation within the constraints can eventually lead to clustering and form structure. The evolution also shows that nonminimal coupling models collapse slower than the minimal coupling one.« less
Influence of asymmetric magnetic perturbation on the nonlinear evolution of double tearing modes

NASA Astrophysics Data System (ADS)

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

2017-06-01

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

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

Mazuet, Charles; Volkov, Mikhail S.; Mukohyama, Shinji, E-mail: charles.mazuet@lmpt.univ-tours.fr, E-mail: shinji.mukohyama@yukawa.kyoto-u.ac.jp, E-mail: volkov@lmpt.univ-tours.fr

We combine analytical and numerical methods to study anisotropic deformations of the spatially open homogeneous and isotropic cosmology in the ghost free massive gravity theory with flat reference metric. We find that if the initial perturbations are not too strong then the physical metric relaxes back to the isotropic de Sitter state. However, the dumping of the anisotropies is achieved at the expense of exciting the Stueckelberg fields in such a way that the reference metric changes and does not share anymore with the physical metric the same rotational and translational symmetries. As a result, the universe evolves towards amore » fixed point which does not coincide with the original solution, but for which the physical metric is still de Sitter. If the initial perturbation is strong, then its evolution generically leads to a singular anisotropic state or, for some parameter values, to a decay into flat spacetime. We also present an infinite dimensional family of new homogeneous and isotropic cosmologies in the theory.« less

Quasi-most unstable modes: a window to 'À la carte' ensemble diversity?

NASA Astrophysics Data System (ADS)

Homar Santaner, Victor; Stensrud, David J.

2010-05-01

The atmospheric scientific community is nowadays facing the ambitious challenge of providing useful forecasts of atmospheric events that produce high societal impact. The low level of social resilience to false alarms creates tremendous pressure on forecasting offices to issue accurate, timely and reliable warnings.Currently, no operational numerical forecasting system is able to respond to the societal demand for high-resolution (in time and space) predictions in the 12-72h time span. The main reasons for such deficiencies are the lack of adequate observations and the high non-linearity of the numerical models that are currently used. The whole weather forecasting problem is intrinsically probabilistic and current methods aim at coping with the various sources of uncertainties and the error propagation throughout the forecasting system. This probabilistic perspective is often created by generating ensembles of deterministic predictions that are aimed at sampling the most important sources of uncertainty in the forecasting system. The ensemble generation/sampling strategy is a crucial aspect of their performance and various methods have been proposed. Although global forecasting offices have been using ensembles of perturbed initial conditions for medium-range operational forecasts since 1994, no consensus exists regarding the optimum sampling strategy for high resolution short-range ensemble forecasts. Bred vectors, however, have been hypothesized to better capture the growing modes in the highly nonlinear mesoscale dynamics of severe episodes than singular vectors or observation perturbations. Yet even this technique is not able to produce enough diversity in the ensembles to accurately and routinely predict extreme phenomena such as severe weather. Thus, we propose a new method to generate ensembles of initial conditions perturbations that is based on the breeding technique. Given a standard bred mode, a set of customized perturbations is derived with specified amplitudes and horizontal scales. This allows the ensemble to excite growing modes across a wider range of scales. Results show that this approach produces significantly more spread in the ensemble prediction than standard bred modes alone. Several examples that illustrate the benefits from this approach for severe weather forecasts will be provided.
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.
Timescales of isotropic and anisotropic cluster collapse

NASA Astrophysics Data System (ADS)

Bartelmann, M.; Ehlers, J.; Schneider, P.

1993-12-01

From a simple estimate for the formation time of galaxy clusters, Richstone et al. have recently concluded that the evidence for non-virialized structures in a large fraction of observed clusters points towards a high value for the cosmological density parameter Omega0. This conclusion was based on a study of the spherical collapse of density perturbations, assumed to follow a Gaussian probability distribution. In this paper, we extend their treatment in several respects: first, we argue that the collapse does not start from a comoving motion of the perturbation, but that the continuity equation requires an initial velocity perturbation directly related to the density perturbation. This requirement modifies the initial condition for the evolution equation and has the effect that the collapse proceeds faster than in the case where the initial velocity perturbation is set to zero; the timescale is reduced by a factor of up to approximately equal 0.5. Our results thus strengthens the conclusion of Richstone et al. for a high Omega0. In addition, we study the collapse of density fluctuations in the frame of the Zel'dovich approximation, using as starting condition the analytically known probability distribution of the eigenvalues of the deformation tensor, which depends only on the (Gaussian) width of the perturbation spectrum. Finally, we consider the anisotropic collapse of density perturbations dynamically, again with initial conditions drawn from the probability distribution of the deformation tensor. We find that in both cases of anisotropic collapse, in the Zel'dovich approximation and in the dynamical calculations, the resulting distribution of collapse times agrees remarkably well with the results from spherical collapse. We discuss this agreement and conclude that it is mainly due to the properties of the probability distribution for the eigenvalues of the Zel'dovich deformation tensor. Hence, the conclusions of Richstone et al. on the value of Omega0 can be verified and strengthened, even if a more general approach to the collapse of density perturbations is employed. A simple analytic formula for the cluster redshift distribution in an Einstein-deSitter universe is derived.
Effects of ocean initial perturbation on developing phase of ENSO in a coupled seasonal prediction model

NASA Astrophysics Data System (ADS)

Lee, Hyun-Chul; Kumar, Arun; Wang, Wanqiu

2018-03-01

Coupled prediction systems for seasonal and inter-annual variability in the tropical Pacific are initialized from ocean analyses. In ocean initial states, small scale perturbations are inevitably smoothed or distorted by the observational limits and data assimilation procedures, which tends to induce potential ocean initial errors for the El Nino-Southern Oscillation (ENSO) prediction. Here, the evolution and effects of ocean initial errors from the small scale perturbation on the developing phase of ENSO are investigated by an ensemble of coupled model predictions. Results show that the ocean initial errors at the thermocline in the western tropical Pacific grow rapidly to project on the first mode of equatorial Kelvin wave and propagate to the east along the thermocline. In boreal spring when the surface buoyancy flux weakens in the eastern tropical Pacific, the subsurface errors influence sea surface temperature variability and would account for the seasonal dependence of prediction skill in the NINO3 region. It is concluded that the ENSO prediction in the eastern tropical Pacific after boreal spring can be improved by increasing the observational accuracy of subsurface ocean initial states in the western tropical Pacific.
A comparative study of Rayleigh-Taylor and Richtmyer-Meshkov instabilities in 2D and 3D in tantalum

NASA Astrophysics Data System (ADS)

Sternberger, Z.; Maddox, B. R.; Opachich, Y. P.; Wehrenberg, C. E.; Kraus, R. G.; Remington, B. A.; Randall, G. C.; Farrell, M.; Ravichandran, G.

2017-01-01

Driving a shock wave through the interface between two materials with different densities can result in the Richtmyer-Meshkov or Rayleigh-Taylor instability and initial perturbations at the interface will grow. If the shock wave is sufficiently strong, the instability will lead to plastic flow at the interface. Material strength will reduce the amount of plastic flow and suppress growth. While such instabilities have been investigated in 2D, no studies of this phenomena have been performed in 3D on materials with strength. Initial perturbations to seed the hydrodynamic instability were coined into tantalum recovery targets. Two types of perturbations were used, two dimensional (2D) perturbations (hill and valley) and three-dimensional (3D) perturbations (egg crate pattern). The targets were subjected to dynamic loading using the Janus laser at the Jupiter Laser Facility. Shock pressures ranged from 50 GPa up to 150 GPa and were calibrated using VISAR drive targets.
Threshold resummation of soft gluons in hadronic reactions - an introduction.

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

Berger, E. L.

The authors discuss the motivation for resummation of the effects of initial-state soft gluon radiation, to all orders in the strong coupling strength, for processes in which the near-threshold region in the partonic subenergy is important. The author summarizes the method of perturbative resummation and its application to the calculation of the total cross section for top quark production at hadron colliders. Comments are included on the differences between the treatment of subleading logarithmic terms in this method and in other approaches.
Eigenmode computation of cavities with perturbed geometry using matrix perturbation methods applied on generalized eigenvalue problems

NASA Astrophysics Data System (ADS)

Gorgizadeh, Shahnam; Flisgen, Thomas; van Rienen, Ursula

2018-07-01

Generalized eigenvalue problems are standard problems in computational sciences. They may arise in electromagnetic fields from the discretization of the Helmholtz equation by for example the finite element method (FEM). Geometrical perturbations of the structure under concern lead to a new generalized eigenvalue problems with different system matrices. Geometrical perturbations may arise by manufacturing tolerances, harsh operating conditions or during shape optimization. Directly solving the eigenvalue problem for each perturbation is computationally costly. The perturbed eigenpairs can be approximated using eigenpair derivatives. Two common approaches for the calculation of eigenpair derivatives, namely modal superposition method and direct algebraic methods, are discussed in this paper. Based on the direct algebraic methods an iterative algorithm is developed for efficiently calculating the eigenvalues and eigenvectors of the perturbed geometry from the eigenvalues and eigenvectors of the unperturbed geometry.
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.
Excitability in chemical and biochemical pH-autocatalytic systems.

PubMed

Zagora, J; Voslar, M; Schreiberová, L; Schreiber, I

2001-01-01

Using two different kinds of pH systems--the papain catalyzed hydrolysis of N-benzoyl-L-arginine ethyl ester in a membrane reactor and the bromate-sulfite-ferrocyanide (BSF) reaction in the CSTR--we study the relation among excitability, oscillations and bistability, and the ability of the system to respond to external periodic perturbations. Excitable properties of dynamical systems are examined in terms of a threshold set which is used to characterise dynamics in the reactor subject to external periodic stimuli. A precise definition and a method of calculating the threshold set are formulated. Two kinds of excitability distinguished by either direct or indirect initiation of the activatory process are found in both pH systems. Periodic pulsed perturbations of the BSF system display a nontrivial dependence of an excitation number on the forcing period. We examined this system also in oscillatory mode by looking at the phase shifts caused by single-pulse perturbations and constructing the phase transition curves (PTCs).
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.
Communication: An efficient and accurate perturbative correction to initiator full configuration interaction quantum Monte Carlo

NASA Astrophysics Data System (ADS)

Blunt, Nick S.

2018-06-01

We present a perturbative correction within initiator full configuration interaction quantum Monte Carlo (i-FCIQMC). In the existing i-FCIQMC algorithm, a significant number of spawned walkers are discarded due to the initiator criteria. Here we show that these discarded walkers have a form that allows the calculation of a second-order Epstein-Nesbet correction, which may be accumulated in a trivial and inexpensive manner, yet substantially improves i-FCIQMC results. The correction is applied to the Hubbard model and the uniform electron gas and molecular systems.
DOE Office of Scientific and Technical Information (OSTI.GOV)

Wang, L. F., E-mail: wang-lifeng@iapcm.ac.cn; Ye, W. H.; Liu, Jie

In this research, a weakly nonlinear (WN) model has been developed considering the growth of a small perturbation on a cylindrical interface between two incompressible fluids which is subject to arbitrary radial motion. We derive evolution equations for the perturbation amplitude up to third order, which can depict the linear growth of the fundamental mode, the generation of the second and third harmonics, and the third-order (second-order) feedback to the fundamental mode (zero-order). WN solutions are obtained for a special uniformly convergent case. WN analyses are performed to address the dependence of interface profiles, amplitudes of inward-going and outward-going parts,more » and saturation amplitudes of linear growth of the fundamental mode on the Atwood number, the mode number (m), and the initial perturbation. The difference of WN evolution in cylindrical geometry from that in planar geometry is discussed in some detail. It is shown that interface profiles are determined mainly by the inward and outward motions rather than bubbles and spikes. The amplitudes of inward-going and outward-going parts are strongly dependent on the Atwood number and the initial perturbation. For low-mode perturbations, the linear growth of fundamental mode cannot be saturated by the third-order feedback. For fixed Atwood numbers and initial perturbations, the linear growth of fundamental mode can be saturated with increasing m. The saturation amplitude of linear growth of the fundamental mode is typically 0.2λ–0.6λ for m < 100, with λ being the perturbation wavelength. Thus, it should be included in applications where Bell-Plesset [G. I. Bell, Los Alamos Scientific Laboratory Report No. LA-1321, 1951; M. S. Plesset, J. Appl. Phys. 25, 96 (1954)] converging geometry effects play a pivotal role, such as inertial confinement fusion implosions.« less
Nonlinear Saturation Amplitude in Classical Planar Richtmyer-Meshkov Instability

NASA Astrophysics Data System (ADS)

Liu, Wan-Hai; Wang, Xiang; Jiang, Hong-Bin; Ma, Wen-Fang

2016-04-01

The classical planar Richtmyer-Meshkov instability (RMI) at a fluid interface supported by a constant pressure is investigated by a formal perturbation expansion up to the third order, and then according to definition of nonlinear saturation amplitude (NSA) in Rayleigh-Taylor instability (RTI), the NSA in planar RMI is obtained explicitly. It is found that the NSA in planar RMI is affected by the initial perturbation wavelength and the initial amplitude of the interface, while the effect of the initial amplitude of the interface on the NSA is less than that of the initial perturbation wavelength. Without marginal influence of the initial amplitude, the NSA increases linearly with wavelength. The NSA normalized by the wavelength in planar RMI is about 0.11, larger than that corresponding to RTI. Supported by the National Natural Science Foundation of China under Grant Nos. 11472278 and 11372330, the Scientific Research Foundation of Education Department of Sichuan Province under Grant No. 15ZA0296, the Scientific Research Foundation of Mianyang Normal University under Grant Nos. QD2014A009 and 2014A02, and the National High-Tech ICF Committee
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.
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).
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
Stochastic Approaches Within a High Resolution Rapid Refresh Ensemble

NASA Astrophysics Data System (ADS)

Jankov, I.

2017-12-01

It is well known that global and regional numerical weather prediction (NWP) ensemble systems are under-dispersive, producing unreliable and overconfident ensemble forecasts. Typical approaches to alleviate this problem include the use of multiple dynamic cores, multiple physics suite configurations, or a combination of the two. While these approaches may produce desirable results, they have practical and theoretical deficiencies and are more difficult and costly to maintain. An active area of research that promotes a more unified and sustainable system is the use of stochastic physics. Stochastic approaches include Stochastic Parameter Perturbations (SPP), Stochastic Kinetic Energy Backscatter (SKEB), and Stochastic Perturbation of Physics Tendencies (SPPT). The focus of this study is to assess model performance within a convection-permitting ensemble at 3-km grid spacing across the Contiguous United States (CONUS) using a variety of stochastic approaches. A single physics suite configuration based on the operational High-Resolution Rapid Refresh (HRRR) model was utilized and ensemble members produced by employing stochastic methods. Parameter perturbations (using SPP) for select fields were employed in the Rapid Update Cycle (RUC) land surface model (LSM) and Mellor-Yamada-Nakanishi-Niino (MYNN) Planetary Boundary Layer (PBL) schemes. Within MYNN, SPP was applied to sub-grid cloud fraction, mixing length, roughness length, mass fluxes and Prandtl number. In the RUC LSM, SPP was applied to hydraulic conductivity and tested perturbing soil moisture at initial time. First iterative testing was conducted to assess the initial performance of several configuration settings (e.g. variety of spatial and temporal de-correlation lengths). Upon selection of the most promising candidate configurations using SPP, a 10-day time period was run and more robust statistics were gathered. SKEB and SPPT were included in additional retrospective tests to assess the impact of using all three stochastic approaches to address model uncertainty. Results from the stochastic perturbation testing were compared to a baseline multi-physics control ensemble. For probabilistic forecast performance the Model Evaluation Tools (MET) verification package was used.
Perturbations of the Kerr spacetime in horizon-penetrating coordinates

NASA Astrophysics Data System (ADS)

Campanelli, Manuela; Khanna, Gaurav; Laguna, Pablo; Pullin, Jorge; Ryan, Michael P.

2001-04-01

We derive the Teukolsky equation for perturbations of a Kerr spacetime when the spacetime metric is written in either ingoing or outgoing Kerr-Schild form. We also write explicit formulae for setting up the initial data for the Teukolsky equation in the time domain in terms of a 3-metric and an extrinsic curvature. The motivation of this work is to have in place a formalism to study the evolution in the `close limit' of two recently proposed solutions to the initial-value problem in general relativity that are based on Kerr-Schild slicings. A perturbative formalism in horizon-penetrating coordinates is also very desirable in connection with numerical relativity simulations using black hole `excision'.

Hybrid perturbation methods based on statistical time series models

NASA Astrophysics Data System (ADS)

San-Juan, Juan Félix; San-Martín, Montserrat; Pérez, Iván; López, Rosario

2016-04-01

In this work we present a new methodology for orbit propagation, the hybrid perturbation theory, based on the combination of an integration method and a prediction technique. The former, which can be a numerical, analytical or semianalytical theory, generates an initial approximation that contains some inaccuracies derived from the fact that, in order to simplify the expressions and subsequent computations, not all the involved forces are taken into account and only low-order terms are considered, not to mention the fact that mathematical models of perturbations not always reproduce physical phenomena with absolute precision. The prediction technique, which can be based on either statistical time series models or computational intelligence methods, is aimed at modelling and reproducing missing dynamics in the previously integrated approximation. This combination results in the precision improvement of conventional numerical, analytical and semianalytical theories for determining the position and velocity of any artificial satellite or space debris object. In order to validate this methodology, we present a family of three hybrid orbit propagators formed by the combination of three different orders of approximation of an analytical theory and a statistical time series model, and analyse their capability to process the effect produced by the flattening of the Earth. The three considered analytical components are the integration of the Kepler problem, a first-order and a second-order analytical theories, whereas the prediction technique is the same in the three cases, namely an additive Holt-Winters method.
A System of ODEs for a Perturbation of a Minimal Mass Soliton

NASA Astrophysics Data System (ADS)

Marzuola, Jeremy L.; Raynor, Sarah; Simpson, Gideon

2010-08-01

We study soliton solutions to the nonlinear Schrödinger equation (NLS) with a saturated nonlinearity. NLS with such a nonlinearity is known to possess a minimal mass soliton. We consider a small perturbation of a minimal mass soliton and identify a system of ODEs extending the work of Comech and Pelinovsky (Commun. Pure Appl. Math. 56:1565-1607, 2003), which models the behavior of the perturbation for short times. We then provide numerical evidence that under this system of ODEs there are two possible dynamical outcomes, in accord with the conclusions of Pelinovsky et al. (Phys. Rev. E 53(2):1940-1953, 1996). Generically, initial data which supports a soliton structure appears to oscillate, with oscillations centered on a stable soliton. For initial data which is expected to disperse, the finite dimensional dynamics initially follow the unstable portion of the soliton curve.
Superdiffusive transport and energy localization in disordered granular crystals

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

Martinez, Alejandro J.; Kevrekidis, Panagiotis G.; Porter, Mason A.

We study the spreading of initially localized excitations in one-dimensional disordered granular crystals. We thereby investigate localization phenomena in strongly nonlinear systems, which we demonstrate to be fundamentally different from localization in linear and weakly nonlinear systems. We conduct a thorough comparison of wave dynamics in chains with three different types of disorder: an uncorrelated (Anderson-like) disorder and two types of correlated disorders (which are produced by random dimer arrangements), and for two families of initial conditions: displacement perturbations and velocity perturbations. We find for strongly precompressed (i.e., weakly nonlinear) chains that the dynamics strongly depends on the initial condition.more » Furthermore, for displacement perturbations, the long-time asymptotic behavior of the second moment m ~2 has oscillations that depend on the type of disorder, with a complex trend that is markedly different from a power law and which is particularly evident for an Anderson-like disorder.« less
Superdiffusive transport and energy localization in disordered granular crystals

DOE PAGES

Martinez, Alejandro J.; Kevrekidis, Panagiotis G.; Porter, Mason A.

2016-02-12

We study the spreading of initially localized excitations in one-dimensional disordered granular crystals. We thereby investigate localization phenomena in strongly nonlinear systems, which we demonstrate to be fundamentally different from localization in linear and weakly nonlinear systems. We conduct a thorough comparison of wave dynamics in chains with three different types of disorder: an uncorrelated (Anderson-like) disorder and two types of correlated disorders (which are produced by random dimer arrangements), and for two families of initial conditions: displacement perturbations and velocity perturbations. We find for strongly precompressed (i.e., weakly nonlinear) chains that the dynamics strongly depends on the initial condition.more » Furthermore, for displacement perturbations, the long-time asymptotic behavior of the second moment m ~2 has oscillations that depend on the type of disorder, with a complex trend that is markedly different from a power law and which is particularly evident for an Anderson-like disorder.« less
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
Multipass Steering: A Reference Implementation

NASA Astrophysics Data System (ADS)

Hennessey, Michael; Tiefenback, Michael

2015-10-01

We introduce a reference implementation of a protocol to compute corrections that bring all beams in one of the CEBAF linear accelerators (linac) to axis, including, with a larger tolerance, the lowest energy pass using measured beam trajectory data. This method relies on linear optics as representation of the system; we treat beamline perturbations as magnetic field errors localized to regions between cryomodules, providing the same transverse momentum kick to each beam. We produce a vector of measured beam position data with which we left-multiply the pseudo-inverse of a coefficient array, A, that describes the transport of the beam through the linac using parameters that include the magnetic offsets of the quadrupole magnets, the instrumental offsets of the BPMs, and the beam initial conditions. This process is repeated using a reduced array to produce values that can be applied to the available correcting magnets and beam initial conditions. We show that this method is effective in steering the beam to a straight axis along the linac by using our values in elegant, the accelerator simulation program, on a model of the linac in question. The algorithms in this reference implementation provide a tool for systematic diagnosis and cataloging of perturbations in the beam line. Supported by Jefferson Lab, Old Dominion University, NSF, DOE.
Wintertime component of the THORPEX Pacific-Asian Regional Campaign (T-PARC)

NASA Astrophysics Data System (ADS)

Song, Y.; Toth, Z.; Asuma, Y.; Reynolds, C.; Lngland, R.; Szunyogh, I.; Colle, B.; Chang, E.; Doyle, C.; Kats, A.

2009-04-01

The winter component of the T-PARC is an international field project that aims at improving high impact weather event forecasts for North America. The main objective is to understand how perturbations from the tropics, Eurasia and polar fronts travel through waveguide and turn into high impact weather events. Through adaptive observations by using manned aircrafts (NOAA G-IV and US Air force C-130s) and Russian rawinsonde network over data sparse regions, it is expected that accurate initial conditions will improve the numerical weather forecasts. Non-adaptive aircraft measurements over the Pacific Rim and part of India are also deployed through E-AMDAR program, which is expected to improve the background field over Asia where perturbations are initiated. The campaign is led by NOAA and joined by agencies and universities from US, Canada, Mexico, Japan, ECWMF, and Russia. While most observational data will be assimilated by operational centers to improve real time numerical weather predictions, post field studies will focus on aspects such as: data impact on forecast and analysis, dry and moist processes that affect the formation and propagation of perturbations, meso-scale storm structure, error growth, forecast "busts" under certain atmospheric regimes, and socio-economic applications such as costs and benefits of improved forecasts and their use by the public for high impact weather events. In particular, a Winter Olympics demonstration project (February 12 - February 28) is expected to be a test bed during winter T-PARC for real user outreach and application purposes. Effectiveness of existing targeting methods as well as new targeting methods in the 3-5 day lead time range will be pursued and other aspects related to data assimilation and numerical forecasts (both deterministic and ensemble forecasts) will be investigated within this project as well.
Cosmic microwave background radiation anisotropies in brane worlds.

PubMed

Koyama, Kazuya

2003-11-28

We propose a new formulation to calculate the cosmic microwave background (CMB) spectrum in the Randall-Sundrum two-brane model based on recent progress in solving the bulk geometry using a low energy approximation. The evolution of the anisotropic stress imprinted on the brane by the 5D Weyl tensor is calculated. An impact of the dark radiation perturbation on the CMB spectrum is investigated in a simple model assuming an initially scale-invariant adiabatic perturbation. The dark radiation perturbation induces isocurvature perturbations, but the resultant spectrum can be quite different from the prediction of simple mixtures of adiabatic and isocurvature perturbations due to Weyl anisotropic stress.
Edgeworth streaming model for redshift space distortions

NASA Astrophysics Data System (ADS)

Uhlemann, Cora; Kopp, Michael; Haugg, Thomas

2015-09-01

We derive the Edgeworth streaming model (ESM) for the redshift space correlation function starting from an arbitrary distribution function for biased tracers of dark matter by considering its two-point statistics and show that it reduces to the Gaussian streaming model (GSM) when neglecting non-Gaussianities. We test the accuracy of the GSM and ESM independent of perturbation theory using the Horizon Run 2 N -body halo catalog. While the monopole of the redshift space halo correlation function is well described by the GSM, higher multipoles improve upon including the leading order non-Gaussian correction in the ESM: the GSM quadrupole breaks down on scales below 30 Mpc /h whereas the ESM stays accurate to 2% within statistical errors down to 10 Mpc /h . To predict the scale-dependent functions entering the streaming model we employ convolution Lagrangian perturbation theory (CLPT) based on the dust model and local Lagrangian bias. Since dark matter halos carry an intrinsic length scale given by their Lagrangian radius, we extend CLPT to the coarse-grained dust model and consider two different smoothing approaches operating in Eulerian and Lagrangian space, respectively. The coarse graining in Eulerian space features modified fluid dynamics different from dust while the coarse graining in Lagrangian space is performed in the initial conditions with subsequent single-streaming dust dynamics, implemented by smoothing the initial power spectrum in the spirit of the truncated Zel'dovich approximation. Finally, we compare the predictions of the different coarse-grained models for the streaming model ingredients to N -body measurements and comment on the proper choice of both the tracer distribution function and the smoothing scale. Since the perturbative methods we considered are not yet accurate enough on small scales, the GSM is sufficient when applied to perturbation theory.
Rarefaction-driven Rayleigh–Taylor instability. Part 1. Diffuse-interface linear stability measurements and theory

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

Morgan, R. V.; Likhachev, O. A.; Jacobs, J. W.

Theory and experiments are reported that explore the behaviour of the Rayleigh–Taylor instability initiated with a diffuse interface. Experiments are performed in which an interface between two gases of differing density is made unstable by acceleration generated by a rarefaction wave. Well-controlled, diffuse, two-dimensional and three-dimensional, single-mode perturbations are generated by oscillating the gases either side to side, or vertically for the three-dimensional perturbations. The puncturing of a diaphragm separating a vacuum tank beneath the test section generates a rarefaction wave that travels upwards and accelerates the interface downwards. This rarefaction wave generates a large, but non-constant, acceleration of the order ofmore » $$1000g_{0}$$, where$$g_{0}$$is the acceleration due to gravity. Initial interface thicknesses are measured using a Rayleigh scattering diagnostic and the instability is visualized using planar laser-induced Mie scattering. Growth rates agree well with theoretical values, and with the inviscid, dynamic diffusion model of Duffet al. (Phys. Fluids, vol. 5, 1962, pp. 417–425) when diffusion thickness is accounted for, and the acceleration is weighted using inviscid Rayleigh–Taylor theory. The linear stability formulation of Chandrasekhar (Proc. Camb. Phil. Soc., vol. 51, 1955, pp. 162–178) is solved numerically with an error function diffusion profile using the Riccati method. This technique exhibits good agreement with the dynamic diffusion model of Duffet al. for small wavenumbers, but produces larger growth rates for large-wavenumber perturbations. Asymptotic analysis shows a$$1/k^{2}$$decay in growth rates as$$k\\rightarrow \\infty$$for large-wavenumber perturbations.« less
Rarefaction-driven Rayleigh–Taylor instability. Part 1. Diffuse-interface linear stability measurements and theory

DOE PAGES

Morgan, R. V.; Likhachev, O. A.; Jacobs, J. W.

2016-02-15

Theory and experiments are reported that explore the behaviour of the Rayleigh–Taylor instability initiated with a diffuse interface. Experiments are performed in which an interface between two gases of differing density is made unstable by acceleration generated by a rarefaction wave. Well-controlled, diffuse, two-dimensional and three-dimensional, single-mode perturbations are generated by oscillating the gases either side to side, or vertically for the three-dimensional perturbations. The puncturing of a diaphragm separating a vacuum tank beneath the test section generates a rarefaction wave that travels upwards and accelerates the interface downwards. This rarefaction wave generates a large, but non-constant, acceleration of the order ofmore » $$1000g_{0}$$, where$$g_{0}$$is the acceleration due to gravity. Initial interface thicknesses are measured using a Rayleigh scattering diagnostic and the instability is visualized using planar laser-induced Mie scattering. Growth rates agree well with theoretical values, and with the inviscid, dynamic diffusion model of Duffet al. (Phys. Fluids, vol. 5, 1962, pp. 417–425) when diffusion thickness is accounted for, and the acceleration is weighted using inviscid Rayleigh–Taylor theory. The linear stability formulation of Chandrasekhar (Proc. Camb. Phil. Soc., vol. 51, 1955, pp. 162–178) is solved numerically with an error function diffusion profile using the Riccati method. This technique exhibits good agreement with the dynamic diffusion model of Duffet al. for small wavenumbers, but produces larger growth rates for large-wavenumber perturbations. Asymptotic analysis shows a$$1/k^{2}$$decay in growth rates as$$k\\rightarrow \\infty$$for large-wavenumber perturbations.« less
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.
Influence of initial conditions on the flow patterns of a shock-accelerated thin fluid layer

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

Budzinski, J.M.; Benjamin, R.F.; Jacobs, J.W.

1994-11-01

Previous observations of three flow patterns generated by shock acceleration of a thin perturbed, fluid layer are now correlated with asymmetries in the initial conditions. Using a different diagnostic (planar laser Rayleigh scattering) than the previous experiments, upstream mushrooms, downstream mushrooms, and sinuous patterns are still observed. For each experiment the initial perturbation amplitude on one side of the layer can either be larger, smaller, or the same as the amplitude on the other side, as observed with two images per experiment, and these differences lead to the formation of the different patterns.
Experiments on the Richtmyer–Meshkov instability with an imposed, random initial perturbation

DOE PAGES

Jacobs, J. W.; Krivets, V. V.; Tsiklashvili, V.; ...

2013-03-16

A vertical shock tube is used to perform experiments on the Richtmyer–Meshkov instability with a three-dimensional random initial perturbation. A membraneless flat interface is formed by opposed gas flows in which the light and heavy gases enter the shock tube from the top and from the bottom of the shock tube driven section. An air/SF6 gas combination is used and a Mach number M = 1.2 incident shock wave impulsively accelerates the interface. Initial perturbations on the interface are created by vertically oscillating the gas column within the shock tube to produce Faraday waves on the interface resulting in amore » short wavelength, three-dimensional perturbation. Planar Mie scattering is used to visualize the flow in which light from a laser sheet is scattered by smoke seeded in the air, and image sequences are captured using three high-speed video cameras. Measurements of the integral penetration depth prior to reshock show two growth behaviors, both having power law growth with growth exponents in the range found in previous experiments and simulations. Following reshock, all experiments showvery consistent linear growth with a growth rate in good agreement with those found in previous studies.« less
Extension to linear dynamics for hybrid stress finite element formulation based on additional displacements

NASA Astrophysics Data System (ADS)

Sumihara, K.

Based upon legitimate variational principles, one microscopic-macroscopic finite element formulation for linear dynamics is presented by Hybrid Stress Finite Element Method. The microscopic application of Geometric Perturbation introduced by Pian and the introduction of infinitesimal limit core element (Baby Element) have been consistently combined according to the flexible and inherent interpretation of the legitimate variational principles initially originated by Pian and Tong. The conceptual development based upon Hybrid Finite Element Method is extended to linear dynamics with the introduction of physically meaningful higher modes.
Energy-momentum tensor of perturbed tachyon matter

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

Jokela, Niko; Department of Mathematics and Physics, University of Haifa at Oranim, Tivon 36006; Jaervinen, Matti

2009-05-15

We add an initial nonhomogeneous perturbation to an otherwise homogeneous condensing tachyon background and compute its spacetime energy-momentum tensor from world-sheet string theory. We show that in the far future the energy-momentum tensor corresponds to nonhomogeneous pressureless tachyon matter.
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.
Solution of the Time-Dependent Schrödinger Equation by the Laplace Transform Method

PubMed Central

Lin, S. H.; Eyring, H.

1971-01-01

The time-dependent Schrödinger equation for two quite general types of perturbation has been solved by introducing the Laplace transforms to eliminate the time variable. The resulting time-independent differential equation can then be solved by the perturbation method, the variation method, the variation-perturbation method, and other methods. PMID:16591898
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.
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.

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.
Statistics of initial density perturbations in heavy ion collisions and their fluid dynamic response

NASA Astrophysics Data System (ADS)

Floerchinger, Stefan; Wiedemann, Urs Achim

2014-08-01

An interesting opportunity to determine thermodynamic and transport properties in more detail is to identify generic statistical properties of initial density perturbations. Here we study event-by-event fluctuations in terms of correlation functions for two models that can be solved analytically. The first assumes Gaussian fluctuations around a distribution that is fixed by the collision geometry but leads to non-Gaussian features after averaging over the reaction plane orientation at non-zero impact parameter. In this context, we derive a three-parameter extension of the commonly used Bessel-Gaussian event-by-event distribution of harmonic flow coefficients. Secondly, we study a model of N independent point sources for which connected n-point correlation functions of initial perturbations scale like 1 /N n-1. This scaling is violated for non-central collisions in a way that can be characterized by its impact parameter dependence. We discuss to what extent these are generic properties that can be expected to hold for any model of initial conditions, and how this can improve the fluid dynamical analysis of heavy ion collisions.
Impact of Inner Surface Perturbations on the Stability of Cylindrical Liner Implosion

NASA Astrophysics Data System (ADS)

Weis, Matthew; Peterson, Kyle; Hess, Mark; Lau, Y. Y.; Zhang, Peng; Gilgenbach, Ronald

2015-11-01

This paper studies the effects of initial perturbations on the inner liner surface (ILS) of an imploding cylindrical liner. In MagLIF, nonuniform preheat of the fuel could provide an additional source of spatial nonuniformity on the ILS. A blast wave generated by the laser preheat might trigger the Richtmyer-Meshkov instability (RM) on the ILS which then serves as another seed to the Rayleigh-Taylor instability (RT) during the stagnation (deceleration) phase of the implosion. Another scenario is that the shock initiated from the outer liner surface, during current rise, propagates inward and is reflected at the ILS. This reflected shock would carry the initial ILS perturbations which then serve as an additional seed for the magneto-RT (MRT) during the acceleration phase of the implosion. These potentially dangerous interactions are analyzed using the 2D HYDRA code. The effects of axial magnetic fields, of the initial surface roughness spectrum, and of gas fill or water fill (to examine deceleration phase RT) are studied. M. R. Weis was supported by the Sandia National Laboratories. This work was also supported by DoE Grant DE-SC0012328.
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.
Film stability in a vertical rotating tube with a core-gas flow.

NASA Technical Reports Server (NTRS)

Sarma, G. S. R.; Lu, P. C.; Ostrach, S.

1971-01-01

The linear hydrodynamic stability of a thin-liquid layer flowing along the inside wall of a vertical tube rotating about its axis in the presence of a core-gas flow is examined. The stability problem is formulated under the conditions that the liquid film is thin, the density and viscosity ratios of gas to liquid are small and the relative (axial) pressure gradient in the gas is of the same order as gravity. The resulting eigenvalue problem is first solved by a perturbation method appropriate to axisymmetric long-wave disturbances. The damped nature (to within the thin-film and other approximations made) of the nonaxisymmetric and short-wave disturbances is noted. In view of the limitations on a truncated perturbation solution when the disturbance wavenumber is not small, an initial value method using digital computer is presented. Stability characteristics of neutral, growing, and damped modes are presented showing the influences of rotation, surface tension, and the core-gas flow. Energy balance in a neutral mode is also illustrated.
Topics in structural dynamics: Nonlinear unsteady transonic flows and Monte Carlo methods in acoustics

NASA Technical Reports Server (NTRS)

Haviland, J. K.

1974-01-01

The results are reported of two unrelated studies. The first was an investigation of the formulation of the equations for non-uniform unsteady flows, by perturbation of an irrotational flow to obtain the linear Green's equation. The resulting integral equation was found to contain a kernel which could be expressed as the solution of the adjoint flow equation, a linear equation for small perturbations, but with non-constant coefficients determined by the steady flow conditions. It is believed that the non-uniform flow effects may prove important in transonic flutter, and that in such cases, the use of doublet type solutions of the wave equation would then prove to be erroneous. The second task covered an initial investigation into the use of the Monte Carlo method for solution of acoustical field problems. Computed results are given for a rectangular room problem, and for a problem involving a circular duct with a source located at the closed end.
Development of MCAERO wing design panel method with interactive graphics module

NASA Technical Reports Server (NTRS)

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

1984-01-01

A reliable and efficient iterative method has been developed for designing wing section contours corresponding to a prescribed subcritical pressure distribution. The design process is initialized by using MCAERO (MCAIR 3-D Subsonic Potential Flow Analysis Code) to analyze a baseline configuration. A second program DMCAERO is then used to calculate a matrix containing the partial derivative of potential at each control point with respect to each unknown geometry parameter by applying a first-order expansion to the baseline equations in MCAERO. This matrix is calculated only once but is used in each iteration cycle to calculate the geometry perturbation and to analyze the perturbed geometry. The potential on the new geometry is calculated by linear extrapolation from the baseline solution. This extrapolated potential is converted to velocity by numerical differentiation, and velocity is converted to pressure by using Bernoulli's equation. There is an interactive graphics option which allows the user to graphically display the results of the design process and to interactively change either the geometry or the prescribed pressure distribution.
An Enhanced Differential Evolution Algorithm Based on Multiple Mutation Strategies.

