Sample records for simple perturbative analysis

  1. 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.

  2. 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.

  3. 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.

  4. Complete Hamiltonian analysis of cosmological perturbations at all orders

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

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

    2016-06-01

    In this work, we present a consistent Hamiltonian analysis of cosmological perturbations at all orders. To make the procedure transparent, we consider a simple model and resolve the 'gauge-fixing' issues and extend the analysis to scalar field models and show that our approach can be applied to any order of perturbation for any first order derivative fields. In the case of Galilean scalar fields, our procedure can extract constrained relations at all orders in perturbations leading to the fact that there is no extra degrees of freedom due to the presence of higher time derivatives of the field in themore » Lagrangian. We compare and contrast our approach to the Lagrangian approach (Chen et al. [2006]) for extracting higher order correlations and show that our approach is efficient and robust and can be applied to any model of gravity and matter fields without invoking slow-roll approximation.« less

  5. Short relaxation times but long transient times in both simple and complex reaction networks

    PubMed Central

    Henry, Adrien; Martin, Olivier C.

    2016-01-01

    When relaxation towards an equilibrium or steady state is exponential at large times, one usually considers that the associated relaxation time τ, i.e. the inverse of the decay rate, is the longest characteristic time in the system. However, that need not be true, other times such as the lifetime of an infinitesimal perturbation can be much longer. In the present work, we demonstrate that this paradoxical property can arise even in quite simple systems such as a linear chain of reactions obeying mass action (MA) kinetics. By mathematical analysis of simple reaction networks, we pin-point the reason why the standard relaxation time does not provide relevant information on the potentially long transient times of typical infinitesimal perturbations. Overall, we consider four characteristic times and study their behaviour in both simple linear chains and in more complex reaction networks taken from the publicly available database ‘Biomodels’. In all these systems, whether involving MA rates, Michaelis–Menten reversible kinetics, or phenomenological laws for reaction rates, we find that the characteristic times corresponding to lifetimes of tracers and of concentration perturbations can be significantly longer than τ. PMID:27411726

  6. Changes in Purkinje cell simple spike encoding of reach kinematics during adaption to a mechanical perturbation.

    PubMed

    Hewitt, Angela L; Popa, Laurentiu S; Ebner, Timothy J

    2015-01-21

    The cerebellum is essential in motor learning. At the cellular level, changes occur in both the simple spike and complex spike firing of Purkinje cells. Because simple spike discharge reflects the main output of the cerebellar cortex, changes in simple spike firing likely reflect the contribution of the cerebellum to the adapted behavior. Therefore, we investigated in Rhesus monkeys how the representation of arm kinematics in Purkinje cell simple spike discharge changed during adaptation to mechanical perturbations of reach movements. Monkeys rapidly adapted to a novel assistive or resistive perturbation along the direction of the reach. Adaptation consisted of matching the amplitude and timing of the perturbation to minimize its effect on the reach. In a majority of Purkinje cells, simple spike firing recorded before and during adaptation demonstrated significant changes in position, velocity, and acceleration sensitivity. The timing of the simple spike representations change within individual cells, including shifts in predictive versus feedback signals. At the population level, feedback-based encoding of position increases early in learning and velocity decreases. Both timing changes reverse later in learning. The complex spike discharge was only weakly modulated by the perturbations, demonstrating that the changes in simple spike firing can be independent of climbing fiber input. In summary, we observed extensive alterations in individual Purkinje cell encoding of reach kinematics, although the movements were nearly identical in the baseline and adapted states. Therefore, adaption to mechanical perturbation of a reaching movement is accompanied by widespread modifications in the simple spike encoding. Copyright © 2015 the authors 0270-6474/15/351106-19$15.00/0.

  7. Changes in Purkinje Cell Simple Spike Encoding of Reach Kinematics during Adaption to a Mechanical Perturbation

    PubMed Central

    Hewitt, Angela L.; Popa, Laurentiu S.

    2015-01-01

    The cerebellum is essential in motor learning. At the cellular level, changes occur in both the simple spike and complex spike firing of Purkinje cells. Because simple spike discharge reflects the main output of the cerebellar cortex, changes in simple spike firing likely reflect the contribution of the cerebellum to the adapted behavior. Therefore, we investigated in Rhesus monkeys how the representation of arm kinematics in Purkinje cell simple spike discharge changed during adaptation to mechanical perturbations of reach movements. Monkeys rapidly adapted to a novel assistive or resistive perturbation along the direction of the reach. Adaptation consisted of matching the amplitude and timing of the perturbation to minimize its effect on the reach. In a majority of Purkinje cells, simple spike firing recorded before and during adaptation demonstrated significant changes in position, velocity, and acceleration sensitivity. The timing of the simple spike representations change within individual cells, including shifts in predictive versus feedback signals. At the population level, feedback-based encoding of position increases early in learning and velocity decreases. Both timing changes reverse later in learning. The complex spike discharge was only weakly modulated by the perturbations, demonstrating that the changes in simple spike firing can be independent of climbing fiber input. In summary, we observed extensive alterations in individual Purkinje cell encoding of reach kinematics, although the movements were nearly identical in the baseline and adapted states. Therefore, adaption to mechanical perturbation of a reaching movement is accompanied by widespread modifications in the simple spike encoding. PMID:25609626

  8. 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

  9. The cognitive domain of a glider in the game of life.

    PubMed

    Beer, Randall D

    2014-01-01

    This article examines in some technical detail the application of Maturana and Varela's biology of cognition to a simple concrete model: a glider in the game of Life cellular automaton. By adopting an autopoietic perspective on a glider, the set of possible perturbations to it can be divided into destructive and nondestructive subsets. From a glider's reaction to each nondestructive perturbation, its cognitive domain is then mapped. In addition, the structure of a glider's possible knowledge of its immediate environment, and the way in which that knowledge is grounded in its constitution, are fully described. The notion of structural coupling is then explored by characterizing the paths of mutual perturbation that a glider and its environment can undergo. Finally, a simple example of a communicative interaction between two gliders is given. The article concludes with a discussion of the potential implications of this analysis for the enactive approach to cognition.

  10. Matrix Perturbation Techniques in Structural Dynamics

    NASA Technical Reports Server (NTRS)

    Caughey, T. K.

    1973-01-01

    Matrix perturbation are developed techniques which can be used in the dynamical analysis of structures where the range of numerical values in the matrices extreme or where the nature of the damping matrix requires that complex valued eigenvalues and eigenvectors be used. The techniques can be advantageously used in a variety of fields such as earthquake engineering, ocean engineering, aerospace engineering and other fields concerned with the dynamical analysis of large complex structures or systems of second order differential equations. A number of simple examples are included to illustrate the techniques.

  11. Simple Perturbation Example for Quantum Chemistry.

    ERIC Educational Resources Information Center

    Goodfriend, P. L.

    1985-01-01

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

  12. Shuttle derived atmospheric density model. Part 2: STS atmospheric implications for AOTV trajectory analysis, a proposed GRAM perturbation density model

    NASA Technical Reports Server (NTRS)

    Findlay, J. T.; Kelly, G. M.; Troutman, P. A.

    1984-01-01

    A perturbation model to the Marshall Space Flight Center (MSFC) Global Reference Atmosphere Model (GRAM) was developed for use in the Aeroassist Orbital Transfer Vehicle (AOTV) trajectory and analysis. The model reflects NASA Space Shuttle experience over the first twelve entry flights. The GRAM was selected over the Air Force 1978 Reference Model because of its more general formulation and wider use throughout NASA. The add-on model, a simple scaling with altitude to reflect density structure encountered by the Shuttle Orbiter was selected principally to simplify implementation. Perturbations, by season, can be utilized to minimize the number of required simulations, however, exact Shuttle flight history can be exercised using the same model if desired. Such a perturbation model, though not meteorologically motivated, enables inclusion of High Resolution Accelerometer Package (HiRAP) results in the thermosphere. Provision is made to incorporate differing perturbations during the AOTV entry and exit phases of the aero-asist maneuver to account for trajectory displacement (geographic) along the ground track.

  13. Cosmic microwave background radiation anisotropies in brane worlds.

    PubMed

    Koyama, Kazuya

    2003-11-28

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

  14. Nonlinear zero-sum differential game analysis by singular perturbation methods

    NASA Technical Reports Server (NTRS)

    Sinar, J.; Farber, N.

    1982-01-01

    A class of nonlinear, zero-sum differential games, exhibiting time-scale separation properties, can be analyzed by singular-perturbation techniques. The merits of such an analysis, leading to an approximate game solution, as well as the 'well-posedness' of the formulation, are discussed. This approach is shown to be attractive for investigating pursuit-evasion problems; the original multidimensional differential game is decomposed to a 'simple pursuit' (free-stream) game and two independent (boundary-layer) optimal-control problems. Using multiple time-scale boundary-layer models results in a pair of uniformly valid zero-order composite feedback strategies. The dependence of suboptimal strategies on relative geometry and own-state measurements is demonstrated by a three dimensional, constant-speed example. For game analysis with realistic vehicle dynamics, the technique of forced singular perturbations and a variable modeling approach is proposed. Accuracy of the analysis is evaluated by comparison with the numerical solution of a time-optimal, variable-speed 'game of two cars' in the horizontal plane.

  15. Optimum performance of hovering rotors

    NASA Technical Reports Server (NTRS)

    Wu, J. C.; Goorjian, P. M.

    1972-01-01

    A theory for the optimum performance of a rotor hovering out of ground effect is developed. The performance problem is formulated using general momentum theory for an infinitely bladed rotor, and the effect of a finite number of blades is estimated. The analysis takes advantage of the fact that a simple relation exists between the radial distributions of static pressure and angular velocity in the ultimate wake, far downstream of the rotor, since the radial velocity vanishes there. This relation permits the establishment of an optimum performance criterion in terms of the ultimate wake velocities by introducing a small local perturbation of the rotational velocity and requiring the resulting ratio of thrust and power changes to be independent of the radial location of the perturbation. This analysis fully accounts for the changes in static pressure distribution and axial velocity distribution throughout the wake as the result of the local perturbation of the rotational velocity component.

  16. Equiparatition of energy for turbulent astrophysical fluids: Accounting for the unseen energy in molecular clouds

    NASA Technical Reports Server (NTRS)

    Zweibel, Ellen G.; Mckee, Christopher F.

    1995-01-01

    Molecular clouds are observed to be partially supported by turbulent pressure. The kinetic energy of the turbulence is directly measurable, but the potential energy, which consists of magnetic, thermal, and gravitational potential energy, is largly unseen. We have extended previous results on equipartition between kinetic and potential energy to show that it is likely to be a very good approximation in molecular clouds. We have used two separate approaches to demonstrate this result: For small-amplitude perturbations of a static equilibrium, we have used the energy principle analysis of Bernstein et al. (1958); this derivation applies to perturbations of arbitary wavelength. To treat perturbations of a nonstatic equilibrium, we have used the Lagrangian analysis of Dewar (1970); this analysis applies only to short-wavelength perturbations. Both analysis assume conservation of energy. Wave damping has only a small effect on equipartition if the wave frequency is small compared to the neutral-ion collision frequency; for the particular case we considered, radiative losses have no effect on equipartition. These results are then incorporated in a simple way into analyses of cloud equilibrium and global stability. We discuss the effect of Alfvenic turbulence on the Jeans mass and show that it has little effect on the magnetic critical mass.

  17. 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.

  18. Alternative Analysis of the Michaelis-Menten Equations

    ERIC Educational Resources Information Center

    Krogstad, Harald E.; Dawed, Mohammed Yiha; Tegegne, Tadele Tesfa

    2011-01-01

    Courses in mathematical modelling are always in need of simple, illustrative examples. The Michaelis-Menten reaction kinetics equations have been considered to be a basic example of scaling and singular perturbation. However, the leading order approximations do not easily show the expected behaviour, and this note proposes a different perturbation…

  19. The Brain Is Faster than the Hand in Split-Second Intentions to Respond to an Impending Hazard: A Simulation of Neuroadaptive Automation to Speed Recovery to Perturbation in Flight Attitude.

    PubMed

    Callan, Daniel E; Terzibas, Cengiz; Cassel, Daniel B; Sato, Masa-Aki; Parasuraman, Raja

    2016-01-01

    The goal of this research is to test the potential for neuroadaptive automation to improve response speed to a hazardous event by using a brain-computer interface (BCI) to decode perceptual-motor intention. Seven participants underwent four experimental sessions while measuring brain activity with magnetoencephalograpy. The first three sessions were of a simple constrained task in which the participant was to pull back on the control stick to recover from a perturbation in attitude in one condition and to passively observe the perturbation in the other condition. The fourth session consisted of having to recover from a perturbation in attitude while piloting the plane through the Grand Canyon constantly maneuvering to track over the river below. Independent component analysis was used on the first two sessions to extract artifacts and find an event related component associated with the onset of the perturbation. These two sessions were used to train a decoder to classify trials in which the participant recovered from the perturbation (motor intention) vs. just passively viewing the perturbation. The BCI-decoder was tested on the third session of the same simple task and found to be able to significantly distinguish motor intention trials from passive viewing trials (mean = 69.8%). The same BCI-decoder was then used to test the fourth session on the complex task. The BCI-decoder significantly classified perturbation from no perturbation trials (73.3%) with a significant time savings of 72.3 ms (Original response time of 425.0-352.7 ms for BCI-decoder). The BCI-decoder model of the best subject was shown to generalize for both performance and time savings to the other subjects. The results of our off-line open loop simulation demonstrate that BCI based neuroadaptive automation has the potential to decode motor intention faster than manual control in response to a hazardous perturbation in flight attitude while ignoring ongoing motor and visual induced activity related to piloting the airplane.

  20. The Brain Is Faster than the Hand in Split-Second Intentions to Respond to an Impending Hazard: A Simulation of Neuroadaptive Automation to Speed Recovery to Perturbation in Flight Attitude

    PubMed Central

    Callan, Daniel E.; Terzibas, Cengiz; Cassel, Daniel B.; Sato, Masa-aki; Parasuraman, Raja

    2016-01-01

    The goal of this research is to test the potential for neuroadaptive automation to improve response speed to a hazardous event by using a brain-computer interface (BCI) to decode perceptual-motor intention. Seven participants underwent four experimental sessions while measuring brain activity with magnetoencephalograpy. The first three sessions were of a simple constrained task in which the participant was to pull back on the control stick to recover from a perturbation in attitude in one condition and to passively observe the perturbation in the other condition. The fourth session consisted of having to recover from a perturbation in attitude while piloting the plane through the Grand Canyon constantly maneuvering to track over the river below. Independent component analysis was used on the first two sessions to extract artifacts and find an event related component associated with the onset of the perturbation. These two sessions were used to train a decoder to classify trials in which the participant recovered from the perturbation (motor intention) vs. just passively viewing the perturbation. The BCI-decoder was tested on the third session of the same simple task and found to be able to significantly distinguish motor intention trials from passive viewing trials (mean = 69.8%). The same BCI-decoder was then used to test the fourth session on the complex task. The BCI-decoder significantly classified perturbation from no perturbation trials (73.3%) with a significant time savings of 72.3 ms (Original response time of 425.0–352.7 ms for BCI-decoder). The BCI-decoder model of the best subject was shown to generalize for both performance and time savings to the other subjects. The results of our off-line open loop simulation demonstrate that BCI based neuroadaptive automation has the potential to decode motor intention faster than manual control in response to a hazardous perturbation in flight attitude while ignoring ongoing motor and visual induced activity related to piloting the airplane. PMID:27199710

  1. Simple atmospheric perturbation models for sonic-boom-signature distortion studies

    NASA Technical Reports Server (NTRS)

    Ehernberger, L. J.; Wurtele, Morton G.; Sharman, Robert D.

    1994-01-01

    Sonic-boom propagation from flight level to ground is influenced by wind and speed-of-sound variations resulting from temperature changes in both the mean atmospheric structure and small-scale perturbations. Meteorological behavior generally produces complex combinations of atmospheric perturbations in the form of turbulence, wind shears, up- and down-drafts and various wave behaviors. Differences between the speed of sound at the ground and at flight level will influence the threshold flight Mach number for which the sonic boom first reaches the ground as well as the width of the resulting sonic-boom carpet. Mean atmospheric temperature and wind structure as a function of altitude vary with location and time of year. These average properties of the atmosphere are well-documented and have been used in many sonic-boom propagation assessments. In contrast, smaller scale atmospheric perturbations are also known to modulate the shape and amplitude of sonic-boom signatures reaching the ground, but specific perturbation models have not been established for evaluating their effects on sonic-boom propagation. The purpose of this paper is to present simple examples of atmospheric vertical temperature gradients, wind shears, and wave motions that can guide preliminary assessments of nonturbulent atmospheric perturbation effects on sonic-boom propagation to the ground. The use of simple discrete atmospheric perturbation structures can facilitate the interpretation of the resulting sonic-boom propagation anomalies as well as intercomparisons among varied flight conditions and propagation models.

  2. Flux transfer events: Reconnection without separators. [magnetopause

    NASA Technical Reports Server (NTRS)

    Hesse, M.; Birn, J.; Schindler, K.

    1989-01-01

    A topological analysis of a simple model magnetic field of a perturbation at the magnetopause modeling an apparent flux transfer event is presented. It is shown that a localized perturbation at the magnetopause can in principle open a closed magnetosphere by establishing magnetic connections across the magnetopause. Although the model field exhibits neutral points, these are not involved in the magnetic connection of the flux tubes. The topological substructure of a localized perturbation is analyzed in a simpler configuration. The presence of both signs of the magnetic field component normal to the magnetopause leads to a linkage of topologically different flux tubes, described as a flux knot, and a filamentary substructure of field lines of different topological types which becomes increasingly complicated for decreasing magnetic shear at the magnetopause.

  3. Tidal interactions in the expanding universe - The formation of prolate systems

    NASA Technical Reports Server (NTRS)

    Binney, J.; Silk, J.

    1979-01-01

    The study estimates the magnitude of the anisotropy that can be tidally induced in neighboring initially spherical protostructures, be they protogalaxies, protoclusters, or even uncollapsed density enhancements in the large-scale structure of the universe. It is shown that the linear analysis of tidal interactions developed by Peebles (1969) predicts that the anisotropy energy of a perturbation grows to first order in a small dimensionless parameter, whereas the net angular momentum acquired is of second order. A simple model is presented for the growth of anisotropy by tidal interactions during the nonlinear stage of the development of perturbations. A possible observational test is described of the alignment predicted by the model between the orientations of large-scale perturbations and the positions of neighboring density enhancements.

  4. Consequences of viscous anisotropy for melt localization in a deforming, two-phase aggregate

    NASA Astrophysics Data System (ADS)

    Takei, Y.; Katz, R. F.

    2012-12-01

    Melt localization in the deforming, partially molten mantle has been of interest because it affects the melt extraction rate, mantle deformability, and chemical interaction between the melt and host rock. Experimental studies have reported the spontaneous segregation of melt into melt-rich bands in samples deformed under simple shear and torsion (Holtzman et al, 2003, King et al, 2010). Efforts to clarify the instability mechanism have so far revealed that rheological properties of partially molten rocks control the occurrence of instability. Porosity-weakening viscosity, empirically written as exp(- λ × f) with porosity f and constant λ(= 25-45), plays an essential role in the destabilization of porosity perturbation in the shear flow of a two-phase aggregate (eg., pure shear flow, simple shear flow): the perturbation growth rate is proportional to the product of shear strain rate and the factor λ (Stevenson, 1989). The stress exponent n of the viscosity affects the angle of the perturbation plane with maximum growthrate, where n=3-6 (power-law creep) explains the experimentally observed low angle to the shear plane (Katz et al, 2006). However, in-situ experimental measurements of n indicate that it takes values as low as unity without affecting the observed orientation of melt bands. Viscous anisotropy provides an alternative explanation for the observed band angles. It is produced by the stress-induced microstructural anisotropy (Daines and Kohlstedt, 1997; Zimmermann et al., 1999; Takei, 2010), and it enhances the coupling between melt migration and matrix shear deformation (Takei and Holtzman, 2009). Even without any porosity perturbation, viscous anisotropy destabilizes simple patterns of two-phase flow with a stress/strain gradient (eg., Poiseuille flow, torsional flow) and gives rise to shear-induced melt localization: the growth rate of this mechanism depends on the shear strain rate and the compaction length relative to the spatial scale of the gradient. When a porosity perturbation is added to the anisotropic system, both localization mechanisms work simultaneously, where the dominant angle of perturbation is decreased by the viscous anisotropy, similarly to the effect of n. Although viscous anisotropy plays an important role in melt localization, previous studies were limited to some simple or linearized cases (Takei and Holtzman, 2009, Butler 2012). Using linearised stability analysis and numerical simulation, we perform a systematic study of viscous anisotropy for behavior of partially molten rocks under forced deformation. Fully nonlinear solutions are obtained for melt localization under simple shear flow, 2D Poiseuille flow, and torsional flow. We show that Poiseuille flow causes melt-lubrication instability, but torsional flow does not. Results for simple shear and torsional flow are compared to the experimental results. Through the comparison between model predictions and experiments, we can test the validity of current theory, ascertain its deficiencies, and refine it to better describe the natural system.

  5. Effects of Normal and Perturbed Social Play on the Duration and Amplitude of Different Types of Infant Smiles

    ERIC Educational Resources Information Center

    Fogel, Alan; Hsu, Hui-Chin; Shapiro, Alyson F.; Nelson-Goens, G. Christina; Secrist, Cory

    2006-01-01

    Different types of smiling varying in amplitude of lip corner retraction were investigated during 2 mother-infant games--peekaboo and tickle--at 6 and 12 months and during normally occurring and perturbed games. Using Facial Action Coding System (FACS), infant smiles were coded as simple (lip corner retraction only), Duchenne (simple plus cheek…

  6. Impact of Anthropogenic CO2 on the Next Glacial Cycle

    NASA Astrophysics Data System (ADS)

    Herrero, C.; García-Olivares, A.; Pelegrí, J. L.

