Hybrid Evidence Theory-based Finite Element/Statistical Energy Analysis method for mid-frequency analysis of built-up systems with epistemic uncertainties

NASA Astrophysics Data System (ADS)

Yin, Shengwen; Yu, Dejie; Yin, Hui; Lü, Hui; Xia, Baizhan

2017-09-01

Considering the epistemic uncertainties within the hybrid Finite Element/Statistical Energy Analysis (FE/SEA) model when it is used for the response analysis of built-up systems in the mid-frequency range, the hybrid Evidence Theory-based Finite Element/Statistical Energy Analysis (ETFE/SEA) model is established by introducing the evidence theory. Based on the hybrid ETFE/SEA model and the sub-interval perturbation technique, the hybrid Sub-interval Perturbation and Evidence Theory-based Finite Element/Statistical Energy Analysis (SIP-ETFE/SEA) approach is proposed. In the hybrid ETFE/SEA model, the uncertainty in the SEA subsystem is modeled by a non-parametric ensemble, while the uncertainty in the FE subsystem is described by the focal element and basic probability assignment (BPA), and dealt with evidence theory. Within the hybrid SIP-ETFE/SEA approach, the mid-frequency response of interest, such as the ensemble average of the energy response and the cross-spectrum response, is calculated analytically by using the conventional hybrid FE/SEA method. Inspired by the probability theory, the intervals of the mean value, variance and cumulative distribution are used to describe the distribution characteristics of mid-frequency responses of built-up systems with epistemic uncertainties. In order to alleviate the computational burdens for the extreme value analysis, the sub-interval perturbation technique based on the first-order Taylor series expansion is used in ETFE/SEA model to acquire the lower and upper bounds of the mid-frequency responses over each focal element. Three numerical examples are given to illustrate the feasibility and effectiveness of the proposed method.

Identification of transmissivity fields using a Bayesian strategy and perturbative approach

NASA Astrophysics Data System (ADS)

Zanini, Andrea; Tanda, Maria Giovanna; Woodbury, Allan D.

2017-10-01

The paper deals with the crucial problem of the groundwater parameter estimation that is the basis for efficient modeling and reclamation activities. A hierarchical Bayesian approach is developed: it uses the Akaike's Bayesian Information Criteria in order to estimate the hyperparameters (related to the covariance model chosen) and to quantify the unknown noise variance. The transmissivity identification proceeds in two steps: the first, called empirical Bayesian interpolation, uses Y* (Y = lnT) observations to interpolate Y values on a specified grid; the second, called empirical Bayesian update, improve the previous Y estimate through the addition of hydraulic head observations. The relationship between the head and the lnT has been linearized through a perturbative solution of the flow equation. In order to test the proposed approach, synthetic aquifers from literature have been considered. The aquifers in question contain a variety of boundary conditions (both Dirichelet and Neuman type) and scales of heterogeneities (σY2 = 1.0 and σY2 = 5.3). The estimated transmissivity fields were compared to the true one. The joint use of Y* and head measurements improves the estimation of Y considering both degrees of heterogeneity. Even if the variance of the strong transmissivity field can be considered high for the application of the perturbative approach, the results show the same order of approximation of the non-linear methods proposed in literature. The procedure allows to compute the posterior probability distribution of the target quantities and to quantify the uncertainty in the model prediction. Bayesian updating has advantages related both to the Monte-Carlo (MC) and non-MC approaches. In fact, as the MC methods, Bayesian updating allows computing the direct posterior probability distribution of the target quantities and as non-MC methods it has computational times in the order of seconds.

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.

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.

The Innisfree meteorite: Dynamical history of the orbit - Possible family of meteor bodies

NASA Astrophysics Data System (ADS)

Galibina, I. V.; Terent'eva, A. K.

1987-09-01

Evolution of the Innisfree meteorite orbit caused by secular perturbations is studied over the time interval of 500000 yrs (from the current epoch backwards). Calculations are made by the Gauss-Halphen-Gorjatschew method taking into account perturbations from the four outer planets - Jupiter, Saturn, Uranus and Neptune. In the above mentioned time interval the meteorite orbit has undergone no essential transformations. The Innisfree orbit intersected in 91 cases the Earth orbit and in 94 - the Mars orbit. A system of small and large meteor bodies (producing ordinary meteors and fireballs) which may be genetically related to the Innisfree meteorite has been found, i.e. there probably exists an Innisfree family of meteor bodies.

A framework for sensitivity analysis of decision trees.

PubMed

Kamiński, Bogumił; Jakubczyk, Michał; Szufel, Przemysław

2018-01-01

In the paper, we consider sequential decision problems with uncertainty, represented as decision trees. Sensitivity analysis is always a crucial element of decision making and in decision trees it often focuses on probabilities. In the stochastic model considered, the user often has only limited information about the true values of probabilities. We develop a framework for performing sensitivity analysis of optimal strategies accounting for this distributional uncertainty. We design this robust optimization approach in an intuitive and not overly technical way, to make it simple to apply in daily managerial practice. The proposed framework allows for (1) analysis of the stability of the expected-value-maximizing strategy and (2) identification of strategies which are robust with respect to pessimistic/optimistic/mode-favoring perturbations of probabilities. We verify the properties of our approach in two cases: (a) probabilities in a tree are the primitives of the model and can be modified independently; (b) probabilities in a tree reflect some underlying, structural probabilities, and are interrelated. We provide a free software tool implementing the methods described.

Theoretical Study of Energy Levels and Transition Probabilities of Boron Atom

NASA Astrophysics Data System (ADS)

Tian Yi, Zhang; Neng Wu, Zheng

2009-08-01

Full Text PDF Though the electrons configuration for boron atom is simple and boron atom has long been of interest for many researchers, the theoretical studies for properties of BI are not systematic, there are only few results reported on energy levels of high excited states of boron, and transition measurements are generally restricted to transitions involving ground states and low excited states without considering fine structure effects, provided only multiplet results, values for transitions between high excited states are seldom performed. In this article, by using the scheme of the weakest bound electron potential model theory calculations for energy levels of five series are performed and with the same method we give the transition probabilities between excited states with considering fine structure effects. The comprehensive set of calculations attempted in this paper could be of some value to workers in the field because of the lack of published calculations for the BI systems. The perturbations coming from foreign perturbers are taken into account in studying the energy levels. Good agreement between our results and the accepted values taken from NIST has been obtained. We also reported some values of energy levels and transition probabilities not existing on the NIST data bases.

A Brownian model for recurrent earthquakes

USGS Publications Warehouse

Matthews, M.V.; Ellsworth, W.L.; Reasenberg, P.A.

2002-01-01

We construct a probability model for rupture times on a recurrent earthquake source. Adding Brownian perturbations to steady tectonic loading produces a stochastic load-state process. Rupture is assumed to occur when this process reaches a critical-failure threshold. An earthquake relaxes the load state to a characteristic ground level and begins a new failure cycle. The load-state process is a Brownian relaxation oscillator. Intervals between events have a Brownian passage-time distribution that may serve as a temporal model for time-dependent, long-term seismic forecasting. This distribution has the following noteworthy properties: (1) the probability of immediate rerupture is zero; (2) the hazard rate increases steadily from zero at t = 0 to a finite maximum near the mean recurrence time and then decreases asymptotically to a quasi-stationary level, in which the conditional probability of an event becomes time independent; and (3) the quasi-stationary failure rate is greater than, equal to, or less than the mean failure rate because the coefficient of variation is less than, equal to, or greater than 1/???2 ??? 0.707. In addition, the model provides expressions for the hazard rate and probability of rupture on faults for which only a bound can be placed on the time of the last rupture. The Brownian relaxation oscillator provides a connection between observable event times and a formal state variable that reflects the macromechanics of stress and strain accumulation. Analysis of this process reveals that the quasi-stationary distance to failure has a gamma distribution, and residual life has a related exponential distribution. It also enables calculation of "interaction" effects due to external perturbations to the state, such as stress-transfer effects from earthquakes outside the target source. The influence of interaction effects on recurrence times is transient and strongly dependent on when in the loading cycle step pertubations occur. Transient effects may be much stronger than would be predicted by the "clock change" method and characteristically decay inversely with elapsed time after the perturbation.

Incremental dynamical downscaling for probabilistic analysis based on multiple GCM projections

NASA Astrophysics Data System (ADS)

Wakazuki, Y.

2015-12-01

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

Estimating the Probability of Rare Events Occurring Using a Local Model Averaging.

PubMed

Chen, Jin-Hua; Chen, Chun-Shu; Huang, Meng-Fan; Lin, Hung-Chih

2016-10-01

In statistical applications, logistic regression is a popular method for analyzing binary data accompanied by explanatory variables. But when one of the two outcomes is rare, the estimation of model parameters has been shown to be severely biased and hence estimating the probability of rare events occurring based on a logistic regression model would be inaccurate. In this article, we focus on estimating the probability of rare events occurring based on logistic regression models. Instead of selecting a best model, we propose a local model averaging procedure based on a data perturbation technique applied to different information criteria to obtain different probability estimates of rare events occurring. Then an approximately unbiased estimator of Kullback-Leibler loss is used to choose the best one among them. We design complete simulations to show the effectiveness of our approach. For illustration, a necrotizing enterocolitis (NEC) data set is analyzed. © 2016 Society for Risk Analysis.

The second Eshelby problem and its solvability

NASA Astrophysics Data System (ADS)

Zou, Wen-Nan; Zheng, Quan-Shui

2012-10-01

It is still a challenge to clarify the dependence of overall elastic properties of heterogeneous materials on the microstructures of non-elliposodal inhomogeneities (cracks, pores, foreign particles). From the theory of elasticity, the formulation of the perturbance elastic fields, coming from a non-ellipsoidal inhomogeneity embedded in an infinitely extended material with remote constant loading, inevitably involve one or more integral equations. Up to now, due to the mathematical difficulty, there is almost no explicit analytical solution obtained except for the ellipsoidal inhomogeneity. In this paper, we point out the impossibility to transform this inhomogeneity problem into a conventional Eshelby problem by the equivalent inclusion method even if the eigenstrain is chosen to be non-uniform. We also build up an equivalent model, called the second Eshelby problem, to investigate the perturbance stress. It is probably a better template to make use of the profound methods and results of conventional Eshelby problems of non-ellipsoidal inclusions.

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

DTIC Science & Technology

1992-12-01

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

Method and Apparatus for Performance Optimization Through Physical Perturbation of Task Elements

NASA Technical Reports Server (NTRS)

Prinzel, Lawrence J., III (Inventor); Pope, Alan T. (Inventor); Palsson, Olafur S. (Inventor); Turner, Marsha J. (Inventor)

2016-01-01

The invention is an apparatus and method of biofeedback training for attaining a physiological state optimally consistent with the successful performance of a task, wherein the probability of successfully completing the task is made is inversely proportional to a physiological difference value, computed as the absolute value of the difference between at least one physiological signal optimally consistent with the successful performance of the task and at least one corresponding measured physiological signal of a trainee performing the task. The probability of successfully completing the task is made inversely proportional to the physiological difference value by making one or more measurable physical attributes of the environment in which the task is performed, and upon which completion of the task depends, vary in inverse proportion to the physiological difference value.

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

NASA Astrophysics Data System (ADS)

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

2016-02-01

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

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.

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

NASA Astrophysics Data System (ADS)

García-Navarro, Encarnación; Fernández, Carlos

2010-05-01

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

Simple and compact expressions for neutrino oscillation probabilities in matter

DOE PAGES

Minakata, Hisakazu; Parke, Stephen J.

2016-01-29

We reformulate perturbation theory for neutrino oscillations in matter with an expansion parameter related to the ratio of the solar to the atmospheric Δm 2 scales. Unlike previous works, use a renormalized basis in which certain first-order effects are taken into account in the zeroth-order Hamiltonian. Using this perturbation theory we derive extremely compact expressions for the neutrino oscillations probabilities in matter. We find, for example, that the ν e disappearance probability at this order is of a simple two flavor form with an appropriately identified mixing angle and Δm 2. Furthermore, despite exceptional simplicity in their forms they accommodatemore » all order effects θ 13 and the matter potential.« less

Quantum transition probabilities during a perturbing pulse: Differences between the nonadiabatic results and Fermi's golden rule forms

NASA Astrophysics Data System (ADS)

Mandal, Anirban; Hunt, Katharine L. C.

2018-05-01

For a perturbed quantum system initially in the ground state, the coefficient ck(t) of excited state k in the time-dependent wave function separates into adiabatic and nonadiabatic terms. The adiabatic term ak(t) accounts for the adjustment of the original ground state to form the new ground state of the instantaneous Hamiltonian H(t), by incorporating excited states of the unperturbed Hamiltonian H0 without transitions; ak(t) follows the adiabatic theorem of Born and Fock. The nonadiabatic term bk(t) describes excitation into another quantum state k; bk(t) is obtained as an integral containing the time derivative of the perturbation. The true transition probability is given by |bk(t)|2, as first stated by Landau and Lifshitz. In this work, we contrast |bk(t)|2 and |ck(t)|2. The latter is the norm-square of the entire excited-state coefficient which is used for the transition probability within Fermi's golden rule. Calculations are performed for a perturbing pulse consisting of a cosine or sine wave in a Gaussian envelope. When the transition frequency ωk0 is on resonance with the frequency ω of the cosine wave, |bk(t)|2 and |ck(t)|2 rise almost monotonically to the same final value; the two are intertwined, but they are out of phase with each other. Off resonance (when ωk0 ≠ ω), |bk(t)|2 and |ck(t)|2 differ significantly during the pulse. They oscillate out of phase and reach different maxima but then fall off to equal final values after the pulse has ended, when ak(t) ≡ 0. If ωk0 < ω, |bk(t)|2 generally exceeds |ck(t)|2, while the opposite is true when ωk0 > ω. While the transition probability is rising, the midpoints between successive maxima and minima fit Gaussian functions of the form a exp[-b(t - d)2]. To our knowledge, this is the first analysis of nonadiabatic transition probabilities during a perturbing pulse.

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

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

Blas, Diego; Garny, Mathias; Sibiryakov, Sergey

2016-07-01

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

Stochastic Inversion of InSAR Data to Assess the Probability of Pressure Penetration into the Lower Caprock at In Salah

DOE PAGES

Ramirez, Abelardo; Foxall, William

2014-05-28

Stochastic inversions of InSAR data were carried out to assess the probability that pressure perturbations resulting from CO 2 injection into well KB-502 at In Salah penetrated into the lower caprock seal above the reservoir. Inversions of synthetic data were employed to evaluate the factors that affect the vertical resolution of overpressure distributions, and to assess the impact of various sources of uncertainty in prior constraints on inverse solutions. These include alternative pressure-driven deformation modes within reservoir and caprock, the geometry of a sub-vertical fracture zone in the caprock identified in previous studies, and imperfect estimates of the rock mechanicalmore » properties. Inversions of field data indicate that there is a high probability that a pressure perturbation during the first phase of injection extended upwards along the fracture zone ~ 150 m above the reservoir, and less than 50% probability that it reached the Hot Shale unit at 1500 m depth. Within the uncertainty bounds considered, it was concluded that it is very unlikely that the pressure perturbation approached within 150 m of the top of the lower caprock at the Hercynian Unconformity. The results are consistent with previous deterministic inversion and forward modeling studies.« less

A matrix-based approach to solving the inverse Frobenius-Perron problem using sequences of density functions of stochastically perturbed dynamical systems

NASA Astrophysics Data System (ADS)

Nie, Xiaokai; Coca, Daniel

2018-01-01

The paper introduces a matrix-based approach to estimate the unique one-dimensional discrete-time dynamical system that generated a given sequence of probability density functions whilst subjected to an additive stochastic perturbation with known density.

A matrix-based approach to solving the inverse Frobenius-Perron problem using sequences of density functions of stochastically perturbed dynamical systems.

PubMed

Nie, Xiaokai; Coca, Daniel

2018-01-01

The paper introduces a matrix-based approach to estimate the unique one-dimensional discrete-time dynamical system that generated a given sequence of probability density functions whilst subjected to an additive stochastic perturbation with known density.

Semiclassical S-matrix for black holes

DOE PAGES

Bezrukov, Fedor; Levkov, Dmitry; Sibiryakov, Sergey

2015-12-01

In this study, we propose a semiclassical method to calculate S-matrix elements for two-stage gravitational transitions involving matter collapse into a black hole and evaporation of the latter. The method consistently incorporates back-reaction of the collapsing and emitted quanta on the metric. We illustrate the method in several toy models describing spherical self-gravitating shells in asymptotically flat and AdS space-times. We find that electrically neutral shells reflect via the above collapse-evaporation process with probability exp(–B), where B is the Bekenstein-Hawking entropy of the intermediate black hole. This is consistent with interpretation of exp(B) as the number of black hole states.more » The same expression for the probability is obtained in the case of charged shells if one takes into account instability of the Cauchy horizon of the intermediate Reissner-Nordström black hole. As a result, our semiclassical method opens a new systematic approach to the gravitational S-matrix in the non-perturbative regime.« less

Protecting count queries in study design

PubMed Central

Sarwate, Anand D; Boxwala, Aziz A

2012-01-01

Objective Today's clinical research institutions provide tools for researchers to query their data warehouses for counts of patients. To protect patient privacy, counts are perturbed before reporting; this compromises their utility for increased privacy. The goal of this study is to extend current query answer systems to guarantee a quantifiable level of privacy and allow users to tailor perturbations to maximize the usefulness according to their needs. Methods A perturbation mechanism was designed in which users are given options with respect to scale and direction of the perturbation. The mechanism translates the true count, user preferences, and a privacy level within administrator-specified bounds into a probability distribution from which the perturbed count is drawn. Results Users can significantly impact the scale and direction of the count perturbation and can receive more accurate final cohort estimates. Strong and semantically meaningful differential privacy is guaranteed, providing for a unified privacy accounting system that can support role-based trust levels. This study provides an open source web-enabled tool to investigate visually and numerically the interaction between system parameters, including required privacy level and user preference settings. Conclusions Quantifying privacy allows system administrators to provide users with a privacy budget and to monitor its expenditure, enabling users to control the inevitable loss of utility. While current measures of privacy are conservative, this system can take advantage of future advances in privacy measurement. The system provides new ways of trading off privacy and utility that are not provided in current study design systems. PMID:22511018

LightForce Photon-Pressure Collision Avoidance: Efficiency Assessment on an Entire Catalogue of Space Debris

NASA Technical Reports Server (NTRS)

Stupl, Jan Michael; Faber, Nicolas; Foster, Cyrus; Yang Yang, Fan; Levit, Creon

2013-01-01

The potential to perturb debris orbits using photon pressure from ground-based lasers has been confirmed by independent research teams. Two useful applications of this scheme are protecting space assets from impacts with debris and stabilizing the orbital debris environment, both relying on collision avoidance rather than de-orbiting debris. This paper presents the results of a new assessment method to analyze the efficiency of the concept for collision avoidance. Earlier research concluded that one ground based system consisting of a 10 kW class laser, directed by a 1.5 m telescope with adaptive optics, can prevent a significant fraction of debris-debris collisions in low Earth orbit. That research used in-track displacement to measure efficiency and restricted itself to an analysis of a limited number of objects. As orbit prediction error is dependent on debris object properties, a static displacement threshold should be complemented with another measure to assess the efficiency of the scheme. In this paper we present the results of an approach using probability of collision. Using a least-squares fitting method, we improve the quality of the original TLE catalogue in terms of state and co-state accuracy. We then calculate collision probabilities for all the objects in the catalogue. The conjunctions with the highest risk of collision are then engaged by a simulated network of laser ground stations. After those engagements, the perturbed orbits are used to re-assess the collision probability in a 20 minute window around the original conjunction. We then use different criteria to evaluate the utility of the laser-based collision avoidance scheme and assess the number of base-line ground stations needed to mitigate a significant number of high probability conjunctions. Finally, we also give an account how a laser ground station can be used for both orbit deflection and debris tracking.

A new probability distribution model of turbulent irradiance based on Born perturbation theory

NASA Astrophysics Data System (ADS)

Wang, Hongxing; Liu, Min; Hu, Hao; Wang, Qian; Liu, Xiguo

2010-10-01

The subject of the PDF (Probability Density Function) of the irradiance fluctuations in a turbulent atmosphere is still unsettled. Theory reliably describes the behavior in the weak turbulence regime, but theoretical description in the strong and whole turbulence regimes are still controversial. Based on Born perturbation theory, the physical manifestations and correlations of three typical PDF models (Rice-Nakagami, exponential-Bessel and negative-exponential distribution) were theoretically analyzed. It is shown that these models can be derived by separately making circular-Gaussian, strong-turbulence and strong-turbulence-circular-Gaussian approximations in Born perturbation theory, which denies the viewpoint that the Rice-Nakagami model is only applicable in the extremely weak turbulence regime and provides theoretical arguments for choosing rational models in practical applications. In addition, a common shortcoming of the three models is that they are all approximations. A new model, called the Maclaurin-spread distribution, is proposed without any approximation except for assuming the correlation coefficient to be zero. So, it is considered that the new model can exactly reflect the Born perturbation theory. Simulated results prove the accuracy of this new model.

An extended car-following model considering the appearing probability of truck and driver's characteristics

NASA Astrophysics Data System (ADS)

Rong, Ying; Wen, Huiying

2018-05-01

In this paper, the appearing probability of truck is introduced and an extended car-following model is presented to analyze the traffic flow based on the consideration of driver's characteristics, under honk environment. The stability condition of this proposed model is obtained through linear stability analysis. In order to study the evolution properties of traffic wave near the critical point, the mKdV equation is derived by the reductive perturbation method. The results show that the traffic flow will become more disorder for the larger appearing probability of truck. Besides, the appearance of leading truck affects not only the stability of traffic flow, but also the effect of other aspects on traffic flow, such as: driver's reaction and honk effect. The effects of them on traffic flow are closely correlated with the appearing probability of truck. Finally, the numerical simulations under the periodic boundary condition are carried out to verify the proposed model. And they are consistent with the theoretical findings.

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

PubMed

Lingala, N; Namachchivaya, N Sri

2016-06-01

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

Collective motion in prolate γ-rigid nuclei within minimal length concept via a quantum perturbation method

NASA Astrophysics Data System (ADS)

Chabab, M.; El Batoul, A.; Lahbas, A.; Oulne, M.

2018-05-01

Based on the minimal length concept, inspired by Heisenberg algebra, a closed analytical formula is derived for the energy spectrum of the prolate γ-rigid Bohr-Mottelson Hamiltonian of nuclei, within a quantum perturbation method (QPM), by considering a scaled Davidson potential in β shape variable. In the resulting solution, called X(3)-D-ML, the ground state and the first β-band are all studied as a function of the free parameters. The fact of introducing the minimal length concept with a QPM makes the model very flexible and a powerful approach to describe nuclear collective excitations of a variety of vibrational-like nuclei. The introduction of scaling parameters in the Davidson potential enables us to get a physical minimum of this latter in comparison with previous works. The analysis of the corrected wave function, as well as the probability density distribution, shows that the minimal length parameter has a physical upper bound limit.

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.

Primordial black holes and uncertainties in the choice of the window function

NASA Astrophysics Data System (ADS)

Ando, Kenta; Inomata, Keisuke; Kawasaki, Masahiro

2018-05-01

Primordial black holes (PBHs) can be produced by the perturbations that exit the horizon during the inflationary phase. While inflation models predict the power spectrum of the perturbations in Fourier space, the PBH abundance depends on the probability distribution function of density perturbations in real space. To estimate the PBH abundance in a given inflation model, we must relate the power spectrum in Fourier space to the probability density function in real space by coarse graining the perturbations with a window function. However, there are uncertainties on what window function should be used, which could change the relation between the PBH abundance and the power spectrum. This is particularly important in considering PBHs with mass 30 M⊙, which account for the LIGO events because the required power spectrum is severely constrained by the observations. In this paper, we investigate how large an influence the uncertainties on the choice of a window function has over the power spectrum required for LIGO PBHs. As a result, it is found that the uncertainties significantly affect the prediction for the stochastic gravitational waves induced by the second-order effect of the perturbations. In particular, the pulsar timing array constraints on the produced gravitational waves could disappear for the real-space top-hat window function.

Information retrieval from wide-band meteorological data - An example

NASA Technical Reports Server (NTRS)

Adelfang, S. I.; Smith, O. E.

1983-01-01

The methods proposed by Smith and Adelfang (1981) and Smith et al. (1982) are used to calculate probabilities over rectangles and sectors of the gust magnitude-gust length plane; probabilities over the same regions are also calculated from the observed distributions and a comparison is also presented to demonstrate the accuracy of the statistical model. These and other statistical results are calculated from samples of Jimsphere wind profiles at Cape Canaveral. The results are presented for a variety of wavelength bands, altitudes, and seasons. It is shown that wind perturbations observed in Jimsphere wind profiles in various wavelength bands can be analyzed by using digital filters. The relationship between gust magnitude and gust length is modeled with the bivariate gamma distribution. It is pointed out that application of the model to calculate probabilities over specific areas of the gust magnitude-gust length plane can be useful in aerospace design.

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.

Promise and problems in using stress triggering models for time-dependent earthquake hazard assessment

NASA Astrophysics Data System (ADS)

Cocco, M.

2001-12-01

Earthquake stress changes can promote failures on favorably oriented faults and modify the seismicity pattern over broad regions around the causative faults. Because the induced stress perturbations modify the rate of production of earthquakes, they alter the probability of seismic events in a specified time window. Comparing the Coulomb stress changes with the seismicity rate changes and aftershock patterns can statistically test the role of stress transfer in earthquake occurrence. The interaction probability may represent a further tool to test the stress trigger or shadow model. The probability model, which incorporate stress transfer, has the main advantage to include the contributions of the induced stress perturbation (a static step in its present formulation), the loading rate and the fault constitutive properties. Because the mechanical conditions of the secondary faults at the time of application of the induced load are largely unkown, stress triggering can only be tested on fault populations and not on single earthquake pairs with a specified time delay. The interaction probability can represent the most suitable tool to test the interaction between large magnitude earthquakes. Despite these important implications and the stimulating perspectives, there exist problems in understanding earthquake interaction that should motivate future research but at the same time limit its immediate social applications. One major limitation is that we are unable to predict how and if the induced stress perturbations modify the ratio between small versus large magnitude earthquakes. In other words, we cannot distinguish between a change in this ratio in favor of small events or of large magnitude earthquakes, because the interaction probability is independent of magnitude. Another problem concerns the reconstruction of the stressing history. The interaction probability model is based on the response to a static step; however, we know that other processes contribute to the stressing history perturbing the faults (such as dynamic stress changes, post-seismic stress changes caused by viscolelastic relaxation or fluid flow). If, for instance, we believe that dynamic stress changes can trigger aftershocks or earthquakes years after the passing of the seismic waves through the fault, the perspective of calculating interaction probability is untenable. It is therefore clear we have learned a lot on earthquake interaction incorporating fault constitutive properties, allowing to solve existing controversy, but leaving open questions for future research.

Do recent observations of very large electromagnetic dissociation cross sections signify a transition towards non-perturbative QED?

NASA Technical Reports Server (NTRS)

Norbury, John W.

1992-01-01

The very large electromagnetic dissociation (EMD) cross section recently observed by Hill, Wohn, Schwellenbach, and Smith do not agree with Weizsacker-Williams (WW) theory or any simple modification thereof. Calculations are presented for the reaction probabilities for this experiment and the entire single and double nucleon removal EMD data set. It is found that for those few reactions where theory and experiment disagree, the probabilities are exceptionally large. This indicates that WW theory is not valid for these reactions and that one must consider higher order corrections and perhaps even a non-perturbative approach to quantum electrodynamics (QED).

Monte Carlo simulation of errors in the anisotropy of magnetic susceptibility - A second-rank symmetric tensor. [for grains in sedimentary and volcanic rocks

NASA Technical Reports Server (NTRS)

Lienert, Barry R.

1991-01-01

Monte Carlo perturbations of synthetic tensors to evaluate the Hext/Jelinek elliptical confidence regions for anisotropy of magnetic susceptibility (AMS) eigenvectors are used. When the perturbations are 33 percent of the minimum anisotropy, both the shapes and probability densities of the resulting eigenvector distributions agree with the elliptical distributions predicted by the Hext/Jelinek equations. When the perturbation size is increased to 100 percent of the minimum eigenvalue difference, the major axis of the 95 percent confidence ellipse underestimates the observed eigenvector dispersion by about 10 deg. The observed distributions of the principal susceptibilities (eigenvalues) are close to being normal, with standard errors that agree well with the calculated Hext/Jelinek errors. The Hext/Jelinek ellipses are also able to describe the AMS dispersions due to instrumental noise and provide reasonable limits for the AMS dispersions observed in two Hawaiian basaltic dikes. It is concluded that the Hext/Jelinek method provides a satisfactory description of the errors in AMS data and should be a standard part of any AMS data analysis.

Girsanov reweighting for path ensembles and Markov state models

NASA Astrophysics Data System (ADS)

Donati, L.; Hartmann, C.; Keller, B. G.

2017-06-01

The sensitivity of molecular dynamics on changes in the potential energy function plays an important role in understanding the dynamics and function of complex molecules. We present a method to obtain path ensemble averages of a perturbed dynamics from a set of paths generated by a reference dynamics. It is based on the concept of path probability measure and the Girsanov theorem, a result from stochastic analysis to estimate a change of measure of a path ensemble. Since Markov state models (MSMs) of the molecular dynamics can be formulated as a combined phase-space and path ensemble average, the method can be extended to reweight MSMs by combining it with a reweighting of the Boltzmann distribution. We demonstrate how to efficiently implement the Girsanov reweighting in a molecular dynamics simulation program by calculating parts of the reweighting factor "on the fly" during the simulation, and we benchmark the method on test systems ranging from a two-dimensional diffusion process and an artificial many-body system to alanine dipeptide and valine dipeptide in implicit and explicit water. The method can be used to study the sensitivity of molecular dynamics on external perturbations as well as to reweight trajectories generated by enhanced sampling schemes to the original dynamics.

Quantum mechanical reaction probability of triplet ketene at the multireference second-order perturbation level of theory.

PubMed

Ogihara, Yusuke; Yamamoto, Takeshi; Kato, Shigeki

2010-09-23

Triplet ketene exhibits a steplike structure in the experimentally observed dissociation rates, but its mechanism is still unknown despite many theoretical efforts in the past decades. In this paper we revisit this problem by quantum mechanically calculating the reaction probability with multireference-based electronic structure theory. Specifically, we first construct an analytical potential energy surface of triplet state by fitting it to about 6000 ab initio energies computed at the multireference second-order Mller-Plesset perturbation (MRMP2) level. We then evaluate the cumulative reaction probability by using the transition state wave packet method together with an adiabatically constrained Hamiltonian. The result shows that the imaginary barrier frequency on the triplet surface is 328i cm-1, which is close to the CCSD(T) result (321i cm-1) but is likely too large for reproducing the experimentally observed steps. Indeed, our calculated reaction probability exhibits no signature of steps, reflecting too strong tunneling effect along the reaction coordinate. Nevertheless, it is emphasized that the flatness of the potential profile in the transition-state region (which governs the degree of tunneling) depends strongly on the level of electronic structure calculation, thus leaving some possibility that the use of more accurate theories might lead to the observed steps. We also demonstrate that the triplet potential surface differs significantly between the CASSCF and MRMP2 results, particularly in the transition-state region. This fact seems to require more attention when studying the "nonadiabatic" scenario for the steps, in which the crossing seam between S0 and T1 surfaces is assumed to play a central role.

Statistical analysis of the ionospheric ion density recorded by DEMETER in the epicenter areas of earthquakes as well as in their magnetically conjugate point areas

NASA Astrophysics Data System (ADS)

Li, Mei; Parrot, Michel

2018-02-01

Results of a statistical variation of total ion density observed in the vicinity of epicenters as well as around magnetically conjugated points of earthquakes are presented in this paper. Two data sets are used: the ion density measured by DEMETER during about 6.5 years and the list of strong earthquakes (MW ≥ 4.8) occurring globally during this period (14,764 earthquakes in total). First of all, ionospheric perturbations with 23-120 s observation time corresponding to spatial scales of 160-840 km are automatically detected by a software (64,287 anomalies in total). Second, it is checked if a perturbation could be associated either with the epicenter of an earthquake or with its magnetically conjugated point (distance < 1500 km and time < 15 days before the earthquake). The index Kp < 3 is also considered in order to reduce the effect of the geomagnetic activity on the ionosphere during this period. The results show that it is possible to detect variations of the ionospheric parameters above the epicenter areas as well as above their conjugated points. About one third of the earthquakes are detected with ionospheric influence on both sides of the Earth. There is a trend showing that the perturbation length increases as the magnitude of the detected EQs but it is more obvious for large magnitude. The probability that a perturbation appears is higher on the day of the earthquake and then gradually decreases when the time before the earthquake increases. The spatial distribution of perturbations shows that the probability of perturbations appearing southeast of the epicenter before an earthquake is a little bit higher and that there is an obvious trend because perturbations appear west of the conjugated point of an earthquake.

Non-Gaussian statistics of soliton timing jitter induced by amplifier noise.

PubMed

Ho, Keang-Po

2003-11-15

Based on first-order perturbation theory of the soliton, the Gordon-Haus timing jitter induced by amplifier noise is found to be non-Gaussian distributed. Both frequency and timing jitter have larger tail probabilities than Gaussian distribution given by the linearized perturbation theory. The timing jitter has a larger discrepancy from Gaussian distribution than does the frequency jitter.

Wave propagation in a random medium

NASA Technical Reports Server (NTRS)

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

1969-01-01

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

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

The condition of a finite Markov chain and perturbation bounds for the limiting probabilities

NASA Technical Reports Server (NTRS)

Meyer, C. D., Jr.

1979-01-01

The inequalities bounding the relative error the norm of w- w squiggly/the norm of w are exhibited by a very simple function of E and A. Let T denote the transition matrix of an ergodic chain, C, and let A = I - T. Let E be a perturbation matrix such that T squiggly = T - E is also the transition matrix of an ergodic chain, C squiggly. Let w and w squiggly denote the limiting probability (row) vectors for C and C squiggly. The inequality is the best one possible. This bound can be significant in the numerical determination of the limiting probabilities for an ergodic chain. In addition to presenting a sharp bound for the norm of w-w squiggly/the norm of w an explicit expression for w squiggly will be derived in which w squiggly is given as a function of E, A, w and some other related terms.

Nonperturbative Quantum Physics from Low-Order Perturbation Theory.

PubMed

Mera, Héctor; Pedersen, Thomas G; Nikolić, Branislav K

2015-10-02

The Stark effect in hydrogen and the cubic anharmonic oscillator furnish examples of quantum systems where the perturbation results in a certain ionization probability by tunneling processes. Accordingly, the perturbed ground-state energy is shifted and broadened, thus acquiring an imaginary part which is considered to be a paradigm of nonperturbative behavior. Here we demonstrate how the low order coefficients of a divergent perturbation series can be used to obtain excellent approximations to both real and imaginary parts of the perturbed ground state eigenenergy. The key is to use analytic continuation functions with a built-in singularity structure within the complex plane of the coupling constant, which is tailored by means of Bender-Wu dispersion relations. In the examples discussed the analytic continuation functions are Gauss hypergeometric functions, which take as input fourth order perturbation theory and return excellent approximations to the complex perturbed eigenvalue. These functions are Borel consistent and dramatically outperform widely used Padé and Borel-Padé approaches, even for rather large values of the coupling constant.

Perturbation analysis for patch occupancy dynamics

USGS Publications Warehouse

Martin, Julien; Nichols, James D.; McIntyre, Carol L.; Ferraz, Goncalo; Hines, James E.

2009-01-01

Perturbation analysis is a powerful tool to study population and community dynamics. This article describes expressions for sensitivity metrics reflecting changes in equilibrium occupancy resulting from small changes in the vital rates of patch occupancy dynamics (i.e., probabilities of local patch colonization and extinction). We illustrate our approach with a case study of occupancy dynamics of Golden Eagle (Aquila chrysaetos) nesting territories. Examination of the hypothesis of system equilibrium suggests that the system satisfies equilibrium conditions. Estimates of vital rates obtained using patch occupancy models are used to estimate equilibrium patch occupancy of eagles. We then compute estimates of sensitivity metrics and discuss their implications for eagle population ecology and management. Finally, we discuss the intuition underlying our sensitivity metrics and then provide examples of ecological questions that can be addressed using perturbation analyses. For instance, the sensitivity metrics lead to predictions about the relative importance of local colonization and local extinction probabilities in influencing equilibrium occupancy for rare and common species.

Compensatory effects of recruitment and survival when amphibian populations are perturbed by disease

USGS Publications Warehouse

Muths, E.; Scherer, R. D.; Pilliod, D.S.

2011-01-01

The need to increase our understanding of factors that regulate animal population dynamics has been catalysed by recent, observed declines in wildlife populations worldwide. Reliable estimates of demographic parameters are critical for addressing basic and applied ecological questions and understanding the response of parameters to perturbations (e.g. disease, habitat loss, climate change). However, to fully assess the impact of perturbation on population dynamics, all parameters contributing to the response of the target population must be estimated. We applied the reverse-time model of Pradel in Program mark to 6years of capture-recapture data from two populations of Anaxyrus boreas (boreal toad) populations, one with disease and one without. We then assessed a priori hypotheses about differences in survival and recruitment relative to local environmental conditions and the presence of disease. We further explored the relative contribution of survival probability and recruitment rate to population growth and investigated how shifts in these parameters can alter population dynamics when a population is perturbed. High recruitment rates (0??41) are probably compensating for low survival probability (range 0??51-0??54) in the population challenged by an emerging pathogen, resulting in a relatively slow rate of decline. In contrast, the population with no evidence of disease had high survival probability (range 0??75-0??78) but lower recruitment rates (0??25). Synthesis and applications.We suggest that the relationship between survival and recruitment may be compensatory, providing evidence that populations challenged with disease are not necessarily doomed to extinction. A better understanding of these interactions may help to explain, and be used to predict, population regulation and persistence for wildlife threatened with disease. Further, reliable estimates of population parameters such as recruitment and survival can guide the formulation and implementation of conservation actions such as repatriations or habitat management aimed to improve recruitment. ?? 2011 The Authors. Journal of Applied Ecology ?? 2011 British Ecological Society.

Deuteron Coulomb Excitation in Peripheral Collisions with a Heavy Ion

NASA Astrophysics Data System (ADS)

Du, Weijie; Yin, Peng; Li, Yang; Chen, Guangyao; Zuo, Wei; Zhao, Xingbo; Vary, James P.

2017-09-01

We develop an ab initio time-dependent Basis Function (tBF) method to solve non-perturbative and time-dependent problems in non-relativistic quantum mechanics. As a test problem, we apply this method to the Coulomb excitation of a deuteron by an impinging heavy ion. We employ wave functions for the bound and excited states of the deuterium system based on a realistic nucleon-nucleon interaction and study the evolution of the transition probability, the r.m.s. radius and the r.m.s. momentum of the system during the scattering process. The dependencies of these quantities on the external field strength and the bombarding energy are also analyzed and compared to corresponding results obtained from first-order perturbation theory. The time evolution of both the charge and the momentum distributions is shown. This work was supported in part by the U. S. Department of Energy (DOE) under Grants No. DESC0008485 (SciDAC/NUCLEI) and DE-FG02-87ER40371. W. Zuo and P. Yin are supported by the National Natural Science Foundation of China (11435014).

Formation of primordial black holes from non-Gaussian perturbations produced in a waterfall transition

NASA Astrophysics Data System (ADS)

Bugaev, Edgar; Klimai, Peter

2012-05-01

We consider the process of primordial black hole (PBH) formation originated from primordial curvature perturbations produced during waterfall transition (with tachyonic instability), at the end of hybrid inflation. It is known that in such inflation models, rather large values of curvature perturbation amplitudes can be reached, which can potentially cause a significant PBH production in the early Universe. The probability distributions of density perturbation amplitudes in this case can be strongly non-Gaussian, which requires a special treatment. We calculated PBH abundances and PBH mass spectra for the model and analyzed their dependence on model parameters. We obtained the constraints on the parameters of the inflationary potential, using the available limits on βPBH.

New stochastic approach for extreme response of slow drift motion of moored floating structures

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

Kato, Shunji; Okazaki, Takashi

1995-12-31

A new stochastic method for investigating the flow drift response statistics of moored floating structures is described. Assuming that wave drift excitation process can be driven by a Gaussian white noise process, an exact stochastic equation governing a time evolution of the response Probability Density Function (PDF) is derived on a basis of Projection operator technique in the field of statistical physics. In order to get an approximate solution of the GFP equation, the authors develop the renormalized perturbation technique which is a kind of singular perturbation methods and solve the GFP equation taken into account up to third ordermore » moments of a non-Gaussian excitation. As an example of the present method, a closed form of the joint PDF is derived for linear response in surge motion subjected to a non-Gaussian wave drift excitation and it is represented by the product of a form factor and the quasi-Cauchy PDFs. In this case, the motion displacement and velocity processes are not mutually independent if the excitation process has a significant third order moment. From a comparison between the response PDF by the present solution and the exact one derived by Naess, it is found that the present solution is effective for calculating both the response PDF and the joint PDF. Furthermore it is shown that the displacement-velocity independence is satisfied if the damping coefficient in equation of motion is not so large and that both the non-Gaussian property of excitation and the damping coefficient should be taken into account for estimating the probability exceedance of the response.« less

On a perturbed Sparre Andersen risk model with multi-layer dividend strategy

NASA Astrophysics Data System (ADS)

Yang, Hu; Zhang, Zhimin

2009-10-01

In this paper, we consider a perturbed Sparre Andersen risk model, in which the inter-claim times are generalized Erlang(n) distributed. Under the multi-layer dividend strategy, piece-wise integro-differential equations for the discounted penalty functions are derived, and a recursive approach is applied to express the solutions. A numerical example to calculate the ruin probabilities is given to illustrate the solution procedure.

Stochastic chaos induced by diffusion processes with identical spectral density but different probability density functions.

PubMed

Lei, Youming; Zheng, Fan

2016-12-01

Stochastic chaos induced by diffusion processes, with identical spectral density but different probability density functions (PDFs), is investigated in selected lightly damped Hamiltonian systems. The threshold amplitude of diffusion processes for the onset of chaos is derived by using the stochastic Melnikov method together with a mean-square criterion. Two quasi-Hamiltonian systems, namely, a damped single pendulum and damped Duffing oscillator perturbed by stochastic excitations, are used as illustrative examples. Four different cases of stochastic processes are taking as the driving excitations. It is shown that in such two systems the spectral density of diffusion processes completely determines the threshold amplitude for chaos, regardless of the shape of their PDFs, Gaussian or otherwise. Furthermore, the mean top Lyapunov exponent is employed to verify analytical results. The results obtained by numerical simulations are in accordance with the analytical results. This demonstrates that the stochastic Melnikov method is effective in predicting the onset of chaos in the quasi-Hamiltonian systems.

Review of probabilistic analysis of dynamic response of systems with random parameters

NASA Technical Reports Server (NTRS)

Kozin, F.; Klosner, J. M.