PubMed

Xiang, Wan-li; Meng, Xue-lei; An, Mei-qing; Li, Yin-zhen; Gao, Ming-xia

2015-01-01

Differential evolution algorithm is a simple yet efficient metaheuristic for global optimization over continuous spaces. However, there is a shortcoming of premature convergence in standard DE, especially in DE/best/1/bin. In order to take advantage of direction guidance information of the best individual of DE/best/1/bin and avoid getting into local trap, based on multiple mutation strategies, an enhanced differential evolution algorithm, named EDE, is proposed in this paper. In the EDE algorithm, an initialization technique, opposition-based learning initialization for improving the initial solution quality, and a new combined mutation strategy composed of DE/current/1/bin together with DE/pbest/bin/1 for the sake of accelerating standard DE and preventing DE from clustering around the global best individual, as well as a perturbation scheme for further avoiding premature convergence, are integrated. In addition, we also introduce two linear time-varying functions, which are used to decide which solution search equation is chosen at the phases of mutation and perturbation, respectively. Experimental results tested on twenty-five benchmark functions show that EDE is far better than the standard DE. In further comparisons, EDE is compared with other five state-of-the-art approaches and related results show that EDE is still superior to or at least equal to these methods on most of benchmark functions.
On Interactions of Oscillation Modes for a Weakly Non-Linear Undamped Elastic Beam with AN External Force

NASA Astrophysics Data System (ADS)

BOERTJENS, G. J.; VAN HORSSEN, W. T.

2000-08-01

In this paper an initial-boundary value problem for the vertical displacement of a weakly non-linear elastic beam with an harmonic excitation in the horizontal direction at the ends of the beam is studied. The initial-boundary value problem can be regarded as a simple model describing oscillations of flexible structures like suspension bridges or iced overhead transmission lines. Using a two-time-scales perturbation method an approximation of the solution of the initial-boundary value problem is constructed. Interactions between different oscillation modes of the beam are studied. It is shown that for certain external excitations, depending on the phase of an oscillation mode, the amplitude of specific oscillation modes changes.
Perturbing Hele-Shaw flow with a small gap gradient

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

Zhao, H.; Casademunt, J.; Yeung, C.

1992-02-15

A controlled perturbation is introduced into the Saffman-Taylor flow problem by adding a gradient to the gap of a Hele-Shaw cell. The stability of the single-finger steady state was found to be strongly affected by such a perturbation. Compared with patterns in a standard Hele-Shaw cell, the single Saffman-Taylor finger was stabilized or destabilized according to the sign of the gap gradient. While a linear stability analysis shows that this perturbation should have a negligible effect on the early-stage pattern formation, the experimental data indicate that the characteristic length for the initial breakup of a flat interface has been changedmore » by the perturbation.« less
Instabilities in a nonstationary model of self-gravitating disks. III. The phenomenon of lopsidedness and a comparison of perturbation modes

NASA Astrophysics Data System (ADS)

Mirtadjieva, K. T.; Nuritdinov, S. N.; Ruzibaev, J. K.; Khalid, Muhammad

2011-06-01

This is an examination of the gravitational instability of the major large-scale perturbation modes for a fixed value of the azimuthal wave number m = 1 in nonlinearly nonstationary disk models with isotropic and anisotropic velocity diagrams for the purpose of explaining the displacement of the nucleus away from the geometric center (lopsidedness) in spiral galaxies. Nonstationary analogs of the dispersion relations for these perturbation modes are obtained. Critical diagrams of the initial virial ratio are constructed from the rotation parameters for the models in each case. A comparative analysis is made of the instability growth rates for the major horizontal perturbation modes in terms of two models, and it is found that, on the average, the instability growth rate for the m = 1 mode with a radial wave number N = 3 almost always has a clear advantage relative to the other modes. An analysis of these results shows that if the initial total kinetic energy in an isotropic model is no more than 12.4% of the initial potential energy, then, regardless of the value of the rotation parameter Ω, an instability of the radial motions always occurs and causes the nucleus to shift away from the geometrical center. This instability is aperiodic when Ω = 0 and is oscillatory when Ω ≠ 0 . For the anisotropic model, this kind of structure involving the nucleus develops when the initial total kinetic energy in the model is no more than 30.6% of the initial potential energy.
Training Rapid Stepping Responses in an Individual With Stroke

PubMed Central

Inness, Elizabeth L.; Komar, Janice; Biasin, Louis; Brunton, Karen; Lakhani, Bimal; McIlroy, William E.

2011-01-01

Background and Purpose Compensatory stepping reactions are important responses to prevent a fall following a postural perturbation. People with hemiparesis following a stroke show delayed initiation and execution of stepping reactions and often are found to be unable to initiate these steps with the more-affected limb. This case report describes a targeted training program involving repeated postural perturbations to improve control of compensatory stepping in an individual with stroke. Case Description Compensatory stepping reactions of a 68-year-old man were examined 52 days after left hemorrhagic stroke. He required assistance to prevent a fall in all trials administered during his initial examination because he showed weight-bearing asymmetry (with more weight borne on the more-affected right side), was unable to initiate stepping with the right leg (despite blocking of the left leg in some trials), and demonstrated delayed response times. The patient completed 6 perturbation training sessions (30–60 minutes per session) that aimed to improve preperturbation weight-bearing symmetry, to encourage stepping with the right limb, and to reduce step initiation and completion times. Outcomes Improved efficacy of compensatory stepping reactions with training and reduced reliance on assistance to prevent falling were observed. Improvements were noted in preperturbation asymmetry and step timing. Blocking the left foot was effective in encouraging stepping with the more-affected right foot. Discussion This case report demonstrates potential short-term adaptations in compensatory stepping reactions following perturbation training in an individual with stroke. Future work should investigate the links between improved compensatory step characteristics and fall risk in this vulnerable population. PMID:21511992
The Lifespan of a Class of Smooth Spherically Symmetric Solutions of the Compressible Euler Equations with Variable Entropy in Three Space Dimensions

NASA Astrophysics Data System (ADS)

Godin, Paul

2005-09-01

We consider smooth three-dimensional spherically symmetric Eulerian flows of ideal polytropic gases with variable entropy, whose initial data are obtained by adding a small smooth perturbation with compact support to a constant state. Under a natural assumption, we obtain precise information on the asymptotic behavior of their lifespan when the size of the initial perturbation tends to 0. This is achieved by the construction and estimate of a suitable approximate flow.
Excursion set mass functions for hierarchical Gaussian fluctuations

NASA Technical Reports Server (NTRS)

Bond, J. R.; Kaiser, N.; Cole, S.; Efstathiou, G.

1991-01-01

It is pointed out that most schemes for determining the mass function of virialized objects from the statistics of the initial density perturbation field suffer from the cloud-in-cloud problem of miscounting the number of low-mass clumps, many of which would have been subsumed into larger objects. The paper proposes a solution based on the theory of the excursion sets of F(r, R sub f), the four-dimensional initial density perturbation field smoothed with a continuous hierarchy of filters of radii R sub f.
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.
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.
Determination of intermediate perturbed orbits of Near-Earth asteroids from range and range rate measurements at three times

NASA Astrophysics Data System (ADS)

Shefer, V. A.

2014-12-01

Two methods that the author developed earlier for finding the intermediate perturbed orbit of a small celestial body from three pairs of range and range rate observations [1, 2] are applied to the determination of orbits of Near-Earth asteroids. The methods are based on using the superosculating orbits with three- and fourth-order tangency. The degrees of approximation of the real motion by the constructed intermediate orbits near the middle measurement time are two and three orders of magnitude higher than by the Keplerian orbit determined with the help of traditional methods. We calculated the orbits of the asteroids 99942 Apophis, 1566 Icarus, 4179 Toutatis, 2007 DN41 and 2012 DA14. For the sake of brevity, we call the method based on the orbit with third-order tangency as Algorithm A1 and the method based on the orbit with fourth-order tangency -- as Algorithm A2. The results of the calculations are compared with the results of the calculations by the version of the methods mentioned that allows us to construct the unperturbed Keplerian orbit. We call this version of the methods as Algorithm A. The observational data were simulated using the nominal trajectories of the selected asteroids. These trajectories were obtained by the numerical integration of the differential equations of motion subject to the perturbations from the eight major planets, Pluto, and the Moon. The integration was carried out with the help of the 15-order Everhart procedure [3]. The main results of the calculations are the following. When the reference time interval is shortened by half (for small sizes of this interval), the errors in the compared algorithms A, A1, A2 decrease approximately by the factors 4, 16, 64 in coordinates and by the factors 2, 8, 16 in velocities, respectively. Such behavior of the errors is most clearly seen with the asteroids 2007 DN41 and 2012 DA14. This leads to a significant increase in the accuracy of the real motion approximation by the intermediate orbits constructed using the A1 and A2 algorithms (2-4 orders of magnitude in coordinates and 4-7 orders of magnitude in velocities higher) compared to the accuracy of the approximation by Keplerian orbits with decreasing the reference arc of the trajectory. Here, the higher is the efficiency of the algorithms A1 and A2, the smaller are the values of the topocentric distances, i.e., the greater are the perturbations caused by the Earth's gravitation. The advantage of Algorithm A2 over Algorithm A1 in accuracy extends approximately one order of magnitude. The minimal methodic errors of the position vector by using the A1 and A2 algorithms range from several meters in the case of the asteroid Apophis to several millimeters in the case of the asteroid 2012 DA14. Hence, the numerical examples analyzed in this work lead us to conclude that the proposed in [1, 2] methods for determination of an intermediate perturbed orbit from range and range rate measurements at three time points allow for significantly raising the accuracy of the calculation of the initial asteroid orbits in comparison with the algorithm based on the finding the unperturbed Keplerian orbit. The shorter is the orbital arc specified by the extreme time points, the greater is the advantage of the algorithms suggested over the algorithms of the traditional approach in the accuracy. The advantage of the algorithms suggested in the accuracy increases with raising the perturbations too, which is especially important for calculation of the initial trajectories of the space objects detected in the Earth's neighbourhood. The work was supported by the Ministry of Education and Science of the Russian Federation, project no. 2014/223(1567).
Simulation and analysis of a geopotential research mission

NASA Technical Reports Server (NTRS)

White, Lisa K.

1987-01-01

Methods for the determination of the initial conditions for the two satellites that will satisfy Geopotential Research Mission (GRM) requirements are investigated. For certain gravitational recovery techniques, the satellites must remain close to a specified separation distance and their groundtracks must repeat after a specified interval of time. Since the objective of the GRM mission is to improve the gravity model, any pre-mission orbit predicted using existing gravity models will be in error. A technique has been developed to eliminate the drift between the two satellites caused by gravitational modeling errors and return them to repeating groundtracks. The concept of frozen orbits, which minimize altitude variations over given latitudes, was investigated. Finally, the effects of temporal perturbations on the relative range-rate signal were studied. At the proposed altitude of 160 km, the range-rate signal produced by perturbations other than the static geopotential field are dominated by the luni-solar effect. This study demonstrates that the combined effects of all the temporal perturbations does not prevent the orbit from being frozen or the satellites from obtaining a repeating groundtrack to within a specified closure distance.
Spectroscopy of the Schwarzschild black hole at arbitrary frequencies.

PubMed

Casals, Marc; Ottewill, Adrian

2012-09-14

Linear field perturbations of a black hole are described by the Green function of the wave equation that they obey. After Fourier decomposing the Green function, its two natural contributions are given by poles (quasinormal modes) and a largely unexplored branch cut in the complex frequency plane. We present new analytic methods for calculating the branch cut on a Schwarzschild black hole for arbitrary values of the frequency. The branch cut yields a power-law tail decay for late times in the response of a black hole to an initial perturbation. We determine explicitly the first three orders in the power-law and show that the branch cut also yields a new logarithmic behavior T(-2ℓ-5)lnT for late times. Before the tail sets in, the quasinormal modes dominate the black hole response. For electromagnetic perturbations, the quasinormal mode frequencies approach the branch cut at large overtone index n. We determine these frequencies up to n(-5/2) and, formally, to arbitrary order. Highly damped quasinormal modes are of particular interest in that they have been linked to quantum properties of black holes.
Nonlinear system guidance in the presence of transmission zero dynamics

NASA Technical Reports Server (NTRS)

Meyer, G.; Hunt, L. R.; Su, R.

1995-01-01

An iterative procedure is proposed for computing the commanded state trajectories and controls that guide a possibly multiaxis, time-varying, nonlinear system with transmission zero dynamics through a given arbitrary sequence of control points. The procedure is initialized by the system inverse with the transmission zero effects nulled out. Then the 'steady state' solution of the perturbation model with the transmission zero dynamics intact is computed and used to correct the initial zero-free solution. Both time domain and frequency domain methods are presented for computing the steady state solutions of the possibly nonminimum phase transmission zero dynamics. The procedure is illustrated by means of linear and nonlinear examples.

Short-term collisional evolution of a disc perturbed by a giant-planet embryo

NASA Astrophysics Data System (ADS)

Charnoz, S.; Thébault, P.; Brahic, A.

2001-07-01

A simple numerical model has been developed to study the evolution of a disc of planetesimals under mutual inelastic collisions in the potential field of a central body and of an embedded giant-planet embryo. Masses for the latter range from 0.5 to 300 Earth masses. A mass of 15 Moplus is typical of the solid-core model for the formation of giant planets. The initially cold disc consists of a few thousand particles. Those initially present between one and three Hill radii from the perturber's orbit are transferred to very eccentric orbits causing violent collisions throughout the disc. The perturbation propagates far from the perturber, like a heat transfer: a 15 Moplus perturber orbiting at 5.2 a.u. heats up the disc from 2.3 to at least 11 a.u. from the central body in a few 105 to 106 years. Relative velocities are typically increased by a factor of 10 to 100. The extent of the heated region increases with the protoplanet's mass while the propagation timescale decreases. The resulting radial mixing has potential applications for the origin of the Asteroid Belt, in particular for the radial distribution of the asteroid's spectroscopic families.
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.
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
Consistent scalar and tensor perturbation power spectra in single fluid matter bounce with dark energy era

NASA Astrophysics Data System (ADS)

Bacalhau, Anna Paula; Pinto-Neto, Nelson; Vitenti, Sandro Dias Pinto

2018-04-01

We investigate cosmological scenarios containing one canonical scalar field with an exponential potential in the context of bouncing models, in which the bounce happens due to quantum cosmological effects. The only possible bouncing solutions in this scenario (discarding an infinitely fine-tuned exception) must have one and only one dark energy phase, occurring either in the contracting era or in the expanding era. Hence, these bounce solutions are necessarily asymmetric. Naturally, the more convenient solution is the one in which the dark energy phase happens in the expanding era, in order to be a possible explanation for the current accelerated expansion indicated by cosmological observations. In this case, one has the picture of a Universe undergoing a classical dust contraction from very large scales, the initial repeller of the model, moving to a classical stiff-matter contraction near the singularity, which is avoided due to the quantum bounce. The Universe is then launched to a dark energy era, after passing through radiation- and dust-dominated phases, finally returning to the dust expanding phase, the final attractor of the model. We calculate the spectral indices and amplitudes of scalar and tensor perturbations numerically, considering the whole history of the model, including the bounce phase itself, without making any approximation nor using any matching condition on the perturbations. As the background model is necessarily dust dominated in the far past, the usual adiabatic vacuum initial conditions can be easily imposed in this era. Hence, this is a cosmological model in which the presence of dark energy behavior in the Universe does not turn the usual vacuum initial conditions prescription for cosmological perturbation in bouncing models problematic. Scalar and tensor perturbations end up being almost scale invariant, as expected. The background parameters can be adjusted, without fine-tunings, to yield the observed amplitude for scalar perturbations and also for the ratio between tensor and scalar amplitudes, r =T /S ≲0.1 . The amplification of scalar perturbations over tensor perturbations takes place only around the bounce, due to quantum effects, and it would not occur if General Relativity has remained valid throughout this phase. Hence, this is a bouncing model in which a single field induces not only an expanding background dark energy phase but also produces all observed features of cosmological perturbations of quantum mechanical origin at linear order.
Use of the adverse outcome pathway framework to represent cross-species consequences of specific pathway perturbations

EPA Science Inventory

The adverse outcome pathway (AOP) framework has been developed as a means for assembling scientifically defensible descriptions of how particular molecular perturbations, termed molecular initiating events (MIEs), can evoke a set of predictable responses at different levels of bi...
Perturbation Facilitated Optical Optical Double Resonance Investigation of the Quintet Manifold of C_2 by Applying Two-Color Four-Wave Mixing

NASA Astrophysics Data System (ADS)

Bornhauser, Peter; Marquardt, Roberto; Radi, Peter

2014-06-01

The potential of four-wave mixing spectroscopy for deperturbation studies has been demonstrated by an analysis of the spin-orbit and L-uncoupling interaction between the d ^3Π_g,v=4 and the b ^3Σ_g^-, v=16 states of C_2. The double-resonance method provides unambiguous assignments of perturbed transitions by intermediate level labeling. Furthermore, the sensitivity of the method unveiled extra transitions that originate from the perturbing b ^3Σ_g^-, v=16 state. A following study has successfully applied the method to deperturb the d ^3Π_g,v=6 state of the dicarbon and lead to the discovery of the first high-spin state of C_2. The energetically lowest quintet (^5Π_g) %and the additionally perturbing b ^3Σ_g^-, v=19 state% has been characterized by applying a conventional Hamiltonian. The detailed study unraveled major issues of the so-called high-pressure band of C_2 which were initially observed back in 1910 and later observed in numerous experimental environments. In this work we take into account our recent studies on tri-carbon where we used perturbation-facilitated two-color resonant four-wave mixing spectroscopy to access the (dark) triplet manifold of C_3 from the singlet tilde{X}^1Σ_g^+ ground state via ``gate-way" levels (i.e. singlet-triplet mixed levels). In a similar way, we performed for this study perturbation-facilitated optical-optical double-resonance experiments to access the first excited quintet state of C_2 via ``gate-way states" in the perturbed d ^3Π_g,v=6. The newly found ^5Π_u state is characterized at rotational resolution by performing a least-squares fit of the observed transitions to a ^5Π_u - ^5Π_g Hamiltionian. The work represents a rare case of a successful analysis of a quintet manifold of a molecule exhibiting a singlet ground state (^1Σ_g^+). P. Bornhauser, G. Knopp, T. Gerber, and P.P. Radi, Journal of Molecular Spectroscopy 262, 69 (2010). P. Bornhauser, Y. Sych, G. Knopp, T. Gerber, and P.P. Radi, J. Chem. Phys. 134, 044302 (2011). A. Fowler, Monthly Notices of the Royal Astronomical Society 70, 484 (1910). Y. Sych, P. Bornhauser, G. Knopp, Y. Liu, T. Gerber, R. Marquardt, and P.P. Radi, J. Chem. Phys. 139, 154203 (2013).
Optimal Initial Perturbations for Ensemble Prediction of the Madden-Julian Oscillation during Boreal Winter

NASA Technical Reports Server (NTRS)

Ham, Yoo-Geun; Schubert, Siegfried; Chang, Yehui

2012-01-01

An initialization strategy, tailored to the prediction of the Madden-Julian oscillation (MJO), is evaluated using the Goddard Earth Observing System Model, version 5 (GEOS-5), coupled general circulation model (CGCM). The approach is based on the empirical singular vectors (ESVs) of a reduced-space statistically determined linear approximation of the full nonlinear CGCM. The initial ESV, extracted using 10 years (1990-99) of boreal winter hindcast data, has zonal wind anomalies over the western Indian Ocean, while the final ESV (at a forecast lead time of 10 days) reflects a propagation of the zonal wind anomalies to the east over the Maritime Continent an evolution that is characteristic of the MJO. A new set of ensemble hindcasts are produced for the boreal winter season from 1990 to 1999 in which the leading ESV provides the initial perturbations. The results are compared with those from a set of control hindcasts generated using random perturbations. It is shown that the ESV-based predictions have a systematically higher bivariate correlation skill in predicting the MJO compared to those using the random perturbations. Furthermore, the improvement in the skill depends on the phase of the MJO. The ESV is particularly effective in increasing the forecast skill during those phases of the MJO in which the control has low skill (with correlations increasing by as much as 0.2 at 20 25-day lead times), as well as during those times in which the MJO is weak.
Evolution of density and velocity profiles of dark matter and dark energy in spherical voids

NASA Astrophysics Data System (ADS)

Novosyadlyj, Bohdan; Tsizh, Maksym; Kulinich, Yurij

2017-02-01

We analyse the evolution of cosmological perturbations which leads to the formation of large isolated voids in the Universe. We assume that initial perturbations are spherical and all components of the Universe (radiation, matter and dark energy) are continuous media with ideal fluid energy-momentum tensors, which interact only gravitationally. Equations of the evolution of perturbations for every component in the comoving to cosmological background reference frame are obtained from equations of energy and momentum conservation and Einstein's ones and are integrated numerically. Initial conditions are set at the early stage of evolution in the radiation-dominated epoch, when the scale of perturbation is much larger than the particle horizon. Results show how the profiles of density and velocity of matter and dark energy are formed and how they depend on parameters of dark energy and initial conditions. In particular, it is shown that final matter density and velocity amplitudes change within range ˜4-7 per cent when the value of equation-of-state parameter of dark energy w vary in the range from -0.8 to -1.2, and change within ˜1 per cent only when the value of effective sound speed of dark energy vary over all allowable range of its values.
On the generation of climate model ensembles

NASA Astrophysics Data System (ADS)

Haughton, Ned; Abramowitz, Gab; Pitman, Andy; Phipps, Steven J.

2014-10-01

Climate model ensembles are used to estimate uncertainty in future projections, typically by interpreting the ensemble distribution for a particular variable probabilistically. There are, however, different ways to produce climate model ensembles that yield different results, and therefore different probabilities for a future change in a variable. Perhaps equally importantly, there are different approaches to interpreting the ensemble distribution that lead to different conclusions. Here we use a reduced-resolution climate system model to compare three common ways to generate ensembles: initial conditions perturbation, physical parameter perturbation, and structural changes. Despite these three approaches conceptually representing very different categories of uncertainty within a modelling system, when comparing simulations to observations of surface air temperature they can be very difficult to separate. Using the twentieth century CMIP5 ensemble for comparison, we show that initial conditions ensembles, in theory representing internal variability, significantly underestimate observed variance. Structural ensembles, perhaps less surprisingly, exhibit over-dispersion in simulated variance. We argue that future climate model ensembles may need to include parameter or structural perturbation members in addition to perturbed initial conditions members to ensure that they sample uncertainty due to internal variability more completely. We note that where ensembles are over- or under-dispersive, such as for the CMIP5 ensemble, estimates of uncertainty need to be treated with care.
DOE Office of Scientific and Technical Information (OSTI.GOV)

Peralta, Pedro; Fortin, Elizabeth; Opie, Saul

Activities for this grant included: 1) Development of dynamic impact experiments to probe strength and phase transition influence on dynamic deformation, 2) development of modern strength and phase aware simulation capabilities, 3) and post-processing of experimental data with simulation and closed form analytical techniques. Two different dynamic experiments were developed to probe material strengths in solid metals (largely copper and iron in this effort). In the first experiment a flyer plate impacts a flat target with an opposite rippled surface that is partially supported by a weaker window material. Post mortem analysis of the target sample showed a strong andmore » repeatable residual plastic deformation dependence on grain orientation. Yield strengths for strain rates near 10 5 s -1 and plastic strains near ~50% were estimated to be around 180 to 240 MPa, varying in this range with grain orientation. Unfortunately dynamic real-time measurements were difficult with this setup due to diagnostic laser scattering; hence, an additional experimental setup was developed to complement these results. In the second set of experiments a rippled surface was ablated by a controlled laser pulsed, which launched a rippled shock front to an opposite initially flat diagnostic surface that was monitored in real-time with spatially resolved velocimetry techniques, e.g., line VISAR in addition to Transient Imaging Displacement Interferometry (TIDI) displacement measurements. This setup limited the displacements at the diagnostic surface to a reasonable level for TIDI measurements (~ less than one micrometer). These experiments coupled with analytical and numerical solutions provided evidence that viscous and elastic deviatoric strength affect shock front perturbation evolution in clearly different ways. Particularly, normalized shock front perturbation amplitudes evolve with viscosity (η) and perturbation wavelength (λ) as η/λ, such that increasing viscosity (or decreasing the initial wavelength) delays the perturbation decay. Conversely our experimental data, analysis and simulations show that for materials with elastic yield strength Y the normalized shock perturbation amplitude evolves with Yλ/A 0, which shows wavelength increases have the opposite effect as in viscous materials and perturbation decay is also dependent on initial amplitude A 0 (viscous materials are independent of this parameter). Materials where strength had clear strain rate dependence, e.g., such as a PTW material law, behaved similarly to materials with only an effective yield stress (elastic-perfectly plastic) in the shock front perturbation studies obeying a Y effλA 0 relationship where Y eff was a constant (near ~400 MPa for Cu for strain rates around 10 6 s -1). Magnitude changes in strain rate would increase Y eff as would be expected from the PTW behavior, but small perturbations (typical of regions behind the shock front) near a mean had little effect. Additional work based on simulations showed that phase transformation kinetics can affect the behavior of the perturbed shock front as well as the evolution of the RM-like instability that develops due to the imprint of the perturbed shock front on the initially flat surface as the shock breaks out.« less
Stable amplitude chimera states in a network of locally coupled Stuart-Landau oscillators

NASA Astrophysics Data System (ADS)

Premalatha, K.; Chandrasekar, V. K.; Senthilvelan, M.; Lakshmanan, M.

2018-03-01

We investigate the occurrence of collective dynamical states such as transient amplitude chimera, stable amplitude chimera, and imperfect breathing chimera states in a locally coupled network of Stuart-Landau oscillators. In an imperfect breathing chimera state, the synchronized group of oscillators exhibits oscillations with large amplitudes, while the desynchronized group of oscillators oscillates with small amplitudes, and this behavior of coexistence of synchronized and desynchronized oscillations fluctuates with time. Then, we analyze the stability of the amplitude chimera states under various circumstances, including variations in system parameters and coupling strength, and perturbations in the initial states of the oscillators. For an increase in the value of the system parameter, namely, the nonisochronicity parameter, the transient chimera state becomes a stable chimera state for a sufficiently large value of coupling strength. In addition, we also analyze the stability of these states by perturbing the initial states of the oscillators. We find that while a small perturbation allows one to perturb a large number of oscillators resulting in a stable amplitude chimera state, a large perturbation allows one to perturb a small number of oscillators to get a stable amplitude chimera state. We also find the stability of the transient and stable amplitude chimera states and traveling wave states for an appropriate number of oscillators using Floquet theory. In addition, we also find the stability of the incoherent oscillation death states.
Stable amplitude chimera states in a network of locally coupled Stuart-Landau oscillators.

PubMed

Premalatha, K; Chandrasekar, V K; Senthilvelan, M; Lakshmanan, M

2018-03-01

We investigate the occurrence of collective dynamical states such as transient amplitude chimera, stable amplitude chimera, and imperfect breathing chimera states in a locally coupled network of Stuart-Landau oscillators. In an imperfect breathing chimera state, the synchronized group of oscillators exhibits oscillations with large amplitudes, while the desynchronized group of oscillators oscillates with small amplitudes, and this behavior of coexistence of synchronized and desynchronized oscillations fluctuates with time. Then, we analyze the stability of the amplitude chimera states under various circumstances, including variations in system parameters and coupling strength, and perturbations in the initial states of the oscillators. For an increase in the value of the system parameter, namely, the nonisochronicity parameter, the transient chimera state becomes a stable chimera state for a sufficiently large value of coupling strength. In addition, we also analyze the stability of these states by perturbing the initial states of the oscillators. We find that while a small perturbation allows one to perturb a large number of oscillators resulting in a stable amplitude chimera state, a large perturbation allows one to perturb a small number of oscillators to get a stable amplitude chimera state. We also find the stability of the transient and stable amplitude chimera states and traveling wave states for an appropriate number of oscillators using Floquet theory. In addition, we also find the stability of the incoherent oscillation death states.
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.
Overheating instability of a thin conductor with respect to stratification

NASA Astrophysics Data System (ADS)

Garanin, S. F.; Kuznetsov, S. D.

2018-04-01

We consider an overheating instability of a thin (compared to the skin depth) conductor with respect to stratification at the stage when its resistivity rises up to an electrical explosion. Temperature perturbations under such conditions are shown to grow in proportion to resistivity. In the model, when resistivity is proportional to temperature, perturbations grow in proportion to temperature and hence exhibit no relative growth. For a conductor with initial thickness perturbations, temperature perturbations grow in proportion to resistivity and current action integral, i.e., somewhat faster than perturbations in the problem of constant thickness conductors. Comparison of our results with simulations of the growth of stratification during electrical heating of foils in warm dense matter generation systems demonstrates their close agreement.
External front instabilities induced by a shocked particle ring.

PubMed

Rodriguez, V; Saurel, R; Jourdan, G; Houas, L

2014-10-01

The dispersion of a cylindrical particle ring by a blast or shock wave induces the formation of coherent structures which take the form of particle jets. A blast wave, issuing from the discharge of a planar shock wave at the exit of a conventional shock tube, is generated in the center of a granular medium ring initially confined inside a Hele-Shaw cell. With the present experimental setup, under impulsive acceleration, a solid particle-jet formation is observed in a quasi-two-dimensional configuration. The aim of the present investigation is to observe in detail the formation of very thin perturbations created around the external surface of the dispersed particle layer. By means of fast flow visualization with an appropriate recording window, we focus solely on the first instants during which the external particle ring becomes unstable. We find that the critical area of the destabilization of the external ring surface is constant regardless of the acceleration of the initial layer. Moreover, we observe in detail the external front perturbation wavelength, rendered dimensionless by the initial ring perimeter, and follow its evolution with the initial particle layer acceleration. We report this quantity to be constant regardless of the evolution of the initial particle layer acceleration. Finally, we can reasonably assert that external front perturbations depend solely on the material of the particles.
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.
Determination of aerodynamic sensitivity coefficients in the transonic and supersonic regimes

NASA Technical Reports Server (NTRS)

Elbanna, Hesham M.; Carlson, Leland A.

1989-01-01

The quasi-analytical approach is developed to compute airfoil aerodynamic sensitivity coefficients in the transonic and supersonic flight regimes. Initial investigation verifies the feasibility of this approach as applied to the transonic small perturbation residual expression. Results are compared to those obtained by the direct (finite difference) approach and both methods are evaluated to determine their computational accuracies and efficiencies. The quasi-analytical approach is shown to be superior and worth further investigation.
High-Order Shock-Capturing Methods for Modeling Dynamics of the Solar Atmosphere

NASA Technical Reports Server (NTRS)

Bryson, Steve; Kosovichev, Alexander; Levy, Doron

2004-01-01

We use one-dimensional high-order central shock capturing numerical methods to study the response of various model solar atmospheres to forcing at the solar surface. The dynamics of the atmosphere is modeled with the Euler equations in a variable-sized flux tube in the presence of gravity. We study dynamics of the atmosphere suggestive of spicule formation and coronal oscillations. These studies are performed on observationally-derived model atmospheres above the quiet sun and above sunspots. To perform these simulations, we provide a new extension of existing second- and third- order shock-capturing methods to irregular grids. We also solve the problem of numerically maintaining initial hydrostatic balance via the introduction of new variables in the model equations and a careful initialization mechanism. We find several striking results: all model atmospheres respond to a single impulsive perturbation with several strong shock waves consistent with the rebound-shock model. These shock waves lift material and the transition region well into the initial corona, and the sensitivity of this lift to the initial impulse depends non-linearly on the details of the atmosphere model. We also reproduce an observed 3-minute coronal oscillation above sunspots compared to 5-minute oscillations above the quiet sun.
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.
Program for the solution of multipoint boundary value problems of quasilinear differential equations

NASA Technical Reports Server (NTRS)

1973-01-01

Linear equations are solved by a method of superposition of solutions of a sequence of initial value problems. For nonlinear equations and/or boundary conditions, the solution is iterative and in each iteration a problem like the linear case is solved. A simple Taylor series expansion is used for the linearization of both nonlinear equations and nonlinear boundary conditions. The perturbation method of solution is used in preference to quasilinearization because of programming ease, and smaller storage requirements; and experiments indicate that the desired convergence properties exist although no proof or convergence is given.

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.
A Comparison of Perturbed Initial Conditions and Multiphysics Ensembles in a Severe Weather Episode in Spain

NASA Technical Reports Server (NTRS)

Tapiador, Francisco; Tao, Wei-Kuo; Angelis, Carlos F.; Martinez, Miguel A.; Cecilia Marcos; Antonio Rodriguez; Hou, Arthur; Jong Shi, Jain

2012-01-01

Ensembles of numerical model forecasts are of interest to operational early warning forecasters as the spread of the ensemble provides an indication of the uncertainty of the alerts, and the mean value is deemed to outperform the forecasts of the individual models. This paper explores two ensembles on a severe weather episode in Spain, aiming to ascertain the relative usefulness of each one. One ensemble uses sensible choices of physical parameterizations (precipitation microphysics, land surface physics, and cumulus physics) while the other follows a perturbed initial conditions approach. The results show that, depending on the parameterizations, large differences can be expected in terms of storm location, spatial structure of the precipitation field, and rain intensity. It is also found that the spread of the perturbed initial conditions ensemble is smaller than the dispersion due to physical parameterizations. This confirms that in severe weather situations operational forecasts should address moist physics deficiencies to realize the full benefits of the ensemble approach, in addition to optimizing initial conditions. The results also provide insights into differences in simulations arising from ensembles of weather models using several combinations of different physical parameterizations.
zeldovich-PLT: Zel'dovich approximation initial conditions generator

NASA Astrophysics Data System (ADS)

Eisenstein, Daniel; Garrison, Lehman

2016-05-01

zeldovich-PLT generates Zel'dovich approximation (ZA) initial conditions (i.e. first-order Lagrangian perturbation theory) for cosmological N-body simulations, optionally applying particle linear theory (PLT) corrections.
Numerical Generation of Dense Plume Fingers in Unsaturated Homogeneous Porous Media

NASA Astrophysics Data System (ADS)

Cremer, C.; Graf, T.

2012-04-01

In nature, the migration of dense plumes typically results in the formation of vertical plume fingers. Flow direction in fingers is downwards, which is counterbalanced by upwards flow of less dense fluid between fingers. In heterogeneous media, heterogeneity itself is known to trigger the formation of fingers. In homogeneous media, however, fingers are also created even if all grains had the same diameter. The reason is that pore-scale heterogeneity leading to different flow velocities also exists in homogeneous media due to two effects: (i) Grains of identical size may randomly arrange differently, e.g. forming tetrahedrons, hexahedrons or octahedrons. Each arrangement creates pores of varying diameter, thus resulting in different average flow velocities. (ii) Random variations of solute concentration lead to varying buoyancy effects, thus also resulting in different velocities. As a continuation of previously made efforts to incorporate pore-scale heterogeneity into fully saturated soil such that dense fingers are realistically generated (Cremer and Graf, EGU Assembly, 2011), the current paper extends the research scope from saturated to unsaturated soil. Perturbation methods are evaluated by numerically re-simulating a laboratory-scale experiment of plume transport in homogeneous unsaturated sand (Simmons et al., Transp. Porous Media, 2002). The following 5 methods are being discussed: (i) homogeneous sand, (ii) initial perturbation of solute concentration, (iii) spatially random, time-constant perturbation of solute source, (iv) spatially and temporally random noise of simulated solute concentration, and (v) random K-field that introduces physically insignificant but numerically significant heterogeneity. Results demonstrate that, as opposed to saturated flow, perturbing the solute source will not result in plume fingering. This is because the location of the perturbed source (domain top) and the location of finger generation (groundwater surface) do not coincide. Alternatively, similar to saturated flow, applying either a random concentration noise (iv) or a random K-field (v) generates realistic plume fingering. Future work will focus on the generation mechanisms of plume finger splitting.
Theoretical study on the photoabsorption in the Herzberg I band system of the O 2 molecule

NASA Astrophysics Data System (ADS)

Takegami, Ryuta; Yabushita, Satoshi

2005-01-01

The Herzberg I band system of the oxygen molecule is electric-dipole forbidden and its absorption strength has been explained by intensity borrowing models which include the spin-orbit (SO) and L-uncoupling (RO) interactions as perturbations. We employed three different levels of theoretical models to evaluate these two interactions, and obtained the rotational and vibronic absorption strengths using the ab initio method. The first model calculates the transition moments induced by the SO interaction variationally with the SO configuration interaction method (SOCI), and uses the first-order perturbation theory for the RO interaction, and is called SOCI. The second is based on the first-order perturbation theory for both the SO and RO interactions, and is called Pert(Full). The last is a limited version of Pert(Full), in that the first-order perturbation wavefunction for the initial and final state is represented by only one dominant basis, namely the 1 3Π g and B3Σu- state, respectively, as originally used by England et al. [Can. J. Phys. 74 (1996) 185], and is called Pert(England). The vibronic oscillator strengths calculated by these three models were in good agreement with the experimental values. As for the integrated rotational linestrengths, the SOCI and Pert(Full) models reproduced the experimental results very well, however the Pert(England) model did not give satisfactory results. Since the Pert(England) model takes only the 1 3Π g and B3Σu- states into consideration, it cannot contain the complicated configuration interactions with highly excited states induced by the SO and RO interaction, which plays an important role for calculating the delicate integrated rotational linestrength. This result suggests that the configuration interaction with highly excited states due to some perturbations cannot be neglected in the case of very weak absorption band systems.
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.
Initial postbuckling analysis of elastoplastic thin-shear structures

NASA Technical Reports Server (NTRS)

Carnoy, E. G.; Panosyan, G.