    2014-12-01

    A simple relaxation-type model (García-Olivares and Herrero, 2013) based on an optimization of Paillard and Parrenin (2004), has been used to predict the future evolution of atmospheric CO2, global ice volume and Antarctic ice cover during the next 300 kyr, with and without the atmospheric CO2 perturbation caused by anthropogenic emissions.The initial atmospheric CO2 condition is obtained after a critical data analysis that sets 1300 Gt as the most realistic carbon Ultimate Recoverable Resources, with the help of a global compartmental model to determine the carbon transfer function to the atmosphere. This analysis sets a peak of emissions on year 2037 AD and a maximum CO2 concentration of 519 ppmv in 2300 AD, leading to 20 kyr of abnormally high greenhouse effect. Weathering compensation and emission of methane from clathrates have also been considered as they have relevant effects on the dynamics of the system after the perturbation.The anthropogenic CO2 pulse clearly perturbs the natural cycle for all model variables during the forthcoming 300 kyr. The present interglacial will be lengthen by 25 kyr, as the anthropogenic perturbation will lead to a delay in the future advance of the ice sheet on the Antarctic shelf and a consequent perturbation of the deep ocean stratification, so the relative maximum of boreal insolation 65 kyr AP will not affect the developing glaciation. Instead, it will be the following insolation peak, about 110 kyr AP, which will find an appropriate climatic state to trigger the next deglaciation. The next glacial maximum will take place about 105 kyr AP and the following interglacial will be delayed forward in time by 44 kyr in relation to unperturbed conditions.This study endorses the idea that relaxation type coupled models, despite their simple structure, may retain the principal Earth's climatic interactions, being capable of accounting for the natural evolution of an externally imposed atmospheric CO2 pulse. - Garcia-Olivares, A. and Herrero, C. (2013) "Simulation of glacial-interglacial cycles by simple relaxation models: consistency with observational results" Clim. Dyn., 41:1307-1331- Paillard, D. and Parrenin, F. (2004) "The Antarctic ice sheet and the triggering of deglaciations" Earth. Planet. Sci. Lett., 227, 263 - 271

  7. 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.

  8. The application of the thermodynamic perturbation theory to study the hydrophobic hydration.

    PubMed

    Mohoric, Tomaz; Urbic, Tomaz; Hribar-Lee, Barbara

    2013-07-14

    The thermodynamic perturbation theory was tested against newly obtained Monte Carlo computer simulations to describe the major features of the hydrophobic effect in a simple 3D-Mercedes-Benz water model: the temperature and hydrophobe size dependence on entropy, enthalpy, and free energy of transfer of a simple hydrophobic solute into water. An excellent agreement was obtained between the theoretical and simulation results. Further, the thermodynamic perturbation theory qualitatively correctly (with respect to the experimental data) describes the solvation thermodynamics under conditions where the simulation results are difficult to obtain with good enough accuracy, e.g., at high pressures.

  9. The application of the thermodynamic perturbation theory to study the hydrophobic hydration

    NASA Astrophysics Data System (ADS)

    Mohorič, Tomaž; Urbic, Tomaz; Hribar-Lee, Barbara

    2013-07-01

    The thermodynamic perturbation theory was tested against newly obtained Monte Carlo computer simulations to describe the major features of the hydrophobic effect in a simple 3D-Mercedes-Benz water model: the temperature and hydrophobe size dependence on entropy, enthalpy, and free energy of transfer of a simple hydrophobic solute into water. An excellent agreement was obtained between the theoretical and simulation results. Further, the thermodynamic perturbation theory qualitatively correctly (with respect to the experimental data) describes the solvation thermodynamics under conditions where the simulation results are difficult to obtain with good enough accuracy, e.g., at high pressures.

  10. Post-game analysis: An initial experiment for heuristic-based resource management in concurrent systems

    NASA Technical Reports Server (NTRS)

    Yan, Jerry C.

    1987-01-01

    In concurrent systems, a major responsibility of the resource management system is to decide how the application program is to be mapped onto the multi-processor. Instead of using abstract program and machine models, a generate-and-test framework known as 'post-game analysis' that is based on data gathered during program execution is proposed. Each iteration consists of (1) (a simulation of) an execution of the program; (2) analysis of the data gathered; and (3) the proposal of a new mapping that would have a smaller execution time. These heuristics are applied to predict execution time changes in response to small perturbations applied to the current mapping. An initial experiment was carried out using simple strategies on 'pipeline-like' applications. The results obtained from four simple strategies demonstrated that for this kind of application, even simple strategies can produce acceptable speed-up with a small number of iterations.

  11. 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…

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

    NASA Astrophysics Data System (ADS)

    Campoamor-Stursberg, Rutwig

    2017-03-01

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

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

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

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

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

  14. 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.

  15. Selective Transient Cooling by Impulse Perturbations in a Simple Toy Model

    NASA Astrophysics Data System (ADS)

    Fabrizio, Michele

    2018-06-01

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

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

    NASA Technical Reports Server (NTRS)

    Rosenfeld, Y.; Ashcroft, N. W.

    1978-01-01

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

  17. On the topology of flux transfer events

    NASA Technical Reports Server (NTRS)

    Hesse, Michael; Birn, Joachim; Schindler, Karl

    1990-01-01

    A topological analysis is made of a simple model magnetic field of a perturbation at the magnetopause that shares magnetic properties with flux transfer events. The aim is to clarify a number of topological aspects that arise in the case of fully three-dimensional magnetic fields. It is shown that a localized perturbation at the magnetopause can in principle open a closed magnetosphere by establishing magnetic connections across the magnetopause by the formation of a ropelike magnetic field structure. For this purpose a global topological model of a closed magnetosphere is considered as the unperturbed state. The topological substructure of the model flux rope is discussed in detail.

  18. Electrostatics of cysteine residues in proteins: Parameterization and validation of a simple model

    PubMed Central

    Salsbury, Freddie R.; Poole, Leslie B.; Fetrow, Jacquelyn S.

    2013-01-01

    One of the most popular and simple models for the calculation of pKas from a protein structure is the semi-macroscopic electrostatic model MEAD. This model requires empirical parameters for each residue to calculate pKas. Analysis of current, widely used empirical parameters for cysteine residues showed that they did not reproduce expected cysteine pKas; thus, we set out to identify parameters consistent with the CHARMM27 force field that capture both the behavior of typical cysteines in proteins and the behavior of cysteines which have perturbed pKas. The new parameters were validated in three ways: (1) calculation across a large set of typical cysteines in proteins (where the calculations are expected to reproduce expected ensemble behavior); (2) calculation across a set of perturbed cysteines in proteins (where the calculations are expected to reproduce the shifted ensemble behavior); and (3) comparison to experimentally determined pKa values (where the calculation should reproduce the pKa within experimental error). Both the general behavior of cysteines in proteins and the perturbed pKa in some proteins can be predicted reasonably well using the newly determined empirical parameters within the MEAD model for protein electrostatics. This study provides the first general analysis of the electrostatics of cysteines in proteins, with specific attention paid to capturing both the behavior of typical cysteines in a protein and the behavior of cysteines whose pKa should be shifted, and validation of force field parameters for cysteine residues. PMID:22777874

  19. Instanton and noninstanton tunneling in periodically perturbed barriers: semiclassical and quantum interpretations.

    PubMed

    Takahashi, Kin'ya; Ikeda, Kensuke S

    2012-11-01

    In multidimensional barrier tunneling, there exist two different types of tunneling mechanisms, instanton-type tunneling and noninstanton tunneling. In this paper we investigate transitions between the two tunneling mechanisms from the semiclassical and quantum viewpoints taking two simple models: a periodically perturbed Eckart barrier for the semiclassical analysis and a periodically perturbed rectangular barrier for the quantum analysis. As a result, similar transitions are observed with change of the perturbation frequency ω for both systems, and we obtain a comprehensive scenario from both semiclassical and quantum viewpoints for them. In the middle range of ω, in which the plateau spectrum is observed, noninstanton tunneling dominates the tunneling process, and the tunneling amplitude takes the maximum value. Noninstanton tunneling explained by stable-unstable manifold guided tunneling (SUMGT) from the semiclassical viewpoint is interpreted as multiphoton-assisted tunneling from the quantum viewpoint. However, in the limit ω→0, instanton-type tunneling takes the place of noninstanton tunneling, and the tunneling amplitude converges on a constant value depending on the perturbation strength. The spectrum localized around the input energy is observed, and there is a scaling law with respect to the width of the spectrum envelope, i.e., the width ∝ℏω. In the limit ω→∞, the tunneling amplitude converges on that of the unperturbed system, i.e., the instanton of the unperturbed system.

  20. The application of the thermodynamic perturbation theory to study the hydrophobic hydration

    PubMed Central

    Mohorič, Tomaž; Urbic, Tomaz; Hribar-Lee, Barbara

    2013-01-01

    The thermodynamic perturbation theory was tested against newly obtained Monte Carlo computer simulations to describe the major features of the hydrophobic effect in a simple 3D-Mercedes-Benz water model: the temperature and hydrophobe size dependence on entropy, enthalpy, and free energy of transfer of a simple hydrophobic solute into water. An excellent agreement was obtained between the theoretical and simulation results. Further, the thermodynamic perturbation theory qualitatively correctly (with respect to the experimental data) describes the solvation thermodynamics under conditions where the simulation results are difficult to obtain with good enough accuracy, e.g., at high pressures. PMID:23862923

  1. Algebraic perturbation theory for dense liquids with discrete potentials

    NASA Astrophysics Data System (ADS)

    Adib, Artur B.

    2007-06-01

    A simple theory for the leading-order correction g1(r) to the structure of a hard-sphere liquid with discrete (e.g., square-well) potential perturbations is proposed. The theory makes use of a general approximation that effectively eliminates four-particle correlations from g1(r) with good accuracy at high densities. For the particular case of discrete perturbations, the remaining three-particle correlations can be modeled with a simple volume-exclusion argument, resulting in an algebraic and surprisingly accurate expression for g1(r) . The structure of a discrete “core-softened” model for liquids with anomalous thermodynamic properties is reproduced as an application.

  2. Calculation of stochastic broadening due to low mn magnetic perturbation in the simple map in action-angle coordinates

    NASA Astrophysics Data System (ADS)

    Hinton, Courtney; Punjabi, Alkesh; Ali, Halima

    2009-11-01

    The simple map is the simplest map that has topology of divertor tokamaks [A. Punjabi, H. Ali, T. Evans, and A. Boozer, Phys. Let. A 364, 140--145 (2007)]. Recently, the action-angle coordinates for simple map are analytically calculated, and simple map is constructed in action-angle coordinates [O. Kerwin, A. Punjabi, and H. Ali, Phys. Plasmas 15, 072504 (2008)]. Action-angle coordinates for simple map cannot be inverted to real space coordinates (R,Z). Because there is logarithmic singularity on the ideal separatrix, trajectories cannot cross separatrix [op cit]. Simple map in action-angle coordinates is applied to calculate stochastic broadening due to the low mn magnetic perturbation with mode numbers m=1, and n=±1. The width of stochastic layer near the X-point scales as 0.63 power of the amplitude δ of low mn perturbation, toroidal flux loss scales as 1.16 power of δ, and poloidal flux loss scales as 1.26 power of δ. Scaling of width deviates from Boozer-Rechester scaling by 26% [A. Boozer, and A. Rechester, Phys. Fluids 21, 682 (1978)]. This work is supported by US Department of Energy grants DE-FG02-07ER54937, DE-FG02-01ER54624 and DE-FG02-04ER54793.

  3. Simple Map with Low MN Perturbation for a Single-Null Divertor Tokamak with Constant Width of Stochastic Layer

    NASA Astrophysics Data System (ADS)

    Verma, Arun; Smith, Terry; Punjabi, Alkesh; Boozer, Allen

    1996-11-01

    In this work, we investigate the effects of low MN perturbations in a single-null divertor tokamak with stochastic scrape-off layer. The unperturbed magnetic topology of a single-null divertor tokamak is represented by Simple Map (Punjabi A, Verma A and Boozer A, Phys Rev Lett), 69, 3322 (1992) and J Plasma Phys, 52, 91 (1994). We choose the combinations of the map parameter k, and the strength of the low MN perturbation such that the width of stochastic layer remains unchanged. We give detailed results on the effects of low MN perturbation on the magnetic topology of the stochastic layer and on the footprint of field lines on the divertor plate given the constraint of constant width of the stochastic layer. The low MN perturbations occur naturally and therefore their effects are of considerable importance in tokamak divertor physics. This work is supported by US DOE OFES. Use of CRAY at HU and at NERSC is gratefully acknowledged.

  4. 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.

  5. Galileon bounce after ekpyrotic contraction

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

    Osipov, M.; Rubakov, V., E-mail: osipov@ms2.inr.ac.ru, E-mail: rubakov@ms2.inr.ac.ru

    We consider a simple cosmological model that includes a long ekpyrotic contraction stage and smooth bounce after it. Ekpyrotic behavior is due to a scalar field with a negative exponential potential, whereas the Galileon field produces bounce. We give an analytical picture of how the bounce occurs within the weak gravity regime, and then perform numerical analysis to extend our results to a non-perturbative regime.

  6. Generalized moment analysis of magnetic field correlations for accumulations of spherical and cylindrical magnetic pertubers

    NASA Astrophysics Data System (ADS)

    Kurz, Felix; Kampf, Thomas; Buschle, Lukas; Schlemmer, Heinz-Peter; Bendszus, Martin; Heiland, Sabine; Ziener, Christian

    2016-12-01

    In biological tissue, an accumulation of similarly shaped objects with a susceptibility difference to the surrounding tissue generates a local distortion of the external magnetic field in magnetic resonance imaging. It induces stochastic field fluctuations that characteristically influence proton spin diffusion in the vicinity of these magnetic perturbers. The magnetic field correlation that is associated with such local magnetic field inhomogeneities can be expressed in the form of a dynamic frequency autocorrelation function that is related to the time evolution of the measured magnetization. Here, an eigenfunction expansion for two simple magnetic perturber shapes, that of spheres and cylinders, is considered for restricted spin diffusion in a simple model geometry. Then, the concept of generalized moment analysis, an approximation technique that is applied in the study of (non-)reactive processes that involve Brownian motion, allows to provide analytical expressions for the correlation function for different exponential decay forms. Results for the biexponential decay for both spherical and cylindrical magnetized objects are derived and compared with the frequently used (less accurate) monoexponential decay forms. They are in asymptotic agreement with the numerically exact value of the correlation function for long and short times.

  7. 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.

  8. Transverse momentum in double parton scattering: factorisation, evolution and matching

    NASA Astrophysics Data System (ADS)

    Buffing, Maarten G. A.; Diehl, Markus; Kasemets, Tomas

    2018-01-01

    We give a description of double parton scattering with measured transverse momenta in the final state, extending the formalism for factorisation and resummation developed by Collins, Soper and Sterman for the production of colourless particles. After a detailed analysis of their colour structure, we derive and solve evolution equations in rapidity and renormalisation scale for the relevant soft factors and double parton distributions. We show how in the perturbative regime, transverse momentum dependent double parton distributions can be expressed in terms of simpler nonperturbative quantities and compute several of the corresponding perturbative kernels at one-loop accuracy. We then show how the coherent sum of single and double parton scattering can be simplified for perturbatively large transverse momenta, and we discuss to which order resummation can be performed with presently available results. As an auxiliary result, we derive a simple form for the square root factor in the Collins construction of transverse momentum dependent parton distributions.

  9. A new approach to the stability analysis of transient natural convection in porous media

    NASA Astrophysics Data System (ADS)

    Tilton, Nils

    2016-11-01

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

  10. Preliminary assessment of the robustness of dynamic inversion based flight control laws

    NASA Technical Reports Server (NTRS)

    Snell, S. A.

    1992-01-01

    Dynamic-inversion-based flight control laws present an attractive alternative to conventional gain-scheduled designs for high angle-of-attack maneuvering, where nonlinearities dominate the dynamics. Dynamic inversion is easily applied to the aircraft dynamics requiring a knowledge of the nonlinear equations of motion alone, rather than an extensive set of linearizations. However, the robustness properties of the dynamic inversion are questionable especially when considering the uncertainties involved with the aerodynamic database during post-stall flight. This paper presents a simple analysis and some preliminary results of simulations with a perturbed database. It is shown that incorporating integrators into the control loops helps to improve the performance in the presence of these perturbations.

  11. Electrostatics of cysteine residues in proteins: parameterization and validation of a simple model.

    PubMed

    Salsbury, Freddie R; Poole, Leslie B; Fetrow, Jacquelyn S

    2012-11-01

    One of the most popular and simple models for the calculation of pK(a) s from a protein structure is the semi-macroscopic electrostatic model MEAD. This model requires empirical parameters for each residue to calculate pK(a) s. Analysis of current, widely used empirical parameters for cysteine residues showed that they did not reproduce expected cysteine pK(a) s; thus, we set out to identify parameters consistent with the CHARMM27 force field that capture both the behavior of typical cysteines in proteins and the behavior of cysteines which have perturbed pK(a) s. The new parameters were validated in three ways: (1) calculation across a large set of typical cysteines in proteins (where the calculations are expected to reproduce expected ensemble behavior); (2) calculation across a set of perturbed cysteines in proteins (where the calculations are expected to reproduce the shifted ensemble behavior); and (3) comparison to experimentally determined pK(a) values (where the calculation should reproduce the pK(a) within experimental error). Both the general behavior of cysteines in proteins and the perturbed pK(a) in some proteins can be predicted reasonably well using the newly determined empirical parameters within the MEAD model for protein electrostatics. This study provides the first general analysis of the electrostatics of cysteines in proteins, with specific attention paid to capturing both the behavior of typical cysteines in a protein and the behavior of cysteines whose pK(a) should be shifted, and validation of force field parameters for cysteine residues. Copyright © 2012 Wiley Periodicals, Inc.

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

    NASA Astrophysics Data System (ADS)

    Suárez, Abril; Chavanis, Pierre-Henri

    2015-07-01

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

  13. Dynamic characteristics of a vibrating beam with periodic variation in bending stiffness

    NASA Technical Reports Server (NTRS)

    Townsend, John S.

    1987-01-01

    A detailed dynamic analysis is performed of a vibrating beam with bending stiffness periodic in the spatial coordinate. The effects of system parameters on beam response are explored with a perturbation expansion technique. It is found that periodic stiffness acts to modulate the modal displacements from the characteristic shape of a simple sine wave. The results are verified by a finite element solution and through experimental testing.

  14. Roles of dark energy perturbations in dynamical dark energy models: can we ignore them?

    PubMed

    Park, Chan-Gyung; Hwang, Jai-chan; Lee, Jae-heon; Noh, Hyerim

    2009-10-09

    We show the importance of properly including the perturbations of the dark energy component in the dynamical dark energy models based on a scalar field and modified gravity theories in order to meet with present and future observational precisions. Based on a simple scaling scalar field dark energy model, we show that observationally distinguishable substantial differences appear by ignoring the dark energy perturbation. By ignoring it the perturbed system of equations becomes inconsistent and deviations in (gauge-invariant) power spectra depend on the gauge choice.

  15. 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.

  16. Noncolocated Time-Reversal MUSIC: High-SNR Distribution of Null Spectrum

    NASA Astrophysics Data System (ADS)

    Ciuonzo, Domenico; Rossi, Pierluigi Salvo

    2017-04-01

    We derive the asymptotic distribution of the null spectrum of the well-known Multiple Signal Classification (MUSIC) in its computational Time-Reversal (TR) form. The result pertains to a single-frequency non-colocated multistatic scenario and several TR-MUSIC variants are here investigated. The analysis builds upon the 1st-order perturbation of the singular value decomposition and allows a simple characterization of null-spectrum moments (up to the 2nd order). This enables a comparison in terms of spectrums stability. Finally, a numerical analysis is provided to confirm the theoretical findings.

  17. On the resonance amplification of magnetic perturbations near the threshold of tearing instability in a tokamak

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

    Arsenin, V. V., E-mail: arsenin-vv@nrcki.ru; Skovoroda, A. A., E-mail: skovoroda-aa@nrcki.ru

    2015-12-15

    Using a cylindrical model, a relatively simple description is presented of how a magnetic field perturbation stimulated by a low external helical current or a small helical distortion of the boundary and generating magnetic islands penetrates into a plasma column with a magnetic surface q=m/n to which tearing instability is attached. Linear analysis of the classical instability with an aperiodic growth of the perturbation in time shows that the perturbation amplitude in plasma increases in a resonant manner as the discharge parameters approach the threshold of tearing instability. In a stationary case, under the assumption on the helical character ofmore » equilibrium, which can be found from the two-dimensional nonlinear equation for the helical flux, there is no requirement for the small size of the island. Examples of calculations in which magnetic islands are large near the threshold of tearing instability are presented. The bifurcation of equilibrium near the threshold of tearing instability in plasma with a cylindrical boundary, i.e., the existence of helical equilibrium (along with cylindrical equilibrium) with large islands, is described. Moreover, helical equilibrium can also exist in the absence of instability.« less

  18. A Pedagogical Approach to the Magnus Expansion

    ERIC Educational Resources Information Center

    Blanes, S.; Casas, F.; Oteo, J. A.; Ros, J.

    2010-01-01

    Time-dependent perturbation theory as a tool to compute approximate solutions of the Schrodinger equation does not preserve unitarity. Here we present, in a simple way, how the "Magnus expansion" (also known as "exponential perturbation theory") provides such unitary approximate solutions. The purpose is to illustrate the importance and…

  19. On the comparison of perturbation-iteration algorithm and residual power series method to solve fractional Zakharov-Kuznetsov equation

    NASA Astrophysics Data System (ADS)

    Şenol, Mehmet; Alquran, Marwan; Kasmaei, Hamed Daei

    2018-06-01

    In this paper, we present analytic-approximate solution of time-fractional Zakharov-Kuznetsov equation. This model demonstrates the behavior of weakly nonlinear ion acoustic waves in a plasma bearing cold ions and hot isothermal electrons in the presence of a uniform magnetic field. Basic definitions of fractional derivatives are described in the Caputo sense. Perturbation-iteration algorithm (PIA) and residual power series method (RPSM) are applied to solve this equation with success. The convergence analysis is also presented for both methods. Numerical results are given and then they are compared with the exact solutions. Comparison of the results reveal that both methods are competitive, powerful, reliable, simple to use and ready to apply to wide range of fractional partial differential equations.

  20. The growth of aspherical structure in the universe - Is the Local Supercluster an unusual system

    NASA Technical Reports Server (NTRS)

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

    1979-01-01

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

  1. A unitary convolution approximation for the impact-parameter dependent electronic energy loss

    NASA Astrophysics Data System (ADS)

    Schiwietz, G.; Grande, P. L.

    1999-06-01

    In this work, we propose a simple method to calculate the impact-parameter dependence of the electronic energy loss of bare ions for all impact parameters. This perturbative convolution approximation (PCA) is based on first-order perturbation theory, and thus, it is only valid for fast particles with low projectile charges. Using Bloch's stopping-power result and a simple scaling, we get rid of the restriction to low charge states and derive the unitary convolution approximation (UCA). Results of the UCA are then compared with full quantum-mechanical coupled-channel calculations for the impact-parameter dependent electronic energy loss.