1989-01-01

The various methods that have been studied in the past to allow probabilistic analysis of dynamic response for systems with random parameters are reviewed. Dynamic response may have been obtained deterministically if the variations about the nominal values were small; however, for space structures which require precise pointing, the variations about the nominal values of the structural details and of the environmental conditions are too large to be considered as negligible. These uncertainties are accounted for in terms of probability distributions about their nominal values. The quantities of concern for describing the response of the structure includes displacements, velocities, and the distributions of natural frequencies. The exact statistical characterization of the response would yield joint probability distributions for the response variables. Since the random quantities will appear as coefficients, determining the exact distributions will be difficult at best. Thus, certain approximations will have to be made. A number of techniques that are available are discussed, even in the nonlinear case. The methods that are described were: (1) Liouville's equation; (2) perturbation methods; (3) mean square approximate systems; and (4) nonlinear systems with approximation by linear systems.

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.

Large leptonic Dirac CP phase from broken democracy with random perturbations

NASA Astrophysics Data System (ADS)

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

2018-06-01

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

Parton Densities: A Personal Retrospective

NASA Astrophysics Data System (ADS)

Petronzio, R.

The beginning of perturbative QCD and the generalisation of parton evolution probabilities beyond leading order are briefly recalled, together with my personal experience of collaboration and friendships with Gabriele.

Dynamical Evolution of Meteoroid Streams, Developments Over the Last 30 Years

NASA Technical Reports Server (NTRS)

Williams, I. P.

2011-01-01

As soon as reliable methods for observationally determining the heliocentric orbits of meteoroids and hence the mean orbit of a meteoroid stream in the 1950s and 60s, astronomers strived to investigate the evolution of the orbit under the effects of gravitational perturbations from the planets. At first, the limitations in the capabilities of computers, both in terms of speed and memory, placed severe restrictions on what was possible to do. As a consequence, secular perturbation methods, where the perturbations are averaged over one orbit became the norm. The most popular of these is the Halphen- Goryachev method which was used extensively until the early 1980s. The main disadvantage of these methods lies in the fact that close encounter can be missed, however they remain useful for performing very long-term integrations. Direct integration methods determine the effects of the perturbing forces at many points on an orbit. This give a better picture of the orbital evolution of an individual meteoroid, but many meteoroids have to be integrated in order to obtain a realistic picture of the evolution of a meteoroid stream. The notion of generating a family of hypothetical meteoroids to represent a stream and directly integrate the motion of each was probably first used by Williams Murray & Hughes (1979), to investigate the Quadrantids. Because of computing limitations, only 10 test meteoroids were used. Only two years later, Hughes et. al. (1981) had increased the number of particles 20-fold to 200 while after a further year, Fox Williams and Hughes used 500 000 test meteoroids to model the Geminid stream. With such a number of meteoroids it was possible for the first time to produce a realistic cross-section of the stream on the ecliptic. From that point on there has been a continued increase in the number of meteoroids, the length of time over which integration is carried out and the frequency with which results can be plotted so that it is now possible to produce moving images of the stream. As a consequence, over recent years, emphasis has moved to considering stream formation and the role fragmentation plays in this.

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

Kelly, Kevin J.; Parke, Stephen J.

Quantum mechanical interactions between neutrinos and matter along the path of propagation, the Wolfenstein matter effect, are of particular importance for the upcoming long-baseline neutrino oscillation experiments, specifically the Deep Underground Neutrino Experiment (DUNE). Here, we explore specifically what about the matter density profile can be measured by DUNE, considering both the shape and normalization of the profile between the neutrinos' origin and detection. Additionally, we explore the capability of a perturbative method for calculating neutrino oscillation probabilities and whether this method is suitable for DUNE. We also briefly quantitatively explore the ability of DUNE to measure the Earth's mattermore » density, and the impact of performing this measurement on measuring standard neutrino oscillation parameters.« less

The 1/ N Expansion of Tensor Models Beyond Perturbation Theory

NASA Astrophysics Data System (ADS)

Gurau, Razvan

2014-09-01

We analyze in full mathematical rigor the most general quartically perturbed invariant probability measure for a random tensor. Using a version of the Loop Vertex Expansion (which we call the mixed expansion) we show that the cumulants write as explicit series in 1/ N plus bounded rest terms. The mixed expansion recasts the problem of determining the subleading corrections in 1/ N into a simple combinatorial problem of counting trees decorated by a finite number of loop edges. As an aside, we use the mixed expansion to show that the (divergent) perturbative expansion of the tensor models is Borel summable and to prove that the cumulants respect an uniform scaling bound. In particular the quartically perturbed measures fall, in the N→ ∞ limit, in the universality class of Gaussian tensor models.

Simulating large-scale crop yield by using perturbed-parameter ensemble method

NASA Astrophysics Data System (ADS)

Iizumi, T.; Yokozawa, M.; Sakurai, G.; Nishimori, M.

2010-12-01

Toshichika Iizumi, Masayuki Yokozawa, Gen Sakurai, Motoki Nishimori Agro-Meteorology Division, National Institute for Agro-Environmental Sciences, Japan Abstract One of concerning issues of food security under changing climate is to predict the inter-annual variation of crop production induced by climate extremes and modulated climate. To secure food supply for growing world population, methodology that can accurately predict crop yield on a large scale is needed. However, for developing a process-based large-scale crop model with a scale of general circulation models (GCMs), 100 km in latitude and longitude, researchers encounter the difficulties in spatial heterogeneity of available information on crop production such as cultivated cultivars and management. This study proposed an ensemble-based simulation method that uses a process-based crop model and systematic parameter perturbation procedure, taking maize in U.S., China, and Brazil as examples. The crop model was developed modifying the fundamental structure of the Soil and Water Assessment Tool (SWAT) to incorporate the effect of heat stress on yield. We called the new model PRYSBI: the Process-based Regional-scale Yield Simulator with Bayesian Inference. The posterior probability density function (PDF) of 17 parameters, which represents the crop- and grid-specific features of the crop and its uncertainty under given data, was estimated by the Bayesian inversion analysis. We then take 1500 ensemble members of simulated yield values based on the parameter sets sampled from the posterior PDF to describe yearly changes of the yield, i.e. perturbed-parameter ensemble method. The ensemble median for 27 years (1980-2006) was compared with the data aggregated from the county yield. On a country scale, the ensemble median of the simulated yield showed a good correspondence with the reported yield: the Pearson’s correlation coefficient is over 0.6 for all countries. In contrast, on a grid scale, the correspondence is still high in most grids regardless of the countries. However, the model showed comparatively low reproducibility in the slope areas, such as around the Rocky Mountains in South Dakota, around the Great Xing'anling Mountains in Heilongjiang, and around the Brazilian Plateau. As there is a wide-ranging local climate conditions in the complex terrain, such as the slope of mountain, the GCM grid-scale weather inputs is likely one of major sources of error. The results of this study highlight the benefits of the perturbed-parameter ensemble method in simulating crop yield on a GCM grid scale: (1) the posterior PDF of parameter could quantify the uncertainty of parameter value of the crop model associated with the local crop production aspects; (2) the method can explicitly account for the uncertainty of parameter value in the crop model simulations; (3) the method achieve a Monte Carlo approximation of probability of sub-grid scale yield, accounting for the nonlinear response of crop yield to weather and management; (4) the method is therefore appropriate to aggregate the simulated sub-grid scale yields to a grid-scale yield and it may be a reason for high performance of the model in capturing inter-annual variation of yield.

Sauter-Schwinger pair creation dynamically assisted by a plane wave

NASA Astrophysics Data System (ADS)

Torgrimsson, Greger; Schneider, Christian; Schützhold, Ralf

2018-05-01

We study electron-positron pair creation by a strong and constant electric field superimposed with a weaker transversal plane wave which is incident perpendicularly (or under some angle). Comparing the fully nonperturbative approach based on the world-line instanton method with a perturbative expansion into powers of the strength of the weaker plane wave, we find good agreement—provided that the latter is carried out to sufficiently high orders. As usual for the dynamically assisted Sauter-Schwinger effect, the additional plane wave induces an exponential enhancement of the pair-creation probability if the combined Keldysh parameter exceeds a certain threshold.

Reemission spectra and inelastic processes at interaction of attosecond and shorter duration electromagnetic pulses with atoms

NASA Astrophysics Data System (ADS)

Makarov, D. N.; Matveev, V. I.

2017-01-01

Inelastic processes and the reemission of attosecond and shorter electromagnetic pulses by atoms have been considered within the analytical solution of the Schrödinger equation in the sudden perturbation approximation. A method of calculations with the exact inclusion of spatial inhomogeneity of the field of an ultrashort pulse and the momenta of photons in the reemission processes has been developed. The probabilities of inelastic processes and spectra of reemission of ultrashort electromagnetic pulses by one- and many-electron atoms have been calculated. The results have been presented in the form of analytical formulas.

New method of computing the contributions of graphs without lepton loops to the electron anomalous magnetic moment in QED

NASA Astrophysics Data System (ADS)

Volkov, Sergey

2017-11-01

This paper presents a new method of numerical computation of the mass-independent QED contributions to the electron anomalous magnetic moment which arise from Feynman graphs without closed electron loops. The method is based on a forestlike subtraction formula that removes all ultraviolet and infrared divergences in each Feynman graph before integration in Feynman-parametric space. The integration is performed by an importance sampling Monte-Carlo algorithm with the probability density function that is constructed for each Feynman graph individually. The method is fully automated at any order of the perturbation series. The results of applying the method to 2-loop, 3-loop, 4-loop Feynman graphs, and to some individual 5-loop graphs are presented, as well as the comparison of this method with other ones with respect to Monte Carlo convergence speed.

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.

RESEARCH PAPERS : Ionospheric signature of surface mine blasts from Global Positioning System measurements

NASA Astrophysics Data System (ADS)

Calais, Eric; Bernard Minster, J.; Hofton, Michelle; Hedlin, Michael

1998-01-01

Sources such as atmospheric or buried explosions and shallow earthquakes are known to produce infrasonic pressure waves in the atmosphere Because of the coupling between neutral particles and electrons at ionospheric altitudes, these acoustic and gravity waves induce variations of the ionospheric electron density. The Global Positioning System (GPS) provides a way of directly measuring the total electron content in the ionosphere and, therefore, of detecting such perturbations in the upper atmosphere. In July and August 1996, three large surface mine blasts (1.5 Kt each) were detonated at the Black Thunder coal mine in eastern Wyoming. As part of a seismic and acoustic monitoring experiment, we deployed five dual-frequency GPS receivers at distances ranging from 50 to 200 km from the mine and were able to detect the ionospheric perturbation caused by the blasts. The perturbation starts 10 to 15 min after the blast, lasts for about 30 min, and propagates with an apparent horizontal velocity of 1200 m s- 1. Its amplitude reaches 3 × 1014 el m- 2 in the 7-3 min period band, a value close to the ionospheric perturbation caused by the M=6.7 Northridge earthquake (Calais & Minster 1995). The small signal-to-noise ratio of the perturbation can be improved by slant-stacking the electron content time-series recorded by the different GPS receivers taking into account the horizontal propagation of the perturbation. The energy of the perturbation is concentrated in the 200 to 300 s period band, a result consistent with previous observations and numerical model predictions. The 300 s band probably corresponds to gravity modes and shorter periods to acoustic modes, respectively. Using a 1-D stratified velocity model of the atmosphere we show that linear acoustic ray tracing fits arrival times at all GPS receivers. We interpret the perturbation as a direct acoustic wave caused by the explosion itself. This study shows that even relatively small subsurface events can produce ionospheric perturbations that are above the detection threshold of the GPS technique. By sensing derivative signals, which can be detected over a relatively broad region, it appears that GPS might be particularly useful for source characterization within the first acoustic quiet zone where infrasound would probably be ineffective. This suggests that dual-frequency GPS monitoring could contribute to Comprehensive Nuclear Test Ban Treaty verification.

Ionospheric Signature of Surface Mine Blasts from Global Positioning System Measurements

NASA Technical Reports Server (NTRS)

Calais, Eric; Minster, J. Bernard; Hofton, Michelle A.; Hedlin, Michael A. H.

1998-01-01

Sources such as atmospheric or buried explosions and shallow earthquakes are known to produce infrasonic pressure waves in the atmosphere. Because of the coupling between neutral particles and electrons at ionospheric altitudes, these acoustic and gravity waves induce variations of the ionospheric electron density. The Global Positioning System (GPS) provides a way of directly measuring the total electron content in the ionosphere and, therefore, of detecting such perturbations in the upper atmosphere. In July and August 1996, three large surface mine blasts (1.5 Kt each) were detonated at the Black Thunder coal mine in eastern Wyoming. As part of a seismic and acoustic monitoring- experiment, we deployed five dual-frequency GPS receivers at distances ranging from 50 to 200 km from the mine and were able to detect the ionospheric perturbation caused by the blasts. The perturbation starts 10 to 15 min after the blast, lasts for about 30 min, and propagates with an apparent horizontal velocity of 1200 meters per second. Its amplitude reaches 3 x 10 (exp 14) el per square meters in the 7-3 min period band, a value close to the ionospheric perturbation caused by the M = 6.7 Northridge earthquake. The small signal-to-noise ratio of the perturbation can be improved by slant-stacking the electron content time-series recorded by the different GPS receivers taking into account the horizontal propagation of the perturbation. The energy of the perturbation is concentrated in the 200 to 300 second period band, a result consistent with previous observations and numerical model predictions. The 300 second band probably corresponds to gravity modes and shorter periods to acoustic modes, respectively. Using a 1-D stratified velocity model of the atmosphere we show that linear acoustic ray tracing fits arrival times at all GPS receivers. We interpret the perturbation as a direct acoustic wave caused by the explosion itself. This study shows that even relatively small subsurface events can produce ionospheric perturbations that are above the detection threshold of the GPS technique. By sensing derivative signals, which can be detected over a relatively broad region, it appears that GPS might be particularly useful for source characterization within the first acoustic quiet zone where infrasound would probably be ineffective. This suggests that dual-frequency GPS monitoring could contribute to Comprehensive Nuclear Test Ban Treaty verification.

Mode perturbation method for optimal guided wave mode and frequency selection.

PubMed

Philtron, J H; Rose, J L

2014-09-01

With a thorough understanding of guided wave mechanics, researchers can predict which guided wave modes will have a high probability of success in a particular nondestructive evaluation application. However, work continues to find optimal mode and frequency selection for a given application. This "optimal" mode could give the highest sensitivity to defects or the greatest penetration power, increasing inspection efficiency. Since material properties used for modeling work may be estimates, in many cases guided wave mode and frequency selection can be adjusted for increased inspection efficiency in the field. In this paper, a novel mode and frequency perturbation method is described and used to identify optimal mode points based on quantifiable wave characteristics. The technique uses an ultrasonic phased array comb transducer to sweep in phase velocity and frequency space. It is demonstrated using guided interface waves for bond evaluation. After searching nearby mode points, an optimal mode and frequency can be selected which has the highest sensitivity to a defect, or gives the greatest penetration power. The optimal mode choice for a given application depends on the requirements of the inspection. Copyright © 2014 Elsevier B.V. All rights reserved.

Monte Carlo Bayesian inference on a statistical model of sub-gridcolumn moisture variability using high-resolution cloud observations. Part 1: Method.

PubMed

Norris, Peter M; da Silva, Arlindo M

2016-07-01

A method is presented to constrain a statistical model of sub-gridcolumn moisture variability using high-resolution satellite cloud data. The method can be used for large-scale model parameter estimation or cloud data assimilation. The gridcolumn model includes assumed probability density function (PDF) intra-layer horizontal variability and a copula-based inter-layer correlation model. The observables used in the current study are Moderate Resolution Imaging Spectroradiometer (MODIS) cloud-top pressure, brightness temperature and cloud optical thickness, but the method should be extensible to direct cloudy radiance assimilation for a small number of channels. The algorithm is a form of Bayesian inference with a Markov chain Monte Carlo (MCMC) approach to characterizing the posterior distribution. This approach is especially useful in cases where the background state is clear but cloudy observations exist. In traditional linearized data assimilation methods, a subsaturated background cannot produce clouds via any infinitesimal equilibrium perturbation, but the Monte Carlo approach is not gradient-based and allows jumps into regions of non-zero cloud probability. The current study uses a skewed-triangle distribution for layer moisture. The article also includes a discussion of the Metropolis and multiple-try Metropolis versions of MCMC.

Monte Carlo Bayesian Inference on a Statistical Model of Sub-Gridcolumn Moisture Variability Using High-Resolution Cloud Observations. Part 1: Method

NASA Technical Reports Server (NTRS)

Norris, Peter M.; Da Silva, Arlindo M.

2016-01-01

A method is presented to constrain a statistical model of sub-gridcolumn moisture variability using high-resolution satellite cloud data. The method can be used for large-scale model parameter estimation or cloud data assimilation. The gridcolumn model includes assumed probability density function (PDF) intra-layer horizontal variability and a copula-based inter-layer correlation model. The observables used in the current study are Moderate Resolution Imaging Spectroradiometer (MODIS) cloud-top pressure, brightness temperature and cloud optical thickness, but the method should be extensible to direct cloudy radiance assimilation for a small number of channels. The algorithm is a form of Bayesian inference with a Markov chain Monte Carlo (MCMC) approach to characterizing the posterior distribution. This approach is especially useful in cases where the background state is clear but cloudy observations exist. In traditional linearized data assimilation methods, a subsaturated background cannot produce clouds via any infinitesimal equilibrium perturbation, but the Monte Carlo approach is not gradient-based and allows jumps into regions of non-zero cloud probability. The current study uses a skewed-triangle distribution for layer moisture. The article also includes a discussion of the Metropolis and multiple-try Metropolis versions of MCMC.

Monte Carlo Bayesian inference on a statistical model of sub-gridcolumn moisture variability using high-resolution cloud observations. Part 1: Method

PubMed Central

Norris, Peter M.; da Silva, Arlindo M.

2018-01-01

A method is presented to constrain a statistical model of sub-gridcolumn moisture variability using high-resolution satellite cloud data. The method can be used for large-scale model parameter estimation or cloud data assimilation. The gridcolumn model includes assumed probability density function (PDF) intra-layer horizontal variability and a copula-based inter-layer correlation model. The observables used in the current study are Moderate Resolution Imaging Spectroradiometer (MODIS) cloud-top pressure, brightness temperature and cloud optical thickness, but the method should be extensible to direct cloudy radiance assimilation for a small number of channels. The algorithm is a form of Bayesian inference with a Markov chain Monte Carlo (MCMC) approach to characterizing the posterior distribution. This approach is especially useful in cases where the background state is clear but cloudy observations exist. In traditional linearized data assimilation methods, a subsaturated background cannot produce clouds via any infinitesimal equilibrium perturbation, but the Monte Carlo approach is not gradient-based and allows jumps into regions of non-zero cloud probability. The current study uses a skewed-triangle distribution for layer moisture. The article also includes a discussion of the Metropolis and multiple-try Metropolis versions of MCMC. PMID:29618847

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.

The Theory of Quantized Fields. III

DOE R&D Accomplishments Database

Schwinger, J.

1953-05-01

In this paper we discuss the electromagnetic field, as perturbed by a prescribed current. All quantities of physical interest in various situations, eigenvalues, eigenfunctions, and transformation probabilities, are derived from a general transformation function which is expressed in a non-Hermitian representation. The problems treated are: the determination of the energy-momentum eigenvalues and eigenfunctions for the isolated electromagnetic field, and the energy eigenvalues and eigenfunctions for the field perturbed by a time-independent current that departs from zero only within a finite time interval, and for a time-dependent current that assumes non-vanishing time-independent values initially and finally. The results are applied in a discussion of the intra-red catastrophe and of the adiabatic theorem. It is shown how the latter can be exploited to give a uniform formulation for all problems requiring the evaluation of transition probabilities or eigenvalue displacements.

A new approach to analytic, non-perturbative and gauge-invariant QCD

NASA Astrophysics Data System (ADS)

Fried, H. M.; Grandou, T.; Sheu, Y.-M.

2012-11-01

Following a previous calculation of quark scattering in eikonal approximation, this paper presents a new, analytic and rigorous approach to the calculation of QCD phenomena. In this formulation a basic distinction between the conventional "idealistic" description of QCD and a more "realistic" description is brought into focus by a non-perturbative, gauge-invariant evaluation of the Schwinger solution for the QCD generating functional in terms of the exact Fradkin representations of Green's functional G(x,y|A) and the vacuum functional L[A]. Because quarks exist asymptotically only in bound states, their transverse coordinates can never be measured with arbitrary precision; the non-perturbative neglect of this statement leads to obstructions that are easily corrected by invoking in the basic Lagrangian a probability amplitude which describes such transverse imprecision. The second result of this non-perturbative analysis is the appearance of a new and simplifying output called "Effective Locality", in which the interactions between quarks by the exchange of a "gluon bundle"-which "bundle" contains an infinite number of gluons, including cubic and quartic gluon interactions-display an exact locality property that reduces the several functional integrals of the formulation down to a set of ordinary integrals. It should be emphasized that "non-perturbative" here refers to the effective summation of all gluons between a pair of quark lines-which may be the same quark line, as in a self-energy graph-but does not (yet) include a summation over all closed-quark loops which are tied by gluon-bundle exchange to the rest of the "Bundle Diagram". As an example of the power of these methods we offer as a first analytic calculation the quark-antiquark binding potential of a pion, and the corresponding three-quark binding potential of a nucleon, obtained in a simple way from relevant eikonal scattering approximations. A second calculation, analytic, non-perturbative and gauge-invariant, of a nucleon-nucleon binding potential to form a model deuteron, will appear separately.

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).

Dynamical Response of Networks Under External Perturbations: Exact Results

NASA Astrophysics Data System (ADS)

Chinellato, David D.; Epstein, Irving R.; Braha, Dan; Bar-Yam, Yaneer; de Aguiar, Marcus A. M.

2015-04-01

We give exact statistical distributions for the dynamic response of influence networks subjected to external perturbations. We consider networks whose nodes have two internal states labeled 0 and 1. We let nodes be frozen in state 0, in state 1, and the remaining nodes change by adopting the state of a connected node with a fixed probability per time step. The frozen nodes can be interpreted as external perturbations to the subnetwork of free nodes. Analytically extending and to be smaller than 1 enables modeling the case of weak coupling. We solve the dynamical equations exactly for fully connected networks, obtaining the equilibrium distribution, transition probabilities between any two states and the characteristic time to equilibration. Our exact results are excellent approximations for other topologies, including random, regular lattice, scale-free and small world networks, when the numbers of fixed nodes are adjusted to take account of the effect of topology on coupling to the environment. This model can describe a variety of complex systems, from magnetic spins to social networks to population genetics, and was recently applied as a framework for early warning signals for real-world self-organized economic market crises.

Eigenpairs of Toeplitz and Disordered Toeplitz Matrices with a Fisher-Hartwig Symbol

NASA Astrophysics Data System (ADS)

Movassagh, Ramis; Kadanoff, Leo P.

2017-05-01

Toeplitz matrices have entries that are constant along diagonals. They model directed transport, are at the heart of correlation function calculations of the two-dimensional Ising model, and have applications in quantum information science. We derive their eigenvalues and eigenvectors when the symbol is singular Fisher-Hartwig. We then add diagonal disorder and study the resulting eigenpairs. We find that there is a "bulk" behavior that is well captured by second order perturbation theory of non-Hermitian matrices. The non-perturbative behavior is classified into two classes: Runaways type I leave the complex-valued spectrum and become completely real because of eigenvalue attraction. Runaways type II leave the bulk and move very rapidly in response to perturbations. These have high condition numbers and can be predicted. Localization of the eigenvectors are then quantified using entropies and inverse participation ratios. Eigenvectors corresponding to Runaways type II are most localized (i.e., super-exponential), whereas Runaways type I are less localized than the unperturbed counterparts and have most of their probability mass in the interior with algebraic decays. The results are corroborated by applying free probability theory and various other supporting numerical studies.

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

Effects of Shocks on Emission from Central Engines of Active Galactic Nuclei. I

NASA Technical Reports Server (NTRS)

Sivron, R.; Caditz, D.; Tsuruta, S.

1996-01-01

In this paper we show that perturbations of the accretion flow within the central engines of some active galactic nuclei (AGNS) are likely to form shock waves in the accreting plasma. Such shocks, which may be either collisional or collisionless, can contribute to the observed high-energy temporal and spectral variability. Our rationale is the following: Observations show that the continuum emission probably originates in an optically thin, hot plasma in the AGN central engine. The flux and spectrum from this hot plasma varies significantly over light crossing timescales. Several authors have suggested that macroscopic perturbations contained within this plasma are the sources of this variability. In order to produce the observed emission the perturbations must be radiatively coupled with the optically thin hot matter and must also move with high velocities. We suggest that shocks, which can be very effective in randomizing the bulk motion of the perturbations, are responsible for this coupling. Shocks should form in the central engine, because the temperatures and magnetic fields are probably reduced below their virial values by radiative dissipation. Perturbations moving at Keplerian speeds, or strong non-linear excitations, result in supersonic and super-Alfvenic velocities leading to shock waves within the hot plasma. We show that even a perturbation smaller than the emitting region can form a shock that significantly modifies the continuum emission in an AGN, and that the spectral and temporal variability from such a shock generally resembles those of radio-quiet AGNS. As an example, the shock inducing perturbation in our model is a small main-sequence star, the capturing and eventual accretion of which are known to be a plausible process. We argue that shocks in the central engine may also provide a natural triggering mechanism for the "cold" component of Guilbert & Rees two-phase medium and an efficient mecha- nism for angular momentum transfer. Current and future missions, such as ASCA, XTE, XMM, AXAF, and ASTRO-E may determine the importance of shock-related emission from the central engines of AGNS.

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.

A stratospheric aerosol model with perturbations induced by the space shuttle particulate effluents

NASA Technical Reports Server (NTRS)

Rosen, J. M.; Hofmann, D. J.

1977-01-01

A one dimensional steady state stratospheric aerosol model is developed that considers the subsequent perturbations caused by including the expected space shuttle particulate effluents. Two approaches to the basic modeling effort were made: in one, enough simplifying assumptions were introduced so that a more or less exact solution to the descriptive equations could be obtained; in the other approach very few simplifications were made and a computer technique was used to solve the equations. The most complex form of the model contains the effects of sedimentation, diffusion, particle growth and coagulation. Results of the perturbation calculations show that there will probably be an immeasurably small increase in the stratospheric aerosol concentration for particles larger than about 0.15 micrometer radius.

A statistical analysis of RNA folding algorithms through thermodynamic parameter perturbation.

PubMed

Layton, D M; Bundschuh, R

2005-01-01

Computational RNA secondary structure prediction is rather well established. However, such prediction algorithms always depend on a large number of experimentally measured parameters. Here, we study how sensitive structure prediction algorithms are to changes in these parameters. We found already that for changes corresponding to the actual experimental error to which these parameters have been determined, 30% of the structure are falsely predicted whereas the ground state structure is preserved under parameter perturbation in only 5% of all the cases. We establish that base-pairing probabilities calculated in a thermal ensemble are viable although not a perfect measure for the reliability of the prediction of individual structure elements. Here, a new measure of stability using parameter perturbation is proposed, and its limitations are discussed.

Acute alcohol intoxication impairs segmental body alignment in upright standing.

PubMed

Hafstrom, A; Patel, M; Modig, F; Magnusson, M; Fransson, P A

2014-01-01

Balance control when standing upright is a complex process requiring input from several partly independent mechanisms such as coordination, feedback and feedforward control, and adaptation. Acute alcohol intoxication from ethanol is recognized as a major contributor to accidental falls requiring medical care. This study aimed to investigate if intoxication at 0.06 and 0.10% blood alcohol concentration affected body alignment. Mean angular positions of the head, shoulder, hip, and knee were measured with 3D-motion analysis and compared with the ankle position in 25 healthy adults during standing with or without perturbations, and with eyes open or closed. Alcohol intoxication had significant effects on body alignment during perturbed and unperturbed stance, and on adaptation to perturbations. It induced a significantly more posterior alignment of the knees and shoulders, and a tendency for a more posterior and left deviated head alignment in perturbed stance than when sober. The impact of alcohol intoxication was most apparent on the knee alignment, where availability of visual information deteriorated the adaptation to perturbations. Thus, acute alcohol intoxication resulted in inadequate balance control strategies with increased postural rigidity and impaired adaptation to perturbations. These factors probably contribute to the increased risk of falling when intoxicated with alcohol.

A Guided Tour of Mathematical Methods for the Physical Sciences

NASA Astrophysics Data System (ADS)

Snieder, Roel; van Wijk, Kasper

2015-05-01

1. Introduction; 2. Dimensional analysis; 3. Power series; 4. Spherical and cylindrical coordinates; 5. Gradient; 6. Divergence of a vector field; 7. Curl of a vector field; 8. Theorem of Gauss; 9. Theorem of Stokes; 10. The Laplacian; 11. Scale analysis; 12. Linear algebra; 13. Dirac delta function; 14. Fourier analysis; 15. Analytic functions; 16. Complex integration; 17. Green's functions: principles; 18. Green's functions: examples; 19. Normal modes; 20. Potential-field theory; 21. Probability and statistics; 22. Inverse problems; 23. Perturbation theory; 24. Asymptotic evaluation of integrals; 25. Conservation laws; 26. Cartesian tensors; 27. Variational calculus; 28. Epilogue on power and knowledge.

The nuclear size and mass effects on muonic hydrogen-like atoms embedded in Debye plasma

NASA Astrophysics Data System (ADS)

Poszwa, A.; Bahar, M. K.; Soylu, A.

2016-10-01

Effects of finite nuclear size and finite nuclear mass are investigated for muonic atoms and muonic ions embedded in the Debye plasma. Both nuclear charge radii and nuclear masses are taken into account with experimentally determined values. In particular, isotope shifts of bound state energies, radial probability densities, transition energies, and binding energies for several atoms are studied as functions of Debye length. The theoretical model based on semianalytical calculations, the Sturmian expansion method, and the perturbative approach has been constructed, in the nonrelativistic frame. For some limiting cases, the comparison with previous most accurate literature results has been made.

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.

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.

Interrelated structure of high altitude atmospheric profiles

NASA Technical Reports Server (NTRS)

Engler, N. A.; Goldschmidt, M. A.

1972-01-01

A preliminary development of a mathematical model to compute probabilities of thermodynamic profiles is presented. The model assumes an exponential expression for pressure and utilizes the hydrostatic law and equation of state in the determination of density and temperature. It is shown that each thermodynamic variable can be factored into the produce of steady state and perturbation functions. The steady state functions have profiles similar to those of the 1962 standard atmosphere while the perturbation functions oscillate about 1. Limitations of the model and recommendations for future work are presented.

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.

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.

Patient observers and non-perturbative infrared dynamics in inflation

NASA Astrophysics Data System (ADS)

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

2018-02-01

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

Heuristics can produce surprisingly rational probability estimates: Comment on Costello and Watts (2014).

PubMed

Nilsson, Håkan; Juslin, Peter; Winman, Anders

2016-01-01

Costello and Watts (2014) present a model assuming that people's knowledge of probabilities adheres to probability theory, but that their probability judgments are perturbed by a random noise in the retrieval from memory. Predictions for the relationships between probability judgments for constituent events and their disjunctions and conjunctions, as well as for sums of such judgments were derived from probability theory. Costello and Watts (2014) report behavioral data showing that subjective probability judgments accord with these predictions. Based on the finding that subjective probability judgments follow probability theory, Costello and Watts (2014) conclude that the results imply that people's probability judgments embody the rules of probability theory and thereby refute theories of heuristic processing. Here, we demonstrate the invalidity of this conclusion by showing that all of the tested predictions follow straightforwardly from an account assuming heuristic probability integration (Nilsson, Winman, Juslin, & Hansson, 2009). We end with a discussion of a number of previous findings that harmonize very poorly with the predictions by the model suggested by Costello and Watts (2014). (c) 2015 APA, all rights reserved).

Time-dependent earthquake probabilities

USGS Publications Warehouse

Gomberg, J.; Belardinelli, M.E.; Cocco, M.; Reasenberg, P.

2005-01-01

We have attempted to provide a careful examination of a class of approaches for estimating the conditional probability of failure of a single large earthquake, particularly approaches that account for static stress perturbations to tectonic loading as in the approaches of Stein et al. (1997) and Hardebeck (2004). We have loading as in the framework based on a simple, generalized rate change formulation and applied it to these two approaches to show how they relate to one another. We also have attempted to show the connection between models of seismicity rate changes applied to (1) populations of independent faults as in background and aftershock seismicity and (2) changes in estimates of the conditional probability of failures of different members of a the notion of failure rate corresponds to successive failures of different members of a population of faults. The latter application requires specification of some probability distribution (density function of PDF) that describes some population of potential recurrence times. This PDF may reflect our imperfect knowledge of when past earthquakes have occurred on a fault (epistemic uncertainty), the true natural variability in failure times, or some combination of both. We suggest two end-member conceptual single-fault models that may explain natural variability in recurrence times and suggest how they might be distinguished observationally. When viewed deterministically, these single-fault patch models differ significantly in their physical attributes, and when faults are immature, they differ in their responses to stress perturbations. Estimates of conditional failure probabilities effectively integrate over a range of possible deterministic fault models, usually with ranges that correspond to mature faults. Thus conditional failure probability estimates usually should not differ significantly for these models. Copyright 2005 by the American Geophysical Union.

Crossover from isotropic to directed percolation

NASA Astrophysics Data System (ADS)

Zhou, Zongzheng; Yang, Ji; Ziff, Robert M.; Deng, Youjin

2012-08-01

We generalize the directed percolation (DP) model by relaxing the strict directionality of DP such that propagation can occur in either direction but with anisotropic probabilities. We denote the probabilities as p↓=ppd and p↑=p(1-pd), with p representing the average occupation probability and pd controlling the anisotropy. The Leath-Alexandrowicz method is used to grow a cluster from an active seed site. We call this model with two main growth directions biased directed percolation (BDP). Standard isotropic percolation (IP) and DP are the two limiting cases of the BDP model, corresponding to pd=1/2 and pd=0,1 respectively. In this work, besides IP and DP, we also consider the 1/2

Observations of height-dependent pressure-perturbation structure of a strong mesoscale gravity wave

NASA Technical Reports Server (NTRS)

Starr, David O'C.; Korb, C. L.; Schwemmer, Geary K.; Weng, Chi Y.

1992-01-01

Airborne observations using a downward-looking, dual-frequency, near-infrared, differential absorption lidar system provide the first measurements of the height-dependent pressure-perturbation field associated with a strong mesoscale gravity wave. A pressure-perturbation amplitude of 3.5 mb was measured within the lowest 1.6 km of the atmosphere over a 52-km flight line. Corresponding vertical displacements of 250-500 m were inferred from lidar-observed displacement of aerosol layers. Accounting for probable wave orientation, a horizontal wavelength of about 40 km was estimated. Satellite observations reveal wave structure of a comparable scale in concurrent cirrus cloud fields over an extended area. Smaller-scale waves were also observed. Local meteorological soundings are analyzed to confirm the existence of a suitable wave duct. Potential wave-generation mechanisms are examined and discussed. The large pressure-perturbation wave is attributed to rapid amplification or possible wave breaking of a gravity wave as it propagated offshore and interacted with a very stable marine boundary layer capped by a strong shear layer.

Identifying early-warning signals of critical transitions with strong noise by dynamical network markers

PubMed Central

Liu, Rui; Chen, Pei; Aihara, Kazuyuki; Chen, Luonan

2015-01-01

Identifying early-warning signals of a critical transition for a complex system is difficult, especially when the target system is constantly perturbed by big noise, which makes the traditional methods fail due to the strong fluctuations of the observed data. In this work, we show that the critical transition is not traditional state-transition but probability distribution-transition when the noise is not sufficiently small, which, however, is a ubiquitous case in real systems. We present a model-free computational method to detect the warning signals before such transitions. The key idea behind is a strategy: “making big noise smaller” by a distribution-embedding scheme, which transforms the data from the observed state-variables with big noise to their distribution-variables with small noise, and thus makes the traditional criteria effective because of the significantly reduced fluctuations. Specifically, increasing the dimension of the observed data by moment expansion that changes the system from state-dynamics to probability distribution-dynamics, we derive new data in a higher-dimensional space but with much smaller noise. Then, we develop a criterion based on the dynamical network marker (DNM) to signal the impending critical transition using the transformed higher-dimensional data. We also demonstrate the effectiveness of our method in biological, ecological and financial systems. PMID:26647650

Regulation of autonomic nervous system in space and magnetic storms.

PubMed

Baevsky, R M; Petrov, V M; Chernikova, A G

1998-01-01

Variations in the earth's magnetic field and magnetic storms are known to be a risk factor for the development of cardiovascular disorders. The main "targets" for geomagnetic perturbations are the central nervous system and the neural regulation of vascular tone and heart rate variability. This paper presents the data about effect of geomagnetic fluctuations on human body in space. As a method for research the analysis of heart rate variability was used, which allows evaluating the state of the sympathetic and parasympathetic parts of the autonomic nervous system, vasomotor center and subcortical neural centers activity. Heart rate variability data were analyzed for 30 cosmonauts at the 2nd day of space flight on transport spaceship Soyuz (32nd orbit). There were formed three groups of cosmonauts: without magnetic storm (n=9), on a day with magnetic storm (n=12) and 1-2 days after magnetic storm (n=9). The present study was the first to demonstrate a specific impact of geomagnetic perturbations on the system of autonomic circulatory control in cosmonauts during space flight. The increasing of highest nervous centers activity was shown for group with magnetic storms, which was more significant on 1-2 days after magnetic storm. The use of discriminate analysis allowed to classify indicated three groups with 88% precision. Canonical variables are suggested to be used as criterions for evaluation of specific and non-specific components of cardiovascular reactions to geomagnetic perturbations. The applied aspect of the findings from the present study should be emphasized. They show, in particular, the need to supplement the medical monitoring of cosmonauts with predictions of probable geomagnetic perturbations in view of the prevention of unfavorable states appearances if the adverse reactions to geomagnetic perturbations are added to the tension experienced by regulatory systems during various stresses situations (such as work in the open space).

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.

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.

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.

SPECIAL ISSUE ON OPTICAL PROCESSING OF INFORMATION: Analysis of the precision parameters of an optoelectronic vector-matrix processor of digital information

NASA Astrophysics Data System (ADS)

Odinokov, S. B.; Petrov, A. V.

1995-10-01

Mathematical models of components of a vector-matrix optoelectronic multiplier are considered. Perturbing factors influencing a real optoelectronic system — noise and errors of radiation sources and detectors, nonlinearity of an analogue—digital converter, nonideal optical systems — are taken into account. Analytic expressions are obtained for relating the precision of such a multiplier to the probability of an error amounting to one bit, to the parameters describing the quality of the multiplier components, and to the quality of the optical system of the processor. Various methods of increasing the dynamic range of a multiplier are considered at the technical systems level.

spsann - optimization of sample patterns using spatial simulated annealing

NASA Astrophysics Data System (ADS)

Samuel-Rosa, Alessandro; Heuvelink, Gerard; Vasques, Gustavo; Anjos, Lúcia

2015-04-01

There are many algorithms and computer programs to optimize sample patterns, some private and others publicly available. A few have only been presented in scientific articles and text books. This dispersion and somewhat poor availability is holds back to their wider adoption and further development. We introduce spsann, a new R-package for the optimization of sample patterns using spatial simulated annealing. R is the most popular environment for data processing and analysis. Spatial simulated annealing is a well known method with widespread use to solve optimization problems in the soil and geo-sciences. This is mainly due to its robustness against local optima and easiness of implementation. spsann offers many optimizing criteria for sampling for variogram estimation (number of points or point-pairs per lag distance class - PPL), trend estimation (association/correlation and marginal distribution of the covariates - ACDC), and spatial interpolation (mean squared shortest distance - MSSD). spsann also includes the mean or maximum universal kriging variance (MUKV) as an optimizing criterion, which is used when the model of spatial variation is known. PPL, ACDC and MSSD were combined (PAN) for sampling when we are ignorant about the model of spatial variation. spsann solves this multi-objective optimization problem scaling the objective function values using their maximum absolute value or the mean value computed over 1000 random samples. Scaled values are aggregated using the weighted sum method. A graphical display allows to follow how the sample pattern is being perturbed during the optimization, as well as the evolution of its energy state. It is possible to start perturbing many points and exponentially reduce the number of perturbed points. The maximum perturbation distance reduces linearly with the number of iterations. The acceptance probability also reduces exponentially with the number of iterations. R is memory hungry and spatial simulated annealing is a computationally intensive method. As such, many strategies were used to reduce the computation time and memory usage: a) bottlenecks were implemented in C++, b) a finite set of candidate locations is used for perturbing the sample points, and c) data matrices are computed only once and then updated at each iteration instead of being recomputed. spsann is available at GitHub under a licence GLP Version 2.0 and will be further developed to: a) allow the use of a cost surface, b) implement other sensitive parts of the source code in C++, c) implement other optimizing criteria, d) allow to add or delete points to/from an existing point pattern.

Maximum of a Fractional Brownian Motion: Analytic Results from Perturbation Theory.

PubMed

Delorme, Mathieu; Wiese, Kay Jörg

2015-11-20

Fractional Brownian motion is a non-Markovian Gaussian process X_{t}, indexed by the Hurst exponent H. It generalizes standard Brownian motion (corresponding to H=1/2). We study the probability distribution of the maximum m of the process and the time t_{max} at which the maximum is reached. They are encoded in a path integral, which we evaluate perturbatively around a Brownian, setting H=1/2+ϵ. This allows us to derive analytic results beyond the scaling exponents. Extensive numerical simulations for different values of H test these analytical predictions and show excellent agreement, even for large ϵ.

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.

Structure theorems for game trees

PubMed Central

Govindan, Srihari; Wilson, Robert

2002-01-01

Kohlberg and Mertens [Kohlberg, E. & Mertens, J. (1986) Econometrica 54, 1003–1039] proved that the graph of the Nash equilibrium correspondence is homeomorphic to its domain when the domain is the space of payoffs in normal-form games. A counterexample disproves the analog for the equilibrium outcome correspondence over the space of payoffs in extensive-form games, but we prove an analog when the space of behavior strategies is perturbed so that every path in the game tree has nonzero probability. Without such perturbations, the graph is the closure of the union of a finite collection of its subsets, each diffeomorphic to a corresponding path-connected open subset of the space of payoffs. As an application, we construct an algorithm for computing equilibria of an extensive-form game with a perturbed strategy space, and thus approximate equilibria of the unperturbed game. PMID:12060702

Structure theorems for game trees.

PubMed

Govindan, Srihari; Wilson, Robert

2002-06-25

Kohlberg and Mertens [Kohlberg, E. & Mertens, J. (1986) Econometrica 54, 1003-1039] proved that the graph of the Nash equilibrium correspondence is homeomorphic to its domain when the domain is the space of payoffs in normal-form games. A counterexample disproves the analog for the equilibrium outcome correspondence over the space of payoffs in extensive-form games, but we prove an analog when the space of behavior strategies is perturbed so that every path in the game tree has nonzero probability. Without such perturbations, the graph is the closure of the union of a finite collection of its subsets, each diffeomorphic to a corresponding path-connected open subset of the space of payoffs. As an application, we construct an algorithm for computing equilibria of an extensive-form game with a perturbed strategy space, and thus approximate equilibria of the unperturbed game.