1984-01-01

The design of thin shell structures with respect to elastoplastic buckling requires an extended analysis of the influence of initial imperfections. For conservative design, the most critical defect should be assumed with the maximum allowable magnitude. This defect is closely related to the initial postbuckling behavior. An algorithm is given for the quasi-static analysis of the postbuckling behavior of structures that exhibit multiple buckling points. the algorithm based upon an energy criterion allows the computation of the critical perturbation which will be employed for the definition of the critical defect. For computational efficiency, the algorithm uses the reduced basis technique with automatic update of the modal basis. The method is applied to the axisymmetric buckling of cylindrical shells under axial compression, and conclusions are given for future research.
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.
Initial Results of an MDO Method Evaluation Study

NASA Technical Reports Server (NTRS)

Alexandrov, Natalia M.; Kodiyalam, Srinivas

1998-01-01

The NASA Langley MDO method evaluation study seeks to arrive at a set of guidelines for using promising MDO methods by accumulating and analyzing computational data for such methods. The data are collected by conducting a series of re- producible experiments. In the first phase of the study, three MDO methods were implemented in the SIGHT: framework and used to solve a set of ten relatively simple problems. In this paper, we comment on the general considerations for conducting method evaluation studies and report some initial results obtained to date. In particular, although the results are not conclusive because of the small initial test set, other formulations, optimality conditions, and sensitivity of solutions to various perturbations. Optimization algorithms are used to solve a particular MDO formulation. It is then appropriate to speak of local convergence rates and of global convergence properties of an optimization algorithm applied to a specific formulation. An analogous distinction exists in the field of partial differential equations. On the one hand, equations are analyzed in terms of regularity, well-posedness, and the existence and unique- ness of solutions. On the other, one considers numerous algorithms for solving differential equations. The area of MDO methods studies MDO formulations combined with optimization algorithms, although at times the distinction is blurred. It is important to
Bounded relative motion under zonal harmonics perturbations

NASA Astrophysics Data System (ADS)

Baresi, Nicola; Scheeres, Daniel J.

2017-04-01

The problem of finding natural bounded relative trajectories between the different units of a distributed space system is of great interest to the astrodynamics community. This is because most popular initialization methods still fail to establish long-term bounded relative motion when gravitational perturbations are involved. Recent numerical searches based on dynamical systems theory and ergodic maps have demonstrated that bounded relative trajectories not only exist but may extend up to hundreds of kilometers, i.e., well beyond the reach of currently available techniques. To remedy this, we introduce a novel approach that relies on neither linearized equations nor mean-to-osculating orbit element mappings. The proposed algorithm applies to rotationally symmetric bodies and is based on a numerical method for computing quasi-periodic invariant tori via stroboscopic maps, including extra constraints to fix the average of the nodal period and RAAN drift between two consecutive equatorial plane crossings of the quasi-periodic solutions. In this way, bounded relative trajectories of arbitrary size can be found with great accuracy as long as these are allowed by the natural dynamics and the physical constraints of the system (e.g., the surface of the gravitational attractor). This holds under any number of zonal harmonics perturbations and for arbitrary time intervals as demonstrated by numerical simulations about an Earth-like planet and the highly oblate primary of the binary asteroid (66391) 1999 KW4.
Dependence of image quality on image operator and noise for optical diffusion tomography

NASA Astrophysics Data System (ADS)

Chang, Jenghwa; Graber, Harry L.; Barbour, Randall L.

1998-04-01

By applying linear perturbation theory to the radiation transport equation, the inverse problem of optical diffusion tomography can be reduced to a set of linear equations, W(mu) equals R, where W is the weight function, (mu) are the cross- section perturbations to be imaged, and R is the detector readings perturbations. We have studied the dependence of image quality on added systematic error and/or random noise in W and R. Tomographic data were collected from cylindrical phantoms, with and without added inclusions, using Monte Carlo methods. Image reconstruction was accomplished using a constrained conjugate gradient descent method. Result show that accurate images containing few artifacts are obtained when W is derived from a reference states whose optical thickness matches that of the unknown teste medium. Comparable image quality was also obtained for unmatched W, but the location of the target becomes more inaccurate as the mismatch increases. Results of the noise study show that image quality is much more sensitive to noise in W than in R, and the impact of noise increase with the number of iterations. Images reconstructed after pure noise was substituted for R consistently contain large peaks clustered about the cylinder axis, which was an initially unexpected structure. In other words, random input produces a non- random output. This finding suggests that algorithms sensitive to the evolution of this feature could be developed to suppress noise effects.
Perturbation method for the second-order nonlinear effect of focused acoustic field around a scatterer in an ideal fluid.

PubMed

Liu, Gang; Jayathilake, Pahala Gedara; Khoo, Boo Cheong

2014-02-01

Two nonlinear models are proposed to investigate the focused acoustic waves that the nonlinear effects will be important inside the liquid around the scatterer. Firstly, the one dimensional solutions for the widely used Westervelt equation with different coordinates are obtained based on the perturbation method with the second order nonlinear terms. Then, by introducing the small parameter (Mach number), a dimensionless formulation and asymptotic perturbation expansion via the compressible potential flow theory is applied. This model permits the decoupling between the velocity potential and enthalpy to second order, with the first potential solutions satisfying the linear wave equation (Helmholtz equation), whereas the second order solutions are associated with the linear non-homogeneous equation. Based on the model, the local nonlinear effects of focused acoustic waves on certain volume are studied in which the findings may have important implications for bubble cavitation/initiation via focused ultrasound called HIFU (High Intensity Focused Ultrasound). The calculated results show that for the domain encompassing less than ten times the radius away from the center of the scatterer, the non-linear effect exerts a significant influence on the focused high intensity acoustic wave. Moreover, at the comparatively higher frequencies, for the model of spherical wave, a lower Mach number may result in stronger nonlinear effects. Copyright © 2013 Elsevier B.V. All rights reserved.
Domain of validity of the perturbative approach to femtosecond optical spectroscopy

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

Gelin, Maxim F.; Rao, B. Jayachander; Nest, Mathias

2013-12-14

We have performed numerical nonperturbative simulations of transient absorption pump-probe responses for a series of molecular model systems. The resulting signals as a function of the laser field strength and the pump-probe delay time are compared with those obtained in the perturbative response function formalism. The simulations and their theoretical analysis indicate that the perturbative description remains valid up to moderately strong laser pulses, corresponding to a rather substantial depopulation (population) of the initial (final) electronic states.
Scalar perturbation in symmetric Lee-Wick bouncing universe

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

Cho, Inyong; Kwon, O-Kab, E-mail: iycho@seoultech.ac.kr, E-mail: okab@skku.edu

2011-11-01

We investigate the scalar perturbation in the Lee-Wick bouncing universe driven by an ordinary scalar field plus a ghost field. We consider only a symmetric evolution of the universe and the scalar fields about the bouncing point. The gauge invariant Sasaki-Mukhanov variable is numerically solved in the spatially flat gauge. We find a new form of the initial perturbation growing during the contracting phase. After the bouncing, this growing mode stabilizes to a constant mode which is responsible for the late-time power spectrum.
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.
Opposing and following responses in sensorimotor speech control: Why responses go both ways.

PubMed

Franken, Matthias K; Acheson, Daniel J; McQueen, James M; Hagoort, Peter; Eisner, Frank

2018-06-04

When talking, speakers continuously monitor and use the auditory feedback of their own voice to control and inform speech production processes. When speakers are provided with auditory feedback that is perturbed in real time, most of them compensate for this by opposing the feedback perturbation. But some responses follow the perturbation. In the present study, we investigated whether the state of the speech production system at perturbation onset may determine what type of response (opposing or following) is made. The results suggest that whether a perturbation-related response is opposing or following depends on ongoing fluctuations of the production system: The system initially responds by doing the opposite of what it was doing. This effect and the nontrivial proportion of following responses suggest that current production models are inadequate: They need to account for why responses to unexpected sensory feedback depend on the production system's state at the time of perturbation.
A high-fidelity method to analyze perturbation evolution in turbulent flows

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

Unnikrishnan, S., E-mail: sasidharannair.1@osu.edu; Gaitonde, Datta V., E-mail: gaitonde.3@osu.edu

2016-04-01

Small perturbation propagation in fluid flows is usually examined by linearizing the governing equations about a steady basic state. It is often useful, however, to study perturbation evolution in the unsteady evolving turbulent environment. Such analyses can elucidate the role of perturbations in the generation of coherent structures or the production of noise from jet turbulence. The appropriate equations are still the linearized Navier–Stokes equations, except that the linearization must be performed about the instantaneous evolving turbulent state, which forms the coefficients of the linearized equations. This is a far more difficult problem since in addition to the turbulent state,more » its rate of change and the perturbation field are all required at each instant. In this paper, we develop and use a novel technique for this problem by using a pair (denoted “baseline” and “twin”) of simultaneous synchronized Large-Eddy Simulations (LES). At each time-step, small disturbances whose propagation characteristics are to be studied, are introduced into the twin through a forcing term. At subsequent time steps, the difference between the two simulations is shown to be equivalent to solving the forced Navier–Stokes equations, linearized about the instantaneous turbulent state. The technique does not put constraints on the forcing, which could be arbitrary, e.g., white noise or other stochastic variants. We consider, however, “native” forcing having properties of disturbances that exist naturally in the turbulent environment. The method then isolates the effect of turbulence in a particular region on the rest of the field, which is useful in the study of noise source localization. The synchronized technique is relatively simple to implement into existing codes. In addition to minimizing the storage and retrieval of large time-varying datasets, it avoids the need to explicitly linearize the governing equations, which can be a very complicated task for viscous terms or turbulence closures. The method is illustrated by application to a well-validated Mach 1.3 jet. Specifically, the effects of turbulence on the jet lipline and core collapse regions on the near-acoustic field are isolated. The properties of the method, including linearity and effect of initial transients, are discussed. The results provide insight into how turbulence from different parts of the jet contribute to the observed dominance of low and high frequency content at shallow and sideline angles, respectively.« less
A high-fidelity method to analyze perturbation evolution in turbulent flows

NASA Astrophysics Data System (ADS)

Unnikrishnan, S.; Gaitonde, Datta V.

2016-04-01

Small perturbation propagation in fluid flows is usually examined by linearizing the governing equations about a steady basic state. It is often useful, however, to study perturbation evolution in the unsteady evolving turbulent environment. Such analyses can elucidate the role of perturbations in the generation of coherent structures or the production of noise from jet turbulence. The appropriate equations are still the linearized Navier-Stokes equations, except that the linearization must be performed about the instantaneous evolving turbulent state, which forms the coefficients of the linearized equations. This is a far more difficult problem since in addition to the turbulent state, its rate of change and the perturbation field are all required at each instant. In this paper, we develop and use a novel technique for this problem by using a pair (denoted "baseline" and "twin") of simultaneous synchronized Large-Eddy Simulations (LES). At each time-step, small disturbances whose propagation characteristics are to be studied, are introduced into the twin through a forcing term. At subsequent time steps, the difference between the two simulations is shown to be equivalent to solving the forced Navier-Stokes equations, linearized about the instantaneous turbulent state. The technique does not put constraints on the forcing, which could be arbitrary, e.g., white noise or other stochastic variants. We consider, however, "native" forcing having properties of disturbances that exist naturally in the turbulent environment. The method then isolates the effect of turbulence in a particular region on the rest of the field, which is useful in the study of noise source localization. The synchronized technique is relatively simple to implement into existing codes. In addition to minimizing the storage and retrieval of large time-varying datasets, it avoids the need to explicitly linearize the governing equations, which can be a very complicated task for viscous terms or turbulence closures. The method is illustrated by application to a well-validated Mach 1.3 jet. Specifically, the effects of turbulence on the jet lipline and core collapse regions on the near-acoustic field are isolated. The properties of the method, including linearity and effect of initial transients, are discussed. The results provide insight into how turbulence from different parts of the jet contribute to the observed dominance of low and high frequency content at shallow and sideline angles, respectively.
Phase dynamics of single long Josephson junction in MgB2 superconductor

NASA Astrophysics Data System (ADS)

Chimouriya, Shanker Pd.; Ghimire, Bal Ram; Kim, Ju H.

2018-05-01

A system of perturbed sine Gordon equations is derived to a superconductor-insulator-superconductor (SIS) long Joseph-son junction as an extension of the Ambegaokar-Baratoff relation, following the long route of path integral formalism. A computer simulation is performed by discretizing the equations using finite difference approximation and applied to the MgB2 superconductor with SiO2 as the junction material. The solution of unperturbed sG equation is taken as the initial profile for the simulation and observed how the perturbation terms play the role to modify it. It is found initial profile deformed as time goes on. The variation of total Josephson current has also been observed. It is found that, the perturbation terms play the role for phase frustration. The phase frustration achieves quicker for high tunneling current.
A hybrid perturbation-Galerkin method for differential equations containing a parameter

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 differential equations which involve a parameter is presented and discussed. The method consists of: (1) the use of a perturbation method to determine the asymptotic expansion of the solution about one or more values of the parameter; and (2) the use of some of the perturbation coefficient functions as trial functions in the classical Bubnov-Galerkin method. 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 illustrated first with a simple linear two-point boundary value problem and is then applied to a nonlinear two-point boundary value problem in lubrication theory. The results obtained from the hybrid method are compared with approximate solutions obtained by purely numerical methods. Some general features of the method, as well as some special tips for its implementation, are discussed. A survey of some current research application areas is presented and its degree of applicability to broader problem areas is discussed.

The correlation function for density perturbations in an expanding universe. III The three-point and predictions of the four-point and higher order correlation functions

NASA Technical Reports Server (NTRS)

Mcclelland, J.; Silk, J.

1978-01-01

Higher-order correlation functions for the large-scale distribution of galaxies in space are investigated. It is demonstrated that the three-point correlation function observed by Peebles and Groth (1975) is not consistent with a distribution of perturbations that at present are randomly distributed in space. The two-point correlation function is shown to be independent of how the perturbations are distributed spatially, and a model of clustered perturbations is developed which incorporates a nonuniform perturbation distribution and which explains the three-point correlation function. A model with hierarchical perturbations incorporating the same nonuniform distribution is also constructed; it is found that this model also explains the three-point correlation function, but predicts different results for the four-point and higher-order correlation functions than does the model with clustered perturbations. It is suggested that the model of hierarchical perturbations might be explained by the single assumption of having density fluctuations or discrete objects all of the same mass randomly placed at some initial epoch.
Continued-fraction representation of the Kraus map for non-Markovian reservoir damping

NASA Astrophysics Data System (ADS)

van Wonderen, A. J.; Suttorp, L. G.

2018-04-01

Quantum dissipation is studied for a discrete system that linearly interacts with a reservoir of harmonic oscillators at thermal equilibrium. Initial correlations between system and reservoir are assumed to be absent. The dissipative dynamics as determined by the unitary evolution of system and reservoir is described by a Kraus map consisting of an infinite number of matrices. For all Laplace-transformed Kraus matrices exact solutions are constructed in terms of continued fractions that depend on the pair correlation functions of the reservoir. By performing factorizations in the Kraus map a perturbation theory is set up that conserves in arbitrary perturbative order both positivity and probability of the density matrix. The latter is determined by an integral equation for a bitemporal matrix and a finite hierarchy for Kraus matrices. In the lowest perturbative order this hierarchy reduces to one equation for one Kraus matrix. Its solution is given by a continued fraction of a much simpler structure as compared to the non-perturbative case. In the lowest perturbative order our non-Markovian evolution equations are applied to the damped Jaynes–Cummings model. From the solution for the atomic density matrix it is found that the atom may remain in the state of maximum entropy for a significant time span that depends on the initial energy of the radiation field.
Suppressing Transients In Digital Phase-Locked Loops

NASA Technical Reports Server (NTRS)

Thomas, J. B.

1993-01-01

Loop of arbitrary order starts in steady-state lock. Method for initializing variables of digital phase-locked loop reduces or eliminates transients in phase and frequency typically occurring during acquisition of lock on signal or when changes made in values of loop-filter parameters called "loop constants". Enables direct acquisition by third-order loop without prior acquisition by second-order loop of greater bandwidth, and eliminates those perturbations in phase and frequency lock occurring when loop constants changed by arbitrarily large amounts.
Neighboring extremal optimal control design including model mismatch errors

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

Kim, T.J.; Hull, D.G.

1994-11-01

The mismatch control technique that is used to simplify model equations of motion in order to determine analytic optimal control laws is extended using neighboring extremal theory. The first variation optimal control equations are linearized about the extremal path to account for perturbations in the initial state and the final constraint manifold. A numerical example demonstrates that the tuning procedure inherent in the mismatch control method increases the performance of the controls to the level of a numerically-determined piecewise-linear controller.
Validation of zero-order feedback strategies for medium range air-to-air interception in a horizontal plane

NASA Technical Reports Server (NTRS)

Shinar, J.

1982-01-01

A zero order feedback solution of a variable speed interception game between two aircraft in the horizontal plane, obtained by using the method of forced singular perturbation (FSP), is compared with the exact open loop solution. The comparison indicates that for initial distances of separation larger than eight turning radii of the evader, the accuracy of the feedback approximation is better than one percent. The result validates the zero order FSP approximation for medium range air combat analysis.
Control of vibrations of a moving beam

NASA Astrophysics Data System (ADS)

Banichuk, N. V.; Ivanova, S. Yu; Makeev, E. V.; Sinitsyn, A. V.

2018-04-01

The translational motion of a thermoelastic beam under transverse vibrations caused by initial perturbations is considered. It is assumed that a beam moving at a constant translational speed is described by a model of a thermoelastic panel supported at the edges of the considered span. The problem of optimal suppression of vibrations is formulated when applying active transverse influences to the panel. To solve the optimization problem, modern methods developed in the theory of control of systems with distributed parameters described by partial differential equations are used.
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
Generalized hydromechanical model for stomatal responses to hydraulic perturbations.

PubMed

Kwon, H W; Choi, M Y

2014-01-07

Stomata respond in a common pattern to various hydraulic perturbations on any part of the 'soil-plant-air' system: initial transient 'wrong-way' responses and final stationary 'right-way' responses. In order to describe this pattern on the basis of statistical physics, we propose a simple model where turgor pressure of a cell is taken to be a power function of its volume, and obtain results in qualitative agreement with experimental data for responses to a variety of hydraulic perturbations: Firstly, stationary stomatal conductance as a function of the vapor pressure deficit divides into three regimes characterized by sensitivities of the stomatal conductance and the transpiration rate with respect to vapor pressure deficit; secondly, for every hydraulic perturbation, the initial transient 'wrong-way' responses always appear; thirdly, on condition that water is supplied insufficiently, stomatal oscillations are often observed; finally, stomatal responses following leaf excision exhibit, after the initial transient wrong-way responses, slow relaxation to stomatal closing. In particular, comparison of areoles having different numbers of stomata demonstrates that areoles with small numbers of stomata tend to provoke lack of water in the soil as well as in the plant. In addition, our model also describes well dependence of the stomatal conductance on temperature. It may be extended further to describe stomatal responses to other environmental factors such as carbon dioxide, light, and temperature. © 2013 Elsevier Ltd. All rights reserved.
Magneto-Rayleigh-Taylor instability in solid media

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

Sun, Y. B.; School of Physical Science and Technology, Lanzhou University, Lanzhou 73000; University of Chinese Academy of Sciences, Beijing 100049

2014-07-15

A linear analysis of the magneto-Rayleigh-Taylor instability at the interface between a Newtonian fluid and an elastic-plastic solid is performed by considering a uniform magnetic B{sup →}, parallel to the interface, which has diffused into the fluid but not into the solid. It is found that the magnetic field attributes elastic properties to the viscous fluid which enhance the stability region by stabilizing all the perturbation wavelengths shorter than λ{sub 0}∝B{sup 2} for any initial perturbation amplitude. Longer wavelengths are stabilized by the mechanical properties of the solid provided that the initial perturbation wavelength is smaller than a threshold valuemore » determined by the yield strength and the shear modulus of the solid. Beyond this threshold, the amplitude grows initially with a growth rate reduced by the solid strength properties. However, such properties do not affect the asymptotic growth rate which is only determined by the magnetic field and the fluid viscosity. The described physical situation intends to resemble some of the features present in recent experiments involving the magnetic shockless acceleration of flyers plates.« less
Stellar metallicity variations across spiral arms in disk galaxies with multiple populations

NASA Astrophysics Data System (ADS)

Khoperskov, S.; Di Matteo, P.; Haywood, M.; Combes, F.

2018-03-01

This Letter studies the formation of azimuthal metallicity variations in the disks of spiral galaxies in the absence of initial radial metallicity gradients. Using high-resolution N-body simulations, we model composite stellar discs, made of kinematically cold and hot stellar populations, and study their response to spiral arm perturbations. We find that, as expected, disk populations with different kinematics respond differently to a spiral perturbation, with the tendency for dynamically cooler populations to show a larger fractional contribution to spiral arms than dynamically hotter populations. By assuming a relation between kinematics and metallicity, namely the hotter the population, the more metal-poor it is, this differential response to the spiral arm perturbations naturally leads to azimuthal variations in the mean metallicity of stars in the simulated disk. Thus, azimuthal variations in the mean metallicity of stars across a spiral galaxy are not necessarily a consequence of the reshaping, by radial migration, of an initial radial metallicity gradient. They indeed arise naturally also in stellar disks which have initially only a negative vertical metallicity gradient.
Competition Between Transients in the Rate of Approach to a Fixed Point

NASA Astrophysics Data System (ADS)

Day, Judy; Rubin, Jonathan E.; Chow, Carson C.

2009-01-01

The goal of this paper is to provide and apply tools for analyzing a specific aspect of transient dynamics not covered by previous theory. The question we address is whether one component of a perturbed solution to a system of differential equations can overtake the corresponding component of a reference solution as both converge to a stable node at the origin, given that the perturbed solution was initially farther away and that both solutions are nonnegative for all time. We call this phenomenon tolerance, for its relation to a biological effect. We show using geometric arguments that tolerance will exist in generic linear systems with a complete set of eigenvectors and in excitable nonlinear systems. We also define a notion of inhibition that may constrain the regions in phase space where the possibility of tolerance arises in general systems. However, these general existence theorems do not not yield an assessment of tolerance for specific initial conditions. To address that issue, we develop some analytical tools for determining if particular perturbed and reference solution initial conditions will exhibit tolerance.
Numerical theory of the motion of Jupiter's Galilean satellites

NASA Astrophysics Data System (ADS)

Kosmodamianskii, G. A.

2009-12-01

A numerical theory of the motion of Jupiter’s Galilean satellites was constructed using 3767 absolute observations of the satellites. The theory was based on the numerical integration of the equations of motion of the satellites. The integration was carried out by Everhart’s method using the ERA software package developed at the Institute of Applied Astronomy (IAA). Perturbations due to the oblateness of the central planet, perturbations from Saturn and the Sun, and the mutual attraction of the satellites were taken into account in the integration. As a result, the coefficients of the Chebyshev series expansion for coordinates and velocities were found for the period from 1962 to 2010. The initial coordinates and velocities of the satellites, as well as their masses, the mass of Jupiter, and the harmonic coefficient J 2 of the potential of Jupiter, were adjusted. The resulting ephemerides were compared to those of Lieske and Lainey.
The Stabilizing Effect of Spacetime Expansion on Relativistic Fluids With Sharp Results for the Radiation Equation of State

NASA Astrophysics Data System (ADS)

Speck, Jared

2013-07-01

In this article, we study the 1 + 3-dimensional relativistic Euler equations on a pre-specified conformally flat expanding spacetime background with spatial slices that are diffeomorphic to {R}^3. We assume that the fluid verifies the equation of state {p = c2s ρ,} where {0 ≤ cs ≤ √{1/3}} is the speed of sound. We also assume that the reciprocal of the scale factor associated with the expanding spacetime metric verifies a c s -dependent time-integrability condition. Under these assumptions, we use the vector field energy method to prove that an explicit family of physically motivated, spatially homogeneous, and spatially isotropic fluid solutions are globally future-stable under small perturbations of their initial conditions. The explicit solutions corresponding to each scale factor are analogs of the well-known spatially flat Friedmann-Lemaître-Robertson-Walker family. Our nonlinear analysis, which exploits dissipative terms generated by the expansion, shows that the perturbed solutions exist for all future times and remain close to the explicit solutions. This work is an extension of previous results, which showed that an analogous stability result holds when the spacetime is exponentially expanding. In the case of the radiation equation of state p = (1/3)ρ, we also show that if the time-integrability condition for the reciprocal of the scale factor fails to hold, then the explicit fluid solutions are unstable. More precisely, we show the existence of an open family of initial data such that (i) it contains arbitrarily small smooth perturbations of the explicit solutions' data and (ii) the corresponding perturbed solutions necessarily form shocks in finite time. The shock formation proof is based on the conformal invariance of the relativistic Euler equations when {c2s = 1/3,} which allows for a reduction to a well-known result of Christodoulou.
Nonlinear structure formation in flat cosmological models

NASA Technical Reports Server (NTRS)

Martel, Hugo

1995-01-01

This paper describes the formation of nonlinear structure in flat (zero curvature) Friedmann cosmological models. We consider models with two components: the usual nonrelativistic component that evolves under gravity and eventually forms the large-scale structure of the universe, and a uniform dark matter component that does not clump under gravity, and whose energy density varies with the scale factor a(t) like a(t)(sup -n), where n is a free parameter. Each model is characterized by two parameters: the exponent n and the present density parameter Omega(sub 0) of the nonrelativistic component. The linear perturbation equations are derived and solved for these models, for the three different cases n = 3, n is greater than 3, and n is less than 3. The case n = 3 is relevant to model with massive neutrinos. The presence of the uniform component strongly reduces the growth of the perturbation compared with the Einstein-de Sitter model. We show that the Meszaros effect (suppression of growth at high redshift) holds not only for n = 4, radiation-dominated models, but for all models with n is greater than 3. This essentially rules out any such model. For the case n is less than 3, we numerically integrate the perturbation equations from the big bang to the present, for 620 different models with various values of Omega(sub 0) and n. Using these solutions, we show that the function f(Omega(sub 0), n) = (a/delta(sub +))d(delta)(sub +)/da, which enters in the relationship between the present density contrast delta(sub 0) and peculiar velocity field u(sub 0) is essentially independent of n. We derive approximate solutions for the second-order perturbation equations. These second-order solutions are tested against the exact solutions and the Zel'dovich approximation for spherically symmetric perturbations in the marginally nonlinear regime (the absolute value of delta is less than or approximately 1). The second-order and Zel'dovich solutions have comparable accuracy, significantly higher than the accuracy of the linear solutions. We then investigate the dependence of the delta(sub 0) - u(sub 0) relationship upon the value of n in the nonlinear regime using the second-order solutions for marginally nonlinear, general perturbations, and the exact solutions for strongly nonlinear, spherically symmetric perturbations. In both cases, we find that the delta(sub 0) - u(sub 0) relationship remains independent of n. We speculate that this result extends to strongly nonlinear, general perturbations as well. This eliminates any hope to determine the presence of the uniform component or the value of n using dynamical methods. Finally, we compute the nonlinear evolution of the skewness of the distribution of values of delta, assuming Gaussian initial conditions. We find that the skewness is not only independent of n, but also of Omega(sub 0). Thus the skewness cannot be used to discriminate among various models with Gaussian initial conditions. However, it can be used for testing the Gaussianity of the initial conditions themselves. We conclude that the uniform component leaves no observable signature in the present large-scale structure of the universe. To determine its presence and nature, we must investigate the relationship between the past and present universe, using redshift-dependent tests.
Accurate computation and continuation of homoclinic and heteroclinic orbits for singular perturbation problems

NASA Technical Reports Server (NTRS)

Vaughan, William W.; Friedman, Mark J.; Monteiro, Anand C.

1993-01-01

In earlier papers, Doedel and the authors have developed a numerical method and derived error estimates for the computation of branches of heteroclinic orbits for a system of autonomous ordinary differential equations in R(exp n). The idea of the method is to reduce a boundary value problem on the real line to a boundary value problem on a finite interval by using a local (linear or higher order) approximation of the stable and unstable manifolds. A practical limitation for the computation of homoclinic and heteroclinic orbits has been the difficulty in obtaining starting orbits. Typically these were obtained from a closed form solution or via a homotopy from a known solution. Here we consider extensions of our algorithm which allow us to obtain starting orbits on the continuation branch in a more systematic way as well as make the continuation algorithm more flexible. In applications, we use the continuation software package AUTO in combination with some initial value software. The examples considered include computation of homoclinic orbits in a singular perturbation problem and in a turbulent fluid boundary layer in the wall region problem.
On the Convenience of Using the Complete Linearization Method in Modelling the BLR of AGN

NASA Astrophysics Data System (ADS)

Patriarchi, P.; Perinotto, M.

The Complete Linearization Method (Mihalas, 1978) consists in the determination of the radiation field (at a set of frequency points), atomic level populations, temperature, electron density etc., by resolving the system of radiative transfer, thermal equilibrium, statistical equilibrium equations simultaneously and self-consistently. Since the system is not linear, it must be solved by iteration after linearization, using a perturbative method, starting from an initial guess solution. Of course the Complete Linearization Method is more time consuming than the previous one. But how great can this disadvantage be in the age of supercomputers? It is possible to approximately evaluate the CPU time needed to run a model by computing the number of multiplications necessary to solve the system.
Perturbations in the initial soil moisture conditions: Impacts on hydrologic simulation in a large river basin

NASA Astrophysics Data System (ADS)

Niroula, Sundar; Halder, Subhadeep; Ghosh, Subimal

2018-06-01

Real time hydrologic forecasting requires near accurate initial condition of soil moisture; however, continuous monitoring of soil moisture is not operational in many regions, such as, in Ganga basin, extended in Nepal, India and Bangladesh. Here, we examine the impacts of perturbation/error in the initial soil moisture conditions on simulated soil moisture and streamflow in Ganga basin and its propagation, during the summer monsoon season (June to September). This provides information regarding the required minimum duration of model simulation for attaining the model stability. We use the Variable Infiltration Capacity model for hydrological simulations after validation. Multiple hydrologic simulations are performed, each of 21 days, initialized on every 5th day of the monsoon season for deficit, surplus and normal monsoon years. Each of these simulations is performed with the initial soil moisture condition obtained from long term runs along with positive and negative perturbations. The time required for the convergence of initial errors is obtained for all the cases. We find a quick convergence for the year with high rainfall as well as for the wet spells within a season. We further find high spatial variations in the time required for convergence; the region with high precipitation such as Lower Ganga basin attains convergence at a faster rate. Furthermore, deeper soil layers need more time for convergence. Our analysis is the first attempt on understanding the sensitivity of hydrological simulations of Ganga basin on initial soil moisture conditions. The results obtained here may be useful in understanding the spin-up requirements for operational hydrologic forecasts.
Evolution of Rotor Wake in Swirling Flow

NASA Technical Reports Server (NTRS)

El-Haldidi, Basman; Atassi, Hafiz; Envia, Edmane; Podboy, Gary

2000-01-01

A theory is presented for modeling the evolution of rotor wakes as a function of axial distance in swirling mean flows. The theory, which extends an earlier work to include arbitrary radial distributions of mean swirl, indicates that swirl can significantly alter the wake structure of the rotor especially at large downstream distances (i.e., for moderate to large rotor-stator spacings). Using measured wakes of a representative scale model fan stage to define the mean swirl and initial wake perturbations, the theory is used to predict the subsequent evolution of the wakes. The results indicate the sensitivity of the wake evolution to the initial profile and the need to have complete and consistent initial definition of both velocity and pressure perturbations.
Improved ensemble-mean forecasting of ENSO events by a zero-mean stochastic error model of an intermediate coupled model

NASA Astrophysics Data System (ADS)

Zheng, Fei; Zhu, Jiang

2017-04-01

How to design a reliable ensemble prediction strategy with considering the major uncertainties of a forecasting system is a crucial issue for performing an ensemble forecast. In this study, a new stochastic perturbation technique is developed to improve the prediction skills of El Niño-Southern Oscillation (ENSO) through using an intermediate coupled model. We first estimate and analyze the model uncertainties from the ensemble Kalman filter analysis results through assimilating the observed sea surface temperatures. Then, based on the pre-analyzed properties of model errors, we develop a zero-mean stochastic model-error model to characterize the model uncertainties mainly induced by the missed physical processes of the original model (e.g., stochastic atmospheric forcing, extra-tropical effects, Indian Ocean Dipole). Finally, we perturb each member of an ensemble forecast at each step by the developed stochastic model-error model during the 12-month forecasting process, and add the zero-mean perturbations into the physical fields to mimic the presence of missing processes and high-frequency stochastic noises. The impacts of stochastic model-error perturbations on ENSO deterministic predictions are examined by performing two sets of 21-yr hindcast experiments, which are initialized from the same initial conditions and differentiated by whether they consider the stochastic perturbations. The comparison results show that the stochastic perturbations have a significant effect on improving the ensemble-mean prediction skills during the entire 12-month forecasting process. This improvement occurs mainly because the nonlinear terms in the model can form a positive ensemble-mean from a series of zero-mean perturbations, which reduces the forecasting biases and then corrects the forecast through this nonlinear heating mechanism.
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.

MHD thermal instabilities in cool inhomogeneous atmospheres

NASA Technical Reports Server (NTRS)

Bodo, G.; Ferrari, A.; Massaglia, S.; Rosner, R.

1983-01-01

The formation of a coronal state in a stellar atmosphere is investigated. A numerical code is used to study the effects of atmospheric gradients and finite loop dimension on the scale of unstable perturbations, solving for oscillatory perturbations as eigenfunctions of a boundary value problem. The atmosphere is considered as initially isothermal, with density and pressure having scale heights fixed by the hydrostatic equations. Joule mode instability is found to be an efficient mechanism for current filamentation and subsequent heating in initially cool atmospheres. This instability is mainly effective at the top of magnetic loops and is not suppressed by thermal conduction.
Modal interactions between a large-wavelength inclined interface and small-wavelength multimode perturbations in a Richtmyer-Meshkov instability

NASA Astrophysics Data System (ADS)

McFarland, Jacob A.; Reilly, David; Black, Wolfgang; Greenough, Jeffrey A.; Ranjan, Devesh

2015-07-01

The interaction of a small-wavelength multimodal perturbation with a large-wavelength inclined interface perturbation is investigated for the reshocked Richtmyer-Meshkov instability using three-dimensional simulations. The ares code, developed at Lawrence Livermore National Laboratory, was used for these simulations and a detailed comparison of simulation results and experiments performed at the Georgia Tech Shock Tube facility is presented first for code validation. Simulation results are presented for four cases that vary in large-wavelength perturbation amplitude and the presence of secondary small-wavelength multimode perturbations. Previously developed measures of mixing and turbulence quantities are presented that highlight the large variation in perturbation length scales created by the inclined interface and the multimode complex perturbation. Measures are developed for entrainment, and turbulence anisotropy that help to identify the effects of and competition between each perturbations type. It is shown through multiple measures that before reshock the flow processes a distinct memory of the initial conditions that is present in both large-scale-driven entrainment measures and small-scale-driven mixing measures. After reshock the flow develops to a turbulentlike state that retains a memory of high-amplitude but not low-amplitude large-wavelength perturbations. It is also shown that the high-amplitude large-wavelength perturbation is capable of producing small-scale mixing and turbulent features similar to the small-wavelength multimode perturbations.
Pumping approximately integrable systems

PubMed Central

Lange, Florian; Lenarčič, Zala; Rosch, Achim

2017-01-01

Weak perturbations can drive an interacting many-particle system far from its initial equilibrium state if one is able to pump into degrees of freedom approximately protected by conservation laws. This concept has for example been used to realize Bose–Einstein condensates of photons, magnons and excitons. Integrable quantum systems, like the one-dimensional Heisenberg model, are characterized by an infinite set of conservation laws. Here, we develop a theory of weakly driven integrable systems and show that pumping can induce large spin or heat currents even in the presence of integrability breaking perturbations, since it activates local and quasi-local approximate conserved quantities. The resulting steady state is qualitatively captured by a truncated generalized Gibbs ensemble with Lagrange parameters that depend on the structure but not on the overall amplitude of perturbations nor the initial state. We suggest to use spin-chain materials driven by terahertz radiation to realize integrability-based spin and heat pumps. PMID:28598444
Stability analysis of a pressure-solution surface

NASA Astrophysics Data System (ADS)

Gal, Doron; Nur, Amos; Aharonov, Einat

We present a linear stability analysis of a dissolution surface subjected to non-hydrostatic stress. A sinusoidal perturbation is imposed on an initially flat solid/fluid interface, and the consequent changes in elastic strain energy and surface energy are calculated. Our results demonstrate that if the far-field lateral stresses are either greater, or much smaller than the fluid pressure, the perturbed configuration has a lower strain energy than the initial one. For wavelengths greater than a critical wavelength this energy decrease may be large enough to offset the increased surface energy. Under these conditions, the perturbation grows unstably. If these conditions are not met, the surface becomes flat. The growth rate and wavelength of the maximally unstable mode depend on the mechanism of matter transport. We conclude that the instability discussed in this paper may account for the formation of stylolites and other pressure-solution phenomena, such as roughening of grain contacts.
Large-scale galaxy flow from a non-gravitational impulse

NASA Technical Reports Server (NTRS)

Hogan, Craig J.; Kaiser, Nick

1989-01-01

A theory is presented describing linear perturbations of an expanding universe containing multiple, independently perturbed, collisionless, gravitationally coupled constituents. Solutions are found in the limit where one initially unperturbed component dominates the total density. The theory is applied to perturbations generated by a nongravitational process in one or more of the light components, as would occur in explosive or radiation-pressure-instability theories of galaxy formation. The apparent dynamical density parameter and correlations between density and velocity amplitude for various populations, are evaluated as a function of cosmic scale factor.
Magnetic perturbation inspection of inner bearing races

NASA Technical Reports Server (NTRS)

Barton, J. R.; Lankford, J.