  2. Protein side chain rotational isomerization: A minimum perturbation mapping study

    NASA Astrophysics Data System (ADS)

    Haydock, Christopher

    1993-05-01

    A theory of the rotational isomerization of the indole side chain of tryptophan-47 of variant-3 scorpion neurotoxin is presented. The isomerization potential energy, entropic part of the isomerization free energy, isomer probabilities, transition state theory reaction rates, and indole order parameters are calculated from a minimum perturbation mapping over tryptophan-47 χ1×χ2 torsion space. A new method for calculating the fluorescence anisotropy from molecular dynamics simulations is proposed. The method is based on an expansion that separates transition dipole orientation from chromophore dynamics. The minimum perturbation potential energy map is inverted and applied as a bias potential for a 100 ns umbrella sampling simulation. The entropic part of the isomerization free energy as calculated by minimum perturbation mapping and umbrella sampling are in fairly close agreement. Throughout, the approximation is made that two glutamine and three tyrosine side chains neighboring tryptophan-47 are truncated at the Cβ atom. Comparison with the previous combination thermodynamic perturbation and umbrella sampling study suggests that this truncated neighbor side chain approximation leads to at least a qualitatively correct theory of tryptophan-47 rotational isomerization in the wild type variant-3 scorpion neurotoxin. Analysis of van der Waals interactions in a transition state region indicates that for the simulation of barrier crossing trajectories a linear combination of three specially defined dihedral angles will be superior to a simple side chain dihedral reaction coordinate.

  3. Structure formation beyond shell-crossing: nonperturbative expansions and late-time attractors

    NASA Astrophysics Data System (ADS)

    Pietroni, Massimo

    2018-06-01

    Structure formation in 1+1 dimensions is considered, with emphasis on the effects of shell-crossing. The breakdown of the perturbative expansion beyond shell-crossing is discussed, and it is shown, in a simple example, that the perturbative series can be extended to a transseries including nonperturbative terms. The latter converges to the exact result well beyond the range of validity of perturbation theory. The crucial role of the divergences induced by shell-crossing is discussed. They provide constraints on the structure of the transseries and act as a bridge between the perturbative and the nonperturbative sectors. Then, we show that the dynamics in the deep multistreaming regime is governed by attractors. In the case of simple initial conditions, these attractors coincide with the asymptotic configurations of the adhesion model, but in general they may differ. These results are applied to a cosmological setting, and an algorithm to build the attractor solution starting from the Zel'dovich approximation is developed. Finally, this algorithm is applied to the search of `haloes' and the results are compared with those obtained from the exact dynamical equations.

  4. Response of an oscillatory differential delay equation to a single stimulus.

    PubMed

    Mackey, Michael C; Tyran-Kamińska, Marta; Walther, Hans-Otto

    2017-04-01

    Here we analytically examine the response of a limit cycle solution to a simple differential delay equation to a single pulse perturbation of the piecewise linear nonlinearity. We construct the unperturbed limit cycle analytically, and are able to completely characterize the perturbed response to a pulse of positive amplitude and duration with onset at different points in the limit cycle. We determine the perturbed minima and maxima and period of the limit cycle and show how the pulse modifies these from the unperturbed case.

  5. Preheating and entropy perturbations in axion monodromy inflation

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

    McDonough, Evan; Moghaddam, Hossein Bazrafshan; Brandenberger, Robert H.

    2016-05-04

    We study the preheating of gauge fields in a simple axion monodromy model and compute the induced entropy perturbations and their effect on the curvature fluctuations. We find that the correction to the spectrum of curvature perturbations has a blue spectrum with index n{sub s}=5/2. Hence, these induced modes are harmless for the observed structure of the universe. Since the spectrum is blue, there is the danger of overproduction of primordial black holes. However, we show that the observational constraints are easily satisfied.

  6. A ground track control algorithm for the Topographic Mapping Laser Altimeter (TMLA)

    NASA Technical Reports Server (NTRS)

    Blaes, V.; Mcintosh, R.; Roszman, L.; Cooley, J.

    1993-01-01

    The results of an analysis of an algorithm that will provide autonomous onboard orbit control using orbits determined with Global Positioning System (GPS) data. The algorithm uses the GPS data to (1) compute the ground track error relative to a fixed longitude grid, and (2) determine the altitude adjustment required to correct the longitude error. A program was written on a personal computer (PC) to test the concept for numerous altitudes and values of solar flux using a simplified orbit model including only the J sub 2 zonal harmonic and simple orbit decay computations. The algorithm was then implemented in a precision orbit propagation program having a full range of perturbations. The analysis showed that, even with all perturbations (including actual time histories of solar flux variation), the algorithm could effectively control the spacecraft ground track and yield more than 99 percent Earth coverage in the time required to complete one coverage cycle on the fixed grid (220 to 230 days depending on altitude and overlap allowance).

  7. 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.

  8. Kinematic strategies for mitigating gust perturbations in insects.

    PubMed

    Vance, J T; Faruque, I; Humbert, J S

    2013-03-01

    Insects are attractive models for the development of micro-aerial vehicles (MAVs) due to their relatively simple sensing, actuation and control architectures as compared to vertebrates, and because of their robust flight ability in dynamic and heterogeneous environments, characterized by turbulence and gusts of wind. How do insects respond to gust perturbations? We investigated this question by perturbing freely-flying honey bees and stalk-eye flies with low-pressure bursts of compressed air to simulate a wind gust. Body and wing kinematics were analyzed from flight sequences, recorded using three high-speed digital video cameras. Bees quickly responded to body rotations caused by gusts through bilateral asymmetry in stroke amplitude, whereas stalk-eye flies used a combination of asymmetric stroke amplitude and wing rotation angle. Both insects coordinated asymmetric and symmetric kinematics in response to gusts, which provides model strategies for simple yet robust flight characteristics for MAVs.

  9. Simple map in action-angle coordinates

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

    Kerwin, Olivia; Punjabi, Alkesh; Ali, Halima

    A simple map [A. Punjabi, A. Verma, and A. Boozer, Phys. Rev. Lett. 69, 3322 (1992)] is the simplest map that has the topology of divertor tokamaks [A. Punjabi, H. Ali, T. Evans, and A. Boozer, Phys. Lett. A 364, 140 (2007)]. Here, action-angle coordinates, the safety factor, and the equilibrium generating function for the simple map are calculated analytically. The simple map in action-angle coordinates is derived from canonical transformations. This map cannot be integrated across the separatrix surface because of the singularity in the safety factor there. The stochastic broadening of the ideal separatrix surface in action-angle representationmore » is calculated by adding a perturbation to the simple map equilibrium generating function. This perturbation represents the spatial noise and field errors typical of the DIII-D [J. L. Luxon and L. E. Davis, Fusion Technol. 8, 441 (1985)] tokamak. The stationary Fourier modes of the perturbation have poloidal and toroidal mode numbers (m,n,)=((3,1),(4,1),(6,2),(7,2),(8,2),(9,3),(10,3),(11,3)) with amplitude {delta}=0.8x10{sup -5}. Near the X-point, about 0.12% of toroidal magnetic flux inside the separatrix, and about 0.06% of the poloidal flux inside the separatrix is lost. When the distance from the O-point to the X-point is 1 m, the width of stochastic layer near the X-point is about 1.4 cm. The average value of the action on the last good surface is 0.19072 compared to the action value of 3/5{pi} on the separatrix. The average width of stochastic layer in action coordinate is 2.7x10{sup -4}, while the average area of the stochastic layer in action-angle phase space is 1.69017x10{sup -3}. On average, about 0.14% of action or toroidal flux inside the ideal separatrix is lost due to broadening. Roughly five times more toroidal flux is lost in the simple map than in DIII-D for the same perturbation [A. Punjabi, H. Ali, A. Boozer, and T. Evans, Bull. Amer. Phys. Soc. 52, 124 (2007)].« less

  10. Simple map in action-angle coordinates

    NASA Astrophysics Data System (ADS)

    Kerwin, Olivia; Punjabi, Alkesh; Ali, Halima

    2008-07-01

    A simple map [A. Punjabi, A. Verma, and A. Boozer, Phys. Rev. Lett. 69, 3322 (1992)] is the simplest map that has the topology of divertor tokamaks [A. Punjabi, H. Ali, T. Evans, and A. Boozer, Phys. Lett. A 364, 140 (2007)]. Here, action-angle coordinates, the safety factor, and the equilibrium generating function for the simple map are calculated analytically. The simple map in action-angle coordinates is derived from canonical transformations. This map cannot be integrated across the separatrix surface because of the singularity in the safety factor there. The stochastic broadening of the ideal separatrix surface in action-angle representation is calculated by adding a perturbation to the simple map equilibrium generating function. This perturbation represents the spatial noise and field errors typical of the DIII-D [J. L. Luxon and L. E. Davis, Fusion Technol. 8, 441 (1985)] tokamak. The stationary Fourier modes of the perturbation have poloidal and toroidal mode numbers (m,n,)={(3,1),(4,1),(6,2),(7,2),(8,2),(9,3),(10,3),(11,3)} with amplitude δ =0.8×10-5. Near the X-point, about 0.12% of toroidal magnetic flux inside the separatrix, and about 0.06% of the poloidal flux inside the separatrix is lost. When the distance from the O-point to the X-point is 1m, the width of stochastic layer near the X-point is about 1.4cm. The average value of the action on the last good surface is 0.19072 compared to the action value of 3/5π on the separatrix. The average width of stochastic layer in action coordinate is 2.7×10-4, while the average area of the stochastic layer in action-angle phase space is 1.69017×10-3. On average, about 0.14% of action or toroidal flux inside the ideal separatrix is lost due to broadening. Roughly five times more toroidal flux is lost in the simple map than in DIII-D for the same perturbation [A. Punjabi, H. Ali, A. Boozer, and T. Evans, Bull. Amer. Phys. Soc. 52, 124 (2007)].

  11. Tokamak plasma high field side response to an n = 3 magnetic perturbation: a comparison of 3D equilibrium solutions from seven different codes

    NASA Astrophysics Data System (ADS)

    Reiman, A.; Ferraro, N. M.; Turnbull, A.; Park, J. K.; Cerfon, A.; Evans, T. E.; Lanctot, M. J.; Lazarus, E. A.; Liu, Y.; McFadden, G.; Monticello, D.; Suzuki, Y.

    2015-06-01

    In comparing equilibrium solutions for a DIII-D shot that is amenable to analysis by both stellarator and tokamak three-dimensional (3D) equilibrium codes, a significant disagreement has been seen between solutions of the VMEC stellarator equilibrium code and solutions of tokamak perturbative 3D equilibrium codes. The source of that disagreement has been investigated, and that investigation has led to new insights into the domain of validity of the different equilibrium calculations, and to a finding that the manner in which localized screening currents at low order rational surfaces are handled can affect global properties of the equilibrium solution. The perturbative treatment has been found to break down at surprisingly small perturbation amplitudes due to overlap of the calculated perturbed flux surfaces, and that treatment is not valid in the pedestal region of the DIII-D shot studied. The perturbative treatment is valid, however, further into the interior of the plasma, and flux surface overlap does not account for the disagreement investigated here. Calculated equilibrium solutions for simple model cases and comparison of the 3D equilibrium solutions with those of other codes indicate that the disagreement arises from a difference in handling of localized currents at low order rational surfaces, with such currents being absent in VMEC and present in the perturbative codes. The significant differences in the global equilibrium solutions associated with the presence or absence of very localized screening currents at rational surfaces suggests that it may be possible to extract information about localized currents from appropriate measurements of global equilibrium plasma properties. That would require improved diagnostic capability on the high field side of the tokamak plasma, a region difficult to access with diagnostics.

  12. 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.

  13. Perturbation-theory analysis of ionization by a chirped few-cycle attosecond pulse

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

    Pronin, E. A.; Starace, Anthony F.; Peng Liangyou

    2011-07-15

    The angular distribution of electrons ionized from an atom by a chirped few-cycle attosecond pulse is analyzed using perturbation theory (PT), keeping terms in the transition amplitude up to second order in the pulse electric field. The dependence of the asymmetry in the ionized electron distributions on both the chirp and the carrier-envelope phase (CEP) of the pulse are explained using a simple analytical formula that approximates the exact PT result. This approximate formula (in which the chirp dependence is explicit) reproduces reasonably well the chirp-dependent oscillations of the electron angular distribution asymmetries found numerically by Peng et al. [Phys.more » Rev. A 80, 013407 (2009)]. It can also be used to determine the chirp rate of the attosecond pulse from the measured electron angular distribution asymmetry.« less

  14. 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…

  15. Predicting perturbation patterns from the topology of biological networks.

    PubMed

    Santolini, Marc; Barabási, Albert-László

    2018-06-20

    High-throughput technologies, offering an unprecedented wealth of quantitative data underlying the makeup of living systems, are changing biology. Notably, the systematic mapping of the relationships between biochemical entities has fueled the rapid development of network biology, offering a suitable framework to describe disease phenotypes and predict potential drug targets. However, our ability to develop accurate dynamical models remains limited, due in part to the limited knowledge of the kinetic parameters underlying these interactions. Here, we explore the degree to which we can make reasonably accurate predictions in the absence of the kinetic parameters. We find that simple dynamically agnostic models are sufficient to recover the strength and sign of the biochemical perturbation patterns observed in 87 biological models for which the underlying kinetics are known. Surprisingly, a simple distance-based model achieves 65% accuracy. We show that this predictive power is robust to topological and kinetic parameter perturbations, and we identify key network properties that can increase up to 80% the recovery rate of the true perturbation patterns. We validate our approach using experimental data on the chemotactic pathway in bacteria, finding that a network model of perturbation spreading predicts with ∼80% accuracy the directionality of gene expression and phenotype changes in knock-out and overproduction experiments. These findings show that the steady advances in mapping out the topology of biochemical interaction networks opens avenues for accurate perturbation spread modeling, with direct implications for medicine and drug development.

  16. Numerical simulation for solution of space-time fractional telegraphs equations with local fractional derivatives via HAFSTM

    NASA Astrophysics Data System (ADS)

    Pandey, Rishi Kumar; Mishra, Hradyesh Kumar

    2017-11-01

    In this paper, the semi-analytic numerical technique for the solution of time-space fractional telegraph equation is applied. This numerical technique is based on coupling of the homotopy analysis method and sumudu transform. It shows the clear advantage with mess methods like finite difference method and also with polynomial methods similar to perturbation and Adomian decomposition methods. It is easily transform the complex fractional order derivatives in simple time domain and interpret the results in same meaning.

  17. Dynamic characteristics of a vibrating beam with periodic variation in bending stiffness

    NASA Technical Reports Server (NTRS)

    Townsend, John S.

    1987-01-01

    A detailed dynamic analysis is performed of a vibrating beam with bending stiffness periodic in the spatial coordinate. Using a perturbation expansion technique the free vibration solution is obtained in a closed-form, and the effects of system parameters on beam response are explored. It is found that periodic stiffness acts to modulate the modal displacements from the characteristic shape of a simple sine wave. The results are verified by a finite element solution and through experimental testing.

  18. Simple Astronomical Theory of Climate.

    ERIC Educational Resources Information Center

    Benumof, Reuben

    1979-01-01

    The author derives, applying perturbation theory, from a simple astronomical model the approximate periods of secular variation of some of the parameters of the Earth's orbit and relates these periods to the past climate of the Earth, indicating the difficulties in predicting the climate of the future. (GA)

  19. Load alleviation maneuvers for a launch vehicle

    NASA Technical Reports Server (NTRS)

    Seywald, Hans; Bless, Robert

    1993-01-01

    This paper addresses the design of a forward-looking autopilot that is capable of employing a priori knowledge of wind gusts ahead of the flight path to reduce the bending loads experienced by a launch vehicle. The analysis presented in the present paper is only preliminary, employing a very simple vehicle dynamical model and restricting itself to wind gusts of the form of isolated spikes. The main result of the present study is that LQR based feedback laws are inappropriate to handle spike-type wind perturbations with large amplitude and narrow base. The best performance is achieved with an interior-point penalty optimal control formulation which can be well approximated by a simple feedback control law. Reduction of the maximum bending loads by nearly 50 percent is demonstrated.

  20. Ground-state energies of simple metals

    NASA Technical Reports Server (NTRS)

    Hammerberg, J.; Ashcroft, N. W.

    1974-01-01

    A structural expansion for the static ground-state energy of a simple metal is derived. Two methods are presented, one an approach based on single-particle band structure which treats the electron gas as a nonlinear dielectric, the other a more general many-particle analysis using finite-temperature perturbation theory. The two methods are compared, and it is shown in detail how band-structure effects, Fermi-surface distortions, and chemical-potential shifts affect the total energy. These are of special interest in corrections to the total energy beyond third order in the electron-ion interaction and hence to systems where differences in energies for various crystal structures are exceptionally small. Preliminary calculations using these methods for the zero-temperature thermodynamic functions of atomic hydrogen are reported.

  1. Structural expansions for the ground state energy of a simple metal

    NASA Technical Reports Server (NTRS)

    Hammerberg, J.; Ashcroft, N. W.

    1973-01-01

    A structural expansion for the static ground state energy of a simple metal is derived. An approach based on single particle band structure which treats the electron gas as a non-linear dielectric is presented, along with a more general many particle analysis using finite temperature perturbation theory. The two methods are compared, and it is shown in detail how band-structure effects, Fermi surface distortions, and chemical potential shifts affect the total energy. These are of special interest in corrections to the total energy beyond third order in the electron ion interaction, and hence to systems where differences in energies for various crystal structures are exceptionally small. Preliminary calculations using these methods for the zero temperature thermodynamic functions of atomic hydrogen are reported.

  2. SHARP ENTRYWISE PERTURBATION BOUNDS FOR MARKOV CHAINS.

    PubMed

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

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

  3. Linear stable unity-feedback system - Necessary and sufficient conditions for stability under nonlinear plant perturbations

    NASA Technical Reports Server (NTRS)

    Desoer, C. A.; Kabuli, M. G.

    1989-01-01

    The authors consider a linear (not necessarily time-invariant) stable unity-feedback system, where the plant and the compensator have normalized right-coprime factorizations. They study two cases of nonlinear plant perturbations (additive and feedback), with four subcases resulting from: (1) allowing exogenous input to Delta P or not; 2) allowing the observation of the output of Delta P or not. The plant perturbation Delta P is not required to be stable. Using the factorization approach, the authors obtain necessary and sufficient conditions for all cases in terms of two pairs of nonlinear pseudostate maps. Simple physical considerations explain the form of these necessary and sufficient conditions. Finally, the authors obtain the characterization of all perturbations Delta P for which the perturbed system remains stable.

  4. 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.

  5. Leading temperature dependence of the conductance in Kondo-correlated quantum dots.

    PubMed

    Aligia, A A

    2018-04-18

    Using renormalized perturbation theory in the Coulomb repulsion, we derive an analytical expression for the leading term in the temperature dependence of the conductance through a quantum dot described by the impurity Anderson model, in terms of the renormalized parameters of the model. Taking these parameters from the literature, we compare the results with published ones calculated using the numerical renormalization group obtaining a very good agreement. The approach is superior to alternative perturbative treatments. We compare in particular to the results of a simple interpolative perturbation approach.

  6. Relaxational effects in radiating stellar collapse

    NASA Astrophysics Data System (ADS)

    Govender, Megan; Maartens, Roy; Maharaj, Sunil D.

    1999-12-01

    Relaxational effects in stellar heat transport can in many cases be significant. Relativistic Fourier-Eckart theory is inherently quasi-stationary, and cannot incorporate these effects. The effects are naturally accounted for in causal relativistic thermodynamics, which provides an improved approximation to kinetic theory. Recent results, based on perturbations of a static star, show that relaxation effects can produce a significant increase in the central temperature and temperature gradient for a given luminosity. We use a simple stellar model that allows for non-perturbative deviations from staticity, and confirms qualitatively the predictions of the perturbative models.

  7. Equivalent circuit models for interpreting impedance perturbation spectroscopy data

    NASA Astrophysics Data System (ADS)

    Smith, R. Lowell

    2004-07-01

    As in-situ structural integrity monitoring disciplines mature, there is a growing need to process sensor/actuator data efficiently in real time. Although smaller, faster embedded processors will contribute to this, it is also important to develop straightforward, robust methods to reduce the overall computational burden for practical applications of interest. This paper addresses the use of equivalent circuit modeling techniques for inferring structure attributes monitored using impedance perturbation spectroscopy. In pioneering work about ten years ago significant progress was associated with the development of simple impedance models derived from the piezoelectric equations. Using mathematical modeling tools currently available from research in ultrasonics and impedance spectroscopy is expected to provide additional synergistic benefits. For purposes of structural health monitoring the objective is to use impedance spectroscopy data to infer the physical condition of structures to which small piezoelectric actuators are bonded. Features of interest include stiffness changes, mass loading, and damping or mechanical losses. Equivalent circuit models are typically simple enough to facilitate the development of practical analytical models of the actuator-structure interaction. This type of parametric structure model allows raw impedance/admittance data to be interpreted optimally using standard multiple, nonlinear regression analysis. One potential long-term outcome is the possibility of cataloging measured viscoelastic properties of the mechanical subsystems of interest as simple lists of attributes and their statistical uncertainties, whose evolution can be followed in time. Equivalent circuit models are well suited for addressing calibration and self-consistency issues such as temperature corrections, Poisson mode coupling, and distributed relaxation processes.

  8. Simple turbulence measurements with azopolymer thin films.

    PubMed

    Barillé, Regis; Pérez, Darío G; Morille, Yohann; Zielińska, Sonia; Ortyl, Ewelina

    2013-04-01

    A simple method to measure the influence on the laser beam propagation by a turbid medium is proposed. This measurement is based on the inscription of a surface relief grating (SRG) on an azopolymer thin film. The grating obtained with a single laser beam after propagation into a turbulent medium is perturbed and directly analyzed by a CCD camera through its diffraction pattern. Later, by scanning the surface pattern with an atomic force microscope, the inscribed SRG is analyzed with the Radon transform. This method has the advantage of using a single beam to remotely inscribe a grating detecting perturbations during the beam path. A method to evaluate the refractive index constant structure is developed.