Bethe/Gauge correspondence in odd dimension: modular double, non-perturbative corrections and open topological strings

NASA Astrophysics Data System (ADS)

Sciarappa, Antonio

2016-10-01

Bethe/Gauge correspondence as it is usually stated is ill-defined in five dimensions and needs a "non-perturbative" completion; a related problem also appears in three dimensions. It has been suggested that this problem, probably due to incompleteness of Omega background regularization in odd dimension, may be solved if we consider gauge theory on compact S 5 and S 3 geometries. We will develop this idea further by giving a full Bethe/Gauge correspondence dictionary on S 5 and S 3 focussing mainly on the eigenfunctions of (open and closed) relativistic 2-particle Toda chain and its quantized spectral curve: these are most properly written in terms of non-perturbatively completed NS open topological strings. A key ingredient is Faddeev's modular double structure which is naturally implemented by the S 5 and S 3 geometries.

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.

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.

A modified hybrid uncertain analysis method for dynamic response field of the LSOAAC with random and interval parameters

NASA Astrophysics Data System (ADS)

Zi, Bin; Zhou, Bin

2016-07-01

For the prediction of dynamic response field of the luffing system of an automobile crane (LSOAAC) with random and interval parameters, a hybrid uncertain model is introduced. In the hybrid uncertain model, the parameters with certain probability distribution are modeled as random variables, whereas, the parameters with lower and upper bounds are modeled as interval variables instead of given precise values. Based on the hybrid uncertain model, the hybrid uncertain dynamic response equilibrium equation, in which different random and interval parameters are simultaneously included in input and output terms, is constructed. Then a modified hybrid uncertain analysis method (MHUAM) is proposed. In the MHUAM, based on random interval perturbation method, the first-order Taylor series expansion and the first-order Neumann series, the dynamic response expression of the LSOAAC is developed. Moreover, the mathematical characteristics of extrema of bounds of dynamic response are determined by random interval moment method and monotonic analysis technique. Compared with the hybrid Monte Carlo method (HMCM) and interval perturbation method (IPM), numerical results show the feasibility and efficiency of the MHUAM for solving the hybrid LSOAAC problems. The effects of different uncertain models and parameters on the LSOAAC response field are also investigated deeply, and numerical results indicate that the impact made by the randomness in the thrust of the luffing cylinder F is larger than that made by the gravity of the weight in suspension Q . In addition, the impact made by the uncertainty in the displacement between the lower end of the lifting arm and the luffing cylinder a is larger than that made by the length of the lifting arm L .

Ab initio theoretical study of dipole-bound anions of molecular complexes: (HF)3- and (HF)4- anions

NASA Astrophysics Data System (ADS)

Ramaekers, Riet; Smith, Dayle M. A.; Smets, Johan; Adamowicz, Ludwik

1997-12-01

Ab initio calculations have been performed to determine structures and vertical electron detachment energy (VDE) of the hydrogen fluoride trimer and tetramer anions, (HF)3- and (HF)4-. In these systems the excess electron is bound by the dipole field of the complex. It was determined that, unlike the neutral complexes which prefer the cyclic structures, the equilibrium geometries of the anions have "zig-zag" shapes. For both complexes the predicted VDEs are positive [210 meV and 363 meV for (HF)3- and (HF)4-, respectively], indicating that the anions are stable systems with respect to the vertical electron detachment. These results were obtained at the coupled-cluster level of theory with single, double and triple excitations [CCSD(T) method; the triple-excitation contribution in this method is calculated approximately using the perturbation approach] with the anion geometries obtained using the second-order Møller-Plesset perturbation theory (MP2) method. The same approach was also used to determine the adiabatic electron affinities (AEA) of (HF)3 and (HF)4. In addition to the electronic contribution, we also calculated the contributions (using the harmonic approximation) resulting from different zero-point vibration energies of the neutral and anionic clusters. The calculations predicted that while the AEA of (HF)3 is positive (44 meV), the AEA for (HF)4 is marginally negative (-16 meV). This suggests that the (HF)3- anion should be a stable system, while the (HF)4- is probably metastable.

Exact Maximum-Entropy Estimation with Feynman Diagrams

NASA Astrophysics Data System (ADS)

Netser Zernik, Amitai; Schlank, Tomer M.; Tessler, Ran J.

2018-02-01

A longstanding open problem in statistics is finding an explicit expression for the probability measure which maximizes entropy with respect to given constraints. In this paper a solution to this problem is found, using perturbative Feynman calculus. The explicit expression is given as a sum over weighted trees.

Statistics of cosmic density profiles from perturbation theory

NASA Astrophysics Data System (ADS)

Bernardeau, Francis; Pichon, Christophe; Codis, Sandrine

2014-11-01

The joint probability distribution function (PDF) of the density within multiple concentric spherical cells is considered. It is shown how its cumulant generating function can be obtained at tree order in perturbation theory as the Legendre transform of a function directly built in terms of the initial moments. In the context of the upcoming generation of large-scale structure surveys, it is conjectured that this result correctly models such a function for finite values of the variance. Detailed consequences of this assumption are explored. In particular the corresponding one-cell density probability distribution at finite variance is computed for realistic power spectra, taking into account its scale variation. It is found to be in agreement with Λ -cold dark matter simulations at the few percent level for a wide range of density values and parameters. Related explicit analytic expansions at the low and high density tails are given. The conditional (at fixed density) and marginal probability of the slope—the density difference between adjacent cells—and its fluctuations is also computed from the two-cell joint PDF; it also compares very well to simulations. It is emphasized that this could prove useful when studying the statistical properties of voids as it can serve as a statistical indicator to test gravity models and/or probe key cosmological parameters.

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

NASA Astrophysics Data System (ADS)

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

2018-06-01

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

Structural stability and chaotic solutions of perturbed Benjamin-Ono equations

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

Birnir, B.; Morrison, P.J.

1986-11-01

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

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

Effects of nuclear electromagnetic pulse (EMP) on synchronous stability of the electric power system

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

Manweiler, R.W.

1975-11-01

The effects of a nuclear electromagnetic pulse (EMP) on the synchronous stability of the electric power transmission and distribution systems are evaluated. The various modes of coupling of EMP to the power system are briefly discussed, with particular emphasis on those perturbations affecting the synchronous stability of the transmission system. A brief review of the fundamental concepts of the stability problem is given, with a discussion of the general characteristics of transient analysis. A model is developed to represent single sets as well as repetitive sets of multiple faults on the distribution systems, as might be produced by EMP. Themore » results of many numerical stability calculations are presented to illustrate the transmission system's response from different types of perturbations. The important parameters of both multiple and repetitive faults are studied, including the dependence of the response on the size of the perturbed area, the fault density, and the effective impedance between the fault location and the transmission system. Both major load reduction and the effect of the opening of tie lines at the time of perturbation are also studied. We conclude that there is a high probability that EMP can induce perturbations on the distribution networks causing a large portion of the transmission network in the perturbed area to lose synchronism. The result would be an immediate and massive power failure. (auth)« less

Stochastic Modelling of Past Volcanic Crises

NASA Astrophysics Data System (ADS)

Woo, Gordon

2017-04-01

It is customary to have continuous monitoring of volcanoes showing signs of unrest that might lead to an eruption threatening local populations. Despite scientific progress in estimating the probability of an eruption occurring, the concept of continuously tracking eruption probability remains a future aspiration for volcano risk analysts. During some recent major volcanic crises, attempts have been made to estimate the eruption probability in real time to support government decision-making. These include the possibility of an eruption of Katla linked with the eruption of Eyjafjallajökull in 2010, and the Santorini crisis of 2011-2012. However, once a crisis fades, interest in analyzing the probability that there might have been an eruption tends to wane. There is an inherent outcome bias well known to psychologists: if disaster was avoided, there is perceived to be little purpose in exploring scenarios where a disaster might have happened. Yet the better that previous periods of unrest are understood and modelled, the better that the risk associated with future periods of unrest will be quantified. Scenarios are counterfactual histories of the future. The task of quantifying the probability of an eruption for a past period of unrest should not be merely a statistical calculation, but should serve to elucidate and refine geophysical models of the eruptive processes. This is achieved by using a Bayesian Belief Network approach, in which monitoring observations are used to draw inferences on the underlying causal factors. Specifically, risk analysts are interested in identifying what dynamical perturbations might have tipped an unrest period in history over towards an eruption, and assessing what was the likelihood of such perturbations. Furthermore, in what ways might a historical volcano crisis have turned for the worse? Such important counterfactual questions are addressed in this paper.

The complexity of divisibility.

PubMed

Bausch, Johannes; Cubitt, Toby

2016-09-01

We address two sets of long-standing open questions in linear algebra and probability theory, from a computational complexity perspective: stochastic matrix divisibility, and divisibility and decomposability of probability distributions. We prove that finite divisibility of stochastic matrices is an NP-complete problem, and extend this result to nonnegative matrices, and completely-positive trace-preserving maps, i.e. the quantum analogue of stochastic matrices. We further prove a complexity hierarchy for the divisibility and decomposability of probability distributions, showing that finite distribution divisibility is in P, but decomposability is NP-hard. For the former, we give an explicit polynomial-time algorithm. All results on distributions extend to weak-membership formulations, proving that the complexity of these problems is robust to perturbations.

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.

Communications/Electronics Receiver Performance Degradation Handbook (Second Edition)

DTIC Science & Technology

1975-08-01

receiver to another in the Rf and IF filter characteristics modify the transfer of inter- forence power through the receiver to the IF output, and so the...modulation system the transmitted and received messages arce in general different bemaus* of small inte, forence or noise perturbations. The probability of

Space-time-modulated stochastic processes

NASA Astrophysics Data System (ADS)

Giona, Massimiliano

2017-10-01

Starting from the physical problem associated with the Lorentzian transformation of a Poisson-Kac process in inertial frames, the concept of space-time-modulated stochastic processes is introduced for processes possessing finite propagation velocity. This class of stochastic processes provides a two-way coupling between the stochastic perturbation acting on a physical observable and the evolution of the physical observable itself, which in turn influences the statistical properties of the stochastic perturbation during its evolution. The definition of space-time-modulated processes requires the introduction of two functions: a nonlinear amplitude modulation, controlling the intensity of the stochastic perturbation, and a time-horizon function, which modulates its statistical properties, providing irreducible feedback between the stochastic perturbation and the physical observable influenced by it. The latter property is the peculiar fingerprint of this class of models that makes them suitable for extension to generic curved-space times. Considering Poisson-Kac processes as prototypical examples of stochastic processes possessing finite propagation velocity, the balance equations for the probability density functions associated with their space-time modulations are derived. Several examples highlighting the peculiarities of space-time-modulated processes are thoroughly analyzed.

Scattering of particles in the presence of harmonic confinement perturbed by a complex absorbing potential

NASA Astrophysics Data System (ADS)

Maghari, A.; Kermani, M. M.

2018-04-01

A system of two interacting atoms confined in 1D harmonic trap and perturbed by an absorbing boundary potential is studied using the Lippmann-Schwinger formalism. The atom-atom interaction potential was considered as a nonlocal separable model. The perturbed absorbing boundary potential was also assumed in the form of Scarf II complex absorbing potential. The model is used for the study of 1D optical lattices that support the trapping of a pair atom within a unit cell. Moreover, it allows to describe the scattering particles in a tight smooth trapping surface and to analyze the bound and resonance states. The analytical expressions for wavefunctions and transition matrix as well as the absorption probabilities are calculated. A demonstration of how the complex absorbing potential affecting the bound states and resonances of particles confined in a harmonic trap is described.

Secured network sensor-based defense system

NASA Astrophysics Data System (ADS)

Wei, Sixiao; Shen, Dan; Ge, Linqiang; Yu, Wei; Blasch, Erik P.; Pham, Khanh D.; Chen, Genshe

2015-05-01

Network sensor-based defense (NSD) systems have been widely used to defend against cyber threats. Nonetheless, if the adversary finds ways to identify the location of monitor sensors, the effectiveness of NSD systems can be reduced. In this paper, we propose both temporal and spatial perturbation based defense mechanisms to secure NSD systems and make the monitor sensor invisible to the adversary. The temporal-perturbation based defense manipulates the timing information of published data so that the probability of successfully recognizing monitor sensors can be reduced. The spatial-perturbation based defense dynamically redeploys monitor sensors in the network so that the adversary cannot obtain the complete information to recognize all of the monitor sensors. We carried out experiments using real-world traffic traces to evaluate the effectiveness of our proposed defense mechanisms. Our data shows that our proposed defense mechanisms can reduce the attack accuracy of recognizing detection sensors.

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

Remote chance of recontact

NASA Technical Reports Server (NTRS)

Elkin, D.; Abeyagunawardene, S.; Defazio, R.

1988-01-01

The ejection of appendages with uncertain drag characteristics presents a concern for eventual recontact. Recontact shortly after release can be prevented by avoiding ejection in a plane perpendicular to the velocity. For ejection tangential to the orbit, the likelihood of recontact within a year is high in the absence of drag and oblateness. The optimum direction of ejection of the thermal shield cable and an overestimate of the recontact probability are determined for the Cosmic Background Explorer (COBE) mission when drag, oblateness, and solar/lunar perturbations are present. The probability is small but possibly significant.

A New Interpretation of Effects of the Probabilistic Delayed Start on the One-Dimensional Traffic Flow

NASA Astrophysics Data System (ADS)

Ishibashi, Yoshihiro; Fukui, Minoru

2018-03-01

The effect of the probabilistic delayed start on the one-dimensional traffic flow is investigated on the basis of several models. Analogy with the degeneracy of the states and its resolution, as well as that with the mathematical procedures adopted for them, is utilized. The perturbation is assumed to be proportional to the probability of the delayed start, and the perturbation function is determined so that imposed conditions are fulfilled. The obtained formulas coincide with those previously derived on the basis of the mean-field analyses of the Nagel-Schreckenberg and Fukui-Ishibashi models, and reproduce the cellular automaton simulation results.

A geophysiologist's thoughts on geoengineering.

PubMed

Lovelock, James

2008-11-13

The Earth is now recognized as a self-regulating system that includes a reactive biosphere; the system maintains a long-term steady-state climate and surface chemical composition favourable for life. We are perturbing the steady state by changing the land surface from mainly forests to farm land and by adding greenhouse gases and aerosol pollutants to the air. We appear to have exceeded the natural capacity to counter our perturbation and consequently the system is changing to a new and as yet unknown but probably adverse state. I suggest here that we regard the Earth as a physiological system and consider amelioration techniques, geoengineering, as comparable to nineteenth century medicine.

GPS detection of ionospheric perturbation before the 13 February 2001, El Salvador earthquake

NASA Astrophysics Data System (ADS)

Plotkin, V. V.

A large earthquake of M6.6 occurred on 13 February 2001 at 14:22:05 UT in El Salvador. We detected ionospheric perturbation before this earthquake using GPS data received from CORS network. Systematic decreases of ionospheric total electron content during two days before the earthquake onset were observed at set of stations near the earthquake location and probably in region of about 1000 km from epicenter. This result is consistent with that of investigators, which studied these phenomena with several observational techniques. However it is possible, that such TEC changes are simultaneously accompanied by changes due to solar wind parameters and Kp -index.

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.

Uncertainty Quantification of Non-linear Oscillation Triggering in a Multi-injector Liquid-propellant Rocket Combustion Chamber

NASA Astrophysics Data System (ADS)

Popov, Pavel; Sideris, Athanasios; Sirignano, William

2014-11-01

We examine the non-linear dynamics of the transverse modes of combustion-driven acoustic instability in a liquid-propellant rocket engine. Triggering can occur, whereby small perturbations from mean conditions decay, while larger disturbances grow to a limit-cycle of amplitude that may compare to the mean pressure. For a deterministic perturbation, the system is also deterministic, computed by coupled finite-volume solvers at low computational cost for a single realization. The randomness of the triggering disturbance is captured by treating the injector flow rates, local pressure disturbances, and sudden acceleration of the entire combustion chamber as random variables. The combustor chamber with its many sub-fields resulting from many injector ports may be viewed as a multi-scale complex system wherein the developing acoustic oscillation is the emergent structure. Numerical simulation of the resulting stochastic PDE system is performed using the polynomial chaos expansion method. The overall probability of unstable growth is assessed in different regions of the parameter space. We address, in particular, the seven-injector, rectangular Purdue University experimental combustion chamber. In addition to the novel geometry, new features include disturbances caused by engine acceleration and unsteady thruster nozzle flow.

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

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.

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.

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…

Spectral theory of extreme statistics in birth-death systems

NASA Astrophysics Data System (ADS)

Meerson, Baruch

2008-03-01

Statistics of rare events, or large deviations, in chemical reactions and systems of birth-death type have attracted a great deal of interest in many areas of science including cell biochemistry, astrochemistry, epidemiology, population biology, etc. Large deviations become of vital importance when discrete (non-continuum) nature of a population of ``particles'' (molecules, bacteria, cells, animals or even humans) and stochastic character of interactions can drive the population to extinction. I will briefly review the novel spectral method [1-3] for calculating the extreme statistics of a broad class of birth-death processes and reactions involving a single species. The spectral method combines the probability generating function formalism with the Sturm-Liouville theory of linear differential operators. It involves a controlled perturbative treatment based on a natural large parameter of the problem: the average number of particles/individuals in a stationary or metastable state. For extinction (the first passage) problems the method yields accurate results for the extinction statistics and for the quasi-stationary probability distribution, including the tails, of metastable states. I will demonstrate the power of the method on the example of a branching and annihilation reaction, A ->-2.8mm2mm2A,,A ->-2.8mm2mm , representative of a rather general class of processes. *M. Assaf and B. Meerson, Phys. Rev. Lett. 97, 200602 (2006). *M. Assaf and B. Meerson, Phys. Rev. E 74, 041115 (2006). *M. Assaf and B. Meerson, Phys. Rev. E 75, 031122 (2007).

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.

Convolutionless Nakajima-Zwanzig equations for stochastic analysis in nonlinear dynamical systems.

PubMed

Venturi, D; Karniadakis, G E

2014-06-08

Determining the statistical properties of stochastic nonlinear systems is of major interest across many disciplines. Currently, there are no general efficient methods to deal with this challenging problem that involves high dimensionality, low regularity and random frequencies. We propose a framework for stochastic analysis in nonlinear dynamical systems based on goal-oriented probability density function (PDF) methods. The key idea stems from techniques of irreversible statistical mechanics, and it relies on deriving evolution equations for the PDF of quantities of interest, e.g. functionals of the solution to systems of stochastic ordinary and partial differential equations. Such quantities could be low-dimensional objects in infinite dimensional phase spaces. We develop the goal-oriented PDF method in the context of the time-convolutionless Nakajima-Zwanzig-Mori formalism. We address the question of approximation of reduced-order density equations by multi-level coarse graining, perturbation series and operator cumulant resummation. Numerical examples are presented for stochastic resonance and stochastic advection-reaction problems.

Convolutionless Nakajima–Zwanzig equations for stochastic analysis in nonlinear dynamical systems

PubMed Central

Venturi, D.; Karniadakis, G. E.

2014-01-01

Determining the statistical properties of stochastic nonlinear systems is of major interest across many disciplines. Currently, there are no general efficient methods to deal with this challenging problem that involves high dimensionality, low regularity and random frequencies. We propose a framework for stochastic analysis in nonlinear dynamical systems based on goal-oriented probability density function (PDF) methods. The key idea stems from techniques of irreversible statistical mechanics, and it relies on deriving evolution equations for the PDF of quantities of interest, e.g. functionals of the solution to systems of stochastic ordinary and partial differential equations. Such quantities could be low-dimensional objects in infinite dimensional phase spaces. We develop the goal-oriented PDF method in the context of the time-convolutionless Nakajima–Zwanzig–Mori formalism. We address the question of approximation of reduced-order density equations by multi-level coarse graining, perturbation series and operator cumulant resummation. Numerical examples are presented for stochastic resonance and stochastic advection–reaction problems. PMID:24910519

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.

Link Prediction in Evolving Networks Based on Popularity of Nodes.

PubMed

Wang, Tong; He, Xing-Sheng; Zhou, Ming-Yang; Fu, Zhong-Qian

2017-08-02

Link prediction aims to uncover the underlying relationship behind networks, which could be utilized to predict missing edges or identify the spurious edges. The key issue of link prediction is to estimate the likelihood of potential links in networks. Most classical static-structure based methods ignore the temporal aspects of networks, limited by the time-varying features, such approaches perform poorly in evolving networks. In this paper, we propose a hypothesis that the ability of each node to attract links depends not only on its structural importance, but also on its current popularity (activeness), since active nodes have much more probability to attract future links. Then a novel approach named popularity based structural perturbation method (PBSPM) and its fast algorithm are proposed to characterize the likelihood of an edge from both existing connectivity structure and current popularity of its two endpoints. Experiments on six evolving networks show that the proposed methods outperform state-of-the-art methods in accuracy and robustness. Besides, visual results and statistical analysis reveal that the proposed methods are inclined to predict future edges between active nodes, rather than edges between inactive nodes.

Evaluation of tranche in securitization and long-range Ising model

NASA Astrophysics Data System (ADS)

Kitsukawa, K.; Mori, S.; Hisakado, M.

2006-08-01

This econophysics work studies the long-range Ising model of a finite system with N spins and the exchange interaction J/N and the external field H as a model for homogeneous credit portfolio of assets with default probability Pd and default correlation ρd. Based on the discussion on the (J,H) phase diagram, we develop a perturbative calculation method for the model and obtain explicit expressions for Pd,ρd and the normalization factor Z in terms of the model parameters N and J,H. The effect of the default correlation ρd on the probabilities P(Nd,ρd) for Nd defaults and on the cumulative distribution function D(i,ρd) are discussed. The latter means the average loss rate of the“tranche” (layered structure) of the securities (e.g. CDO), which are synthesized from a pool of many assets. We show that the expected loss rate of the subordinated tranche decreases with ρd and that of the senior tranche increases linearly, which are important in their pricing and ratings.

Default risk modeling with position-dependent killing

NASA Astrophysics Data System (ADS)

Katz, Yuri A.

2013-04-01

Diffusion in a linear potential in the presence of position-dependent killing is used to mimic a default process. Different assumptions regarding transport coefficients, initial conditions, and elasticity of the killing measure lead to diverse models of bankruptcy. One “stylized fact” is fundamental for our consideration: empirically default is a rather rare event, especially in the investment grade categories of credit ratings. Hence, the action of killing may be considered as a small parameter. In a number of special cases we derive closed-form expressions for the entire term structure of the cumulative probability of default, its hazard rate, and intensity. Comparison with historical data on aggregate global corporate defaults confirms the validity of the perturbation method for estimations of long-term probability of default for companies with high credit quality. On a single company level, we implement the derived formulas to estimate the one-year likelihood of default of Enron on a daily basis from August 2000 to August 2001, three months before its default, and compare the obtained results with forecasts of traditional structural models.

Fire and aquatic ecosystems in forested biomes of North America

USGS Publications Warehouse

Gresswell, Robert E.

1999-01-01

Synthesis of the literature suggests that physical, chemical, and biological elements of a watershed interact with long-term climate to influence fire regime, and that these factors, in concordance with the postfire vegetation mosaic, combine with local-scale weather to govern the trajectory and magnitude of change following a fire event. Perturbation associated with hydrological processes is probably the primary factor influencing postfire persistence of fishes, benthic macroinvertebrates, and diatoms in fluvial systems. It is apparent that salmonids have evolved strategies to survive perturbations occurring at the frequency of wildland fires (100a??102 years), but local populations of a species may be more ephemeral. Habitat alteration probably has the greatest impact on individual organisms and local populations that are the least mobile, and reinvasion will be most rapid by aquatic organisms with high mobility. It is becoming increasingly apparent that during the past century fire suppression has altered fire regimes in some vegetation types, and consequently, the probability of large stand-replacing fires has increased in those areas. Current evidence suggests, however, that even in the case of extensive high-severity fires, local extirpation of fishes is patchy, and recolonization is rapid. Lasting detrimental effects on fish populations have been limited to areas where native populations have declined and become increasingly isolated because of anthropogenic activities. A strategy of protecting robust aquatic communities and restoring aquatic habitat structure and life history complexity in degraded areas may be the most effective means for insuring the persistence of native biota where the probability of large-scale fires has increased.

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.

Evaluating a linearized Euler equations model for strong turbulence effects on sound propagation.

PubMed

Ehrhardt, Loïc; Cheinet, Sylvain; Juvé, Daniel; Blanc-Benon, Philippe

2013-04-01

Sound propagation outdoors is strongly affected by atmospheric turbulence. Under strongly perturbed conditions or long propagation paths, the sound fluctuations reach their asymptotic behavior, e.g., the intensity variance progressively saturates. The present study evaluates the ability of a numerical propagation model based on the finite-difference time-domain solving of the linearized Euler equations in quantitatively reproducing the wave statistics under strong and saturated intensity fluctuations. It is the continuation of a previous study where weak intensity fluctuations were considered. The numerical propagation model is presented and tested with two-dimensional harmonic sound propagation over long paths and strong atmospheric perturbations. The results are compared to quantitative theoretical or numerical predictions available on the wave statistics, including the log-amplitude variance and the probability density functions of the complex acoustic pressure. The match is excellent for the evaluated source frequencies and all sound fluctuations strengths. Hence, this model captures these many aspects of strong atmospheric turbulence effects on sound propagation. Finally, the model results for the intensity probability density function are compared with a standard fit by a generalized gamma function.

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.

Protecting count queries in study design.

PubMed

Vinterbo, Staal A; Sarwate, Anand D; Boxwala, Aziz A

2012-01-01

Today's clinical research institutions provide tools for researchers to query their data warehouses for counts of patients. To protect patient privacy, counts are perturbed before reporting; this compromises their utility for increased privacy. The goal of this study is to extend current query answer systems to guarantee a quantifiable level of privacy and allow users to tailor perturbations to maximize the usefulness according to their needs. A perturbation mechanism was designed in which users are given options with respect to scale and direction of the perturbation. The mechanism translates the true count, user preferences, and a privacy level within administrator-specified bounds into a probability distribution from which the perturbed count is drawn. Users can significantly impact the scale and direction of the count perturbation and can receive more accurate final cohort estimates. Strong and semantically meaningful differential privacy is guaranteed, providing for a unified privacy accounting system that can support role-based trust levels. This study provides an open source web-enabled tool to investigate visually and numerically the interaction between system parameters, including required privacy level and user preference settings. Quantifying privacy allows system administrators to provide users with a privacy budget and to monitor its expenditure, enabling users to control the inevitable loss of utility. While current measures of privacy are conservative, this system can take advantage of future advances in privacy measurement. The system provides new ways of trading off privacy and utility that are not provided in current study design systems.

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.

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

NASA Technical Reports Server (NTRS)

Stahara, S. S.

1984-01-01

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

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

NASA Technical Reports Server (NTRS)

Garcia, F., Jr.

1974-01-01

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

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.

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.

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.

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.

Addendum to "Compact Perturbative Expressions for Neutrino Oscillations in Matter"

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

Denton, Peter B.; Minakata, Hisakazu; Parke, Stephen J.

2018-01-19

In this paper we rewrite the neutrino mixing angles and mass squared differences in matter given, in our original paper, in a notation that is more conventional for the reader. Replacing the usual neutrino mixing angles and mass squared differences in the expressions for the vacuum oscillation probabilities with these matter mixing angles and mass squared differences gives an excellent approximation to the oscillation probabilities in matter. Comparisons for T2K, NOvA, T2HKK and DUNE are also given for neutrinos and anti-neutrinos, disappearance and appearance channels, normal ordering and inverted ordering.

Higher-dimensional attractors with absolutely continuous invariant probability

NASA Astrophysics Data System (ADS)

Bocker, Carlos; Bortolotti, Ricardo

2018-05-01

Consider a dynamical system given by , where E is a linear expanding map of , C is a linear contracting map of and f is in . We provide sufficient conditions for E that imply the existence of an open set of pairs for which the corresponding dynamic T admits a unique absolutely continuous invariant probability. A geometrical characteristic of transversality between self-intersections of images of is present in the dynamic of the maps in . In addition, we give a condition between E and C under which it is possible to perturb f to obtain a pair in .

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.

Seeing the hand while reaching speeds up on-line responses to a sudden change in target position

PubMed Central

Reichenbach, Alexandra; Thielscher, Axel; Peer, Angelika; Bülthoff, Heinrich H; Bresciani, Jean-Pierre

2009-01-01

Goal-directed movements are executed under the permanent supervision of the central nervous system, which continuously processes sensory afferents and triggers on-line corrections if movement accuracy seems to be compromised. For arm reaching movements, visual information about the hand plays an important role in this supervision, notably improving reaching accuracy. Here, we tested whether visual feedback of the hand affects the latency of on-line responses to an external perturbation when reaching for a visual target. Two types of perturbation were used: visual perturbation consisted in changing the spatial location of the target and kinesthetic perturbation in applying a force step to the reaching arm. For both types of perturbation, the hand trajectory and the electromyographic (EMG) activity of shoulder muscles were analysed to assess whether visual feedback of the hand speeds up on-line corrections. Without visual feedback of the hand, on-line responses to visual perturbation exhibited the longest latency. This latency was reduced by about 10% when visual feedback of the hand was provided. On the other hand, the latency of on-line responses to kinesthetic perturbation was independent of the availability of visual feedback of the hand. In a control experiment, we tested the effect of visual feedback of the hand on visual and kinesthetic two-choice reaction times – for which coordinate transformation is not critical. Two-choice reaction times were never facilitated by visual feedback of the hand. Taken together, our results suggest that visual feedback of the hand speeds up on-line corrections when the position of the visual target with respect to the body must be re-computed during movement execution. This facilitation probably results from the possibility to map hand- and target-related information in a common visual reference frame. PMID:19675067

Model of Selective and Non-Selective Management of Badgers (Meles meles) to Control Bovine Tuberculosis in Badgers and Cattle

PubMed Central

Smith, Graham C.; Delahay, Richard J.; McDonald, Robbie A.

2016-01-01

Bovine tuberculosis (bTB) causes substantial economic losses to cattle farmers and taxpayers in the British Isles. Disease management in cattle is complicated by the role of the European badger (Meles meles) as a host of the infection. Proactive, non-selective culling of badgers can reduce the incidence of disease in cattle but may also have negative effects in the area surrounding culls that have been associated with social perturbation of badger populations. The selective removal of infected badgers would, in principle, reduce the number culled, but the effects of selective culling on social perturbation and disease outcomes are unclear. We used an established model to simulate non-selective badger culling, non-selective badger vaccination and a selective trap and vaccinate or remove (TVR) approach to badger management in two distinct areas: South West England and Northern Ireland. TVR was simulated with and without social perturbation in effect. The lower badger density in Northern Ireland caused no qualitative change in the effect of management strategies on badgers, although the absolute number of infected badgers was lower in all cases. However, probably due to differing herd density in Northern Ireland, the simulated badger management strategies caused greater variation in subsequent cattle bTB incidence. Selective culling in the model reduced the number of badgers killed by about 83% but this only led to an overall benefit for cattle TB incidence if there was no social perturbation of badgers. We conclude that the likely benefit of selective culling will be dependent on the social responses of badgers to intervention but that other population factors including badger and cattle density had little effect on the relative benefits of selective culling compared to other methods, and that this may also be the case for disease management in other wild host populations. PMID:27893809

Model of Selective and Non-Selective Management of Badgers (Meles meles) to Control Bovine Tuberculosis in Badgers and Cattle.

PubMed

Smith, Graham C; Delahay, Richard J; McDonald, Robbie A; Budgey, Richard

2016-01-01

Bovine tuberculosis (bTB) causes substantial economic losses to cattle farmers and taxpayers in the British Isles. Disease management in cattle is complicated by the role of the European badger (Meles meles) as a host of the infection. Proactive, non-selective culling of badgers can reduce the incidence of disease in cattle but may also have negative effects in the area surrounding culls that have been associated with social perturbation of badger populations. The selective removal of infected badgers would, in principle, reduce the number culled, but the effects of selective culling on social perturbation and disease outcomes are unclear. We used an established model to simulate non-selective badger culling, non-selective badger vaccination and a selective trap and vaccinate or remove (TVR) approach to badger management in two distinct areas: South West England and Northern Ireland. TVR was simulated with and without social perturbation in effect. The lower badger density in Northern Ireland caused no qualitative change in the effect of management strategies on badgers, although the absolute number of infected badgers was lower in all cases. However, probably due to differing herd density in Northern Ireland, the simulated badger management strategies caused greater variation in subsequent cattle bTB incidence. Selective culling in the model reduced the number of badgers killed by about 83% but this only led to an overall benefit for cattle TB incidence if there was no social perturbation of badgers. We conclude that the likely benefit of selective culling will be dependent on the social responses of badgers to intervention but that other population factors including badger and cattle density had little effect on the relative benefits of selective culling compared to other methods, and that this may also be the case for disease management in other wild host populations.

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

What drives the perceptual change resulting from speech motor adaptation? Evaluation of hypotheses in a Bayesian modeling framework

PubMed Central

Perrier, Pascal; Schwartz, Jean-Luc; Diard, Julien

2018-01-01

Shifts in perceptual boundaries resulting from speech motor learning induced by perturbations of the auditory feedback were taken as evidence for the involvement of motor functions in auditory speech perception. Beyond this general statement, the precise mechanisms underlying this involvement are not yet fully understood. In this paper we propose a quantitative evaluation of some hypotheses concerning the motor and auditory updates that could result from motor learning, in the context of various assumptions about the roles of the auditory and somatosensory pathways in speech perception. This analysis was made possible thanks to the use of a Bayesian model that implements these hypotheses by expressing the relationships between speech production and speech perception in a joint probability distribution. The evaluation focuses on how the hypotheses can (1) predict the location of perceptual boundary shifts once the perturbation has been removed, (2) account for the magnitude of the compensation in presence of the perturbation, and (3) describe the correlation between these two behavioral characteristics. Experimental findings about changes in speech perception following adaptation to auditory feedback perturbations serve as reference. Simulations suggest that they are compatible with a framework in which motor adaptation updates both the auditory-motor internal model and the auditory characterization of the perturbed phoneme, and where perception involves both auditory and somatosensory pathways. PMID:29357357

Two-strain competition in quasineutral stochastic disease dynamics.

PubMed

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

2014-10-01

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

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.

Discovery of a missing disease spreader

NASA Astrophysics Data System (ADS)

Maeno, Yoshiharu

2011-10-01

This study presents a method to discover an outbreak of an infectious disease in a region for which data are missing, but which is at work as a disease spreader. Node discovery for the spread of an infectious disease is defined as discriminating between the nodes which are neighboring to a missing disease spreader node, and the rest, given a dataset on the number of cases. The spread is described by stochastic differential equations. A perturbation theory quantifies the impact of the missing spreader on the moments of the number of cases. Statistical discriminators examine the mid-body or tail-ends of the probability density function, and search for the disturbance from the missing spreader. They are tested with computationally synthesized datasets, and applied to the SARS outbreak and flu pandemic.

Statistical properties of Charney-Hasegawa-Mima zonal flows

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

Anderson, Johan, E-mail: anderson.johan@gmail.com; Botha, G. J. J.

2015-05-15

A theoretical interpretation of numerically generated probability density functions (PDFs) of intermittent plasma transport events in unforced zonal flows is provided within the Charney-Hasegawa-Mima (CHM) model. The governing equation is solved numerically with various prescribed density gradients that are designed to produce different configurations of parallel and anti-parallel streams. Long-lasting vortices form whose flow is governed by the zonal streams. It is found that the numerically generated PDFs can be matched with analytical predictions of PDFs based on the instanton method by removing the autocorrelations from the time series. In many instances, the statistics generated by the CHM dynamics relaxesmore » to Gaussian distributions for both the electrostatic and vorticity perturbations, whereas in areas with strong nonlinear interactions it is found that the PDFs are exponentially distributed.« less

An Aircraft Separation Algorithm with Feedback and Perturbation

NASA Technical Reports Server (NTRS)

White, Allan L.

2010-01-01

A separation algorithm is a set of rules that tell aircraft how to maneuver in order to maintain a minimum distance between them. This paper investigates demonstrating that separation algorithms satisfy the FAA requirement for the occurrence of incidents by means of simulation. Any demonstration that a separation algorithm, or any other aspect of flight, satisfies the FAA requirement is a challenge because of the stringent nature of the requirement and the complexity of airspace operations. The paper begins with a probability and statistical analysis of both the FAA requirement and demonstrating meeting it by a Monte Carlo approach. It considers the geometry of maintaining separation when one plane must change its flight path. It then develops a simple feedback control law that guides the planes on their paths. The presence of feedback control permits the introduction of perturbations, and the stochastic nature of the chosen perturbation is examined. The simulation program is described. This paper is an early effort in the realistic demonstration of a stringent requirement. Much remains to be done.

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.

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).

Eclipsing Stellar Binaries in the Galactic Center

NASA Astrophysics Data System (ADS)

Li, Gongjie; Ginsburg, Idan; Naoz, Smadar; Loeb, Abraham

2017-12-01

Compact stellar binaries are expected to survive in the dense environment of the Galactic center. The stable binaries may undergo Kozai–Lidov oscillations due to perturbations from the central supermassive black hole (Sgr A*), yet the general relativistic precession can suppress the Kozai–Lidov oscillations and keep the stellar binaries from merging. However, it is challenging to resolve the binary sources and distinguish them from single stars. The close separations of the stable binaries allow higher eclipse probabilities. Here, we consider the massive star SO-2 as an example and calculate the probability of detecting eclipses, assuming it is a binary. We find that the eclipse probability is ∼30%–50%, reaching higher values when the stellar binary is more eccentric or highly inclined relative to its orbit around Sgr A*.

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.

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.

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)

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.

Nonperturbative Time Dependent Solution of a Simple Ionization Model

NASA Astrophysics Data System (ADS)

Costin, Ovidiu; Costin, Rodica D.; Lebowitz, Joel L.

2018-02-01

We present a non-perturbative solution of the Schrödinger equation {iψ_t(t,x)=-ψ_{xx}(t,x)-2(1 +α sinω t) δ(x)ψ(t,x)} , written in units in which \\hbar=2m=1, describing the ionization of a model atom by a parametric oscillating potential. This model has been studied extensively by many authors, including us. It has surprisingly many features in common with those observed in the ionization of real atoms and emission by solids, subjected to microwave or laser radiation. Here we use new mathematical methods to go beyond previous investigations and to provide a complete and rigorous analysis of this system. We obtain the Borel-resummed transseries (multi-instanton expansion) valid for all values of α, ω, t for the wave function, ionization probability, and energy distribution of the emitted electrons, the latter not studied previously for this model. We show that for large t and small α the energy distribution has sharp peaks at energies which are multiples of ω, corresponding to photon capture. We obtain small α expansions that converge for all t, unlike those of standard perturbation theory. We expect that our analysis will serve as a basis for treating more realistic systems revealing a form of universality in different emission processes.

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.

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.

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.

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

Cai, H.

In this dissertation we study a procedure which restarts a Markov process when the process is killed by some arbitrary multiplicative functional. The regenerative nature of this revival procedure is characterized through a Markov renewal equation. An interesting duality between the revival procedure and the classical killing operation is found. Under the condition that the multiplicative functional possesses an intensity, the generators of the revival process can be written down explicitly. An intimate connection is also found between the perturbation of the sample path of a Markov process and the perturbation of a generator (in Kato's sense). The applications ofmore » the theory include the study of the processes like piecewise-deterministic Markov process, virtual waiting time process and the first entrance decomposition (taboo probability).« less

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

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.

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.

Good Practices in Free-energy Calculations

NASA Technical Reports Server (NTRS)

Pohorille, Andrew; Jarzynski, Christopher; Chipot, Christopher

2013-01-01

As access to computational resources continues to increase, free-energy calculations have emerged as a powerful tool that can play a predictive role in drug design. Yet, in a number of instances, the reliability of these calculations can be improved significantly if a number of precepts, or good practices are followed. For the most part, the theory upon which these good practices rely has been known for many years, but often overlooked, or simply ignored. In other cases, the theoretical developments are too recent for their potential to be fully grasped and merged into popular platforms for the computation of free-energy differences. The current best practices for carrying out free-energy calculations will be reviewed demonstrating that, at little to no additional cost, free-energy estimates could be markedly improved and bounded by meaningful error estimates. In energy perturbation and nonequilibrium work methods, monitoring the probability distributions that underlie the transformation between the states of interest, performing the calculation bidirectionally, stratifying the reaction pathway and choosing the most appropriate paradigms and algorithms for transforming between states offer significant gains in both accuracy and precision. In thermodynamic integration and probability distribution (histogramming) methods, properly designed adaptive techniques yield nearly uniform sampling of the relevant degrees of freedom and, by doing so, could markedly improve efficiency and accuracy of free energy calculations without incurring any additional computational expense.

Hard and Soft Constraints in Reliability-Based Design Optimization

NASA Technical Reports Server (NTRS)

Crespo, L.uis G.; Giesy, Daniel P.; Kenny, Sean P.

2006-01-01

This paper proposes a framework for the analysis and design optimization of models subject to parametric uncertainty where design requirements in the form of inequality constraints are present. Emphasis is given to uncertainty models prescribed by norm bounded perturbations from a nominal parameter value and by sets of componentwise bounded uncertain variables. These models, which often arise in engineering problems, allow for a sharp mathematical manipulation. Constraints can be implemented in the hard sense, i.e., constraints must be satisfied for all parameter realizations in the uncertainty model, and in the soft sense, i.e., constraints can be violated by some realizations of the uncertain parameter. In regard to hard constraints, this methodology allows (i) to determine if a hard constraint can be satisfied for a given uncertainty model and constraint structure, (ii) to generate conclusive, formally verifiable reliability assessments that allow for unprejudiced comparisons of competing design alternatives and (iii) to identify the critical combination of uncertain parameters leading to constraint violations. In regard to soft constraints, the methodology allows the designer (i) to use probabilistic uncertainty models, (ii) to calculate upper bounds to the probability of constraint violation, and (iii) to efficiently estimate failure probabilities via a hybrid method. This method integrates the upper bounds, for which closed form expressions are derived, along with conditional sampling. In addition, an l(sub infinity) formulation for the efficient manipulation of hyper-rectangular sets is also proposed.

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.

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,…

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

PubMed

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

2014-11-01

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

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

NASA Astrophysics Data System (ADS)

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

2014-11-01

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

A PDF-based classification of gait cadence patterns in patients with amyotrophic lateral sclerosis.

PubMed

Wu, Yunfeng; Ng, Sin Chun

2010-01-01

Amyotrophic lateral sclerosis (ALS) is a type of neurological disease due to the degeneration of motor neurons. During the course of such a progressive disease, it would be difficult for ALS patients to regulate normal locomotion, so that the gait stability becomes perturbed. This paper presents a pilot statistical study on the gait cadence (or stride interval) in ALS, based on the statistical analysis method. The probability density functions (PDFs) of stride interval were first estimated with the nonparametric Parzen-window method. We computed the mean of the left-foot stride interval and the modified Kullback-Leibler divergence (MKLD) from the PDFs estimated. The analysis results suggested that both of these two statistical parameters were significantly altered in ALS, and the least-squares support vector machine (LS-SVM) may effectively distinguish the stride patterns between the ALS patients and healthy controls, with an accurate rate of 82.8% and an area of 0.87 under the receiver operating characteristic curve.

Linear chirp phase perturbing approach for finding binary phased codes

NASA Astrophysics Data System (ADS)

Li, Bing C.