1972-01-01

Approximately 100 inner race bearings were inspected nondestructively prior to endurance testing. Two of the bearings which failed during testing spalled at the sites of subsurface inclusions previously detected by using magnetic field perturbation. At other sites initially judged to be suspect, subsurface inclusion-nucleated cracking was observed. Inspection records and metallurgical sectioning results are presented and discussed.
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
Recovering the full velocity and density fields from large-scale redshift-distance samples

NASA Technical Reports Server (NTRS)

Bertschinger, Edmund; Dekel, Avishai

1989-01-01

A new method for extracting the large-scale three-dimensional velocity and mass density fields from measurements of the radial peculiar velocities is presented. Galaxies are assumed to trace the velocity field rather than the mass. The key assumption made is that the Lagrangian velocity field has negligible vorticity, as might be expected from perturbations that grew by gravitational instability. By applying the method to cosmological N-body simulations, it is demonstrated that it accurately reconstructs the velocity field. This technique promises a direct determination of the mass density field and the initial conditions for the formation of large-scale structure from galaxy peculiar velocity surveys.
Hydrodynamic instability growth of three-dimensional modulations in radiation-driven implosions with “low-foot” and “high-foot” drives at the National Ignition Facility

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

Smalyuk, V. A.; Weber, C. R.; Robey, H. F.

Hydrodynamic instability growth has been studied using three-dimensional (3-D) broadband modulations by comparing “high-foot” and “low-foot” spherical plastic (CH) capsule implosions at the National Ignition Facility (NIF). The initial perturbations included capsule outer-surface roughness and capsule-mounting membranes (“tents”) that were similar to those used in a majority of implosions on NIF. The tents with thicknesses of 31-nm, 46-nm, and 109-nm were used in the experiments. The outer-surface roughness in the “low-foot” experiment was similar to the standard specification, while it was increased by ~4 times in the “high-foot” experiment to compensate for the reduced growth. The ablation-front instability growth wasmore » measured using a Hydrodynamic Growth Radiography platform at a convergence ratio of 3. The dominant capsule perturbations, generated by the tent mountings, had measured perturbation amplitudes comparable to the capsule thickness with the “low-foot” drive. These tent perturbations were reduced by ~3 to 10 times in implosions with the “high-foot” drive. Unexpectedly, the measured perturbations with initially thinner tents were either larger or similar to the measured perturbations with thicker tents for both “high-foot” and “low-foot” drives. While the measured instability growth of 3-D broadband perturbations was also significantly reduced by ~5 to 10 times with the “high-foot” drive, compared to the “low-foot” drive, the growth mitigation was stronger than expected based on previous “growth-factor” results measured with two-dimensional modulations. Lastly, one of the hypotheses to explain the results is based on the 3-D modulations of the oxygen content in the bulk of the capsule having a stronger effect on the overall growth of capsule perturbations than the outer-surface capsule roughness.« less
Hydrodynamic instability growth of three-dimensional modulations in radiation-driven implosions with “low-foot” and “high-foot” drives at the National Ignition Facility

DOE PAGES

Smalyuk, V. A.; Weber, C. R.; Robey, H. F.; ...

2017-04-11

Hydrodynamic instability growth has been studied using three-dimensional (3-D) broadband modulations by comparing “high-foot” and “low-foot” spherical plastic (CH) capsule implosions at the National Ignition Facility (NIF). The initial perturbations included capsule outer-surface roughness and capsule-mounting membranes (“tents”) that were similar to those used in a majority of implosions on NIF. The tents with thicknesses of 31-nm, 46-nm, and 109-nm were used in the experiments. The outer-surface roughness in the “low-foot” experiment was similar to the standard specification, while it was increased by ~4 times in the “high-foot” experiment to compensate for the reduced growth. The ablation-front instability growth wasmore » measured using a Hydrodynamic Growth Radiography platform at a convergence ratio of 3. The dominant capsule perturbations, generated by the tent mountings, had measured perturbation amplitudes comparable to the capsule thickness with the “low-foot” drive. These tent perturbations were reduced by ~3 to 10 times in implosions with the “high-foot” drive. Unexpectedly, the measured perturbations with initially thinner tents were either larger or similar to the measured perturbations with thicker tents for both “high-foot” and “low-foot” drives. While the measured instability growth of 3-D broadband perturbations was also significantly reduced by ~5 to 10 times with the “high-foot” drive, compared to the “low-foot” drive, the growth mitigation was stronger than expected based on previous “growth-factor” results measured with two-dimensional modulations. Lastly, one of the hypotheses to explain the results is based on the 3-D modulations of the oxygen content in the bulk of the capsule having a stronger effect on the overall growth of capsule perturbations than the outer-surface capsule roughness.« less
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
Visco-acoustic wave-equation traveltime inversion and its sensitivity to attenuation errors

NASA Astrophysics Data System (ADS)

Yu, Han; Chen, Yuqing; Hanafy, Sherif M.; Huang, Jiangping

2018-04-01

A visco-acoustic wave-equation traveltime inversion method is presented that inverts for the shallow subsurface velocity distribution. Similar to the classical wave equation traveltime inversion, this method finds the velocity model that minimizes the squared sum of the traveltime residuals. Even though, wave-equation traveltime inversion can partly avoid the cycle skipping problem, a good initial velocity model is required for the inversion to converge to a reasonable tomogram with different attenuation profiles. When Q model is far away from the real model, the final tomogram is very sensitive to the starting velocity model. Nevertheless, a minor or moderate perturbation of the Q model from the true one does not strongly affect the inversion if the low wavenumber information of the initial velocity model is mostly correct. These claims are validated with numerical tests on both the synthetic and field data sets.
Correlation Between the Field Line and Particle Diffusion Coefficients in the Stochastic Fields of a Tokamak

NASA Astrophysics Data System (ADS)

Calvin, Mark; Punjabi, Alkesh

1996-11-01

We use the method of quasi-magnetic surfaces to calculate the correlation between the field line and particle diffusion coefficients. The magnetic topology of a tokamak is perturbed by a spectrum of neighboring resonant resistive modes. The Hamiltonian equations of motion for the field line are integrated numerically. Poincare plots of the quasi-magnetic surfaces are generated initially and after the field line has traversed a considerable distance. From the areas of the quasi-magnetic surfaces and the field line distance, we estimate the field line diffusion coefficient. We start plasma particles on the initial quasi-surface, and calculate the particle diffusion coefficient from our Monte Carlo method (Punjabi A., Boozer A., Lam M., Kim H. and Burke K., J. Plasma Phys.), 44, 405 (1990). We then estimate the correlation between the particle and field diffusion as the strength of the resistive modes is varied.
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.
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.
Evolution of helical perturbations in a thin-shell model of an imploding liner

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

Ryutov, D. D.; Dorf, M. A.

A thin-shell model of the liner stability has been revisited and applied to the stability of the helical perturbations. Several stages of the implosion have been identified, starting from a long initial “latent” phase of an almost resting liner, continuing to the second stage of a rapid contraction and significant perturbation growth, and then transitioning to the third stage where perturbations become ballistic and highly non-linear. The stage of stagnation and rebound is beyond the scope of this paper. An importance of vorticity conservation during the late stages is emphasized. Nonlinear evolution of perturbations is followed up to the pointmore » of the formation of cusp structures. Effects of in-surface flows and of their enhancement due to the vorticity conservation are discussed. It is shown that the pre-machined perturbations created only on the outer surface of the liner grow much slower than one could anticipate. The limitations on the thin-shell description are discussed.« less
The influence of Monte Carlo source parameters on detector design and dose perturbation in small field dosimetry

NASA Astrophysics Data System (ADS)

Charles, P. H.; Crowe, S. B.; Kairn, T.; Knight, R.; Hill, B.; Kenny, J.; Langton, C. M.; Trapp, J. V.

2014-03-01

To obtain accurate Monte Carlo simulations of small radiation fields, it is important model the initial source parameters (electron energy and spot size) accurately. However recent studies have shown that small field dosimetry correction factors are insensitive to these parameters. The aim of this work is to extend this concept to test if these parameters affect dose perturbations in general, which is important for detector design and calculating perturbation correction factors. The EGSnrc C++ user code cavity was used for all simulations. Varying amounts of air between 0 and 2 mm were deliberately introduced upstream to a diode and the dose perturbation caused by the air was quantified. These simulations were then repeated using a range of initial electron energies (5.5 to 7.0 MeV) and electron spot sizes (0.7 to 2.2 FWHM). The resultant dose perturbations were large. For example 2 mm of air caused a dose reduction of up to 31% when simulated with a 6 mm field size. However these values did not vary by more than 2 % when simulated across the full range of source parameters tested. If a detector is modified by the introduction of air, one can be confident that the response of the detector will be the same across all similar linear accelerators and the Monte Carlo modelling of each machine is not required.
Estimation of metal strength at very high rates using free-surface Richtmyer–Meshkov Instabilities

DOE PAGES

Prime, Michael Bruce; Buttler, William Tillman; Buechler, Miles Allen; ...

2017-03-08

Recently, Richtmyer–Meshkov Instabilities (RMI) have been proposed for studying the average strength at strain rates up to at least 10 7/s. RMI experiments involve shocking a metal interface that has initial sinusoidal perturbations. The perturbations invert and grow subsequent to shock and may arrest because of strength effects. In this work we present new RMI experiments and data on a copper target that had five regions with different perturbation amplitudes on the free surface opposite the shock. We estimate the high-rate, low-pressure copper strength by comparing experimental data with Lagrangian numerical simulations. From a detailed computational study we find thatmore » mesh convergence must be carefully addressed to accurately compare with experiments, and numerical viscosity has a strong influence on convergence. We also find that modeling the as-built perturbation geometry rather than the nominal makes a significant difference. Because of the confounding effect of tensile damage on total spike growth, which has previously been used as the metric for estimating strength, we instead use a new strength metric: the peak velocity during spike growth. Furthermore, this new metric also allows us to analyze a broader set of experimental results that are sensitive to strength because some larger initial perturbations grow unstably to failure and so do not have a finite total spike growth.« less
Estimation of metal strength at very high rates using free-surface Richtmyer–Meshkov Instabilities

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

Prime, Michael Bruce; Buttler, William Tillman; Buechler, Miles Allen

Recently, Richtmyer–Meshkov Instabilities (RMI) have been proposed for studying the average strength at strain rates up to at least 10 7/s. RMI experiments involve shocking a metal interface that has initial sinusoidal perturbations. The perturbations invert and grow subsequent to shock and may arrest because of strength effects. In this work we present new RMI experiments and data on a copper target that had five regions with different perturbation amplitudes on the free surface opposite the shock. We estimate the high-rate, low-pressure copper strength by comparing experimental data with Lagrangian numerical simulations. From a detailed computational study we find thatmore » mesh convergence must be carefully addressed to accurately compare with experiments, and numerical viscosity has a strong influence on convergence. We also find that modeling the as-built perturbation geometry rather than the nominal makes a significant difference. Because of the confounding effect of tensile damage on total spike growth, which has previously been used as the metric for estimating strength, we instead use a new strength metric: the peak velocity during spike growth. Furthermore, this new metric also allows us to analyze a broader set of experimental results that are sensitive to strength because some larger initial perturbations grow unstably to failure and so do not have a finite total spike growth.« less
Numerical and experimental investigation on static electric charge model at stable cone-jet region

NASA Astrophysics Data System (ADS)

Hashemi, Ali Reza; Pishevar, Ahmad Reza; Valipouri, Afsaneh; Pǎrǎu, Emilian I.

2018-03-01

In a typical electro-spinning process, the steady stretching process of the jet beyond the Taylor cone has a significant effect on the dimensions of resulting nanofibers. Also, it sets up the conditions for the onset of the bending instability. The focus of this work is the modeling and simulation of the initial stable jet phase seen during the electro-spinning process. The perturbation method was applied to solve hydrodynamic equations, and the electrostatic equation was solved by a boundary integral method. These equations were coupled with the stress boundary conditions derived appropriate at the fluid-fluid interface. Perturbation equations were discretized by the second-order finite difference method, and the Newton method was implemented to solve the discretized nonlinear system. Also, the boundary element method was utilized to solve the electrostatic equation. In the theoretical study, the fluid is described as a leaky dielectric with charges only on the jet surface in dielectric air. In this study, electric charges were modeled as static. Comparison of numerical and experimental results shows that at low flow rates and high electric field, good agreement was achieved because of the superior importance of the charge transport by conduction rather than convection and charge concentration. In addition, the effect of unevenness of the electric field around the nozzle tip was experimentally studied through plate-plate geometry as well as point-plate geometry.

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).
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.
Perturbation Selection and Local Influence Analysis for Nonlinear Structural Equation Model

ERIC Educational Resources Information Center

Chen, Fei; Zhu, Hong-Tu; Lee, Sik-Yum

2009-01-01

Local influence analysis is an important statistical method for studying the sensitivity of a proposed model to model inputs. One of its important issues is related to the appropriate choice of a perturbation vector. In this paper, we develop a general method to select an appropriate perturbation vector and a second-order local influence measure…
Orbit Stability of OSIRIS-REx in the Vicinity of Bennu Using a High-Fidelity Solar Radiation Model

NASA Technical Reports Server (NTRS)

Williams, Trevor W.; Hughes, Kyle M.; Mashiku, Alinda K.; Longuski, James M.

2015-01-01

Solar radiation pressure is one of the largest perturbing forces on the OSIRISRex trajectory as it orbits the asteroid Bennu. In this work, we investigate how forces due to solar radiation perturb the OSIRIS-REx trajectory in a high-fidelity model. The model accounts for Bennu's non-spherical gravity field, third-body gravity forces from the Sun and Jupiter, as well as solar radiation forces acting on a simplified spacecraft model. Such high-fidelity simulations indicate significant solar radiation pressure perturbations from the nominal orbit. Modifications to the initial design of the nominal orbit are found using a variation of parameters approach that reduce the perturbation in eccentricity by a factor of one-half.
Simulations of the Richtmyer-Meshkov Instability with experimentally measured volumetric initial conditions

NASA Astrophysics Data System (ADS)

Ferguson, Kevin; Sewell, Everest; Krivets, Vitaliy; Greenough, Jeffrey; Jacobs, Jeffrey

2016-11-01

Initial conditions for the Richtmyer-Meshkov instability (RMI) are measured in three dimensions in the University of Arizona Vertical Shock Tube using a moving magnet galvanometer system. The resulting volumetric data is used as initial conditions for the simulation of the RMI using ARES at Lawrence-Livermore National Laboratory (LLNL). The heavy gas is sulfur hexafluoride (SF6), and the light gas is air. The perturbations are generated by harmonically oscillating the gasses vertically using two loudspeakers mounted to the shock tube which cause Faraday resonance, producing a random short wavelength perturbation on the interface. Planar Mie scattering is used to illuminate the flow field through the addition of propylene glycol particles seeded in the heavy gas. An M=1.2 shock impulsively accelerates the interface, initiating instability growth. Images of the initial condition and instability growth are captured at a rate of 6 kHz using high speed cameras. Comparisons between experimental and simulation results, mixing diagnostics, and mixing zone growth are presented.
Axisymmetric capillary-gravity waves at the interface of two viscous, immiscible fluids - Initial value problem

NASA Astrophysics Data System (ADS)

Farsoiya, Palas Kumar; Dasgupta, Ratul

2017-11-01

When the interface between two radially unbounded, viscous fluids lying vertically in a stable configuration (denser fluid below) at rest, is perturbed, radially propagating capillary-gravity waves are formed which damp out with time. We study this process analytically using a recently developed linearised theory. For small amplitude initial perturbations, the analytical solution to the initial value problem, represented as a linear superposition of Bessel modes at time t = 0 , is found to agree very well with results obtained from direct numerical simulations of the Navier-Stokes equations, for a range of initial conditions. Our study extends the earlier work by John W. Miles who studied this initial value problem analytically, taking into account, a single viscous fluid only. Implications of this study for the mechanistic understanding of droplet impact into a deep pool, will be discussed. Some preliminary, qualitative comparison with experiments will also be presented. We thank SERB Dept. Science & Technology, Govt. of India, Grant No. EMR/2016/000830 for financial support.
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.
Specific sine-Gordon soliton dynamics in the presence of external driving forces

NASA Astrophysics Data System (ADS)

Reinisch, Gilbert; Fernandez, Jean Claude

1981-07-01

We consider the acceleration of a single sine-Gordon (SG) soliton kink wave by an external time-dependent force χ(t), first without any dissipation, and then in the presence of a weak damping effect. We use the method of Fogel, Trullinger, Bishop, and Krumhansl [FTBK,
Phys. Rev. B 45, 1578 (1977)]
which consists in perturbing the SG equation about its kink solution and solving the resulting linear inhomogeneous equation for the perturbation function by expanding it in the complete set of eigenfunctions of the Schrödinger operator with potential 1-2 2x. Our results concerning the accelerated soliton dynamics strongly disagree with the FTBK conclusion that the soliton should undergo an acceleration proportional to χ (this is the so-called Newtonian dynamical behavior of SG soliton, which is also predicted by all existing perturbation theories dealing with the perturbed SG equation). On the contrary, we find that this Newtonian acceleration is exactly balanced by a reaction effect of the continuous phonon spectrum excited by the external force χ, upon the moving kink, so that there is no soliton acceleration at all within the frame of this linear perturbation theory, i.e., for small time values. Actually, we show by the simple example of a static external force that the acceleration of an initially static kink is a higher-order effect (proportional to χt2, where t is the time, instead of being constant and proportional to χ). We emphasize that this last result has already been checked by numerical experiments and show, both by theory and by numerical simulations, that it does not qualitatively change when a small damping effect is taken into account.
Nonlinear oscillations of compact stars in the vicinity of the maximum mass configuration

NASA Astrophysics Data System (ADS)

Brillante, A.; Mishustin, I. N.

2015-07-01

We solve the dynamical GR equations for the spherically symmetric evolution of compact stars in the vicinity of the maximum mass, for which instability sets in according to linear perturbation theory. The calculations are done with the analytical Zeldovich-like EOS P=a≤ft(ρ-ρ_0\\right) and with the TM1 parametrisation of the RMF model. The initial configurations for the dynamical calculations are represented by spherical stars with equilibrium density profile, which are perturbed by either i) an artificially added inward velocity field proportional to the radial coordinate, or ii) a rarefaction corresponding to a static and expanded star. These configurations are evolved using a one-dimensional GR hydro code for ideal and barotropic fluids. Depending on the initial conditions we obtain either stable oscillations or the collapse to a black hole. The minimal amplitude of the perturbation, needed to trigger gravitational collapse is evaluated. The approximate independence of this energy on the type of perturbation is pointed out. At the threshold we find type-I critical behaviour for all stellar models considered and discuss the dependence of the time scaling exponent on the baryon mass and EOS.
Multiple spacecraft configuration designs for coordinated flight missions

NASA Astrophysics Data System (ADS)

Fumenti, Federico; Theil, Stephan

2018-06-01

Coordinated flight allows the replacement of a single monolithic spacecraft with multiple smaller ones, based on the principle of distributed systems. According to the mission objectives and to ensure a safe relative motion, constraints on the relative distances need to be satisfied. Initially, differential perturbations are limited by proper orbit design. Then, the induced differential drifts can be properly handled through corrective maneuvers. In this work, several designs are surveyed, defining the initial configuration of a group of spacecraft while counteracting the differential perturbations. For each of the investigated designs, focus is placed upon the number of deployable spacecraft and on the possibility to ensure safe relative motion through station keeping of the initial configuration, with particular attention to the required Δ V budget and the constraints violations.
Fast and slow coherent cascades in anti-de Sitter spacetime

NASA Astrophysics Data System (ADS)

Dimitrakopoulos, Fotios V.; Freivogel, Ben; Pedraza, Juan F.

2018-06-01

We study the phase and amplitude dynamics of small perturbations in 3 + 1 dimensional anti-de Sitter spacetime using the truncated resonant approximation, also known as the two time framework. We analyse the phase spectrum for different classes of initial data and find that higher frequency modes turn on with coherently aligned phases. Combining numerical and analytical results, we conjecture that there is a class of initial conditions that collapse in infinite slow time and to which the well-studied case of the two-mode, equal energy initial data belongs. We additionally study perturbations that collapse in finite time, and find that the energy spectrum approaches a power law, with the energy per mode scaling approximately as the inverse first power of the frequency.
Simulations of the Richtmyer-Meshkov Instability in a two-shock vertical shock tube

NASA Astrophysics Data System (ADS)

Ferguson, Kevin; Olson, Britton; Jacobs, Jeffrey

2017-11-01

Simulations of the Richtmyer-Meshkov Instability (RMI) in a new two-shock vertical shock tube configuration are presented. The simulations are performed using the ARES code at Lawrence-Livermore National Laboratory (LLNL). Two M=1.2 shock waves travel in opposing directions and impact an initially stationary interface formed by sulfur hexaflouride (SF6) and air. The delay between the two shocks is controlled to achieve a prescribed temporal separation in shock wave arrival time. Initial interface perturbations and diffusion profiles are generated in keeping with previously gathered experimental data. The effect of varying the inter-shock delay and initial perturbation structure on instability growth and mixing parameters is examined. Information on the design, construction, and testing of a new two-shock vertical shock tube are also presented.
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.
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.
Physics with charmonium - Highlights of BESIII and PANDA

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

Messchendorp, Johan

2014-11-11

The physics of the strong interaction is undoubtedly one of the most challenging areas of modern science. Quantum ChromoDynamics (QCD) is reproducing successfully the physics phenomena at distances much shorter than the size of the nucleon, where perturbation theory can be used yielding results of high precision and predictive power. At larger distance scales, however, perturbative methods cannot be applied anymore, although spectacular phenomena, such as the generation of hadron masses and quark confinement, occur. Studies using charmed quarks and gluon-rich matter have the potential to connect the perturbative and the non-perturbative QCD region. The annihilation of matter with antimattermore » in the mass regime of charmonium is an ideal environment to discover new states or transitions that could reveal the secrets of the strong interaction. Hadronic and electromagnetic transitions between charmonium states and their decays have been measured with a world-record in precision with the BESIII spectrometer at the electron-positron collider at IHEP Beijing, China. Moreover, unconventional narrow charmonium-rich states have been discovered recently in an energy regime above the open-charm threshold, thereby, possibly initiating a new era in charmonium spectroscopy. The near future experiment, PANDA, at the research facility FAIR in Germany, Darmstadt, will exploit the annihilation of cooled anti-protons with protons to perform charmonium spectroscopy with an incredible precision. I will present the most promising results that have been recently obtained with BESIII together with the future perspectives of PANDA in the field of charmonium spectroscopy.« less
Physics with charmonium - Highlights of BESIII and PANDA

NASA Astrophysics Data System (ADS)

Messchendorp, Johan

2014-11-01

The physics of the strong interaction is undoubtedly one of the most challenging areas of modern science. Quantum ChromoDynamics (QCD) is reproducing successfully the physics phenomena at distances much shorter than the size of the nucleon, where perturbation theory can be used yielding results of high precision and predictive power. At larger distance scales, however, perturbative methods cannot be applied anymore, although spectacular phenomena, such as the generation of hadron masses and quark confinement, occur. Studies using charmed quarks and gluon-rich matter have the potential to connect the perturbative and the non-perturbative QCD region. The annihilation of matter with antimatter in the mass regime of charmonium is an ideal environment to discover new states or transitions that could reveal the secrets of the strong interaction. Hadronic and electromagnetic transitions between charmonium states and their decays have been measured with a world-record in precision with the BESIII spectrometer at the electron-positron collider at IHEP Beijing, China. Moreover, unconventional narrow charmonium-rich states have been discovered recently in an energy regime above the open-charm threshold, thereby, possibly initiating a new era in charmonium spectroscopy. The near future experiment, PANDA, at the research facility FAIR in Germany, Darmstadt, will exploit the annihilation of cooled anti-protons with protons to perform charmonium spectroscopy with an incredible precision. I will present the most promising results that have been recently obtained with BESIII together with the future perspectives of PANDA in the field of charmonium spectroscopy.
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.
The decay of motor adaptation to novel movement dynamics reveals an asymmetry in the stability of motion state-dependent learning

PubMed Central

Hosseini, Eghbal A.; Nguyen, Katrina P.; Joiner, Wilsaan M.

2017-01-01

Motor adaptation paradigms provide a quantitative method to study short-term modification of motor commands. Despite the growing understanding of the role motion states (e.g., velocity) play in this form of motor learning, there is little information on the relative stability of memories based on these movement characteristics, especially in comparison to the initial adaptation. Here, we trained subjects to make reaching movements perturbed by force patterns dependent upon either limb position or velocity. Following training, subjects were exposed to a series of error-clamp trials to measure the temporal characteristics of the feedforward motor output during the decay of learning. The compensatory force patterns were largely based on the perturbation kinematic (e.g., velocity), but also showed a small contribution from the other motion kinematic (e.g., position). However, the velocity contribution in response to the position-based perturbation decayed at a slower rate than the position contribution to velocity-based training, suggesting a difference in stability. Next, we modified a previous model of motor adaptation to reflect this difference and simulated the behavior for different learning goals. We were interested in the stability of learning when the perturbations were based on different combinations of limb position or velocity that subsequently resulted in biased amounts of motion-based learning. We trained additional subjects on these combined motion-state perturbations and confirmed the predictions of the model. Specifically, we show that (1) there is a significant separation between the observed gain-space trajectories for the learning and decay of adaptation and (2) for combined motion-state perturbations, the gain associated to changes in limb position decayed at a faster rate than the velocity-dependent gain, even when the position-dependent gain at the end of training was significantly greater. Collectively, these results suggest that the state-dependent adaptation associated with movement velocity is relatively more stable than that based on position. PMID:28481891
Forced Ignition Study Based On Wavelet Method

NASA Astrophysics Data System (ADS)

Martelli, E.; Valorani, M.; Paolucci, S.; Zikoski, Z.

2011-05-01

The control of ignition in a rocket engine is a critical problem for combustion chamber design. Therefore it is essential to fully understand the mechanism of ignition during its earliest stages. In this paper the characteristics of flame kernel formation and initial propagation in a hydrogen-argon-oxygen mixing layer are studied using 2D direct numerical simulations with detailed chemistry and transport properties. The flame kernel is initiated by adding an energy deposition source term in the energy equation. The effect of unsteady strain rate is studied by imposing a 2D turbulence velocity field, which is initialized by means of a synthetic field. An adaptive wavelet method, based on interpolating wavelets is used in this study to solve the compressible reactive Navier- Stokes equations. This method provides an alternative means to refine the computational grid points according to local demands of the physical solution. The present simulations show that in the very early instants the kernel perturbed by the turbulent field is characterized by an increased burning area and a slightly increased rad- ical formation. In addition, the calculations show that the wavelet technique yields a significant reduction in the number of degrees of freedom necessary to achieve a pre- scribed solution accuracy.

Measurement-based perturbation theory and differential equation parameter estimation with applications to satellite gravimetry

NASA Astrophysics Data System (ADS)

Xu, Peiliang

2018-06-01

The numerical integration method has been routinely used by major institutions worldwide, for example, NASA Goddard Space Flight Center and German Research Center for Geosciences (GFZ), to produce global gravitational models from satellite tracking measurements of CHAMP and/or GRACE types. Such Earth's gravitational products have found widest possible multidisciplinary applications in Earth Sciences. The method is essentially implemented by solving the differential equations of the partial derivatives of the orbit of a satellite with respect to the unknown harmonic coefficients under the conditions of zero initial values. From the mathematical and statistical point of view, satellite gravimetry from satellite tracking is essentially the problem of estimating unknown parameters in the Newton's nonlinear differential equations from satellite tracking measurements. We prove that zero initial values for the partial derivatives are incorrect mathematically and not permitted physically. The numerical integration method, as currently implemented and used in mathematics and statistics, chemistry and physics, and satellite gravimetry, is groundless, mathematically and physically. Given the Newton's nonlinear governing differential equations of satellite motion with unknown equation parameters and unknown initial conditions, we develop three methods to derive new local solutions around a nominal reference orbit, which are linked to measurements to estimate the unknown corrections to approximate values of the unknown parameters and the unknown initial conditions. Bearing in mind that satellite orbits can now be tracked almost continuously at unprecedented accuracy, we propose the measurement-based perturbation theory and derive global uniformly convergent solutions to the Newton's nonlinear governing differential equations of satellite motion for the next generation of global gravitational models. Since the solutions are global uniformly convergent, theoretically speaking, they are able to extract smallest possible gravitational signals from modern and future satellite tracking measurements, leading to the production of global high-precision, high-resolution gravitational models. By directly turning the nonlinear differential equations of satellite motion into the nonlinear integral equations, and recognizing the fact that satellite orbits are measured with random errors, we further reformulate the links between satellite tracking measurements and the global uniformly convergent solutions to the Newton's governing differential equations as a condition adjustment model with unknown parameters, or equivalently, the weighted least squares estimation of unknown differential equation parameters with equality constraints, for the reconstruction of global high-precision, high-resolution gravitational models from modern (and future) satellite tracking measurements.
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.
A SCILAB Program for Computing General-Relativistic Models of Rotating Neutron Stars by Implementing Hartle's Perturbation Method

NASA Astrophysics Data System (ADS)

Papasotiriou, P. J.; Geroyannis, V. S.

We implement Hartle's perturbation method to the computation of relativistic rigidly rotating neutron star models. The program has been written in SCILAB (© INRIA ENPC), a matrix-oriented high-level programming language. The numerical method is described in very detail and is applied to many models in slow or fast rotation. We show that, although the method is perturbative, it gives accurate results for all practical purposes and it should prove an efficient tool for computing rapidly rotating pulsars.
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.
A high-fidelity satellite ephemeris program for Earth satellites in eccentric orbits

NASA Technical Reports Server (NTRS)

Simmons, David R.

1990-01-01

A program for mission planning called the Analytic Satellite Ephemeris Program (ASEP), produces projected data for orbits that remain fairly close to the Earth. ASEP does not take into account lunar and solar perturbations. These perturbations are accounted for in another program called GRAVE, which incorporates more flexible means of input for initial data, provides additional kinds of output information, and makes use of structural programming techniques to make the program more understandable and reliable. GRAVE was revised, and a new program called ORBIT was developed. It is divided into three major phases: initialization, integration, and output. Results of the program development are presented.
Non-modal analysis of the diocotron instability for cylindrical geometry with conducting boundary

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

Mikhailenko, V. V.; Seok Kim, Jin; Jo, Younghyun

2014-05-15

The temporal evolution of the linear diocotron instability of a cylindrical annular plasma column surrounded by a conducting boundary has been investigated by using the methodology of the cylindrical shearing modes. The linear solution of the initial and boundary-value problems is obtained which is valid for any time at which linear effects dominate. The solution reveals that the initial perturbations of the electron density pass through the stage of the non-modal evolution when the perturbation experiences spatio-temporal distortion pertinent to the considered geometry of the electron column. The result is confirmed by a two-dimensional cylindrical particle-in-cell simulation.
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.
DOE Office of Scientific and Technical Information (OSTI.GOV)

Field, Scott E.; Hesthaven, Jan S.; Lau, Stephen R.

In the context of metric perturbation theory for nonspinning black holes, extreme mass ratio binary systems are described by distributionally forced master wave equations. Numerical solution of a master wave equation as an initial boundary value problem requires initial data. However, because the correct initial data for generic-orbit systems is unknown, specification of trivial initial data is a common choice, despite being inconsistent and resulting in a solution which is initially discontinuous in time. As is well known, this choice leads to a burst of junk radiation which eventually propagates off the computational domain. We observe another potential consequence ofmore » trivial initial data: development of a persistent spurious solution, here referred to as the Jost junk solution, which contaminates the physical solution for long times. This work studies the influence of both types of junk on metric perturbations, waveforms, and self-force measurements, and it demonstrates that smooth modified source terms mollify the Jost solution and reduce junk radiation. Our concluding section discusses the applicability of these observations to other numerical schemes and techniques used to solve distributionally forced master wave equations.« less
A structural model of polyglutamine determined from a host-guest method combining experiments and landscape theory.

PubMed

Finke, John M; Cheung, Margaret S; Onuchic, José N

2004-09-01

Modeling the structure of natively disordered peptides has proved difficult due to the lack of structural information on these peptides. In this work, we use a novel application of the host-guest method, combining folding theory with experiments, to model the structure of natively disordered polyglutamine peptides. Initially, a minimalist molecular model (C(alpha)C(beta)) of CI2 is developed with a structurally based potential and captures many of the folding properties of CI2 determined from experiments. Next, polyglutamine "guest" inserts of increasing length are introduced into the CI2 "host" model and the polyglutamine is modeled to match the resultant change in CI2 thermodynamic stability between simulations and experiments. The polyglutamine model that best mimics the experimental changes in CI2 thermodynamic stability has 1), a beta-strand dihedral preference and 2), an attractive energy between polyglutamine atoms 0.75-times the attractive energy between the CI2 host Go-contacts. When free-energy differences in the CI2 host-guest system are correctly modeled at varying lengths of polyglutamine guest inserts, the kinetic folding rates and structural perturbation of these CI2 insert mutants are also correctly captured in simulations without any additional parameter adjustment. In agreement with experiments, the residues showing structural perturbation are located in the immediate vicinity of the loop insert. The simulated polyglutamine loop insert predominantly adopts extended random coil conformations, a structural model consistent with low resolution experimental methods. The agreement between simulation and experimental CI2 folding rates, CI2 structural perturbation, and polyglutamine insert structure show that this host-guest method can select a physically realistic model for inserted polyglutamine. If other amyloid peptides can be inserted into stable protein hosts and the stabilities of these host-guest mutants determined, this novel host-guest method may prove useful to determine structural preferences of these intractable but biologically relevant protein fragments.
Local influence for generalized linear models with missing covariates.

PubMed

Shi, Xiaoyan; Zhu, Hongtu; Ibrahim, Joseph G

2009-12-01

In the analysis of missing data, sensitivity analyses are commonly used to check the sensitivity of the parameters of interest with respect to the missing data mechanism and other distributional and modeling assumptions. In this article, we formally develop a general local influence method to carry out sensitivity analyses of minor perturbations to generalized linear models in the presence of missing covariate data. We examine two types of perturbation schemes (the single-case and global perturbation schemes) for perturbing various assumptions in this setting. We show that the metric tensor of a perturbation manifold provides useful information for selecting an appropriate perturbation. We also develop several local influence measures to identify influential points and test model misspecification. Simulation studies are conducted to evaluate our methods, and real datasets are analyzed to illustrate the use of our local influence measures.
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.
Hill Problem Analytical Theory to the Order Four. Application to the Computation of Frozen Orbits around Planetary Satellites

NASA Technical Reports Server (NTRS)

Lara, Martin; Palacian, Jesus F.

2007-01-01

Frozen orbits of the Hill problem are determined in the double averaged problem, where short and long period terms are removed by means of Lie transforms. The computation of initial conditions of corresponding quasi periodic solutions in the non-averaged problem is straightforward for the perturbation method used provides the explicit equations of the transformation that connects the averaged and non-averaged models. A fourth order analytical theory reveals necessary for the accurate computation of quasi periodic, frozen orbits.
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.
Feedback Integrators

NASA Astrophysics Data System (ADS)

Chang, Dong Eui; Jiménez, Fernando; Perlmutter, Matthew

2016-12-01

A new method is proposed to numerically integrate a dynamical system on a manifold such that the trajectory stably remains on the manifold and preserves the first integrals of the system. The idea is that given an initial point in the manifold we extend the dynamics from the manifold to its ambient Euclidean space and then modify the dynamics outside the intersection of the manifold and the level sets of the first integrals containing the initial point such that the intersection becomes a unique local attractor of the resultant dynamics. While the modified dynamics theoretically produces the same trajectory as the original dynamics, it yields a numerical trajectory that stably remains on the manifold and preserves the first integrals. The big merit of our method is that the modified dynamics can be integrated with any ordinary numerical integrator such as Euler or Runge-Kutta. We illustrate this method by applying it to three famous problems: the free rigid body, the Kepler problem and a perturbed Kepler problem with rotational symmetry. We also carry out simulation studies to demonstrate the excellence of our method and make comparisons with the standard projection method, a splitting method and Störmer-Verlet schemes.
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.
Postural responses to unexpected perturbations of balance during reaching

PubMed Central

Trivedi, Hari; Leonard, Julia A.; Ting, Lena H.; Stapley, Paul J.

2014-01-01

To study the interaction between feedforward and feedback modes of postural control, we investigated postural responses during unexpected perturbations of the support surface that occurred during forward reaching in a standing position. We examined postural responses in lower limb muscles of 9 human subjects. Baseline measures were obtained when subjects executed reaching movements to a target placed in front of them (R condition) and during postural responses to forward and backward support-surface perturbations (no reaching, P condition) during quiet stance. Perturbations were also given at different delays after the onset of reaching movements (RP conditions) as well as with the arm extended in the direction of the target, but not reaching (P/AE condition). Results showed that during perturbations to reaching (RP), the initial automatic postural response, occurring around 100 ms after the onset of perturbations, was relatively unchanged in latency or amplitude compared to control conditions (P and P/AE). However, longer latency postural responses were modulated to aid in the reaching movements during forward perturbations but not during backward perturbations. Our results suggest that the nervous system prioritizes the maintenance of a stable postural base during reaching, and that later components of the postural responses can be modulated to ensure the performance of the voluntary task. PMID:20035321
The association between later cortical potentials and later phases of postural reactions evoked by perturbations to upright stance.