  9. Coherent states, quantum gravity, and the Born-Oppenheimer approximation. I. General considerations

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

    Stottmeister, Alexander, E-mail: alexander.stottmeister@gravity.fau.de; Thiemann, Thomas, E-mail: thomas.thiemann@gravity.fau.de

    2016-06-15

    This article, as the first of three, aims at establishing the (time-dependent) Born-Oppenheimer approximation, in the sense of space adiabatic perturbation theory, for quantum systems constructed by techniques of the loop quantum gravity framework, especially the canonical formulation of the latter. The analysis presented here fits into a rather general framework and offers a solution to the problem of applying the usual Born-Oppenheimer ansatz for molecular (or structurally analogous) systems to more general quantum systems (e.g., spin-orbit models) by means of space adiabatic perturbation theory. The proposed solution is applied to a simple, finite dimensional model of interacting spin systems,more » which serves as a non-trivial, minimal model of the aforesaid problem. Furthermore, it is explained how the content of this article and its companion affect the possible extraction of quantum field theory on curved spacetime from loop quantum gravity (including matter fields).« less

  10. Clustering of arc volcanoes caused by temperature perturbations in the back-arc mantle

    PubMed Central

    Lee, Changyeol; Wada, Ikuko

    2017-01-01

    Clustering of arc volcanoes in subduction zones indicates along-arc variation in the physical condition of the underlying mantle where majority of arc magmas are generated. The sub-arc mantle is brought in from the back-arc largely by slab-driven mantle wedge flow. Dynamic processes in the back-arc, such as small-scale mantle convection, are likely to cause lateral variations in the back-arc mantle temperature. Here we use a simple three-dimensional numerical model to quantify the effects of back-arc temperature perturbations on the mantle wedge flow pattern and sub-arc mantle temperature. Our model calculations show that relatively small temperature perturbations in the back-arc result in vigorous inflow of hotter mantle and subdued inflow of colder mantle beneath the arc due to the temperature dependence of the mantle viscosity. This causes a three-dimensional mantle flow pattern that amplifies the along-arc variations in the sub-arc mantle temperature, providing a simple mechanism for volcano clustering. PMID:28660880

  11. Clustering of arc volcanoes caused by temperature perturbations in the back-arc mantle.

    PubMed

    Lee, Changyeol; Wada, Ikuko

    2017-06-29

    Clustering of arc volcanoes in subduction zones indicates along-arc variation in the physical condition of the underlying mantle where majority of arc magmas are generated. The sub-arc mantle is brought in from the back-arc largely by slab-driven mantle wedge flow. Dynamic processes in the back-arc, such as small-scale mantle convection, are likely to cause lateral variations in the back-arc mantle temperature. Here we use a simple three-dimensional numerical model to quantify the effects of back-arc temperature perturbations on the mantle wedge flow pattern and sub-arc mantle temperature. Our model calculations show that relatively small temperature perturbations in the back-arc result in vigorous inflow of hotter mantle and subdued inflow of colder mantle beneath the arc due to the temperature dependence of the mantle viscosity. This causes a three-dimensional mantle flow pattern that amplifies the along-arc variations in the sub-arc mantle temperature, providing a simple mechanism for volcano clustering.

  12. Cosmological perturbations in mimetic Horndeski gravity

    NASA Astrophysics Data System (ADS)

    Arroja, Frederico; Bartolo, Nicola; Karmakar, Purnendu; Matarrese, Sabino

    2016-04-01

    We study linear scalar perturbations around a flat FLRW background in mimetic Horndeski gravity. In the absence of matter, we show that the Newtonian potential satisfies a second-order differential equation with no spatial derivatives. This implies that the sound speed for scalar perturbations is exactly zero on this background. We also show that in mimetic G3 theories the sound speed is equally zero. We obtain the equation of motion for the comoving curvature perturbation (first order differential equation) and solve it to find that the comoving curvature perturbation is constant on all scales in mimetic Horndeski gravity. We find solutions for the Newtonian potential evolution equation in two simple models. Finally we show that the sound speed is zero on all backgrounds and therefore the system does not have any wave-like scalar degrees of freedom.

  13. Load alleviation maneuvers for a launch vehicle

    NASA Technical Reports Server (NTRS)

    Seywald, Hans; Bless, Robert R.

    1993-01-01

    This paper addresses the design of a forward-looking autopilot that is capable of employing a priori knowledge of wind gusts ahead of the flight path to reduce the bending loads experienced by a launch vehicle. The analysis presented in the present paper is only preliminary, employing a very simple vehicle dynamical model and restricting itself to wind gusts of the form of isolated spikes. The main result of the present study is that linear quadratic regulator (LQR) based feedback laws are inappropriate to handle spike-type wind perturbations with large amplitude and narrow base. The best performance is achieved with an interior-point penalty optimal control formulation which can be well approximated by a simple feedback control law. Reduction of the maximum bending loads by nearly 50% is demonstrated.

  14. An on-board near-optimal climb-dash energy management

    NASA Technical Reports Server (NTRS)

    Weston, A. R.; Cliff, E. M.; Kelley, H. J.

    1982-01-01

    On-board real time flight control is studied in order to develop algorithms which are simple enough to be used in practice, for a variety of missions involving three dimensional flight. The intercept mission in symmetric flight is emphasized. Extensive computation is required on the ground prior to the mission but the ensuing on-board exploitation is extremely simple. The scheme takes advantage of the boundary layer structure common in singular perturbations, arising with the multiple time scales appropriate to aircraft dynamics. Energy modelling of aircraft is used as the starting point for the analysis. In the symmetric case, a nominal path is generated which fairs into the dash or cruise state. Feedback coefficients are found as functions of the remaining energy to go (dash energy less current energy) along the nominal path.

  15. On the Treatment of l-changing Proton-hydrogen Rydberg Atom Collisions

    NASA Astrophysics Data System (ADS)

    Vrinceanu, Daniel; Onofrio, Roberto; Sadeghpour, Hossein

    2018-01-01

    Energy-conserving, angular momentum-changing collisions between protons and highly excited Rydberg hydrogen atoms are important for precise understanding of the primordial recombination cascade, and the elemental abundance.Early approaches to l-changing collisions used perturbation theory for only dipole-allowed (Δl = ±1) transitions. An exact non-perturbative quantum mechanical treatment is possible, but it comes at computational cost for highly excited Rydberg states. In this note we show how to obtain a semi-classical limit that is accurate and simple, and develop further physical insights afforded by the non-perturbative quantum mechanical treatment.

  16. Perturbative computation in a generalized quantum field theory

    NASA Astrophysics Data System (ADS)

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

    2002-10-01

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

  17. Compensation for large tensor modes with iso-curvature perturbations in CMB anisotropies

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

    Kawasaki, Masahiro; Yokoyama, Shuichiro, E-mail: kawasaki@icrr.u-tokyo.ac.jp, E-mail: shu@icrr.u-tokyo.ac.jp

    Recently, BICEP2 has reported the large tensor-to-scalar ratio r = 0.2{sup +0.07}{sub −0.05} from the observation of the cosmic microwave background (CMB) B-mode at degree-scales. Since tensor modes induce not only CMB B-mode but also the temperature fluctuations on large scales, to realize the consistent temperature fluctuations with the Planck result we should consider suppression of scalar perturbations on corresponding large scales. To realize such a suppression, we consider anti-correlated iso-curvature perturbations which could be realized in the simple curvaton model.

  18. Correlated perturbations from inflation and the cosmic microwave background.

    PubMed

    Amendola, Luca; Gordon, Christopher; Wands, David; Sasaki, Misao

    2002-05-27

    We compare the latest cosmic microwave background data with theoretical predictions including correlated adiabatic and cold dark matter (CDM) isocurvature perturbations with a simple power-law dependence. We find that there is a degeneracy between the amplitude of correlated isocurvature perturbations and the spectral tilt. A negative (red) tilt is found to be compatible with a larger isocurvature contribution. Estimates of the baryon and CDM densities are found to be almost independent of the isocurvature amplitude. The main result is that current microwave background data do not exclude a dominant contribution from CDM isocurvature fluctuations on large scales.

  19. Sound produced by an oscillating arc in a high-pressure gas

    NASA Astrophysics Data System (ADS)

    Popov, Fedor K.; Shneider, Mikhail N.

    2017-08-01

    We suggest a simple theory to describe the sound generated by small periodic perturbations of a cylindrical arc in a dense gas. Theoretical analysis was done within the framework of the non-self-consistent channel arc model and supplemented with time-dependent gas dynamic equations. It is shown that an arc with power amplitude oscillations on the order of several percent is a source of sound whose intensity is comparable with external ultrasound sources used in experiments to increase the yield of nanoparticles in the high pressure arc systems for nanoparticle synthesis.

  20. Scaling rates of true polar wander in convecting planets and moons

    NASA Astrophysics Data System (ADS)

    Rose, Ian; Buffett, Bruce

    2017-12-01

    Mass redistribution in the convecting mantle of a planet causes perturbations in its moment of inertia tensor. Conservation of angular momentum dictates that these perturbations change the direction of the rotation vector of the planet, a process known as true polar wander (TPW). Although the existence of TPW on Earth is firmly established, its rate and magnitude over geologic time scales remain controversial. Here we present scaling analyses and numerical simulations of TPW due to mantle convection over a range of parameter space relevant to planetary interiors. For simple rotating convection, we identify a set of dimensionless parameters that fully characterize true polar wander. We use these parameters to define timescales for the growth of moment of inertia perturbations due to convection and for their relaxation due to true polar wander. These timescales, as well as the relative sizes of convective anomalies, control the rate and magnitude of TPW. This analysis also clarifies the nature of so called "inertial interchange" TPW events, and relates them to a broader class of events that enable large and often rapid TPW. We expect these events to have been more frequent in Earth's past.

  1. NLO perturbativity bounds on quartic couplings in renormalizable theories with Φ 4 -like scalar sectors

    DOE PAGES

    Murphy, Christopher W.

    2017-08-17

    The apparent breakdown of unitarity in low order perturbation theory is often is used to place bounds on the parameters of a theory. In this work we give an algorithm for approximately computing the next-to-leading order (NLO) perturbativity bounds on the quartic couplings of a renormalizable theory whose scalar sector is Φ 4 -like. And by this we mean theories where either there are no cubic scalar interactions, or the cubic couplings are related to the quartic couplings through spontaneous symmetry breaking. Furthermore, the quantity that tests where perturbation theory breaks down itself can be written as a perturbative series,more » and having the NLO terms allows one to test how well the series converges. We also present a simple example to illustrate the effect of considering these bounds at different orders in perturbation theory. For example, there is a noticeable difference in the viable parameter when the square of the NLO piece is included versus when it is not.« less

  2. Hamilton-Jacobi modelling of relative motion for formation flying.

    PubMed

    Kolemen, Egemen; Kasdin, N Jeremy; Gurfil, Pini

    2005-12-01

    A precise analytic model for the relative motion of a group of satellites in slightly elliptic orbits is introduced. With this aim, we describe the relative motion of an object relative to a circular or slightly elliptic reference orbit in the rotating Hill frame via a low-order Hamiltonian, and solve the Hamilton-Jacobi equation. This results in a first-order solution to the relative motion identical to the Clohessy-Wiltshire approach; here, however, rather than using initial conditions as our constants of the motion, we utilize the canonical momenta and coordinates. This allows us to treat perturbations in an identical manner, as in the classical Delaunay formulation of the two-body problem. A precise analytical model for the base orbit is chosen with the included effect of zonal harmonics (J(2), J(3), J(4)). A Hamiltonian describing the real relative motion is formed and by differing this from the nominal Hamiltonian, the perturbing Hamiltonian is obtained. Using the Hamilton equations, the variational equations for the new constants are found. In a manner analogous to the center manifold reduction procedure, the non-periodic part of the motion is canceled through a magnitude analysis leading to simple boundedness conditions that cancel the drift terms due to the higher order perturbations. Using this condition, the variational equations are integrated to give periodic solutions that closely approximate the results from numerical integration (1 mm/per orbit for higher order and eccentricity perturbations and 30 cm/per orbit for zonal perturbations). This procedure provides a compact and insightful analytic description of the resulting relative motion.

  3. 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.

  4. 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

  5. Stability of the line preserving flows

    NASA Astrophysics Data System (ADS)

    Figura, Przemysław

    2017-11-01

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

  6. Simple Climate Model Evaluation Using Impulse Response Tests

    NASA Astrophysics Data System (ADS)

    Schwarber, A.; Hartin, C.; Smith, S. J.

    2017-12-01

    Simple climate models (SCMs) are central tools used to incorporate climate responses into human-Earth system modeling. SCMs are computationally inexpensive, making them an ideal tool for a variety of analyses, including consideration of uncertainty. Despite their wide use, many SCMs lack rigorous testing of their fundamental responses to perturbations. Here, following recommendations of a recent National Academy of Sciences report, we compare several SCMs (Hector-deoclim, MAGICC 5.3, MAGICC 6.0, and the IPCC AR5 impulse response function) to diagnose model behavior and understand the fundamental system responses within each model. We conduct stylized perturbations (emissions and forcing/concentration) of three different chemical species: CO2, CH4, and BC. We find that all 4 models respond similarly in terms of overall shape, however, there are important differences in the timing and magnitude of the responses. For example, the response to a BC pulse differs over the first 20 years after the pulse among the models, a finding that is due to differences in model structure. Such perturbation experiments are difficult to conduct in complex models due to internal model noise, making a direct comparison with simple models challenging. We can, however, compare the simplified model response from a 4xCO2 step experiment to the same stylized experiment carried out by CMIP5 models, thereby testing the ability of SCMs to emulate complex model results. This work allows an assessment of how well current understanding of Earth system responses are incorporated into multi-model frameworks by way of simple climate models.

  7. Cosmological Perturbation Theory and the Spherical Collapse model - I. Gaussian initial conditions

    NASA Astrophysics Data System (ADS)

    Fosalba, Pablo; Gaztanaga, Enrique

    1998-12-01

    We present a simple and intuitive approximation for solving the perturbation theory (PT) of small cosmic fluctuations. We consider only the spherically symmetric or monopole contribution to the PT integrals, which yields the exact result for tree-graphs (i.e. at leading order). We find that the non-linear evolution in Lagrangian space is then given by a simple local transformation over the initial conditions, although it is not local in Euler space. This transformation is found to be described by the spherical collapse (SC) dynamics, as it is the exact solution in the shearless (and therefore local) approximation in Lagrangian space. Taking advantage of this property, it is straightforward to derive the one-point cumulants, xi_J, for both the unsmoothed and smoothed density fields to arbitrary order in the perturbative regime. To leading-order this reproduces, and provides us with a simple explanation for, the exact results obtained by Bernardeau. We then show that the SC model leads to accurate estimates for the next corrective terms when compared with the results derived in the exact perturbation theory making use of the loop calculations. The agreement is within a few per cent for the hierarchical ratios S_J=xi_J/xi^J-1_2. We compare our analytic results with N-body simulations, which turn out to be in very good agreement up to scales where sigma~1. A similar treatment is presented to estimate higher order corrections in the Zel'dovich approximation. These results represent a powerful and readily usable tool to produce analytical predictions that describe the gravitational clustering of large-scale structure in the weakly non-linear regime.

  8. Spheroidal and Toroidal Modes for Tidal Kinetic Energy in Spherical Elastic Bodies

    NASA Astrophysics Data System (ADS)

    Getino, Juan; Escapa, Alberto; Garcia, Amelia

    In this work, the total expression of the perturbation of the kinetic energy of rotation, when an elastic spherical solid is deformed due to the gravitational attraction of external bodies, is studied. We do not limit this study to any order in the expansion of the perturbing potential in spherical harmonics, and we consider in the expression of the displacement vector the complete solution, composed by spheroidal and toroidal modes. We show in a very simple way, by using the properties of the Legendre polynomials, that the toroidal modes have no contribution at all under the hypothesis of spherical body, and, among the spheroidal modes, only the term n=2 acts, therefore the perturbation produced by the spheroidal component for n=2 gathers the total perturbation.

  9. 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.

  10. On the treatment of ℓ-changing proton-hydrogen Rydberg atom collisions

    NASA Astrophysics Data System (ADS)

    Vrinceanu, D.; Onofrio, R.; Sadeghpour, H. R.

    2017-11-01

    Energy-conserving, angular momentum changing collisions between protons and highly excited Rydberg hydrogen atoms are important for precise understanding of atomic recombination at the photon decoupling era and the elemental abundance after primordial nucleosynthesis. Early approaches to ℓ-changing collisions used perturbation theory only for dipole-allowed (Δℓ = ±1) transitions. An exact non-perturbative quantum mechanical treatment is possible, but it comes at a computational cost for highly excited Rydberg states. In this paper, we show how to obtain a semiclassical limit that is accurate and simple, and develop further physical insights afforded by the non-perturbative quantum mechanical treatment.

  11. A gauge-independent zeroth-order regular approximation to the exact relativistic Hamiltonian—Formulation and applications

    NASA Astrophysics Data System (ADS)

    Filatov, Michael; Cremer, Dieter

    2005-01-01

    A simple modification of the zeroth-order regular approximation (ZORA) in relativistic theory is suggested to suppress its erroneous gauge dependence to a high level of approximation. The method, coined gauge-independent ZORA (ZORA-GI), can be easily installed in any existing nonrelativistic quantum chemical package by programming simple one-electron matrix elements for the quasirelativistic Hamiltonian. Results of benchmark calculations obtained with ZORA-GI at the Hartree-Fock (HF) and second-order Møller-Plesset perturbation theory (MP2) level for dihalogens X2 (X=F,Cl,Br,I,At) are in good agreement with the results of four-component relativistic calculations (HF level) and experimental data (MP2 level). ZORA-GI calculations based on MP2 or coupled-cluster theory with single and double perturbations and a perturbative inclusion of triple excitations [CCSD(T)] lead to accurate atomization energies and molecular geometries for the tetroxides of group VIII elements. With ZORA-GI/CCSD(T), an improved estimate for the atomization energy of hassium (Z=108) tetroxide is obtained.

  12. 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.

  13. Timescales of isotropic and anisotropic cluster collapse

    NASA Astrophysics Data System (ADS)

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

    1993-12-01

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

  14. 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.

  15. Monitoring Mars LOD Variations from a High Altitude Circular Equatorial Orbit: Theory and Simulation

    NASA Astrophysics Data System (ADS)

    Barriot, J.; Dehant, V.; Duron, J.

    2003-12-01

    We compute the perturbations of a high altitude circular equatorial orbit of a martian probe under the influence of an annual variation of the martian lenght of day. For this purpose, we use the first order perturbations of the newtonian equations of motion, where the small parameter is given from the hourglass model of Chao and Rubincam, which allow a simple computation of CO2 exchanges during the martian year. We are able to demonstrate that the perturbations contains two components: the first one is a sine/cosine modulation at the orbit frequency, the second one is composed of terms of the form exp(t)*sin(t), so the orbit may not stable in the long term (several martian years), with perturbations growing exponentially. We give the full theory and numbers.

  16. A preliminary experiment for the long-term regional reanalysis over Japan assimilating conventional observations with NHM-LETKF

    NASA Astrophysics Data System (ADS)

    Fukui, Shin; Iwasaki, Toshiki; Saito, Kazuo; Seko, Hiromu; Kunii, Masaru

    2016-04-01

    Several long-term global reanalyses have been produced by major operational centres and have contributed to the advance of weather and climate researches considerably. Although the horizontal resolutions of these global reanalyses are getting higher partly due to the development of computing technology, they are still too coarse to reproduce local circulations and precipitation realistically. To solve this problem, dynamical downscaling is often employed. However, the forcing from lateral boundaries only cannot necessarily control the inner fields especially in long-term dynamical downscaling. Regional reanalysis is expected to overcome the difficulty. To maintain the long-term consistency of the analysis quality, it is better to assimilate only the conventional observations that are available in long period. To confirm the effectiveness of the regional reanalysis, some assimilation experiments are performed. In the experiments, only conventional observations (SYNOP, SHIP, BUOY, TEMP, PILOT, TC-Bogus) are assimilated with the NHM-LETKF system, which consists of the nonhydrostatic model (NHM) of the Japan Meteorological Agency (JMA) and the local ensemble transform Kalman filter (LETKF). The horizontal resolution is 25 km and the domain covers Japan and its surroundings. Japanese 55-year reanalysis (JRA-55) is adopted as the initial and lateral boundary conditions for the NHM-LETKF forecast-analysis cycles. The ensemble size is 10. The experimental period is August 2014 as a representative of warm season for the region. The results are verified against the JMA's operational Meso-scale Analysis, which is produced with assimilating observation data including various remote sensing observations using a 4D-Var scheme, and compared with those of the simple dynamical downscaling experiment without data assimilation. Effects of implementation of lateral boundary perturbations derived from an EOF analysis of JRA-55 over the targeted domain are also examined. The comparison proposes that the assimilation system can reproduce more accurate fields than dynamical downscaling. The implementation of the lateral boundary perturbations implies that the perturbations contribute to providing more appropriate ensemble spreads, though the perturbations are not necessarily consistent to those of the inner fields given by NHM-LETKF.

  17. Gauge Fields in Homogeneous and Inhomogeneous Cosmologies

    NASA Astrophysics Data System (ADS)

    Darian, Bahman K.

    Despite its formidable appearance, the study of classical Yang-Mills (YM) fields on homogeneous cosmologies is amenable to a formal treatment. This dissertation is a report on a systematic approach to the general construction of invariant YM fields on homogeneous cosmologies undertaken for the first time in this context. This construction is subsequently followed by the investigation of the behavior of YM field variables for the most simple of self-gravitating YM fields. Particularly interesting was a dynamical system analysis and the discovery of chaotic signature in the axially symmetric Bianchi I-YM cosmology. Homogeneous YM fields are well studied and are known to have chaotic properties. The chaotic behavior of YM field variables in homogeneous cosmologies might eventually lead to an invariant definition of chaos in (general) relativistic cosmological models. By choosing the gauge fields to be Abelian, the construction and the field equations presented so far reduce to that of electromagnetic field in homogeneous cosmologies. A perturbative analysis of gravitationally interacting electromagnetic and scalar fields in inhomogeneous cosmologies is performed via the Hamilton-Jacobi formulation of general relativity. An essential feature of this analysis is the spatial gradient expansion of the generating functional (Hamilton principal function) to solve the Hamiltonian constraint. Perturbations of a spatially flat Friedman-Robertson-Walker cosmology with an exponential potential for the scalar field are presented.