2017-05-01

Binary phased codes have many applications in communication and radar systems. These applications require binary phased codes to have low sidelobes in order to reduce interferences and false detection. Barker codes are the ones that satisfy these requirements and they have lowest maximum sidelobes. However, Barker codes have very limited code lengths (equal or less than 13) while many applications including low probability of intercept radar, and spread spectrum communication, require much higher code lengths. The conventional techniques of finding binary phased codes in literatures include exhaust search, neural network, and evolutionary methods, and they all require very expensive computation for large code lengths. Therefore these techniques are limited to find binary phased codes with small code lengths (less than 100). In this paper, by analyzing Barker code, linear chirp, and P3 phases, we propose a new approach to find binary codes. Experiments show that the proposed method is able to find long low sidelobe binary phased codes (code length >500) with reasonable computational cost.

Deriving photometric redshifts using fuzzy archetypes and self-organizing maps - I. Methodology

NASA Astrophysics Data System (ADS)

Speagle, Joshua S.; Eisenstein, Daniel J.

2017-07-01

We propose a method to substantially increase the flexibility and power of template fitting-based photometric redshifts by transforming a large number of galaxy spectral templates into a corresponding collection of 'fuzzy archetypes' using a suitable set of perturbative priors designed to account for empirical variation in dust attenuation and emission-line strengths. To bypass widely separated degeneracies in parameter space (e.g. the redshift-reddening degeneracy), we train self-organizing maps (SOMs) on large 'model catalogues' generated from Monte Carlo sampling of our fuzzy archetypes to cluster the predicted observables in a topologically smooth fashion. Subsequent sampling over the SOM then allows full reconstruction of the relevant probability distribution functions (PDFs). This combined approach enables the multimodal exploration of known variation among galaxy spectral energy distributions with minimal modelling assumptions. We demonstrate the power of this approach to recover full redshift PDFs using discrete Markov chain Monte Carlo sampling methods combined with SOMs constructed from Large Synoptic Survey Telescope ugrizY and Euclid YJH mock photometry.

Cross sections and rate coefficients for inner-shell excitation of Li-like ions with 6 < Z < 42

NASA Astrophysics Data System (ADS)

Safronova, U. I.; Safronova, M. S.; Kato, T.

1996-07-01

Excitation cross sections and rate coefficients by electron impact were calculated for the 1s22s-1s2s2p, 1s22s-1s2s2 and 1s22s-1s2p2 transitions of the Li-like ions (C IV, N V, O VI, Ne VIII, Mg X, Al XI, Si XII, S XIV, Ar XVI, Ca XVIII, Ti XX, Fe XXIV, Ni XXVI, Zn XXVIII, Ge XXX, Se XXXII, Kr XXXIV and Mo XXXX) in the Coulomb-Born approximation with exchange including relativistic effects and configuration interaction. Level energies, mixing coefficients and transition wavelengths and probabilities were also computed. Calculations performed by the 1/Z perturbation theory and Coulomb-Born approximation are compared with the R-matrix method and the distorted-wave approximation were Z is the nuclear charge. Formulae obtained for the angular factors of n-electron atomic system allow one to generalize this method to an arbitrary system of highly charged ions.

Nonlinear gyrokinetics: a powerful tool for the description of microturbulence in magnetized plasmas

NASA Astrophysics Data System (ADS)

Krommes, John A.

2010-12-01

Gyrokinetics is the description of low-frequency dynamics in magnetized plasmas. In magnetic-confinement fusion, it provides the most fundamental basis for numerical simulations of microturbulence; there are astrophysical applications as well. In this tutorial, a sketch of the derivation of the novel dynamical system comprising the nonlinear gyrokinetic (GK) equation (GKE) and the coupled electrostatic GK Poisson equation will be given by using modern Lagrangian and Lie perturbation methods. No background in plasma physics is required in order to appreciate the logical development. The GKE describes the evolution of an ensemble of gyrocenters moving in a weakly inhomogeneous background magnetic field and in the presence of electromagnetic perturbations with wavelength of the order of the ion gyroradius. Gyrocenters move with effective drifts, which may be obtained by an averaging procedure that systematically, order by order, removes gyrophase dependence. To that end, the use of the Lagrangian differential one-form as well as the content and advantages of Lie perturbation theory will be explained. The electromagnetic fields follow via Maxwell's equations from the charge and current density of the particles. Particle and gyrocenter densities differ by an important polarization effect. That is calculated formally by a 'pull-back' (a concept from differential geometry) of the gyrocenter distribution to the laboratory coordinate system. A natural truncation then leads to the closed GK dynamical system. Important properties such as GK energy conservation and fluctuation noise will be mentioned briefly, as will the possibility (and difficulties) of deriving nonlinear gyrofluid equations suitable for rapid numerical solution—although it is probably best to directly simulate the GKE. By the end of the tutorial, students should appreciate the GKE as an extremely powerful tool and will be prepared for later lectures describing its applications to physical problems.

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.

The angular electronic band structure and free particle model of aromatic molecules: High-frequency photon-induced ring current

NASA Astrophysics Data System (ADS)

Öncan, Mehmet; Koç, Fatih; Şahin, Mehmet; Köksal, Koray

2017-05-01

This work introduces an analysis of the relationship of first-principles calculations based on DFT method with the results of free particle model for ring-shaped aromatic molecules. However, the main aim of the study is to reveal the angular electronic band structure of the ring-shaped molecules. As in the case of spherical molecules such as fullerene, it is possible to observe a parabolic dispersion of electronic states with the variation of angular quantum number in the planar ring-shaped molecules. This work also discusses the transition probabilities between the occupied and virtual states by analyzing the angular electronic band structure and the possibility of ring currents in the case of spin angular momentum (SAM) or orbital angular momentum (OAM) carrying light. Current study focuses on the benzene molecule to obtain its angular electronic band structure. The obtained electronic band structure can be considered as a useful tool to see the transition probabilities between the electronic states and possible contribution of the states to the ring currents. The photoinduced current due to the transfer of SAM into the benzene molecule has been investigated by using analytical calculations within the frame of time-dependent perturbation theory.

Feline immunodeficiency virus and feline leukemia virus infection in free-ranging guignas (Leopardus guigna) and sympatric domestic cats in human perturbed landscapes on Chiloé Island, Chile.

PubMed

Mora, Mónica; Napolitano, Constanza; Ortega, René; Poulin, Elie; Pizarro-Lucero, José

2015-01-01

Feline immunodeficiency virus (FIV) and feline leukemia virus (FeLV) are two of the most common viruses affecting domestic cats (Felis catus). During the last two decades, reports show that both viruses also infect or affect other species of the family Felidae. Human landscape perturbation is one of the main causes of emerging diseases in wild animals, facilitating contact and transmission of pathogens between domestic and wild animals. We investigated FIV and FeLV infection in free-ranging guignas (Leopardus guigna) and sympatric domestic cats in human perturbed landscapes on Chiloé Island, Chile. Samples from 78 domestic cats and 15 guignas were collected from 2008 to 2010 and analyzed by PCR amplification and sequencing. Two guignas and two domestic cats were positive for FIV; three guignas and 26 domestic cats were positive for FeLV. The high percentage of nucleotide identity of FIV and FeLV sequences from both species suggests possible interspecies transmission of viruses, facilitated by increased contact probability through human invasion into natural habitats, fragmentation of guigna habitat, and poultry attacks by guignas. This study enhances our knowledge on the transmission of pathogens from domestic to wild animals in the global scenario of human landscape perturbation and emerging diseases.

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.

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.

Data-driven adaptive fractional order PI control for PMSM servo system with measurement noise and data dropouts.

PubMed

Xie, Yuanlong; Tang, Xiaoqi; Song, Bao; Zhou, Xiangdong; Guo, Yixuan

2018-04-01

In this paper, data-driven adaptive fractional order proportional integral (AFOPI) control is presented for permanent magnet synchronous motor (PMSM) servo system perturbed by measurement noise and data dropouts. The proposed method directly exploits the closed-loop process data for the AFOPI controller design under unknown noise distribution and data missing probability. Firstly, the proposed method constructs the AFOPI controller tuning problem as a parameter identification problem using the modified l p norm virtual reference feedback tuning (VRFT). Then, iteratively reweighted least squares is integrated into the l p norm VRFT to give a consistent compensation solution for the AFOPI controller. The measurement noise and data dropouts are estimated and eliminated by feedback compensation periodically, so that the AFOPI controller is updated online to accommodate the time-varying operating conditions. Moreover, the convergence and stability are guaranteed by mathematical analysis. Finally, the effectiveness of the proposed method is demonstrated both on simulations and experiments implemented on a practical PMSM servo system. Copyright © 2018 ISA. Published by Elsevier Ltd. All rights reserved.

Short term impact risk assessment for asteroids 2011 AG5

NASA Astrophysics Data System (ADS)

Bancelin, D.; Pravec, P.; Nolan, M.

2013-04-01

Among the potentially hazardous asteroids (PHAs) in orbit around the Earth, some of them can become a real threat. The most famous PHA presently known is asteroid (99942) Apophis which briefly presented an unusually high impact probability (up to 2.3 %) for a collision with the Earth in 2029. It remains the only asteroid to have reached level 4 of the Torino Scale. Even if Apophis is not a threat anymore, other PHAs are still monitored and now, only one asteroid is scaled to 1 with the highest impact probability. Asteroid 2011 AG5 has 1 chance over 500 to hit the Earth on 2040. This asteroid is challenging because it will remain of faint magnitude around 23.0 until its close encounter with the Earth in February 2023. It will come close to the Earth by 0.012 AU. Intensive ground-based (optical and mainly radar measurements) will be performed. Before this date, optical measurements would be possible (provided that large telescopes are used) and orbital refinement could be performed in order to improve the orbital uncertainty of this asteroid. Nevertheless, no physical data can be derived before 2023 and therefore, the influence of non gravitational forces, mainly Yarkovsky effect, can not be precisely determined. This non gravitational effect produces a secular drift da/dt (positive or negative) of the semi-major axis due to the anisotropic re-emission of the incident solar radiation. We propose here a dynamical study of the asteroid 2011 AG5. We discuss first the location of primary and secondary keyholes in the target plane of 2023 as well as the quantification of the impact probability. Secondary keyholes are due to two consecutive close encounters, the second usually happening near a keyhole or a resonant return. Then, we will address how those quantities evolve with future dedicated ground-based measurements. In a second part, we will discuss non gravitational perturbations through Yarkovsky effect. Assuming that this asteroid is a C or S-type, we can statistically derive some maximum intensity of Yarkovsky force, without any assumptions on the physical parameters. This will help to assess the maximum deviation expected on the geocentric distance expressed in the 2023 target plane. This deviation will have a direct consequence on the impact probability. Finally, a deeper study will include a Monte Carlo test on the orbital fit in order to compute virtual asteroids (VA) moving under gravity, relativistic and Yarkovsky perturbations. Using a simple model of Yarkovsky force as a perturbation along the transverse component and inversely proportional to the heliocentric square distance of the asteroid, we include a random deviation da/dt to assess the number of VA becoming virtual impactors (VI). We will compare this number to the one obtained with VA moving only under gravity and relativistic perturbations.

Stochastic Modeling of Past Volcanic Crises

NASA Astrophysics Data System (ADS)

Woo, Gordon

2018-01-01

The statistical foundation of disaster risk analysis is past experience. From a scientific perspective, history is just one realization of what might have happened, given the randomness and chaotic dynamics of Nature. Stochastic analysis of the past is an exploratory exercise in counterfactual history, considering alternative possible scenarios. In particular, the dynamic perturbations that might have transitioned a volcano from an unrest to an eruptive state need to be considered. The stochastic modeling of past volcanic crises leads to estimates of eruption probability that can illuminate historical volcanic crisis decisions. It can also inform future economic risk management decisions in regions where there has been some volcanic unrest, but no actual eruption for at least hundreds of years. Furthermore, the availability of a library of past eruption probabilities would provide benchmark support for estimates of eruption probability in future volcanic crises.

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.

Tackling higher derivative ghosts with the Euclidean path integral

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

Fontanini, Michele; Department of Physics, Syracuse University, Syracuse, New York 13244; Trodden, Mark

2011-05-15

An alternative to the effective field theory approach to treat ghosts in higher derivative theories is to attempt to integrate them out via the Euclidean path integral formalism. It has been suggested that this method could provide a consistent framework within which we might tolerate the ghost degrees of freedom that plague, among other theories, the higher derivative gravity models that have been proposed to explain cosmic acceleration. We consider the extension of this idea to treating a class of terms with order six derivatives, and find that for a general term the Euclidean path integral approach works in themore » most trivial background, Minkowski. Moreover we see that even in de Sitter background, despite some difficulties, it is possible to define a probability distribution for tensorial perturbations of the metric.« less

The Experiment of the Clog Reduction in a Plane Silo

NASA Astrophysics Data System (ADS)

Sun, Ai-Le; Zhang, Jie

2017-06-01

The flow of particles may be clogged when they pass through a narrow orifice. Many factors can change the probability of clogging, such as the outlet size, the presence of obstacles and external perturbation, but the detailed mechanisms are still unclear. In this paper, we present an experimental study of reduction of the clogging probability in a horizontal plane silo, which consists of a layer of elastic particles transported on an annular flat plate rotating with a constant angular velocity passing through a hopper structure. We found the exponential distributions of the avalanche size for different sizes of orifice and the power law tails of the passing time between two particles. We did not confirm whether there was a critical size of orifice above which the clogging became impossible. We explored the effect of the obstacle on the probability of clogging: and if we chose a proper obstacle placed at a proper position, the probability of clogging could be reduced by a factor of about seven.

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.

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.

On Graph Isomorphism and the PageRank Algorithm

DTIC Science & Technology

2008-09-01

specifies the probability of visiting each node from any other node. The perturbed matrix satisfies the Perron - Frobenius theorem’s conditions. Therefore... Frobenius and Perron theorems establishes the matrix must yield the dominant eigenvalue, one. Normalizing the unique and associated dominant eigenvector...is constructed such that none of its entries equal zero. An arbitrary PageRank matrix, S, is irreducible and satisfies the Perron - Frobenius

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.

CHARACTERIZATION OF THE RESONANT CAUSTIC PERTURBATION

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

Chung, Sun-Ju, E-mail: sjchung@kasi.re.k

Four of nine exoplanets found by microlensing were detected by the resonant caustic, which represents the merging of the planetary and central caustics at the position when the projected separation of a host star and a bounded planet is s approx 1. One of the resonant caustic lensing events, OGLE-2005-BLG-169, was a caustic-crossing high-magnification event with A {sub max}approx 800 and the source star was much smaller than the caustic, nevertheless the perturbation was not obviously apparent on the light curve of the event. In this paper, we investigate the perturbation pattern of the resonant caustic to understand why themore » perturbations induced by the caustic do not leave strong traces on the light curves of high-magnification events despite a small source/caustic size ratio. From this study, we find that the regions with small magnification excess around the center of the resonant caustic are rather widely formed, and the event passing the small-excess region produces a high-magnification event with a weak perturbation that is small relative to the amplification caused by the star and thus does not noticeably appear on the light curve of the event. We also find that the positive excess of the inside edge of the resonant caustic and the negative excess inside the caustic become stronger and wider as q increases, and thus the resonant caustic-crossing high-magnification events with the weak perturbation occur in the range of q <= 10{sup -4}. We determine the probability of the occurrence of events with the small excess |epsilon| <= 3% in high-magnification events induced by a resonant caustic. As a result, we find that for Earth-mass planets with a separation of approx2.5 AU the resonant caustic high-magnification events with the weak perturbation can occur with a significant frequency.« less

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.

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.

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.

Climate warming, euxinia and carbon isotope perturbations during the Carnian (Triassic) Crisis in South China

NASA Astrophysics Data System (ADS)

Sun, Y. D.; Wignall, P. B.; Joachimski, M. M.; Bond, D. P. G.; Grasby, S. E.; Lai, X. L.; Wang, L. N.; Zhang, Z. T.; Sun, S.

2016-06-01

The Carnian Humid Episode (CHE), also known as the Carnian Pluvial Event, and associated biotic changes are major enigmas of the Mesozoic record in western Tethys. We show that the CHE also occurred in eastern Tethys (South China), suggestive of a much more widespread and probably global climate perturbation. Oxygen isotope records from conodont apatite indicate a double-pulse warming event. The CHE coincided with an initial warming of 4 °C. This was followed by a transient cooling period and then a prolonged ∼7 °C warming in the later Carnian (Tuvalian 2). Carbon isotope perturbations associated with the CHE of western Tethys occurred contemporaneously in South China, and mark the start of a prolonged period of carbon cycle instability that persisted until the late Carnian. The dry-wet transition during the CHE coincides with the negative carbon isotope excursion and the temperature rise, pointing to an intensification of hydrologic cycle activities due to climatic warming. While carbonate platform shutdown in western Tethys is associated with an influx of siliciclastic sediment, the eastern Tethyan carbonate platforms are overlain by deep-water anoxic facies. The transition from oxygenated to euxinic facies was via a condensed, manganiferous carbonate (MnO content up to 15.1 wt%), that records an intense Mn shuttle operating in the basin. Significant siliciclastic influx in South China only occurred after the CHE climatic changes and was probably due to foreland basin development at the onset of the Indosinian Orogeny. The mid-Carnian biotic crisis thus coincided with several phenomena associated with major extinction events: a carbonate production crisis, climate warming, δ13 C oscillations, marine anoxia, biotic turnover and flood basalt eruptions (of the Wrangellia Large Igneous Province).

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.

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.

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.

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.

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.

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.

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.

Generalized Arcsine Laws for Fractional Brownian Motion

NASA Astrophysics Data System (ADS)

Sadhu, Tridib; Delorme, Mathieu; Wiese, Kay Jörg

2018-01-01

The three arcsine laws for Brownian motion are a cornerstone of extreme-value statistics. For a Brownian Bt starting from the origin, and evolving during time T , one considers the following three observables: (i) the duration t+ the process is positive, (ii) the time tlast the process last visits the origin, and (iii) the time tmax when it achieves its maximum (or minimum). All three observables have the same cumulative probability distribution expressed as an arcsine function, thus the name arcsine laws. We show how these laws change for fractional Brownian motion Xt, a non-Markovian Gaussian process indexed by the Hurst exponent H . It generalizes standard Brownian motion (i.e., H =1/2 ). We obtain the three probabilities using a perturbative expansion in ɛ =H -1/2 . While all three probabilities are different, this distinction can only be made at second order in ɛ . Our results are confirmed to high precision by extensive numerical simulations.

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.

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.

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.

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.

Pacific slab beneath northeast China revealed by regional and teleseismic waveform modeling

NASA Astrophysics Data System (ADS)

WANG, X.; Chen, Q. F.; Wei, S.

2015-12-01

Accurate velocity and geometry of the slab is essential for better understanding of the thermal, chemical structure of the mantle earth, as well as geodynamics. Recent tomography studies show similar morphology of the subducting Pacific slab beneath northeast China, which was stagnant in the mantle transition zone with thickness of more than 200km and an average velocity perturbation of ~1.5% [Fukao and Obayashi, 2013]. Meanwhile, waveform-modeling studies reveal that the Pacific slab beneath Japan and Kuril Island has velocity perturbation up to 5% and thickness up to 90km [Chen et al., 2007; Zhan et al., 2014]. These discrepancies are probably caused by the smoothing and limited data coverage in the tomographic inversions. Here we adopted 1D and 2D waveform modeling methods to study the fine structure of Pacific slab beneath northeast China using dense regional permanent and temporary broadband seismic records. The residual S- and P-wave travel time, difference between data and 1D synthetics, shows significant difference between the eastern and western stations. S-wave travel time residuals indicate 5-10s earlier arrivals for stations whose ray path lies within the slab, compared with those out of the slab. Teleseimic waveforms were used to rule out the major contribution of the possible low velocity structure above 200km. Furthermore, we use 2D finite-difference waveform modeling to confirm the velocity perturbation and geometry of the slab. Our result shows that the velocity perturbation in the slab is significantly higher than those reported in travel-time tomography studies. ReferencesChen, M., J. Tromp, D. Helmberger, and H. Kanamori (2007), Waveform modeling of the slab beneath Japan, J. Geophys. Res.-Solid Earth, 112(B2), 19, doi:10.1029/2006jb004394.Fukao, Y., and M. Obayashi (2013), Subducted slabs stagnant above, penetrating through, and trapped below the 660 km discontinuity, J. Geophys. Res.-Solid Earth, 118(11), 5920-5938, doi:10.1002/2013jb010466.Zhan, Z. W., D. V. Helmberger, and D. Z. Li (2014), Imaging subducted slab structure beneath the Sea of Okhotsk with teleseismic waveforms, Phys. Earth Planet. Inter., 232, 30-35, doi:10.1016/j.pepi.2014.03.008.

Topological transitions and freezing in XY models and Coulomb gases with quenched disorder: renormalization via traveling waves

NASA Astrophysics Data System (ADS)

Carpentier, David; Le Doussal, Pierre

2000-11-01

We study the two dimensional XY model with quenched random phases and its Coulomb gas formulation. A novel renormalization group (RG) method is developed which allows to study perturbatively the glassy low temperature XY phase and the transition at which frozen topological defects (vortices) proliferate. This RG approach is constructed both from the replicated Coulomb gas and, equivalently without the use of replicas, using the probability distribution of the local disorder (random defect core energy). By taking into account the fusion of environments (i.e., charge fusion in the replicated Coulomb gas) this distribution is shown to obey a Kolmogorov's type (KPP) non linear RG equation which admits traveling wave solutions and exhibits a freezing phenomenon analogous to glassy freezing in Derrida's random energy models. The resulting physical picture is that the distribution of local disorder becomes broad below a freezing temperature and that the transition is controlled by rare favorable regions for the defects, the density of which can be used as the new perturbative parameter. The determination of marginal directions at the disorder induced transition is shown to be related to the well studied front velocity selection problem in the KPP equation and the universality of the novel critical behaviour obtained here to the known universality of the corrections to the front velocity. Applications to other two dimensional problems are mentioned at the end.

A group evolving-based framework with perturbations for link prediction

NASA Astrophysics Data System (ADS)

Si, Cuiqi; Jiao, Licheng; Wu, Jianshe; Zhao, Jin

2017-06-01

Link prediction is a ubiquitous application in many fields which uses partially observed information to predict absence or presence of links between node pairs. The group evolving study provides reasonable explanations on the behaviors of nodes, relations between nodes and community formation in a network. Possible events in group evolution include continuing, growing, splitting, forming and so on. The changes discovered in networks are to some extent the result of these events. In this work, we present a group evolving-based characterization of node's behavioral patterns, and via which we can estimate the probability they tend to interact. In general, the primary aim of this paper is to offer a minimal toy model to detect missing links based on evolution of groups and give a simpler explanation on the rationality of the model. We first introduce perturbations into networks to obtain stable cluster structures, and the stable clusters determine the stability of each node. Then fluctuations, another node behavior, are assumed by the participation of each node to its own belonging group. Finally, we demonstrate that such characteristics allow us to predict link existence and propose a model for link prediction which outperforms many classical methods with a decreasing computational time in large scales. Encouraging experimental results obtained on real networks show that our approach can effectively predict missing links in network, and even when nearly 40% of the edges are missing, it also retains stationary performance.

Mathematical estimates of recovery after loss of activity: II. Long-range connectivity facilitates rapid functional recovery.

PubMed

Hübler, Merla J; Buchman, Timothy G

2008-02-01

To model the effects of system connectedness on recovery of dysfunctional tissues. One-dimensional elementary cellular automata models with small-world features, where the center-input for a few cells comes not from itself but, with a given probability, from another cell. This probability represents the connectivity of the network. The long-range connections are chosen randomly to survey the potential influences of distant information flowing into a local region. MATLAB and Mathematica computing environments. None. None. We determined the recovery rate of the entropy after perturbing a uniformly dormant system. We observed that the recovery of normal activity after perturbation of a dormant system had the characteristics of an epidemic. Moreover, we found that the rate of recovery to normal steady-state activity increased rapidly even for small amounts of long-range connectivity. Findings obtained through numerical simulation were verified through analytical solutions. This study links our hypothesis that multiple organ function syndromes represent recoupling failure with a mathematical model showing the contribution of such coupling to reactivation of dormant systems. The implication is that strategies aimed not at target tissues or target organs but rather at restoring the quality and quantity of interconnections across those tissues and organs may be a novel therapeutic strategy.

A cluster in a crowded environment: XMM-Newton and Chandra observations of A3558

NASA Astrophysics Data System (ADS)

Rossetti, M.; Ghizzardi, S.; Molendi, S.; Finoguenov, A.

2007-03-01

Combining XMM-Newton and Chandra data, we have performed a detailed study of Abell 3558. Our analysis shows that its dynamical history is more complicated than previously thought. We have found some traits typical of cool core clusters (surface brightness peaked at the center, peaked metal abundance profile) and others that are more common in merging clusters, like deviations from spherical symmetry in the thermodynamic quantities of the ICM. This last result has been achieved with a new technique for deriving temperature maps from images. We have also detected a cold front and, with the combined use of XMM-Newton and Chandra, we have characterized its properties, such as the speed and the metal abundance profile across the edge. This cold front is probably due to the sloshing of the core, induced by the perturbation of the gravitational potential associated with a past merger. The hydrodynamic processes related to this perturbation have presumably produced a tail of lower entropy, higher pressure and metal rich ICM, which extends behind the cold front for~500 kpc. The unique characteristics of A3558 are probably due to the very peculiar environment in which it is located: the core of the Shapley supercluster. Appendices A and B are only available in electronic form at http://www.aanda.org

Fourth-Order Vibrational Transition State Theory and Chemical Kinetics

NASA Astrophysics Data System (ADS)

Stanton, John F.; Matthews, Devin A.; Gong, Justin Z.

2015-06-01

Second-order vibrational perturbation theory (VPT2) is an enormously successful and well-established theory for treating anharmonic effects on the vibrational levels of semi-rigid molecules. Partially as a consequence of the fact that the theory is exact for the Morse potential (which provides an appropriate qualitative model for stretching anharmonicity), VPT2 calculations for such systems with appropriate ab initio potential functions tend to give fundamental and overtone levels that fall within a handful of wavenumbers of experimentally measured positions. As a consequence, the next non-vanishing level of perturbation theory -- VPT4 -- offers only slight improvements over VPT2 and is not practical for most calculations since it requires information about force constants up through sextic. However, VPT4 (as well as VPT2) can be used for other applications such as the next vibrational correction to rotational constants (the ``gammas'') and other spectroscopic parameters. In addition, the marriage of VPT with the semi-classical transition state theory of Miller (SCTST) has recently proven to be a powerful and accurate treatment for chemical kinetics. In this talk, VPT4-based SCTST tunneling probabilities and cumulative reaction probabilities are give for the first time for selected low-dimensional model systems. The prospects for VPT4, both practical and intrinsic, will also be discussed.

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.

LightForce Photon-Pressure Collision Avoidance: Updated Efficiency Analysis Utilizing a Highly Parallel Simulation Approach

NASA Technical Reports Server (NTRS)

Stupl, Jan; Faber, Nicolas; Foster, Cyrus; Yang, Fan Yang; Nelson, Bron; Aziz, Jonathan; Nuttall, Andrew; Henze, Chris; Levit, Creon

2014-01-01

This paper provides an updated efficiency analysis of the LightForce space debris collision avoidance scheme. LightForce aims to prevent collisions on warning by utilizing photon pressure from ground based, commercial off the shelf lasers. Past research has shown that a few ground-based systems consisting of 10 kilowatt class lasers directed by 1.5 meter telescopes with adaptive optics could lower the expected number of collisions in Low Earth Orbit (LEO) by an order of magnitude. Our simulation approach utilizes the entire Two Line Element (TLE) catalogue in LEO for a given day as initial input. Least-squares fitting of a TLE time series is used for an improved orbit estimate. We then calculate the probability of collision for all LEO objects in the catalogue for a time step of the simulation. The conjunctions that exceed a threshold probability of collision are then engaged by a simulated network of laser ground stations. After those engagements, the perturbed orbits are used to re-assess the probability of collision and evaluate the efficiency of the system. This paper describes new simulations with three updated aspects: 1) By utilizing a highly parallel simulation approach employing hundreds of processors, we have extended our analysis to a much broader dataset. The simulation time is extended to one year. 2) We analyze not only the efficiency of LightForce on conjunctions that naturally occur, but also take into account conjunctions caused by orbit perturbations due to LightForce engagements. 3) We use a new simulation approach that is regularly updating the LightForce engagement strategy, as it would be during actual operations. In this paper we present our simulation approach to parallelize the efficiency analysis, its computational performance and the resulting expected efficiency of the LightForce collision avoidance system. Results indicate that utilizing a network of four LightForce stations with 20 kilowatt lasers, 85% of all conjunctions with a probability of collision Pc > 10 (sup -6) can be mitigated.

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.

Probabilistic finite elements for fatigue and fracture analysis

NASA Astrophysics Data System (ADS)

Belytschko, Ted; Liu, Wing Kam

1993-04-01

An overview of the probabilistic finite element method (PFEM) developed by the authors and their colleagues in recent years is presented. The primary focus is placed on the development of PFEM for both structural mechanics problems and fracture mechanics problems. The perturbation techniques are used as major tools for the analytical derivation. The following topics are covered: (1) representation and discretization of random fields; (2) development of PFEM for the general linear transient problem and nonlinear elasticity using Hu-Washizu variational principle; (3) computational aspects; (4) discussions of the application of PFEM to the reliability analysis of both brittle fracture and fatigue; and (5) a stochastic computational tool based on stochastic boundary element (SBEM). Results are obtained for the reliability index and corresponding probability of failure for: (1) fatigue crack growth; (2) defect geometry; (3) fatigue parameters; and (4) applied loads. These results show that initial defect is a critical parameter.

Probabilistic finite elements for fatigue and fracture analysis

NASA Technical Reports Server (NTRS)

Belytschko, Ted; Liu, Wing Kam

1993-01-01

An overview of the probabilistic finite element method (PFEM) developed by the authors and their colleagues in recent years is presented. The primary focus is placed on the development of PFEM for both structural mechanics problems and fracture mechanics problems. The perturbation techniques are used as major tools for the analytical derivation. The following topics are covered: (1) representation and discretization of random fields; (2) development of PFEM for the general linear transient problem and nonlinear elasticity using Hu-Washizu variational principle; (3) computational aspects; (4) discussions of the application of PFEM to the reliability analysis of both brittle fracture and fatigue; and (5) a stochastic computational tool based on stochastic boundary element (SBEM). Results are obtained for the reliability index and corresponding probability of failure for: (1) fatigue crack growth; (2) defect geometry; (3) fatigue parameters; and (4) applied loads. These results show that initial defect is a critical parameter.

SU-F-T-192: Study of Robustness Analysis Method of Multiple Field Optimized IMPT Plans for Head & Neck Patients

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

Li, Y; Wang, X; Li, H

Purpose: Proton therapy is more sensitive to uncertainties than photon treatments due to protons’ finite range depending on the tissue density. Worst case scenario (WCS) method originally proposed by Lomax has been adopted in our institute for robustness analysis of IMPT plans. This work demonstrates that WCS method is sufficient enough to take into account of the uncertainties which could be encountered during daily clinical treatment. Methods: A fast and approximate dose calculation method is developed to calculate the dose for the IMPT plan under different setup and range uncertainties. Effects of two factors, inversed square factor and range uncertainty,more » are explored. WCS robustness analysis method was evaluated using this fast dose calculation method. The worst-case dose distribution was generated by shifting isocenter by 3 mm along x,y and z directions and modifying stopping power ratios by ±3.5%. 1000 randomly perturbed cases in proton range and x, yz directions were created and the corresponding dose distributions were calculated using this approximated method. DVH and dosimetric indexes of all 1000 perturbed cases were calculated and compared with the result using worst case scenario method. Results: The distributions of dosimetric indexes of 1000 perturbed cases were generated and compared with the results using worst case scenario. For D95 of CTVs, at least 97% of 1000 perturbed cases show higher values than the one of worst case scenario. For D5 of CTVs, at least 98% of perturbed cases have lower values than worst case scenario. Conclusion: By extensively calculating the dose distributions under random uncertainties, WCS method was verified to be reliable in evaluating the robustness level of MFO IMPT plans of H&N patients. The extensively sampling approach using fast approximated method could be used in evaluating the effects of different factors on the robustness level of IMPT plans in the future.« less

Perturbative Quantum Gravity and its Relation to Gauge Theory.

PubMed

Bern, Zvi

2002-01-01

In this review we describe a non-trivial relationship between perturbative gauge theory and gravity scattering amplitudes. At the semi-classical or tree-level, the scattering amplitudes of gravity theories in flat space can be expressed as a sum of products of well defined pieces of gauge theory amplitudes. These relationships were first discovered by Kawai, Lewellen, and Tye in the context of string theory, but hold more generally. In particular, they hold for standard Einstein gravity. A method based on D -dimensional unitarity can then be used to systematically construct all quantum loop corrections order-by-order in perturbation theory using as input the gravity tree amplitudes expressed in terms of gauge theory ones. More generally, the unitarity method provides a means for perturbatively quantizing massless gravity theories without the usual formal apparatus associated with the quantization of constrained systems. As one application, this method was used to demonstrate that maximally supersymmetric gravity is less divergent in the ultraviolet than previously thought.

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.

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.

Apparatus and method for microwave processing of materials using field-perturbing tool

DOEpatents

Tucker, Denise A.; Fathi, Zakaryae; Lauf, Robert J.

2001-01-01

A variable frequency microwave heating apparatus designed to allow modulation of the frequency of the microwaves introduced into a multi-mode microwave cavity for heating or other selected applications. A field-perturbing tool is disposed within the cavity to perturb the microwave power distribution in order to apply a desired level of microwave power to the workpiece.

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.

A multiple scales approach to sound generation by vibrating bodies

NASA Technical Reports Server (NTRS)

Geer, James F.; Pope, Dennis S.

1992-01-01

The problem of determining the acoustic field in an inviscid, isentropic fluid generated by a solid body whose surface executes prescribed vibrations is formulated and solved as a multiple scales perturbation problem, using the Mach number M based on the maximum surface velocity as the perturbation parameter. Following the idea of multiple scales, new 'slow' spacial scales are introduced, which are defined as the usual physical spacial scale multiplied by powers of M. The governing nonlinear differential equations lead to a sequence of linear problems for the perturbation coefficient functions. However, it is shown that the higher order perturbation functions obtained in this manner will dominate the lower order solutions unless their dependence on the slow spacial scales is chosen in a certain manner. In particular, it is shown that the perturbation functions must satisfy an equation similar to Burgers' equation, with a slow spacial scale playing the role of the time-like variable. The method is illustrated by a simple one-dimenstional example, as well as by three different cases of a vibrating sphere. The results are compared with solutions obtained by purely numerical methods and some insights provided by the perturbation approach are discussed.

Qualitative reasoning for biological network inference from systematic perturbation experiments.

PubMed

Badaloni, Silvana; Di Camillo, Barbara; Sambo, Francesco

2012-01-01

The systematic perturbation of the components of a biological system has been proven among the most informative experimental setups for the identification of causal relations between the components. In this paper, we present Systematic Perturbation-Qualitative Reasoning (SPQR), a novel Qualitative Reasoning approach to automate the interpretation of the results of systematic perturbation experiments. Our method is based on a qualitative abstraction of the experimental data: for each perturbation experiment, measured values of the observed variables are modeled as lower, equal or higher than the measurements in the wild type condition, when no perturbation is applied. The algorithm exploits a set of IF-THEN rules to infer causal relations between the variables, analyzing the patterns of propagation of the perturbation signals through the biological network, and is specifically designed to minimize the rate of false positives among the inferred relations. Tested on both simulated and real perturbation data, SPQR indeed exhibits a significantly higher precision than the state of the art.

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

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

Herbert, J.M.

1997-02-01

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

Non-perturbative String Theory from Water Waves

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

Iyer, Ramakrishnan; Johnson, Clifford V.; /Southern California U.

2012-06-14

We use a combination of a 't Hooft limit and numerical methods to find non-perturbative solutions of exactly solvable string theories, showing that perturbative solutions in different asymptotic regimes are connected by smooth interpolating functions. Our earlier perturbative work showed that a large class of minimal string theories arise as special limits of a Painleve IV hierarchy of string equations that can be derived by a similarity reduction of the dispersive water wave hierarchy of differential equations. The hierarchy of string equations contains new perturbative solutions, some of which were conjectured to be the type IIA and IIB string theoriesmore » coupled to (4, 4k ? 2) superconformal minimal models of type (A, D). Our present paper shows that these new theories have smooth non-perturbative extensions. We also find evidence for putative new string theories that were not apparent in the perturbative analysis.« less

Tau hadronic spectral function moments: perturbative expansion and αs extractions

NASA Astrophysics Data System (ADS)

Boito, D.

2016-04-01

In the extraction of αs from hadronic τ decays different moments of the spectral functions have been used. Furthermore, the two mainstream renormalization group improvement (RGI) frameworks, namely Fixed Order Perturbation Theory (FOPT) and Contour Improved Perturbation Theory (CIPT), lead to conflicting values of αs. In order to improve the strategy used in αs determinations, we have performed a systematic study of the perturbative behaviour of these spectral moments in the context of FOPT and CIPT. Higher order coefficients of the perturbative series, yet unknown, were modelled using available knowledge of the renormalon content of the QCD Adler function. We conclude that within these RGI frameworks some of the moments often employed in αs extractions should be avoided due to their poor perturbative behaviour. Finally, under reasonable assumptions about higher orders, we conclude that FOPT is the preferred method to perform the renormalization group improvement of the perturbative series.

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

Origin and Evolution of Comet Clouds

NASA Astrophysics Data System (ADS)

Higuchi, Arika

2007-01-01

The Oort cloud (comet cloud) is a spherical comet reservoir surrounding a planetary system. We have investigated the comet cloud formation that consists of two dynamical stages of orbital evolution of planetesimals due to (1) planetary perturbation, and (2) the galactic tide. We investigated the first stage by using numerical calculations and obtained the probabilities of the fates of planetesimals as functions of the orbital parameters of the planets and planetesimals. We investigated the second stage by using the secular perturbation theory and showed the evolution of the structure of a comet cloud from a planetesimal disk. We found that (1) massive planets effectively produce comet cloud candidates by scattering and (2) many planetesimals with semimajor axes larger than 1,000 AU rise up their perihelion distances to the outside of the planetary region and become members of the Oort cloud in 5 Gyr.

First-principles analysis of anharmonic nuclear motion and thermal transport in thermoelectric materials

NASA Astrophysics Data System (ADS)

Tadano, Terumasa; Tsuneyuki, Shinji

2015-12-01

We show a first-principles approach for analyzing anharmonic properties of lattice vibrations in solids. We firstly extract harmonic and anharmonic force constants from accurate first-principles calculations based on the density functional theory. Using the many-body perturbation theory of phonons, we then estimate the phonon scattering probability due to anharmonic phonon-phonon interactions. We show the validity of the approach by computing the lattice thermal conductivity of Si, a typical covalent semiconductor, and selected thermoelectric materials PbTe and Bi2Te3 based on the Boltzmann transport equation. We also show that the phonon lifetime and the lattice thermal conductivity of the high-temperature phase of SrTiO3 can be estimated by employing the perturbation theory on top of the solution of the self-consistent phonon equation.

Perturbations of a close-earth satellite due to sunlight diffusely reflected from the earth. I - Uniform albedo

NASA Technical Reports Server (NTRS)

Lautman, D. A.

1977-01-01

A semianalytic method has been developed to calculate the radiation-pressure perturbations of a close-earth satellite due to sunlight reflected from the earth. The assumptions made are that the satellite is spherically symmetric and that the solar radiation is reflected from the earth according to Lambert's Law with uniform albedo. By using expressions for the components of the radiation-pressure force due to Lochry, the expressions for the perturbations of the elements were developed into series in the true anomaly. The perturbations within a given revolution can be obtained analytically by integrating with respect to v while holding all slowly varying quantities constant. The long-range perturbations are then obtained by accumulating the net perturbations at the end of each revolution.

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

NASA Astrophysics Data System (ADS)

Jaouen, Stéphane

2007-07-01

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

Series Expansion of Functions with He's Homotopy Perturbation Method

ERIC Educational Resources Information Center

Khattri, Sanjay Kumar

2012-01-01

Finding a series expansion, such as Taylor series, of functions is an important mathematical concept with many applications. Homotopy perturbation method (HPM) is a new, easy to use and effective tool for solving a variety of mathematical problems. In this study, we present how to apply HPM to obtain a series expansion of functions. Consequently,…

Application of the Homotopy Perturbation Method to the Nonlinear Pendulum

ERIC Educational Resources Information Center

Belendez, A.; Hernandez, A.; Belendez, T.; Marquez, A.

2007-01-01

The homotopy perturbation method is used to solve the nonlinear differential equation that governs the nonlinear oscillations of a simple pendulum, and an approximate expression for its period is obtained. Only one iteration leads to high accuracy of the solutions and the relative error for the approximate period is less than 2% for amplitudes as…

A Numerical, Literal, and Converged Perturbation Algorithm

NASA Astrophysics Data System (ADS)

Wiesel, William E.

2017-09-01

The KAM theorem and von Ziepel's method are applied to a perturbed harmonic oscillator, and it is noted that the KAM methodology does not allow for necessary frequency or angle corrections, while von Ziepel does. The KAM methodology can be carried out with purely numerical methods, since its generating function does not contain momentum dependence. The KAM iteration is extended to allow for frequency and angle changes, and in the process apparently can be successfully applied to degenerate systems normally ruled out by the classical KAM theorem. Convergence is observed to be geometric, not exponential, but it does proceed smoothly to machine precision. The algorithm produces a converged perturbation solution by numerical methods, while still retaining literal variable dependence, at least in the vicinity of a given trajectory.

Nonplanar dust-ion acoustic shock waves with transverse perturbation

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

Xue Jukui

2005-01-01

The nonlinear dust-ion acoustic shock waves in dusty plasmas with the combined effects of bounded cylindrical/spherical geometry, the transverse perturbation, the dust charge fluctuation, and the nonthermal electrons are studied. Using the perturbation method, a cylindrical/spherical Kadomtsev-Petviashvili Burgers equation that describes the dust-ion acoustic shock waves is deduced. A particular solution of the cylindrical/spherical Kadomtsev-Petviashvili Burgers equation is also obtained. It is shown that the dust-ion acoustic shock wave propagating in cylindrical/spherical geometry with transverse perturbation will be slightly deformed as time goes on.