PubMed

Quant, Sylvia; Maki, Brian E; McIlroy, William E

2005-06-24

Previous studies have suggested that early cortical potentials (e.g. N1) that are evoked by perturbations to upright stance are associated with sensory processing of the initial perturbation and that later potentials may represent cognitive processing of this perturbation. However, it has also been suggested that later cortical potentials could reflect sensory and motor processing of later phases of the postural reaction. The current study set out to provide additional insight into the association between perturbation-evoked cortical potentials and postural reactions evoked by whole-body perturbations. By altering the deceleration onset of the perturbation, which altered the timing of later postural responses, we determined whether changes in later postural responses were associated with changes in later potentials. Based on previous work, we hypothesized that later potentials would not be associated with changes in later postural responses. During stance, seven healthy young adults were instructed to maintain their balance following two types of perturbations: (1) acceleration phase immediately followed by a deceleration phase (TASK 1), and (2) acceleration phase followed by a delayed deceleration phase (TASK 2). In spite of profound task differences in later postural responses, results revealed no significant differences in later potentials. This work provides additional support for the idea that latter elements of perturbation-evoked cortical responses are likely independent of evoked motor reactions required to maintain stability.
Short-Term TEC Perturbations Associated With Planetary Waves Occurrence in the Ionosphere

NASA Astrophysics Data System (ADS)

Shagimuratov, I. I.; Karpov, I.; Krankowski, A.

2008-12-01

Analysis of TEC response to storm showed short-term perturbations which were observed after initial phase of geomagnetic storms. The perturbations demonstrated very well expressed latitudinal structure and were recognized on diurnal variations as surges of TEC enhancement of TEC. Ordinary such storm-time positive effect was associated with TAD. Duration of the perturbations was about 2-4 hours and their amplitude increased toward low latitudes. Such TEC perturbations have the longitudinal dependence. It is important that time location of surges have week dependence on latitude. The observed structure appeared to arrive from high latitudes, but at middle latitudes it was represented as a standing wave. It is assumed that such TEC perturbations can be produced due to superposition of the eastward and westward propagating planetary Poincare waves. The periods of these waves are usually several hours. Poincare waves can be excited at the atmosphere in storm time. At middle latitudes their superposition is as standing wave that forms observing TEC perturbations. In the report, the possibilities of application Poincare waves to the ionosphere dynamics studies are discussed and an explanation of the observed ionospheric effects is given.
Selective Transient Cooling by Impulse Perturbations in a Simple Toy Model

NASA Astrophysics Data System (ADS)

Fabrizio, Michele

2018-06-01

We show in a simple exactly solvable toy model that a properly designed impulse perturbation can transiently cool down low-energy degrees of freedom at the expense of high-energy ones that heat up. The model consists of two infinite-range quantum Ising models: one, the high-energy sector, with a transverse field much bigger than the other, the low-energy sector. The finite-duration perturbation is a spin exchange that couples the two Ising models with an oscillating coupling strength. We find a cooling of the low-energy sector that is optimized by the oscillation frequency in resonance with the spin exchange excitation. After the perturbation is turned off, the Ising model with a low transverse field can even develop a spontaneous symmetry breaking despite being initially above the critical temperature.
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.

Design and Characterization of an Exoskeleton for Perturbing the Knee During Gait.

PubMed

Tucker, Michael R; Shirota, Camila; Lambercy, Olivier; Sulzer, James S; Gassert, Roger

2017-10-01

An improved understanding of mechanical impedance modulation in human joints would provide insights about the neuromechanics underlying functional movements. Experimental estimation of impedance requires specialized tools with highly reproducible perturbation dynamics and reliable measurement capabilities. This paper presents the design and mechanical characterization of the ETH Knee Perturbator: an actuated exoskeleton for perturbing the knee during gait. A novel wearable perturbation device was developed based on specific experimental objectives. Bench-top tests validated the device's torque limiting capability and characterized the time delays of the on-board clutch. Further tests demonstrated the device's ability to perform system identification on passive loads with static initial conditions. Finally, the ability of the device to consistently perturb human gait was evaluated through a pilot study on three unimpaired subjects. The ETH Knee Perturbator is capable of identifying mass-spring systems within 15% accuracy, accounting for over 95% of the variance in the observed torque in 10 out of 16 cases. Five-degree extension and flexion perturbations were executed on human subjects with an onset timing precision of 2.52% of swing phase duration and a rise time of 36.5 ms. The ETH Knee Perturbator can deliver safe, precisely timed, and controlled perturbations, which is a prerequisite for the estimation of knee joint impedance during gait. Tools such as this can enhance models of neuromuscular control, which may improve rehabilitative outcomes following impairments affecting gait and advance the design and control of assistive devices.
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.
Non-radial instabilities and progenitor asphericities in core-collapse supernovae

NASA Astrophysics Data System (ADS)

Müller, B.; Janka, H.-Th.

2015-04-01

Since core-collapse supernova simulations still struggle to produce robust neutrino-driven explosions in 3D, it has been proposed that asphericities caused by convection in the progenitor might facilitate shock revival by boosting the activity of non-radial hydrodynamic instabilities in the post-shock region. We investigate this scenario in depth using 42 relativistic 2D simulations with multigroup neutrino transport to examine the effects of velocity and density perturbations in the progenitor for different perturbation geometries that obey fundamental physical constraints (like the anelastic condition). As a framework for analysing our results, we introduce semi-empirical scaling laws relating neutrino heating, average turbulent velocities in the gain region, and the shock deformation in the saturation limit of non-radial instabilities. The squared turbulent Mach number, , reflects the violence of aspherical motions in the gain layer, and explosive runaway occurs for ≳ 0.3, corresponding to a reduction of the critical neutrino luminosity by ˜ 25 per cent compared to 1D. In the light of this theory, progenitor asphericities aid shock revival mainly by creating anisotropic mass flux on to the shock: differential infall efficiently converts velocity perturbations in the progenitor into density perturbations δρ/ρ at the shock of the order of the initial convective Mach number Maprog. The anisotropic mass flux and ram pressure deform the shock and thereby amplify post-shock turbulence. Large-scale (ℓ = 2, ℓ = 1) modes prove most conducive to shock revival, whereas small-scale perturbations require unrealistically high convective Mach numbers. Initial density perturbations in the progenitor are only of the order of Ma_prog^2 and therefore play a subdominant role.
Motor unit recruitment and firing rate in medial gastrocnemius muscles during external perturbations in standing in humans.

PubMed

Pollock, C L; Ivanova, T D; Hunt, M A; Garland, S J

2014-10-01

There is limited investigation of the interaction between motor unit recruitment and rate coding for modulating force during standing or responding to external perturbations. Fifty-seven motor units were recorded from the medial gastrocnemius muscle with intramuscular electrodes in response to external perturbations in standing. Anteriorly directed perturbations were generated by applying loads in 0.45-kg increments at the pelvis every 25-40 s until 2.25 kg was maintained. Motor unit firing rate was calculated for the initial recruitment load and all subsequent loads during two epochs: 1) dynamic response to perturbation directly following each load drop and 2) maintenance of steady state between perturbations. Joint kinematics and surface electromyography (EMG) from lower extremities and force platform measurements were assessed. Application of the external loads resulted in a significant forward progression of the anterior-posterior center of pressure (AP COP) that was accompanied by modest changes in joint angles (<3°). Surface EMG increased more in medial gastrocnemius than in the other recorded muscles. At initial recruitment, motor unit firing rate immediately after the load drop was significantly lower than during subsequent load drops or during the steady state at the same load. There was a modest increase in motor unit firing rate immediately after the load drop on subsequent load drops associated with regaining balance. There was no effect of maintaining balance with increased load and forward progression of the AP COP on steady-state motor unit firing rate. The medial gastrocnemius utilized primarily motor unit recruitment to achieve the increased levels of activation necessary to maintain standing in the presence of external loads. Copyright © 2014 the American Physiological Society.
Initial conditions for cosmological perturbations

NASA Astrophysics Data System (ADS)

Ashtekar, Abhay; Gupt, Brajesh

2017-02-01

Penrose proposed that the big bang singularity should be constrained by requiring that the Weyl curvature vanishes there. The idea behind this past hypothesis is attractive because it constrains the initial conditions for the universe in geometric terms and is not confined to a specific early universe paradigm. However, the precise statement of Penrose’s hypothesis is tied to classical space-times and furthermore restricts only the gravitational degrees of freedom. These are encapsulated only in the tensor modes of the commonly used cosmological perturbation theory. Drawing inspiration from the underlying idea, we propose a quantum generalization of Penrose’s hypothesis using the Planck regime in place of the big bang, and simultaneously incorporating tensor as well as scalar modes. Initial conditions selected by this generalization constrain the universe to be as homogeneous and isotropic in the Planck regime as permitted by the Heisenberg uncertainty relations.
Exploring the spectrum of planar AdS4 /CFT3 at finite coupling

NASA Astrophysics Data System (ADS)

Bombardelli, Diego; Cavaglià, Andrea; Conti, Riccardo; Tateo, Roberto

2018-04-01

The Quantum Spectral Curve (QSC) equations for planar N=6 super-conformal Chern-Simons (SCS) are solved numerically at finite values of the coupling constant for states in the sl(2\\Big|1) sector. New weak coupling results for conformal dimensions of operators outside the sl(2) -like sector are obtained by adapting a recently proposed algorithm for the QSC perturbative solution. Besides being interesting in their own right, these perturbative results are necessary initial inputs for the numerical algorithm to converge on the correct solution. The non-perturbative numerical outcomes nicely interpolate between the weak coupling and the known semiclassical expansions, and novel strong coupling exact results are deduced from the numerics. Finally, the existence of contour crossing singularities in the TBA equations for the operator 20 is ruled out by our analysis. The results of this paper are an important test of the QSC formalism for this model, open the way to new quantitative studies and provide further evidence in favour of the conjectured weak/strong coupling duality between N=6 SCS and type IIA superstring theory on AdS4 × CP 3. Attached to the arXiv submission, a Mathematica implementation of the numerical method and ancillary files containing the numerical results are provided.
Experimental Approaches to Systematic Discovery and Development of Reproductive Adverse Outcome Pathways in Fish

EPA Science Inventory

Adverse outcome pathways (AOPs) are conceptual frameworks that portray causal and predictive linkages between key events at multiple scales of biological organization that connect molecular initiating events and early cellular perturbations (e.g., initiation of toxicity pathways)...
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
Formation of free round jets with long laminar regions at large Reynolds numbers

NASA Astrophysics Data System (ADS)

Zayko, Julia; Teplovodskii, Sergey; Chicherina, Anastasia; Vedeneev, Vasily; Reshmin, Alexander

2018-04-01

The paper describes a new, simple method for the formation of free round jets with long laminar regions by a jet-forming device of ˜1.5 jet diameters in size. Submerged jets of 0.12 m diameter at Reynolds numbers of 2000-12 560 are experimentally studied. It is shown that for the optimal regime, the laminar region length reaches 5.5 diameters for Reynolds number ˜10 000 which is not achievable for other methods of laminar jet formation. To explain the existence of the optimal regime, a steady flow calculation in the forming unit and a stability analysis of outcoming jet velocity profiles are conducted. The shortening of the laminar regions, compared with the optimal regime, is explained by the higher incoming turbulence level for lower velocities and by the increase of perturbation growth rates for larger velocities. The initial laminar regions of free jets can be used for organising air curtains for the protection of objects in medicine and technologies by creating the air field with desired properties not mixed with ambient air. Free jets with long laminar regions can also be used for detailed studies of perturbation growth and transition to turbulence in round jets.
Thermalization and light cones in a model with weak integrability breaking

DOE PAGES

Bertini, Bruno; Essler, Fabian H. L.; Groha, Stefan; ...

2016-12-09

Here, we employ equation-of-motion techniques to study the nonequilibrium dynamics in a lattice model of weakly interacting spinless fermions. Our model provides a simple setting for analyzing the effects of weak integrability-breaking perturbations on the time evolution after a quantum quench. We establish the accuracy of the method by comparing results at short and intermediate times to time-dependent density matrix renormalization group computations. For sufficiently weak integrability-breaking interactions we always observe prethermalization plateaus, where local observables relax to nonthermal values at intermediate time scales. At later times a crossover towards thermal behavior sets in. We determine the associated time scale,more » which depends on the initial state, the band structure of the noninteracting theory, and the strength of the integrability-breaking perturbation. Our method allows us to analyze in some detail the spreading of correlations and in particular the structure of the associated light cones in our model. We find that the interior and exterior of the light cone are separated by an intermediate region, the temporal width of which appears to scale with a universal power law t 1/3.« less
Optimal Transient Growth of Submesoscale Baroclinic Instabilities

NASA Astrophysics Data System (ADS)

White, Brian; Zemskova, Varvara; Passaggia, Pierre-Yves

2016-11-01

Submesoscale instabilities are analyzed using a transient growth approach to determine the optimal perturbation for a rotating Boussinesq fluid subject to baroclinic instabilities. We consider a base flow with uniform shear and stratification and consider the non-normal evolution over finite-time horizons of linear perturbations in an ageostrophic, non-hydrostatic regime. Stone (1966, 1971) showed that the stability of the base flow to normal modes depends on the Rossby and Richardson numbers, with instabilities ranging from geostrophic (Ro -> 0) and ageostrophic (finite Ro) baroclinic modes to symmetric (Ri < 1 , Ro > 1) and Kelvin-Helmholtz (Ri < 1 / 4) modes. Non-normal transient growth, initiated by localized optimal wave packets, represents a faster mechanism for the growth of perturbations and may provide an energetic link between large-scale flows in geostrophic balance and dissipation scales via submesoscale instabilities. Here we consider two- and three-dimensional optimal perturbations by means of direct-adjoint iterations of the linearized Boussinesq Navier-Stokes equations to determine the form of the optimal perturbation, the optimal energy gain, and the characteristics of the most unstable perturbation.
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.
Pre-inflationary universe in loop quantum cosmology

NASA Astrophysics Data System (ADS)

Zhu, Tao; Wang, Anzhong; Cleaver, Gerald; Kirsten, Klaus; Sheng, Qin

2017-10-01

The evolutions of the flat Friedmann-Lemaître-Robertson-Walker universe and its linear perturbations are studied systematically in the dressed metric approach of loop quantum cosmology. When it is dominated by the kinetic energy of the inflaton at the quantum bounce, the evolution of the background can be divided into three different phases prior to the preheating: bouncing, transition and slow-roll inflation. During the bouncing phase, the evolution is independent of not only the initial conditions, but also the inflationary potentials. In particular, the expansion factor can be well described by the same exact solution in all the cases considered. In contrast, in the potential-dominated case such a universality is lost. It is because of this universality that the linear perturbations are also independent of the inflationary models and obtained exactly. During the transition phase, the evolutions of the background and its linear perturbations are found explicitly, and then matched to the ones given in the other two phases. Hence, once the initial conditions are imposed, the linear scalar and tensor perturbations will be uniquely determined. Considering two different sets of initial conditions, one imposed during the contracting phase and the other at the bounce, we calculate the Bogoliubov coefficients and find that the two sets yield the same results and all lead to particle creations at the onset of the inflation. Due to the preinflationary dynamics, the scalar and tensor power spectra become scale dependent. By comparing our results with the Planck 2015 data, we find constraints on the total number of e -folds since the bounce, in order to be consistent with current observations.
Can superhorizon cosmological perturbations explain the acceleration of the universe?

NASA Astrophysics Data System (ADS)

Hirata, Christopher M.; Seljak, Uroš

2005-10-01

We investigate the recent suggestions by Barausse et al. and Kolb et al. that the acceleration of the universe could be explained by large superhorizon fluctuations generated by inflation. We show that no acceleration can be produced by this mechanism. We begin by showing how the application of Raychaudhuri equation to inhomogeneous cosmologies results in several “no go” theorems for accelerated expansion. Next we derive an exact solution for a specific case of initial perturbations, for which application of the Kolb et al. expressions leads to an acceleration, while the exact solution reveals that no acceleration is present. We show that the discrepancy can be traced to higher-order terms that were dropped in the Kolb et al. analysis. We proceed with the analysis of initial value formulation of general relativity to argue that causality severely limits what observable effects can be derived from superhorizon perturbations. By constructing a Riemann normal coordinate system on initial slice we show that no infrared divergence terms arise in this coordinate system. Thus any divergences found previously can be eliminated by a local rescaling of coordinates and are unobservable. We perform an explicit analysis of the variance of the deceleration parameter for the case of single-field inflation using usual coordinates and show that the infrared-divergent terms found by Barausse et al. and Kolb et al. cancel against several additional terms not considered in their analysis. Finally, we argue that introducing isocurvature perturbations does not alter our conclusion that the accelerating expansion of the universe cannot be explained by superhorizon modes.
Power law inflation with electromagnetism

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

Luo, Xianghui; Isenberg, James, E-mail: isenberg@uoregon.edu

2013-07-15

We generalize Ringström’s global future causal stability results (Ringström 2009) [11] for certain expanding cosmological solutions of the Einstein-scalar field equations to solutions of the Einstein–Maxwell-scalar field system. In particular, after noting that the power law inflationary spacetimes (M{sup n+1},g{sup -hat}, ϕ{sup -hat}) considered by Ringström (2009) in [11] are solutions of the Einstein–Maxwell-scalar field system (with exponential potential) as well as of the Einstein-scalar field system (with the same exponential potential), we consider (nonlinear) perturbations of initial data sets of these spacetimes which include electromagnetic perturbations as well as gravitational and scalar perturbations. We show that if (as inmore » Ringström (2009) [11]) we focus on pairs of relatively scaled open sets U{sub R{sub 0}}⊂U{sub 4R{sub 0}} on an initial slice of (M{sup n+1},g{sup -hat}), and if we choose a set of perturbed data which on U{sub 4R{sub 0}} is sufficiently close to that of (M{sup n+1},g{sup -hat},ϕ{sup -hat}, A{sup -hat} = 0), then in the maximal globally hyperbolic spacetime development (M{sup n+1},g,ϕ,A) of this data via the Einstein–Maxwell-scalar field equations, all causal geodesics emanating from U{sub R{sub 0}} are future complete (just as in (M{sup n+1},g{sup -hat})). We also verify that, in a certain sense, the future asymptotic behavior of the fields in the spacetime developments of the perturbed data sets does not differ significantly from the future asymptotic behavior of (M{sup n+1},g{sup -hat}, ϕ{sup -hat}, A{sup -hat} = 0). -- Highlights: •We prove stability of expanding solutions of the Einstein–Maxwell-scalar field equations. •All nearby solutions are geodesically complete. •The topology of the initial slice is irrelevant to our stability results.« less
Single-Inclusive Jet Production In Electron-Nucleon Collisions Through Next-To-Next-To-Leading Order In Perturbative QCD

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

Abelof, Gabriel; Boughezal, Radja; Liu, Xiaohui

2016-10-17

We compute the Oσ 2σ 2 s perturbative corrections to inclusive jet production in electron-nucleon collisions. This process is of particular interest to the physics program of a future Electron Ion Collider (EIC). We include all relevant partonic processes, including deep-inelastic scattering contributions, photon-initiated corrections, and parton-parton scattering terms that first appear at this order. Upon integration over the final-state hadronic phase space we validate our results for the deep-inelastic corrections against the known next-to-next-to-leading order (NNLO) structure functions. Our calculation uses the N-jettiness subtraction scheme for performing higher-order computations, and allows for a completely differential description of the deep-inelasticmore » scattering process. We describe the application of this method to inclusive jet production in detail, and present phenomenological results for the proposed EIC. The NNLO corrections have a non-trivial dependence on the jet kinematics and arise from an intricate interplay between all contributing partonic channels.« less
A Comparison of Averaged and Full Models to Study the Third-Body Perturbation

PubMed Central

Solórzano, Carlos Renato Huaura; Prado, Antonio Fernando Bertachini de Almeida

2013-01-01

The effects of a third-body travelling in a circular orbit around a main body on a massless satellite that is orbiting the same main body are studied under two averaged models, single and double, where expansions of the disturbing function are made, and the full restricted circular three-body problem. The goal is to compare the behavior of these two averaged models against the full problem for long-term effects, in order to have some knowledge of their differences. The single averaged model eliminates the terms due to the short period of the spacecraft. The double average is taken over the mean motion of the satellite and the mean motion of the disturbing body, so removing both short period terms. As an example of the methods, an artificial satellite around the Earth perturbed by the Moon is used. A detailed study of the effects of different initial conditions in the orbit of the spacecraft is made. PMID:24319348
A comparison of averaged and full models to study the third-body perturbation.

PubMed

Solórzano, Carlos Renato Huaura; Prado, Antonio Fernando Bertachini de Almeida

2013-01-01

The effects of a third-body travelling in a circular orbit around a main body on a massless satellite that is orbiting the same main body are studied under two averaged models, single and double, where expansions of the disturbing function are made, and the full restricted circular three-body problem. The goal is to compare the behavior of these two averaged models against the full problem for long-term effects, in order to have some knowledge of their differences. The single averaged model eliminates the terms due to the short period of the spacecraft. The double average is taken over the mean motion of the satellite and the mean motion of the disturbing body, so removing both short period terms. As an example of the methods, an artificial satellite around the Earth perturbed by the Moon is used. A detailed study of the effects of different initial conditions in the orbit of the spacecraft is made.
Inferring Strength of Tantalum from Hydrodynamic Instability Recovery Experiments

NASA Astrophysics Data System (ADS)

Sternberger, Z.; Maddox, B.; Opachich, Y.; Wehrenberg, C.; Kraus, R.; Remington, B.; Randall, G.; Farrell, M.; Ravichandran, G.

2018-05-01

Hydrodynamic instability experiments allow access to material properties at extreme conditions, where strain rates exceed 105 s-1 and pressures reach 100 GPa. Current hydrodynamic instability experimental methods require in-flight radiography to image the instability growth at high pressure and high strain rate, limiting the facilities where these experiments can be performed. An alternate approach, recovering the sample after loading, allows measurement of the instability growth with profilometry. Tantalum samples were manufactured with different 2D and 3D initial perturbation patterns and dynamically compressed by a blast wave generated by laser ablation. The samples were recovered from peak pressures between 30 and 120 GPa and strain rates on the order of 107 s-1, providing a record of the growth of the perturbations due to hydrodynamic instability. These records are useful validation points for hydrocode simulations using models of material strength at high strain rate. Recovered tantalum samples were analyzed, providing an estimate of the strength of the material at high pressure and strain rate.

Stabilization of Inviscid Vortex Sheets

NASA Astrophysics Data System (ADS)

Protas, Bartosz; Sakajo, Takashi

2017-11-01

In this study we investigate the problem of stabilizing inviscid vortex sheets via feedback control. Such models, expressed in terms of the Birkhoff-Rott equation, are often used to describe the Kevin-Helmholtz instability of shear layers and are known to be strongly unstable to small-scale perturbations. First, we consider the linear stability of a straight vortex sheet in the periodic setting with actuation in the form of an array of point vortices or sources located a certain distance away from the sheet. We establish conditions under which this system is controllable and observable. Next, using methods of the linear control theory, we synthesize a feedback control strategy which stabilizes a straight vortex sheet in the linear regime. Given the poor conditioning of the discretized problem, reliable solution of the resulting algebraic Riccati equation requires the use of high-precision arithmetic. Finally, we demonstrate that this control approach also succeeds in the nonlinear regime, provided the magnitude of the initial perturbation is sufficiently small.
Robust approximate optimal guidance strategies for aeroassisted orbital transfer missions

NASA Astrophysics Data System (ADS)

Ilgen, Marc R.

This thesis presents the application of game theoretic and regular perturbation methods to the problem of determining robust approximate optimal guidance laws for aeroassisted orbital transfer missions with atmospheric density and navigated state uncertainties. The optimal guidance problem is reformulated as a differential game problem with the guidance law designer and Nature as opposing players. The resulting equations comprise the necessary conditions for the optimal closed loop guidance strategy in the presence of worst case parameter variations. While these equations are nonlinear and cannot be solved analytically, the presence of a small parameter in the equations of motion allows the method of regular perturbations to be used to solve the equations approximately. This thesis is divided into five parts. The first part introduces the class of problems to be considered and presents results of previous research. The second part then presents explicit semianalytical guidance law techniques for the aerodynamically dominated region of flight. These guidance techniques are applied to unconstrained and control constrained aeroassisted plane change missions and Mars aerocapture missions, all subject to significant atmospheric density variations. The third part presents a guidance technique for aeroassisted orbital transfer problems in the gravitationally dominated region of flight. Regular perturbations are used to design an implicit guidance technique similar to the second variation technique but that removes the need for numerically computing an optimal trajectory prior to flight. This methodology is then applied to a set of aeroassisted inclination change missions. In the fourth part, the explicit regular perturbation solution technique is extended to include the class of guidance laws with partial state information. This methodology is then applied to an aeroassisted plane change mission using inertial measurements and subject to uncertainties in the initial value of the flight path angle. A summary of performance results for all these guidance laws is presented in the fifth part of this thesis along with recommendations for further research.
Task-specific stability in muscle activation space during unintentional movements.

PubMed

Falaki, Ali; Towhidkhah, Farzad; Zhou, Tao; Latash, Mark L

2014-11-01

We used robot-generated perturbations applied during position-holding tasks to explore stability of induced unintentional movements in a multidimensional space of muscle activations. Healthy subjects held the handle of a robot against a constant bias force and were instructed not to interfere with hand movements produced by changes in the external force. Transient force changes were applied leading to handle displacement away from the initial position and then back toward the initial position. Intertrial variance in the space of muscle modes (eigenvectors in the muscle activations space) was quantified within two subspaces, corresponding to unchanged handle coordinate and to changes in the handle coordinate. Most variance was confined to the former subspace in each of the three phases of movement, the initial steady state, the intermediate position, and the final steady state. The same result was found when the changes in muscle activation were analyzed between the initial and final steady states. Changes in the dwell time between the perturbation force application and removal led to different final hand locations undershooting the initial position. The magnitude of the undershot scaled with the dwell time, while the structure of variance in the muscle activation space did not depend on the dwell time. We conclude that stability of the hand coordinate is ensured during both intentional and unintentional actions via similar mechanisms. Relative equifinality in the external space after transient perturbations may be associated with varying states in the redundant space of muscle activations. The results fit a hierarchical scheme for the control of voluntary movements with referent configurations and redundant mapping between the levels of the hierarchy.
Retrospective qualitative analysis of ecological networks under environmental perturbation: a copper-polluted intertidal community as a case study.

PubMed

Ramos-Jiliberto, Rodrigo; Garay-Narváez, Leslie; Medina, Matías H

2012-01-01

The coast of Chañaral Bay in northern Chile has been affected by copper mine wastes for decades. This sustained perturbation has disrupted the intertidal community in several ways, but the mechanisms behind the observed shifts in local biodiversity remain poorly understood. Our main goal was to identify the species (lumped into trophic groups) belonging to the Chañaral intertidal community that, being directly affected by copper pollution, contributed primarily to the generation of the observed changes in community structure. These groups of species were called initiators. We applied a qualitative modelling approach based only on the sign and direction of effects among species, and present a formula for predicting changes in equilibrium abundances considering stress on multiple variables simultaneously. We then applied this technique retrospectively to identify the most likely set of initiators. Our analyses allowed identification of a unique set of four initiators in the studied intertidal system (a group of algae, sessile invertebrates, a group of herbivores and starfish), which were hypothesized to be the primary drivers of the observed changes in community structure. In addition, a hypothesis was derived about how the perturbation affected these initiators. The hypothesis is that pollution affected negatively the population growth rate of both algae and sessile invertebrates and suppressed the interaction between herbivores and starfish. Our analytic approach, focused on identifying initiators, constitutes an advance towards understanding the mechanisms underlying human-driven ecosystem disruption and permits identifying species that may serve as a focal point for community management and restoration.
Rotational behavior of comet nuclei under gravitational perturbations

NASA Technical Reports Server (NTRS)

Oberti, Pascal; Bois, E.; Froeschle, Claude

1992-01-01

A dynamical qualitative study of the rotational motion for cometary-type bodies submitted to gravitational perturbations has been performed by numerical simulations, including the Sun and Jupiter's disturbing torques in the model. Results show small gravitational disturbing effects from the Sun on Halley-type orbits, as well as from Jupiter on most close-approach configurations. Only a very close-approach induces notable effects, presenting then some interesting sensitivity to initial conditions.
Phase portraits analysis of a barothropic system: The initial value problem

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

Kuetche, Victor Kamgang, E-mail: vkuetche@yahoo.fr; Department of Physics, Faculty of Science, University of Yaounde I, P.O. Box 812, Yaounde; The Abdus Salam International Center for Theoretical Physics, Strada Costiera 11, 34014 Trieste

2014-05-15

In this paper, we investigate the phase portraits features of a barothropic relaxing medium under pressure perturbations. In the starting point, we show within a third-order of accuracy that the previous system is modeled by a “dissipative” cubic nonlinear evolution equation. Paying particular attention to high-frequency perturbations of the system, we solve the initial value problem of the system both analytically and numerically while unveiling the existence of localized multivalued waveguide channels. Accordingly, we find that the “dissipative” term with a “dissipative” parameter less than some limit value does not destroy the ambiguous solutions. We address some physical implications ofmore » the results obtained previously.« less
Primordial inhomogeneities in the expanding universe. I - Density and velocity distributions of galaxies in the vicinities of rich clusters

NASA Technical Reports Server (NTRS)

Silk, J.; Wilson, M. L.

1979-01-01

The density profiles and Hubble flow deviations in the vicinities of rich galaxy clusters are derived for a variety of models of initial density and velocity perturbations at the recombination epoch. The galaxy correlation function, measured with respect to the Abell clusters, is used to normalize the theoretical models. The angular scales of the required primordial inhomogeneities are calculated. It is found that the resulting density profiles around rich clusters are surprisingly insensitive to the shape of the initial perturbations and also to the cosmological density parameter, Omega. However, it is shown that the distribution of galaxy radial velocities can provide a possible means of deriving Omega.
Modulation of Small-scale Turbulence Structure by Large-scale Motions in the Absence of Direct Energy Transfer.

NASA Astrophysics Data System (ADS)

Brasseur, James G.; Juneja, Anurag

1996-11-01

Previous DNS studies indicate that small-scale structure can be directly altered through ``distant'' dynamical interactions by energetic forcing of the large scales. To remove the possibility of stimulating energy transfer between the large- and small-scale motions in these long-range interactions, we here perturb the large scale structure without altering its energy content by suddenly altering only the phases of large-scale Fourier modes. Scale-dependent changes in turbulence structure appear as a non zero difference field between two simulations from identical initial conditions of isotropic decaying turbulence, one perturbed and one unperturbed. We find that the large-scale phase perturbations leave the evolution of the energy spectrum virtually unchanged relative to the unperturbed turbulence. The difference field, on the other hand, is strongly affected by the perturbation. Most importantly, the time scale τ characterizing the change in in turbulence structure at spatial scale r shortly after initiating a change in large-scale structure decreases with decreasing turbulence scale r. Thus, structural information is transferred directly from the large- to the smallest-scale motions in the absence of direct energy transfer---a long-range effect which cannot be explained by a linear mechanism such as rapid distortion theory. * Supported by ARO grant DAAL03-92-G-0117
Nonlinear Equatorial Spread F: Spatially Large Bubbles Resulting from Large Horizontal Scale Initial Perturbations.

DTIC Science & Technology

1980-02-06

Hk~ NAT;ONAL BUR[AUJ (1 STANDARDS 1%3-, $LEVE1 NR L Memomduum Report 4154 ILII Nonlinear Equatorial Spread F: Spatially Large Bubbles Resulting from...Washington, DC 20375 and 67-0883-0-0 _DNA qubtask S99OAXHC 41 II. CONTROLLING OFFICE NAME AND ADDRESS 12 . REPORT DATE Defense Nuclear Agency, Washington...Perturbation A: n(yO) i-e 23 [CIDS ] 8 Ax <Jxj< 16Ax n(x,y,0) 1 1 x1 > 16 Ax n (y,O) ( 12 ) Perturbation B: n(%,y,0) 1 -e 3 cos ( (13) n 0 (y,) \\2xm 7
Inverted initial conditions: Exploring the growth of cosmic structure and voids

DOE PAGES

Pontzen, Andrew; Roth, Nina; Peiris, Hiranya V.; ...

2016-05-18

We introduce and explore “paired” cosmological simulations. A pair consists of an A and B simulation with initial conditions related by the inversion δ A(x,t initial) = –δ B(x,t initial) (underdensities substituted for overdensities and vice versa). We argue that the technique is valuable for improving our understanding of cosmic structure formation. The A and B fields are by definition equally likely draws from ΛCDM initial conditions, and in the linear regime evolve identically up to the overall sign. As nonlinear evolution takes hold, a region that collapses to form a halo in simulation A will tend to expand tomore » create a void in simulation B. Applications include (i) contrasting the growth of A-halos and B-voids to test excursion-set theories of structure formation, (ii) cross-correlating the density field of the A and B universes as a novel test for perturbation theory, and (iii) canceling error terms by averaging power spectra between the two boxes. Furthermore, generalizations of the method to more elaborate field transformations are suggested.« 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.
Fuel-Optimal Altitude Maintenance of Low-Earth-Orbit Spacecrafts by Combined Direct/Indirect Optimization

NASA Astrophysics Data System (ADS)

Kim, Kyung-Ha; Park, Chandeok; Park, Sang-Young

2015-12-01

This work presents fuel-optimal altitude maintenance of Low-Earth-Orbit (LEO) spacecrafts experiencing non-negligible air drag and J2 perturbation. A pseudospectral (direct) method is first applied to roughly estimate an optimal fuel consumption strategy, which is employed as an initial guess to precisely determine itself. Based on the physical specifications of KOrea Multi-Purpose SATellite-2 (KOMPSAT-2), a Korean artificial satellite, numerical simulations show that a satellite ascends with full thrust at the early stage of the maneuver period and then descends with null thrust. While the thrust profile is presumably bang-off, it is difficult to precisely determine the switching time by using a pseudospectral method only. This is expected, since the optimal switching epoch does not coincide with one of the collocation points prescribed by the pseudospectral method, in general. As an attempt to precisely determine the switching time and the associated optimal thrust history, a shooting (indirect) method is then employed with the initial guess being obtained through the pseudospectral method. This hybrid process allows the determination of the optimal fuel consumption for LEO spacecrafts and their thrust profiles efficiently and precisely.
Analysis of a renormalization group method and normal form theory for perturbed ordinary differential equations

NASA Astrophysics Data System (ADS)

DeVille, R. E. Lee; Harkin, Anthony; Holzer, Matt; Josić, Krešimir; Kaper, Tasso J.

2008-06-01

For singular perturbation problems, the renormalization group (RG) method of Chen, Goldenfeld, and Oono [Phys. Rev. E. 49 (1994) 4502-4511] has been shown to be an effective general approach for deriving reduced or amplitude equations that govern the long time dynamics of the system. It has been applied to a variety of problems traditionally analyzed using disparate methods, including the method of multiple scales, boundary layer theory, the WKBJ method, the Poincaré-Lindstedt method, the method of averaging, and others. In this article, we show how the RG method may be used to generate normal forms for large classes of ordinary differential equations. First, we apply the RG method to systems with autonomous perturbations, and we show that the reduced or amplitude equations generated by the RG method are equivalent to the classical Poincaré-Birkhoff normal forms for these systems up to and including terms of O(ɛ2), where ɛ is the perturbation parameter. This analysis establishes our approach and generalizes to higher order. Second, we apply the RG method to systems with nonautonomous perturbations, and we show that the reduced or amplitude equations so generated constitute time-asymptotic normal forms, which are based on KBM averages. Moreover, for both classes of problems, we show that the main coordinate changes are equivalent, up to translations between the spaces in which they are defined. In this manner, our results show that the RG method offers a new approach for deriving normal forms for nonautonomous systems, and it offers advantages since one can typically more readily identify resonant terms from naive perturbation expansions than from the nonautonomous vector fields themselves. Finally, we establish how well the solution to the RG equations approximates the solution of the original equations on time scales of O(1/ɛ).
Numerical and experimental study on the steady cone-jet mode of electro-centrifugal spinning

NASA Astrophysics Data System (ADS)

Hashemi, Ali Reza; Pishevar, Ahmad Reza; Valipouri, Afsaneh; Pǎrǎu, Emilian I.

2018-01-01

This study focuses on a numerical investigation of an initial stable jet through the air-sealed electro-centrifugal spinning process, which is known as a viable method for the mass production of nanofibers. A liquid jet undergoing electric and centrifugal forces, as well as other forces, first travels in a stable trajectory and then goes through an unstable curled path to the collector. In numerical modeling, hydrodynamic equations have been solved using the perturbation method—and the boundary integral method has been implemented to efficiently solve the electric potential equation. Hydrodynamic equations have been coupled with the electric field using stress boundary conditions at the fluid-fluid interface. Perturbation equations were discretized by a second order finite difference method, and the Newton method was implemented to solve the discretized non-linear system. Also, the boundary element method was utilized to solve electrostatic equations. In the theoretical study, the fluid was described as a leaky dielectric with charges only on the surface of the jet traveling in dielectric air. The effect of the electric field induced around the nozzle tip on the jet instability and trajectory deviation was also experimentally studied through plate-plate geometry as well as point-plate geometry. It was numerically found that the centrifugal force prevails on electric force by increasing the rotational speed. Therefore, the alteration of the applied voltage does not significantly affect the jet thinning profile or the jet trajectory.
An initial investigation into methods of computing transonic aerodynamic sensitivity coefficients

NASA Technical Reports Server (NTRS)

Carlson, Leland A.