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

    Rizwan-uddin

    Recently, various branches of engineering and science have seen a rapid increase in the number of dynamical analyses undertaken. This modern phenomenon often obscures the fact that such analyses were sometimes carried out even before the current trend began. Moreover, these earlier analyses, which even now seem very ingenuous, were carried out at a time when the available information about dynamical systems was not as well disseminated as it is today. One such analysis, carried out in the early 1960s, showed the existence of stable limit cycles in a simple model for space-independent xenon dynamics in nuclear reactors. The authors,more » apparently unaware of the now well-known bifurcation theorem by Hopf, could not numerically discover unstable limit cycles, though they did find regions in parameter space where the fixed points are stable for small perturbations but unstable for very large perturbations. The analysis was carried out both analytically and numerically. As a tribute to these early nonlinear dynamicists in the field of nuclear engineering, in this paper, the Hopf theorem and its conclusions are briefly described, and then the solution of the space-independent xenon oscillation problem is presented, which was obtained using the bifurcation analysis BIFDD code. These solutions are presented along with a discussion of the earlier results.« less

  19. Characterization of microscopic deformation through two-point spatial correlation functions

    NASA Astrophysics Data System (ADS)

    Huang, Guan-Rong; Wu, Bin; Wang, Yangyang; Chen, Wei-Ren

    2018-01-01

    The molecular rearrangements of most fluids under flow and deformation do not directly follow the macroscopic strain field. In this work, we describe a phenomenological method for characterizing such nonaffine deformation via the anisotropic pair distribution function (PDF). We demonstrate how the microscopic strain can be calculated in both simple shear and uniaxial extension, by perturbation expansion of anisotropic PDF in terms of real spherical harmonics. Our results, given in the real as well as the reciprocal space, can be applied in spectrum analysis of small-angle scattering experiments and nonequilibrium molecular dynamics simulations of soft matter under flow.

  20. Characterization of microscopic deformation through two-point spatial correlation functions.

    PubMed

    Huang, Guan-Rong; Wu, Bin; Wang, Yangyang; Chen, Wei-Ren

    2018-01-01

    The molecular rearrangements of most fluids under flow and deformation do not directly follow the macroscopic strain field. In this work, we describe a phenomenological method for characterizing such nonaffine deformation via the anisotropic pair distribution function (PDF). We demonstrate how the microscopic strain can be calculated in both simple shear and uniaxial extension, by perturbation expansion of anisotropic PDF in terms of real spherical harmonics. Our results, given in the real as well as the reciprocal space, can be applied in spectrum analysis of small-angle scattering experiments and nonequilibrium molecular dynamics simulations of soft matter under flow.

  1. Wentzel-Kramers-Brillouin method in the Bargmann representation. [of quantum mechanics

    NASA Technical Reports Server (NTRS)

    Voros, A.

    1989-01-01

    It is demonstrated that the Bargmann representation of quantum mechanics is ideally suited for semiclassical analysis, using as an example the WKB method applied to the bound-state problem in a single well of one degree of freedom. For the harmonic oscillator, this WKB method trivially gives the exact eigenfunctions in addition to the exact eigenvalues. For an anharmonic well, a self-consistent variational choice of the representation greatly improves the accuracy of the semiclassical ground state. Also, a simple change of scale illuminates the relationship of semiclassical versus linear perturbative expansions, allowing a variety of multidimensional extensions.

  2. Phase response curves for models of earthquake fault dynamics

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

    Franović, Igor, E-mail: franovic@ipb.ac.rs; Kostić, Srdjan; Perc, Matjaž

    We systematically study effects of external perturbations on models describing earthquake fault dynamics. The latter are based on the framework of the Burridge-Knopoff spring-block system, including the cases of a simple mono-block fault, as well as the paradigmatic complex faults made up of two identical or distinct blocks. The blocks exhibit relaxation oscillations, which are representative for the stick-slip behavior typical for earthquake dynamics. Our analysis is carried out by determining the phase response curves of first and second order. For a mono-block fault, we consider the impact of a single and two successive pulse perturbations, further demonstrating how themore » profile of phase response curves depends on the fault parameters. For a homogeneous two-block fault, our focus is on the scenario where each of the blocks is influenced by a single pulse, whereas for heterogeneous faults, we analyze how the response of the system depends on whether the stimulus is applied to the block having a shorter or a longer oscillation period.« less

  3. Localization of a small change in a multiple scattering environment without modeling of the actual medium.

    PubMed

    Rakotonarivo, S T; Walker, S C; Kuperman, W A; Roux, P

    2011-12-01

    A method to actively localize a small perturbation in a multiple scattering medium using a collection of remote acoustic sensors is presented. The approach requires only minimal modeling and no knowledge of the scatterer distribution and properties of the scattering medium and the perturbation. The medium is ensonified before and after a perturbation is introduced. The coherent difference between the measured signals then reveals all field components that have interacted with the perturbation. A simple single scatter filter (that ignores the presence of the medium scatterers) is matched to the earliest change of the coherent difference to localize the perturbation. Using a multi-source/receiver laboratory setup in air, the technique has been successfully tested with experimental data at frequencies varying from 30 to 60 kHz (wavelength ranging from 0.5 to 1 cm) for cm-scale scatterers in a scattering medium with a size two to five times bigger than its transport mean free path. © 2011 Acoustical Society of America

  4. Numerical analysis of the effect of surface roughness on mechanical fields in polycrystalline aggregates

    NASA Astrophysics Data System (ADS)

    Guilhem, Yoann; Basseville, Stéphanie; Curtit, François; Stéphan, Jean-Michel; Cailletaud, Georges

    2018-06-01

    This paper is dedicated to the study of the influence of surface roughness on local stress and strain fields in polycrystalline aggregates. Finite element computations are performed with a crystal plasticity model on a 316L stainless steel polycrystalline material element with different roughness states on its free surface. The subsequent analysis of the plastic strain localization patterns shows that surface roughness strongly affects the plastic strain localization induced by crystallography. Nevertheless, this effect mainly takes place at the surface and vanishes under the first layer of grains, which implies the existence of a critical perturbed depth. A statistical analysis based on the plastic strain distribution obtained for different roughness levels provides a simple rule to define the size of the affected zone depending on the rough surface parameters.

  5. 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.

  6. On the analytic lunar and solar perturbations of a near earth satellite

    NASA Technical Reports Server (NTRS)

    Estes, R. H.

    1972-01-01

    The disturbing function of the moon (sun) is expanded as a sum of products of two harmonic functions, one depending on the position of the satellite and the other on the position of the moon (sun). The harmonic functions depending on the position of the perturbing body are developed into trigonometric series with the ecliptic elements l, l', F, D, and Gamma of the lunar theory which are nearly linear with respect to time. Perturbation of elements are in the form of trigonometric series with the ecliptic lunar elements and the equatorial elements omega and Omega of the satellite so that analytic integration is simple and the results accurate over a long period of time.

  7. Renormalization scheme dependence of high-order perturbative QCD predictions

    NASA Astrophysics Data System (ADS)

    Ma, Yang; Wu, Xing-Gang

    2018-02-01

    Conventionally, one adopts typical momentum flow of a physical observable as the renormalization scale for its perturbative QCD (pQCD) approximant. This simple treatment leads to renormalization scheme-and-scale ambiguities due to the renormalization scheme and scale dependence of the strong coupling and the perturbative coefficients do not exactly cancel at any fixed order. It is believed that those ambiguities will be softened by including more higher-order terms. In the paper, to show how the renormalization scheme dependence changes when more loop terms have been included, we discuss the sensitivity of pQCD prediction on the scheme parameters by using the scheme-dependent {βm ≥2}-terms. We adopt two four-loop examples, e+e-→hadrons and τ decays into hadrons, for detailed analysis. Our results show that under the conventional scale setting, by including more-and-more loop terms, the scheme dependence of the pQCD prediction cannot be reduced as efficiently as that of the scale dependence. Thus a proper scale-setting approach should be important to reduce the scheme dependence. We observe that the principle of minimum sensitivity could be such a scale-setting approach, which provides a practical way to achieve optimal scheme and scale by requiring the pQCD approximate be independent to the "unphysical" theoretical conventions.

  8. Water quality assessment by means of HFNI valvometry and high-frequency data modeling.

    PubMed

    Sow, Mohamedou; Durrieu, Gilles; Briollais, Laurent; Ciret, Pierre; Massabuau, Jean-Charles

    2011-11-01

    The high-frequency measurements of valve activity in bivalves (e.g., valvometry) over a long period of time and in various environmental conditions allow a very accurate study of their behaviors as well as a global analysis of possible perturbations due to the environment. Valvometry uses the bivalve's ability to close its shell when exposed to a contaminant or other abnormal environmental conditions as an alarm to indicate possible perturbations in the environment. The modeling of such high-frequency serial valvometry data is statistically challenging, and here, a nonparametric approach based on kernel estimation is proposed. This method has the advantage of summarizing complex data into a simple density profile obtained from each animal at every 24-h period to ultimately make inference about time effect and external conditions on this profile. The statistical properties of the estimator are presented. Through an application to a sample of 16 oysters living in the Bay of Arcachon (France), we demonstrate that this method can be used to first estimate the normal biological rhythms of permanently immersed oysters and second to detect perturbations of these rhythms due to changes in their environment. We anticipate that this approach could have an important contribution to the survey of aquatic systems.

  9. 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.

  10. Running of the spectrum of cosmological perturbations in string gas cosmology

    NASA Astrophysics Data System (ADS)

    Brandenberger, Robert; Franzmann, Guilherme; Liang, Qiuyue

    2017-12-01

    We compute the running of the spectrum of cosmological perturbations in string gas cosmology, making use of a smooth parametrization of the transition between the early Hagedorn phase and the later radiation phase. We find that the running has the same sign as in simple models of single scalar field inflation. Its magnitude is proportional to (1 -ns) (ns being the slope index of the spectrum), and it is thus parametrically larger than for inflationary cosmology, where it is proportional to (1 -ns)2 .

  11. THE FIRST FERMI IN A HIGH ENERGY NUCLEAR COLLISION.

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

    KRASNITZ,A.

    1999-08-09

    At very high energies, weak coupling, non-perturbative methods can be used to study classical gluon production in nuclear collisions. One observes in numerical simulations that after an initial formation time, the produced partons are on shell, and their subsequent evolution can be studied using transport theory. At the initial formation time, a simple non-perturbative relation exists between the energy and number densities of the produced partons, and a scale determined by the saturated parton density in the nucleus.

  12. Nonadiabatic exchange dynamics during adiabatic frequency sweeps.

    PubMed

    Barbara, Thomas M

    2016-04-01

    A Bloch equation analysis that includes relaxation and exchange effects during an adiabatic frequency swept pulse is presented. For a large class of sweeps, relaxation can be incorporated using simple first order perturbation theory. For anisochronous exchange, new expressions are derived for exchange augmented rotating frame relaxation. For isochronous exchange between sites with distinct relaxation rate constants outside the extreme narrowing limit, simple criteria for adiabatic exchange are derived and demonstrate that frequency sweeps commonly in use may not be adiabatic with regard to exchange unless the exchange rates are much larger than the relaxation rates. Otherwise, accurate assessment of the sensitivity to exchange dynamics will require numerical integration of the rate equations. Examples of this situation are given for experimentally relevant parameters believed to hold for in-vivo tissue. These results are of significance in the study of exchange induced contrast in magnetic resonance imaging. Copyright © 2016 Elsevier Inc. All rights reserved.

  13. Time-dependent inhomogeneous jet models for BL Lac objects

    NASA Technical Reports Server (NTRS)

    Marlowe, A. T.; Urry, C. M.; George, I. M.

    1992-01-01

    Relativistic beaming can explain many of the observed properties of BL Lac objects (e.g., rapid variability, high polarization, etc.). In particular, the broadband radio through X-ray spectra are well modeled by synchrotron-self Compton emission from an inhomogeneous relativistic jet. We have done a uniform analysis on several BL Lac objects using a simple but plausible inhomogeneous jet model. For all objects, we found that the assumed power-law distribution of the magnetic field and the electron density can be adjusted to match the observed BL Lac spectrum. While such models are typically unconstrained, consideration of spectral variability strongly restricts the allowed parameters, although to date the sampling has generally been too sparse to constrain the current models effectively. We investigate the time evolution of the inhomogeneous jet model for a simple perturbation propagating along the jet. The implications of this time evolution model and its relevance to observed data are discussed.

  14. Time-dependent inhomogeneous jet models for BL Lac objects

    NASA Astrophysics Data System (ADS)

    Marlowe, A. T.; Urry, C. M.; George, I. M.

    1992-05-01

    Relativistic beaming can explain many of the observed properties of BL Lac objects (e.g., rapid variability, high polarization, etc.). In particular, the broadband radio through X-ray spectra are well modeled by synchrotron-self Compton emission from an inhomogeneous relativistic jet. We have done a uniform analysis on several BL Lac objects using a simple but plausible inhomogeneous jet model. For all objects, we found that the assumed power-law distribution of the magnetic field and the electron density can be adjusted to match the observed BL Lac spectrum. While such models are typically unconstrained, consideration of spectral variability strongly restricts the allowed parameters, although to date the sampling has generally been too sparse to constrain the current models effectively. We investigate the time evolution of the inhomogeneous jet model for a simple perturbation propagating along the jet. The implications of this time evolution model and its relevance to observed data are discussed.

  15. 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.

  16. Analysis of pulsating spray flames propagating in lean two-phase mixtures with unity Lewis number

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

    Nicoli, C.; Haldenwang, P.; Suard, S.

    2005-11-01

    Pulsating (or oscillatory) spray flames have recently been observed in experiments on two-phase combustion. Numerical studies have pointed out that such front oscillations can be obtained even with very simple models of homogeneous two-phase mixtures, including elementary vaporization schemes. The paper presents an analytical approach within the simple framework of the thermal-diffusive model, which is complemented by a vaporization rate independent of gas temperature, as soon as the latter reaches a certain thermal threshold ({theta}{sub v} in reduced form). The study involves the Damkoehler number (Da), the ratio of chemical reaction rate to vaporization rate, and the Zeldovich number (Ze)more » as essential parameters. We use the standard asymptotic method based on matched expansions in terms of 1/Ze. Linear analysis of two-phase flame stability is performed by studying, in the absence of differential diffusive effects (unity Lewis number), the linear growth rate of 2-D perturbations added to steady plane solutions and characterized by wavenumber k in the direction transverse to spreading. A domain of existence is found for the pulsating regime. It corresponds to mixture characteristics often met in air-fuel two-phase systems: low boiling temperature ({theta}{sub v} << 1), reaction rate not higher than vaporization rate (Da < 1, i.e., small droplets), and activation temperature assumed to be high compared with flame temperature (Ze {>=} 10). Satisfactory comparison with numerical simulations confirms the validity of the analytical approach; in particular, positive growth rates have been found for planar perturbations (k = 0) and for wrinkled fronts (k {ne} 0). Finally, comparison between predicted frequencies and experimental measurements is discussed.« less

  17. The life of a meander bend: Connecting shape and dynamics via analysis of a numerical model

    NASA Astrophysics Data System (ADS)

    Schwenk, Jon; Lanzoni, Stefano; Foufoula-Georgiou, Efi

    2015-04-01

    Analysis of bend-scale meandering river dynamics is a problem of theoretical and practical interest. This work introduces a method for extracting and analyzing the history of individual meander bends from inception until cutoff (called "atoms") by tracking backward through time the set of two cutoff nodes in numerical meander migration models. Application of this method to a simplified yet physically based model provides access to previously unavailable bend-scale meander dynamics over long times and at high temporal resolutions. We find that before cutoffs, the intrinsic model dynamics invariably simulate a prototypical cutoff atom shape we dub simple. Once perturbations from cutoffs occur, two other archetypal cutoff planform shapes emerge called long and round that are distinguished by a stretching along their long and perpendicular axes, respectively. Three measures of meander migration—growth rate, average migration rate, and centroid migration rate—are introduced to capture the dynamic lives of individual bends and reveal that similar cutoff atom geometries share similar dynamic histories. Specifically, through the lens of the three shape types, simples are seen to have the highest growth and average migration rates, followed by rounds, and finally longs. Using the maximum average migration rate as a metric describing an atom's dynamic past, we show a strong connection between it and two metrics of cutoff geometry. This result suggests both that early formative dynamics may be inferred from static cutoff planforms and that there exists a critical period early in a meander bend's life when its dynamic trajectory is most sensitive to cutoff perturbations. An example of how these results could be applied to Mississippi River oxbow lakes with unknown historic dynamics is shown. The results characterize the underlying model and provide a framework for comparisons against more complex models and observed dynamics.

  18. A simple parameter can switch between different weak-noise-induced phenomena in a simple neuron model

    NASA Astrophysics Data System (ADS)

    Yamakou, Marius E.; Jost, Jürgen

    2017-10-01

    In recent years, several, apparently quite different, weak-noise-induced resonance phenomena have been discovered. Here, we show that at least two of them, self-induced stochastic resonance (SISR) and inverse stochastic resonance (ISR), can be related by a simple parameter switch in one of the simplest models, the FitzHugh-Nagumo (FHN) neuron model. We consider a FHN model with a unique fixed point perturbed by synaptic noise. Depending on the stability of this fixed point and whether it is located to either the left or right of the fold point of the critical manifold, two distinct weak-noise-induced phenomena, either SISR or ISR, may emerge. SISR is more robust to parametric perturbations than ISR, and the coherent spike train generated by SISR is more robust than that generated deterministically. ISR also depends on the location of initial conditions and on the time-scale separation parameter of the model equation. Our results could also explain why real biological neurons having similar physiological features and synaptic inputs may encode very different information.

  19. Uniform function constants of motion and their first-order perturbation

    NASA Astrophysics Data System (ADS)

    Prato, Domingo; Hamity, Victor H.

    2005-05-01

    The main purpose of this work is to present some uniform function constants of motion rather than the well-known quantities arising from spacetime symmetries. These constants are usually associated with the intrinsic characteristics of the trajectories of a particle in a central potential field. We treat two cases. The first is the Lenz vector which sometimes is found in the literature [1, 2]; the other is associated with the isotropic harmonic oscillator, of relative importance in some simple models of the classical molecular interaction. The first example is applied to describe the perturbation of the trajectories in the Rutherford scattering and the precession of the Keplerian orbit of a planet. In the other case the conserved quantity is a symmetric tensor. We find the eigenvectors and eigenvalues of that tensor while at the same time we obtain the solution to the problem of calculating the rotation rate of the orbits in first order of a perturbation parameter in the potential energy, by performing a simple coordinate transformation in the Cartesian plane. We think that the present work addresses many aspects of mechanics with a didactical interest in other physics or mathematics courses.

  20. Computer modeling of pulsed CO2 lasers for lidar applications

    NASA Technical Reports Server (NTRS)

    Spiers, Gary D.; Smithers, Martin E.; Murty, Rom

    1991-01-01

    The experimental results will enable a comparison of the numerical code output with experimental data. This will ensure verification of the validity of the code. The measurements were made on a modified commercial CO2 laser. Results are listed as following. (1) The pulse shape and energy dependence on gas pressure were measured. (2) The intrapulse frequency chirp due to plasma and laser induced medium perturbation effects were determined. A simple numerical model showed quantitative agreement with these measurements. The pulse to pulse frequency stability was also determined. (3) The dependence was measured of the laser transverse mode stability on cavity length. A simple analysis of this dependence in terms of changes to the equivalent fresnel number and the cavity magnification was performed. (4) An analysis was made of the discharge pulse shape which enabled the low efficiency of the laser to be explained in terms of poor coupling of the electrical energy into the vibrational levels. And (5) the existing laser resonator code was changed to allow it to run on the Cray XMP under the new operating system.

  1. The Effects of Aperiodic Perturbation on the Last Good Surface of a Single-Null Divertor Tokamak

    NASA Astrophysics Data System (ADS)

    Jordan, Joseph; Punjabi, Alkesh; Ali, Halima

    2003-10-01

    An area-preserving discrete mapping, called the Simple Map is used to analyze the effects of aperiodic perturbation on the last good magnetic surface of a single-null divertor tokamak. The SM was developed by Punjabi and Boozer /1/. The SM equations are modified to reflect the effect of aperiodic perturbation: Xn + 1 = Xn - (k+δ_aperiodics(n))Y_n(1-Y_n), Y_n+1 = Yn + kX_n+1 where δ_aperiodic is the amplitude of the aperiodic perturbation. The equations are coded into FORTRAN and used in conjunction with a graphing program to show the trajectories for different amplitudes of aperiodic perturbation. As the aperiodic perturbation is increased, the trajectories break from a clean curve and develop strange behavior as they approach chaos. The progression of the trajectories from a clean curve to a chaotic one is observed, and the results are presented in this paper. This project is supported by NASA SHARP and US DOE Grant Number DE-F02-02ER54673. The research was done under the mentorship of Profs. Punjabi and Ali. 1. Punjabi A., Verma A., and Boozer A., Phys. Rev. Lett, 69, 3322 (1992)

  2. 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.

  3. On the Propagation of Small Perturbations in Two Simple Aeroelastic Systems

    NASA Technical Reports Server (NTRS)

    Iollo, Angelo; Salas, Manuel D.

    1998-01-01

    In this paper we investigate the wave propagation patterns for two simple flow-structure problems. We focus on the study of the propagation speeds of the waves in the fluid and in the structure, as the rigidity of the structure and the Mach number of the undisturbed flow are changing. Some implications concerning the sound emission by inhomogeneities eventually present in the structure are discussed.

  4. 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.

  5. A relativistic signature in large-scale structure

    NASA Astrophysics Data System (ADS)

    Bartolo, Nicola; Bertacca, Daniele; Bruni, Marco; Koyama, Kazuya; Maartens, Roy; Matarrese, Sabino; Sasaki, Misao; Verde, Licia; Wands, David

    2016-09-01

    In General Relativity, the constraint equation relating metric and density perturbations is inherently nonlinear, leading to an effective non-Gaussianity in the dark matter density field on large scales-even if the primordial metric perturbation is Gaussian. Intrinsic non-Gaussianity in the large-scale dark matter overdensity in GR is real and physical. However, the variance smoothed on a local physical scale is not correlated with the large-scale curvature perturbation, so that there is no relativistic signature in the galaxy bias when using the simplest model of bias. It is an open question whether the observable mass proxies such as luminosity or weak lensing correspond directly to the physical mass in the simple halo bias model. If not, there may be observables that encode this relativistic signature.

  6. Long-lived light mediator to dark matter and primordial small scale spectrum

    DOE PAGES

    Zhang, Yue

    2015-05-01

    We calculate the early universe evolution of perturbations in the dark matter energy density in the context of simple dark sector models containing a GeV scale light mediator. We consider the case that the mediator is long-lived, with lifetime up to a second, and before decaying it temporarily dominates the energy density of the universe. We show that for primordial perturbations that enter the horizon around this period, the interplay between linear growth during matter domination and collisional damping can generically lead to a sharp peak in the spectrum of dark matter density perturbation. Finally, as a result, the populationmore » of the smallest DM halos gets enhanced. Possible implications of this scenario are discussed.« less

  7. An improved thermodynamic perturbation theory for Mercedes-Benz water

    NASA Astrophysics Data System (ADS)

    Urbic, T.; Vlachy, V.; Kalyuzhnyi, Yu. V.; Dill, K. A.