Testing approximate predictions of displacements of cosmological dark matter halos

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

Munari, Emiliano; Monaco, Pierluigi; Borgani, Stefano

We present a test to quantify how well some approximate methods, designed to reproduce the mildly non-linear evolution of perturbations, are able to reproduce the clustering of DM halos once the grouping of particles into halos is defined and kept fixed. The following methods have been considered: Lagrangian Perturbation Theory (LPT) up to third order, Truncated LPT, Augmented LPT, MUSCLE and COLA. The test runs as follows: halos are defined by applying a friends-of-friends (FoF) halo finder to the output of an N-body simulation. The approximate methods are then applied to the same initial conditions of the simulation, producing formore » all particles displacements from their starting position and velocities. The position and velocity of each halo are computed by averaging over the particles that belong to that halo, according to the FoF halo finder. This procedure allows us to perform a well-posed test of how clustering of the matter density and halo density fields are recovered, without asking to the approximate method an accurate reconstruction of halos. We have considered the results at z =0,0.5,1, and we have analysed power spectrum in real and redshift space, object-by-object difference in position and velocity, density Probability Distribution Function (PDF) and its moments, phase difference of Fourier modes. We find that higher LPT orders are generally able to better reproduce the clustering of halos, while little or no improvement is found for the matter density field when going to 2LPT and 3LPT. Augmentation provides some improvement when coupled with 2LPT, while its effect is limited when coupled with 3LPT. Little improvement is brought by MUSCLE with respect to Augmentation. The more expensive particle-mesh code COLA outperforms all LPT methods, and this is true even for mesh sizes as large as the inter-particle distance. This test sets an upper limit on the ability of these methods to reproduce the clustering of halos, for the cases when these objects are reconstructed at the object-by-object level.« less

Testing approximate predictions of displacements of cosmological dark matter halos

NASA Astrophysics Data System (ADS)

Munari, Emiliano; Monaco, Pierluigi; Koda, Jun; Kitaura, Francisco-Shu; Sefusatti, Emiliano; Borgani, Stefano

2017-07-01

We present a test to quantify how well some approximate methods, designed to reproduce the mildly non-linear evolution of perturbations, are able to reproduce the clustering of DM halos once the grouping of particles into halos is defined and kept fixed. The following methods have been considered: Lagrangian Perturbation Theory (LPT) up to third order, Truncated LPT, Augmented LPT, MUSCLE and COLA. The test runs as follows: halos are defined by applying a friends-of-friends (FoF) halo finder to the output of an N-body simulation. The approximate methods are then applied to the same initial conditions of the simulation, producing for all particles displacements from their starting position and velocities. The position and velocity of each halo are computed by averaging over the particles that belong to that halo, according to the FoF halo finder. This procedure allows us to perform a well-posed test of how clustering of the matter density and halo density fields are recovered, without asking to the approximate method an accurate reconstruction of halos. We have considered the results at z=0,0.5,1, and we have analysed power spectrum in real and redshift space, object-by-object difference in position and velocity, density Probability Distribution Function (PDF) and its moments, phase difference of Fourier modes. We find that higher LPT orders are generally able to better reproduce the clustering of halos, while little or no improvement is found for the matter density field when going to 2LPT and 3LPT. Augmentation provides some improvement when coupled with 2LPT, while its effect is limited when coupled with 3LPT. Little improvement is brought by MUSCLE with respect to Augmentation. The more expensive particle-mesh code COLA outperforms all LPT methods, and this is true even for mesh sizes as large as the inter-particle distance. This test sets an upper limit on the ability of these methods to reproduce the clustering of halos, for the cases when these objects are reconstructed at the object-by-object level.

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.

TWINTAN: A program for transonic wall interference assessment in two-dimensional wind tunnels

NASA Technical Reports Server (NTRS)

Kemp, W. B., Jr.

1980-01-01

A method for assessing the wall interference in transonic two dimensional wind tunnel test was developed and implemented in a computer program. The method involves three successive solutions of the transonic small disturbance potential equation to define the wind tunnel flow, the perturbation attriburable to the model, and the equivalent free air flow around the model. Input includes pressure distributions on the model and along the top and bottom tunnel walls which are used as boundary conditions for the wind tunnel flow. The wall induced perturbation fields is determined as the difference between the perturbation in the tunnel flow solution and the perturbation attributable to the model. The methodology used in the program is described and detailed descriptions of the computer program input and output are presented. Input and output for a sample case are given.

Current distribution in a three-dimensional IC analyzed by a perturbation method. Part 1: A simple steady state theory

NASA Technical Reports Server (NTRS)

Edmonds, Larry D.

1987-01-01

The steady state current distribution in a three dimensional integrated circuit is presented. A device physics approach, based on a perturbation method rather than an equivalent lumped circuit approach, is used. The perturbation method allows the various currents to be expressed in terms of elementary solutions which are solutions to very simple boundary value problems. A Simple Steady State Theory is the subtitle because the most obvious limitation of the present version of the analysis is that all depletion region boundary surfaces are treated as equipotential surfaces. This may be an adequate approximation in some applications but it is an obvious weakness in the theory when applied to latched states. Examples that illustrate the use of these analytical methods are not given because they will be presented in detail in the future.

Using satellite radiotelemetry data to delineate and manage wildlife populations

USGS Publications Warehouse

Amstrup, Steven C.; McDonald, T.L.; Durner, George M.

2004-01-01

The greatest promise of radiotelemetry always has been a better understanding of animal movements. Telemetry has helped us know when animals are active, how active they are, how far and how fast they move, the geographic areas they occupy, and whether individuals vary in these traits. Unfortunately, the inability to estimate the error in animals utilization distributions (UDs), has prevented probabilistic linkage of movements data, which are always retrospective, with future management actions. We used the example of the harvested population of polar bears (Ursus maritimus) in the Southern Beaufort Sea to illustrate a method that provides that linkage. We employed a 2-dimensional Gaussian kernel density estimator to smooth and scale frequencies of polar bear radio locations within cells of a grid overlying our study area. True 2-dimensional smoothing allowed us to create accurate descriptions of the UDs of individuals and groups of bears. We used a new method of clustering, based upon the relative use collared bears made of each cell in our grid, to assign individual animals to populations. We applied the fast Fourier transform to make bootstrapped estimates of the error in UDs computationally feasible. Clustering and kernel smoothing identified 3 populations of polar bears in the region between Wrangel Island, Russia, and Banks Island, Canada. The relative probability of occurrence of animals from each population varied significantly among grid cells distributed across the study area. We displayed occurrence probabilities as contour maps wherein each contour line corresponded with a change in relative probability. Only at the edges of our study area and in some offshore regions were bootstrapped estimates of error in occurrence probabilities too high to allow prediction. Error estimates, which also were displayed as contours, allowed us to show that occurrence probabilities did not vary by season. Near Barrow, Alaska, 50% of bears observed are predicted to be from the Chukchi Sea population and 50% from the Southern Beaufort Sea population. At Tuktoyaktuk, Northwest Territories, Canada, 50% are from the Southern Beaufort Sea and 50% from the Northern Beaufort Sea population. The methods described here will aid managers of all wildlife that can be studied by telemetry to allocate harvests and other human perturbations to the appropriate populations, make risk assessments, and predict impacts of human activities. They will aid researchers by providing the refined descriptions of study populations that are necessary for population estimation and other investigative tasks. Arctic, Beaufort Sea, boundaries, clustering, Fourier transform, kernel, management, polar bears, population delineation, radiotelemetry, satellite, smoothing, Ursus maritimus

Møller-Plesset perturbation theory gradient in the generalized hybrid orbital quantum mechanical and molecular mechanical method

NASA Astrophysics Data System (ADS)

Jung, Jaewoon; Sugita, Yuji; Ten-no, S.

2010-02-01

An analytic gradient expression is formulated and implemented for the second-order Møller-Plesset perturbation theory (MP2) based on the generalized hybrid orbital QM/MM method. The method enables us to obtain an accurate geometry at a reasonable computational cost. The performance of the method is assessed for various isomers of alanine dipepetide. We also compare the optimized structures of fumaramide-derived [2]rotaxane and cAMP-dependent protein kinase with experiment.

Left passage probability of Schramm-Loewner Evolution

NASA Astrophysics Data System (ADS)

Najafi, M. N.

2013-06-01

SLE(κ,ρ⃗) is a variant of Schramm-Loewner Evolution (SLE) which describes the curves which are not conformal invariant, but are self-similar due to the presence of some other preferred points on the boundary. In this paper we study the left passage probability (LPP) of SLE(κ,ρ⃗) through field theoretical framework and find the differential equation governing this probability. This equation is numerically solved for the special case κ=2 and hρ=0 in which hρ is the conformal weight of the boundary changing (bcc) operator. It may be referred to loop erased random walk (LERW) and Abelian sandpile model (ASM) with a sink on its boundary. For the curve which starts from ξ0 and conditioned by a change of boundary conditions at x0, we find that this probability depends significantly on the factor x0-ξ0. We also present the perturbative general solution for large x0. As a prototype, we apply this formalism to SLE(κ,κ-6) which governs the curves that start from and end on the real axis.

Left passage probability of Schramm-Loewner Evolution.

PubMed

Najafi, M N

2013-06-01

SLE(κ,ρ[over arrow]) is a variant of Schramm-Loewner Evolution (SLE) which describes the curves which are not conformal invariant, but are self-similar due to the presence of some other preferred points on the boundary. In this paper we study the left passage probability (LPP) of SLE(κ,ρ[over arrow]) through field theoretical framework and find the differential equation governing this probability. This equation is numerically solved for the special case κ=2 and h(ρ)=0 in which h(ρ) is the conformal weight of the boundary changing (bcc) operator. It may be referred to loop erased random walk (LERW) and Abelian sandpile model (ASM) with a sink on its boundary. For the curve which starts from ξ(0) and conditioned by a change of boundary conditions at x(0), we find that this probability depends significantly on the factor x(0)-ξ(0). We also present the perturbative general solution for large x(0). As a prototype, we apply this formalism to SLE(κ,κ-6) which governs the curves that start from and end on the real axis.

Prediction of probable mutations in influenza virus hemagglutinin protein based on large-scale ab initio fragment molecular orbital calculations.

PubMed

Yoshioka, Akio; Fukuzawa, Kaori; Mochizuki, Yuji; Yamashita, Katsumi; Nakano, Tatsuya; Okiyama, Yoshio; Nobusawa, Eri; Nakajima, Katsuhisa; Tanaka, Shigenori

2011-09-01

Ab initio electronic-state calculations for influenza virus hemagglutinin (HA) trimer complexed with Fab antibody were performed on the basis of the fragment molecular orbital (FMO) method at the second and third-order Møller-Plesset (MP2 and MP3) perturbation levels. For the protein complex containing 2351 residues and 36,160 atoms, the inter-fragment interaction energies (IFIEs) were evaluated to illustrate the effective interactions between all the pairs of amino acid residues. By analyzing the calculated data on the IFIEs, we first discussed the interactions and their fluctuations between multiple domains contained in the trimer complex. Next, by combining the IFIE data between the Fab antibody and each residue in the HA antigen with experimental data on the hemadsorption activity of HA mutants, we proposed a protocol to predict probable mutations in HA. The proposed protocol based on the FMO-MP2.5 calculation can explain the historical facts concerning the actual mutations after the emergence of A/Hong Kong/1/68 influenza virus with subtype H3N2, and thus provides a useful methodology to enumerate those residue sites likely to mutate in the future. Copyright © 2011 Elsevier Inc. All rights reserved.

Yarkovsky-driven Impact Predictions: Apophis and 1950 DA

NASA Astrophysics Data System (ADS)

Farnocchia, Davide; Chesley, S. R.; Chodas, P.; Milani, A.

2013-05-01

Abstract (2,250 Maximum Characters): Orbit determination for Near-Earth Asteroids presents unique technical challenges due to the imperative of early detection and careful assessment of the risk posed by specific Earth close approaches. The occurrence of an Earth impact can be decisively driven by the Yarkovsky effect, which is the most important nongravitational perturbation as it causes asteroids to undergo a secular variation in semimajor axis resulting in a quadratic effect in anomaly. We discuss the cases of (99942) Apophis and (29075) 1950 DA. The relevance of the Yarkovsky effect for Apophis is due to a scattering close approach in 2029 with minimum geocentric distance ~38000 km. For 1950 DA the influence of the Yarkovsky effect in 2880 is due to the long time interval preceding the impact. We use the available information on the asteroids' physical models as a starting point for a Monte Carlo method that allow us to measure how the Yarkovsky effect affects orbital predictions. For Apophis we map onto the 2029 close approach b-plane and analyze the keyholes corresponding to resonant close approaches. For 1950 DA we use the b-plane corresponding to the possible impact in 2880. We finally compute the impact probability from the mapped probability density function on the considered b-plane.

A comparison of methods to estimate seismic phase delays--Numerical examples for coda wave interferometry

USGS Publications Warehouse

Mikesell, T. Dylan; Malcolm, Alison E.; Yang, Di; Haney, Matthew M.

2015-01-01

Time-shift estimation between arrivals in two seismic traces before and after a velocity perturbation is a crucial step in many seismic methods. The accuracy of the estimated velocity perturbation location and amplitude depend on this time shift. Windowed cross correlation and trace stretching are two techniques commonly used to estimate local time shifts in seismic signals. In the work presented here, we implement Dynamic Time Warping (DTW) to estimate the warping function – a vector of local time shifts that globally minimizes the misfit between two seismic traces. We illustrate the differences of all three methods compared to one another using acoustic numerical experiments. We show that DTW is comparable to or better than the other two methods when the velocity perturbation is homogeneous and the signal-to-noise ratio is high. When the signal-to-noise ratio is low, we find that DTW and windowed cross correlation are more accurate than the stretching method. Finally, we show that the DTW algorithm has better time resolution when identifying small differences in the seismic traces for a model with an isolated velocity perturbation. These results impact current methods that utilize not only time shifts between (multiply) scattered waves, but also amplitude and decoherence measurements. DTW is a new tool that may find new applications in seismology and other geophysical methods (e.g., as a waveform inversion misfit function).

Process for computing geometric perturbations for probabilistic analysis

DOEpatents

Fitch, Simeon H. K. [Charlottesville, VA; Riha, David S [San Antonio, TX; Thacker, Ben H [San Antonio, TX

2012-04-10

A method for computing geometric perturbations for probabilistic analysis. The probabilistic analysis is based on finite element modeling, in which uncertainties in the modeled system are represented by changes in the nominal geometry of the model, referred to as "perturbations". These changes are accomplished using displacement vectors, which are computed for each node of a region of interest and are based on mean-value coordinate calculations.

A numerical scheme for singularly perturbed reaction-diffusion problems with a negative shift via numerov method

NASA Astrophysics Data System (ADS)

Dinesh Kumar, S.; Nageshwar Rao, R.; Pramod Chakravarthy, P.

2017-11-01

In this paper, we consider a boundary value problem for a singularly perturbed delay differential equation of reaction-diffusion type. We construct an exponentially fitted numerical method using Numerov finite difference scheme, which resolves not only the boundary layers but also the interior layers arising from the delay term. An extensive amount of computational work has been carried out to demonstrate the applicability of the proposed method.

Numerical-analytic implementation of the higher-order canonical Van Vleck perturbation theory for the interpretation of medium-sized molecule vibrational spectra.

PubMed

Krasnoshchekov, Sergey V; Isayeva, Elena V; Stepanov, Nikolay F

2012-04-12

Anharmonic vibrational states of semirigid polyatomic molecules are often studied using the second-order vibrational perturbation theory (VPT2). For efficient higher-order analysis, an approach based on the canonical Van Vleck perturbation theory (CVPT), the Watson Hamiltonian and operators of creation and annihilation of vibrational quanta is employed. This method allows analysis of the convergence of perturbation theory and solves a number of theoretical problems of VPT2, e.g., yields anharmonic constants y(ijk), z(ijkl), and allows the reliable evaluation of vibrational IR and Raman anharmonic intensities in the presence of resonances. Darling-Dennison and higher-order resonance coupling coefficients can be reliably evaluated as well. The method is illustrated on classic molecules: water and formaldehyde. A number of theoretical conclusions results, including the necessity of using sextic force field in the fourth order (CVPT4) and the nearly vanishing CVPT4 contributions for bending and wagging modes. The coefficients of perturbative Dunham-type Hamiltonians in high-orders of CVPT are found to conform to the rules of equality at different orders as earlier proven analytically for diatomic molecules. The method can serve as a good substitution of the more traditional VPT2.

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

PubMed

Fink, Reinhold F

2010-11-07

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

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

PubMed

Xu, Enhua; Zhao, Dongbo; Li, Shuhua

2015-10-13

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

Markovian queue optimisation analysis with an unreliable server subject to working breakdowns and impatient customers

NASA Astrophysics Data System (ADS)

Liou, Cheng-Dar

2015-09-01

This study investigates an infinite capacity Markovian queue with a single unreliable service station, in which the customers may balk (do not enter) and renege (leave the queue after entering). The unreliable service station can be working breakdowns even if no customers are in the system. The matrix-analytic method is used to compute the steady-state probabilities for the number of customers, rate matrix and stability condition in the system. The single-objective model for cost and bi-objective model for cost and expected waiting time are derived in the system to fit in with practical applications. The particle swarm optimisation algorithm is implemented to find the optimal combinations of parameters in the pursuit of minimum cost. Two different approaches are used to identify the Pareto optimal set and compared: the epsilon-constraint method and non-dominate sorting genetic algorithm. Compared results allow using the traditional optimisation approach epsilon-constraint method, which is computationally faster and permits a direct sensitivity analysis of the solution under constraint or parameter perturbation. The Pareto front and non-dominated solutions set are obtained and illustrated. The decision makers can use these to improve their decision-making quality.

Direct computation of stochastic flow in reservoirs with uncertain parameters

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

Dainton, M.P.; Nichols, N.K.; Goldwater, M.H.

1997-01-15

A direct method is presented for determining the uncertainty in reservoir pressure, flow, and net present value (NPV) using the time-dependent, one phase, two- or three-dimensional equations of flow through a porous medium. The uncertainty in the solution is modelled as a probability distribution function and is computed from given statistical data for input parameters such as permeability. The method generates an expansion for the mean of the pressure about a deterministic solution to the system equations using a perturbation to the mean of the input parameters. Hierarchical equations that define approximations to the mean solution at each point andmore » to the field convariance of the pressure are developed and solved numerically. The procedure is then used to find the statistics of the flow and the risked value of the field, defined by the NPV, for a given development scenario. This method involves only one (albeit complicated) solution of the equations and contrasts with the more usual Monte-Carlo approach where many such solutions are required. The procedure is applied easily to other physical systems modelled by linear or nonlinear partial differential equations with uncertain data. 14 refs., 14 figs., 3 tabs.« less

Analytic Approximations to the Free Boundary and Multi-dimensional Problems in Financial Derivatives Pricing

NASA Astrophysics Data System (ADS)

Lau, Chun Sing

This thesis studies two types of problems in financial derivatives pricing. The first type is the free boundary problem, which can be formulated as a partial differential equation (PDE) subject to a set of free boundary condition. Although the functional form of the free boundary condition is given explicitly, the location of the free boundary is unknown and can only be determined implicitly by imposing continuity conditions on the solution. Two specific problems are studied in details, namely the valuation of fixed-rate mortgages and CEV American options. The second type is the multi-dimensional problem, which involves multiple correlated stochastic variables and their governing PDE. One typical problem we focus on is the valuation of basket-spread options, whose underlying asset prices are driven by correlated geometric Brownian motions (GBMs). Analytic approximate solutions are derived for each of these three problems. For each of the two free boundary problems, we propose a parametric moving boundary to approximate the unknown free boundary, so that the original problem transforms into a moving boundary problem which can be solved analytically. The governing parameter of the moving boundary is determined by imposing the first derivative continuity condition on the solution. The analytic form of the solution allows the price and the hedging parameters to be computed very efficiently. When compared against the benchmark finite-difference method, the computational time is significantly reduced without compromising the accuracy. The multi-stage scheme further allows the approximate results to systematically converge to the benchmark results as one recasts the moving boundary into a piecewise smooth continuous function. For the multi-dimensional problem, we generalize the Kirk (1995) approximate two-asset spread option formula to the case of multi-asset basket-spread option. Since the final formula is in closed form, all the hedging parameters can also be derived in closed form. Numerical examples demonstrate that the pricing and hedging errors are in general less than 1% relative to the benchmark prices obtained by numerical integration or Monte Carlo simulation. By exploiting an explicit relationship between the option price and the underlying probability distribution, we further derive an approximate distribution function for the general basket-spread variable. It can be used to approximate the transition probability distribution of any linear combination of correlated GBMs. Finally, an implicit perturbation is applied to reduce the pricing errors by factors of up to 100. When compared against the existing methods, the basket-spread option formula coupled with the implicit perturbation turns out to be one of the most robust and accurate approximation methods.

Mapping Health Data: Improved Privacy Protection With Donut Method Geomasking

PubMed Central

Hampton, Kristen H.; Fitch, Molly K.; Allshouse, William B.; Doherty, Irene A.; Gesink, Dionne C.; Leone, Peter A.; Serre, Marc L.; Miller, William C.

2010-01-01

A major challenge in mapping health data is protecting patient privacy while maintaining the spatial resolution necessary for spatial surveillance and outbreak identification. A new adaptive geomasking technique, referred to as the donut method, extends current methods of random displacement by ensuring a user-defined minimum level of geoprivacy. In donut method geomasking, each geocoded address is relocated in a random direction by at least a minimum distance, but less than a maximum distance. The authors compared the donut method with current methods of random perturbation and aggregation regarding measures of privacy protection and cluster detection performance by masking multiple disease field simulations under a range of parameters. Both the donut method and random perturbation performed better than aggregation in cluster detection measures. The performance of the donut method in geoprivacy measures was at least 42.7% higher and in cluster detection measures was less than 4.8% lower than that of random perturbation. Results show that the donut method provides a consistently higher level of privacy protection with a minimal decrease in cluster detection performance, especially in areas where the risk to individual geoprivacy is greatest. PMID:20817785

Mapping health data: improved privacy protection with donut method geomasking.

PubMed

Hampton, Kristen H; Fitch, Molly K; Allshouse, William B; Doherty, Irene A; Gesink, Dionne C; Leone, Peter A; Serre, Marc L; Miller, William C

2010-11-01

A major challenge in mapping health data is protecting patient privacy while maintaining the spatial resolution necessary for spatial surveillance and outbreak identification. A new adaptive geomasking technique, referred to as the donut method, extends current methods of random displacement by ensuring a user-defined minimum level of geoprivacy. In donut method geomasking, each geocoded address is relocated in a random direction by at least a minimum distance, but less than a maximum distance. The authors compared the donut method with current methods of random perturbation and aggregation regarding measures of privacy protection and cluster detection performance by masking multiple disease field simulations under a range of parameters. Both the donut method and random perturbation performed better than aggregation in cluster detection measures. The performance of the donut method in geoprivacy measures was at least 42.7% higher and in cluster detection measures was less than 4.8% lower than that of random perturbation. Results show that the donut method provides a consistently higher level of privacy protection with a minimal decrease in cluster detection performance, especially in areas where the risk to individual geoprivacy is greatest.

Calculation of a fluctuating entropic force by phase space sampling.

PubMed

Waters, James T; Kim, Harold D

2015-07-01

A polymer chain pinned in space exerts a fluctuating force on the pin point in thermal equilibrium. The average of such fluctuating force is well understood from statistical mechanics as an entropic force, but little is known about the underlying force distribution. Here, we introduce two phase space sampling methods that can produce the equilibrium distribution of instantaneous forces exerted by a terminally pinned polymer. In these methods, both the positions and momenta of mass points representing a freely jointed chain are perturbed in accordance with the spatial constraints and the Boltzmann distribution of total energy. The constraint force for each conformation and momentum is calculated using Lagrangian dynamics. Using terminally pinned chains in space and on a surface, we show that the force distribution is highly asymmetric with both tensile and compressive forces. Most importantly, the mean of the distribution, which is equal to the entropic force, is not the most probable force even for long chains. Our work provides insights into the mechanistic origin of entropic forces, and an efficient computational tool for unbiased sampling of the phase space of a constrained system.

Head stabilisation in fast running lizards.

PubMed

Goyens, Jana; Aerts, Peter

2018-04-01

The cyclic patterns of terrestrial animal locomotion are frequently perturbed in natural environments. The terrain can be complex or inclined, the substrate can move unexpectedly and animals can misjudge situations. Loosing stability due to perturbations increases the probability of capture by predators and decreases the chance of successful prey capture and winning intraspecific battles. When controlled corrective actions are necessary to negotiate perturbations, animals rely on their exteroceptive and proprioceptive senses to monitor the environment and their own body movements. The vestibular system in the inner ear perceives linear and angular accelerations. This information enables gaze stabilisation and the creation of a stable, world-bound reference frame for the integration of the information of other senses. During locomotion, both functions are known to be facilitated by head stabilisation in several animals with an erect posture. Animals with a sprawled body posture, however, undergo very large body undulations while running. Using high speed video recordings, we tested whether they nevertheless stabilise their head during running, and how this is influenced by perturbations. We found that running Acanthodactylus boskianus lizards strongly stabilise their head yaw rotations when running on a flat, straight runway: the head rotation amplitude is only 4.76±0.99°, while the adjacent trunk part rotates over 27.0±3.8°. Lateral head translations are not stabilised (average amplitude of 7.4±2.0mm). When the lizards are experimentally perturbed by a large and unexpected lateral substrate movement, lateral translations of both the head and the body decrease (on average by 1.52±0.81mm). At the same time, the rotations of the head and trunk also decrease (on average by 1.62°±7.21°). These results show that head stabilisation intensifies because of the perturbation, which emphasises the importance of vestibular perception and balance in these fast and manoeuvrable animals. Copyright © 2017 Elsevier GmbH. All rights reserved.

Perturbation solutions of combustion instability problems

NASA Technical Reports Server (NTRS)

Googerdy, A.; Peddieson, J., Jr.; Ventrice, M.

1979-01-01

A method involving approximate modal analysis using the Galerkin method followed by an approximate solution of the resulting modal-amplitude equations by the two-variable perturbation method (method of multiple scales) is applied to two problems of pressure-sensitive nonlinear combustion instability in liquid-fuel rocket motors. One problem exhibits self-coupled instability while the other exhibits mode-coupled instability. In both cases it is possible to carry out the entire linear stability analysis and significant portions of the nonlinear stability analysis in closed form. In the problem of self-coupled instability the nonlinear stability boundary and approximate forms of the limit-cycle amplitudes and growth and decay rates are determined in closed form while the exact limit-cycle amplitudes and growth and decay rates are found numerically. In the problem of mode-coupled instability the limit-cycle amplitudes are found in closed form while the growth and decay rates are found numerically. The behavior of the solutions found by the perturbation method are in agreement with solutions obtained using complex numerical methods.

New Methods in Non-Perturbative QCD

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

Unsal, Mithat

2017-01-31

In this work, we investigate the properties of quantum chromodynamics (QCD), by using newly developing mathematics and physics formalisms. Almost all of the mass in the visible universe emerges from a quantum chromodynamics (QCD), which has a completely negligible microscopic mass content. An intimately related issue in QCD is the quark confinement problem. Answers to non-perturbative questions in QCD remained largely elusive despite much effort over the years. It is also believed that the usual perturbation theory is inadequate to address these kinds of problems. Perturbation theory gives a divergent asymptotic series (even when the theory is properly renormalized), andmore » there are non-perturbative phenomena which never appear at any order in perturbation theory. Recently, a fascinating bridge between perturbation theory and non-perturbative effects has been found: a formalism called resurgence theory in mathematics tells us that perturbative data and non-perturbative data are intimately related. Translating this to the language of quantum field theory, it turns out that non-perturbative information is present in a coded form in perturbation theory and it can be decoded. We take advantage of this feature, which is particularly useful to understand some unresolved mysteries of QCD from first principles. In particular, we use: a) Circle compactifications which provide a semi-classical window to study confinement and mass gap problems, and calculable prototypes of the deconfinement phase transition; b) Resurgence theory and transseries which provide a unified framework for perturbative and non-perturbative expansion; c) Analytic continuation of path integrals and Lefschetz thimbles which may be useful to address sign problem in QCD at finite density.« less

Internal wave energy flux from density perturbations in nonlinear stratifications

NASA Astrophysics Data System (ADS)

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

2017-11-01

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

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

PubMed

Pakdemirli, Mehmet

2016-01-01

The recently developed perturbation iteration method is applied to boundary layer type singular problems for the first time. As a preliminary work on the topic, the simplest algorithm of PIA(1,1) is employed in the calculations. Linear and nonlinear problems are solved to outline the basic ideas of the new solution technique. The inner and outer solutions are determined with the iteration algorithm and matched to construct a composite expansion valid within all parts of the domain. The solutions are contrasted with the available exact or numerical solutions. It is shown that the perturbation-iteration algorithm can be effectively used for solving boundary layer type problems.

Analogies in electronic properties of graphene wormhole and perturbed nanocylinder

NASA Astrophysics Data System (ADS)

Pincak, R.; Smotlacha, J.

2013-11-01

The electronic properties of the wormhole and the perturbed nanocylinder were investigated using two different methods: the continuum gauge field-theory model that deals with the continuum approximation of the surface and the Haydock recursion method that transforms the surface into a simplier structure and deals with the nearest-neighbor interactions. Furthermore, the changes of the electronic properties were investigated for the case of enclosing the appropriate structure, and possible substitutes for the encloser were derived. Finally, the character of the electron flux through the perturbed wormhole was predicted from the model based on the multiwalled nanotubes. The effect of the "graphene blackhole" is introduced.

Reconstructing the ideal results of a perturbed analog quantum simulator

NASA Astrophysics Data System (ADS)

Schwenk, Iris; Reiner, Jan-Michael; Zanker, Sebastian; Tian, Lin; Leppäkangas, Juha; Marthaler, Michael

2018-04-01

Well-controlled quantum systems can potentially be used as quantum simulators. However, a quantum simulator is inevitably perturbed by coupling to additional degrees of freedom. This constitutes a major roadblock to useful quantum simulations. So far there are only limited means to understand the effect of perturbation on the results of quantum simulation. Here we present a method which, in certain circumstances, allows for the reconstruction of the ideal result from measurements on a perturbed quantum simulator. We consider extracting the value of the correlator 〈Ôi(t ) Ôj(0 ) 〉 from the simulated system, where Ôi are the operators which couple the system to its environment. The ideal correlator can be straightforwardly reconstructed by using statistical knowledge of the environment, if any n -time correlator of operators Ôi of the ideal system can be written as products of two-time correlators. We give an approach to verify the validity of this assumption experimentally by additional measurements on the perturbed quantum simulator. The proposed method can allow for reliable quantum simulations with systems subjected to environmental noise without adding an overhead to the quantum system.

Spatial Distribution Measurement of Heart Wall Vibrations Generated by Remote Perturbation of Inner Pressure

NASA Astrophysics Data System (ADS)

Kanai, Hiroshi; Hasegawa, Hideyuki; Imamura, Kohsuke

2006-05-01

It is essential for the diagnosis of heart diseases to noninvasively measure instantaneous myocardial movability and transition properties during one cardiac cycle. This study proposes a novel method of noninvasively perturbing left ventricle (LV) internal pressure by remotely actuating the brachium artery with sinusoidal vibration for the diagnosis of myocardial movability. By attaching an actuator to the brachium artery and driving it with a sinusoidal wave of f0 Hz, the internal pressure of the artery is perturbed. The perturbation propagates along the artery to the LV of the heart and the sinusoidal perturbation of the LV internal pressure is induced. Using an ultrasound-based phased tracking method, the resultant minute motion of the heart wall can be noninvasively measured. Because the vibration mode of the heart wall depends on actuation frequency, by phantom experiments using a spherical shell made of silicone rubber, to which a silicone rubber tube is connected, the vibration mode was identified from the measurement of the spatial distribution of the motions by scanning with an ultrasonic beam. From an in vivo experiment, the principle of remote actuation was confirmed.

Bayesian Sensitivity Analysis of Statistical Models with Missing Data

PubMed Central

ZHU, HONGTU; IBRAHIM, JOSEPH G.; TANG, NIANSHENG

2013-01-01

Methods for handling missing data depend strongly on the mechanism that generated the missing values, such as missing completely at random (MCAR) or missing at random (MAR), as well as other distributional and modeling assumptions at various stages. It is well known that the resulting estimates and tests may be sensitive to these assumptions as well as to outlying observations. In this paper, we introduce various perturbations to modeling assumptions and individual observations, and then develop a formal sensitivity analysis to assess these perturbations in the Bayesian analysis of statistical models with missing data. We develop a geometric framework, called the Bayesian perturbation manifold, to characterize the intrinsic structure of these perturbations. We propose several intrinsic influence measures to perform sensitivity analysis and quantify the effect of various perturbations to statistical models. We use the proposed sensitivity analysis procedure to systematically investigate the tenability of the non-ignorable missing at random (NMAR) assumption. Simulation studies are conducted to evaluate our methods, and a dataset is analyzed to illustrate the use of our diagnostic measures. PMID:24753718

The Effect of Stochastic Perturbation of Fuel Distribution on the Criticality of a One Speed Reactor and the Development of Multi-Material Multinomial Line Statistics

NASA Technical Reports Server (NTRS)

Jahshan, S. N.; Singleterry, R. C.

2001-01-01

The effect of random fuel redistribution on the eigenvalue of a one-speed reactor is investigated. An ensemble of such reactors that are identical to a homogeneous reference critical reactor except for the fissile isotope density distribution is constructed such that it meets a set of well-posed redistribution requirements. The average eigenvalue, , is evaluated when the total fissile loading per ensemble element, or realization, is conserved. The perturbation is proven to increase the reactor criticality on average when it is uniformly distributed. The various causes of the change in reactivity, and their relative effects are identified and ranked. From this, a path towards identifying the causes. and relative effects of reactivity fluctuations for the energy dependent problem is pointed to. The perturbation method of using multinomial distributions for representing the perturbed reactor is developed. This method has some advantages that can be of use in other stochastic problems. Finally, some of the features of this perturbation problem are related to other techniques that have been used for addressing similar problems.

Characterizing heterogeneous cellular responses to perturbations.

PubMed

Slack, Michael D; Martinez, Elisabeth D; Wu, Lani F; Altschuler, Steven J

2008-12-09

Cellular populations have been widely observed to respond heterogeneously to perturbation. However, interpreting the observed heterogeneity is an extremely challenging problem because of the complexity of possible cellular phenotypes, the large dimension of potential perturbations, and the lack of methods for separating meaningful biological information from noise. Here, we develop an image-based approach to characterize cellular phenotypes based on patterns of signaling marker colocalization. Heterogeneous cellular populations are characterized as mixtures of phenotypically distinct subpopulations, and responses to perturbations are summarized succinctly as probabilistic redistributions of these mixtures. We apply our method to characterize the heterogeneous responses of cancer cells to a panel of drugs. We find that cells treated with drugs of (dis-)similar mechanism exhibit (dis-)similar patterns of heterogeneity. Despite the observed phenotypic diversity of cells observed within our data, low-complexity models of heterogeneity were sufficient to distinguish most classes of drug mechanism. Our approach offers a computational framework for assessing the complexity of cellular heterogeneity, investigating the degree to which perturbations induce redistributions of a limited, but nontrivial, repertoire of underlying states and revealing functional significance contained within distinct patterns of heterogeneous responses.

On the Tesseral-Harmonics Resonance Problem in Artificial-Satellite Theory, Part 2

NASA Technical Reports Server (NTRS)

Romanowicz, B. A.

1976-01-01

Equations were derived for the perturbations on an artificial satellite when the motion of the satellite is commensurable with that of the earth. This was done by first selecting the tesseral harmonics that contribute the most to the perturbations and then by applying Hori's method by use of Lie series. Here, are introduced some modifications to the perturbations, which now result in better agreement with numerical integration.

Communication: Extended multi-state complete active space second-order perturbation theory: Energy and nuclear gradients

NASA Astrophysics Data System (ADS)

Shiozaki, Toru; Győrffy, Werner; Celani, Paolo; Werner, Hans-Joachim

2011-08-01

The extended multireference quasi-degenerate perturbation theory, proposed by Granovsky [J. Chem. Phys. 134, 214113 (2011)], is combined with internally contracted multi-state complete active space second-order perturbation theory (XMS-CASPT2). The first-order wavefunction is expanded in terms of the union of internally contracted basis functions generated from all the reference functions, which guarantees invariance of the theory with respect to unitary rotations of the reference functions. The method yields improved potentials in the vicinity of avoided crossings and conical intersections. The theory for computing nuclear energy gradients for MS-CASPT2 and XMS-CASPT2 is also presented and the first implementation of these gradient methods is reported. A number of illustrative applications of the new methods are presented.

Adaptation to sensory-motor reflex perturbations is blind to the source of errors.

PubMed

Hudson, Todd E; Landy, Michael S

2012-01-06

In the study of visual-motor control, perhaps the most familiar findings involve adaptation to externally imposed movement errors. Theories of visual-motor adaptation based on optimal information processing suppose that the nervous system identifies the sources of errors to effect the most efficient adaptive response. We report two experiments using a novel perturbation based on stimulating a visually induced reflex in the reaching arm. Unlike adaptation to an external force, our method induces a perturbing reflex within the motor system itself, i.e., perturbing forces are self-generated. This novel method allows a test of the theory that error source information is used to generate an optimal adaptive response. If the self-generated source of the visually induced reflex perturbation is identified, the optimal response will be via reflex gain control. If the source is not identified, a compensatory force should be generated to counteract the reflex. Gain control is the optimal response to reflex perturbation, both because energy cost and movement errors are minimized. Energy is conserved because neither reflex-induced nor compensatory forces are generated. Precision is maximized because endpoint variance is proportional to force production. We find evidence against source-identified adaptation in both experiments, suggesting that sensory-motor information processing is not always optimal.

TWINTN4: A program for transonic four-wall interference assessment in two-dimensional wind tunnels

NASA Technical Reports Server (NTRS)

Kemp, W. B., Jr.

1984-01-01

A method for assessing the wall interference in transonic two-dimensional wind tunnel tests including the effects of the tunnel sidewall boundary layer was developed and implemented in a computer program named TWINTN4. The method involves three successive solutions of the transonic small disturbance potential equation to define the wind tunnel flow, the equivalent free air flow around the model, and the perturbation attributable to the model. Required input includes pressure distributions on the model and along the top and bottom tunnel walls which are used as boundary conditions for the wind tunnel flow. The wall-induced perturbation field is determined as the difference between the perturbation in the tunnel flow solution and the perturbation attributable to the model. The methodology used in the program is described and detailed descriptions of the computer program input and output are presented. Input and output for a sample case are given.

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

Yarkovsky-driven Impact Predictions: Apophis and 1950 DA

NASA Astrophysics Data System (ADS)

Chesley, Steven R.; Farnocchia, D.; Chodas, P. W.; Milani, A.

2013-10-01

Orbit determination for Near-Earth Asteroids presents unique technical challenges due to the imperative of early detection and careful assessment of the risk posed by specific Earth close approaches. The occurrence of an Earth impact can be decisively driven by the Yarkovsky effect, which is the most important nongravitational perturbation as it causes asteroids to undergo a secular variation in semimajor axis resulting in a quadratic effect in anomaly. We discuss the cases of (99942) Apophis and (29075) 1950 DA. The relevance of the Yarkovsky effect for Apophis is due to a scattering close approach in 2029 with minimum geocentric distance ~38000 km. For 1950 DA the influence of the Yarkovsky effect in 2880 is due to the long time interval preceding the impact. We use the available information from the astrometry and the asteroids' physical models and dynamical evolution as a starting point for a Monte Carlo method that allows us to measure how the Yarkovsky effect affects orbital predictions. We also find that 1950 DA has a 98% likelihood of being a retrograde rotator. For Apophis we map onto the 2029 close approach b-plane and analyze the keyholes corresponding to resonant close approaches. For 1950 DA we use the b-plane corresponding to the possible impact in 2880. We finally compute the impact probability from the mapped probability density function on the considered b-plane. For Apophis we have 4 in a million chances of an impact in 2068, while the probability of Earth impact in 2880 for 1950 DA is 0.04%.

A Perturbation Analysis of Harmonics Generation from Saturated Elements in Power Systems

NASA Astrophysics Data System (ADS)

Kumano, Teruhisa

Nonlinear phenomena such as saturation in magnetic flux give considerable effects in power system analysis. It is reported that a failure in a real 500kV system triggered islanding operation, where resultant even harmonics caused malfunctions in protective relays. It is also reported that the major origin of this wave distortion is nothing but unidirectional magnetization of the transformer iron core. Time simulation is widely used today to analyze this type of phenomena, but it has basically two shortcomings. One is that the time simulation takes two much computing time in the vicinity of inflection points in the saturation characteristic curve because certain iterative procedure such as N-R (Newton-Raphson) should be used and such methods tend to be caught in an ill conditioned numerical hunting. The other is that such simulation methods sometimes do not help intuitive understanding of the studied phenomenon because the whole nonlinear equations are treated in a matrix form and not properly divided into understandable parts as done in linear systems. This paper proposes a new computation scheme which is based on so called perturbation method. Magnetic saturation in iron cores in a generator and a transformer are taken into account. The proposed method has a special feature against the first shortcoming of the N-R based time simulation method stated above. In the proposed method no iterative process is used to reduce the equation residue but uses perturbation series, which means free from the ill condition problem. Users have only to calculate each perturbation terms one by one until he reaches necessary accuracy. In a numerical example treated in the present paper the first order perturbation can make reasonably high accuracy, which means very fast computing. In numerical study three nonlinear elements are considered. Calculated results are almost identical to the conventional Newton-Raphson based time simulation, which shows the validity of the method. The proposed method would be effectively used in a screening where many case studies are needed.

On optimizing the treatment of exchange perturbations.

NASA Technical Reports Server (NTRS)

Hirschfelder, J. O.; Chipman, D. M.

1972-01-01

Most theories of exchange perturbations would give the exact energy and wave function if carried out to an infinite order. However, the different methods give different values for the second-order energy, and different values for E(1), the expectation value of the Hamiltonian corresponding to the zeroth- plus first-order wave function. In the presented paper, it is shown that the zeroth- plus first-order wave function obtained by optimizing the basic equation which is used in most exchange perturbation treatments is the exact wave function for the perturbation system and E(1) is the exact energy.

Ozone response to a CO2 doubling - Results from a stratospheric circulation model with heterogeneous chemistry

NASA Technical Reports Server (NTRS)

Pitari, G.; Palermi, S.; Visconti, G.; Prinn, R. G.

1992-01-01

A spectral 3D model of the stratosphere has been used to study the sensitivity of polar ozone with respect to a carbon dioxide increase. The lower stratospheric cooling associated with an imposed CO2 doubling may increase the probability of polar stratospheric cloud (PSC) formation and this affect ozone. The ozone perturbation obtained with the inclusion of a simple parameterization for heterogeneous chemistry on PSCs is compared to that relative to a pure homogeneous chemistry. In both cases the temperature perturbation is determined by a CO2 doubling, while the total chlorine content is kept at the present level. It is shown that the lower temperature may increase the depth and the extension of the ozone hole by extending the area amenable to PSC formation. It may be argued that this effect, coupled with an increasing amount of chlorine, may produce a positive feedback on the ozone destruction.

Sprites and Early ionospheric VLF perturbations

NASA Astrophysics Data System (ADS)

Haldoupis, Christos; Amvrosiadi, Nino; Cotts, Ben; van der Velde, Oscar; Chanrion, Olivier; Neubert, Torsten

2010-05-01

Past studies have shown a correlation between sprites and early VLF perturbations, but the reported correlation varies widely from ~ 50% to 100%. The present study resolves these large discrepancies by analyzing several case studies of sprite and narrowband VLF observations, in which multiple transmitter-receiver VLF links with great circle paths (GCPs) passing near a sprite-producing thunderstorm were available. In this setup, the multiple links act in a complementary way that makes the detection of early VLF perturbations much more probable compared to a single VLF link that can miss several of them, a fact that was overlooked in past studies. The evidence shows that sprites are accompanied by early VLF perturbations in a one-to-one correspondence. This implies that the sprite generation mechanism may cause also sub-ionospheric conductivity disturbances that produce early VLF events. However, the one-to-one "sprite to early" event relationship, if viewed conversely as "early to sprite", appears not to be always reciprocal. This is because the number of early events detected in some cases was considerably larger than the number of sprites. Since the great majority of the early events not accompanied by sprites was caused by positive cloud to ground (+CG) lightning discharges, it is possible that sprites or sprite halos were concurrently present in these events as well but were missed by the sprite-watch detection system. In order for this option to be resolved we need more studies using highly sensitive optical systems capable of detecting weaker sprites, sprite halos and elves.