1994-01-01

The primary accomplishments of the project are as follows: (1) Using the transonic small perturbation equation as a flowfield model, the project demonstrated that the quasi-analytical method could be used to obtain aerodynamic sensitivity coefficients for airfoils at subsonic, transonic, and supersonic conditions for design variables such as Mach number, airfoil thickness, maximum camber, angle of attack, and location of maximum camber. It was established that the quasi-analytical approach was an accurate method for obtaining aerodynamic sensitivity derivatives for airfoils at transonic conditions and usually more efficient than the finite difference approach. (2) The usage of symbolic manipulation software to determine the appropriate expressions and computer coding associated with the quasi-analytical method for sensitivity derivatives was investigated. Using the three dimensional fully conservative full potential flowfield model, it was determined that symbolic manipulation along with a chain rule approach was extremely useful in developing a combined flowfield and quasi-analytical sensitivity derivative code capable of considering a large number of realistic design variables. (3) Using the three dimensional fully conservative full potential flowfield model, the quasi-analytical method was applied to swept wings (i.e. three dimensional) at transonic flow conditions. (4) The incremental iterative technique has been applied to the three dimensional transonic nonlinear small perturbation flowfield formulation, an equivalent plate deflection model, and the associated aerodynamic and structural discipline sensitivity equations; and coupled aeroelastic results for an aspect ratio three wing in transonic flow have been obtained.
Approximate analytic method for high-apogee twelve-hour orbits of artificial Earth's satellites

NASA Astrophysics Data System (ADS)

Vashkovyaka, M. A.; Zaslavskii, G. S.

2016-09-01

We propose an approach to the study of the evolution of high-apogee twelve-hour orbits of artificial Earth's satellites. We describe parameters of the motion model used for the artificial Earth's satellite such that the principal gravitational perturbations of the Moon and Sun, nonsphericity of the Earth, and perturbations from the light pressure force are approximately taken into account. To solve the system of averaged equations describing the evolution of the orbit parameters of an artificial satellite, we use both numeric and analytic methods. To select initial parameters of the twelve-hour orbit, we assume that the path of the satellite along the surface of the Earth is stable. Results obtained by the analytic method and by the numerical integration of the evolving system are compared. For intervals of several years, we obtain estimates of oscillation periods and amplitudes for orbital elements. To verify the results and estimate the precision of the method, we use the numerical integration of rigorous (not averaged) equations of motion of the artificial satellite: they take into account forces acting on the satellite substantially more completely and precisely. The described method can be applied not only to the investigation of orbit evolutions of artificial satellites of the Earth; it can be applied to the investigation of the orbit evolution for other planets of the Solar system provided that the corresponding research problem will arise in the future and the considered special class of resonance orbits of satellites will be used for that purpose.
Camera pose estimation to improve accuracy and reliability of joint angles assessed with attitude and heading reference systems.

PubMed

Lebel, Karina; Hamel, Mathieu; Duval, Christian; Nguyen, Hung; Boissy, Patrick

2018-01-01

Joint kinematics can be assessed using orientation estimates from Attitude and Heading Reference Systems (AHRS). However, magnetically-perturbed environments affect the accuracy of the estimated orientations. This study investigates, both in controlled and human mobility conditions, a trial calibration technic based on a 2D photograph with a pose estimation algorithm to correct initial difference in AHRS Inertial reference frames and improve joint angle accuracy. In controlled conditions, two AHRS were solidly affixed onto a wooden stick and a series of static and dynamic trials were performed in varying environments. Mean accuracy of relative orientation between the two AHRS was improved from 24.4° to 2.9° using the proposed correction method. In human conditions, AHRS were placed on the shank and the foot of a participant who performed repeated trials of straight walking and walking while turning, varying the level of magnetic perturbation in the starting environment and the walking speed. Mean joint orientation accuracy went from 6.7° to 2.8° using the correction algorithm. The impact of starting environment was also greatly reduced, up to a point where one could consider it as non-significant from a clinical point of view (maximum mean difference went from 8° to 0.6°). The results obtained demonstrate that the proposed method improves significantly the mean accuracy of AHRS joint orientation estimations in magnetically-perturbed environments and can be implemented in post processing of AHRS data collected during biomechanical evaluation of motion. Copyright © 2017 Elsevier B.V. All rights reserved.
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.
Study of the Reynolds Number Effect on the Process of Instability Transition Into the Turbulent Stage.

PubMed

Nevmerzhitskiy, N V; Sotskov, E A; Sen'kovskiy, E D; Krivonos, O L; Polovnikov, A A; Levkina, E V; Frolov, S V; Abakumov, S A; Marmyshev, V V

2014-09-01

The results of the experimental study of the Reynolds number effect on the process of the Rayleigh-Taylor (R-T) instability transition into the turbulent stage are presented. The experimental liquid layer was accelerated by compressed gas. Solid particles were scattered on the layer free surface to specify the initial perturbations in some experiments. The process was recorded with the use of a high-speed motion picture camera. The following results were obtained in experiments: (1) Long-wave perturbation is developed at the interface at the Reynolds numbers Re < 10 4 . If such perturbation growth is limited by a hard wall, the jet directed in gas is developed. If there is no such limitation, this perturbation is resolved into the short-wave ones with time, and their growth results in gas-liquid mixing. (2) Short-wave perturbations specified at the interface significantly reduce the Reynolds number Re for instability to pass into the turbulent mixing stage.
The correlation function for density perturbations in an expanding universe. IV - The evolution of the correlation function. [galaxy distribution

NASA Technical Reports Server (NTRS)

Mcclelland, J.; Silk, J.

1979-01-01

The evolution of the two-point correlation function for the large-scale distribution of galaxies in an expanding universe is studied on the assumption that the perturbation densities lie in a Gaussian distribution centered on any given mass scale. The perturbations are evolved according to the Friedmann equation, and the correlation function for the resulting distribution of perturbations at the present epoch is calculated. It is found that: (1) the computed correlation function gives a satisfactory fit to the observed function in cosmological models with a density parameter (Omega) of approximately unity, provided that a certain free parameter is suitably adjusted; (2) the power-law slope in the nonlinear regime reflects the initial fluctuation spectrum, provided that the density profile of individual perturbations declines more rapidly than the -2.4 power of distance; and (3) both positive and negative contributions to the correlation function are predicted for cosmological models with Omega less than unity.

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.
Dynamic stability of passive dynamic walking on an irregular surface.

PubMed

Su, Jimmy Li-Shin; Dingwell, Jonathan B

2007-12-01

Falls that occur during walking are a significant health problem. One of the greatest impediments to solve this problem is that there is no single obviously "correct" way to quantify walking stability. While many people use variability as a proxy for stability, measures of variability do not quantify how the locomotor system responds to perturbations. The purpose of this study was to determine how changes in walking surface variability affect changes in both locomotor variability and stability. We modified an irreducibly simple model of walking to apply random perturbations that simulated walking over an irregular surface. Because the model's global basin of attraction remained fixed, increasing the amplitude of the applied perturbations directly increased the risk of falling in the model. We generated ten simulations of 300 consecutive strides of walking at each of six perturbation amplitudes ranging from zero (i.e., a smooth continuous surface) up to the maximum level the model could tolerate without falling over. Orbital stability defines how a system responds to small (i.e., "local") perturbations from one cycle to the next and was quantified by calculating the maximum Floquet multipliers for the model. Local stability defines how a system responds to similar perturbations in real time and was quantified by calculating short-term and long-term local exponential rates of divergence for the model. As perturbation amplitudes increased, no changes were seen in orbital stability (r(2)=2.43%; p=0.280) or long-term local instability (r(2)=1.0%; p=0.441). These measures essentially reflected the fact that the model never actually "fell" during any of our simulations. Conversely, the variability of the walker's kinematics increased exponentially (r(2)>or=99.6%; p<0.001) and short-term local instability increased linearly (r(2)=88.1%; p<0.001). These measures thus predicted the increased risk of falling exhibited by the model. For all simulated conditions, the walker remained orbitally stable, while exhibiting substantial local instability. This was because very small initial perturbations diverged away from the limit cycle, while larger initial perturbations converged toward the limit cycle. These results provide insight into how these different proposed measures of walking stability are related to each other and to risk of falling.
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)
Online automatic tuning and control for fed-batch cultivation

PubMed Central

van Straten, Gerrit; van der Pol, Leo A.; van Boxtel, Anton J. B.

2007-01-01

Performance of controllers applied in biotechnological production is often below expectation. Online automatic tuning has the capability to improve control performance by adjusting control parameters. This work presents automatic tuning approaches for model reference specific growth rate control during fed-batch cultivation. The approaches are direct methods that use the error between observed specific growth rate and its set point; systematic perturbations of the cultivation are not necessary. Two automatic tuning methods proved to be efficient, in which the adaptation rate is based on a combination of the error, squared error and integral error. These methods are relatively simple and robust against disturbances, parameter uncertainties, and initialization errors. Application of the specific growth rate controller yields a stable system. The controller and automatic tuning methods are qualified by simulations and laboratory experiments with Bordetella pertussis. PMID:18157554
Diffusion-driven fluid dynamics in ideal gases and plasmas

NASA Astrophysics Data System (ADS)

Vold, E. L.; Yin, L.; Taitano, W.; Molvig, K.; Albright, B. J.

2018-06-01

The classical transport theory based on Chapman-Enskog methods provides self-consistent approximations for the kinetic flux of mass, heat, and momentum in a fluid limit characterized with a small Knudsen number. The species mass fluxes relative to the center of mass, or "diffusive fluxes," are expressed as functions of known gradient quantities with kinetic coefficients evaluated using similar analyses for mixtures of gases or plasma components. The sum over species of the diffusive mass fluxes is constrained to be zero in the Lagrange frame, and thus results in a non-zero molar flux leading to a pressure perturbation. At an interface between two species initially in pressure equilibrium, the pressure perturbation driven by the diffusive molar flux induces a center of mass velocity directed from the species of greater atomic mass towards the lighter atomic mass species. As the ratio of the species particle masses increases, this center of mass velocity carries an increasingly greater portion of the mass across the interface and for a particle mass ratio greater than about two, the center of mass velocity carries more mass than the gradient driven diffusion flux. Early time transients across an interface between two species in a 1D plasma regime and initially in equilibrium are compared using three methods; a fluid code with closure in a classical transport approximation, a particle in cell simulation, and an implicit Fokker-Planck solver for the particle distribution functions. The early time transient phenomenology is shown to be similar in each of the computational simulation methods, including a pressure perturbation associated with the stationary "induced" component of the center of mass velocity which decays to pressure equilibrium during diffusion. At early times, the diffusive process generates pressure and velocity waves which propagate outward from the interface and are required to maintain momentum conservation. The energy in the outgoing waves dissipates as heat in viscous regions, and it is hypothesized that these diffusion driven waves may sustain fluctuations in less viscid finite domains after reflections from the boundaries. These fluid dynamic phenomena are similar in gases or plasmas and occur in flow transients with a moderate Knudsen number. The analysis and simulation results show how the kinetic flux, represented in the fluid transport closure, directly modifies the mass averaged flow described with the Euler equations.
Bubble nucleation and inflationary perturbations

NASA Astrophysics Data System (ADS)

Firouzjahi, Hassan; Jazayeri, Sadra; Karami, Asieh; Rostami, Tahereh

2017-12-01

In this work we study the imprints of bubble nucleation on primordial inflationary perturbations. We assume that the bubble is formed via the tunneling of a spectator field from the false vacuum of its potential to its true vacuum. We consider the configuration in which the observable CMB sphere is initially outside of the bubble. As the bubble expands, more and more regions of the exterior false vacuum, including our CMB sphere, fall into the interior of the bubble. The modes which leave the horizon during inflation at the time when the bubble wall collides with the observable CMB sphere are affected the most. The bubble wall induces non-trivial anisotropic and scale dependent corrections in the two point function of the curvature perturbation. The corrections in the curvature perturbation and the diagonal and off-diagonal elements of CMB power spectrum are estimated.
Further Experimental Investigations of the Richtmyer-Meshkov Instability

NASA Astrophysics Data System (ADS)

Miller, P. L.; Peyser, T. A.; Stry, P. E.; Logory, L. M.; Farley, D. R.

1996-11-01

We report on further experimental investigations of the Richtmyer-Meshkov instability from an initially nonlinear perturbation, conducted on the Nova laser. The experiments use a Nova hohlraum as a driver source for a strong shock in a miniature shock tube attached to the hohlraum. The shock tube contains brominated plastic and low-density carbon foam as the two working fluids, with a micro-machined sawtooth interface between them serving as the perturbation. The shock, upon crossing the interface, instigates the Richtmyer-Meshkov instability from the perturbation. The resulting growth of the mixing layer is diagnosed radiographically. We have previously reported upon a results from a single wavelength and amplitude of perturbation (T. A. Peyser et al., Phys. Rev. Lett.) 75, 2332 (1996).. A study of the effect of variations in amplitude and wavelength on the nonlinear growth of the instability will be discussed.
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.
Aircraft Range Optimization Using Singular Perturbations

NASA Technical Reports Server (NTRS)

Oconnor, Joseph Taffe

1973-01-01

An approximate analytic solution is developed for the problem of maximizing the range of an aircraft for a fixed end state. The problem is formulated as a singular perturbation and solved by matched inner and outer asymptotic expansions and the minimum principle of Pontryagin. Cruise in the stratosphere, and on transition to and from cruise at constant Mach number are discussed. The state vector includes altitude, flight path angle, and mass. Specific fuel consumption becomes a linear function of power approximating that of the cruise values. Cruise represents the outer solution; altitude and flight path angle are constants, and only mass changes. Transitions between cruise and the specified initial and final conditions correspond to the inner solutions. The mass is constant and altitude and velocity vary. A solution is developed which is valid for cruise but which is not for the initial and final conditions. Transforming of the independent variable near the initial and final conditions result in solutions which are valid for the two inner solutions but not for cruise. The inner solutions can not be obtained without simplifying the state equations. The singular perturbation approach overcomes this difficulty. A quadratic approximation of the state equations is made. The resulting problem is solved analytically, and the two inner solutions are matched to the outer solution.
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.
Streamer properties and associated x-rays in perturbed air

NASA Astrophysics Data System (ADS)

Köhn, C.; Chanrion, O.; Babich, L. P.; Neubert, T.

2018-01-01

Streamers are ionization waves in electric discharges. One of the key ingredients of streamer propagation is an ambient gas that serves as a source of free electrons. Here, we explore the dependence of streamer dynamics on different spatial distributions of ambient air molecules. We vary the spatial profile of air parallel and perpendicular to the ambient electric field. We consider local sinusoidal perturbations of 5%-100%, as induced from discharge shock waves. We use a cylindrically symmetric particle-in-cell code to simulate the evolution of bidirectional streamers and compare the electron density, electric field, streamer velocity and electron energy of streamers in uniform air and in perturbed air. In all considered cases, the motion is driven along in decreasing air density and damped along increasing air density. Perturbations of at most 5%-10% change the velocity differences by up to approximately 40%. Perturbations perpendicular to the electric field additionally squeeze or branch streamers. Air variations can thus partly explain the difference of velocities and morphologies of streamer discharges. In cases with large perturbations, electrons gain energies of up to 30 keV compared to 100 eV in uniformly distributed air. For such perturbations parallel to the ambient electric field, we see the spontaneous initiation of a negative streamer; for perpendicular perturbations, x-rays with energies of up to 20 keV are emitted within 0.17 ns.
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.
Silent initial conditions for cosmological perturbations with a change of spacetime signature

NASA Astrophysics Data System (ADS)

Mielczarek, Jakub; Linsefors, Linda; Barrau, Aurelien

Recent calculations in loop quantum cosmology suggest that a transition from a Lorentzian to a Euclidean spacetime might take place in the very early universe. The transition point leads to a state of silence, characterized by a vanishing speed of light. This behavior can be interpreted as a decoupling of different space points, similar to the one characterizing the BKL phase. In this study, we address the issue of imposing initial conditions for the cosmological perturbations at the transition point between the Lorentzian and Euclidean phases. Motivated by the decoupling of space points, initial conditions characterized by a lack of correlations are investigated. We show that the “white noise” gains some support from analysis of the vacuum state in the deep Euclidean regime. Furthermore, the possibility of imposing the silent initial conditions at the trans-Planckian surface, characterized by a vanishing speed for the propagation of modes with wavelengths of the order of the Planck length, is studied. Such initial conditions might result from the loop deformations of the Poincaré algebra. The conversion of the silent initial power spectrum to a scale-invariant one is also examined.
A review for identification of initiating events in event tree development process on nuclear power plants

NASA Astrophysics Data System (ADS)

Riyadi, Eko H.

2014-09-01

Initiating event is defined as any event either internal or external to the nuclear power plants (NPPs) that perturbs the steady state operation of the plant, if operating, thereby initiating an abnormal event such as transient or loss of coolant accident (LOCA) within the NPPs. These initiating events trigger sequences of events that challenge plant control and safety systems whose failure could potentially lead to core damage or large early release. Selection for initiating events consists of two steps i.e. first step, definition of possible events, such as by evaluating a comprehensive engineering, and by constructing a top level logic model. Then the second step, grouping of identified initiating event's by the safety function to be performed or combinations of systems responses. Therefore, the purpose of this paper is to discuss initiating events identification in event tree development process and to reviews other probabilistic safety assessments (PSA). The identification of initiating events also involves the past operating experience, review of other PSA, failure mode and effect analysis (FMEA), feedback from system modeling, and master logic diagram (special type of fault tree). By using the method of study for the condition of the traditional US PSA categorization in detail, could be obtained the important initiating events that are categorized into LOCA, transients and external events.
Effects of Initial Conditions on Shock Driven Flows

NASA Astrophysics Data System (ADS)

Martinez, Adam A.; Mula, Swathi M.; Charonko, John; Prestridge, Kathy

2017-11-01

The spatial and temporal evolution of shock-driven, variable density flows, such as the Richtmyer Meshkov (RM) instability, are strongly influenced by the initial conditions (IC's) of the flow at the time of interaction with shockwave. We study the effects of the IC's on the Vertical Shock Tube (VST) and on flows from Mach =1.2 to Mach =9. Experiments at the VST are of an Air-SF6 (At =0.6) multimode interface. Perturbations are generated using a shear layer with a flapper plate. Planar Laser Induced Fluorescence (PLIF) is used to characterize the IC's. New experiments are occurring using the Powder Gun driver at LANL Proton Radiography (pRad) facility. Mach number up to M =9 accelerate a Xenon-Helium (At =0.94) interface that is perturbed using a membrane supported by different sized grids. This presentation focuses on how to design and characterize different types of initial conditions for experiments.
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
A method of initial orbit determination from three or more observations on a short arc. (Russian Title: Метод определения первоначальной орбиты по трем и более наблюдениям на короткой дуге)

NASA Astrophysics Data System (ADS)

Shefer, V. A.

2010-12-01

A new method is suggested for computing the initial orbit of a small celestial body from its three or more pairs of angular measurements at three times. The method is based on using the approach that we previously developed for constructing the intermediate orbit from minimal number of observations. This intermediate orbit allows for most of the perturbations in the motion of the body under study. The method proposed uses the Herget's algorithmic scheme that makes it possible to involve additional observations as well. The methodical error of orbit computation by the proposed method is two orders smaller than the corresponding error of the Herget's approach based on the construction of the unperturbed Keplerian orbit. The new method is especially efficient if applied to high-accuracy observational data covering short orbital arcs.
Control of aperture closure during reach-to-grasp movements in parkinson’s disease

PubMed Central

Rand, M. K.; Smiley-Oyen, A. L.; Shimansky, Y. P.; Bloedel, J. R.; Stelmach, G. E.

2007-01-01

This study examined whether the pattern of coordination between arm-reaching toward an object (hand transport) and the initiation of aperture closure for grasping is different between PD patients and healthy individuals, and whether that pattern is affected by the necessity to quickly adjust the reach-to-grasp movement in response to an unexpected shift of target location. Subjects reached for and grasped a vertical dowel, the location of which was indicated by illuminating one of the three dowels placed on a horizontal plane. In control conditions, target location was fixed during the trial. In perturbation conditions, target location was shifted instantaneously by switching the illumination to a different dowel during the reach. The hand distance from the target at which the subject initiated aperture closure (aperture closure distance) was similar for both the control and perturbation conditions within each group of subjects. However, that distance was significantly closer to the target in the PD group than in the control group. The timing of aperture closure initiation varied considerably across the trials in both groups of subjects. In contrast, aperture closure distance was relatively invariant, suggesting that aperture closure initiation was determined by spatial parameters of arm kinematics rather than temporal parameters. The linear regression analysis of aperture closure distance showed that the distance was highly predictable based on the following three parameters: the amplitude of maximum grip aperture, hand velocity, and hand acceleration. This result implies that a control law, the arguments of which include the above parameters, governs the initiation of aperture closure. Further analysis revealed that the control law was very similar between the subject groups under each condition as well as between the control and perturbation conditions for each group. Consequently, the shorter aperture closure distance observed in PD patients apparently is a result of the hypometria of their grip aperture and bradykinesia of hand transport movement, rather than a consequence of a deficit in transport-grasp coordination. It is also concluded that the perturbation of target location does not disrupt the transport-grasp coordination in either healthy individuals or PD patients. PMID:16307233

Control of aperture closure during reach-to-grasp movements in Parkinson's disease.

PubMed

Rand, M K; Smiley-Oyen, A L; Shimansky, Y P; Bloedel, J R; Stelmach, G E

2006-01-01

This study examined whether the pattern of coordination between arm-reaching toward an object (hand transport) and the initiation of aperture closure for grasping is different between PD patients and healthy individuals, and whether that pattern is affected by the necessity to quickly adjust the reach-to-grasp movement in response to an unexpected shift of target location. Subjects reached for and grasped a vertical dowel, the location of which was indicated by illuminating one of the three dowels placed on a horizontal plane. In control conditions, target location was fixed during the trial. In perturbation conditions, target location was shifted instantaneously by switching the illumination to a different dowel during the reach. The hand distance from the target at which the subject initiated aperture closure (aperture closure distance) was similar for both the control and perturbation conditions within each group of subjects. However, that distance was significantly closer to the target in the PD group than in the control group. The timing of aperture closure initiation varied considerably across the trials in both groups of subjects. In contrast, aperture closure distance was relatively invariant, suggesting that aperture closure initiation was determined by spatial parameters of arm kinematics rather than temporal parameters. The linear regression analysis of aperture closure distance showed that the distance was highly predictable based on the following three parameters: the amplitude of maximum grip aperture, hand velocity, and hand acceleration. This result implies that a control law, the arguments of which include the above parameters, governs the initiation of aperture closure. Further analysis revealed that the control law was very similar between the subject groups under each condition as well as between the control and perturbation conditions for each group. Consequently, the shorter aperture closure distance observed in PD patients apparently is a result of the hypometria of their grip aperture and bradykinesia of hand transport movement, rather than a consequence of a deficit in transport-grasp coordination. It is also concluded that the perturbation of target location does not disrupt the transport-grasp coordination in either healthy individuals or PD patients.
Application of functional analysis to perturbation theory of differential equations. [nonlinear perturbation of the harmonic oscillator

NASA Technical Reports Server (NTRS)

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

1980-01-01

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

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

Pipin, V. V.; Kosovichev, A. G.

2015-11-10

We explore the response of a nonlinear non-axisymmetric mean-field solar dynamo model to shallow non-axisymmetric perturbations. After a relaxation period, the amplitude of the non-axisymmetric field depends on the initial condition, helicity conservation, and the depth of perturbation. It is found that a perturbation that is anchored at 0.9 R{sub ⊙} has a profound effect on the dynamo process, producing a transient magnetic cycle of the axisymmetric magnetic field, if it is initiated at the growing phase of the cycle. The non-symmetric, with respect to the equator, perturbation results in a hemispheric asymmetry of the magnetic activity. The evolution ofmore » the axisymmetric and non-axisymmetric fields depends on the turbulent magnetic Reynolds number R{sub m}. In the range of R{sub m} = 10{sup 4}–10{sup 6} the evolution returns to the normal course in the next cycle, in which the non-axisymmetric field is generated due to a nonlinear α-effect and magnetic buoyancy. In the stationary state, the large-scale magnetic field demonstrates a phenomenon of “active longitudes” with cyclic 180° “flip-flop” changes of the large-scale magnetic field orientation. The flip-flop effect is known from observations of solar and stellar magnetic cycles. However, this effect disappears in the model, which includes the meridional circulation pattern determined by helioseismology. The rotation rate of the non-axisymmetric field components varies during the relaxation period and carries important information about the dynamo process.« less
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.
Stability of stationary solutions for inflow problem on the micropolar fluid model

NASA Astrophysics Data System (ADS)

Yin, Haiyan

2017-04-01

In this paper, we study the asymptotic behavior of solutions to the initial boundary value problem for the micropolar fluid model in a half-line R+:=(0,∞). We prove that the corresponding stationary solutions of the small amplitude to the inflow problem for the micropolar fluid model are time asymptotically stable under small H1 perturbations in both the subsonic and degenerate cases. The microrotation velocity brings us some additional troubles compared with Navier-Stokes equations in the absence of the microrotation velocity. The proof of asymptotic stability is based on the basic energy method.
Numerical methods for stiff systems of two-point boundary value problems

NASA Technical Reports Server (NTRS)

Flaherty, J. E.; Omalley, R. E., Jr.

1983-01-01

Numerical procedures are developed for constructing asymptotic solutions of certain nonlinear singularly perturbed vector two-point boundary value problems having boundary layers at one or both endpoints. The asymptotic approximations are generated numerically and can either be used as is or to furnish a general purpose two-point boundary value code with an initial approximation and the nonuniform computational mesh needed for such problems. The procedures are applied to a model problem that has multiple solutions and to problems describing the deformation of thin nonlinear elastic beam that is resting on an elastic foundation.
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.
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,…
Overview of the ToxCast Research Program: Applications to Predictive Toxicology and Chemical Prioritization

EPA Science Inventory

EPA’s ToxCast program, the NTP’s HTS initiative, and the NCGC’s Molecular Libraries Initiative into a collaborative research program focused on identifying toxicity pathways and developing in vitro assays to characterize the ability of chemicals to perturb those pathways. The go...
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.
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.
Rarefaction-driven Rayleigh–Taylor instability. Part 2. Experiments and simulations in the nonlinear regime

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

Morgan, R. V.; Cabot, W. H.; Greenough, J. A.

Experiments and large eddy simulation (LES) were performed to study the development of the Rayleigh–Taylor instability into the saturated, nonlinear regime, produced between two gases accelerated by a rarefaction wave. Single-mode two-dimensional, and single-mode three-dimensional initial perturbations were introduced on the diffuse interface between the two gases prior to acceleration. The rarefaction wave imparts a non-constant acceleration, and a time decreasing Atwood number,more » $$A=(\\unicode[STIX]{x1D70C}_{2}-\\unicode[STIX]{x1D70C}_{1})/(\\unicode[STIX]{x1D70C}_{2}+\\unicode[STIX]{x1D70C}_{1})$$, where$$\\unicode[STIX]{x1D70C}_{2}$$and$$\\unicode[STIX]{x1D70C}_{1}$$are the densities of the heavy and light gas, respectively. Experiments and simulations are presented for initial Atwood numbers of$A=0.49$$,$$A=0.63$$,$$A=0.82$$and$$A=0.94$$. Nominally two-dimensional (2-D) experiments (initiated with nearly 2-D perturbations) and 2-D simulations are observed to approach an intermediate-time velocity plateau that is in disagreement with the late-time velocity obtained from the incompressible model of Goncharov (Phys. Rev. Lett., vol. 88, 2002, 134502). Reacceleration from an intermediate velocity is observed for 2-D bubbles in large wavenumber,$$k=2\\unicode[STIX]{x03C0}/\\unicode[STIX]{x1D706}=0.247~\\text{mm}^{-1}$$, experiments and simulations, where$$\\unicode[STIX]{x1D706}$is the wavelength of the initial perturbation. At moderate Atwood numbers, the bubble and spike velocities approach larger values than those predicted by Goncharov’s model. These late-time velocity trends are predicted well by numerical simulations using the LLNL Miranda code, and by the 2009 model of Mikaelian (Phys. Fluids., vol. 21, 2009, 024103) that extends Layzer type models to variable acceleration and density. Large Atwood number experiments show a delayed roll up, and exhibit a free-fall like behaviour. Finally, experiments initiated with three-dimensional perturbations tend to agree better with models and a simulation using the LLNL Ares code initiated with an axisymmetric rather than Cartesian symmetry.« less
Rarefaction-driven Rayleigh–Taylor instability. Part 2. Experiments and simulations in the nonlinear regime

DOE PAGES

Morgan, R. V.; Cabot, W. H.; Greenough, J. A.; ...

2018-01-12

Experiments and large eddy simulation (LES) were performed to study the development of the Rayleigh–Taylor instability into the saturated, nonlinear regime, produced between two gases accelerated by a rarefaction wave. Single-mode two-dimensional, and single-mode three-dimensional initial perturbations were introduced on the diffuse interface between the two gases prior to acceleration. The rarefaction wave imparts a non-constant acceleration, and a time decreasing Atwood number,more » $$A=(\\unicode[STIX]{x1D70C}_{2}-\\unicode[STIX]{x1D70C}_{1})/(\\unicode[STIX]{x1D70C}_{2}+\\unicode[STIX]{x1D70C}_{1})$$, where$$\\unicode[STIX]{x1D70C}_{2}$$and$$\\unicode[STIX]{x1D70C}_{1}$$are the densities of the heavy and light gas, respectively. Experiments and simulations are presented for initial Atwood numbers of$A=0.49$$,$$A=0.63$$,$$A=0.82$$and$$A=0.94$$. Nominally two-dimensional (2-D) experiments (initiated with nearly 2-D perturbations) and 2-D simulations are observed to approach an intermediate-time velocity plateau that is in disagreement with the late-time velocity obtained from the incompressible model of Goncharov (Phys. Rev. Lett., vol. 88, 2002, 134502). Reacceleration from an intermediate velocity is observed for 2-D bubbles in large wavenumber,$$k=2\\unicode[STIX]{x03C0}/\\unicode[STIX]{x1D706}=0.247~\\text{mm}^{-1}$$, experiments and simulations, where$$\\unicode[STIX]{x1D706}$is the wavelength of the initial perturbation. At moderate Atwood numbers, the bubble and spike velocities approach larger values than those predicted by Goncharov’s model. These late-time velocity trends are predicted well by numerical simulations using the LLNL Miranda code, and by the 2009 model of Mikaelian (Phys. Fluids., vol. 21, 2009, 024103) that extends Layzer type models to variable acceleration and density. Large Atwood number experiments show a delayed roll up, and exhibit a free-fall like behaviour. Finally, experiments initiated with three-dimensional perturbations tend to agree better with models and a simulation using the LLNL Ares code initiated with an axisymmetric rather than Cartesian symmetry.« less

Dynamics of landslide model with time delay and periodic parameter perturbations

NASA Astrophysics Data System (ADS)

Kostić, Srđan; Vasović, Nebojša; Franović, Igor; Jevremović, Dragutin; Mitrinovic, David; Todorović, Kristina

2014-09-01

In present paper, we analyze the dynamics of a single-block model on an inclined slope with Dieterich-Ruina friction law under the variation of two new introduced parameters: time delay Td and initial shear stress μ. It is assumed that this phenomenological model qualitatively simulates the motion along the infinite creeping slope. The introduction of time delay is proposed to mimic the memory effect of the sliding surface and it is generally considered as a function of history of sliding. On the other hand, periodic perturbation of initial shear stress emulates external triggering effect of long-distant earthquakes or some non-natural vibration source. The effects of variation of a single observed parameter, Td or μ, as well as their co-action, are estimated for three different sliding regimes: β < 1, β = 1 and β > 1, where β stands for the ratio of long-term to short-term stress changes. The results of standard local bifurcation analysis indicate the onset of complex dynamics for very low values of time delay. On the other side, numerical approach confirms an additional complexity that was not observed by local analysis, due to the possible effect of global bifurcations. The most complex dynamics is detected for β < 1, with a complete Ruelle-Takens-Newhouse route to chaos under the variation of Td, or the co-action of both parameters Td and μ. These results correspond well with the previous experimental observations on clay and siltstone with low clay fraction. In the same regime, the perturbation of only a single parameter, μ, renders the oscillatory motion of the block. Within the velocity-independent regime, β = 1, the inclusion and variation of Td generates a transition to equilibrium state, whereas the small oscillations of μ induce oscillatory motion with decreasing amplitude. The co-action of both parameters, in the same regime, causes the decrease of block's velocity. As for β > 1, highly-frequent, limit-amplitude oscillations of initial stress give rise to oscillatory motion. Also for β > 1, in case of perturbing only the initial shear stress, with smaller amplitude, velocity of the block changes exponentially fast. If the time delay is introduced, besides the stress perturbation, within the same regime, the co-action of Td (Td < 0.1) and small oscillations of μ induce the onset of deterministic chaos.
Newton to Einstein — dust to dust

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

Kopp, Michael; Uhlemann, Cora; Haugg, Thomas, E-mail: michael.kopp@physik.lmu.de, E-mail: cora.uhlemann@physik.lmu.de, E-mail: thomas.haugg@physik.lmu.de

We investigate the relation between the standard Newtonian equations for a pressureless fluid (dust) and the Einstein equations in a double expansion in small scales and small metric perturbations. We find that parts of the Einstein equations can be rewritten as a closed system of two coupled differential equations for the scalar and transverse vector metric perturbations in Poisson gauge. It is then shown that this system is equivalent to the Newtonian system of continuity and Euler equations. Brustein and Riotto (2011) conjectured the equivalence of these systems in the special case where vector perturbations were neglected. We show thatmore » this approach does not lead to the Euler equation but to a physically different one with large deviations already in the 1-loop power spectrum. We show that it is also possible to consistently set to zero the vector perturbations which strongly constrains the allowed initial conditions, in particular excluding Gaussian ones such that inclusion of vector perturbations is inevitable in the cosmological context. In addition we derive nonlinear equations for the gravitational slip and tensor perturbations, thereby extending Newtonian gravity of a dust fluid to account for nonlinear light propagation effects and dust-induced gravitational waves.« less
Sub-structure formation in starless cores

NASA Astrophysics Data System (ADS)

Toci, C.; Galli, D.; Verdini, A.; Del Zanna, L.; Landi, S.

2018-02-01

Motivated by recent observational searches of sub-structure in starless molecular cloud cores, we investigate the evolution of density perturbations on scales smaller than the Jeans length embedded in contracting isothermal clouds, adopting the same formalism developed for the expanding Universe and the solar wind. We find that initially small amplitude, Jeans-stable perturbations (propagating as sound waves in the absence of a magnetic field) are amplified adiabatically during the contraction, approximately conserving the wave action density, until they either become non-linear and steepen into shocks at a time tnl, or become gravitationally unstable when the Jeans length decreases below the scale of the perturbations at a time tgr. We evaluate analytically the time tnl at which the perturbations enter the non-linear stage using a Burgers' equation approach, and we verify numerically that this time marks the beginning of the phase of rapid dissipation of the kinetic energy of the perturbations. We then show that for typical values of the rms Mach number in molecular cloud cores, tnl is smaller than tgr, and therefore density perturbations likely dissipate before becoming gravitational unstable. Solenoidal modes grow at a faster rate than compressible modes, and may eventually promote fragmentation through the formation of vortical structures.
Properties of convective oxygen and silicon burning shells in supernova progenitors

NASA Astrophysics Data System (ADS)

Collins, Christine; Müller, Bernhard; Heger, Alexander

2018-01-01

Recent 3D simulations have suggested that convective seed perturbations from shell burning can play an important role in triggering neutrino-driven supernova explosions. Since isolated simulations cannot determine whether this perturbation-aided mechanism is of general relevance across the progenitor mass range, we here investigate the pertinent properties of convective oxygen and silicon burning shells in a broad range of pre-supernova stellar evolution models. We find that conditions for perturbation-aided explosions are most favourable in the extended oxygen shells of progenitors between about 16 and 26 solar masses, which exhibit large-scale convective overturn with high convective Mach numbers. Although the highest convective Mach numbers of up to 0.3 are reached in the oxygen shells of low-mass progenitors, convection is typically dominated by small-scale modes in these shells, which implies a more modest role of initial perturbations in the explosion mechanism. Convective silicon burning rarely provides the high Mach numbers and large-scale perturbations required for perturbation-aided explosions. We also find that about 40 per cent of progenitors between 16 and 26 solar masses exhibit simultaneous oxygen and neon burning in the same convection zone as a result of a shell merger shortly before collapse.
Adaptation of reach-to-grasp movement in response to force perturbations.