    2007-11-01

    We previously applied Wertheim's thermodynamic perturbation theory for associative fluids to the simple Mercedes-Benz model of water. We found that the theory reproduced well the physical properties of hot water, but was less successful in capturing the more structured hydrogen bonding that occurs in cold water. Here, we propose an improved version of the thermodynamic perturbation theory in which the effective density of the reference system is calculated self-consistently. The new theory is a significant improvement, giving good agreement with Monte Carlo simulations of the model, and predicting key anomalies of cold water, such as minima in the molar volume and large heat capacity, in addition to giving good agreement with the isothermal compressibility and thermal expansion coefficient.

  8. An improved thermodynamic perturbation theory for Mercedes-Benz water.

    PubMed

    Urbic, T; Vlachy, V; Kalyuzhnyi, Yu V; Dill, K A

    2007-11-07

    We previously applied Wertheim's thermodynamic perturbation theory for associative fluids to the simple Mercedes-Benz model of water. We found that the theory reproduced well the physical properties of hot water, but was less successful in capturing the more structured hydrogen bonding that occurs in cold water. Here, we propose an improved version of the thermodynamic perturbation theory in which the effective density of the reference system is calculated self-consistently. The new theory is a significant improvement, giving good agreement with Monte Carlo simulations of the model, and predicting key anomalies of cold water, such as minima in the molar volume and large heat capacity, in addition to giving good agreement with the isothermal compressibility and thermal expansion coefficient.

  9. Shot noise perturbations and mean first passage times between stable states.

    PubMed

    Drury, Kevin L S

    2007-08-01

    Predicting crossings between stable states is a central issue in population biology. Crossings from low-density to high-density equilibria are often associated with pest outbreaks, while the opposite crossings are often associated with population collapse of harvested species. Here I use a simple, bistable model to demonstrate a technique for estimating mean first passage times (MFPT) of thresholds, including boundaries between stable equilibria. The approach is based on stochastic "shot-noise" perturbations to the population and the MFPTs compare favorably with mean crossing times from Monte Carlo numerical solutions of the stochastically perturbed model. This agreement suggests that MFPT approximations can be used to quantify expected effects of species manipulations, whether the goal is pest control or sustainable harvest.

  10. Perturbations i have Known and Loved

    NASA Astrophysics Data System (ADS)

    Field, Robert W.

    2011-06-01

    A spectroscopic perturbation is a disruption of a ^1Σ-^1Σ-like regular pattern that can embody level-shifts, extra lines, and intensity anomalies. Once upon a time, when a band was labeled ``perturbed,'' it was considered worthless because it could at best yield molecular constants unsuited for archival tables. Nevertheless, a few brave spectroscopists, notably Albin Lagerqvist and Richard Barrow, collected perturbations because they knew that the pattern of multiple perturbations formed an intricate puzzle that would eventually reveal the presence and electronic symmetry of otherwise unobservable electronic states. There are many kinds of patterns of broken patterns. In my PhD thesis I showed how to determine absolute vibrational assignments for the perturber from patterns among the observed values of perturbation matrix elements. When a ^3Π state is perturbed, its six (Ω, parity) components capture a pattern of level shifts and intensity anomalies that reveals more about the nature of the perturber than a simple perturbation of the single component of a ^1Σ state. In perturbation-facilitated OODR, a perturbed singlet level acts as a spectroscopic doorway through which the entire triplet manifold may be systematically explored. For polyatomic molecule vibrations, a vibrational polyad (a group of mutually perturbing vibrational levels, among which the perturbation matrix elements are expected to follow harmonic oscillator scaling rules) can contain more components than a ^3Π state and intrapolyad patterns can be exquisitely sensitive not merely to the nature of an interloper within the polyad but also to the eigenvector character of the vibronic state from which the polyad is viewed. Variation of scaled polyad interaction parameters from one polyad to the next, a pattern of patterns, can signal proximity to an isomerization barrier. Everything in Rydberg-land seems to scale as N⋆-3, yet a trespassing valence state causes all scaling and propensity rules go out the window.

  11. Cooling of a sunspot

    NASA Technical Reports Server (NTRS)

    Boruta, N.

    1977-01-01

    The question of whether a perturbed photospheric area can grow into a region of reduced temperature resembling a sunspot is investigated by considering whether instabilities exist that can lead to a growing temperature change and corresponding magnetic-field concentration in some region of the photosphere. After showing that Alfven cooling can lead to these instabilities, the effect of a heat sink on the temperature development of a perturbed portion of the photosphere is studied. A simple form of Alfven-wave cooling is postulated, and computations are performed to determine whether growing modes exist for physically relevant boundary conditions. The results indicate that simple inhibition of convection does not give growing modes, but Alfven-wave production can result in cooling that leads to growing field concentration. It is concluded that since growing instabilities can occur with strong enough cooling, it is quite possible that energy loss through Alfven waves gives rise to a self-generating temperature change and sunspot formation.

  12. Coronal Mass Ejection early-warning mission by solar-photon sailcraft

    NASA Astrophysics Data System (ADS)

    Vulpetti, Giovanni; Circi, Christian; Pino, Tommaso

    2017-11-01

    A preliminary investigation of the early warning of solar storms caused by Coronal Mass Ejection has been carried out. A long warning time could be obtained with a sailcraft synchronous with the Earth-Moon barycenter, and stationed well below the L1 point. In this paper, the theory of heliocentric synchronous sailcraft is set up, its perturbed orbit is analyzed, and a potential solution capable of providing an annual synchrony is carried out. A simple analysis of the response from a low-mass electrochromic actuator for the realization of station-keeping attitude maneuvers is put forwards, and an example of propellantless re-orientation maneuver is studied.

  13. VENTURE: a code block for solving multigroup neutronics problems applying the finite-difference diffusion-theory approximation to neutron transport

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

    Vondy, D.R.; Fowler, T.B.; Cunningham, G.W.

    1975-10-01

    The computer code block VENTURE, designed to solve multigroup neutronics problems with application of the finite-difference diffusion-theory approximation to neutron transport (or alternatively simple P$sub 1$) in up to three- dimensional geometry is described. A variety of types of problems may be solved: the usual eigenvalue problem, a direct criticality search on the buckling, on a reciprocal velocity absorber (prompt mode), or on nuclide concentrations, or an indirect criticality search on nuclide concentrations, or on dimensions. First- order perturbation analysis capability is available at the macroscopic cross section level. (auth)

  14. Dynamic Considerations for Control of Closed Life Support Systems

    NASA Technical Reports Server (NTRS)

    Babcock, P. S.; Auslander, D. M.; Spear, R. C.

    1985-01-01

    Reliability of closed life support systems depend on their ability to continue supplying the crew's needs during perturbations and equipment failures. The dynamic considerations interact with the basic static design through the sizing of storages, the specification of excess capacities in processors, and the choice of system initial state. A very simple system flow model was used to examine the possibilities for system failures even when there is sufficient storage to buffer the immediate effects of the perturbation. Two control schemes are shown which have different dynamic consequences in response to component failures.

  15. Single-particle dynamics of the Anderson model: a local moment approach

    NASA Astrophysics Data System (ADS)

    Glossop, Matthew T.; Logan, David E.

    2002-07-01

    A non-perturbative local moment approach to single-particle dynamics of the general asymmetric Anderson impurity model is developed. The approach encompasses all energy scales and interaction strengths. It captures thereby strong coupling Kondo behaviour, including the resultant universal scaling behaviour of the single-particle spectrum; as well as the mixed valence and essentially perturbative empty orbital regimes. The underlying approach is physically transparent and innately simple, and as such is capable of practical extension to lattice-based models within the framework of dynamical mean-field theory.

  16. CMB in the river frame and gauge invariance at second order

    NASA Astrophysics Data System (ADS)

    Roldan, Omar

    2018-03-01

    Gauge invariance: the Sachs-Wolfe formula describing the Cosmic Microwave Background (CMB) temperature anisotropies is one of the most important relations in cosmology. Despite its importance, the gauge invariance of this formula has only been discussed at first order. Here we discuss the subtle issue of second-order gauge transformations on the CMB. By introducing two rules (needed to handle the subtle issues), we prove the gauge invariance of the second-order Sachs-Wolfe formula and provide several compact expressions which can be useful for the study of gauge transformations on cosmology. Our results go beyond a simple technicality: we discuss from a physical point of view several aspects that improve our understanding of the CMB. We also elucidate how crucial it is to understand gauge transformations on the CMB in order to avoid errors and/or misconceptions as occurred in the past. The river frame: we introduce a cosmological frame which we call the river frame. In this frame, photons and any object can be thought as fishes swimming in the river and relations are easily expressed in either the metric or the covariant formalism then ensuring a transparent geometric meaning. Finally, our results show that the river frame is useful to make perturbative and non-perturbative analysis. In particular, it was already used to obtain the fully nonlinear generalization of the Sachs-Wolfe formula and is used here to describe second-order perturbations.

  17. Framework for network modularization and Bayesian network analysis to investigate the perturbed metabolic network

    PubMed Central

    2011-01-01

    Background Genome-scale metabolic network models have contributed to elucidating biological phenomena, and predicting gene targets to engineer for biotechnological applications. With their increasing importance, their precise network characterization has also been crucial for better understanding of the cellular physiology. Results We herein introduce a framework for network modularization and Bayesian network analysis (FMB) to investigate organism’s metabolism under perturbation. FMB reveals direction of influences among metabolic modules, in which reactions with similar or positively correlated flux variation patterns are clustered, in response to specific perturbation using metabolic flux data. With metabolic flux data calculated by constraints-based flux analysis under both control and perturbation conditions, FMB, in essence, reveals the effects of specific perturbations on the biological system through network modularization and Bayesian network analysis at metabolic modular level. As a demonstration, this framework was applied to the genetically perturbed Escherichia coli metabolism, which is a lpdA gene knockout mutant, using its genome-scale metabolic network model. Conclusions After all, it provides alternative scenarios of metabolic flux distributions in response to the perturbation, which are complementary to the data obtained from conventionally available genome-wide high-throughput techniques or metabolic flux analysis. PMID:22784571

  18. Framework for network modularization and Bayesian network analysis to investigate the perturbed metabolic network.

    PubMed

    Kim, Hyun Uk; Kim, Tae Yong; Lee, Sang Yup

    2011-01-01

    Genome-scale metabolic network models have contributed to elucidating biological phenomena, and predicting gene targets to engineer for biotechnological applications. With their increasing importance, their precise network characterization has also been crucial for better understanding of the cellular physiology. We herein introduce a framework for network modularization and Bayesian network analysis (FMB) to investigate organism's metabolism under perturbation. FMB reveals direction of influences among metabolic modules, in which reactions with similar or positively correlated flux variation patterns are clustered, in response to specific perturbation using metabolic flux data. With metabolic flux data calculated by constraints-based flux analysis under both control and perturbation conditions, FMB, in essence, reveals the effects of specific perturbations on the biological system through network modularization and Bayesian network analysis at metabolic modular level. As a demonstration, this framework was applied to the genetically perturbed Escherichia coli metabolism, which is a lpdA gene knockout mutant, using its genome-scale metabolic network model. After all, it provides alternative scenarios of metabolic flux distributions in response to the perturbation, which are complementary to the data obtained from conventionally available genome-wide high-throughput techniques or metabolic flux analysis.

  19. 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.

  20. A new convergence analysis and perturbation resilience of some accelerated proximal forward-backward algorithms with errors

    NASA Astrophysics Data System (ADS)

    Reem, Daniel; De Pierro, Alvaro

    2017-04-01

    Many problems in science and engineering involve, as part of their solution process, the consideration of a separable function which is the sum of two convex functions, one of them possibly non-smooth. Recently a few works have discussed inexact versions of several accelerated proximal methods aiming at solving this minimization problem. This paper shows that inexact versions of a method of Beck and Teboulle (fast iterative shrinkable tresholding algorithm) preserve, in a Hilbert space setting, the same (non-asymptotic) rate of convergence under some assumptions on the decay rate of the error terms The notion of inexactness discussed here seems to be rather simple, but, interestingly, when comparing to related works, closely related decay rates of the errors terms yield closely related convergence rates. The derivation sheds some light on the somewhat mysterious origin of some parameters which appear in various accelerated methods. A consequence of the analysis is that the accelerated method is perturbation resilient, making it suitable, in principle, for the superiorization methodology. By taking this into account, we re-examine the superiorization methodology and significantly extend its scope. This work was supported by FAPESP 2013/19504-9. The second author was supported also by CNPq grant 306030/2014-4.

  1. Robust and novel two degree of freedom fractional controller based on two-loop topology for inverted pendulum.

    PubMed

    Dwivedi, Prakash; Pandey, Sandeep; Junghare, A S

    2018-04-01

    A rotary single inverted pendulum (RSIP) typically represents a space booster rocket, Segway and similar systems with unstable equilibrium. This paper proposes a novel two degree of freedom (2-DOF) fractional control strategy based on 2-loop topology for RSIP system which can be extended to control the systems with unstable equilibrium. It comprises feedback and feed-forward paths. Primary controller relates the perturbation attenuation while the secondary controller is accountable for set point tracking. To tune the parameters of proposed fractional controller a simple graphical tuning method based on frequency response is used. The study will serve the outstanding experimental results for both, stabilization and trajectory tracking tasks. The study will also serve to present a comparison of the performance of the proposed controller with the 1-DOF FOPID controller and sliding mode controller (SMC) for the RSIP system. Further to confirm the usability of the proposed controller and to avoid the random perturbations sensitivity, robustness, and stability analysis through fractional root-locus and Bode-plot is investigated. Copyright © 2018 ISA. Published by Elsevier Ltd. All rights reserved.

  2. The Multiple Resonance Probe: A Novel Device for Industry Compatible Plasma Diagnostics

    NASA Astrophysics Data System (ADS)

    Brinkmann, Ralf Peter; Storch, Robert; Lapke, Martin; Oberrath, Jens; Schulz, Christian; Styrnoll, Tim; Zietz, Christian; Awakowicz, Peter; Musch, Thomas; Mussenbrock, Thomas; Rolfes, Ilona

    2012-10-01

    To be useful for the supervision or control of technical plasmas, a diagnostic method must be i) robust and stable, ii) insensitive to perturbation by the process, iii) itself not perturbing the process, iv) clearly and easily interpretable without the need for calibration, v) compliant with the requirements of process integration, and, last but not least, vi) economical in terms of investment, footprint, and maintenance. Plasma resonance spectroscopy, exploiting the natural ability of plasmas to resonate on or near the electron plasma frequency, provides a good basis for such an ``industry compatible'' plasma diagnostics. The contribution will describe the general idea of active plasma resonance spectroscopy and introduce a mathematical formalism for its analysis. It will then focus on the novel multipole resonance probe (MRP), where the excited resonances can be classified explicitly and the connection between the probe response and the desired electron density can be cast as a simple formula. The current state of the MRP project will be described, including the experimental characterization of a prototype in comparison with Langmuir probes, and the development of a specialized measurement circuit.

  3. Boundary formulations for sensitivity analysis without matrix derivatives

    NASA Technical Reports Server (NTRS)

    Kane, J. H.; Guru Prasad, K.

    1993-01-01

    A new hybrid approach to continuum structural shape sensitivity analysis employing boundary element analysis (BEA) is presented. The approach uses iterative reanalysis to obviate the need to factor perturbed matrices in the determination of surface displacement and traction sensitivities via a univariate perturbation/finite difference (UPFD) step. The UPFD approach makes it possible to immediately reuse existing subroutines for computation of BEA matrix coefficients in the design sensitivity analysis process. The reanalysis technique computes economical response of univariately perturbed models without factoring perturbed matrices. The approach provides substantial computational economy without the burden of a large-scale reprogramming effort.

  4. Symmetric Simple Map with Dipole Map for a Single-Null Divertor Tokamak

    NASA Astrophysics Data System (ADS)

    Ali, Halima; Watson, Michael; Punjabi, Alkesh; Boozer, Allen

    1996-11-01

    This investigation focuses on the effects of an externally placed dipole coil on the magnetic topology of a single-null divertor tokamak with a stochastic scrape-off layer using the Method of Maps (Punjabi A, Verma A and Boozer A, Phys Rev Lett), 69, 3322 (1992) and J Plasma Phys, 52, 91 (1994). The unperturbed magnetic topology is represented by the Symmetric Simple Map (Ali H, Watson M, Mayer C, Punjabi A and Boozer A, Bull Am Phys Soc), 40, 1855 (1995). The effect of dipole perturbation is repesented by the Dipole Map (Ali H, Watson M, Punjabi A and Boozer A, Sherwood Mtg), paper 1C20 (1996). A single dipole coil is placed across from the X-point below the last good surface. The strength of the dipole perturbation and the distance of the coil from the last good surface are varied. We observe that the dipole perturbation causes spatially intermittent chaos. This has significant implications for radiative divertor concepts as well for impurity control. We also present the detailed results on the effects of the dipole coil on the properties of the stochastic layer and the footprint of the field lines on the divertor plate. This work is supported by the US DOE OFES.

  5. Perturbation Biology: Inferring Signaling Networks in Cellular Systems

    PubMed Central

    Miller, Martin L.; Gauthier, Nicholas P.; Jing, Xiaohong; Kaushik, Poorvi; He, Qin; Mills, Gordon; Solit, David B.; Pratilas, Christine A.; Weigt, Martin; Braunstein, Alfredo; Pagnani, Andrea; Zecchina, Riccardo; Sander, Chris

    2013-01-01

    We present a powerful experimental-computational technology for inferring network models that predict the response of cells to perturbations, and that may be useful in the design of combinatorial therapy against cancer. The experiments are systematic series of perturbations of cancer cell lines by targeted drugs, singly or in combination. The response to perturbation is quantified in terms of relative changes in the measured levels of proteins, phospho-proteins and cellular phenotypes such as viability. Computational network models are derived de novo, i.e., without prior knowledge of signaling pathways, and are based on simple non-linear differential equations. The prohibitively large solution space of all possible network models is explored efficiently using a probabilistic algorithm, Belief Propagation (BP), which is three orders of magnitude faster than standard Monte Carlo methods. Explicit executable models are derived for a set of perturbation experiments in SKMEL-133 melanoma cell lines, which are resistant to the therapeutically important inhibitor of RAF kinase. The resulting network models reproduce and extend known pathway biology. They empower potential discoveries of new molecular interactions and predict efficacious novel drug perturbations, such as the inhibition of PLK1, which is verified experimentally. This technology is suitable for application to larger systems in diverse areas of molecular biology. PMID:24367245

  6. Cosmological perturbations in teleparallel Loop Quantum Cosmology

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

    Haro, Jaime, E-mail: jaime.haro@upc.edu

    2013-11-01

    Cosmological perturbations in Loop Quantum Cosmology (LQC) are usually studied incorporating either holonomy corrections, where the Ashtekar connection is replaced by a suitable sinus function in order to have a well-defined quantum analogue, or inverse-volume corrections coming from the eigenvalues of the inverse-volume operator. In this paper we will develop an alternative approach to calculate cosmological perturbations in LQC based on the fact that, holonomy corrected LQC in the flat Friedmann-Lemaître-Robertson-Walker (FLRW) geometry could be also obtained as a particular case of teleparallel F(T) gravity (teleparallel LQC). The main idea of our approach is to mix the simple bounce providedmore » by holonomy corrections in LQC with the non-singular perturbation equations given by F(T) gravity, in order to obtain a matter bounce scenario as a viable alternative to slow-roll inflation. In our study, we have obtained an scale invariant power spectrum of cosmological perturbations. However, the ratio of tensor to scalar perturbations is of order 1, which does not agree with the current observations. For this reason, we suggest a model where a transition from the matter domination to a quasi de Sitter phase is produced in order to enhance the scalar power spectrum.« less

  7. A simple non-perturbing cell migration assay insensitive to proliferation effects.

    PubMed

    Glenn, Honor L; Messner, Jacob; Meldrum, Deirdre R

    2016-08-18

    Migration is a fundamental cellular behavior that plays an indispensable role in development and homeostasis, but can also contribute to pathology such as cancer metastasis. Due to its relevance to many aspects of human health, the ability to accurately measure cell migration is of broad interest, and numerous approaches have been developed. One of the most commonly employed approaches, because of its simplicity and throughput, is the exclusion zone assay in which cells are allowed to migrate into an initially cell-free region. A major drawback of this assay is that it relies on simply counting cells in the exclusion zone and therefore cannot distinguish the effects of proliferation from migration. We report here a simple modification to the exclusion zone migration assay that exclusively measures cell migration and is not affected by proliferation. This approach makes use of a lineage-tracing vital stain that is retained through cell generations and effectively reads out migration relative to the original, parental cell population. This modification is simple, robust, non-perturbing, and inexpensive. We validate the method in a panel of cell lines under conditions that inhibit or promote migration and demonstrate its use in normal and cancer cell lines as well as primary cells.

  8. Simple, explicitly time-dependent, and regular solutions of the linearized vacuum Einstein equations in Bondi-Sachs coordinates

    NASA Astrophysics Data System (ADS)

    Mädler, Thomas

    2013-05-01

    Perturbations of the linearized vacuum Einstein equations in the Bondi-Sachs formulation of general relativity can be derived from a single master function with spin weight two, which is related to the Weyl scalar Ψ0, and which is determined by a simple wave equation. By utilizing a standard spin representation of tensors on a sphere and two different approaches to solve the master equation, we are able to determine two simple and explicitly time-dependent solutions. Both solutions, of which one is asymptotically flat, comply with the regularity conditions at the vertex of the null cone. For the asymptotically flat solution we calculate the corresponding linearized perturbations, describing all multipoles of spin-2 waves that propagate on a Minkowskian background spacetime. We also analyze the asymptotic behavior of this solution at null infinity using a Penrose compactification and calculate the Weyl scalar Ψ4. Because of its simplicity, the asymptotically flat solution presented here is ideally suited for test bed calculations in the Bondi-Sachs formulation of numerical relativity. It may be considered as a sibling of the Bergmann-Sachs or Teukolsky-Rinne solutions, on spacelike hypersurfaces, for a metric adapted to null hypersurfaces.

  9. Energy Expansion for the Period of Anharmonic Oscillators by the Method of Lindstedt-Poincare

    ERIC Educational Resources Information Center

    Fernandez, Francisco M.

    2004-01-01

    A simple, straightforward and efficient method is proposed for the calculation of the period of anharmonic oscillators as an energy series. The approach is based on perturbation theory and the method of Lindstedt-Poincare.