Wealth distribution of simple exchange models coupled with extremal dynamics

NASA Astrophysics Data System (ADS)

Bagatella-Flores, N.; Rodríguez-Achach, M.; Coronel-Brizio, H. F.; Hernández-Montoya, A. R.

2015-01-01

Punctuated Equilibrium (PE) states that after long periods of evolutionary quiescence, species evolution can take place in short time intervals, where sudden differentiation makes new species emerge and some species extinct. In this paper, we introduce and study the effect of punctuated equilibrium on two different asset exchange models: the yard sale model (YS, winner gets a random fraction of a poorer player's wealth) and the theft and fraud model (TF, winner gets a random fraction of the loser's wealth). The resulting wealth distribution is characterized using the Gini index. In order to do this, we consider PE as a perturbation with probability ρ of being applied. We compare the resulting values of the Gini index at different increasing values of ρ in both models. We found that in the case of the TF model, the Gini index reduces as the perturbation ρ increases, not showing dependence with the agents number. While for YS we observe a phase transition which happens around ρc = 0.79. For perturbations ρ <ρc the Gini index reaches the value of one as time increases (an extreme wealth condensation state), whereas for perturbations greater than or equal to ρc the Gini index becomes different to one, avoiding the system reaches this extreme state. We show that both simple exchange models coupled with PE dynamics give more realistic results. In particular for YS, we observe a power low decay of wealth distribution.

Restoration of dimensional reduction in the random-field Ising model at five dimensions

NASA Astrophysics Data System (ADS)

Fytas, Nikolaos G.; Martín-Mayor, Víctor; Picco, Marco; Sourlas, Nicolas

2017-04-01

The random-field Ising model is one of the few disordered systems where the perturbative renormalization group can be carried out to all orders of perturbation theory. This analysis predicts dimensional reduction, i.e., that the critical properties of the random-field Ising model in D dimensions are identical to those of the pure Ising ferromagnet in D -2 dimensions. It is well known that dimensional reduction is not true in three dimensions, thus invalidating the perturbative renormalization group prediction. Here, we report high-precision numerical simulations of the 5D random-field Ising model at zero temperature. We illustrate universality by comparing different probability distributions for the random fields. We compute all the relevant critical exponents (including the critical slowing down exponent for the ground-state finding algorithm), as well as several other renormalization-group invariants. The estimated values of the critical exponents of the 5D random-field Ising model are statistically compatible to those of the pure 3D Ising ferromagnet. These results support the restoration of dimensional reduction at D =5 . We thus conclude that the failure of the perturbative renormalization group is a low-dimensional phenomenon. We close our contribution by comparing universal quantities for the random-field problem at dimensions 3 ≤D <6 to their values in the pure Ising model at D -2 dimensions, and we provide a clear verification of the Rushbrooke equality at all studied dimensions.

Restoration of dimensional reduction in the random-field Ising model at five dimensions.

PubMed

Fytas, Nikolaos G; Martín-Mayor, Víctor; Picco, Marco; Sourlas, Nicolas

2017-04-01

The random-field Ising model is one of the few disordered systems where the perturbative renormalization group can be carried out to all orders of perturbation theory. This analysis predicts dimensional reduction, i.e., that the critical properties of the random-field Ising model in D dimensions are identical to those of the pure Ising ferromagnet in D-2 dimensions. It is well known that dimensional reduction is not true in three dimensions, thus invalidating the perturbative renormalization group prediction. Here, we report high-precision numerical simulations of the 5D random-field Ising model at zero temperature. We illustrate universality by comparing different probability distributions for the random fields. We compute all the relevant critical exponents (including the critical slowing down exponent for the ground-state finding algorithm), as well as several other renormalization-group invariants. The estimated values of the critical exponents of the 5D random-field Ising model are statistically compatible to those of the pure 3D Ising ferromagnet. These results support the restoration of dimensional reduction at D=5. We thus conclude that the failure of the perturbative renormalization group is a low-dimensional phenomenon. We close our contribution by comparing universal quantities for the random-field problem at dimensions 3≤D<6 to their values in the pure Ising model at D-2 dimensions, and we provide a clear verification of the Rushbrooke equality at all studied dimensions.

δ M formalism: a new approach to cosmological perturbation theory in anisotropic inflation

NASA Astrophysics Data System (ADS)

Talebian-Ashkezari, A.; Ahmadi, N.; Abolhasani, A. A.

2018-03-01

We study the evolution of the metric perturbations in a Bianchi background in the long-wavelength limit. By applying the gradient expansion to the equations of motion we exhibit a generalized "Separate Universe" approach to the cosmological perturbation theory. Having found this consistent separate universe picture, we introduce the δ M formalism for calculating the evolution of the linear tensor perturbations in anisotropic inflation models in almost the same way that the so-called δ N formula is applied to the super-horizon dynamics of the curvature perturbations. Similar to her twin formula, δ N, this new method can substantially reduce the amount of calculations related to the evolution of tensor modes. However, it is not as general as δ N it is a "perturbative" formula and solves the shear only to linear order. In other words, it is restricted to weak shear limit.

Noise Reduction in High-Throughput Gene Perturbation Screens

USDA-ARS?s Scientific Manuscript database

Motivation: Accurate interpretation of perturbation screens is essential for a successful functional investigation. However, the screened phenotypes are often distorted by noise, and their analysis requires specialized statistical analysis tools. The number and scope of statistical methods available...

The alcoholism generator.

PubMed

Miller, Michael W; Spear, Linda P

2006-09-01

Alcohol exposure largely affects 3 populations: fetuses, adolescents, and adults. These 3 developmental stages are inextricably intertwined such that elevated alcohol exposure at any time increases the probability of exposure at the others. This circular interdependency is called the alcoholism generator. Furthermore, exposure to large amounts of alcohol at these 3 times can cause cognitive dysfunction, largely through mechanisms of alcohol-induced perturbations in neurogenesis and synaptogenesis. Breaking this cycle is key to reducing problem alcohol drinking and the associated sequelae.

How decoherence affects the probability of slow-roll eternal inflation

NASA Astrophysics Data System (ADS)

Boddy, Kimberly K.; Carroll, Sean M.; Pollack, Jason

2017-07-01

Slow-roll inflation can become eternal if the quantum variance of the inflaton field around its slowly rolling classical trajectory is converted into a distribution of classical spacetimes inflating at different rates, and if the variance is large enough compared to the rate of classical rolling that the probability of an increased rate of expansion is sufficiently high. Both of these criteria depend sensitively on whether and how perturbation modes of the inflaton interact and decohere. Decoherence is inevitable as a result of gravitationally sourced interactions whose strength are proportional to the slow-roll parameters. However, the weakness of these interactions means that decoherence is typically delayed until several Hubble times after modes grow beyond the Hubble scale. We present perturbative evidence that decoherence of long-wavelength inflaton modes indeed leads to an ensemble of classical spacetimes with differing cosmological evolutions. We introduce the notion of per-branch observables—expectation values with respect to the different decohered branches of the wave function—and show that the evolution of modes on individual branches varies from branch to branch. Thus, single-field slow-roll inflation fulfills the quantum-mechanical criteria required for the validity of the standard picture of eternal inflation. For a given potential, the delayed decoherence can lead to slight quantitative adjustments to the regime in which the inflaton undergoes eternal inflation.

Cerebellar associative sensory learning defects in five mouse autism models

PubMed Central

Kloth, Alexander D; Badura, Aleksandra; Li, Amy; Cherskov, Adriana; Connolly, Sara G; Giovannucci, Andrea; Bangash, M Ali; Grasselli, Giorgio; Peñagarikano, Olga; Piochon, Claire; Tsai, Peter T; Geschwind, Daniel H; Hansel, Christian; Sahin, Mustafa; Takumi, Toru; Worley, Paul F; Wang, Samuel S-H

2015-01-01

Sensory integration difficulties have been reported in autism, but their underlying brain-circuit mechanisms are underexplored. Using five autism-related mouse models, Shank3+/ΔC, Mecp2R308/Y, Cntnap2−/−, L7-Tsc1 (L7/Pcp2Cre::Tsc1flox/+), and patDp(15q11-13)/+, we report specific perturbations in delay eyeblink conditioning, a form of associative sensory learning requiring cerebellar plasticity. By distinguishing perturbations in the probability and characteristics of learned responses, we found that probability was reduced in Cntnap2−/−, patDp(15q11-13)/+, and L7/Pcp2Cre::Tsc1flox/+, which are associated with Purkinje-cell/deep-nuclear gene expression, along with Shank3+/ΔC. Amplitudes were smaller in L7/Pcp2Cre::Tsc1flox/+ as well as Shank3+/ΔC and Mecp2R308/Y, which are associated with granule cell pathway expression. Shank3+/ΔC and Mecp2R308/Y also showed aberrant response timing and reduced Purkinje-cell dendritic spine density. Overall, our observations are potentially accounted for by defects in instructed learning in the olivocerebellar loop and response representation in the granule cell pathway. Our findings indicate that defects in associative temporal binding of sensory events are widespread in autism mouse models. DOI: http://dx.doi.org/10.7554/eLife.06085.001 PMID:26158416

Generalized Arcsine Laws for Fractional Brownian Motion.

PubMed

Sadhu, Tridib; Delorme, Mathieu; Wiese, Kay Jörg

2018-01-26

The three arcsine laws for Brownian motion are a cornerstone of extreme-value statistics. For a Brownian B_{t} starting from the origin, and evolving during time T, one considers the following three observables: (i) the duration t_{+} the process is positive, (ii) the time t_{last} the process last visits the origin, and (iii) the time t_{max} when it achieves its maximum (or minimum). All three observables have the same cumulative probability distribution expressed as an arcsine function, thus the name arcsine laws. We show how these laws change for fractional Brownian motion X_{t}, a non-Markovian Gaussian process indexed by the Hurst exponent H. It generalizes standard Brownian motion (i.e., H=1/2). We obtain the three probabilities using a perturbative expansion in ϵ=H-1/2. While all three probabilities are different, this distinction can only be made at second order in ϵ. Our results are confirmed to high precision by extensive numerical simulations.

Generation of intervention strategy for a genetic regulatory network represented by a family of Markov Chains.

PubMed

Berlow, Noah; Pal, Ranadip

2011-01-01

Genetic Regulatory Networks (GRNs) are frequently modeled as Markov Chains providing the transition probabilities of moving from one state of the network to another. The inverse problem of inference of the Markov Chain from noisy and limited experimental data is an ill posed problem and often generates multiple model possibilities instead of a unique one. In this article, we address the issue of intervention in a genetic regulatory network represented by a family of Markov Chains. The purpose of intervention is to alter the steady state probability distribution of the GRN as the steady states are considered to be representative of the phenotypes. We consider robust stationary control policies with best expected behavior. The extreme computational complexity involved in search of robust stationary control policies is mitigated by using a sequential approach to control policy generation and utilizing computationally efficient techniques for updating the stationary probability distribution of a Markov chain following a rank one perturbation.

A semi-analytical method of computation of oceanic tidal perturbations in the motion of artificial satellites

NASA Technical Reports Server (NTRS)

Musen, P.

1973-01-01

The method of expansion of the satellite's perturbations, as caused by the oceanic tides, into Fourier series is discussed. The coefficients of the expansion are purely numerical and peculiar to each particular satellite. Such a method is termed as semi-analytical in celestial mechanics. Gaussian form of the differential equations for variation of elements, with the right hand sides averaged over the orbit of the satellite, is convenient to use with the semi-analytical expansion.

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.

Development of a methodology for probable maximum precipitation estimation over the American River watershed using the WRF model

NASA Astrophysics Data System (ADS)

Tan, Elcin

A new physically-based methodology for probable maximum precipitation (PMP) estimation is developed over the American River Watershed (ARW) using the Weather Research and Forecast (WRF-ARW) model. A persistent moisture flux convergence pattern, called Pineapple Express, is analyzed for 42 historical extreme precipitation events, and it is found that Pineapple Express causes extreme precipitation over the basin of interest. An average correlation between moisture flux convergence and maximum precipitation is estimated as 0.71 for 42 events. The performance of the WRF model is verified for precipitation by means of calibration and independent validation of the model. The calibration procedure is performed only for the first ranked flood event 1997 case, whereas the WRF model is validated for 42 historical cases. Three nested model domains are set up with horizontal resolutions of 27 km, 9 km, and 3 km over the basin of interest. As a result of Chi-square goodness-of-fit tests, the hypothesis that "the WRF model can be used in the determination of PMP over the ARW for both areal average and point estimates" is accepted at the 5% level of significance. The sensitivities of model physics options on precipitation are determined using 28 microphysics, atmospheric boundary layer, and cumulus parameterization schemes combinations. It is concluded that the best triplet option is Thompson microphysics, Grell 3D ensemble cumulus, and YSU boundary layer (TGY), based on 42 historical cases, and this TGY triplet is used for all analyses of this research. Four techniques are proposed to evaluate physically possible maximum precipitation using the WRF: 1. Perturbations of atmospheric conditions; 2. Shift in atmospheric conditions; 3. Replacement of atmospheric conditions among historical events; and 4. Thermodynamically possible worst-case scenario creation. Moreover, climate change effect on precipitation is discussed by emphasizing temperature increase in order to determine the physically possible upper limits of precipitation due to climate change. The simulation results indicate that the meridional shift in atmospheric conditions is the optimum method to determine maximum precipitation in consideration of cost and efficiency. Finally, exceedance probability analyses of the model results of 42 historical extreme precipitation events demonstrate that the 72-hr basin averaged probable maximum precipitation is 21.72 inches for the exceedance probability of 0.5 percent. On the other hand, the current operational PMP estimation for the American River Watershed is 28.57 inches as published in the hydrometeorological report no. 59 and a previous PMP value was 31.48 inches as published in the hydrometeorological report no. 36. According to the exceedance probability analyses of this proposed method, the exceedance probabilities of these two estimations correspond to 0.036 percent and 0.011 percent, respectively.

A Jeziorski-Monkhorst fully uncontracted multi-reference perturbative treatment. I. Principles, second-order versions, and tests on ground state potential energy curves

NASA Astrophysics Data System (ADS)

Giner, Emmanuel; Angeli, Celestino; Garniron, Yann; Scemama, Anthony; Malrieu, Jean-Paul

2017-06-01

The present paper introduces a new multi-reference perturbation approach developed at second order, based on a Jeziorski-Mokhorst expansion using individual Slater determinants as perturbers. Thanks to this choice of perturbers, an effective Hamiltonian may be built, allowing for the dressing of the Hamiltonian matrix within the reference space, assumed here to be a CAS-CI. Such a formulation accounts then for the coupling between the static and dynamic correlation effects. With our new definition of zeroth-order energies, these two approaches are strictly size-extensive provided that local orbitals are used, as numerically illustrated here and formally demonstrated in the Appendix. Also, the present formalism allows for the factorization of all double excitation operators, just as in internally contracted approaches, strongly reducing the computational cost of these two approaches with respect to other determinant-based perturbation theories. The accuracy of these methods has been investigated on ground-state potential curves up to full dissociation limits for a set of six molecules involving single, double, and triple bond breaking together with an excited state calculation. The spectroscopic constants obtained with the present methods are found to be in very good agreement with the full configuration interaction results. As the present formalism does not use any parameter or numerically unstable operation, the curves obtained with the two methods are smooth all along the dissociation path.

Unsteady hovering wake parameters identified from dynamic model tests, part 1

NASA Technical Reports Server (NTRS)

Hohenemser, K. H.; Crews, S. T.

1977-01-01

The development of a 4-bladed model rotor is reported that can be excited with a simple eccentric mechanism in progressing and regressing modes with either harmonic or transient inputs. Parameter identification methods were applied to the problem of extracting parameters for linear perturbation models, including rotor dynamic inflow effects, from the measured blade flapping responses to transient pitch stirring excitations. These perturbation models were then used to predict blade flapping response to other pitch stirring transient inputs, and rotor wake and blade flapping responses to harmonic inputs. The viability and utility of using parameter identification methods for extracting the perturbation models from transients are demonstrated through these combined analytical and experimental studies.

Numerical solution of Euler's equation by perturbed functionals

NASA Technical Reports Server (NTRS)

Dey, S. K.

1985-01-01

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

Galilean invariant resummation schemes of cosmological perturbations

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

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

2017-01-01

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

Analytic energy gradients for the orbital-optimized third-order Møller-Plesset perturbation theory

NASA Astrophysics Data System (ADS)

Bozkaya, Uǧur

2013-09-01

Analytic energy gradients for the orbital-optimized third-order Møller-Plesset perturbation theory (OMP3) [U. Bozkaya, J. Chem. Phys. 135, 224103 (2011)], 10.1063/1.3665134 are presented. The OMP3 method is applied to problematic chemical systems with challenging electronic structures. The performance of the OMP3 method is compared with those of canonical second-order Møller-Plesset perturbation theory (MP2), third-order Møller-Plesset perturbation theory (MP3), coupled-cluster singles and doubles (CCSD), and coupled-cluster singles and doubles with perturbative triples [CCSD(T)] for investigating equilibrium geometries, vibrational frequencies, and open-shell reaction energies. For bond lengths, the performance of OMP3 is in between those of MP3 and CCSD. For harmonic vibrational frequencies, the OMP3 method significantly eliminates the singularities arising from the abnormal response contributions observed for MP3 in case of symmetry-breaking problems, and provides noticeably improved vibrational frequencies for open-shell molecules. For open-shell reaction energies, OMP3 exhibits a better performance than MP3 and CCSD as in case of barrier heights and radical stabilization energies. As discussed in previous studies, the OMP3 method is several times faster than CCSD in energy computations. Further, in analytic gradient computations for the CCSD method one needs to solve λ-amplitude equations, however for OMP3 one does not since λ _{ab}^{ij(1)} = t_{ij}^{ab(1)} and λ _{ab}^{ij(2)} = t_{ij}^{ab(2)}. Additionally, one needs to solve orbital Z-vector equations for CCSD, but for OMP3 orbital response contributions are zero owing to the stationary property of OMP3. Overall, for analytic gradient computations the OMP3 method is several times less expensive than CCSD (roughly ˜4-6 times). Considering the balance of computational cost and accuracy we conclude that the OMP3 method emerges as a very useful tool for the study of electronically challenging chemical systems.

Analytic energy gradients for the orbital-optimized third-order Møller-Plesset perturbation theory.

PubMed

Bozkaya, Uğur

2013-09-14

Analytic energy gradients for the orbital-optimized third-order Møller-Plesset perturbation theory (OMP3) [U. Bozkaya, J. Chem. Phys. 135, 224103 (2011)] are presented. The OMP3 method is applied to problematic chemical systems with challenging electronic structures. The performance of the OMP3 method is compared with those of canonical second-order Møller-Plesset perturbation theory (MP2), third-order Møller-Plesset perturbation theory (MP3), coupled-cluster singles and doubles (CCSD), and coupled-cluster singles and doubles with perturbative triples [CCSD(T)] for investigating equilibrium geometries, vibrational frequencies, and open-shell reaction energies. For bond lengths, the performance of OMP3 is in between those of MP3 and CCSD. For harmonic vibrational frequencies, the OMP3 method significantly eliminates the singularities arising from the abnormal response contributions observed for MP3 in case of symmetry-breaking problems, and provides noticeably improved vibrational frequencies for open-shell molecules. For open-shell reaction energies, OMP3 exhibits a better performance than MP3 and CCSD as in case of barrier heights and radical stabilization energies. As discussed in previous studies, the OMP3 method is several times faster than CCSD in energy computations. Further, in analytic gradient computations for the CCSD method one needs to solve λ-amplitude equations, however for OMP3 one does not since λ(ab)(ij(1))=t(ij)(ab(1)) and λ(ab)(ij(2))=t(ij)(ab(2)). Additionally, one needs to solve orbital Z-vector equations for CCSD, but for OMP3 orbital response contributions are zero owing to the stationary property of OMP3. Overall, for analytic gradient computations the OMP3 method is several times less expensive than CCSD (roughly ~4-6 times). Considering the balance of computational cost and accuracy we conclude that the OMP3 method emerges as a very useful tool for the study of electronically challenging chemical systems.

An automated integration-free path-integral method based on Kleinert's variational perturbation theory

NASA Astrophysics Data System (ADS)

Wong, Kin-Yiu; Gao, Jiali

2007-12-01

Based on Kleinert's variational perturbation (KP) theory [Path Integrals in Quantum Mechanics, Statistics, Polymer Physics, and Financial Markets, 3rd ed. (World Scientific, Singapore, 2004)], we present an analytic path-integral approach for computing the effective centroid potential. The approach enables the KP theory to be applied to any realistic systems beyond the first-order perturbation (i.e., the original Feynman-Kleinert [Phys. Rev. A 34, 5080 (1986)] variational method). Accurate values are obtained for several systems in which exact quantum results are known. Furthermore, the computed kinetic isotope effects for a series of proton transfer reactions, in which the potential energy surfaces are evaluated by density-functional theory, are in good accordance with experiments. We hope that our method could be used by non-path-integral experts or experimentalists as a "black box" for any given system.

Impulsive control of stochastic systems with applications in chaos control, chaos synchronization, and neural networks.

PubMed

Li, Chunguang; Chen, Luonan; Aihara, Kazuyuki

2008-06-01

Real systems are often subject to both noise perturbations and impulsive effects. In this paper, we study the stability and stabilization of systems with both noise perturbations and impulsive effects. In other words, we generalize the impulsive control theory from the deterministic case to the stochastic case. The method is based on extending the comparison method to the stochastic case. The method presented in this paper is general and easy to apply. Theoretical results on both stability in the pth mean and stability with disturbance attenuation are derived. To show the effectiveness of the basic theory, we apply it to the impulsive control and synchronization of chaotic systems with noise perturbations, and to the stability of impulsive stochastic neural networks. Several numerical examples are also presented to verify the theoretical results.

Dynamical study of low Earth orbit debris collision avoidance using ground based laser

NASA Astrophysics Data System (ADS)

Khalifa, N. S.

2015-06-01

The objective of this paper was to investigate the orbital velocity changes due to the effect of ground based laser force. The resulting perturbations of semi-major axis, miss distance and collision probability of two approaching objects are studied. The analytical model is applied for low Earth orbit debris of different eccentricities and area to mass ratio and the numerical test shows that laser of medium power ∼5 kW can perform a small change Δ V ‾ of an average magnitude of 0.2 cm/s which can be accumulated over time to be about 3 cm/day. Moreover, it is confirmed that applying laser Δ V ‾ results in decreasing collision probability and increasing miss distance in order to avoid collision.

Do gravity waves significantly impact PSC occurrence in the Antarctic?

NASA Astrophysics Data System (ADS)

McDonald, A. J.; George, S. E.; Woollands, R. M.

2009-02-01

This study uses a combination of POAM III aerosol extinction measurements and CHAMP GPS/RO temperature measurements to examine the role of atmospheric gravity waves in Polar Stratospheric Cloud (PSC) formation in the Antarctic. POAM III aerosol extinction observations are used to identify Type I Polar Stratospheric Clouds using an unsupervised clustering algorithm. The seasonal and spatial distribution of PSCs observed by POAM III is examined to determine whether there is a bias towards regions of high wave activity early in the Antarctic winter which may enhance PSC formation. Examination of the probability of temperatures below the Type Ia formation temperature threshold based on UKMO analyses displays a good correspondence to the PSC occurrence derived from POAM III extinction data in general. However, in June the POAM III observations of PSC are more abundant than expected from temperature thresholds. In addition the PSC occurrence based on temperature thresholds in September and October is often significantly higher than the PSC occurrence observed by POAM III, this observation probably being due to dehydration and denitrification. Use of high resolution temperatures from CHAMP GPS/RO observations provide a slightly improved relationship to the POAM III derived values. Analysis of the CHAMP temperature observations indicates that temperature perturbations associated with gravity waves may explain the enhanced PSC incidence observed in June compared to the UKMO analyses. Comparison of the UKMO analyses temperatures relative to corresponding CHAMP observations also suggests a small warm bias in the UKMO analyses during June. Examination of the longitudinal structure PSC occurrence in June 2005 also shows that regions of enhancement are associated with data near the Antarctic peninsula a known Mountain wave "hotspot". The impact of temperature perturbations causing enhanced temperature threshold crossings is shown to be particularly important early in the Antarctic winter while later in the season temperature perturbations associated with gravity waves could contribute to about 15% of the PSC observed, a value which corresponds well to several previous studies.

Conditioning geostatistical simulations of a heterogeneous paleo-fluvial bedrock aquifer using lithologs and pumping tests

NASA Astrophysics Data System (ADS)

Niazi, A.; Bentley, L. R.; Hayashi, M.

2016-12-01

Geostatistical simulations are used to construct heterogeneous aquifer models. Optimally, such simulations should be conditioned with both lithologic and hydraulic data. We introduce an approach to condition lithologic geostatistical simulations of a paleo-fluvial bedrock aquifer consisting of relatively high permeable sandstone channels embedded in relatively low permeable mudstone using hydraulic data. The hydraulic data consist of two-hour single well pumping tests extracted from the public water well database for a 250-km2 watershed in Alberta, Canada. First, lithologic models of the entire watershed are simulated and conditioned with hard lithological data using transition probability - Markov chain geostatistics (TPROGS). Then, a segment of the simulation around a pumping well is used to populate a flow model (FEFLOW) with either sand or mudstone. The values of the hydraulic conductivity and specific storage of sand and mudstone are then adjusted to minimize the difference between simulated and actual pumping test data using the parameter estimation program PEST. If the simulated pumping test data do not adequately match the measured data, the lithologic model is updated by locally deforming the lithology distribution using the probability perturbation method and the model parameters are again updated with PEST. This procedure is repeated until the simulated and measured data agree within a pre-determined tolerance. The procedure is repeated for each well that has pumping test data. The method creates a local groundwater model that honors both the lithologic model and pumping test data and provides estimates of hydraulic conductivity and specific storage. Eventually, the simulations will be integrated into a watershed-scale groundwater model.

Multiple Revolution Solutions for the Perturbed Lambert Problem using the Method of Particular Solutions and Picard Iteration

NASA Astrophysics Data System (ADS)

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

2017-12-01

We present a new method for solving the multiple revolution perturbed Lambert problem using the method of particular solutions and modified Chebyshev-Picard iteration. The method of particular solutions differs from the well-known Newton-shooting method in that integration of the state transition matrix (36 additional differential equations) is not required, and instead it makes use of a reference trajectory and a set of n particular solutions. Any numerical integrator can be used for solving two-point boundary problems with the method of particular solutions, however we show that using modified Chebyshev-Picard iteration affords an avenue for increased efficiency that is not available with other step-by-step integrators. We take advantage of the path approximation nature of modified Chebyshev-Picard iteration (nodes iteratively converge to fixed points in space) and utilize a variable fidelity force model for propagating the reference trajectory. Remarkably, we demonstrate that computing the particular solutions with only low fidelity function evaluations greatly increases the efficiency of the algorithm while maintaining machine precision accuracy. Our study reveals that solving the perturbed Lambert's problem using the method of particular solutions with modified Chebyshev-Picard iteration is about an order of magnitude faster compared with the classical shooting method and a tenth-twelfth order Runge-Kutta integrator. It is well known that the solution to Lambert's problem over multiple revolutions is not unique and to ensure that all possible solutions are considered we make use of a reliable preexisting Keplerian Lambert solver to warm start our perturbed algorithm.

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.

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.

Perturbation-free measurement of in situ di-nitrogen emissions from denitrification in nitrate-rich aquatic ecosystems.

PubMed

Qin, Shuping; Clough, Timothy; Luo, Jiafa; Wrage-Mönnig, Nicole; Oenema, Oene; Zhang, Yuming; Hu, Chunsheng

2017-02-01

Increased production of reactive nitrogen (Nr) from atmospheric di-nitrogen (N 2 ) has greatly contributed to increased food production. However, enriching the biosphere with Nr has also caused a series of negative effects on global ecosystems, especially aquatic ecosystems. The main pathway converting Nr back into the atmospheric N 2 pool is the last step in the denitrification process. Despite several attempts, there is still a need for perturbation-free methods for measuring in situ N 2 fluxes from denitrification in aquatic ecosystems at the field scale. Such a method is needed to comprehensively quantify the N 2 fluxes from aquatic ecosystems. Here we observed linear relationships between the δ 15 N-N 2 O signatures and the logarithmically transformed N 2 O/(N 2 +N 2 O) emission ratios. Through independent measurements, we verified that the perturbation-free N 2 flux from denitrification in nitrate-rich aquatic ecosystems can be inferred from these linear relationships. Our method allowed the determination of field-scale in situ N 2 fluxes from nitrate-rich aquatic ecosystems both with and without overlaying water. The perturbation-free in situ N 2 fluxes observed by the new method were almost one order of magnitude higher than those by the sediment core method. The ability of aquatic ecosystems to remove Nr may previously have been severely underestimated. Copyright © 2016 Elsevier Ltd. All rights reserved.

Stability of Alfvén wings in uniform plasmas

NASA Astrophysics Data System (ADS)

Sallago, P. A.; Platzeck, A. M.

2007-12-01

A conducting source moving uniformly through a magnetized plasma generates, among a variety of perturbations, Alfvén waves. An interesting characteristic of Alfvén waves is that they can build up structures in the plasma called Alfvén wings. These wings have been detected and measured in many solar system bodies, and their existence has also been theoretically proven. However, their stability remains to be studied. The aim of this paper is to analyze the stability of an Alfvén wing developed in a uniform background field, in the presence of an incompressible perturbation that has the same symmetry as the Alfvén wing, in the magnetohydrodynamic approximation. The study of the stability of a magnetohydrodynamic system is often performed by linearizing the equations and using either the normal modes method or the energy method. In spite of being applicable for many problems, both methods become algebraically complicated if the structure under analysis is a highly non-uniform one. Palumbo has developed an analytical method for the study of the stability of static structures with a symmetry in magnetized plasmas, in the presence of incompressible perturbations with the same symmetry as the structure (Palumbo 1998 Thesis, Universidad de Firenze, Italia). In the present paper we extend this method for Alfvén wings that are stationary structures, and conclude that in the presence of this kind of perturbation they are stable.

Significance of stress transfer in time-dependent earthquake probability calculations

USGS Publications Warehouse

Parsons, T.

2005-01-01

A sudden change in stress is seen to modify earthquake rates, but should it also revise earthquake probability? Data used to derive input parameters permits an array of forecasts; so how large a static stress change is require to cause a statistically significant earthquake probability change? To answer that question, effects of parameter and philosophical choices are examined through all phases of sample calculations, Drawing at random from distributions of recurrence-aperiodicity pairs identifies many that recreate long paleoseismic and historic earthquake catalogs. Probability density funtions built from the recurrence-aperiodicity pairs give the range of possible earthquake forecasts under a point process renewal model. Consequences of choices made in stress transfer calculations, such as different slip models, fault rake, dip, and friction are, tracked. For interactions among large faults, calculated peak stress changes may be localized, with most of the receiving fault area changed less than the mean. Thus, to avoid overstating probability change on segments, stress change values should be drawn from a distribution reflecting the spatial pattern rather than using the segment mean. Disparity resulting from interaction probability methodology is also examined. For a fault with a well-understood earthquake history, a minimum stress change to stressing rate ratio of 10:1 to 20:1 is required to significantly skew probabilities with >80-85% confidence. That ratio must be closer to 50:1 to exceed 90-95% confidence levels. Thus revision to earthquake probability is achievable when a perturbing event is very close to the fault in question or the tectonic stressing rate is low.

A numerical assessment of rough surface scattering theories. I - Horizontal polarization. II - Vertical polarization

NASA Technical Reports Server (NTRS)

Rodriguez, Ernesto; Kim, Yunjin; Durden, Stephen L.

1992-01-01

A numerical evaluation is presented of the regime of validity for various rough surface scattering theories against numerical results obtained by employing the method of moments. The contribution of each theory is considered up to second order in the perturbation expansion for the surface current. Considering both vertical and horizontal polarizations, the unified perturbation method provides best results among all theories weighed.

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

PubMed

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

2017-02-14

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

Stellarator Coil Design and Plasma Sensitivity

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

Long-Poe Ku and Allen H. Boozer

2010-11-03

The rich information contained in the plasma response to external magnetic perturbations can be used to help design stellarator coils more effectively. We demonstrate the feasibility by first devel- oping a simple, direct method to study perturbations in stellarators that do not break stellarator symmetry and periodicity. The method applies a small perturbation to the plasma boundary and evaluates the resulting perturbed free-boundary equilibrium to build up a sensitivity matrix for the important physics attributes of the underlying configuration. Using this sensitivity information, design methods for better stellarator coils are then developed. The procedure and a proof-of-principle application are givenmore » that (1) determine the spatial distributions of external normal magnetic field at the location of the unperturbed plasma boundary to which the plasma properties are most sen- sitive, (2) determine the distributions of external normal magnetic field that can be produced most efficiently by distant coils, (3) choose the ratios of the magnitudes of the the efficiently produced magnetic distributions so the sensitive plasma properties can be controlled. Using these methods, sets of modular coils are found for the National Compact Stellarator Experiment (NCSX) that are either smoother or can be located much farther from the plasma boundary than those of the present design.« less

Statistical State Dynamics Based Study of the Role of Nonlinearity in the Maintenance of Turbulence in Couette Flow

NASA Astrophysics Data System (ADS)

Farrell, Brian; Ioannou, Petros; Nikolaidis, Marios-Andreas

2017-11-01

While linear non-normality underlies the mechanism of energy transfer from the externally driven flow to the perturbation field, nonlinearity is also known to play an essential role in sustaining turbulence. We report a study based on the statistical state dynamics of Couette flow turbulence with the goal of better understanding the role of nonlinearity in sustaining turbulence. The statistical state dynamics implementations used are ensemble closures at second order in a cumulant expansion of the Navier-Stokes equations in which the averaging operator is the streamwise mean. Two fundamentally non-normal mechanisms potentially contributing to maintaining the second cumulant are identified. These are essentially parametric perturbation growth arising from interaction of the perturbations with the fluctuating mean flow and transient growth of perturbations arising from nonlinear interaction between components of the perturbation field. By the method of selectively including these mechanisms parametric growth is found to maintain the perturbation field in the turbulent state while the more commonly invoked mechanism associated with transient growth of perturbations arising from scattering by nonlinear interaction is found to suppress perturbation variance. Funded by ERC Coturb Madrid Summer Program and NSF AGS-1246929.

A general theory of linear cosmological perturbations: bimetric theories

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

Lagos, Macarena; Ferreira, Pedro G., E-mail: m.lagos13@imperial.ac.uk, E-mail: p.ferreira1@physics.ox.ac.uk

2017-01-01

We implement the method developed in [1] to construct the most general parametrised action for linear cosmological perturbations of bimetric theories of gravity. Specifically, we consider perturbations around a homogeneous and isotropic background, and identify the complete form of the action invariant under diffeomorphism transformations, as well as the number of free parameters characterising this cosmological class of theories. We discuss, in detail, the case without derivative interactions, and compare our results with those found in massive bigravity.

Desynchronization of stochastically synchronized chemical oscillators

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

Snari, Razan; Tinsley, Mark R., E-mail: mark.tinsley@mail.wvu.edu, E-mail: kshowalt@wvu.edu; Faramarzi, Sadegh

Experimental and theoretical studies are presented on the design of perturbations that enhance desynchronization in populations of oscillators that are synchronized by periodic entrainment. A phase reduction approach is used to determine optimal perturbation timing based upon experimentally measured phase response curves. The effectiveness of the perturbation waveforms is tested experimentally in populations of periodically and stochastically synchronized chemical oscillators. The relevance of the approach to therapeutic methods for disrupting phase coherence in groups of stochastically synchronized neuronal oscillators is discussed.

Creation of a magnetic barrier at a noble q close to physical midpoint between two resonant surfaces in the ASDEX UG tokamak

NASA Astrophysics Data System (ADS)

Vazquez, Justin; Ali, Halima; Punjabi, Alkesh

2009-11-01

Ciraolo, Vittot and Chandre method of building invariant manifolds inside chaos in Hamiltonian systems [Ali H. and Punjabi A, Plasma Phys. Control. Fusion, 49, 1565--1582 (2007)] is used in the ASDEX UG tokamak. In this method, a second order perturbation is added to the perturbed Hamiltonian [op cit]. It creates an invariant torus inside the chaos, and reduces the plasma transport. The perturbation that is added to the equilibrium Hamiltonian is at least an order of magnitude smaller than the perturbation that causes chaos. This additional term has a finite, limited number of Fourier modes. Resonant magnetic perturbations (m,n) = (3,2)+(4,3) are added to the field line Hamiltonian for the ASDEX UG. An area-preserving map for the field line trajectories in the ASDEX UG is used. The common amplitude δ of these modes that gives complete chaos between the resonant surfaces ψ43 and ψ32 is determined. A magnetic barrier is built at a surface with noble q that is very nearly equals to the q at the physical midpoint between the two resonant surfaces. The maximum amplitude of magnetic perturbation for which this barrier can be sustained is determined. This work is supported by US Department of Energy grants DE-FG02-07ER54937, DE-FG02-01ER54624 and DE-FG02-04ER54793.

Asteroid mass estimation using Markov-chain Monte Carlo

NASA Astrophysics Data System (ADS)

Siltala, Lauri; Granvik, Mikael

2017-11-01

Estimates for asteroid masses are based on their gravitational perturbations on the orbits of other objects such as Mars, spacecraft, or other asteroids and/or their satellites. In the case of asteroid-asteroid perturbations, this leads to an inverse problem in at least 13 dimensions where the aim is to derive the mass of the perturbing asteroid(s) and six orbital elements for both the perturbing asteroid(s) and the test asteroid(s) based on astrometric observations. We have developed and implemented three different mass estimation algorithms utilizing asteroid-asteroid perturbations: the very rough 'marching' approximation, in which the asteroids' orbital elements are not fitted, thereby reducing the problem to a one-dimensional estimation of the mass, an implementation of the Nelder-Mead simplex method, and most significantly, a Markov-chain Monte Carlo (MCMC) approach. We describe each of these algorithms with particular focus on the MCMC algorithm, and present example results using both synthetic and real data. Our results agree with the published mass estimates, but suggest that the published uncertainties may be misleading as a consequence of using linearized mass-estimation methods. Finally, we discuss remaining challenges with the algorithms as well as future plans.

Automatic Screening for Perturbations in Boolean Networks.

PubMed

Schwab, Julian D; Kestler, Hans A

2018-01-01

A common approach to address biological questions in systems biology is to simulate regulatory mechanisms using dynamic models. Among others, Boolean networks can be used to model the dynamics of regulatory processes in biology. Boolean network models allow simulating the qualitative behavior of the modeled processes. A central objective in the simulation of Boolean networks is the computation of their long-term behavior-so-called attractors. These attractors are of special interest as they can often be linked to biologically relevant behaviors. Changing internal and external conditions can influence the long-term behavior of the Boolean network model. Perturbation of a Boolean network by stripping a component of the system or simulating a surplus of another element can lead to different attractors. Apparently, the number of possible perturbations and combinations of perturbations increases exponentially with the size of the network. Manually screening a set of possible components for combinations that have a desired effect on the long-term behavior can be very time consuming if not impossible. We developed a method to automatically screen for perturbations that lead to a user-specified change in the network's functioning. This method is implemented in the visual simulation framework ViSiBool utilizing satisfiability (SAT) solvers for fast exhaustive attractor search.

Permeability Sensitivity Functions and Rapid Simulation of Hydraulic-Testing Measurements Using Perturbation Theory

NASA Astrophysics Data System (ADS)

Escobar Gómez, J. D.; Torres-Verdín, C.

2018-03-01

Single-well pressure-diffusion simulators enable improved quantitative understanding of hydraulic-testing measurements in the presence of arbitrary spatial variations of rock properties. Simulators of this type implement robust numerical algorithms which are often computationally expensive, thereby making the solution of the forward modeling problem onerous and inefficient. We introduce a time-domain perturbation theory for anisotropic permeable media to efficiently and accurately approximate the transient pressure response of spatially complex aquifers. Although theoretically valid for any spatially dependent rock/fluid property, our single-phase flow study emphasizes arbitrary spatial variations of permeability and anisotropy, which constitute key objectives of hydraulic-testing operations. Contrary to time-honored techniques, the perturbation method invokes pressure-flow deconvolution to compute the background medium's permeability sensitivity function (PSF) with a single numerical simulation run. Subsequently, the first-order term of the perturbed solution is obtained by solving an integral equation that weighs the spatial variations of permeability with the spatial-dependent and time-dependent PSF. Finally, discrete convolution transforms the constant-flow approximation to arbitrary multirate conditions. Multidimensional numerical simulation studies for a wide range of single-well field conditions indicate that perturbed solutions can be computed in less than a few CPU seconds with relative errors in pressure of <5%, corresponding to perturbations in background permeability of up to two orders of magnitude. Our work confirms that the proposed joint perturbation-convolution (JPC) method is an efficient alternative to analytical and numerical solutions for accurate modeling of pressure-diffusion phenomena induced by Neumann or Dirichlet boundary conditions.

A Cascaded Approach for Correcting Ionospheric Contamination with Large Amplitude in HF Skywave Radars

PubMed Central

Wei, Yinsheng; Guo, Rujiang; Xu, Rongqing; Tang, Xiudong

2014-01-01

Ionospheric phase perturbation with large amplitude causes broadening sea clutter's Bragg peaks to overlap each other; the performance of traditional decontamination methods about filtering Bragg peak is poor, which greatly limits the detection performance of HF skywave radars. In view of the ionospheric phase perturbation with large amplitude, this paper proposes a cascaded approach based on improved S-method to correct the ionospheric phase contamination. This approach consists of two correction steps. At the first step, a time-frequency distribution method based on improved S-method is adopted and an optimal detection method is designed to obtain a coarse ionospheric modulation estimation from the time-frequency distribution. At the second correction step, based on the phase gradient algorithm (PGA) is exploited to eliminate the residual contamination. Finally, use the measured data to verify the effectiveness of the method. Simulation results show the time-frequency resolution of this method is high and is not affected by the interference of the cross term; ionospheric phase perturbation with large amplitude can be corrected in low signal-to-noise (SNR); such a cascade correction method has a good effect. PMID:24578656

Computing induced velocity perturbations due to a helicopter fuselage in a free stream

NASA Technical Reports Server (NTRS)

Berry, John D.; Althoff, Susan L.

1989-01-01

The velocity field of a representative helicopter fuselage in a free stream is computed. Perturbation velocities due to the fuselage are computed in a plan above the location of the helicopter rotor (rotor removed). The velocity perturbations computed by a source-panel model of the fuselage are compared with experimental measurements taken with a laser velocimeter. Three paneled fuselage models are studied: fuselage shape, fuselage shape with hub shape, and a body of revolution. The velocity perturbations computed for both fuselage shape models agree well with the measured velocity field except in the close vicinity of the rotor hub. In the hub region, without knowing the extent of separation, modeling of the effective source shape is difficult. The effects of the fuselage perturbations are not well-predicted with a simplified ellipsoid fuselage. The velocity perturbations due to the fuselage at the plane of the measurements have magnitudes of less than 8 percent of free-stream velocity. The velocity perturbations computed by the panel method are tabulated for the same locations at which previously reported rotor-inflow velocity measurements were made.