PubMed

Rand, M K; Shimansky, Y; Stelmach, G E; Bloedel, J R

2004-01-01

This study examined how reach-to-grasp movements are modified during adaptation to external force perturbations applied on the arm during reach. Specifically, we examined whether the organization of these movements was dependent upon the condition under which the perturbation was applied. In response to an auditory signal, all subjects were asked to reach for a vertical dowel, grasp it between the index finger and thumb, and lift it a short distance off the table. The subjects were instructed to do the task as fast as possible. The perturbation was an elastic load acting on the wrist at an angle of 105 deg lateral to the reaching direction. The condition was modified by changing the predictability with which the perturbation was applied in a given trial. After recording unperturbed control trials, perturbations were applied first on successive trials (predictable perturbations) and then were applied randomly (unpredictable perturbations). In the early predictable perturbation trials, reach path length became longer and reaching duration increased. As more predictable perturbations were applied, the reach path length gradually decreased and became similar to that of control trials. Reaching duration also decreased gradually as the subjects adapted by exerting force against the perturbation. In addition, the amplitude of peak grip aperture during arm transport initially increased in response to repeated perturbations. During the course of learning, it reached its maximum and thereafter slightly decreased. However, it did not return to the normal level. The subjects also adapted to the unpredictable perturbations through changes in both arm transport and grasping components, indicating that they can compensate even when the occurrence of the perturbation cannot be predicted during the inter-trial interval. Throughout random perturbation trials, large grip aperture values were observed, suggesting that a conservative aperture level is set regardless of whether the reaching arm is perturbed or not. In addition, the results of the predictable perturbations showed that the time from movement onset to the onset of grip aperture closure changed as adaptation occurred. However, the spatial location where the onset of finger closure occurred showed minimum changes with perturbation. These data suggest that the onset of finger closure is dependent upon distance to target rather than the temporal relationship of the grasp relative to the transport phase of the movement.
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.
Cosmic rays from primordial black holes

NASA Technical Reports Server (NTRS)

Macgibbon, Jane H.; Carr, B. J.

1991-01-01

The quark and gluon emission from primordial black holes (PBHs) which may have formed from initial density perturbations or phase transitions in the early universe are investigated. If the PBHs formed from scale-invariant initial density perturbations in the radiation dominated era, it is found that the emission can explain or contribute significantly to the extragalactic photon and interstellar cosmic-ray electron, positron, and antiproton spectra around 0.1-1 GeV. In particular, the PBH emission strongly resembles the cosmic-ray gamma-ray spectrum between 50 and 170 MeV. The upper limits on the PBH density today from the gamma-ray, e(+), e(-), and antiproton data are comparable, provided that the PBHs cluster to the same degree as the other matter in the Galactic halo.
Transient spatiotemporal chaos in the Morris-Lecar neuronal ring network.

PubMed

Keplinger, Keegan; Wackerbauer, Renate

2014-03-01

Transient behavior is thought to play an integral role in brain functionality. Numerical simulations of the firing activity of diffusively coupled, excitable Morris-Lecar neurons reveal transient spatiotemporal chaos in the parameter regime below the saddle-node on invariant circle bifurcation point. The neighborhood of the chaotic saddle is reached through perturbations of the rest state, in which few initially active neurons at an effective spatial distance can initiate spatiotemporal chaos. The system escapes from the neighborhood of the chaotic saddle to either the rest state or to a state of pulse propagation. The lifetime of the chaotic transients is manipulated in a statistical sense through a singular application of a synchronous perturbation to a group of neurons.
The in-phase states of Josephson junctions stacks as attractors

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

Hristov, I.; Dimova, S.; Hristova, R.

2014-11-12

The aim of this investigation is to show that the coherent, in-phase states of intrinsic Josephson junctions stacks are attractors of the stacks' states when the applied external magnetic field h{sub e} and the external current γ vary within certain domains. Mathematically the problem is to find the solutions of the system of perturbed sine-Gordon equations for fixed other parameters and zero or random initial conditions. We determine the region in the plane (h{sub e}, γ), where the in-phase states are attractors of the stack's states for arbitrary initial perturbations. This is important, because the in-phase states are required formore » achieving terahertz radiation from the Josephson stacks.« less
DOE Office of Scientific and Technical Information (OSTI.GOV)

Kuzmina, L.K.

The research deals with different aspects of mathematical modelling and the analysis of complex dynamic non-linear systems as a consequence of applied problems in mechanics (in particular those for gyrosystems, for stabilization and orientation systems, control systems of movable objects, including the aviation and aerospace systems) Non-linearity, multi-connectedness and high dimensionness of dynamical problems, that occur at the initial full statement lead to the need of the problem narrowing, and of the decomposition of the full model, but with safe-keeping of main properties and of qualitative equivalence. The elaboration of regular methods for modelling problems in dynamics, the generalization ofmore » reduction principle are the main aims of the investigations. Here, uniform methodology, based on Lyapunov`s methods, founded by N.G.Ohetayev, is developed. The objects of the investigations are considered with exclusive positions, as systems of singularly perturbed class, treated as ones with singular parametrical perturbations. It is the natural extension of the statements of N.G.Chetayev and P.A.Kuzmin for parametrical stability. In paper the systematical procedures for construction of correct simplified models (comparison ones) are developed, the validity conditions of the transition are determined the appraisals are received, the regular algorithms of engineering level are obtained. Applicabilitelly to the stabilization and orientation systems with the gyroscopic controlling subsystems, these methods enable to build the hierarchical sequence of admissible simplified models; to determine the conditions of their correctness.« less
Synthesizing Virtual Oscillators to Control Islanded Inverters

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

Johnson, Brian B.; Sinha, Mohit; Ainsworth, Nathan G.

Virtual oscillator control (VOC) is a decentralized control strategy for islanded microgrids where inverters are regulated to emulate the dynamics of weakly nonlinear oscillators. Compared to droop control, which is only well defined in sinusoidal steady state, VOC is a time-domain controller that enables interconnected inverters to stabilize arbitrary initial conditions to a synchronized sinusoidal limit cycle. However, the nonlinear oscillators that are elemental to VOC cannot be designed with conventional linear-control design methods. We address this challenge by applying averaging- and perturbation-based nonlinear analysis methods to extract the sinusoidal steady-state and harmonic behavior of such oscillators. The averaged modelsmore » reveal conclusive links between real- and reactive-power outputs and the terminal-voltage dynamics. Similarly, the perturbation methods aid in quantifying higher order harmonics. The resultant models are then leveraged to formulate a design procedure for VOC such that the inverter satisfies standard ac performance specifications related to voltage regulation, frequency regulation, dynamic response, and harmonic content. Experimental results for a single-phase 750 VA, 120 V laboratory prototype demonstrate the validity of the design approach. They also demonstrate that droop laws are, in fact, embedded within the equilibria of the nonlinear-oscillator dynamics. This establishes the backward compatibility of VOC in that, while acting on time-domain waveforms, it subsumes droop control in sinusoidal steady state.« less
Optimal error analysis of the intraseasonal convection due to uncertainties of the sea surface temperature in a coupled model

NASA Astrophysics Data System (ADS)

Li, Xiaojing; Tang, Youmin; Yao, Zhixiong

2017-04-01

The predictability of the convection related to the Madden-Julian Oscillation (MJO) is studied using a coupled model CESM (Community Earth System Model) and the climatically relevant singular vector (CSV) approach. The CSV approach is an ensemble-based strategy to calculate the optimal initial error on climate scale. In this study, we focus on the optimal initial error of the sea surface temperature in Indian Ocean, where is the location of the MJO onset. Six MJO events are chosen from the 10 years model simulation output. The results show that the large values of the SVs are mainly located in the bay of Bengal and the south central IO (around (25°S, 90°E)), which is a meridional dipole-like pattern. The fast error growth of the CSVs have important impacts on the prediction of the convection related to the MJO. The initial perturbations with the SV pattern result in the deep convection damping more quickly in the east Pacific Ocean. Moreover, the sensitivity studies of the CSVs show that different initial fields do not affect the CSVs obviously, while the perturbation domain is a more responsive factor to the CSVs. The rapid growth of the CSVs is found to be related to the west bay of Bengal, where the wind stress starts to be perturbed due to the CSV initial error. These results contribute to the establishment of an ensemble prediction system, as well as the optimal observation network. In addition, the analysis of the error growth can provide us some enlightment about the relationship between SST and the intraseasonal convection related to the MJO.
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.
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.
The Predictability of Advection-dominated Flux-transport Solar Dynamo Models

NASA Astrophysics Data System (ADS)

Sanchez, Sabrina; Fournier, Alexandre; Aubert, Julien

2014-01-01

Space weather is a matter of practical importance in our modern society. Predictions of forecoming solar cycles mean amplitude and duration are currently being made based on flux-transport numerical models of the solar dynamo. Interested in the forecast horizon of such studies, we quantify the predictability window of a representative, advection-dominated, flux-transport dynamo model by investigating its sensitivity to initial conditions and control parameters through a perturbation analysis. We measure the rate associated with the exponential growth of an initial perturbation of the model trajectory, which yields a characteristic timescale known as the e-folding time τ e . The e-folding time is shown to decrease with the strength of the α-effect, and to increase with the magnitude of the imposed meridional circulation. Comparing the e-folding time with the solar cycle periodicity, we obtain an average estimate for τ e equal to 2.76 solar cycle durations. From a practical point of view, the perturbations analyzed in this work can be interpreted as uncertainties affecting either the observations or the physical model itself. After reviewing these, we discuss their implications for solar cycle prediction.
Nonsingular cosmology with a scale-invariant spectrum of cosmological perturbations from Lee-Wick theory

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

Cai Yifu; Qiu Taotao; Brandenberger, Robert

2009-07-15

We study the cosmology of a Lee-Wick type scalar field theory. First, we consider homogeneous and isotropic background solutions and find that they are nonsingular, leading to cosmological bounces. Next, we analyze the spectrum of cosmological perturbations which result from this model. Unless either the potential of the Lee-Wick theory or the initial conditions are finely tuned, it is impossible to obtain background solutions which have a sufficiently long period of inflation after the bounce. More interestingly, however, we find that in the generic noninflationary bouncing cosmology, perturbations created from quantum vacuum fluctuations in the contracting phase have the correctmore » form to lead to a scale-invariant spectrum of metric inhomogeneities in the expanding phase. Since the background is nonsingular, the evolution of the fluctuations is defined unambiguously through the bounce. We also analyze the evolution of fluctuations which emerge from thermal initial conditions in the contracting phase. The spectrum of gravitational waves stemming from quantum vacuum fluctuations in the contracting phase is also scale-invariant, and the tensor to scalar ratio is not suppressed.« less
Kurtosis, skewness, and non-Gaussian cosmological density perturbations

NASA Technical Reports Server (NTRS)

Luo, Xiaochun; Schramm, David N.

1993-01-01

Cosmological topological defects as well as some nonstandard inflation models can give rise to non-Gaussian density perturbations. Skewness and kurtosis are the third and fourth moments that measure the deviation of a distribution from a Gaussian. Measurement of these moments for the cosmological density field and for the microwave background temperature anisotropy can provide a test of the Gaussian nature of the primordial fluctuation spectrum. In the case of the density field, the importance of measuring the kurtosis is stressed since it will be preserved through the weakly nonlinear gravitational evolution epoch. Current constraints on skewness and kurtosis of primeval perturbations are obtained from the observed density contrast on small scales and from recent COBE observations of temperature anisotropies on large scales. It is also shown how, in principle, future microwave anisotropy experiments might be able to reveal the initial skewness and kurtosis. It is shown that present data argue that if the initial spectrum is adiabatic, then it is probably Gaussian, but non-Gaussian isocurvature fluctuations are still allowed, and these are what topological defects provide.
Surfing gravitational waves: can bigravity survive growing tensor modes?

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

Amendola, Luca; Könnig, Frank; Martinelli, Matteo

The theory of bigravity offers one of the simplest possibilities to describe a massive graviton while having self-accelerating cosmological solutions without a cosmological constant. However, it has been shown recently that bigravity is affected by early-time fast growing modes on the tensor sector. Here we argue that we can only trust the linear analysis up to when perturbations are in the linear regime and use a cut-off to stop the growing of the metric perturbations. This analysis, although more consistent, still leads to growing tensor modes that are unacceptably large for the theory to be compatible with measurements of themore » cosmic microwave background (CMB), both in temperature and polarization spectra. In order to suppress the growing modes and make the model compatible with CMB spectra, we find it necessary to either fine-tune the initial conditions, modify the theory or set the cut-off for the tensor perturbations of the second metric much lower than unity. Initial conditions such that the growing mode is sufficiently suppresed can be achieved in scenarios in which inflation ends at the GeV scale.« less

Primordial power spectra for scalar perturbations in loop quantum cosmology

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

De Blas, Daniel Martín; Olmedo, Javier, E-mail: d.martindeblas@uandresbello.edu, E-mail: jolmedo@lsu.edu

We provide the power spectrum of small scalar perturbations propagating in an inflationary scenario within loop quantum cosmology. We consider the hybrid quantization approach applied to a Friedmann-Robertson-Walker spacetime with flat spatial sections coupled to a massive scalar field. We study the quantum dynamics of scalar perturbations on an effective background within this hybrid approach. We consider in our study adiabatic states of different orders. For them, we find that the hybrid quantization is in good agreement with the predictions of the dressed metric approach. We also propose an initial vacuum state for the perturbations, and compute the primordial andmore » the anisotropy power spectrum in order to qualitatively compare with the current observations of Planck mission. We find that our vacuum state is in good agreement with them, showing a suppression of the power spectrum for large scale anisotropies. We compare with other choices already studied in the literature.« less
A water-based training program that include perturbation exercises to improve stepping responses in older adults: study protocol for a randomized controlled cross-over trial

PubMed Central

Melzer, Itshak; Elbar, Ori; Tsedek, Irit; Oddsson, Lars IE

2008-01-01

Background Gait and balance impairments may increase the risk of falls, the leading cause of accidental death in the elderly population. Fall-related injuries constitute a serious public health problem associated with high costs for society as well as human suffering. A rapid step is the most important protective postural strategy, acting to recover equilibrium and prevent a fall from initiating. It can arise from large perturbations, but also frequently as a consequence of volitional movements. We propose to use a novel water-based training program which includes specific perturbation exercises that will target the stepping responses that could potentially have a profound effect in reducing risk of falling. We describe the water-based balance training program and a study protocol to evaluate its efficacy (Trial registration number #NCT00708136). Methods/Design The proposed water-based training program involves use of unpredictable, multi-directional perturbations in a group setting to evoke compensatory and volitional stepping responses. Perturbations are made by pushing slightly the subjects and by water turbulence, in 24 training sessions conducted over 12 weeks. Concurrent cognitive tasks during movement tasks are included. Principles of physical training and exercise including awareness, continuity, motivation, overload, periodicity, progression and specificity were used in the development of this novel program. Specific goals are to increase the speed of stepping responses and improve the postural control mechanism and physical functioning. A prospective, randomized, cross-over trial with concealed allocation, assessor blinding and intention-to-treat analysis will be performed to evaluate the efficacy of the water-based training program. A total of 36 community-dwelling adults (age 65–88) with no recent history of instability or falling will be assigned to either the perturbation-based training or a control group (no training). Voluntary step reaction times and postural stability using stabiliogram diffusion analysis will be tested before and after the 12 weeks of training. Discussion This study will determine whether a water-based balance training program that includes perturbation exercises, in a group setting, can improve speed of voluntary stepping responses and improve balance control. Results will help guide the development of more cost-effective interventions that can prevent the occurrence of falls in the elderly. PMID:18706103
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.
Dynamic postural stability during advancing pregnancy.

PubMed

McCrory, J L; Chambers, A J; Daftary, A; Redfern, M S

2010-08-26

Pregnant women are at an increased risk of experiencing a fall. Numerous anatomical, physiological, and hormonal alterations occur during pregnancy, but the influence of these factors on dynamic postural stability has not been explored. The purpose of this study was to examine dynamic postural stability in pregnant women during their second and third trimesters as well as in a group of non-pregnant control women. Eighty-one women (41 pregnant, 40 controls) participated stood on a force plate that translated anteroposteriorly at small, medium, and large magnitudes. Reaction time and center of pressure (COP) movement during the translations were analyzed. Trimester, perturbation direction, and perturbation magnitude were the independent variables in a mixed-model analysis of variance on each of the following dependent variables: reaction time, initial sway, total sway, and sway velocity. Reaction time to the perturbation was not significantly different between the groups. Initial sway, total sway, and sway velocity were significantly less during the third trimester than during the second trimester and when compared to the non-pregnant controls (P<0.05). No differences were found in any of the measures between the pregnant women in their second trimesters and the control group. Alterations in sway responses to perturbations are seen in the third trimester in healthy women with uncomplicated pregnancies. Further study is needed to examine the biomechanical and physiological reasons behind this altered dynamic postural stability. 2010 Elsevier Ltd. All rights reserved.
Perturbation theory for BAO reconstructed fields: One-loop results in the real-space matter density field

NASA Astrophysics Data System (ADS)

Hikage, Chiaki; Koyama, Kazuya; Heavens, Alan

2017-08-01

We compute the power spectrum at one-loop order in standard perturbation theory for the matter density field to which a standard Lagrangian baryonic acoustic oscillation (BAO) reconstruction technique is applied. The BAO reconstruction method corrects the bulk motion associated with the gravitational evolution using the inverse Zel'dovich approximation (ZA) for the smoothed density field. We find that the overall amplitude of one-loop contributions in the matter power spectrum substantially decreases after reconstruction. The reconstructed power spectrum thereby approaches the initial linear spectrum when the smoothed density field is close enough to linear, i.e., the smoothing scale Rs≳10 h-1 Mpc . On smaller Rs, however, the deviation from the linear spectrum becomes significant on large scales (k ≲Rs-1 ) due to the nonlinearity in the smoothed density field, and the reconstruction is inaccurate. Compared with N-body simulations, we show that the reconstructed power spectrum at one-loop order agrees with simulations better than the unreconstructed power spectrum. We also calculate the tree-level bispectrum in standard perturbation theory to investigate non-Gaussianity in the reconstructed matter density field. We show that the amplitude of the bispectrum significantly decreases for small k after reconstruction and that the tree-level bispectrum agrees well with N-body results in the weakly nonlinear regime.
PARALLEL PERTURBATION MODEL FOR CYCLE TO CYCLE VARIABILITY PPM4CCV

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

Ameen, Muhsin Mohammed; Som, Sibendu

This code consists of a Fortran 90 implementation of the parallel perturbation model to compute cyclic variability in spark ignition (SI) engines. Cycle-to-cycle variability (CCV) is known to be detrimental to SI engine operation resulting in partial burn and knock, and result in an overall reduction in the reliability of the engine. Numerical prediction of cycle-to-cycle variability (CCV) in SI engines is extremely challenging for two key reasons: (i) high-fidelity methods such as large eddy simulation (LES) are required to accurately capture the in-cylinder turbulent flow field, and (ii) CCV is experienced over long timescales and hence the simulations needmore » to be performed for hundreds of consecutive cycles. In the new technique, the strategy is to perform multiple parallel simulations, each of which encompasses 2-3 cycles, by effectively perturbing the simulation parameters such as the initial and boundary conditions. The PPM4CCV code is a pre-processing code and can be coupled with any engine CFD code. PPM4CCV was coupled with Converge CFD code and a 10-time speedup was demonstrated over the conventional multi-cycle LES in predicting the CCV for a motored engine. Recently, the model is also being applied to fired engines including port fuel injected (PFI) and direct injection spark ignition engines and the preliminary results are very encouraging.« less
An Image Encryption Algorithm Utilizing Julia Sets and Hilbert Curves

PubMed Central

Sun, Yuanyuan; Chen, Lina; Xu, Rudan; Kong, Ruiqing

2014-01-01

Image encryption is an important and effective technique to protect image security. In this paper, a novel image encryption algorithm combining Julia sets and Hilbert curves is proposed. The algorithm utilizes Julia sets’ parameters to generate a random sequence as the initial keys and gets the final encryption keys by scrambling the initial keys through the Hilbert curve. The final cipher image is obtained by modulo arithmetic and diffuse operation. In this method, it needs only a few parameters for the key generation, which greatly reduces the storage space. Moreover, because of the Julia sets’ properties, such as infiniteness and chaotic characteristics, the keys have high sensitivity even to a tiny perturbation. The experimental results indicate that the algorithm has large key space, good statistical property, high sensitivity for the keys, and effective resistance to the chosen-plaintext attack. PMID:24404181
Effect of Swirl on Turbulent Structures in Supersonic Jets

NASA Technical Reports Server (NTRS)

Rao, Ram Mohan; Lundgren, Thomas S.

1998-01-01

Direct Numerical Simulation (DNS) is used to study the mechanism of generation and evolution of turbulence structures in a temporally evolving supersonic swirling round jet and also to examine the resulting acoustic radiations. Fourier spectral expansions are used in the streamwise and azimuthal directions and a 1-D b-spline Galerkin representation is used in the radial direction. Spectral-like accuracy is achieved using this numerical scheme. Direct numerical simulations, using the b-spline spectral method, are carried out starting from mean flow initial conditions which are perturbed by the most unstable linear stability eigenfunctions. It is observed that the initial helical instability waves evolve into helical vortices which eventually breakdown into smaller scales of turbulence. 'Rib' structures similar to those seen in incompressible mixing layer flow of Rogers and Moserl are observed. The jet core breakdown stage exhibits increased acoustic radiations.
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.
Boundary Layer Instabilities Generated by Freestream Laser Perturbations

NASA Technical Reports Server (NTRS)

Chou, Amanda; Schneider, Steven P.

2015-01-01

A controlled, laser-generated, freestream perturbation was created in the freestream of the Boeing/AFOSR Mach-6 Quiet Tunnel (BAM6QT). The freestream perturbation convected downstream in the Mach-6 wind tunnel to interact with a flared cone model. The geometry of the flared cone is a body of revolution bounded by a circular arc with a 3-meter radius. Fourteen PCB 132A31 pressure transducers were used to measure a wave packet generated in the cone boundary layer by the freestream perturbation. This wave packet grew large and became nonlinear before experiencing natural transition in quiet flow. Breakdown of this wave packet occurred when the amplitude of the pressure fluctuations was approximately 10% of the surface pressure for a nominally sharp nosetip. The initial amplitude of the second mode instability on the blunt flared cone is estimated to be on the order of 10 -6 times the freestream static pressure. The freestream laser-generated perturbation was positioned upstream of the model in three different configurations: on the centerline, offset from the centerline by 1.5 mm, and offset from the centerline by 3.0 mm. When the perturbation was offset from the centerline of a blunt flared cone, a larger wave packet was generated on the side toward which the perturbation was offset. The offset perturbation did not show as much of an effect on the wave packet on a sharp flared cone as it did on a blunt flared cone.
Orbital Eccentricity and the Stability of Planets in the Alpha Centauri System

NASA Technical Reports Server (NTRS)

Lissauer, Jack

2016-01-01

Planets on initially circular orbits are typically more dynamically stable than planets initially having nonzero eccentricities. However, the presence of a major perturber that forces periodic oscillations of planetary eccentricity can alter this situation. We investigate the dependance of system lifetime on initial eccentricity for planets orbiting one star within the alpha Centauri system. Our results show that initial conditions chosen to minimize free eccentricity can substantially increase stability compared to planets on circular orbits.
A new model for gravitational potential perturbations in disks of spiral galaxies. An application to our Galaxy

NASA Astrophysics Data System (ADS)

Junqueira, T. C.; Lépine, J. R. D.; Braga, C. A. S.; Barros, D. A.

2013-02-01

Aims: We propose a new, more realistic description of the perturbed gravitational potential of spiral galaxies, with spiral arms having Gaussian-shaped groove profiles. The aim is to reach a self-consistent description of the spiral structure, that is, one in which an initial potential perturbation generates, by means of the stellar orbits, spiral arms with a profile similar to that of the imposed perturbation. Self-consistency is a condition for having long-lived structures. Methods: Using the new perturbed potential, we investigate the stable stellar orbits in galactic disks for galaxies with no bar or with only a weak bar. The model is applied to our Galaxy by making use of the axisymmetric component of the potential computed from the Galactic rotation curve, in addition to other input parameters similar to those of our Galaxy. The influence of the bulge mass on the stellar orbits in the inner regions of a disk is also investigated. Results: The new description offers the advantage of easy control of the parameters of the Gaussian profile of its potential. We compute the density contrast between arm and inter-arm regions. We find a range of values for the perturbation amplitude from 400 to 800 km2 s-2 kpc-1, which implies an approximate maximum ratio of the tangential force to the axisymmetric force between 3% and 6%. Good self-consistency of arm shapes is obtained between the Inner Lindblad resonance (ILR) and the 4:1 resonance. Near the 4:1 resonance the response density starts to deviate from the imposed logarithmic spiral form. This creates bifurcations that appear as short arms. Therefore the deviation from a perfect logarithmic spiral in galaxies can be understood as a natural effect of the 4:1 resonance. Beyond the 4:1 resonance we find closed orbits that have similarities with the arms observed in our Galaxy. In regions near the center, elongated stellar orbits appear naturally, in the presence of a massive bulge, without imposing any bar-shaped potential, but only extending the spiral perturbation a little inward of the ILR. This suggests that a bar is formed with a half-size ~3 kpc by a mechanism similar to that of the spiral arms. Conclusions: The potential energy perturbation that we adopted represents an important step in the direction of self-consistency, compared to previous sine function descriptions of the potential. In addition, our model produces a realistic description of the spiral structure, which is able to explain several details that were not yet understood.
Self-Organizing Global Gene Expression Regulated through Criticality: Mechanism of the Cell-Fate Change

PubMed Central

Tsuchiya, Masa; Giuliani, Alessandro; Hashimoto, Midori; Erenpreisa, Jekaterina; Yoshikawa, Kenichi

2016-01-01

Background A fundamental issue in bioscience is to understand the mechanism that underlies the dynamic control of genome-wide expression through the complex temporal-spatial self-organization of the genome to regulate the change in cell fate. We address this issue by elucidating a physically motivated mechanism of self-organization. Principal Findings Building upon transcriptome experimental data for seven distinct cell fates, including early embryonic development, we demonstrate that self-organized criticality (SOC) plays an essential role in the dynamic control of global gene expression regulation at both the population and single-cell levels. The novel findings are as follows: i) Mechanism of cell-fate changes: A sandpile-type critical transition self-organizes overall expression into a few transcription response domains (critical states). A cell-fate change occurs by means of a dissipative pulse-like global perturbation in self-organization through the erasure of initial-state critical behaviors (criticality). Most notably, the reprogramming of early embryo cells destroys the zygote SOC control to initiate self-organization in the new embryonal genome, which passes through a stochastic overall expression pattern. ii) Mechanism of perturbation of SOC controls: Global perturbations in self-organization involve the temporal regulation of critical states. Quantitative evaluation of this perturbation in terminal cell fates reveals that dynamic interactions between critical states determine the critical-state coherent regulation. The occurrence of a temporal change in criticality perturbs this between-states interaction, which directly affects the entire genomic system. Surprisingly, a sub-critical state, corresponding to an ensemble of genes that shows only marginal changes in expression and consequently are considered to be devoid of any interest, plays an essential role in generating a global perturbation in self-organization directed toward the cell-fate change. Conclusion and Significance ‘Whole-genome’ regulation of gene expression through self-regulatory SOC control complements gene-by-gene fine tuning and represents a still largely unexplored non-equilibrium statistical mechanism that is responsible for the massive reprogramming of genome expression. PMID:27997556
Techniques of orbital decay and long-term ephemeris prediction for satellites in earth orbit

NASA Technical Reports Server (NTRS)

Barry, B. F.; Pimm, R. S.; Rowe, C. K.

1971-01-01

In the special perturbation method, Cowell and variation-of-parameters formulations of the motion equations are implemented and numerically integrated. Variations in the orbital elements due to drag are computed using the 1970 Jacchia atmospheric density model, which includes the effects of semiannual variations, diurnal bulge, solar activity, and geomagnetic activity. In the general perturbation method, two-variable asymptotic series and automated manipulation capabilities are used to obtain analytical solutions to the variation-of-parameters equations. Solutions are obtained considering the effect of oblateness only and the combined effects of oblateness and drag. These solutions are then numerically evaluated by means of a FORTRAN program in which an updating scheme is used to maintain accurate epoch values of the elements. The atmospheric density function is approximated by a Fourier series in true anomaly, and the 1970 Jacchia model is used to periodically update the Fourier coefficients. The accuracy of both methods is demonstrated by comparing computed orbital elements to actual elements over time spans of up to 8 days for the special perturbation method and up to 356 days for the general perturbation method.
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.
Protecting a quantum state from environmental noise by an incompatible finite-time measurement

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

Brasil, Carlos Alexandre; Castro, L. A. de; Napolitano, R. d. J.

We show that measurements of finite duration performed on an open two-state system can protect the initial state from a phase-noisy environment, provided the measured observable does not commute with the perturbing interaction. When the measured observable commutes with the environmental interaction, the finite-duration measurement accelerates the rate of decoherence induced by the phase noise. For the description of the measurement of an observable that is incompatible with the interaction between system and environment, we have found an approximate analytical expression, valid at zero temperature and weak coupling with the measuring device. We have tested the validity of the analyticalmore » predictions against an exact numerical approach, based on the superoperator-splitting method, that confirms the protection of the initial state of the system. When the coupling between the system and the measuring apparatus increases beyond the range of validity of the analytical approximation, the initial state is still protected by the finite-time measurement, according with the exact numerical calculations.« less
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.

SHORT-WAVELENGTH MAGNETIC BUOYANCY INSTABILITY

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

Mizerski, K. A.; Davies, C. R.; Hughes, D. W., E-mail: kamiz@igf.edu.pl, E-mail: tina@maths.leeds.ac.uk, E-mail: d.w.hughes@leeds.ac.uk

2013-04-01

Magnetic buoyancy instability plays an important role in the evolution of astrophysical magnetic fields. Here we revisit the problem introduced by Gilman of the short-wavelength linear stability of a plane layer of compressible isothermal fluid permeated by a horizontal magnetic field of strength decreasing with height. Dissipation of momentum and magnetic field is neglected. By the use of a Rayleigh-Schroedinger perturbation analysis, we explain in detail the limit in which the transverse horizontal wavenumber of the perturbation, denoted by k, is large (i.e., short horizontal wavelength) and show that the fastest growing perturbations become localized in the vertical direction asmore » k is increased. The growth rates are determined by a function of the vertical coordinate z since, in the large k limit, the eigenmodes are strongly localized in the vertical direction. We consider in detail the case of two-dimensional perturbations varying in the directions perpendicular to the magnetic field, which, for sufficiently strong field gradients, are the most unstable. The results of our analysis are backed up by comparison with a series of initial value problems. Finally, we extend the analysis to three-dimensional perturbations.« less
Water content dependence of trapped air in two soils

USGS Publications Warehouse

Stonestrom, David A.; Rubin, Jacob

1989-01-01

An improved air pycnometer method was used to examine the water content dependence of trapped-air volumes in two repacked, nonswelling soils. Trapped-air volumes were determined at a series of hydrostatic equilibrium stages which were attained during water pressure-controlled wetting and drying cycles over a range of 0 to −10 kPa for a sand and 0 to −20 kPa for a loam. Small pressure perturbations, between 0.2 and 0.6 kPa, were used in the air pycnometer method. Volumes of trapped air obtained at each hydrostatic equilibrium stage were independent of perturbation level and remained relatively constant over the time required to make repeated determinations. In contrast with most of the results obtained in previous studies, which often showed irregular relations, in this study the volume fraction of trapped air was found to be a regular, monotonically increasing (though possibly hysteretic) function of water content. For the soils studied, the function definitely exceeded zero only at water contents greater than 70% of saturation. However, during the initial drying from complete water saturation, the volume fraction of trapped air was virtually zero. Air trapping influenced the water retention curves significantly only at water contents higher than about 60% of saturation. Except at zero water pressure, however, not all of the differences between the initial and the other drying retention curves were accounted for by observed differences in trapped-air volumes. Air trapping was not required for the onset of hysteresis in the water retention relation for the cases studied, i.e., when drying-to-wetting reversals were imposed at about 27% and 40% of saturation for the sand and loam soils, respectively.
Evaluation of the observation operator Jacobian for leaf area index data assimilation with an extended Kalman filter

NASA Astrophysics Data System (ADS)

Rüdiger, Christoph; Albergel, CléMent; Mahfouf, Jean-FrançOis; Calvet, Jean-Christophe; Walker, Jeffrey P.

2010-05-01

To quantify carbon and water fluxes between the vegetation and the atmosphere in a consistent manner, land surface models now include interactive vegetation components. These models treat the vegetation biomass as a prognostic model state, allowing the model to dynamically adapt the vegetation states to environmental conditions. However, it is expected that the prediction skill of such models can be greatly increased by assimilating biophysical observations such as leaf area index (LAI). The Jacobian of the observation operator, a central aspect of data assimilation methods such as the extended Kalman filter (EKF) and the variational assimilation methods, provides the required linear relationship between the observation and the model states. In this paper, the Jacobian required for assimilating LAI into the Interaction between the Soil, Biosphere and Atmosphere-A-gs land surface model using the EKF is studied. In particular, sensitivity experiments were undertaken on the size of the initial perturbation for estimating the Jacobian and on the length of the time window between initial state and available observation. It was found that small perturbations (0.1% of the state) typically lead to accurate estimates of the Jacobian. While other studies have shown that the assimilation of LAI with 10 day assimilation windows is possible, 1 day assimilation intervals can be chosen to comply with numerical weather prediction requirements. Moreover, the seasonal dependence of the Jacobian revealed contrasted groups of Jacobian values due to environmental factors. Further analyses showed the Jacobian values to vary as a function of the LAI itself, which has important implications for its assimilation in different seasons, as the size of the LAI increments will subsequently vary due to the variability of the Jacobian.
Tests of oceanic stochastic parameterisation in a seasonal forecast system.

NASA Astrophysics Data System (ADS)

Cooper, Fenwick; Andrejczuk, Miroslaw; Juricke, Stephan; Zanna, Laure; Palmer, Tim

2015-04-01

Over seasonal time scales, our aim is to compare the relative impact of ocean initial condition and model uncertainty, upon the ocean forecast skill and reliability. Over seasonal timescales we compare four oceanic stochastic parameterisation schemes applied in a 1x1 degree ocean model (NEMO) with a fully coupled T159 atmosphere (ECMWF IFS). The relative impacts upon the ocean of the resulting eddy induced activity, wind forcing and typical initial condition perturbations are quantified. Following the historical success of stochastic parameterisation in the atmosphere, two of the parameterisations tested were multiplicitave in nature: A stochastic variation of the Gent-McWilliams scheme and a stochastic diffusion scheme. We also consider a surface flux parameterisation (similar to that introduced by Williams, 2012), and stochastic perturbation of the equation of state (similar to that introduced by Brankart, 2013). The amplitude of the stochastic term in the Williams (2012) scheme was set to the physically reasonable amplitude considered in that paper. The amplitude of the stochastic term in each of the other schemes was increased to the limits of model stability. As expected, variability was increased. Up to 1 month after initialisation, ensemble spread induced by stochastic parameterisation is greater than that induced by the atmosphere, whilst being smaller than the initial condition perturbations currently used at ECMWF. After 1 month, the wind forcing becomes the dominant source of model ocean variability, even at depth.
An iterative analytical technique for the design of interplanetary direct transfer trajectories including perturbations

NASA Astrophysics Data System (ADS)

Parvathi, S. P.; Ramanan, R. V.

2018-06-01

An iterative analytical trajectory design technique that includes perturbations in the departure phase of the interplanetary orbiter missions is proposed. The perturbations such as non-spherical gravity of Earth and the third body perturbations due to Sun and Moon are included in the analytical design process. In the design process, first the design is obtained using the iterative patched conic technique without including the perturbations and then modified to include the perturbations. The modification is based on, (i) backward analytical propagation of the state vector obtained from the iterative patched conic technique at the sphere of influence by including the perturbations, and (ii) quantification of deviations in the orbital elements at periapsis of the departure hyperbolic orbit. The orbital elements at the sphere of influence are changed to nullify the deviations at the periapsis. The analytical backward propagation is carried out using the linear approximation technique. The new analytical design technique, named as biased iterative patched conic technique, does not depend upon numerical integration and all computations are carried out using closed form expressions. The improved design is very close to the numerical design. The design analysis using the proposed technique provides a realistic insight into the mission aspects. Also, the proposed design is an excellent initial guess for numerical refinement and helps arrive at the four distinct design options for a given opportunity.
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.
Aging effect on step adjustments and stability control in visually perturbed gait initiation.

PubMed

Sun, Ruopeng; Cui, Chuyi; Shea, John B

2017-10-01

Gait adaptability is essential for fall avoidance during locomotion. It requires the ability to rapidly inhibit original motor planning, select and execute alternative motor commands, while also maintaining the stability of locomotion. This study investigated the aging effect on gait adaptability and dynamic stability control during a visually perturbed gait initiation task. A novel approach was used such that the anticipatory postural adjustment (APA) during gait initiation were used to trigger the unpredictable relocation of a foot-size stepping target. Participants (10 young adults and 10 older adults) completed visually perturbed gait initiation in three adjustment timing conditions (early, intermediate, late; all extracted from the stereotypical APA pattern) and two adjustment direction conditions (medial, lateral). Stepping accuracy, foot rotation at landing, and Margin of Dynamic Stability (MDS) were analyzed and compared across test conditions and groups using a linear mixed model. Stepping accuracy decreased as a function of adjustment timing as well as stepping direction, with older subjects exhibited a significantly greater undershoot in foot placement to late lateral stepping. Late adjustment also elicited a reaching-like movement (i.e. foot rotation prior to landing in order to step on the target), regardless of stepping direction. MDS measures in the medial-lateral and anterior-posterior direction revealed both young and older adults exhibited reduced stability in the adjustment step and subsequent steps. However, young adults returned to stable gait faster than older adults. These findings could be useful for future study of screening deficits in gait adaptability and preventing falls. Copyright © 2017 Elsevier B.V. All rights reserved.
Perturbation analysis of 6DoF flight dynamics and passive dynamic stability of hovering fruit fly Drosophila melanogaster.