  10. Autofrecuencias de las ecuaciones de Helmholtz y Liouville para un modelo de tierra tipo Jeffreys simplificado.

    NASA Astrophysics Data System (ADS)

    Sevilla, M. J.; González-Camacho, A.

    The authors obtain expressions for the free frequencies of polar motion for an ellipsoidal, rotating and perturbed earth model constituted by an elastic mantle with an homogeneous liquid core of additional simple motion.

  11. Meso-beta scale numerical simulation studies of terrain-induced jet streak mass and momentum perturbations

    NASA Technical Reports Server (NTRS)

    Lin, Yuh-Lang; Kaplan, Michael L.

    1994-01-01

    An in-depth analysis of observed gravity waves and their relationship to precipitation bands over the Montana mesonetwork during the 11-12 July 1981 CCOPE case study indicated two episodes of coherent waves. While geostrophic adjustment, shearing instability, and terrain were all implicated separately or in combination as possible wave generation mechanisms, the lack of upper-air data within the wave genesis region made it difficult to define the genesis processes from observations alone. The first part of this paper, 3D Numerical Modeling Studies of Terrain-Induced Mass/Momentum Perturbations, employs a mesoscale numerical model to help diagnose the intricate early wave generation mechanisms during the first observed gravity wave episode. The meso-beta scale numerical model is used to study various simulations of the role of multiple geostrophic adjustment processes in focusing a region for gravity wave genesis. The second part of this paper, Linear Theory and Theoretical Modeling, investigates the response of non-resting rotating homogeneous and continuously stratified Boussinesq models of the terrestrial atmosphere to temporally impulsive and uniformly propagating three-dimensional localized zonal momentum sources representative of midlatitude jet streaks. The methods of linear perturbation theory applied to the potential vorticity (PV) and wave field equations are used to study the geostrophic adjustment dynamics. The total zonal and meridional wind perturbations are separated into geostrophic and ageostrophic components in order to define and follow the evolution of both the primary and secondary mesocirculations accompanying midlatitude jetogenesis forced by geostrophic adjustment processes. This problem is addressed to help fill the gap in understanding the dynamics and structure of mesoscale inertia-gravity waves forced by geostrophic adjustment processes in simple two-dimensional quiescent current systems and those produced by mesoscale numerical models simulating the orographic and diabatic perturbation of three-dimensional quasi-geostrophically balanced synoptic scale jet streaks associated with complex baroclinic severe storm producing environments.

  12. Irreducible Brillouin conditions and contracted Schrödinger equations for n-electron systems. III. Systems of noninteracting electrons.

    PubMed

    Kutzelnigg, Werner; Mukherjee, Debashis

    2004-04-22

    We analyze the structure and the solutions of the irreducible k-particle Brillouin conditions (IBCk) and the irreducible contracted Schrödinger equations (ICSEk) for an n-electron system without electron interaction. This exercise is very instructive in that it gives one both the perspective and the strategies to be followed in applying the IBC and ICSE to physically realistic systems with electron interaction. The IBC1 leads to a Liouville equation for the one-particle density matrix gamma1=gamma, consistent with our earlier analysis that the IBC1 holds both for a pure and an ensemble state. The IBC1 or the ICSE1 must be solved subject to the constraints imposed by the n-representability condition, which is particularly simple for gamma. For a closed-shell state gamma is idempotent, i.e., all natural spin orbitals (NSO's) have occupation numbers 0 or 1, and all cumulants lambdak with k> or =2 vanish. For open-shell states there are NSO's with fractional occupation number, and at the same time nonvanishing elements of lambda2, which are related to spin and symmetry coupling. It is often useful to describe an open-shell state by a totally symmetric ensemble state. If one wants to treat a one-particle perturbation by means of perturbation theory, this mainly as a run-up for the study of a two-particle perturbation, one is faced with the problem that the perturbation expansion of the Liouville equation gives information only on the nondiagonal elements (in a basis of the unperturbed states) of gamma. There are essentially three possibilities to construct the diagonal elements of gamma: (i) to consider the perturbation expansion of the characteristic polynomial of gamma, especially the idempotency for closed-shell states, (ii) to rely on the ICSE1, which (at variance with the IBC1) also gives information on the diagonal elements, though not in a very efficient manner, and (iii) to formulate the perturbation theory in terms of a unitary transformation in Fock space. The latter is particularly powerful, especially, when one wishes to study realistic Hamiltonians with a two-body interaction. (c) 2004 American Institute of Physics

  13. Investigation into the propagation of Omega very low frequency signals and techniques for improvement of navigation accuracy including differential and composite omega

    NASA Technical Reports Server (NTRS)

    1973-01-01

    An analysis of Very Low Frequency propagation in the atmosphere in the 10-14 kHz range leads to a discussion of some of the more significant causes of phase perturbation. The method of generating sky-wave corrections to predict the Omega phase is discussed. Composite Omega is considered as a means of lane identification and of reducing Omega navigation error. A simple technique for generating trapezoidal model (T-model) phase prediction is presented and compared with the Navy predictions and actual phase measurements. The T-model prediction analysis illustrates the ability to account for the major phase shift created by the diurnal effects on the lower ionosphere. An analysis of the Navy sky-wave correction table is used to provide information about spatial and temporal correlation of phase correction relative to the differential mode of operation.

  14. A finite-element-based perturbation model for the rotordynamic analysis of shrouded pump impellers: Part 2: User's guide

    NASA Technical Reports Server (NTRS)

    Baskharone, Erian A.

    1993-01-01

    This report describes the computational steps involved in executing a finite-element-based perturbation model for computing the rotor dynamic coefficients of a shrouded pump impeller or a simple seal. These arise from the fluid/rotor interaction in the clearance gap. In addition to the sample cases, the computational procedure also applies to a separate category of problems referred to as the 'seal-like' category. The problem, in this case, concerns a shrouded impeller, with the exception that the secondary, or leakage, passage is totally isolated from the primary-flow passage. The difference between this and the pump problem is that the former is analytically of the simple 'seal-like' configuration, with two (inlet and exit) flow-permeable stations, while the latter constitutes a double-entry / double-discharge flow problem. In all cases, the problem is that of a rotor clearance gap. The problem here is that of a rotor excitation in the form of a cylindrical whirl around the housing centerline for a smooth annular seal. In its centered operation mode, the rotor is assumed to give rise to an axisymmetric flow field in the clearance gap. As a result, problems involving longitudinal or helical grooves, in the rotor or housing surfaces, go beyond the code capabilities. Discarding, for the moment, the pre- and post-processing phases, the bulk of the computational procedure consists of two main steps. The first is aimed at producing the axisymmetric 'zeroth-order' flow solution in the given flow domain. Detailed description of this problem, including the flow-governing equations, turbulence closure, boundary conditions, and the finite-element formulation, was covered by Baskharone and Hensel. The second main step is where the perturbation model is implemented, with the input being the centered-rotor 'zeroth-order' flow solution and a prescribed whirl frequency ratio (whirl frequency divided by the impeller speed). The computational domain, in the latter case, is treated as three dimensional, with the number of computational planes in the circumferential direction being specified a priori. The reader is reminded that the deformations in the finite elements are all infinitesimally small because the rotor eccentricity itself is a virtual displacement. This explains why we have generically termed the perturbation model the 'virtually' deformable finite-element category. The primary outcome of implementing the perturbation model is the tangential and radial components, F(sub theta)(sup *) and F(sub r)(sup *) of the fluid-exerted force on the rotor surface due to the whirling motion. Repetitive execution of the perturbation model subprogram over a sufficient range of whirl frequency ratios, and subsequent interpolation of these fluid forces, using the least-square method, finally enable the user to compute the impeller rotor dynamic coefficients of the fluid/rotor interaction. These are the direct and cross-coupled stiffness, damping, and inertia effects of the fluid/rotor interaction.

  15. 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.

  16. Anomalistic Disturbance Torques during the Entry Phase of the Mars Exploration Rover Missions: A Telemetry and Mars-Surface Investigation

    NASA Technical Reports Server (NTRS)

    Tolson, Robert H.; Willcockson, William H.; Desai, Prasun N.; Thomas, Paige

    2006-01-01

    Shortly after landing on Mars, post-flight analysis of the "Spirit" entry data suggested that the vehicle experienced large, anomalistic oscillations in angle-of-attack starting at about M=6. Similar analysis for "Opportunity " found even larger oscillations starting immediately after maximum dynamic pressure at M=14. Where angles-of-attack of 1-2 degrees were expected from maximum dynamic pressure to drogue deployment, the reconstructions suggested 4 to 9 degrees. The next Mars lander, 2007 Phoenix project, was concerned enough to recommend further exploration of the anomalies. Detailed analysis of "Opportunity" data found significant anomalies in the hypersonic aerodynamic torques. The analysis showed that these torques were essentially fixed in the spinning vehicle. Nearly a year after landing, the "Oportunity" rover took pictures of its aeroshell on the surface, which showed that portions of the aeroshell thermal blanket assembly still remained. This blanket assembly was supposed to burn off very early in the entry. An analysis of the aeroshell photographs led to an estimate of the aerodynamic torques that the remnants could have produced. A comparison of two estimates of the aerodynamic torque perturbations (one extracted from telemetry data and the other from Mars surface photographs) showed exceptional agreement. Trajectory simulations using a simple data derived torque perturbation model provided rigid body motions similar to that observed during the "Opportunity" entry. Therefore, the case of the anomalistic attitude behavior for the "Opportunity" EDL is now considered closed and a suggestion is put forth that a similar event occurred for the "Spirit" entry as well.

  17. High-Resolution Study of the First Stretching Overtones of H3Si79Br.

    PubMed

    Ceausu; Graner; Bürger; Mkadmi; Pracna; Lafferty

    1998-11-01

    The Fourier transform infrared spectrum of monoisotopic H3Si79Br (resolution 7.7 x 10(-3) cm-1) was studied from 4200 to 4520 cm-1, in the region of the first overtones of the Si-H stretching vibration. The investigation of the spectrum revealed the presence of two band systems, the first consisting of one parallel (nu0 = 4340.2002 cm-1) and one perpendicular (nu0 = 4342.1432 cm-1) strong component, and the second of one parallel (nu0 = 4405.789 cm-1) and one perpendicular (nu0 = 4416.233 cm-1) weak component. The rovibrational analysis shows strong local perturbations for both strong and weak systems. Seven hundred eighty-one nonzero-weighted transitions belonging to the strong system [the (200) manifold in the local mode picture] were fitted to a simple model involving a perpendicular component interacting by a weak Coriolis resonance with a parallel component. The most severely perturbed transitions (whose ||obs-calc || values exceeded 3 x 10(-3) cm-1) were given zero weights. The standard deviations of the fit were 1.0 x 10(-3) and 0.69 x 10(-3) cm-1 for the parallel and the perpendicular components, respectively. The weak band system, severely perturbed by many "dark" perturbers, was fitted to a model involving one parallel and one perpendicular band, connected by a Coriolis-type resonance. The K" . DeltaK = +10 to +18 subbands of the perpendicular component, which showed very high observed - calculated values ( approximately 0.5 cm-1), were excluded from this calculation. The standard deviations of the fit were 11 x 10(-3) and 13 x 10(-3) cm-1 for the parallel and the perpendicular components, respectively. Copyright 1998 Academic Press.

  18. Compensatory dynamics stabilize aggregate community properties in response to multiple types of perturbations.

    PubMed

    Brown, Bryan L; Downing, Amy L; Leibold, Mathew A

    2016-08-01

    Compensatory dynamics are an important suite of mechanisms that can stabilize community and ecosystem attributes in systems subject to environmental fluctuations. However, few experimental investigations of compensatory dynamics have addressed these mechanisms in systems of real-world complexity, and existing evidence relies heavily on correlative analyses, retrospective examination, and experiments in simple systems. We investigated the potential for compensatory dynamics to stabilize plankton communities in plankton mesocosm systems of real-world complexity. We employed four types of perturbations including two types of nutrient pulses, shading, and acidification. To quantify how communities responded to these perturbations, we used a measure of community-wide synchrony combined with spectral analysis that allowed us to assess timescale-specific community dynamics, for example, whether dynamics were synchronous at some timescales but compensatory at others. The 150-d experiment produced 32-point time series of all zooplankton taxa in the mesocosms. We then used those time series to evaluate total zooplankton biomass as an aggregate property and to evaluate community dynamics. For three of our four perturbation types, total zooplankton biomass was significantly less variable in systems with environmental variation than in constant environments. For the same three perturbation types, community-wide synchrony was much lower in fluctuating environments than in the constant environment, particularly at longer timescales (periods ≈ 60 d). Additionally, there were strong negative correlations between population temporal variances and the level of community-wide synchrony. Taken together, these results strongly imply that compensatory interactions between species stabilized total biomass in response to perturbations. Diversity did not differ significantly across either treatments or perturbation types, thus ruling out several classes of mechanisms driven by changes in diversity. We also used several pieces of secondary evidence to evaluate the particular mechanism behind compensatory responses since a wide variety of mechanisms are hypothesized to produce compensatory dynamics. We concluded that fluctuation dependent endogenous cycles that occur as a consequence of consumer-resource interactions in competitive communities were the most likely explanation for the compensatory dynamics observed in our experiment. As with our previous work, scale-dependent dynamics were also a key to understanding compensatory dynamics in these experimental communities. © 2016 by the Ecological Society of America.

  19. Minimal string theories and integrable hierarchies

    NASA Astrophysics Data System (ADS)

    Iyer, Ramakrishnan

    Well-defined, non-perturbative formulations of the physics of string theories in specific minimal or superminimal model backgrounds can be obtained by solving matrix models in the double scaling limit. They provide us with the first examples of completely solvable string theories. Despite being relatively simple compared to higher dimensional critical string theories, they furnish non-perturbative descriptions of interesting physical phenomena such as geometrical transitions between D-branes and fluxes, tachyon condensation and holography. The physics of these theories in the minimal model backgrounds is succinctly encoded in a non-linear differential equation known as the string equation, along with an associated hierarchy of integrable partial differential equations (PDEs). The bosonic string in (2,2m-1) conformal minimal model backgrounds and the type 0A string in (2,4 m) superconformal minimal model backgrounds have the Korteweg-de Vries system, while type 0B in (2,4m) backgrounds has the Zakharov-Shabat system. The integrable PDE hierarchy governs flows between backgrounds with different m. In this thesis, we explore this interesting connection between minimal string theories and integrable hierarchies further. We uncover the remarkable role that an infinite hierarchy of non-linear differential equations plays in organizing and connecting certain minimal string theories non-perturbatively. We are able to embed the type 0A and 0B (A,A) minimal string theories into this single framework. The string theories arise as special limits of a rich system of equations underpinned by an integrable system known as the dispersive water wave hierarchy. We find that there are several other string-like limits of the system, and conjecture that some of them are type IIA and IIB (A,D) minimal string backgrounds. We explain how these and several other string-like special points arise and are connected. In some cases, the framework endows the theories with a non-perturbative definition for the first time. Notably, we discover that the Painleve IV equation plays a key role in organizing the string theory physics, joining its siblings, Painleve I and II, whose roles have previously been identified in this minimal string context. We then present evidence that the conjectured type II theories have smooth non-perturbative solutions, connecting two perturbative asymptotic regimes, in a 't Hooft limit. Our technique also demonstrates evidence for new minimal string theories that are not apparent in a perturbative analysis.

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

    NASA Astrophysics Data System (ADS)

    Charnoz, S.; Thébault, P.; Brahic, A.

    2001-07-01

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

  1. 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.

  2. A framework for studying transient dynamics of population projection matrix models.

    PubMed

    Stott, Iain; Townley, Stuart; Hodgson, David James

    2011-09-01

    Empirical models are central to effective conservation and population management, and should be predictive of real-world dynamics. Available modelling methods are diverse, but analysis usually focuses on long-term dynamics that are unable to describe the complicated short-term time series that can arise even from simple models following ecological disturbances or perturbations. Recent interest in such transient dynamics has led to diverse methodologies for their quantification in density-independent, time-invariant population projection matrix (PPM) models, but the fragmented nature of this literature has stifled the widespread analysis of transients. We review the literature on transient analyses of linear PPM models and synthesise a coherent framework. We promote the use of standardised indices, and categorise indices according to their focus on either convergence times or transient population density, and on either transient bounds or case-specific transient dynamics. We use a large database of empirical PPM models to explore relationships between indices of transient dynamics. This analysis promotes the use of population inertia as a simple, versatile and informative predictor of transient population density, but criticises the utility of established indices of convergence times. Our findings should guide further development of analyses of transient population dynamics using PPMs or other empirical modelling techniques. © 2011 Blackwell Publishing Ltd/CNRS.

  3. A Novel Shape Parameterization Approach

    NASA Technical Reports Server (NTRS)

    Samareh, Jamshid A.

    1999-01-01

    This paper presents a novel parameterization approach for complex shapes suitable for a multidisciplinary design optimization application. The approach consists of two basic concepts: (1) parameterizing the shape perturbations rather than the geometry itself and (2) performing the shape deformation by means of the soft objects animation algorithms used in computer graphics. Because the formulation presented in this paper is independent of grid topology, we can treat computational fluid dynamics and finite element grids in a similar manner. The proposed approach is simple, compact, and efficient. Also, the analytical sensitivity derivatives are easily computed for use in a gradient-based optimization. This algorithm is suitable for low-fidelity (e.g., linear aerodynamics and equivalent laminated plate structures) and high-fidelity analysis tools (e.g., nonlinear computational fluid dynamics and detailed finite element modeling). This paper contains the implementation details of parameterizing for planform, twist, dihedral, thickness, and camber. The results are presented for a multidisciplinary design optimization application consisting of nonlinear computational fluid dynamics, detailed computational structural mechanics, performance, and a simple propulsion module.

  4. Ultrasensitive dual phosphorylation dephosphorylation cycle kinetics exhibits canonical competition behavior

    NASA Astrophysics Data System (ADS)

    Huang, Qingdao; Qian, Hong

    2009-09-01

    We establish a mathematical model for a cellular biochemical signaling module in terms of a planar differential equation system. The signaling process is carried out by two phosphorylation-dephosphorylation reaction steps that share common kinase and phosphatase with saturated enzyme kinetics. The pair of equations is particularly simple in the present mathematical formulation, but they are singular. A complete mathematical analysis is developed based on an elementary perturbation theory. The dynamics exhibits the canonical competition behavior in addition to bistability. Although widely understood in ecological context, we are not aware of a full range of biochemical competition in a simple signaling network. The competition dynamics has broad implications to cellular processes such as cell differentiation and cancer immunoediting. The concepts of homogeneous and heterogeneous multisite phosphorylation are introduced and their corresponding dynamics are compared: there is no bistability in a heterogeneous dual phosphorylation system. A stochastic interpretation is also provided that further gives intuitive understanding of the bistable behavior inside the cells.

  5. Multidisciplinary Aerodynamic-Structural Shape Optimization Using Deformation (MASSOUD)

    NASA Technical Reports Server (NTRS)

    Samareh, Jamshid A.

    2000-01-01

    This paper presents a multidisciplinary shape parameterization approach. The approach consists of two basic concepts: (1) parameterizing the shape perturbations rather than the geometry itself and (2) performing the shape deformation by means of the soft object animation algorithms used in computer graphics. Because the formulation presented in this paper is independent of grid topology, we can treat computational fluid dynamics and finite element grids in the same manner. The proposed approach is simple, compact, and efficient. Also, the analytical sensitivity derivatives are easily computed for use in a gradient-based optimization. This algorithm is suitable for low-fidelity (e.g., linear aerodynamics and equivalent laminate plate structures) and high-fidelity (e.g., nonlinear computational fluid dynamics and detailed finite element modeling) analysis tools. This paper contains the implementation details of parameterizing for planform, twist, dihedral, thickness, camber, and free-form surface. Results are presented for a multidisciplinary application consisting of nonlinear computational fluid dynamics, detailed computational structural mechanics, and a simple performance module.

  6. Multidisciplinary Aerodynamic-Structural Shape Optimization Using Deformation (MASSOUD)

    NASA Technical Reports Server (NTRS)

    Samareh, Jamshid A.

    2000-01-01

    This paper presents a multidisciplinary shape parameterization approach. The approach consists of two basic concepts: (1) parameterizing the shape perturbations rather than the geometry itself and (2) performing the shape deformation by means of the soft object animation algorithms used in computer graphics. Because the formulation presented in this paper is independent of grid topology, we can treat computational fluid dynamics and finite element grids in a similar manner. The proposed approach is simple, compact, and efficient. Also, the analytical sensitivity derivatives are easily computed for use in a gradient-based optimization. This algorithm is suitable for low-fidelity (e.g., linear aerodynamics and equivalent laminated plate structures) and high-fidelity (e.g., nonlinear computational fluid dynamics and detailed finite element modeling analysis tools. This paper contains the implementation details of parameterizing for planform, twist, dihedral, thickness, camber, and free-form surface. Results are presented for a multidisciplinary design optimization application consisting of nonlinear computational fluid dynamics, detailed computational structural mechanics, and a simple performance module.

  7. Applications of Cosmological Perturbation Theory

    NASA Astrophysics Data System (ADS)

    Christopherson, Adam J.

    2011-06-01

    Cosmological perturbation theory is crucial for our understanding of the universe. The linear theory has been well understood for some time, however developing and applying the theory beyond linear order is currently at the forefront of research in theoretical cosmology. This thesis studies the applications of perturbation theory to cosmology and, specifically, to the early universe. Starting with some background material introducing the well-tested 'standard model' of cosmology, we move on to develop the formalism for perturbation theory up to second order giving evolution equations for all types of scalar, vector and tensor perturbations, both in gauge dependent and gauge invariant form. We then move on to the main result of the thesis, showing that, at second order in perturbation theory, vorticity is sourced by a coupling term quadratic in energy density and entropy perturbations. This source term implies a qualitative difference to linear order. Thus, while at linear order vorticity decays with the expansion of the universe, the same is not true at higher orders. This will have important implications on future measurements of the polarisation of the Cosmic Microwave Background, and could give rise to the generation of a primordial seed magnetic field. Having derived this qualitative result, we then estimate the scale dependence and magnitude of the vorticity power spectrum, finding, for simple power law inputs a small, blue spectrum. The final part of this thesis concerns higher order perturbation theory, deriving, for the first time, the metric tensor, gauge transformation rules and governing equations for fully general third order perturbations. We close with a discussion of natural extensions to this work and other possible ideas for off-shooting projects in this continually growing field.

  8. Chaos and noise in a truncated Toda potential

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

    Habib, S.; Kandrup, H.E.; Mahon, M.E.