Transient statistics in stabilizing periodic orbits

NASA Astrophysics Data System (ADS)

Meucci, R.; Gadomski, W.; Ciofini, M.; Arecchi, F. T.

1995-11-01

The statistics of chaotic and periodic transient time intervals preceding the stabilization of a given periodic orbit have been experimentally studied in a CO2 laser with modulated losses, subjected to a small subharmonic perturbation. As predicted by the theory, an exponential tail has been found in the probability distribution of chaotic transients. Furthermore, a fine periodic structure in the distributions of the periodic transients, resulting from the interaction of the control signal and the local structure of the chaotic attractor, has been revealed.

Mass extinctions and missing matter

NASA Technical Reports Server (NTRS)

Stothers, R. B.

1984-01-01

The possible influence of 'invisible matter' on the solar system's comet halo, and therefore on quasi-periodic cometary bombardment of the earth and consequent mass extinctions, is briefly addressed. Invisible matter consisting of small or cold interstellar molecular clouds could significantly modulate the comet background flux, while invisible matter consisting of a large population of old, dead stars with a relatively small galactic concentration probably could not. It is also shown that the downward force exerted by the Galaxy will perturb the halo, but will not produce any periodicity.

Germanium-Source Tunnel Field Effect Transistors for Ultra-Low Power Digital Logic

DTIC Science & Technology

2012-05-10

carrier injection via band-to-band tunneling (BTBT) and the absence of thermal (kT) dependence allows for the subthreshold swing to be steeper than... tunneling probability was derived by Kane using time- dependent perturbation theory and Fermi’s Golden Rule [8-9]. This section will instead employ a...be based on tunneling across a reverse- biased p-n junction as shown in Fig. 2.2. In order to obtain a closed form solution of the BTBT

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 use of atmospheric measurements to constrain model predictions of ozone change from chlorine perturbations

NASA Technical Reports Server (NTRS)

Douglass, Anne R.; Stolarski, Richard S.

1987-01-01

Atmospheric photochemistry models have been used to predict the sensitivity of the ozone layer to various perturbations. These same models also predict concentrations of chemical species in the present day atmosphere which can be compared to observations. Model results for both present day values and sensitivity to perturbation depend upon input data for reaction rates, photodissociation rates, and boundary conditions. A method of combining the results of a Monte Carlo uncertainty analysis with the existing set of present atmospheric species measurements is developed. The method is used to examine the range of values for the sensitivity of ozone to chlorine perturbations that is possible within the currently accepted ranges for input data. It is found that model runs which predict ozone column losses much greater than 10 percent as a result of present fluorocarbon fluxes produce concentrations and column amounts in the present atmosphere which are inconsistent with the measurements for ClO, HCl, NO, NO2, and HNO3.

Geometric Integration of Weakly Dissipative Systems

NASA Astrophysics Data System (ADS)

Modin, K.; Führer, C.; Soöderlind, G.

2009-09-01

Some problems in mechanics, e.g. in bearing simulation, contain subsystems that are conservative as well as weakly dissipative subsystems. Our experience is that geometric integration methods are often superior for such systems, as long as the dissipation is weak. Here we develop adaptive methods for dissipative perturbations of Hamiltonian systems. The methods are "geometric" in the sense that the form of the dissipative perturbation is preserved. The methods are linearly explicit, i.e., they require the solution of a linear subsystem. We sketch an analysis in terms of backward error analysis and numerical comparisons with a conventional RK method of the same order is given.

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

PubMed

Imperatore, Pasquale; Iodice, Antonio; Riccio, Daniele

2017-12-27

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

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

PubMed Central

2017-01-01

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

Potential Energy Surface of the Chromium Dimer Re-re-revisited with Multiconfigurational Perturbation Theory.

PubMed

Vancoillie, Steven; Malmqvist, Per Åke; Veryazov, Valera

2016-04-12

The chromium dimer has long been a benchmark molecule to evaluate the performance of different computational methods ranging from density functional theory to wave function methods. Among the latter, multiconfigurational perturbation theory was shown to be able to reproduce the potential energy surface of the chromium dimer accurately. However, for modest active space sizes, it was later shown that different definitions of the zeroth-order Hamiltonian have a large impact on the results. In this work, we revisit the system for the third time with multiconfigurational perturbation theory, now in order to increase the active space of the reference wave function. This reduces the impact of the choice of zeroth-order Hamiltonian and improves the shape of the potential energy surface significantly. We conclude by comparing our results of the dissocation energy and vibrational spectrum to those obtained from several highly accurate multiconfigurational methods and experiment. For a meaningful comparison, we used the extrapolation to the complete basis set for all methods involved.

Investigation of the Wave Propagation of Vector Modes of Light in a Spherically Symmetric Refractive Index Profile

NASA Astrophysics Data System (ADS)

Pozderac, Preston; Leary, Cody

We investigated the solutions to the Helmholtz equation in the case of a spherically symmetric refractive index using three different methods. The first method involves solving the Helmholtz equation for a step index profile and applying further constraints contained in Maxwell's equations. Utilizing these equations, we can simultaneously solve for the electric and magnetic fields as well as the allowed energies of photons propagating in this system. The second method applies a perturbative correction to these energies, which surfaces when deriving a Helmholtz type equation in a medium with an inhomogeneous refractive index. Applying first order perturbation theory, we examine how the correction term affects the energy of the photon. In the third method, we investigate the effects of the above perturbation upon solutions to the scalar Helmholtz equation, which are separable with respect to its polarization and spatial degrees of freedom. This work provides insights into the vector field structure of a photon guided by a glass microsphere.

Nonlinear Waves, Dynamical Systems and Other Applied Mathematics Programs

DTIC Science & Technology

1991-10-04

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

Perturbed dark and singular optical solitons in polarization preserving fibers by modified simple equation method

NASA Astrophysics Data System (ADS)

Yaşar, Emrullah; Yıldırım, Yakup; Zhou, Qin; Moshokoa, Seithuti P.; Ullah, Malik Zaka; Triki, Houria; Biswas, Anjan; Belic, Milivoj

2017-11-01

This paper obtains optical soliton solution to perturbed nonlinear Schrödinger's equation by modified simple equation method. There are four types of nonlinear fibers studied in this paper. They are Anti-cubic law, Quadratic-cubic law, Cubic-quintic-septic law and Triple-power law. Dark and singular soliton solutions are derived. Additional solutions such as singular periodic solutions also fall out of the integration scheme.

Applications of direct numerical simulation of turbulence in second order closures

NASA Technical Reports Server (NTRS)

Shih, Tsan-Hsing; Lumley, John L.

1995-01-01

This paper discusses two methods of developing models for the rapid pressure-strain correlation term in the Reynolds stress transport equation using direct numerical simulation (DNS) data. One is a perturbation about isotropic turbulence, the other is a perturbation about two-component turbulence -- an extremely anisotropic turbulence. A model based on the latter method is proposed and is found to be very promising when compared with DNS data and other models.

Bifurcation of small limit cycles in cubic integrable systems using higher-order analysis

NASA Astrophysics Data System (ADS)

Tian, Yun; Yu, Pei

2018-05-01

In this paper, we present a method of higher-order analysis on bifurcation of small limit cycles around an elementary center of integrable systems under perturbations. This method is equivalent to higher-order Melinikov function approach used for studying bifurcation of limit cycles around a center but simpler. Attention is focused on planar cubic polynomial systems and particularly it is shown that the system studied by Żoła¸dek (1995) [24] can indeed have eleven limit cycles under perturbations at least up to 7th order. Moreover, the pattern of numbers of limit cycles produced near the center is discussed up to 39th-order perturbations, and no more than eleven limit cycles are found.

High-fidelity cluster state generation for ultracold atoms in an optical lattice.

PubMed

Inaba, Kensuke; Tokunaga, Yuuki; Tamaki, Kiyoshi; Igeta, Kazuhiro; Yamashita, Makoto

2014-03-21

We propose a method for generating high-fidelity multipartite spin entanglement of ultracold atoms in an optical lattice in a short operation time with a scalable manner, which is suitable for measurement-based quantum computation. To perform the desired operations based on the perturbative spin-spin interactions, we propose to actively utilize the extra degrees of freedom (DOFs) usually neglected in the perturbative treatment but included in the Hubbard Hamiltonian of atoms, such as, (pseudo-)charge and orbital DOFs. Our method simultaneously achieves high fidelity, short operation time, and scalability by overcoming the following fundamental problem: enhancing the interaction strength for shortening the operation time breaks the perturbative condition of the interaction and inevitably induces unwanted correlations among the spin and extra DOFs.

Constraining compensated isocurvature perturbations using the CMB

NASA Astrophysics Data System (ADS)

Smith, Tristan L.; Rhiannon Smith, Kyle Yee, Julian Munoz, Daniel Grin

2017-01-01

Compensated isocurvature perturbations (CIPs) are variations in the cosmic baryon fraction which leave the total non-relativistic matter (and radiation) density unchanged. They are predicted by models of inflation which involve more than one scalar field, such as the curvaton scenario. At linear order, they leave the CMB two-point correlation function nearly unchanged: this is why existing constraints to CIPs are so much more permissive than constraints to typical isocurvature perturbations. Recent work articulated an efficient way to calculate the second order CIP effects on the CMB two-point correlation. We have implemented this method in order to explore constraints to the CIP amplitude using current Planck temperature and polarization data. In addition, we have computed the contribution of CIPs to the CMB lensing estimator which provides us with a novel method to use CMB data to place constraints on CIPs. We find that Planck data places a constraint to the CIP amplitude which is competitive with other methods.

Linear perturbations of a Schwarzschild blackhole by thin disc - convergence

NASA Astrophysics Data System (ADS)

Čížek, P.; Semerák, O.

2012-07-01

In order to find the perturbation of a Schwarzschild space-time due to a rotating thin disc, we try to adjust the method used by [4] in the case of perturbation by a one-dimensional ring. This involves solution of stationary axisymmetric Einstein's equations in terms of spherical-harmonic expansions whose convergence however turned out questionable in numerical examples. Here we show, analytically, that the series are almost everywhere convergent, but in some regions the convergence is not absolute.

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.

Anticipatory and Compensatory Postural Adjustments in Response to External Lateral Shoulder Perturbations in Subjects with Parkinson's Disease.

PubMed

de Azevedo, Alexandre Kretzer E Castro; Claudino, Renato; Conceição, Josilene Souza; Swarowsky, Alessandra; Santos, Márcio José Dos

2016-01-01

The purpose of this study was to investigate the anticipatory (APA) and compensatory (CPA) postural adjustments in individuals with Parkinson's disease (PD) during lateral instability of posture. Twenty-six subjects (13 individuals with PD and 13 healthy matched controls) were exposed to predictable lateral postural perturbations. The electromyographic (EMG) activity of the lateral muscles and the displacement of the center of pressure (COP) were recorded during four time intervals that are typical for postural adjustments, i.e., immediately before (APA1, APA2) and after (CPA1 and CPA2) the postural disturbances. The magnitude of the activity of the lateral muscles in the group with PD was lower only during the CPA time intervals and not during the anticipatory adjustments (APAs). Despite this finding, subjects with PD exhibit smaller COP excursions before and after the disturbance, probably due to lack of flexibility and proprioceptive impairments. The results of this study suggest that postural instability in subjects with PD can be partially explained by decreased postural sway, before and after perturbations, and reduced muscular activity after body disturbances. Our findings can motivate new studies to investigate therapeutic interventions that optimize the use of postural adjustment strategies in subjects with PD.

A novel method to predict current voltage characteristics of positive corona discharges based on a perturbation technique. I. Local analysis

NASA Astrophysics Data System (ADS)

Shibata, Hisaichi; Takaki, Ryoji

2017-11-01

A novel method to compute current-voltage characteristics (CVCs) of direct current positive corona discharges is formulated based on a perturbation technique. We use linearized fluid equations coupled with the linearized Poisson's equation. Townsend relation is assumed to predict CVCs apart from the linearization point. We choose coaxial cylinders as a test problem, and we have successfully predicted parameters which can determine CVCs with arbitrary inner and outer radii. It is also confirmed that the proposed method essentially does not induce numerical instabilities.

Solving the Helmholtz equation in conformal mapped ARROW structures using homotopy perturbation method.

PubMed

Reck, Kasper; Thomsen, Erik V; Hansen, Ole

2011-01-31

The scalar wave equation, or Helmholtz equation, describes within a certain approximation the electromagnetic field distribution in a given system. In this paper we show how to solve the Helmholtz equation in complex geometries using conformal mapping and the homotopy perturbation method. The solution of the mapped Helmholtz equation is found by solving an infinite series of Poisson equations using two dimensional Fourier series. The solution is entirely based on analytical expressions and is not mesh dependent. The analytical results are compared to a numerical (finite element method) solution.

Impact Hazard Monitoring: Theory and Implementation

NASA Astrophysics Data System (ADS)

Farnocchia, Davide

2015-08-01

Impact monitoring is a crucial component of the mitigation or elimination of the hazard posed by asteroid impacts. Once an asteroid is discovered, it is important to achieve an early detection and an accurate assessment of the risk posed by future Earth encounters. Here we review the most standard impact monitoring techniques. Linear methods are the fastest approach but their applicability regime is limited because of the chaotic dynamics of near-Earth asteroids, whose orbits are often scattered by planetary encounters. Among nonlinear methods, Monte Carlo algorithms are the most reliable ones. However, the large number of near-Earth asteroids and the computational load required to detect low probability impact events make Monte Carlo approaches impractical in the framework of monitoring all near-Earth asteroids. In the last 15 years, the Line of Variations (LOV) method has been the most successful technique as it strikes a remarkable compromise between computational efficiency and the capability of detecting low probability events deep in the nonlinear regime. As a matter of fact, the LOV method is the engine of JPL’s Sentry and University of Pisa’s NEODyS, which the two fully automated impact monitoring systems that routinely search for potential impactors among known near-Earth asteroids. We also present some more recent techniques developed to deal with the new challenges arising in the impact hazard assessment problem. In particular, we describe how to use keyhole maps to go beyond strongly scattering encounters and push forward in time the impact prediction horizon. In these cases asteroids usually have a very well constrained orbit and we often need to account for the action of nongravitational perturbations, especially the Yarkovsky effect. Finally, we discuss the short-term hazard assessment problem for newly discovered asteroids, when only a short observed arc is available. The limited amount of observational data generally leads to severe degeneracies in the orbit estimation process. We overcome these degeneracies by employing ranging techniques, which scan the poorly constrained space of topocentric range and range rate.

Emulation of simulations of atmospheric dispersion at Fukushima for Sobol' sensitivity analysis

NASA Astrophysics Data System (ADS)

Girard, Sylvain; Korsakissok, Irène; Mallet, Vivien

2015-04-01

Polyphemus/Polair3D, from which derives IRSN's operational model ldX, was used to simulate the atmospheric dispersion at the Japan scale of radionuclides after the Fukushima disaster. A previous study with the screening method of Morris had shown that - The sensitivities depend a lot on the considered output; - Only a few of the inputs are non-influential on all considered outputs; - Most influential inputs have either non-linear effects or are interacting. These preliminary results called for a more detailed sensitivity analysis, especially regarding the characterization of interactions. The method of Sobol' allows for a precise evaluation of interactions but requires large simulation samples. Gaussian process emulators for each considered outputs were built in order to relieve this computational burden. Globally aggregated outputs proved to be easy to emulate with high accuracy, and associated Sobol' indices are in broad agreement with previous results obtained with the Morris method. More localized outputs, such as temporal averages of gamma dose rates at measurement stations, resulted in lesser emulator performances: tests simulations could not satisfactorily be reproduced by some emulators. These outputs are of special interest because they can be compared to available observations, for instance for calibration purpose. A thorough inspection of prediction residuals hinted that the model response to wind perturbations often behaved in very distinct regimes relatively to some thresholds. Complementing the initial sample with wind perturbations set to the extreme values allowed for sensible improvement of some of the emulators while other remained too unreliable to be used in a sensitivity analysis. Adaptive sampling or regime-wise emulation could be tried to circumvent this issue. Sobol' indices for local outputs revealed interesting patterns, mostly dominated by the winds, with very high interactions. The emulators will be useful for subsequent studies. Indeed, our goal is to characterize the model output uncertainty but too little information is available about input uncertainties. Hence, calibration of the input distributions with observation and a Bayesian approach seem necessary. This would probably involve methods such as MCMC which would be intractable without emulators.

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

NASA Astrophysics Data System (ADS)

Matsubara, Takahiko

2003-02-01

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

More evidence for a one-to-one correlation between Sprites and Early VLF perturbations

NASA Astrophysics Data System (ADS)

Haldoupis, C.; Amvrosiadi, N.; Cotts, B. R. T.; van der Velde, O. A.; Chanrion, O.; Neubert, T.

2010-07-01

Past studies have shown a correlation between sprites and early VLF perturbations, but the reported correlation varies widely from ˜50% to 100%. The present study resolves these large discrepancies by analyzing several case studies of sprite and narrowband VLF observations, in which multiple transmitter-receiver VLF pairs with great circle paths (GCPs) passing near a sprite-producing thunderstorm were available. In this setup, the multiple paths act in a complementary way that makes the detection of early VLF perturbations much more probable compared to a single VLF path that can miss several of them, a fact that was overlooked in past studies. The evidence shows that visible sprite occurrences are accompanied by early VLF perturbations in a one-to-one correspondence. This implies that the sprite generation mechanism may cause also sub-ionospheric conductivity disturbances that produce early VLF events. However, the one-to-one visible sprite to early VLF event correspondence, if viewed conversely, appears not to be always reciprocal. This is because the number of early events detected in some case studies was considerably larger than the number of visible sprites. Since the great majority of the early events not accompanied by visible sprites appeared to be caused by positive cloud to ground (+CG) lightning discharges, it is possible that sprites or sprite halos were concurrently present in these events as well but were missed by the sprite-watch camera detection system. In order for this option to be resolved we need more studies using highly sensitive optical systems capable of detecting weaker sprites, sprite halos and elves.

Stress concentrations at structural discontinuities in active fault zones in the western United States: Implications for permeability and fluid flow in geothermal fields

USGS Publications Warehouse

Siler, Drew; Hinz, Nicholas H.; Faulds, James E.

2018-01-01

Slip can induce concentration of stresses at discontinuities along fault systems. These structural discontinuities, i.e., fault terminations, fault step-overs, intersections, bends, and other fault interaction areas, are known to host fluid flow in ore deposition systems, oil and gas reservoirs, and geothermal systems. We modeled stress transfer associated with slip on faults with Holocene-to-historic slip histories at the Salt Wells and Bradys geothermal systems in western Nevada, United States. Results show discrete locations of stress perturbation within discontinuities along these fault systems. Well field data, surface geothermal manifestations, and subsurface temperature data, each a proxy for modern fluid circulation in the fields, indicate that geothermal fluid flow is focused in these same areas where stresses are most highly perturbed. These results suggest that submeter- to meter-scale slip on these fault systems generates stress perturbations that are sufficiently large to promote slip on an array of secondary structures spanning the footprint of the modern geothermal activity. Slip on these secondary faults and fractures generates permeability through kinematic deformation and allows for transmission of fluids. Still, mineralization is expected to seal permeability along faults and fractures over time scales that are generally shorter than either earthquake recurrence intervals or the estimated life span of geothermal fields. This suggests that though stress perturbations resulting from fault slip are broadly important for defining the location and spatial extent of enhanced permeability at structural discontinuities, continual generation and maintenance of flow conduits throughout these areas are probably dependent on the deformation mechanism(s) affecting individual structures.

Aspects of perturbation theory in quantum mechanics: The BenderWuMATHEMATICA® package

NASA Astrophysics Data System (ADS)

Sulejmanpasic, Tin; Ünsal, Mithat

2018-07-01

We discuss a general setup which allows the study of the perturbation theory of an arbitrary, locally harmonic 1D quantum mechanical potential as well as its multi-variable (many-body) generalization. The latter may form a prototype for regularized quantum field theory. We first generalize the method of Bender-Wu,and derive exact recursion relations which allow the determination of the perturbative wave-function and energy corrections to an arbitrary order, at least in principle. For 1D systems, we implement these equations in an easy to use MATHEMATICA® package we call BenderWu. Our package enables quick home-computer computation of high orders of perturbation theory (about 100 orders in 10-30 s, and 250 orders in 1-2 h) and enables practical study of a large class of problems in Quantum Mechanics. We have two hopes concerning the BenderWu package. One is that due to resurgence, large amount of non-perturbative information, such as non-perturbative energies and wave-functions (e.g. WKB wave functions), can in principle be extracted from the perturbative data. We also hope that the package may be used as a teaching tool, providing an effective bridge between perturbation theory and non-perturbative physics in textbooks. Finally, we show that for the multi-variable case, the recursion relation acquires a geometric character, and has a structure which allows parallelization to computer clusters.

A New Homotopy Perturbation Scheme for Solving Singular Boundary Value Problems Arising in Various Physical Models

NASA Astrophysics Data System (ADS)

Roul, Pradip; Warbhe, Ujwal

2017-08-01

The classical homotopy perturbation method proposed by J. H. He, Comput. Methods Appl. Mech. Eng. 178, 257 (1999) is useful for obtaining the approximate solutions for a wide class of nonlinear problems in terms of series with easily calculable components. However, in some cases, it has been found that this method results in slowly convergent series. To overcome the shortcoming, we present a new reliable algorithm called the domain decomposition homotopy perturbation method (DDHPM) to solve a class of singular two-point boundary value problems with Neumann and Robin-type boundary conditions arising in various physical models. Five numerical examples are presented to demonstrate the accuracy and applicability of our method, including thermal explosion, oxygen-diffusion in a spherical cell and heat conduction through a solid with heat generation. A comparison is made between the proposed technique and other existing seminumerical or numerical techniques. Numerical results reveal that only two or three iterations lead to high accuracy of the solution and this newly improved technique introduces a powerful improvement for solving nonlinear singular boundary value problems (SBVPs).

A Simple Method for Deriving the Confidence Regions for the Penalized Cox's Model via the Minimand Perturbation.

PubMed

Lin, Chen-Yen; Halabi, Susan

2017-01-01

We propose a minimand perturbation method to derive the confidence regions for the regularized estimators for the Cox's proportional hazards model. Although the regularized estimation procedure produces a more stable point estimate, it remains challenging to provide an interval estimator or an analytic variance estimator for the associated point estimate. Based on the sandwich formula, the current variance estimator provides a simple approximation, but its finite sample performance is not entirely satisfactory. Besides, the sandwich formula can only provide variance estimates for the non-zero coefficients. In this article, we present a generic description for the perturbation method and then introduce a computation algorithm using the adaptive least absolute shrinkage and selection operator (LASSO) penalty. Through simulation studies, we demonstrate that our method can better approximate the limiting distribution of the adaptive LASSO estimator and produces more accurate inference compared with the sandwich formula. The simulation results also indicate the possibility of extending the applications to the adaptive elastic-net penalty. We further demonstrate our method using data from a phase III clinical trial in prostate cancer.

THE AXISYMMETRIC FREE-CONVECTION HEAT TRANSFER ALONG A VERTICAL THIN CYLINDER WITH CONSTANT SURFACE TEMPERATURE

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

Viskanta, R.

1963-01-01

Laminar free-convection flow produced by a heated, vertical, circular cylinder for which the temperature at the outer surface of the cylinder is assumed to be uniform is analyzed. The solution of the boundary-layer equations was obtained by the perturbation method of Sparrow and Gregg, which is valid only for small values of the axial distance parameter xi ; and the integral method of Hama et al., for large values of the parameter xi . Heat-transfer results were calculated for Prandtl numbers (Pr) of 100, the Nusselt numbers (Nu) for the cylinder were higher than those for the flat plate, andmore » this difference increased as Pr decreased. It was also found that the perturbation method of solution of the free-convection boundary-layer equations becomes useless for small values of Pr because of the slow convergence of the series. The results obtained by the integral method were in good agreement with those calculated by the perturbation method for Pr approximately 1 and 0.1 < xi < 1 only; they deviated considerably for smaller values of xi . (auth)« less

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

Ioannisian, Ara N.; Kazarian, Narine; Millar, Alexander J.

Axion-photon conversion at dielectric interfaces, immersed in a near-homogeneous magnetic field, is the basis for the dielectric haloscope method to search for axion dark matter. In analogy to transition radiation, this process is possible because the photon wave function is modified by the dielectric layers ('Garibian wave function') and is no longer an eigenstate of momentum. A conventional first-order perturbative calculation of the transition probability between a quantized axion state and these distorted photon states provides the microwave production rate. It agrees with previous results based on solving the classical Maxwell equations for the combined system of axions and electromagneticmore » fields. We argue that in general the average photon production rate is given by our result, independently of the detailed quantum state of the axion field. Moreover, our result provides a new perspective on axion-photon conversion in dielectric haloscopes because the rate is based on an overlap integral between unperturbed axion and photon wave functions, in analogy to the usual treatment of microwave-cavity haloscopes.« less

Local fields and effective conductivity tensor of ellipsoidal particle composite with anisotropic constituents

NASA Astrophysics Data System (ADS)

Kushch, Volodymyr I.; Sevostianov, Igor; Giraud, Albert

2017-11-01

An accurate semi-analytical solution of the conductivity problem for a composite with anisotropic matrix and arbitrarily oriented anisotropic ellipsoidal inhomogeneities has been obtained. The developed approach combines the superposition principle with the multipole expansion of perturbation fields of inhomogeneities in terms of ellipsoidal harmonics and reduces the boundary value problem to an infinite system of linear algebraic equations for the induced multipole moments of inhomogeneities. A complete full-field solution is obtained for the multi-particle models comprising inhomogeneities of diverse shape, size, orientation and properties which enables an adequate account for the microstructure parameters. The solution is valid for the general-type anisotropy of constituents and arbitrary orientation of the orthotropy axes. The effective conductivity tensor of the particulate composite with anisotropic constituents is evaluated in the framework of the generalized Maxwell homogenization scheme. Application of the developed method to composites with imperfect ellipsoidal interfaces is straightforward. Their incorporation yields probably the most general model of a composite that may be considered in the framework of analytical approach.

Computation of Steady-State Probability Distributions in Stochastic Models of Cellular Networks

PubMed Central

Hallen, Mark; Li, Bochong; Tanouchi, Yu; Tan, Cheemeng; West, Mike; You, Lingchong

2011-01-01

Cellular processes are “noisy”. In each cell, concentrations of molecules are subject to random fluctuations due to the small numbers of these molecules and to environmental perturbations. While noise varies with time, it is often measured at steady state, for example by flow cytometry. When interrogating aspects of a cellular network by such steady-state measurements of network components, a key need is to develop efficient methods to simulate and compute these distributions. We describe innovations in stochastic modeling coupled with approaches to this computational challenge: first, an approach to modeling intrinsic noise via solution of the chemical master equation, and second, a convolution technique to account for contributions of extrinsic noise. We show how these techniques can be combined in a streamlined procedure for evaluation of different sources of variability in a biochemical network. Evaluation and illustrations are given in analysis of two well-characterized synthetic gene circuits, as well as a signaling network underlying the mammalian cell cycle entry. PMID:22022252

Robust parameter extraction for decision support using multimodal intensive care data

PubMed Central

Clifford, G.D.; Long, W.J.; Moody, G.B.; Szolovits, P.

2008-01-01

Digital information flow within the intensive care unit (ICU) continues to grow, with advances in technology and computational biology. Recent developments in the integration and archiving of these data have resulted in new opportunities for data analysis and clinical feedback. New problems associated with ICU databases have also arisen. ICU data are high-dimensional, often sparse, asynchronous and irregularly sampled, as well as being non-stationary, noisy and subject to frequent exogenous perturbations by clinical staff. Relationships between different physiological parameters are usually nonlinear (except within restricted ranges), and the equipment used to measure the observables is often inherently error-prone and biased. The prior probabilities associated with an individual's genetics, pre-existing conditions, lifestyle and ongoing medical treatment all affect prediction and classification accuracy. In this paper, we describe some of the key problems and associated methods that hold promise for robust parameter extraction and data fusion for use in clinical decision support in the ICU. PMID:18936019

Impact of distal mutations on the network of coupled motions correlated to hydride transfer in dihydrofolate reductase.

PubMed

Wong, Kim F; Selzer, Tzvia; Benkovic, Stephen J; Hammes-Schiffer, Sharon

2005-05-10

A comprehensive analysis of the network of coupled motions correlated to hydride transfer in dihydrofolate reductase is presented. Hybrid quantum/classical molecular dynamics simulations are combined with a rank correlation analysis method to extract thermally averaged properties that vary along the collective reaction coordinate according to a prescribed target model. Coupled motions correlated to hydride transfer are identified throughout the enzyme. Calculations for wild-type dihydrofolate reductase and a triple mutant, along with the associated single and double mutants, indicate that each enzyme system samples a unique distribution of coupled motions correlated to hydride transfer. These coupled motions provide an explanation for the experimentally measured nonadditivity effects in the hydride transfer rates for these mutants. This analysis illustrates that mutations distal to the active site can introduce nonlocal structural perturbations and significantly impact the catalytic rate by altering the conformational motions of the entire enzyme and the probability of sampling conformations conducive to the catalyzed reaction.

Global asymptotic stability of plant-seed bank models.

PubMed

Eager, Eric Alan; Rebarber, Richard; Tenhumberg, Brigitte

2014-07-01

Many plant populations have persistent seed banks, which consist of viable seeds that remain dormant in the soil for many years. Seed banks are important for plant population dynamics because they buffer against environmental perturbations and reduce the probability of extinction. Viability of the seeds in the seed bank can depend on the seed's age, hence it is important to keep track of the age distribution of seeds in the seed bank. In this paper we construct a general density-dependent plant-seed bank model where the seed bank is age-structured. We consider density dependence in both seedling establishment and seed production, since previous work has highlighted that overcrowding can suppress both of these processes. Under certain assumptions on the density dependence, we prove that there is a globally stable equilibrium population vector which is independent of the initial state. We derive an analytical formula for the equilibrium population using methods from feedback control theory. We apply these results to a model for the plant species Cirsium palustre and its seed bank.

A strategy for evaluating pathway analysis methods.

PubMed

Yu, Chenggang; Woo, Hyung Jun; Yu, Xueping; Oyama, Tatsuya; Wallqvist, Anders; Reifman, Jaques

2017-10-13

Researchers have previously developed a multitude of methods designed to identify biological pathways associated with specific clinical or experimental conditions of interest, with the aim of facilitating biological interpretation of high-throughput data. Before practically applying such pathway analysis (PA) methods, we must first evaluate their performance and reliability, using datasets where the pathways perturbed by the conditions of interest have been well characterized in advance. However, such 'ground truths' (or gold standards) are often unavailable. Furthermore, previous evaluation strategies that have focused on defining 'true answers' are unable to systematically and objectively assess PA methods under a wide range of conditions. In this work, we propose a novel strategy for evaluating PA methods independently of any gold standard, either established or assumed. The strategy involves the use of two mutually complementary metrics, recall and discrimination. Recall measures the consistency of the perturbed pathways identified by applying a particular analysis method to an original large dataset and those identified by the same method to a sub-dataset of the original dataset. In contrast, discrimination measures specificity-the degree to which the perturbed pathways identified by a particular method to a dataset from one experiment differ from those identifying by the same method to a dataset from a different experiment. We used these metrics and 24 datasets to evaluate six widely used PA methods. The results highlighted the common challenge in reliably identifying significant pathways from small datasets. Importantly, we confirmed the effectiveness of our proposed dual-metric strategy by showing that previous comparative studies corroborate the performance evaluations of the six methods obtained by our strategy. Unlike any previously proposed strategy for evaluating the performance of PA methods, our dual-metric strategy does not rely on any ground truth, either established or assumed, of the pathways perturbed by a specific clinical or experimental condition. As such, our strategy allows researchers to systematically and objectively evaluate pathway analysis methods by employing any number of datasets for a variety of conditions.

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.

Maximum Lyapunov exponents as predictors of global gait stability: a modelling approach.

PubMed

Bruijn, Sjoerd M; Bregman, Daan J J; Meijer, Onno G; Beek, Peter J; van Dieën, Jaap H

2012-05-01

To examine the stability of human walking, methods such as local dynamic stability have been adopted from dynamical systems theory. Local dynamic stability is calculated by estimating maximal finite time Lyapunov exponents (λ(S) and λ(L)), which quantify how a system responds continuously to very small (i.e. "local") perturbations. However, it is unknown if, and to what extent, these measures are correlated to global stability, defined operationally as the probability of falling. We studied whether changes in probability of falling of a simple model of human walking (a so-called dynamic walker) could be predicted from maximum finite time Lyapunov exponents. We used an extended version of the simplest walking model with arced feet and a hip spring. This allowed us to change the probability of falling of the model by changing either the foot radius, the slope at which the model walks, the stiffness of the hip spring, or a combination of these factors. Results showed that λ(S) correlated fairly well with global stability, although this relationship was dependent upon differences in the distance between initial nearest neighbours on the divergence curve. A measure independent of such changes (the log(distance between initially nearest neighbours after 50 samples)) correlated better with global stability, and, more importantly, showed a more consistent relationship across conditions. In contrast, λ(L) showed either weak correlations, or correlations opposite to expected, thus casting doubt on the use of this measure as a predictor of global gait stability. Our findings support the use of λ(S), but not of λ(L), as measure of human gait stability. Copyright © 2011 IPEM. Published by Elsevier Ltd. All rights reserved.

Instability of 2D Flows to Hydrostatic 3D Perturbations.

NASA Astrophysics Data System (ADS)

Straub, David N.

2003-01-01

Considered here is the evolution of three-dimensional perturbations to the hydrostatic equations linearized about a two-dimensional base state U. Motivated by an argument by T. Warn, this study begins with the nonrotating, unstratified case, and draws analogies between the perturbation equations and equations describing evolution of material line elements and scalar gradients embedded in the same 2D flow. When U is chaotic, both scalar gradients and line elements are characterized by rapid growth, and this leads one to suspect that the perturbations behave similarly. A generalized Okubo-Weiss parameter is proposed, and it is argued that this gives a reasonable litmus test for identifying regions where growth is most probable. Rotation modifies the generalized Okubo-Weiss parameter and tends to curb growth of the perturbation fields, as expected. It is also pointed out that, in realistic geophysical settings, the stability parameter can be suggestive of growth locally, even when a globally defined Rossby number is small.Also considered is the effect of a constant stratification. The perturbation equations can then be separated into vertical modes that have simple sinusoidal structures. The equations describing the evolution of a given mode take a form analogous to the shallow water equations, linearized about U. Numerical simulations of these, assuming a simple but chaotic prescription of U, are carried out. For sufficiently strong stratification, a balance dynamics similar to that suggested by Riley, Metcalfe, and Weissman is recovered. For a given value of the buoyancy frequency N, however, this balance breaks down at high vertical wavenumbers. For high vertical wavenumbers, the modified Okubo-Weiss parameter once again appears to give a potentially useful indication of when growth should be expected. When the Rossby number is small, this criterion predicts stability, and growth occurs only when stratification effects are comparable to or larger than rotational effects. More specifically, growth is seen when the relevant Rossby radius is comparable to or larger than the characteristic length scale of U. It is also found in this limit that approximate geostrophic adjustment occurs prior to growth.

Local indicators of geocoding accuracy (LIGA): theory and application

PubMed Central

Jacquez, Geoffrey M; Rommel, Robert

2009-01-01

Background Although sources of positional error in geographic locations (e.g. geocoding error) used for describing and modeling spatial patterns are widely acknowledged, research on how such error impacts the statistical results has been limited. In this paper we explore techniques for quantifying the perturbability of spatial weights to different specifications of positional error. Results We find that a family of curves describes the relationship between perturbability and positional error, and use these curves to evaluate sensitivity of alternative spatial weight specifications to positional error both globally (when all locations are considered simultaneously) and locally (to identify those locations that would benefit most from increased geocoding accuracy). We evaluate the approach in simulation studies, and demonstrate it using a case-control study of bladder cancer in south-eastern Michigan. Conclusion Three results are significant. First, the shape of the probability distributions of positional error (e.g. circular, elliptical, cross) has little impact on the perturbability of spatial weights, which instead depends on the mean positional error. Second, our methodology allows researchers to evaluate the sensitivity of spatial statistics to positional accuracy for specific geographies. This has substantial practical implications since it makes possible routine sensitivity analysis of spatial statistics to positional error arising in geocoded street addresses, global positioning systems, LIDAR and other geographic data. Third, those locations with high perturbability (most sensitive to positional error) and high leverage (that contribute the most to the spatial weight being considered) will benefit the most from increased positional accuracy. These are rapidly identified using a new visualization tool we call the LIGA scatterplot. Herein lies a paradox for spatial analysis: For a given level of positional error increasing sample density to more accurately follow the underlying population distribution increases perturbability and introduces error into the spatial weights matrix. In some studies positional error may not impact the statistical results, and in others it might invalidate the results. We therefore must understand the relationships between positional accuracy and the perturbability of the spatial weights in order to have confidence in a study's results. PMID:19863795

Protonation States of Homocitrate and Nearby Residues in Nitrogenase Studied by Computational Methods and Quantum Refinement.

PubMed

Cao, Lili; Caldararu, Octav; Ryde, Ulf

2017-09-07

Nitrogenase is the only enzyme that can break the triple bond in N 2 to form two molecules of ammonia. The enzyme has been thoroughly studied with both experimental and computational methods, but there is still no consensus regarding the atomic details of the reaction mechanism. In the most common form, the active site is a MoFe 7 S 9 C(homocitrate) cluster. The homocitrate ligand contains one alcohol and three carboxylate groups. In water solution, the triply deprotonated form dominates, but because the alcohol (and one of the carboxylate groups) coordinate to the Mo ion, this may change in the enzyme. We have performed a series of computational calculations with molecular dynamics (MD), quantum mechanical (QM) cluster, combined QM and molecular mechanics (QM/MM), QM/MM with Poisson-Boltzmann and surface area solvation, QM/MM thermodynamic cycle perturbations, and quantum refinement methods to settle the most probable protonation state of the homocitrate ligand in nitrogenase. The results quite conclusively point out a triply deprotonated form (net charge -3) with a proton shared between the alcohol and one of the carboxylate groups as the most stable at pH 7. Moreover, we have studied eight ionizable protein residues close to the active site with MD simulations and determined the most likely protonation states.

Active Time-Domain Reflectometry for Unattended Safeguards Systems FY15 Report

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

Tedeschi, Jonathan R.; Smith, Leon E.; Moore, David E.

2015-09-01

The International Atomic Energy Agency (IAEA) continues to expand its use of unattended measurement systems. An increasing number of systems and an expanding family of instruments create challenges in terms of deployment efficiency and the implementation of data authentication measures. In collaboration with the IAEA, tamper-indicating measures to address data-transmission authentication challenges with unattended safeguards systems are under investigation. Pacific Northwest National Laboratory (PNNL) is studying the viability of active time-domain reflectometry (TDR) along two parallel but interconnected paths: (1) swept-frequency TDR as the highly flexible, laboratory gold standard to which field-deployable options can be compared, and (2) a low-costmore » commercially available spread-spectrum TDR technology as one option for field implementation. This report describes PNNL’s FY15 progress in the viability study including: an overview of the TDR methods under investigation; description of the testing configurations and mock tampering scenarios; results from a preliminary sensitivity comparison of the two TDR methods; demonstration of a quantitative metric for estimating field performance that acknowledges the need for high detection probability while minimizing false alarms. FY15 progress reported here sets the stage for a rigorous comparison of the candidate TDR methods, over a range of deployment scenarios and perturbing effects typical of IAEA unattended monitoring systems.« less

Probabilistic homogenization of random composite with ellipsoidal particle reinforcement by the iterative stochastic finite element method

NASA Astrophysics Data System (ADS)

Sokołowski, Damian; Kamiński, Marcin

2018-01-01

This study proposes a framework for determination of basic probabilistic characteristics of the orthotropic homogenized elastic properties of the periodic composite reinforced with ellipsoidal particles and a high stiffness contrast between the reinforcement and the matrix. Homogenization problem, solved by the Iterative Stochastic Finite Element Method (ISFEM) is implemented according to the stochastic perturbation, Monte Carlo simulation and semi-analytical techniques with the use of cubic Representative Volume Element (RVE) of this composite containing single particle. The given input Gaussian random variable is Young modulus of the matrix, while 3D homogenization scheme is based on numerical determination of the strain energy of the RVE under uniform unit stretches carried out in the FEM system ABAQUS. The entire series of several deterministic solutions with varying Young modulus of the matrix serves for the Weighted Least Squares Method (WLSM) recovery of polynomial response functions finally used in stochastic Taylor expansions inherent for the ISFEM. A numerical example consists of the High Density Polyurethane (HDPU) reinforced with the Carbon Black particle. It is numerically investigated (1) if the resulting homogenized characteristics are also Gaussian and (2) how the uncertainty in matrix Young modulus affects the effective stiffness tensor components and their PDF (Probability Density Function).

Measurements of effective delayed neutron fraction in a fast neutron reactor using the perturbation method

NASA Astrophysics Data System (ADS)

Zhou, Hao-Jun; Yin, Yan-Peng; Fan, Xiao-Qiang; Li, Zheng-Hong; Pu, Yi-Kang

2016-06-01

A perturbation method is proposed to obtain the effective delayed neutron fraction β eff of a cylindrical highly enriched uranium reactor. Based on reactivity measurements with and without a sample at a specified position using the positive period technique, the reactor reactivity perturbation Δρ of the sample in β eff units is measured. Simulations of the perturbation experiments are performed using the MCNP program. The PERT card is used to provide the difference dk of effective neutron multiplication factors with and without the sample inside the reactor. Based on the relationship between the effective multiplication factor and the reactivity, the equation β eff = dk/Δρ is derived. In this paper, the reactivity perturbations of 13 metal samples at the designable position of the reactor are measured and calculated. The average β eff value of the reactor is given as 0.00645, and the standard uncertainty is 3.0%. Additionally, the perturbation experiments for β eff can be used to evaluate the reliabilities of the delayed neutron parameters. This work shows that the delayed neutron data of 235U and 238U from G.R. Keepin’s publication are more reliable than those from ENDF-B6.0, ENDF-B7.0, JENDL3.3 and CENDL2.2. Supported by Foundation of Key Laboratory of Neutron Physics, China Academy of Engineering Physics (2012AA01, 2014AA01), National Natural Science Foundation (11375158, 91326104)

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

NASA Astrophysics Data System (ADS)

Vallinotto, Alberto

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

Wave theory of turbulence in compressible media (acoustic theory of turbulence)

NASA Technical Reports Server (NTRS)

Kentzer, C. P.

1975-01-01

The generation and the transmission of sound in turbulent flows are treated as one of the several aspects of wave propagation in turbulence. Fluid fluctuations are decomposed into orthogonal Fourier components, with five interacting modes of wave propagation: two vorticity modes, one entropy mode, and two acoustic modes. Wave interactions, governed by the inhomogeneous and nonlinear terms of the perturbed Navier-Stokes equations, are modeled by random functions which give the rates of change of wave amplitudes equal to the averaged interaction terms. The statistical framework adopted is a quantum-like formulation in terms of complex distribution functions. The spatial probability distributions are given by the squares of the absolute values of the complex characteristic functions. This formulation results in nonlinear diffusion-type transport equations for the probability densities of the five modes of wave propagation.