PubMed

Gao, Na; Aono, Hikaru; Liu, Hao

2011-02-07

Insects exhibit exquisite control of their flapping flight, capable of performing precise stability and steering maneuverability. Here we develop an integrated computational model to investigate flight dynamics of insect hovering based on coupling the equations of 6 degree of freedom (6DoF) motion with the Navier-Stokes (NS) equations. Unsteady aerodynamics is resolved by using a biology-inspired dynamic flight simulator that integrates models of realistic wing-body morphology and kinematics, and a NS solver. We further develop a dynamic model to solve the rigid body equations of 6DoF motion by using a 4th-order Runge-Kutta method. In this model, instantaneous forces and moments based on the NS-solutions are represented in terms of Fourier series. With this model, we perform a systematic simulation-based analysis on the passive dynamic stability of a hovering fruit fly, Drosophila melanogaster, with a specific focus on responses of state variables to six one-directional perturbation conditions during latency period. Our results reveal that the flight dynamics of fruit fly hovering does not have a straightforward dynamic stability in a conventional sense that perturbations damp out in a manner of monotonous convergence. However, it is found to exist a transient interval containing an initial converging response observed for all the six perturbation variables and a terminal instability that at least one state variable subsequently tends to diverge after several wing beat cycles. Furthermore, our results illustrate that a fruit fly does have sufficient time to apply some active mediation to sustain a steady hovering before losing body attitudes. Copyright Â© 2010 Elsevier Ltd. All rights reserved.
Patterns of HIV-1 Protein Interaction Identify Perturbed Host-Cellular Subsystems

PubMed Central

MacPherson, Jamie I.; Dickerson, Jonathan E.; Pinney, John W.; Robertson, David L.

2010-01-01

Human immunodeficiency virus type 1 (HIV-1) exploits a diverse array of host cell functions in order to replicate. This is mediated through a network of virus-host interactions. A variety of recent studies have catalogued this information. In particular the HIV-1, Human Protein Interaction Database (HHPID) has provided a unique depth of protein interaction detail. However, as a map of HIV-1 infection, the HHPID is problematic, as it contains curation error and redundancy; in addition, it is based on a heterogeneous set of experimental methods. Based on identifying shared patterns of HIV-host interaction, we have developed a novel methodology to delimit the core set of host-cellular functions and their associated perturbation from the HHPID. Initially, using biclustering, we identify 279 significant sets of host proteins that undergo the same types of interaction. The functional cohesiveness of these protein sets was validated using a human protein-protein interaction network, gene ontology annotation and sequence similarity. Next, using a distance measure, we group host protein sets and identify 37 distinct higher-level subsystems. We further demonstrate the biological significance of these subsystems by cross-referencing with global siRNA screens that have been used to detect host factors necessary for HIV-1 replication, and investigate the seemingly small intersect between these data sets. Our results highlight significant host-cell subsystems that are perturbed during the course of HIV-1 infection. Moreover, we characterise the patterns of interaction that contribute to these perturbations. Thus, our work disentangles the complex set of HIV-1-host protein interactions in the HHPID, reconciles these with siRNA screens and provides an accessible and interpretable map of infection. PMID:20686668
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.
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.
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
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.
Cosmological explosions from cold dark matter perturbations

NASA Technical Reports Server (NTRS)

Scherrer, Robert J.

1992-01-01

The cosmological-explosion model is examined for a universe dominated by cold dark matter in which explosion seeds are produced from the growth of initial density perturbations of a given form. Fragmentation of the exploding shells is dominated by the dark-matter potential wells rather than the self-gravity of the shells, and particular conditions are required for the explosions to bootstrap up to very large scales. The final distribution of dark matter is strongly correlated with the baryons on small scales, but uncorrelated on large scales.
Scattering transform for nonstationary Schroedinger equation with bidimensionally perturbed N-soliton potential

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

Boiti, M.; Pempinelli, F.; Pogrebkov, A. K.

2006-12-15

In the framework of the extended resolvent approach the direct and inverse scattering problems for the nonstationary Schroedinger equation with a potential being a perturbation of the N-soliton potential by means of a generic bidimensional smooth function decaying at large spaces are introduced and investigated. The initial value problem of the Kadomtsev-Petviashvili I equation for a solution describing N wave solitons on a generic smooth decaying background is then linearized, giving the time evolution of the spectral data.
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.
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.

TOPEX/POSEIDON orbit maintenance maneuver design

NASA Technical Reports Server (NTRS)

Bhat, R. S.; Frauenholz, R. B.; Cannell, Patrick E.

1990-01-01

The Ocean Topography Experiment (TOPEX/POSEIDON) mission orbit requirements are outlined, as well as its control and maneuver spacing requirements including longitude and time targeting. A ground-track prediction model dealing with geopotential, luni-solar gravity, and atmospheric-drag perturbations is considered. Targeting with all modeled perturbations is discussed, and such ground-track prediction errors as initial semimajor axis, orbit-determination, maneuver-execution, and atmospheric-density modeling errors are assessed. A longitude targeting strategy for two extreme situations is investigated employing all modeled perturbations and prediction errors. It is concluded that atmospheric-drag modeling errors are the prevailing ground-track prediction error source early in the mission during high solar flux, and that low solar-flux levels expected late in the experiment stipulate smaller maneuver magnitudes.
A review for identification of initiating events in event tree development process on nuclear power plants

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

Riyadi, Eko H., E-mail: e.riyadi@bapeten.go.id

2014-09-30

Initiating event is defined as any event either internal or external to the nuclear power plants (NPPs) that perturbs the steady state operation of the plant, if operating, thereby initiating an abnormal event such as transient or loss of coolant accident (LOCA) within the NPPs. These initiating events trigger sequences of events that challenge plant control and safety systems whose failure could potentially lead to core damage or large early release. Selection for initiating events consists of two steps i.e. first step, definition of possible events, such as by evaluating a comprehensive engineering, and by constructing a top level logicmore » model. Then the second step, grouping of identified initiating event's by the safety function to be performed or combinations of systems responses. Therefore, the purpose of this paper is to discuss initiating events identification in event tree development process and to reviews other probabilistic safety assessments (PSA). The identification of initiating events also involves the past operating experience, review of other PSA, failure mode and effect analysis (FMEA), feedback from system modeling, and master logic diagram (special type of fault tree). By using the method of study for the condition of the traditional US PSA categorization in detail, could be obtained the important initiating events that are categorized into LOCA, transients and external events.« less
Application of Numerical Integration and Data Fusion in Unit Vector Method

NASA Astrophysics Data System (ADS)

Zhang, J.

2012-01-01

The Unit Vector Method (UVM) is a series of orbit determination methods which are designed by Purple Mountain Observatory (PMO) and have been applied extensively. It gets the conditional equations for different kinds of data by projecting the basic equation to different unit vectors, and it suits for weighted process for different kinds of data. The high-precision data can play a major role in orbit determination, and accuracy of orbit determination is improved obviously. The improved UVM (PUVM2) promoted the UVM from initial orbit determination to orbit improvement, and unified the initial orbit determination and orbit improvement dynamically. The precision and efficiency are improved further. In this thesis, further research work has been done based on the UVM: Firstly, for the improvement of methods and techniques for observation, the types and decision of the observational data are improved substantially, it is also asked to improve the decision of orbit determination. The analytical perturbation can not meet the requirement. So, the numerical integration for calculating the perturbation has been introduced into the UVM. The accuracy of dynamical model suits for the accuracy of the real data, and the condition equations of UVM are modified accordingly. The accuracy of orbit determination is improved further. Secondly, data fusion method has been introduced into the UVM. The convergence mechanism and the defect of weighted strategy have been made clear in original UVM. The problem has been solved in this method, the calculation of approximate state transition matrix is simplified and the weighted strategy has been improved for the data with different dimension and different precision. Results of orbit determination of simulation and real data show that the work of this thesis is effective: (1) After the numerical integration has been introduced into the UVM, the accuracy of orbit determination is improved obviously, and it suits for the high-accuracy data of available observation apparatus. Compare with the classical differential improvement with the numerical integration, its calculation speed is also improved obviously. (2) After data fusion method has been introduced into the UVM, weighted distribution accords rationally with the accuracy of different kinds of data, all data are fully used and the new method is also good at numerical stability and rational weighted distribution.
Unveiling the excited state energy transfer pathways in peridinin-chlorophyll a-protein by ultrafast multi-pulse transient absorption spectroscopy.

PubMed

Redeckas, Kipras; Voiciuk, Vladislava; Zigmantas, Donatas; Hiller, Roger G; Vengris, Mikas

2017-04-01

Time-resolved multi-pulse methods were applied to investigate the excited state dynamics, the interstate couplings, and the excited state energy transfer pathways between the light-harvesting pigments in peridinin-chlorophyll a-protein (PCP). The utilized pump-dump-probe techniques are based on perturbation of the regular PCP energy transfer pathway. The PCP complexes were initially excited with an ultrashort pulse, resonant to the S 0 →S 2 transition of the carotenoid peridinin. A portion of the peridinin-based emissive intramolecular charge transfer (ICT) state was then depopulated by applying an ultrashort NIR pulse that perturbed the interaction between S 1 and ICT states and the energy flow from the carotenoids to the chlorophylls. The presented data indicate that the peridinin S 1 and ICT states are spectrally distinct and coexist in an excited state equilibrium in the PCP complex. Moreover, numeric analysis of the experimental data asserts ICT→Chl-a as the main energy transfer pathway in the photoexcited PCP systems. Copyright © 2017 Elsevier B.V. All rights reserved.
Two-dimensional simulations of thermonuclear burn in ignition-scale inertial confinement fusion targets under compressed axial magnetic fields

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

Perkins, L. J.; Logan, B. G.; Zimmerman, G. B.

2013-07-15

We report for the first time on full 2-D radiation-hydrodynamic implosion simulations that explore the impact of highly compressed imposed magnetic fields on the ignition and burn of perturbed spherical implosions of ignition-scale cryogenic capsules. Using perturbations that highly convolute the cold fuel boundary of the hotspot and prevent ignition without applied fields, we impose initial axial seed fields of 20–100 T (potentially attainable using present experimental methods) that compress to greater than 4 × 10{sup 4} T (400 MG) under implosion, thereby relaxing hotspot areal densities and pressures required for ignition and propagating burn by ∼50%. The compressed fieldmore » is high enough to suppress transverse electron heat conduction, and to allow alphas to couple energy into the hotspot even when highly deformed by large low-mode amplitudes. This might permit the recovery of ignition, or at least significant alpha particle heating, in submarginal capsules that would otherwise fail because of adverse hydrodynamic instabilities.« less
On the tesseral-harmonics resonance problem in artificial-satellite theory

NASA Technical Reports Server (NTRS)

Romanowicz, B. A.

1975-01-01

The longitude-dependent part of the geopotential usually gives rise only to short-period effects in the motion of an artificial satellite. However, when the motion of the satellite is commensurable with that of the earth, the path of the satellite repeats itself relative to the earth and perturbations build up at each passage of the satellite in the same spot, so that there can be important long-period effects. In order to take these effects into account in deriving a theoretical solution to the equations of motion of an artificial satellite, it is necessary to select terms in the longitude-dependent part of the geopotential that will contribute significantly to the perturbations. Attempts made to obtain a selection that is valid in a general case, regardless of the initial eccentricity of the orbit and of the order of the resonance, are reported. The solution to the equations of motion of an artificial satellite, in a geopotential thus determined, is then derived by using Hori's method by Lie series, which, by its properties regarding canonical invariance, has proved advantageous in the classical theory.
Perturbation schedule does not alter retention of a locomotor adaptation across days.

PubMed

Hussain, Sara J; Morton, Susanne M

2014-06-15

Motor adaptation in response to gradual vs. abrupt perturbation schedules may involve different neural mechanisms, potentially leading to different levels of motor memory. However, no study has investigated whether perturbation schedules alter memory of a locomotor adaptation across days. We measured adaptation and retention (memory) of altered interlimb symmetry during walking in two groups of participants over 2 days. On day 1, participants adapted to either a single, large perturbation (abrupt schedule) or a series of small perturbations that increased in size over time (gradual schedule). Retention was examined on day 2. On day 1, initial swing time and foot placement symmetry error sizes differed between groups but overall adaptation magnitudes were similar. On day 2, participants in both groups showed similar retention, readaptation, and aftereffect sizes, although there were some trends for improved memory in the abrupt group. These results conflict with previous data but are consistent with newer studies reporting no behavioral differences following adaptation using abrupt vs. gradual schedules. Although memory levels were very similar between groups, we cannot rule out the possibility that the neural mechanisms underlying this memory storage differ. Overall, it appears that adaptation of locomotor patterns via abrupt and gradual perturbation schedules produces similar expression of locomotor memories across days. Copyright © 2014 the American Physiological Society.
Adiabatic invariants in stellar dynamics, 3: Application to globular cluster evolution

NASA Technical Reports Server (NTRS)

Weinberg, Martin D.

1994-01-01

The previous two companion papers demonstrate that slowly varying perturbations may not result in adiabatic cutoffs and provide a formalism for computing the long-term effects of time-dependent perturbations on stellar systems. Here, the theory is implemented in a Fokker-Planck code and a suite of runs illustrating the effects of shock heating on globular cluster evolution are described. Shock heating alone results in considerable mass loss for clusters with R(sub g) less than or approximately 8 kpc: a concentration c = 1.5 cluster with R(sub g) kpc loses up to 95% of its initial mass in 15 Gyr. Only those with concentration c greater than or approximately 1.3 survive disk shocks inside of this radius. Other effects, such as mass loss by stellar evolution, will decrease this survival bound. Loss of the initial halo together with mass segregation leads to mass spectral indices, x, which may be considerably larger than their initial values.
Cosmological perturbation theory and the spherical collapse model - II. Non-Gaussian initial conditions

NASA Astrophysics Data System (ADS)

Gaztanaga, Enrique; Fosalba, Pablo

1998-12-01

In Paper I of this series, we introduced the spherical collapse (SC) approximation in Lagrangian space as a way of estimating the cumulants xi_J of density fluctuations in cosmological perturbation theory (PT). Within this approximation, the dynamics is decoupled from the statistics of the initial conditions, so we are able to present here the cumulants for generic non-Gaussian initial conditions, which can be estimated to arbitrary order including the smoothing effects. The SC model turns out to recover the exact leading-order non-linear contributions up to terms involving non-local integrals of the J-point functions. We argue that for the hierarchical ratios S_J, these non-local terms are subdominant and tend to compensate each other. The resulting predictions show a non-trivial time evolution that can be used to discriminate between models of structure formation. We compare these analytic results with non-Gaussian N-body simulations, which turn out to be in very good agreement up to scales where sigma<~1.
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.
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.
4D Hybrid Ensemble-Variational Data Assimilation for the NCEP GFS: Outer Loops and Variable Transforms

NASA Astrophysics Data System (ADS)

Kleist, D. T.; Ide, K.; Mahajan, R.; Thomas, C.

2014-12-01

The use of hybrid error covariance models has become quite popular for numerical weather prediction (NWP). One such method for incorporating localized covariances from an ensemble within the variational framework utilizes an augmented control variable (EnVar), and has been implemented in the operational NCEP data assimilation system (GSI). By taking the existing 3D EnVar algorithm in GSI and allowing for four-dimensional ensemble perturbations, coupled with the 4DVAR infrastructure already in place, a 4D EnVar capability has been developed. The 4D EnVar algorithm has a few attractive qualities relative to 4DVAR, including the lack of need for tangent-linear and adjoint model as well as reduced computational cost. Preliminary results using real observations have been encouraging, showing forecast improvements nearly as large as were found in moving from 3DVAR to hybrid 3D EnVar. 4D EnVar is the method of choice for the next generation assimilation system for use with the operational NCEP global model, the global forecast system (GFS). The use of an outer-loop has long been the method of choice for 4DVar data assimilation to help address nonlinearity. An outer loop involves the re-running of the (deterministic) background forecast from the updated initial condition at the beginning of the assimilation window, and proceeding with another inner loop minimization. Within 4D EnVar, a similar procedure can be adopted since the solver evaluates a 4D analysis increment throughout the window, consistent with the valid times of the 4D ensemble perturbations. In this procedure, the ensemble perturbations are kept fixed and centered about the updated background state. This is analogous to the quasi-outer loop idea developed for the EnKF. Here, we present results for both toy model and real NWP systems demonstrating the impact from incorporating outer loops to address nonlinearity within the 4D EnVar context. The appropriate amplitudes for observation and background error covariances in subsequent outer loops will be explored. Lastly, variable transformations on the ensemble perturbations will be utilized to help address issues of non-Gaussianity. This may be particularly important for variables that clearly have non-Gaussian error characteristics such as water vapor and cloud condensate.
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.
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.
Existence and exponential stability of traveling waves for delayed reaction-diffusion systems

NASA Astrophysics Data System (ADS)

Hsu, Cheng-Hsiung; Yang, Tzi-Sheng; Yu, Zhixian

2018-03-01

The purpose of this work is to investigate the existence and exponential stability of traveling wave solutions for general delayed multi-component reaction-diffusion systems. Following the monotone iteration scheme via an explicit construction of a pair of upper and lower solutions, we first obtain the existence of monostable traveling wave solutions connecting two different equilibria. Then, applying the techniques of weighted energy method and comparison principle, we show that all solutions of the Cauchy problem for the considered systems converge exponentially to traveling wave solutions provided that the initial perturbations around the traveling wave fronts belong to a suitable weighted Sobolev space.
Control of vertical posture while standing on a sliding board and pushing an object.

PubMed

Lee, Yun-Ju; Chen, Bing; Liang, Jing-Nong; Aruin, Alexander S

2018-03-01

Voluntary pushing or translation perturbation of the support surface each induces a body perturbation that affects postural control. The objective of the study was to investigate anticipatory (APA) and compensatory (CPA) postural adjustments when pushing an object (that induces self-initiated perturbation) and standing on a sliding board (that induces translational perturbation). Thirteen healthy young participants were instructed to push a handle with both hands while standing on a sliding board that was either free to move in the anterior-posterior direction or stationary. Electromyographic activity (EMG) of trunk and lower extremity muscles, center of pressure (COP) displacements, and the forces exerted by the hand were recorded and analyzed during the APA and CPA phases. When the sliding board was free to move during pushing (translation perturbation), onsets of activity of ventral leg muscles and COP displacement were delayed as compared to pushing when standing on a stationary board. Moreover, magnitudes of shank muscle activity and the COP displacement were decreased. When pushing heavier weight, magnitudes of muscle activity, COP displacement, and pushing force increased. The magnitude of activity of the shank muscles during the APA and CPA phases in conditions with translational perturbation varied with the magnitude of the pushing weight. The outcome of the study suggests that the central nervous system prioritizes the pushing task while attenuates the source of additional perturbation induced by translation perturbation. These results could be used in the development of balance re-training paradigms involving pushing weight while standing on a sliding surface.
Manual physical therapy and perturbation exercises in knee osteoarthritis.

PubMed

Rhon, Daniel; Deyle, Gail; Gill, Norman; Rendeiro, Daniel

2013-11-01

Knee osteoarthritis (OA) causes disability among the elderly and is often associated with impaired balance and proprioception. Perturbation exercises may help improve these impairments. Although manual physical therapy is generally a well-tolerated treatment for knee OA, perturbation exercises have not been evaluated when used with a manual physical therapy approach. The purpose of this study was to observe tolerance to perturbation exercises and the effect of a manual physical therapy approach with perturbation exercises on patients with knee OA. This was a prospective observational cohort study of 15 patients with knee OA. The Western Ontario and McMaster Universities Arthritis Index (WOMAC), global rating of change (GROC), and 72-hour post-treatment tolerance were primary outcome measures. Patients received perturbation balance exercises along with a manual physical therapy approach, twice weekly for 4 weeks. Follow-up evaluation was done at 1, 3, and 6 months after beginning the program. Mean total WOMAC score significantly improved (P = 0.001) after the 4-week program (total WOMAC: initial, 105; 4 weeks, 56; 3 months, 54; 6 months, 57). Mean improvements were similar to previously published trials of manual physical therapy without perturbation exercises. The GROC score showed a minimal clinically important difference (MCID)≥+3 in 13 patients (87%) at 4 weeks, 12 patients (80%) at 3 months, and 9 patients (60%) at 6 months. No patients reported exacerbation of symptoms within 72 hours following each treatment session. A manual physical therapy approach that also included perturbation exercises was well tolerated and resulted in improved outcome scores in patients with knee OA.
Linear analysis on the growth of non-spherical perturbations in supersonic accretion flows

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

Takahashi, Kazuya; Yamada, Shoichi, E-mail: ktakahashi@heap.phys.waseda.ac.jp

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

NASA Astrophysics Data System (ADS)

Huo, Jing; Okada, Kazunori; Pope, Whitney; Brown, Matthew

2011-03-01

Inconsistency and a lack of reproducibility are commonly associated with semi-automated segmentation methods. In this study, we developed an ensemble approach to improve reproducibility and applied it to glioblastoma multiforme (GBM) brain tumor segmentation on T1-weigted contrast enhanced MR volumes. The proposed approach combines samplingbased simulations and ensemble segmentation into a single framework; it generates a set of segmentations by perturbing user initialization and user-specified internal parameters, then fuses the set of segmentations into a single consensus result. Three combination algorithms were applied: majority voting, averaging and expectation-maximization (EM). The reproducibility of the proposed framework was evaluated by a controlled experiment on 16 tumor cases from a multicenter drug trial. The ensemble framework had significantly better reproducibility than the individual base Otsu thresholding method (p<.001).

Method and apparatus for control of coherent synchrotron radiation effects during recirculation with bunch compression

DOEpatents

Douglas, David R; Tennant, Christopher

2015-11-10

A modulated-bending recirculating system that avoids CSR-driven breakdown in emittance compensation by redistributing the bending along the beamline. The modulated-bending recirculating system includes a) larger angles of bending in initial FODO cells, thereby enhancing the impact of CSR early on in the beam line while the bunch is long, and 2) a decreased bending angle in the final FODO cells, reducing the effect of CSR while the bunch is short. The invention describes a method for controlling the effects of CSR during recirculation and bunch compression including a) correcting chromatic aberrations, b) correcting lattice and CSR-induced curvature in the longitudinal phase space by compensating T.sub.566, and c) using lattice perturbations to compensate obvious linear correlations x-dp/p and x'-dp/p.
Readout signals calculated for near-field optical pickups with land and groove recording.

PubMed

Saito, K; Kishima, K; Ichimura, I

2000-08-10

Optical disk readout signals with a solid immersion lens (SIL) and the land-groove recording technique are calculated by use of a simplified vector-diffraction theory. In this method the full vector-diffraction theory is applied to calculate the diffracted light from the initial state of the disk, and the light scattered from the recorded marks is regarded as a perturbation. Using this method, we confirmed that the land-groove recording technique is effective as a means of cross-talk reduction even when the numerical aperture is more than 1. However, the top surface of the disk under the SIL must be flat, or the readout signal from marks recorded on a groove decays when the optical depth of the groove is greater than lambda/8.
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.
Optimal perturbations of a finite-width mixing layer near the trailing edge

NASA Astrophysics Data System (ADS)

Gumbart, James C.; Rabchuk, James

2002-03-01

The trailing edge of a surface separating two fluid flows can act as an efficient receptor for acoustic or other disturbances. The incident wave energy is converted by a linear mechanism into incipient flow instabilities which lead further downstream to the transition to turbulence. Understanding this process is essential for analyzing feedback loops and other resonances which can cause unwanted structural vibrations in the surface material or directed acoustic emissions from the mixing region. Previously, the modes of instability in a finite-width mixing layer near the trailing edge were studied as a function of frequency by assuming that vorticity was continually being introduced into the flow at the trailing edge by the forcing field. It was found that the initial amplitude of the growing instability mode was a sharply decreasing function of forcing frequency, and that the initial amplitude was a minimum for the frequency at which the rate of instability growth was a maximum^1. This result has led to a study of the adjoint equation for the perturbation stream function, whose eigensolutions are known to be associated with the optimal perturbation field for the frequency of forcing leading to the greatest instability growth downstream. We have obtained these solutions for a piecewise linear velocity profile near the trailing edge using group-theoretic techniques and have shown that they are indeed optimal. We have also analyzed the nature of the physical forcing field that might produce these optimal perturbations. ^1 Rabchuk, J.A., July 2000, Physics of Fluids.
Perturbational formulation of principal component analysis in molecular dynamics simulation.

PubMed

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.
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.
Shock front distortion and Richtmyer-Meshkov-type growth caused by a small preshock nonuniformity

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

Velikovich, A. L.; Wouchuk, J. G.; Huete Ruiz de Lira, C.

The response of a shock front to small preshock nonuniformities of density, pressure, and velocity is studied theoretically and numerically. These preshock nonuniformities emulate imperfections of a laser target, due either to its manufacturing, like joints or feeding tubes, or to preshock perturbation seeding/growth, as well as density fluctuations in foam targets, ''thermal layers'' near heated surfaces, etc. Similarly to the shock-wave interaction with a small nonuniformity localized at a material interface, which triggers a classical Richtmyer-Meshkov (RM) instability, interaction of a shock wave with periodic or localized preshock perturbations distributed in the volume distorts the shape of the shockmore » front and can cause a RM-type instability growth. Explicit asymptotic formulas describing distortion of the shock front and the rate of RM-type growth are presented. These formulas are favorably compared both to the exact solutions of the corresponding initial-boundary-value problem and to numerical simulations. It is demonstrated that a small density modulation localized sufficiently close to a flat target surface produces the same perturbation growth as an 'equivalent' ripple on the surface of a uniform target, characterized by the same initial areal mass modulation amplitude.« less
Formation of rogue waves from a locally perturbed condensate.

PubMed

Gelash, A A

2018-02-01

The one-dimensional focusing nonlinear Schrödinger equation (NLSE) on an unstable condensate background is the fundamental physical model that can be applied to study the development of modulation instability (MI) and formation of rogue waves. The complete integrability of the NLSE via inverse scattering transform enables the decomposition of the initial conditions into elementary nonlinear modes: breathers and continuous spectrum waves. The small localized condensate perturbations (SLCP) that grow as a result of MI have been of fundamental interest in nonlinear physics for many years. Here, we demonstrate that Kuznetsov-Ma and superregular NLSE breathers play the key role in the dynamics of a wide class of SLCP. During the nonlinear stage of MI development, collisions of these breathers lead to the formation of rogue waves. We present new scenarios of rogue wave formation for randomly distributed breathers as well as for artificially prepared initial conditions. For the latter case, we present an analytical description based on the exact expressions found for the space-phase shifts that breathers acquire after collisions with each other. Finally, the presence of Kuznetsov-Ma and superregular breathers in arbitrary-type condensate perturbations is demonstrated by solving the Zakharov-Shabat eigenvalue problem with high numerical accuracy.
Formation of rogue waves from a locally perturbed condensate

NASA Astrophysics Data System (ADS)

Gelash, A. Â. A.

2018-02-01

The one-dimensional focusing nonlinear Schrödinger equation (NLSE) on an unstable condensate background is the fundamental physical model that can be applied to study the development of modulation instability (MI) and formation of rogue waves. The complete integrability of the NLSE via inverse scattering transform enables the decomposition of the initial conditions into elementary nonlinear modes: breathers and continuous spectrum waves. The small localized condensate perturbations (SLCP) that grow as a result of MI have been of fundamental interest in nonlinear physics for many years. Here, we demonstrate that Kuznetsov-Ma and superregular NLSE breathers play the key role in the dynamics of a wide class of SLCP. During the nonlinear stage of MI development, collisions of these breathers lead to the formation of rogue waves. We present new scenarios of rogue wave formation for randomly distributed breathers as well as for artificially prepared initial conditions. For the latter case, we present an analytical description based on the exact expressions found for the space-phase shifts that breathers acquire after collisions with each other. Finally, the presence of Kuznetsov-Ma and superregular breathers in arbitrary-type condensate perturbations is demonstrated by solving the Zakharov-Shabat eigenvalue problem with high numerical accuracy.
Time-resolved particle image velocimetry measurements of the 3D single-mode Richtmyer-Meshkov instability

NASA Astrophysics Data System (ADS)

Xu, Qian; Krivets, Vitaliy V.; Sewell, Everest G.; Jacobs, Jeffrey W.

2016-11-01

A vertical shock tube is used to perform experiments on the single-mode three-dimensional Richtmyer-Meshkov Instability (RMI). The light gas (Air) and the heavy gas (SF6) enter from the top and the bottom of the shock tube driven section to form the interface. The initial perturbation is then generated by oscillating the gases vertically. Both gases are seeded with particles generated through vaporizing propylene glycol. An incident shock wave (M 1.2) impacts the interface to create an impulsive acceleration. The seeded particles are illuminated by a dual cavity 75W, Nd: YLF laser. Three high-speed CMOS cameras record time sequences of image pairs at a rate of 2 kHz. The initial perturbation used is that of a single, square-mode perturbation with either a single spike or a single bubble positioned at the center of the shock tube. The full time dependent velocity field is obtained allowing the determination of the circulation versus time. In addition, the evolution of time dependent amplitude is also determined. The results are compared with PIV measurements from previous two-dimensional single mode experiments along with PLIF measurements from previous three-dimensional single mode experiments.
Weakly nonlinear incompressible Rayleigh-Taylor instability in spherical geometry

NASA Astrophysics Data System (ADS)

Zhang, J.; Wang, L. F.; Ye, W. H.; Wu, J. F.; Guo, H. Y.; Zhang, W. Y.; He, X. T.

2017-06-01

In this research, a weakly nonlinear (WN) model for the incompressible Rayleigh-Taylor instability in cylindrical geometry [Wang et al., Phys. Plasmas 20, 042708 (2013)] is generalized to spherical geometry. The evolution of the interface with an initial small-amplitude single-mode perturbation in the form of Legendre mode (Pn) is analysed with the third-order WN solutions. The transition of the small-amplitude perturbed spherical interface to the bubble-and-spike structure can be observed by our model. For single-mode perturbation Pn, besides the generation of P 2 n and P 3 n , which are similar to the second and third harmonics in planar and cylindrical geometries, many other modes in the range of P0- P 3 n are generated by mode-coupling effects up to the third order. With the same initial amplitude, the bubbles at the pole grow faster than those at the equator in the WN regime. Furthermore, it is found that the behavior of the bubbles at the pole is similar to that of three-dimensional axisymmetric bubbles, while the behavior of the bubbles at the equator is similar to that of two-dimensional bubbles.
Imprinting of Pre-Imposed Laser Perturbations on Targets With a High-Z Overcoat

NASA Astrophysics Data System (ADS)

Karasik, Max; Weaver, J. L.; Aglitskiy, Y.; Oh, J.; Schmitt, A. J.; Bates, J. W.; Serlin, V.; Obenschain, S. P.

2014-10-01

In direct drive ICF, most of the laser imprint is expected to occur during the initial part of the laser pulse, which generates the first shocks necessary to compress the target to achieve high gain. Previous experiments found that a thin (400-800Å) high-Z (Au or Pd) overcoat on the laser side of the target is effective in suppressing broadband imprint. The overcoat initially absorbs the laser and emits soft x-rays that ablate the target, forming a large stand-off distance between laser absorption and ablation and smoothing the drive perturbations. We investigate the effectiveness of imprint suppression for different spatial wavelengths via perturbations imposed on top of the beams smoothed by Induced Spatial Incoherence (ISI). Measurements of areal mass non-uniformity on planar targets driven by the Nike KrF laser are made by curved crystal x-ray radiography. Simultaneous side-on radiography allows observation of the layer dynamics and monitoring of the laser absorption - target ablation stand-off. X-ray flux from the high-Z layer is monitored using absolutely calibrated time-resolved x-ray spectrometers. Work supported by the Department of Energy/NNSA.
Coarse-grained description of cosmic structure from Szekeres models

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

Sussman, Roberto A.; Gaspar, I. Delgado; Hidalgo, Juan Carlos, E-mail: sussman@nucleares.unam.mx, E-mail: ismael.delgadog@uaem.edu.mx, E-mail: hidalgo@fis.unam.mx

2016-03-01

We show that the full dynamical freedom of the well known Szekeres models allows for the description of elaborated 3-dimensional networks of cold dark matter structures (over-densities and/or density voids) undergoing ''pancake'' collapse. By reducing Einstein's field equations to a set of evolution equations, which themselves reduce in the linear limit to evolution equations for linear perturbations, we determine the dynamics of such structures, with the spatial comoving location of each structure uniquely specified by standard early Universe initial conditions. By means of a representative example we examine in detail the density contrast, the Hubble flow and peculiar velocities ofmore » structures that evolved, from linear initial data at the last scattering surface, to fully non-linear 10–20 Mpc scale configurations today. To motivate further research, we provide a qualitative discussion on the connection of Szekeres models with linear perturbations and the pancake collapse of the Zeldovich approximation. This type of structure modelling provides a coarse grained—but fully relativistic non-linear and non-perturbative —description of evolving large scale cosmic structures before their virialisation, and as such it has an enormous potential for applications in cosmological research.« less
The renormalization scale-setting problem in QCD

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

Wu, Xing-Gang; Brodsky, Stanley J.; Mojaza, Matin

2013-09-01

A key problem in making precise perturbative QCD predictions is to set the proper renormalization scale of the running coupling. The conventional scale-setting procedure assigns an arbitrary range and an arbitrary systematic error to fixed-order pQCD predictions. In fact, this ad hoc procedure gives results which depend on the choice of the renormalization scheme, and it is in conflict with the standard scale-setting procedure used in QED. Predictions for physical results should be independent of the choice of the scheme or other theoretical conventions. We review current ideas and points of view on how to deal with the renormalization scalemore » ambiguity and show how to obtain renormalization scheme- and scale-independent estimates. We begin by introducing the renormalization group (RG) equation and an extended version, which expresses the invariance of physical observables under both the renormalization scheme and scale-parameter transformations. The RG equation provides a convenient way for estimating the scheme- and scale-dependence of a physical process. We then discuss self-consistency requirements of the RG equations, such as reflexivity, symmetry, and transitivity, which must be satisfied by a scale-setting method. Four typical scale setting methods suggested in the literature, i.e., the Fastest Apparent Convergence (FAC) criterion, the Principle of Minimum Sensitivity (PMS), the Brodsky–Lepage–Mackenzie method (BLM), and the Principle of Maximum Conformality (PMC), are introduced. Basic properties and their applications are discussed. We pay particular attention to the PMC, which satisfies all of the requirements of RG invariance. Using the PMC, all non-conformal terms associated with the β-function in the perturbative series are summed into the running coupling, and one obtains a unique, scale-fixed, scheme-independent prediction at any finite order. The PMC provides the principle underlying the BLM method, since it gives the general rule for extending BLM up to any perturbative order; in fact, they are equivalent to each other through the PMC–BLM correspondence principle. Thus, all the features previously observed in the BLM literature are also adaptable to the PMC. The PMC scales and the resulting finite-order PMC predictions are to high accuracy independent of the choice of the initial renormalization scale, and thus consistent with RG invariance. The PMC is also consistent with the renormalization scale-setting procedure for QED in the zero-color limit. The use of the PMC thus eliminates a serious systematic scale error in perturbative QCD predictions, greatly improving the precision of empirical tests of the Standard Model and their sensitivity to new physics.« less
Bäcklund transformation, analytic soliton solutions and numerical simulation for a (2+1)-dimensional complex Ginzburg-Landau equation in a nonlinear fiber

NASA Astrophysics Data System (ADS)

Yu, Ming-Xiao; Tian, Bo; Chai, Jun; Yin, Hui-Min; Du, Zhong

2017-10-01

In this paper, we investigate a nonlinear fiber described by a (2+1)-dimensional complex Ginzburg-Landau equation with the chromatic dispersion, optical filtering, nonlinear and linear gain. Bäcklund transformation in the bilinear form is constructed. With the modified bilinear method, analytic soliton solutions are obtained. For the soliton, the amplitude can decrease or increase when the absolute value of the nonlinear or linear gain is enlarged, and the width can be compressed or amplified when the absolute value of the chromatic dispersion or optical filtering is enhanced. We study the stability of the numerical solutions numerically by applying the increasing amplitude, embedding the white noise and adding the Gaussian pulse to the initial values based on the analytic solutions, which shows that the numerical solutions are stable, not influenced by the finite initial perturbations.
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.
High-order tail in Schwarzschild spacetime

NASA Astrophysics Data System (ADS)

Casals, Marc; Ottewill, Adrian

2015-12-01

We present an analysis of the behavior at late times of linear field perturbations of a Schwarzschild black hole spacetime. In particular, we give explicit analytic expressions for the field perturbations (for a specific ℓ-multipole) of general spin up to the first four orders at late times. These expressions are valid at arbitrary radius and include, apart from the well-known power-law tail decay at leading order (˜t-2 ℓ-3), a new logarithmic behavior at third leading order (˜t-2 ℓ-5ln t ). We obtain these late-time results by developing an analytical formalism initially formulated by Mano, Suzuki and Takasugi (MST) [Prog. Theor. Phys. 95, 1079 (1996); 96, 549 (1996)] formalism and by expanding the various MST Fourier-mode quantities for small frequency. While we give explicit expansions up to the first four leading orders (for small frequency for the Fourier modes, for late time for the field perturbation), we give a prescription for obtaining expressions to arbitrary order within a "perturbative regime."

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