Periodic solutions of second-order nonlinear difference equations containing a small parameter. III - Perturbation theory

NASA Technical Reports Server (NTRS)

Mickens, R. E.

1986-01-01

A technique to construct a uniformly valid perturbation series solution to a particular class of nonlinear difference equations is shown. The method allows the determination of approximations to the periodic solutions to these equations. An example illustrating the technique is presented.

Prosodic Adaptations to Pitch Perturbation in Running Speech

ERIC Educational Resources Information Center

Patel, Rupal; Niziolek, Caroline; Reilly, Kevin; Guenther, Frank H.

2011-01-01

Purpose: A feedback perturbation paradigm was used to investigate whether prosodic cues are controlled independently or in an integrated fashion during sentence production. Method: Twenty-one healthy speakers of American English were asked to produce sentences with emphatic stress while receiving real-time auditory feedback of their productions.…

Exact Solution of a Faraday's Law Problem that Includes a Nonlinear Term and Its Implication for Perturbation Theory.

ERIC Educational Resources Information Center

Fulcher, Lewis P.

1979-01-01

Presents an exact solution to the nonlinear Faraday's law problem of a rod sliding on frictionless rails with resistance. Compares the results with perturbation calculations based on the methods of Poisson and Pincare and of Kryloff and Bogoliuboff. (Author/GA)

Control of spiral waves and turbulent states in a cardiac model by travelling-wave perturbations

NASA Astrophysics Data System (ADS)

Wang, Peng-Ye; Xie, Ping; Yin, Hua-Wei

2003-06-01

We propose a travelling-wave perturbation method to control the spatiotemporal dynamics in a cardiac model. It is numerically demonstrated that the method can successfully suppress the wave instability (alternans in action potential duration) in the one-dimensional case and convert spiral waves and turbulent states to the normal travelling wave states in the two-dimensional case. An experimental scheme is suggested which may provide a new design for a cardiac defibrillator.

Controlling spiral waves and turbulent states in cardiac tissue by traveling wave perturbations

NASA Astrophysics Data System (ADS)

Wang, Peng-Ye; Xie, Ping

2000-03-01

We propose a traveling wave perturbation method to control the spatiotemporal dynamics in cardiac tissue. With a two-variable model we demonstrate that the method can successfully suppress the wave instability (alternans in action potential duration) in the one-dimensional case and convert spiral waves and turbulent states to the normal traveling wave state in the two-dimensional case. An experimental scheme is suggested which may provide a new design for a cardiac defibrillator.

Computation of diverging sums based on a finite number of terms

NASA Astrophysics Data System (ADS)

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

2017-10-01

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

Quantitative posturography in altered sensory conditions: a way to assess balance instability in patients with chronic whiplash injury.

PubMed

Madeleine, Pascal; Prietzel, Hanne; Svarrer, Heine; Arendt-Nielsen, Lars

2004-03-01

To quantify neck mobility and posture with and without various postural perturbations. A multivariable 2-group study with repeated measures and treatments. A human performance laboratory. Eleven patients with chronic whiplash injury (mean age, 33.3+/-6.7 y; weight, 73.4+/-11.4 kg; height, 173.3+/-7.2 cm) with a sex- and age-matched control group (mean age, 33.1+/-6.8 y; weight, 68+/-12.5 kg; height, 171.5+/-6.3 cm). Neck mobility and the effects of postural perturbations affecting the visual, vestibular, cutaneous, proprioceptive, and nociceptive systems were measured. Active range of motion, neck position sense, and postural activity. We found significantly reduced neck mobility and increased postural activity in the patient group compared with the control group. In patients, there was significantly greater postural activity with eyes closed, eyes open and speaking, and eyes closed with Achilles' tendons vibrations compared with eyes open with no vibrations. In the controls, there was no significant effect of experimental muscle pain on postural activity. Patients with chronic whiplash injury had a protective response to neck movement and different tuning, sequencing, and execution of the postural synergies probably because of excessive reliance on visual input despite a possible deficit and altered vestibular and/or proprioceptive activity. In healthy volunteers, the pain induced by a single bolus injection of hypertonic saline was probably too limited in intensity and spreading to decrease postural stability.

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.

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

Zhu, Z. W., E-mail: zhuzhiwen@tju.edu.cn; Li, X. M., E-mail: lixinmiaotju@163.com; Xu, J., E-mail: xujia-ld@163.com

A kind of magnetic shape memory alloy (MSMA) microgripper is proposed in this paper, and its nonlinear dynamic characteristics are studied when the stochastic perturbation is considered. Nonlinear differential items are introduced to explain the hysteretic phenomena of MSMA, and the constructive relationships among strain, stress, and magnetic field intensity are obtained by the partial least-square regression method. The nonlinear dynamic model of a MSMA microgripper subjected to in-plane stochastic excitation is developed. The stationary probability density function of the system’s response is obtained, the transition sets of the system are determined, and the conditions of stochastic bifurcation are obtained.more » The homoclinic and heteroclinic orbits of the system are given, and the boundary of the system’s safe basin is obtained by stochastic Melnikov integral method. The numerical and experimental results show that the system’s motion depends on its parameters, and stochastic Hopf bifurcation appears in the variation of the parameters; the area of the safe basin decreases with the increase of the stochastic excitation, and the boundary of the safe basin becomes fractal. The results of this paper are helpful for the application of MSMA microgripper in engineering fields.« less

Impact of Eccentricity on East-west Stationkeeping for GPS Class of Orbits

NASA Technical Reports Server (NTRS)

Ely, Todd A.

1999-01-01

There exists a strong relationship between eccentricity and the potential for a repeating groundtrack orbit to exhibit chaotic motion. This is true at all values of eccentricity, but, perhaps most dramatic, is that it is true even for orbits that are nearly circular. These complex motions can have a significant impact on the east-west stationkeeping process for maintaining the repeating groundtrack property of a commensurate orbit. Ely and Howell have shown that traditional stationkeeping (SK) methods are unable to maintain a repeating groundtrack in the presence of complex dynamics, such as with chaotic motion. They developed an alternate SK method that is able to maintain a repeating groundtrack for eccentric, commensurate orbits. The focus of the current study is to investigate orbits with characteristics that are similar to GPS satellites except with modestly larger eccentricities. It will be shown that at eccentricities larger than approx. .01 the chaotic regions become significant, and the need arises for a robust stationkeeping approach, such as developed in. FurtheRmore, the investigation will reveal that the influence of luni-solar perturbations contributes to the growth of eccentricity, thus increasing the probability of encountering chaotic motion during a typical satellite lifetime.

Experimental and CFD evidence of multiple solutions in a naturally ventilated building.

PubMed

Heiselberg, P; Li, Y; Andersen, A; Bjerre, M; Chen, Z

2004-02-01

This paper considers the existence of multiple solutions to natural ventilation of a simple one-zone building, driven by combined thermal and opposing wind forces. The present analysis is an extension of an earlier analytical study of natural ventilation in a fully mixed building, and includes the effect of thermal stratification. Both computational and experimental investigations were carried out in parallel with an analytical investigation. When flow is dominated by thermal buoyancy, it was found experimentally that there is thermal stratification. When the flow is wind-dominated, the room is fully mixed. Results from all three methods have shown that the hysteresis phenomena exist. Under certain conditions, two different stable steady-state solutions are found to exist by all three methods for the same set of parameters. As shown by both the computational fluid dynamics (CFD) and experimental results, one of the solutions can shift to another when there is a sufficient perturbation. These results have probably provided the strongest evidence so far for the conclusion that multiple states exist in natural ventilation of simple buildings. Different initial conditions in the CFD simulations led to different solutions, suggesting that caution must be taken when adopting the commonly used 'zero initialization'.

Phonon dispersions, band structures, and dielectric functions of BeO and BeS polymorphs

NASA Astrophysics Data System (ADS)

Wang, Ke-Long; Gao, Shang-Peng

2018-07-01

Structures, phonon dispersions, electronic structures, and dielectric functions of beryllium oxide (BeO) and beryllium sulfide (BeS) polymorphs are investigated by density functional theory and many-body perturbation theory. Phonon calculations indicate that both wurtzite (w-) and zincblende (zb-) structures are dynamically stable for BeO and BeS, whereas rocksalt (rs-) structures for both BeO and BeS have imaginary phonon frequencies and thus are dynamically unstable at zero pressure. Band structures for the 4 dynamically stable phases show that only w-BeO has a direct band gap. Both the one-shot G0W0 and quasiparticle self-consistent GW methods are used to correct band energies at high symmetry k-points. Bethe-Salpeter equation (BSE), which considers Coulomb correlated electron-hole pairs, is employed to deal with the computation of macroscopic dielectric functions. It is shown that BSE calculation, employing scissors operator derived by self-consistent GW method, can give dielectric functions agreeing very well with experimental measurement of w-BeO. Weak anisotropic characters can be observed for w-BeO and w-BeS. Both zb-BeS and w-BeS show high optical transition probabilities within a narrow ultraviolet energy range.

Realization of the three-qubit quantum controlled gate based on matching Hermitian generators

NASA Astrophysics Data System (ADS)

Gautam, Kumar; Rawat, Tarun Kumar; Parthasarathy, Harish; Sharma, Navneet; Upadhyaya, Varun

2017-05-01

This paper deals with the design of quantum unitary gate by matching the Hermitian generators. A given complicated quantum controlled gate is approximated by perturbing a simple quantum system with a small time-varying potential. The basic idea is to evaluate the generator H_φ of the perturbed system approximately using first-order perturbation theory in the interaction picture. H_φ depends on a modulating signal φ(t){:} 0≤t≤T which modulates a known potential V. The generator H_φ of the given gate U_g is evaluated using H_g=ι log U_g. The optimal modulating signal φ(t) is chosen so that \\Vert H_g - H_φ \\Vert is a minimum. The simple quantum system chosen for our simulation is harmonic oscillator with charge perturbed by an electric field that is a constant in space but time varying and is controlled externally. This is used to approximate the controlled unitary gate obtained by perturbing the oscillator with an anharmonic term proportional to q^3. Simulations results show significantly small noise-to-signal ratio. Finally, we discuss how the proposed method is particularly suitable for designing some commonly used unitary gates. Another example was chosen to illustrate this method of gate design is the ion-trap model.

Asteroid mass estimation using Markov-Chain Monte Carlo techniques

NASA Astrophysics Data System (ADS)

Siltala, Lauri; Granvik, Mikael

2016-10-01

Estimates for asteroid masses are based on their gravitational perturbations on the orbits of other objects such as Mars, spacecraft, or other asteroids and/or their satellites. In the case of asteroid-asteroid perturbations, this leads to a 13-dimensional inverse problem where the aim is to derive the mass of the perturbing asteroid and six orbital elements for both the perturbing asteroid and the test asteroid using astrometric observations. We have developed and implemented three different mass estimation algorithms utilizing asteroid-asteroid perturbations into the OpenOrb asteroid-orbit-computation software: the very rough 'marching' approximation, in which the asteroid orbits are fixed at a given epoch, reducing the problem to a one-dimensional estimation of the mass, an implementation of the Nelder-Mead simplex method, and most significantly, a Markov-Chain Monte Carlo (MCMC) approach. We will introduce each of these algorithms with particular focus on the MCMC algorithm, and present example results for both synthetic and real data. Our results agree with the published mass estimates, but suggest that the published uncertainties may be misleading as a consequence of using linearized mass-estimation methods. Finally, we discuss remaining challenges with the algorithms as well as future plans, particularly in connection with ESA's Gaia mission.

Differentially Private Empirical Risk Minimization

PubMed Central

Chaudhuri, Kamalika; Monteleoni, Claire; Sarwate, Anand D.

2011-01-01

Privacy-preserving machine learning algorithms are crucial for the increasingly common setting in which personal data, such as medical or financial records, are analyzed. We provide general techniques to produce privacy-preserving approximations of classifiers learned via (regularized) empirical risk minimization (ERM). These algorithms are private under the ε-differential privacy definition due to Dwork et al. (2006). First we apply the output perturbation ideas of Dwork et al. (2006), to ERM classification. Then we propose a new method, objective perturbation, for privacy-preserving machine learning algorithm design. This method entails perturbing the objective function before optimizing over classifiers. If the loss and regularizer satisfy certain convexity and differentiability criteria, we prove theoretical results showing that our algorithms preserve privacy, and provide generalization bounds for linear and nonlinear kernels. We further present a privacy-preserving technique for tuning the parameters in general machine learning algorithms, thereby providing end-to-end privacy guarantees for the training process. We apply these results to produce privacy-preserving analogues of regularized logistic regression and support vector machines. We obtain encouraging results from evaluating their performance on real demographic and benchmark data sets. Our results show that both theoretically and empirically, objective perturbation is superior to the previous state-of-the-art, output perturbation, in managing the inherent tradeoff between privacy and learning performance. PMID:21892342

Robust fuzzy control subject to state variance and passivity constraints for perturbed nonlinear systems with multiplicative noises.

PubMed

Chang, Wen-Jer; Huang, Bo-Jyun

2014-11-01

The multi-constrained robust fuzzy control problem is investigated in this paper for perturbed continuous-time nonlinear stochastic systems. The nonlinear system considered in this paper is represented by a Takagi-Sugeno fuzzy model with perturbations and state multiplicative noises. The multiple performance constraints considered in this paper include stability, passivity and individual state variance constraints. The Lyapunov stability theory is employed to derive sufficient conditions to achieve the above performance constraints. By solving these sufficient conditions, the contribution of this paper is to develop a parallel distributed compensation based robust fuzzy control approach to satisfy multiple performance constraints for perturbed nonlinear systems with multiplicative noises. At last, a numerical example for the control of perturbed inverted pendulum system is provided to illustrate the applicability and effectiveness of the proposed multi-constrained robust fuzzy control method. Copyright © 2014 ISA. Published by Elsevier Ltd. All rights reserved.

Electron density increases due to Lightning activity as deduced from LWPC code and VLF signal perturbations.

NASA Astrophysics Data System (ADS)

Samir, Nait Amor; Bouderba, Yasmina

VLF signal perturbations in association with thunderstorm activity appear as changes in the signal amplitude and phase. Several papers reported on the characteristics of thus perturbations and their connection to the lightning strokes amplitude and polarity. In this contribution, we quantified the electrons density increases due to lightning activity by the use of the LWPC code and VLF signal perturbations parameters. The method is similar to what people did in studying the solar eruptions effect. the results showed that the reference height (h') decreased to lower altitudes (between 70 and 80 km). From the LWPC code results the maximum of the electron density was then deduced. Therefore, a numerical simulation of the atmospheric species times dependences was performed to study the recovery times of the electrons density at different heights. The results showed that the recovery time last for several minutes and explain the observation of long recovery Early signal perturbations.

Analytic-continuation approach to the resummation of divergent series in Rayleigh-Schrödinger perturbation theory

NASA Astrophysics Data System (ADS)

Mihálka, Zsuzsanna É.; Surján, Péter R.

2017-12-01

The method of analytic continuation is applied to estimate eigenvalues of linear operators from finite order results of perturbation theory even in cases when the latter is divergent. Given a finite number of terms E(k ),k =1 ,2 ,⋯M resulting from a Rayleigh-Schrödinger perturbation calculation, scaling these numbers by μk (μ being the perturbation parameter) we form the sum E (μ ) =∑kμkE(k ) for small μ values for which the finite series is convergent to a certain numerical accuracy. Extrapolating the function E (μ ) to μ =1 yields an estimation of the exact solution of the problem. For divergent series, this procedure may serve as resummation tool provided the perturbation problem has a nonzero radius of convergence. As illustrations, we treat the anharmonic (quartic) oscillator and an example from the many-electron correlation problem.

Evolution of almost circular orbits of satellites under the action of noncentral gravitational field of the Earth and lunisolar perturbations

NASA Astrophysics Data System (ADS)

Dulliev, A. M.

2011-02-01

Based on the results of paper [1] by G.V. Mozhaev, joint perturbations produced by nonsphericity of the Earth and by attraction of the Moon and the Sun are investigated using the method of averaging. Arbitrary number of spherical harmonics was taken into account in the force function of the Earth’s gravitational filed, and only the principal term was retained in the perturbing function of the Sun. In the perturbing function of the Moon two parallactic terms were considered in addition to the dominant term. The flight altitude was chosen in such a way that perturbations produced by the Sun and Moon would have the second order of smallness relative to the polar oblateness of the Earth. As a result, the formulas for calculation of satellite coordinates are derived that give a high precision on long time intervals.

A uniformly valid approximation algorithm for nonlinear ordinary singular perturbation problems with boundary layer solutions.

PubMed

Cengizci, Süleyman; Atay, Mehmet Tarık; Eryılmaz, Aytekin

2016-01-01

This paper is concerned with two-point boundary value problems for singularly perturbed nonlinear ordinary differential equations. The case when the solution only has one boundary layer is examined. An efficient method so called Successive Complementary Expansion Method (SCEM) is used to obtain uniformly valid approximations to this kind of solutions. Four test problems are considered to check the efficiency and accuracy of the proposed method. The numerical results are found in good agreement with exact and existing solutions in literature. The results confirm that SCEM has a superiority over other existing methods in terms of easy-applicability and effectiveness.

Propagation of sound in turbulent media

NASA Technical Reports Server (NTRS)

Wenzel, A. R.

1976-01-01

Perturbation methods commonly used to study the propagation of acoustic waves in turbulent media are reviewed. Emphasis is on those techniques which are applicable to problems involving long-range propagation in the atmosphere and ocean. Characteristic features of the various methods are illustrated by applying them to particular problems. It is shown that conventional perturbation techniques, such as the Born approximation, yield solutions which contain secular terms, and which therefore have a relatively limited range of validity. In contrast, it is found that solutions obtained with the aid of the Rytov method or the smoothing method do not contain secular terms, and consequently have a much greater range of validity.

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.

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

BRST quantization of cosmological perturbations

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

Armendariz-Picon, Cristian; Şengör, Gizem

2016-11-08

BRST quantization is an elegant and powerful method to quantize theories with local symmetries. In this article we study the Hamiltonian BRST quantization of cosmological perturbations in a universe dominated by a scalar field, along with the closely related quantization method of Dirac. We describe how both formalisms apply to perturbations in a time-dependent background, and how expectation values of gauge-invariant operators can be calculated in the in-in formalism. Our analysis focuses mostly on the free theory. By appropriate canonical transformations we simplify and diagonalize the free Hamiltonian. BRST quantization in derivative gauges allows us to dramatically simplify the structuremore » of the propagators, whereas Dirac quantization, which amounts to quantization in synchronous gauge, dispenses with the need to introduce ghosts and preserves the locality of the gauge-fixed action.« less

Knowledge of damage identification about tensegrities via flexibility disassembly

NASA Astrophysics Data System (ADS)

Jiang, Ge; Feng, Xiaodong; Du, Shigui

2017-12-01

Tensegrity structures composing of continuous cables and discrete struts are under tension and compression, respectively. In order to determine the damage extents of tensegrity structures, a new method for tensegrity structural damage identification is presented based on flexibility disassembly. To decompose a tensegrity structural flexibility matrix into the matrix represention of the connectivity between degress-of-freedoms and the diagonal matrix comprising of magnitude informations. Step 1: Calculate perturbation flexibility; Step 2: Compute the flexibility connectivity matrix and perturbation flexibility parameters; Step 3: Calculate the perturbation stiffness parameters. The efficiency of the proposed method is demonstrated by a numeical example comprising of 12 cables and 4 struts with pretensioned. Accurate identification of local damage depends on the availability of good measured data, an accurate and reasonable algorithm.

Photonic Crystals from Order to Disorder: Perturbative Methods in Nanophotonics

ScienceCinema

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

2017-12-09

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

ASP: Automated symbolic computation of approximate symmetries of differential equations

NASA Astrophysics Data System (ADS)

Jefferson, G. F.; Carminati, J.

2013-03-01

A recent paper (Pakdemirli et al. (2004) [12]) compared three methods of determining approximate symmetries of differential equations. Two of these methods are well known and involve either a perturbation of the classical Lie symmetry generator of the differential system (Baikov, Gazizov and Ibragimov (1988) [7], Ibragimov (1996) [6]) or a perturbation of the dependent variable/s and subsequent determination of the classical Lie point symmetries of the resulting coupled system (Fushchych and Shtelen (1989) [11]), both up to a specified order in the perturbation parameter. The third method, proposed by Pakdemirli, Yürüsoy and Dolapçi (2004) [12], simplifies the calculations required by Fushchych and Shtelen's method through the assignment of arbitrary functions to the non-linear components prior to computing symmetries. All three methods have been implemented in the new MAPLE package ASP (Automated Symmetry Package) which is an add-on to the MAPLE symmetry package DESOLVII (Vu, Jefferson and Carminati (2012) [25]). To our knowledge, this is the first computer package to automate all three methods of determining approximate symmetries for differential systems. Extensions to the theory have also been suggested for the third method and which generalise the first method to systems of differential equations. Finally, a number of approximate symmetries and corresponding solutions are compared with results in the literature.

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

Range of validity for perturbative treatments of relativistic sum rules

NASA Astrophysics Data System (ADS)

Cohen, Scott M.

2003-10-01

The range of validity of perturbative calculations of relativistic sum rules is investigated by calculating the second-order relativistic corrections to the Bethe sum rule and its small momentum limit, the Thomas-Reiche-Kuhn (TRK) sum rule. For the TRK sum rule and atomic systems, the second-order correction is found to be less than 0.5% up to about Z=70. The total relativistic corrections should then be accurate at least through this range of Z, and probably beyond this range if the second-order terms are included. For Rn (Z=86), however, the second-order corrections are nearly 1%. The total corrections to the Bethe sum rule are largest at small momentum, never being significantly larger than the corresponding corrections to the TRK sum rule. The first-order corrections to the Bethe sum rule also give better than 0.5% accuracy for Z<70, and inclusion of the second-order corrections should extend this range, as well.

Trigonometrically-fitted Scheifele two-step methods for perturbed oscillators

NASA Astrophysics Data System (ADS)

You, Xiong; Zhang, Yonghui; Zhao, Jinxi

2011-07-01

In this paper, a new family of trigonometrically-fitted Scheifele two-step (TFSTS) methods for the numerical integration of perturbed oscillators is proposed and investigated. An essential feature of TFSTS methods is that they are exact in both the internal stages and the updates when solving the unperturbed harmonic oscillator y″ = -ω2 y for known frequency ω. Based on the linear operator theory, the necessary and sufficient conditions for TFSTS methods of up to order five are derived. Two specific TFSTS methods of orders four and five respectively are constructed and their stability and phase properties are examined. In the five numerical experiments carried out the new integrators are shown to be more efficient and competent than some well-known methods in the literature.

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.

Alien calculus and non perturbative effects in Quantum Field Theory

NASA Astrophysics Data System (ADS)

Bellon, Marc P.

2016-12-01

In many domains of physics, methods for dealing with non-perturbative aspects are required. Here, I want to argue that a good approach for this is to work on the Borel transforms of the quantities of interest, the singularities of which give non-perturbative contributions. These singularities in many cases can be largely determined by using the alien calculus developed by Jean Écalle. My main example will be the two point function of a massless theory given as a solution of a renormalization group equation.

System, device, and methods for real-time screening of live cells, biomarkers, and chemical signatures

DOEpatents

Sundaram, S Kamakshi [Richland, WA; Riley, Brian J [West Richland, WA; Weber, Thomas J [Richland, WA; Sacksteder, Colette A [West Richland, WA; Addleman, R Shane [Benton City, WA

2011-06-07

An ATR-FTIR device and system are described that defect live-cell responses to stimuli and perturbations in real-time. The system and device can monitor perturbations resulting from exposures to various physical, chemical, and biological materials in real-time, as well as those sustained over a long period of time, including those associated with stimuli having unknown modes-of-action (e.g. nanoparticles). The device and system can also be used to identify specific chemical species or substances that profile cellular responses to these perturbations.

Quaternion Regularization of the Equations of the Perturbed Spatial Restricted Three-Body Problem: I

NASA Astrophysics Data System (ADS)

Chelnokov, Yu. N.

2017-11-01

We develop a quaternion method for regularizing the differential equations of the perturbed spatial restricted three-body problem by using the Kustaanheimo-Stiefel variables, which is methodologically closely related to the quaternion method for regularizing the differential equations of perturbed spatial two-body problem, which was proposed by the author of the present paper. A survey of papers related to the regularization of the differential equations of the two- and threebody problems is given. The original Newtonian equations of perturbed spatial restricted three-body problem are considered, and the problem of their regularization is posed; the energy relations and the differential equations describing the variations in the energies of the system in the perturbed spatial restricted three-body problem are given, as well as the first integrals of the differential equations of the unperturbed spatial restricted circular three-body problem (Jacobi integrals); the equations of perturbed spatial restricted three-body problem written in terms of rotating coordinate systems whose angular motion is described by the rotation quaternions (Euler (Rodrigues-Hamilton) parameters) are considered; and the differential equations for angular momenta in the restricted three-body problem are given. Local regular quaternion differential equations of perturbed spatial restricted three-body problem in the Kustaanheimo-Stiefel variables, i.e., equations regular in a neighborhood of the first and second body of finite mass, are obtained. The equations are systems of nonlinear nonstationary eleventhorder differential equations. These equations employ, as additional dependent variables, the energy characteristics of motion of the body under study (a body of a negligibly small mass) and the time whose derivative with respect to a new independent variable is equal to the distance from the body of negligibly small mass to the first or second body of finite mass. The equations obtained in the paper permit developing regular methods for determining solutions, in analytical or numerical form, of problems difficult for classicalmethods, such as the motion of a body of negligibly small mass in a neighborhood of the other two bodies of finite masses.

Cosmological perturbations during the Bose-Einstein condensation of dark matter

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

Freitas, R.C.; Gonçalves, S.V.B., E-mail: rodolfo.camargo@pq.cnpq.br, E-mail: sergio.vitorino@pq.cnpq.br

In the present work, we analyze the evolution of the scalar and tensorial perturbations and the quantities relevant for the physical description of the Universe, as the density contrast of the scalar perturbations and the gravitational waves energy density during the Bose-Einstein condensation of dark matter. The behavior of these parameters during the Bose-Einstein phase transition of dark matter is analyzed in details. To study the cosmological dynamics and evolution of scalar and tensorial perturbations in a Universe with and without cosmological constant we use both analytical and numerical methods. The Bose-Einstein phase transition modifies the evolution of gravitational wavesmore » of cosmological origin, as well as the process of large-scale structure formation.« less

Feedback linearization of singularly perturbed systems based on canonical similarity transformations

NASA Astrophysics Data System (ADS)

Kabanov, A. A.

2018-05-01

This paper discusses the problem of feedback linearization of a singularly perturbed system in a state-dependent coefficient form. The result is based on the introduction of a canonical similarity transformation. The transformation matrix is constructed from separate blocks for fast and slow part of an original singularly perturbed system. The transformed singular perturbed system has a linear canonical form that significantly simplifies a control design problem. Proposed similarity transformation allows accomplishing linearization of the system without considering the virtual output (as it is needed for normal form method), a technique of a transition from phase coordinates of the transformed system to state variables of the original system is simpler. The application of the proposed approach is illustrated through example.

The scalar and electromagnetic form factors of the nucleon in dispersively improved Chiral EFT

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

Alarcon, Jose Manuel

We present a method for calculating the nucleon form factors of G-parity-even operators. This method combines chiral effective field theory (χEFT) and dispersion theory. Through unitarity we factorize the imaginary part of the form factors into a perturbative part, calculable with χEFT, and a non-perturbative part, obtained through other methods. We consider the scalar and electromagnetic (EM) form factors of the nucleon. The results show an important improvement compared to standard chiral calculations, and can be used in analysis of the low-energy properties of the nucleon.

Probability Current in Hydrogen with Spin-Orbit Interaction

NASA Astrophysics Data System (ADS)

Hodge, William; Migirditch, Sam; Kerr, William

2013-03-01

The spin-orbit interaction is a coupling between a particle's spin and its motion. The Hamiltonian for a spin- 1 / 2 particle which includes this coupling is H =p2/2 m + V (x) +∇/V (x) × p 2m2c2 . S . To describe the flow of probability in this system, we derive the continuity equation, which takes the usual form. In this case, however, we find the probability current density j (x , t) to be the sum of two terms. The first term is the one obtained by most quantum mechanics textbooks during their derivation of the continuity equation. The second term, js (x , t) =1/2m2c2 ∑ σ , σ ' = ↑ , ↓ [ ψ* (x , σ , t) < σ | S | σ ' > ψ (x , σ ' , t) ] × ∇ V (x) , arises due to the inclusion of the spin-orbit term in the Hamiltonian and is small compared to the first. Using a perturbative treatment, we calculate j (x , t) for hydrogenlike atoms; for states with l = 0 , we find that j (x , t) =js (x , t) .

Two-Photon Emission of a Hydrogenlike Atom with Photon Polarization and Electron Spin States Taken into Account

NASA Astrophysics Data System (ADS)

Skobelev, V. V.

2017-02-01

The process of two-photon emission ( Ze)* → ( Ze) + 2 γ of a hydrogenlike atom is considered with spin states of the electron and polarization of the photons taken into account, which had not been done before. A general expression for the probability of the process per unit time has been obtained for different polarization states of the photons with a formulation of hard and soft selection rules for the quantum numbers m and l. It is shown that by virtue of the established specifics of the properties of the two-photon emission process (absence of a Zeeman effect and dependence of the probability on the polarization states of the photons), it can in principle be identified against the background of single-photon emission ( Ze)* → ( Ze) + γ, despite the presence of additional small factors: 1) α = e 2/ ћc ≈ 1/137 of the perturbation theory in e, and 2) the square of the atomic expansion parameter ( Zα)2 in the expression for the probability.

Effects of the Voice over Internet Protocol on Perturbation Analysis of Normal and Pathological Phonation

PubMed Central

Zhu, Yanmei; Witt, Rachel E.; MacCallum, Julia K.; Jiang, Jack J.

2010-01-01

Objective In this study, a Voice over Internet Protocol (VoIP) communication based on G.729 protocol was simulated to determine the effects of this system on acoustic perturbation parameters of normal and pathological voice signals. Patients and Methods: Fifty recordings of normal voice and 48 recordings of pathological voice affected by laryngeal paralysis were transmitted through a VoIP communication system. The acoustic analysis programs of CSpeech and MDVP were used to determine the percent jitter and percent shimmer from the voice samples before and after VoIP transmission. The effects of three frequently used audio compression protocols (MP3, WMA, and FLAC) on the perturbation measures were also studied. Results It was found that VoIP transmission disrupts the waveform and increases the percent jitter and percent shimmer of voice samples. However, after VoIP transmission, significant discrimination between normal and pathological voices affected by laryngeal paralysis was still possible. It was found that the lossless compression method FLAC does not exert any influence on the perturbation measures. The lossy compression methods MP3 and WMA increase percent jitter and percent shimmer values. Conclusion This study validates the feasibility of these transmission and compression protocols in developing remote voice signal data collection and assessment systems. PMID:20588051

An Improved Perturb and Observe Algorithm for Photovoltaic Motion Carriers

NASA Astrophysics Data System (ADS)

Peng, Lele; Xu, Wei; Li, Liming; Zheng, Shubin

2018-03-01

An improved perturbation and observation algorithm for photovoltaic motion carriers is proposed in this paper. The model of the proposed algorithm is given by using Lambert W function and tangent error method. Moreover, by using matlab and experiment of photovoltaic system, the tracking performance of the proposed algorithm is tested. And the results demonstrate that the improved algorithm has fast tracking speed and high efficiency. Furthermore, the energy conversion efficiency by the improved method has increased by nearly 8.2%.

An algorithm for full parametric solution of problems on the statics of orthotropic plates by the method of boundary states with perturbations

NASA Astrophysics Data System (ADS)

Penkov, V. B.; Ivanychev, D. A.; Novikova, O. S.; Levina, L. V.

2018-03-01

The article substantiates the possibility of building full parametric analytical solutions of mathematical physics problems in arbitrary regions by means of computer systems. The suggested effective means for such solutions is the method of boundary states with perturbations, which aptly incorporates all parameters of an orthotropic medium in a general solution. We performed check calculations of elastic fields of an anisotropic rectangular region (test and calculation problems) for a generalized plane stress state.

Scattering by Artificial Wind and Rain Roughened Water Surfaces at Oblique Incidences

NASA Technical Reports Server (NTRS)

Craeye, C.; Sobieski, P. W.; Bliven, L. F.

1997-01-01

Rain affects wind retrievals from scatterometric measurements of the sea surface. To depict the additional roughness caused by rain on a wind driven surface, we use a ring-wave spectral model. This enables us to analyse the rain effect on K(u) band scatterometric observations from two laboratory experiments. Calculations based on the small perturbation method provide good simulation of scattering measurements for the rain-only case, whereas for combined wind and rain cases, the boundary perturbation method is appropriate.

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.

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.

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

NASA Astrophysics Data System (ADS)

Finster, Felix; Tolksdorf, Jürgen

2014-05-01

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

Statistical Mechanics of the Delayed Reward-Based Learning with Node Perturbation

NASA Astrophysics Data System (ADS)

Hiroshi Saito,; Kentaro Katahira,; Kazuo Okanoya,; Masato Okada,

2010-06-01

In reward-based learning, reward is typically given with some delay after a behavior that causes the reward. In machine learning literature, the framework of the eligibility trace has been used as one of the solutions to handle the delayed reward in reinforcement learning. In recent studies, the eligibility trace is implied to be important for difficult neuroscience problem known as the “distal reward problem”. Node perturbation is one of the stochastic gradient methods from among many kinds of reinforcement learning implementations, and it searches the approximate gradient by introducing perturbation to a network. Since the stochastic gradient method does not require a objective function differential, it is expected to be able to account for the learning mechanism of a complex system, like a brain. We study the node perturbation with the eligibility trace as a specific example of delayed reward-based learning, and analyzed it using a statistical mechanics approach. As a result, we show the optimal time constant of the eligibility trace respect to the reward delay and the existence of unlearnable parameter configurations.

A multireference perturbation method using non-orthogonal Hartree-Fock determinants for ground and excited states

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

Yost, Shane R.; Kowalczyk, Tim; Van Voorhis, Troy, E-mail: tvan@mit.edu

2013-11-07

In this article we propose the ΔSCF(2) framework, a multireference strategy based on second-order perturbation theory, for ground and excited electronic states. Unlike the complete active space family of methods, ΔSCF(2) employs a set of self-consistent Hartree-Fock determinants, also known as ΔSCF states. Each ΔSCF electronic state is modified by a first-order correction from Møller-Plesset perturbation theory and used to construct a Hamiltonian in a configuration interactions like framework. We present formulas for the resulting matrix elements between nonorthogonal states that scale as N{sub occ}{sup 2}N{sub virt}{sup 3}. Unlike most active space methods, ΔSCF(2) treats the ground and excited statemore » determinants even-handedly. We apply ΔSCF(2) to the H{sub 2}, hydrogen fluoride, and H{sub 4} systems and show that the method provides accurate descriptions of ground- and excited-state potential energy surfaces with no single active space containing more than 10 ΔSCF states.« less

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

NASA Astrophysics Data System (ADS)

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

2018-02-01

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

Step length after discrete perturbation predicts accidental falls and fall-related injury in elderly people with a range of peripheral neuropathy

PubMed Central

Allet, L; Kim, H; Ashton-Miller, JA; De Mott, T; Richardson, JK

2013-01-01

Aims Distal symmetric polyneuropathy increases fall risk due to inability to cope with perturbations. We aimed to 1) identify the frontal plane lower limb sensorimotor functions which are necessary for robustness to a discrete, underfoot perturbation during gait; and 2) determine whether changes in the post-perturbed step parameters could distinguish between fallers and non fallers. Methods Forty-two subjects (16 healthy old and 26 with diabetic PN) participated. Frontal plane lower limb sensorimotor functions were determined using established laboratory-based techniques. The subjects' most extreme alterations in step width or step length in response to a perturbation were measured. In addition, falls and fall-related injuries were prospectively recorded. Results Ankle proprioceptive threshold (APrT; p=.025) and hip abduction rate of torque generation (RTG; p=.041) independently predicted extreme step length after medial perturbation, with precise APrT and greater hip RTG allowing maintenance of step length. Fallers demonstrated greater extreme step length changes after medial perturbation than non fallers (percent change = 16.41±8.42 vs 11.0±4.95; p=.06) Conclusions The ability to rapidly generate frontal plane hip strength and/or precisely perceive motion at the ankle is needed to maintain a normal step length after perturbation, a parameter, which distinguishes between fallers and non fallers. PMID:24183899

Nonconvergence to Saddle Boundary Points under Perturbed Reinforcement Learning

DTIC Science & Technology

2012-12-07

of the ODE (12). Note that for some games not all stationary points of the ODE (12) are Nash equilibria. For example, if you consider the Typewriter ...B A 4, 4 2, 2 B 2, 2 3, 3 Table 1: The Typewriter Game. On the other hand, any stationary point in the interior of the probability simplex will... Typewriter Game of Table 1. We observe that it is possible for the process to converge to a pure strategy profile which is not a Nash equilibrium when Ri(α

Infrasonic ray tracing applied to mesoscale atmospheric structures: refraction by hurricanes.

PubMed

Bedard, Alfred J; Jones, R Michael

2013-11-01

A ray-tracing program is used to estimate the refraction of infrasound by the temperature structure of the atmosphere and by hurricanes represented by a Rankine-combined vortex wind plus a temperature perturbation. Refraction by the hurricane winds is significant, giving rise to regions of focusing, defocusing, and virtual sources. The refraction of infrasound by the temperature anomaly associated with a hurricane is small, probably no larger than that from uncertainties in the wind field. The results are pertinent to interpreting ocean wave generated infrasound in the vicinities of tropical cyclones.

The role of advection and diffusion in waste disposal by sea urchin embryos

NASA Astrophysics Data System (ADS)

Clark, Aaron; Licata, Nicholas

2014-03-01

We determine the first passage probability for the absorption of waste molecules released from the microvilli of sea urchin embryos. We calculate a perturbative solution of the advection-diffusion equation for a linear shear profile similar to the fluid environment which the embryos inhabit. Rapid rotation of the embryo results in a concentration boundary layer of comparable thickness to the length of the microvilli. A comparison of the results to the regime of diffusion limited transport indicates that fluid flow is advantageous for efficient waste disposal.

Molecular collision processes in the presence of picosecond laser pulses

NASA Technical Reports Server (NTRS)

Lee, H. W.; George, T. F.

1979-01-01

Radiative transitions in molecular collision processes taking place in the presence of picosecond pulses are studied within a semiclassical formalism. An expression for adiabatic potential surfaces in the electronic-field representation is obtained, which directly leads to the evaluation of transition probabilities. Calculations with a Landau-Zener-type model indicate that picosecond pulses can be much more effective in inducing transitions than a single long pulse of the same intensity and the same total energy, if the intensity is sufficiently high that the perturbation treatment is not valid.

The quark-hadron phase transition and primordial nucleosynthesis

NASA Technical Reports Server (NTRS)

Hogan, Craig J.

1987-01-01

After presenting the current view of the processes taking place during the cosmological transition from 'quark soup' to normal hadron matter, attention is given to what happens to cosmological nucleosynthesis in the presence of small-scale baryon inhomogeneities. The QCD phase transition is among the plausible sources of this inhomogeneity. It is concluded that the formation of primordial 'quark nuggets' and other cold exotica requires very low entropy regions at the outset, and that even the more modest nonlinearities perturbing nucleosynthesis probably require some ingredient in addition to a quiescent, mildly supercooled transition.

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

PubMed

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

2013-01-01

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

Stability basin estimates fall risk from observed kinematics, demonstrated on the Sit-to-Stand task.

PubMed

Shia, Victor; Moore, Talia Yuki; Holmes, Patrick; Bajcsy, Ruzena; Vasudevan, Ram

2018-04-27

The ability to quantitatively measure stability is essential to ensuring the safety of locomoting systems. While the response to perturbation directly reflects the stability of a motion, this experimental method puts human subjects at risk. Unfortunately, existing indirect methods for estimating stability from unperturbed motion have been shown to have limited predictive power. This paper leverages recent advances in dynamical systems theory to accurately estimate the stability of human motion without requiring perturbation. This approach relies on kinematic observations of a nominal Sit-to-Stand motion to construct an individual-specific dynamic model, input bounds, and feedback control that are then used to compute the set of perturbations from which the model can recover. This set, referred to as the stability basin, was computed for 14 individuals, and was able to successfully differentiate between less and more stable Sit-to-Stand strategies for each individual with greater accuracy than existing methods. Copyright © 2018 Elsevier Ltd. All rights reserved.

A stable high-order perturbation of surfaces method for numerical simulation of diffraction problems in triply layered media

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

Hong, Youngjoon, E-mail: hongy@uic.edu; Nicholls, David P., E-mail: davidn@uic.edu

The accurate numerical simulation of linear waves interacting with periodic layered media is a crucial capability in engineering applications. In this contribution we study the stable and high-order accurate numerical simulation of the interaction of linear, time-harmonic waves with a periodic, triply layered medium with irregular interfaces. In contrast with volumetric approaches, High-Order Perturbation of Surfaces (HOPS) algorithms are inexpensive interfacial methods which rapidly and recursively estimate scattering returns by perturbation of the interface shape. In comparison with Boundary Integral/Element Methods, the stable HOPS algorithm we describe here does not require specialized quadrature rules, periodization strategies, or the solution ofmore » dense non-symmetric positive definite linear systems. In addition, the algorithm is provably stable as opposed to other classical HOPS approaches. With numerical experiments we show the remarkable efficiency, fidelity, and accuracy one can achieve with an implementation of this algorithm.« less

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

PubMed Central

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

2013-01-01

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

Applying dynamic Bayesian networks to perturbed gene expression data.

PubMed

Dojer, Norbert; Gambin, Anna; Mizera, Andrzej; Wilczyński, Bartek; Tiuryn, Jerzy

2006-05-08

A central goal of molecular biology is to understand the regulatory mechanisms of gene transcription and protein synthesis. Because of their solid basis in statistics, allowing to deal with the stochastic aspects of gene expressions and noisy measurements in a natural way, Bayesian networks appear attractive in the field of inferring gene interactions structure from microarray experiments data. However, the basic formalism has some disadvantages, e.g. it is sometimes hard to distinguish between the origin and the target of an interaction. Two kinds of microarray experiments yield data particularly rich in information regarding the direction of interactions: time series and perturbation experiments. In order to correctly handle them, the basic formalism must be modified. For example, dynamic Bayesian networks (DBN) apply to time series microarray data. To our knowledge the DBN technique has not been applied in the context of perturbation experiments. We extend the framework of dynamic Bayesian networks in order to incorporate perturbations. Moreover, an exact algorithm for inferring an optimal network is proposed and a discretization method specialized for time series data from perturbation experiments is introduced. We apply our procedure to realistic simulations data. The results are compared with those obtained by standard DBN learning techniques. Moreover, the advantages of using exact learning algorithm instead of heuristic methods are analyzed. We show that the quality of inferred networks dramatically improves when using data from perturbation experiments. We also conclude that the exact algorithm should be used when it is possible, i.e. when considered set of genes is small enough.

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.