    Results are reported from a numerical investigation of orbits in a truncated Toda potential that is perturbed by weak friction and noise. Aside from the perturbations displaying a simple scaling in the amplitude of the friction and noise, it is found that even very weak friction and noise can induce an extrinsic diffusion through cantori on a time scale that is much shorter than that associated with intrinsic diffusion in the unperturbed system. The results have applications in galactic dynamics and in the formation of a beam halo in charged particle beams. {copyright} {ital 1996 The American Physical Society.}

  9. Asymptotic stability and instability of large-scale systems. [using vector Liapunov functions

    NASA Technical Reports Server (NTRS)

    Grujic, L. T.; Siljak, D. D.

    1973-01-01

    The purpose of this paper is to develop new methods for constructing vector Lyapunov functions and broaden the application of Lyapunov's theory to stability analysis of large-scale dynamic systems. The application, so far limited by the assumption that the large-scale systems are composed of exponentially stable subsystems, is extended via the general concept of comparison functions to systems which can be decomposed into asymptotically stable subsystems. Asymptotic stability of the composite system is tested by a simple algebraic criterion. By redefining interconnection functions among the subsystems according to interconnection matrices, the same mathematical machinery can be used to determine connective asymptotic stability of large-scale systems under arbitrary structural perturbations.

  10. Perturbative studies of toroidal momentum transport in KSTAR H-mode and the effect of ion temperature perturbation

    NASA Astrophysics Data System (ADS)

    Yang, S. M.; Na, Yong-Su; Na, D. H.; Park, J.-K.; Shi, Y. J.; Ko, W. H.; Lee, S. G.; Hahm, T. S.

    2018-06-01

    Perturbative experiments have been carried out using tangential neutral beam injection (NBI) and non-resonant magnetic perturbation (NRMP) to analyze the momentum transport properties in KSTAR H-modes. Diffusive and non-diffusive terms of momentum transport are evaluated from the transient analysis. Although the operating conditions and methodologies applied in the two cases are similar, the momentum transport properties obtained show clear differences. The estimated momentum diffusivity and pinch obtained in the NBI modulation experiments is larger than that in the NRMP modulation experiments. We found that this discrepancy could be a result of uncertainties in the assumption for the analysis. By introducing time varying momentum transport coefficients depending on the temperature gradient, the linearized equation shows that if the temperature perturbation exists, the evolution of toroidal rotation perturbation could be faster than the transport rate of mean quantity, since the evolution of toroidal rotation perturbation is related to , a momentum diffusivity from perturbative analysis. This could explain the estimated higher momentum diffusivity using time independent transport coefficients in NBI experiments with higher ion temperature perturbation compared to that in NRMP modulation experiments. The differences in the momentum transport coefficient with NRMP and NBI are much reduced by considering time varying momentum transport coefficients in the time dependent transport simulation.

  11. Canonical Representations of the Simple Map

    NASA Astrophysics Data System (ADS)

    Kerwin, Olivia; Punjabi, Alkesh; Ali, Halima; Boozer, Allen

    2007-11-01

    The simple map is the simplest map that has the topology of a divertor tokamak. The simple map has three canonical representations: (i) toroidal flux and poloidal angle (ψ,θ) as canonical coordinates, (ii) the physical variables (R,Z) or (X,Y) as canonical coordinates, and (iii) the action-angle (J,ζ) or magnetic variables (ψ,θ) as canonical coordinates. We give the derivation of the simple map in the (X,Y) representation. The simple map in this representation has been studied extensively (Ref. 1 and references therein). We calculate the magnetic coordinates for the simple map, construct the simple map in magnetic coordinates, and calculate generic topological effects of magnetic perturbations in divertor tokamaks using the map. We also construct the simple map in (ψ,θ) representation. Preliminary results of these studies will be presented. This work is supported by US DOE OFES DE-FG02-01ER54624 and DE-FG02-04ER54793. [1] A. Punjabi, H. Ali, T. Evans, and A. Boozer, Phys Lett A 364 140--145 (2007).

  12. Ultrasonic monitoring of droplets' evaporation: Application to human whole blood.

    PubMed

    Laux, D; Ferrandis, J Y; Brutin, D

    2016-09-01

    During a colloidal droplet evaporation, a sol-gel transition can be observed and is described by the desiccation time τD and the gelation time τG. These characteristic times, which can be linked to viscoelastic properties of the droplet and to its composition, are classically rated by analysis of mass droplet evolution during evaporation. Even if monitoring mass evolution versus time seems straightforward, this approach is very sensitive to environmental conditions (vibrations, air flow…) as mass has to be evaluated very accurately using ultra-sensitive weighing scales. In this study we investigated the potentialities of ultrasonic shear reflectometry to assess τD and τG in a simple and reliable manner. In order to validate this approach, our study has focused on blood droplets evaporation on which a great deal of work has recently been published. Desiccation and gelation times measured with shear ultrasonic reflectometry have been perfectly correlated to values obtained from mass versus time analysis. This ultrasonic method which is not very sensitive to environmental perturbations is therefore very interesting to monitor the drying of blood droplets in a simple manner and is more generally suitable for complex fluid droplets evaporation investigation. Copyright © 2016 Elsevier B.V. All rights reserved.

  13. Approximate analytical solution for induction heating of solid cylinders

    DOE PAGES

    Jankowski, Todd Andrew; Pawley, Norma Helen; Gonzales, Lindsey Michal; ...

    2015-10-20

    An approximate solution to the mathematical model for induction heating of a solid cylinder in a cylindrical induction coil is presented here. The coupled multiphysics model includes equations describing the electromagnetic field in the heated object, a heat transfer simulation to determine temperature of the heated object, and an AC circuit simulation of the induction heating power supply. A multiple-scale perturbation method is used to solve the multiphysics model. The approximate analytical solution yields simple closed-form expressions for the electromagnetic field and heat generation rate in the solid cylinder, for the equivalent impedance of the associated tank circuit, and formore » the frequency response of a variable frequency power supply driving the tank circuit. The solution developed here is validated by comparing predicted power supply frequency to both experimental measurements and calculated values from finite element analysis for heating of graphite cylinders in an induction furnace. The simple expressions from the analytical solution clearly show the functional dependence of the power supply frequency on the material properties of the load and the geometrical characteristics of the furnace installation. In conclusion, the expressions developed here provide physical insight into observations made during load signature analysis of induction heating.« less

  14. Singularity perturbed zero dynamics of nonlinear systems

    NASA Technical Reports Server (NTRS)

    Isidori, A.; Sastry, S. S.; Kokotovic, P. V.; Byrnes, C. I.

    1992-01-01

    Stability properties of zero dynamics are among the crucial input-output properties of both linear and nonlinear systems. Unstable, or 'nonminimum phase', zero dynamics are a major obstacle to input-output linearization and high-gain designs. An analysis of the effects of regular perturbations in system equations on zero dynamics shows that whenever a perturbation decreases the system's relative degree, it manifests itself as a singular perturbation of zero dynamics. Conditions are given under which the zero dynamics evolve in two timescales characteristic of a standard singular perturbation form that allows a separate analysis of slow and fast parts of the zero dynamics.

  15. 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.

  16. Singular perturbation analysis of AOTV-related trajectory optimization problems

    NASA Technical Reports Server (NTRS)

    Calise, Anthony J.; Bae, Gyoung H.

    1990-01-01

    The problem of real time guidance and optimal control of Aeroassisted Orbit Transfer Vehicles (AOTV's) was addressed using singular perturbation theory as an underlying method of analysis. Trajectories were optimized with the objective of minimum energy expenditure in the atmospheric phase of the maneuver. Two major problem areas were addressed: optimal reentry, and synergetic plane change with aeroglide. For the reentry problem, several reduced order models were analyzed with the objective of optimal changes in heading with minimum energy loss. It was demonstrated that a further model order reduction to a single state model is possible through the application of singular perturbation theory. The optimal solution for the reduced problem defines an optimal altitude profile dependent on the current energy level of the vehicle. A separate boundary layer analysis is used to account for altitude and flight path angle dynamics, and to obtain lift and bank angle control solutions. By considering alternative approximations to solve the boundary layer problem, three guidance laws were derived, each having an analytic feedback form. The guidance laws were evaluated using a Maneuvering Reentry Research Vehicle model and all three laws were found to be near optimal. For the problem of synergetic plane change with aeroglide, a difficult terminal boundary layer control problem arises which to date is found to be analytically intractable. Thus a predictive/corrective solution was developed to satisfy the terminal constraints on altitude and flight path angle. A composite guidance solution was obtained by combining the optimal reentry solution with the predictive/corrective guidance method. Numerical comparisons with the corresponding optimal trajectory solutions show that the resulting performance is very close to optimal. An attempt was made to obtain numerically optimized trajectories for the case where heating rate is constrained. A first order state variable inequality constraint was imposed on the full order AOTV point mass equations of motion, using a simple aerodynamic heating rate model.

  17. Lensing in the geodesic light-cone coordinates and its (exact) illustration to an off-center observer in Lemaȋtre-Tolman-Bondi models

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

    Fanizza, G.; Nugier, F., E-mail: giuseppe.fanizza@ba.infn.it, E-mail: fabienjean.nugier@unibo.it

    We present in this paper a new application of the geodesic light-cone (GLC) gauge for weak lensing calculations. Using interesting properties of this gauge, we derive an exact expression of the amplification matrix—involving convergence, magnification and shear—and of the deformation matrix—involving the optical scalars. These expressions are simple and non-perturbative as long as no caustics are created on the past light-cone and are, by construction, free from the thin lens approximation. We apply these general expressions on the example of an Lemaȋtre-Tolman-Bondi (LTB) model with an off-center observer and obtain explicit forms for the lensing quantities as a direct consequencemore » of the non-perturbative transformation between GLC and LTB coordinates. We show their evolution in redshift after a numerical integration, for underdense and overdense LTB models, and interpret their respective variations in the simple non-curvature case.« less

  18. Sensitivity studies and a simple ozone perturbation experiment with a truncated two-dimensional model of the stratosphere

    NASA Technical Reports Server (NTRS)

    Stordal, Frode; Garcia, Rolando R.

    1987-01-01

    The 1-1/2-D model of Holton (1986), which is actually a highly truncated two-dimensional model, describes latitudinal variations of tracer mixing ratios in terms of their projections onto second-order Legendre polynomials. The present study extends the work of Holton by including tracers with photochemical production in the stratosphere (O3 and NOy). It also includes latitudinal variations in the photochemical sources and sinks, improving slightly the calculated global mean profiles for the long-lived tracers studied by Holton and improving substantially the latitudinal behavior of ozone. Sensitivity tests of the dynamical parameters in the model are performed, showing that the response of the model to changes in vertical residual meridional winds and horizontal diffusion coefficients is similar to that of a full two-dimensional model. A simple ozone perturbation experiment shows the model's ability to reproduce large-scale latitudinal variations in total ozone column depletions as well as ozone changes in the chemically controlled upper stratosphere.

  19. Robust vortex lines, vortex rings, and hopfions in three-dimensional Bose-Einstein condensates

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

    Bisset, R. N.; Wang, Wenlong; Ticknor, Christopher

    Performing a systematic Bogoliubov–de Gennes spectral analysis, we illustrate that stationary vortex lines, vortex rings, and more exotic states, such as hopfions, are robust in three-dimensional atomic Bose-Einstein condensates, for large parameter intervals. Importantly, we find that the hopfion can be stabilized in a simple parabolic trap, without the need for trap rotation or inhomogeneous interactions. We supplement our spectral analysis by studying the dynamics of such stationary states; we find them to be robust against significant perturbations of the initial state. In the unstable regimes, we not only identify the unstable mode, such as a quadrupolar or hexapolar mode,more » but we also observe the corresponding instability dynamics. Moreover, deep in the Thomas-Fermi regime, we investigate the particlelike behavior of vortex rings and hopfions.« less

  20. Robust vortex lines, vortex rings, and hopfions in three-dimensional Bose-Einstein condensates

    DOE PAGES

    Bisset, R. N.; Wang, Wenlong; Ticknor, Christopher; ...

    2015-12-07

    Performing a systematic Bogoliubov–de Gennes spectral analysis, we illustrate that stationary vortex lines, vortex rings, and more exotic states, such as hopfions, are robust in three-dimensional atomic Bose-Einstein condensates, for large parameter intervals. Importantly, we find that the hopfion can be stabilized in a simple parabolic trap, without the need for trap rotation or inhomogeneous interactions. We supplement our spectral analysis by studying the dynamics of such stationary states; we find them to be robust against significant perturbations of the initial state. In the unstable regimes, we not only identify the unstable mode, such as a quadrupolar or hexapolar mode,more » but we also observe the corresponding instability dynamics. Moreover, deep in the Thomas-Fermi regime, we investigate the particlelike behavior of vortex rings and hopfions.« less

  1. Black hole binary inspiral: Analysis of the plunge

    NASA Astrophysics Data System (ADS)

    Price, Richard H.; Nampalliwar, Sourabh; Khanna, Gaurav

    2016-02-01

    Binary black hole coalescence has its peak of gravitational-wave generation during the "plunge," the transition from quasicircular early motion to late quasinormal ringing (QNR). Although advances in numerical relativity have provided plunge waveforms, there is still no intuitive or phenomenological understanding of plunge comparable to that of the early and late stages. Here we make progress in developing such understanding by relying on insights of the linear mathematics of the particle perturbation model for the extreme mass limit. Our analysis, based on the Fourier-domain Green function, and a simple initial model, point to the crucial role played by the kinematics near the "light ring" (the circular photon orbit) in determining the plunge radiation and the excitation of QNR. That insight is then shown to successfully explain results obtained for particle motion in a Schwarzschild background.

  2. Quasi-steady-state analysis of coupled flashing ratchets.

    PubMed

    Levien, Ethan; Bressloff, Paul C

    2015-10-01

    We perform a quasi-steady-state (QSS) reduction of a flashing ratchet to obtain a Brownian particle in an effective potential. The resulting system is analytically tractable and yet preserves essential dynamical features of the full model. We first use the QSS reduction to derive an explicit expression for the velocity of a simple two-state flashing ratchet. In particular, we determine the relationship between perturbations from detailed balance, which are encoded in the transitions rates of the flashing ratchet, and a tilted-periodic potential. We then perform a QSS analysis of a pair of elastically coupled flashing ratchets, which reduces to a Brownian particle moving in a two-dimensional vector field. We suggest that the fixed points of this vector field accurately approximate the metastable spatial locations of the coupled ratchets, which are, in general, impossible to identify from the full system.

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

    NASA Technical Reports Server (NTRS)

    Murphy, J. P.

    1972-01-01

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

  4. Differential Dynamic Engagement within 24 SH3 Domain: Peptide Complexes Revealed by Co-Linear Chemical Shift Perturbation Analysis

    PubMed Central

    Stollar, Elliott J.; Lin, Hong; Davidson, Alan R.; Forman-Kay, Julie D.

    2012-01-01

    There is increasing evidence for the functional importance of multiple dynamically populated states within single proteins. However, peptide binding by protein-protein interaction domains, such as the SH3 domain, has generally been considered to involve the full engagement of peptide to the binding surface with minimal dynamics and simple methods to determine dynamics at the binding surface for multiple related complexes have not been described. We have used NMR spectroscopy combined with isothermal titration calorimetry to comprehensively examine the extent of engagement to the yeast Abp1p SH3 domain for 24 different peptides. Over one quarter of the domain residues display co-linear chemical shift perturbation (CCSP) behavior, in which the position of a given chemical shift in a complex is co-linear with the same chemical shift in the other complexes, providing evidence that each complex exists as a unique dynamic rapidly inter-converting ensemble. The extent the specificity determining sub-surface of AbpSH3 is engaged as judged by CCSP analysis correlates with structural and thermodynamic measurements as well as with functional data, revealing the basis for significant structural and functional diversity amongst the related complexes. Thus, CCSP analysis can distinguish peptide complexes that may appear identical in terms of general structure and percent peptide occupancy but have significant local binding differences across the interface, affecting their ability to transmit conformational change across the domain and resulting in functional differences. PMID:23251481

  5. Insights into Volcanic Tremor: A Linear Stability Analysis of Waves Propagating Along Fluid-Filled Cracks

    NASA Astrophysics Data System (ADS)

    Lipovsky, B.; Dunham, E. M.

    2012-12-01

    Crack waves are guided waves along fluid-filled cracks that propagate with phase velocity less than the sound wave speed. Chouet (JGR, 1986) and Ferrazzini and Aki (JGR, 1977) have shown that such waves could explain volcanic tremor in terms of the resonant modes of a finite length magma-filled crack. Based on an idealized lumped-parameter model, Julian (JGR, 1994) further proposed that the steady flow of a viscous magma in a volcanic conduit is unstable to perturbations, leading to self-excited oscillations of the conduit walls and radiation of seismic waves. Our objective is to evaluate the possibility of self-excited oscillations within a rigorous, continuum framework. Our specific focus has been on basaltic fissure eruptions. In a typical basaltic fissure system, the magnitudes of the wave restoring forces, fluid compressibility and wall elasticity, are highly depth dependent. Because of the elevated fluid compressibility from gas exsolution at shallow depths, fluid pressure perturbations in this regime propagate as acoustic waves with effectively rigid conduit walls. Below the exsolution depth, the conduit walls are more compliant relative to the magma compressibility and perturbations propagate as dispersive crack waves. Viscous magma flow through such a fissure will evolve to a fully developed state characterized by a parabolic velocity profile in several to tens of seconds. This time scale is greater than harmonic tremor periods, typically 0.1 to 1 second. A rigorous treatment of the wave response to pressure perturbations therefore requires a general analysis of conduit flow that is not in a fully developed state. We present a linearized analysis of the coupled fluid and elastic response to general flow perturbations. We assume that deformation of the wall is linear elastic. As our focus is on wavelengths greatly exceeding the crack width, fluid flow is described by a quasi-one dimensional, or width-averaged, model. We account for conservation of magma mass and momentum including compressibility and viscous drag. Our analysis further assumes small perturbations about a steady background flow, a linearized isothermal equation of state, and a nominally constant width channel. We confirm Julian's results that sufficiently rapid flow through a deformable-walled conduit is unstable to perturbations in the form of crack waves. Instability occurs when drag reduction from opening the conduit exceeds the increase in drag from increased fluid velocity. Crack waves are most unstable at long wavelengths, where the conduit becomes more compliant. In the long wavelength limit, we find a simple expression for the critical flow speed beyond which crack waves are unstable: u = c / 2, where c is the crack wave phase velocity. The instability condition is remarkably independent of viscosity. This result more rigorously confirms the conclusion of Dunham and Ogden (2012, J. App. Mech.), who found the same instability criterion under the limiting assumption of fully developed flow. In a typical basaltic system the occurrence of this instability requires flow speeds exceeding ~50 m/s at depths where magma is primarily liquid melt with little exsolved gas. At these depths, flow speeds of this order are unlikely to occur. We conclude that harmonic tremor due to self-excited oscillations is unlikely to occur in nature.

  6. The accommodation index measures the perturbation associated with insertions and deletions in coiled‐coils: Application to understand signaling in histidine kinases

    PubMed Central

    Schmidt, Nathan W.; Grigoryan, Gevorg

    2017-01-01

    Abstract Coiled‐coils are essential components of many protein complexes. First discovered in structural proteins such as keratins, they have since been found to figure largely in the assembly and dynamics required for diverse functions, including membrane fusion, signal transduction and motors. Coiled‐coils have a characteristic repeating seven‐residue geometric and sequence motif, which is sometimes interrupted by the insertion of one or more residues. Such insertions are often highly conserved and critical to interdomain communication in signaling proteins such as bacterial histidine kinases. Here we develop the “accommodation index” as a parameter that allows automatic detection and classification of insertions based on the three dimensional structure of a protein. This method allows precise identification of the type of insertion and the “accommodation length” over which the insertion is structurally accommodated. A simple theory is presented that predicts the structural perturbations of 1, 3, 4 residue insertions as a function of the length over which the insertion is accommodated. Analysis of experimental structures is in good agreement with theory, and shows that short accommodation lengths give rise to greater perturbation of helix packing angles, changes in local helical phase, and increased structural asymmetry relative to long accommodation lengths. Cytoplasmic domains of histidine kinases in different signaling states display large changes in their accommodation lengths, which can now be seen to underlie diverse structural transitions including symmetry/asymmetry and local variations in helical phase that accompany signal transduction. PMID:27977891

  7. 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.

  8. 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.

  9. A simple non-perturbing cell migration assay insensitive to proliferation effects

    PubMed Central

    Glenn, Honor L.; Messner, Jacob; Meldrum, Deirdre R.

    2016-01-01

    Migration is a fundamental cellular behavior that plays an indispensable role in development and homeostasis, but can also contribute to pathology such as cancer metastasis. Due to its relevance to many aspects of human health, the ability to accurately measure cell migration is of broad interest, and numerous approaches have been developed. One of the most commonly employed approaches, because of its simplicity and throughput, is the exclusion zone assay in which cells are allowed to migrate into an initially cell-free region. A major drawback of this assay is that it relies on simply counting cells in the exclusion zone and therefore cannot distinguish the effects of proliferation from migration. We report here a simple modification to the exclusion zone migration assay that exclusively measures cell migration and is not affected by proliferation. This approach makes use of a lineage-tracing vital stain that is retained through cell generations and effectively reads out migration relative to the original, parental cell population. This modification is simple, robust, non-perturbing, and inexpensive. We validate the method in a panel of cell lines under conditions that inhibit or promote migration and demonstrate its use in normal and cancer cell lines as well as primary cells. PMID:27535324

  10. 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…

  11. A dynamical stabilizer in the climate system: a mechanism suggested by a simple model

    NASA Astrophysics Data System (ADS)

    Bates, J. R.

    1999-05-01

    A simple zonally averaged hemispheric model of the climate system is constructed, based on energy equations for two ocean basins separated at 30° latitude with the surface fluxes calculated explicitly. A combination of empirical input and theoretical calculation is used to determine an annual mean equilibrium climate for the model and to study its stability with respect to small perturbations. The insolation, the mean albedos and the equilibrium temperatures for the two model zones are prescribed from observation. The principal agent of interaction between the zones is the vertically integrated poleward transport of atmospheric angular momentum across their common boundary. This is parameterized using an empirical formula derived from a multiyear atmospheric data set. The surface winds are derived from the angular momentum transport assuming the atmosphere to be in a state of dynamic balance on the climatic timescales of interest. A further assumption that the air sea temperature difference and low level relative humidity remain fixed at their mean observed values then allows the surface fluxes of latent and sensible heat to be calculated. Results from a radiative model, which show a positive lower tropospheric water vapour/infrared radiative feedback on SST perturbations in both zones, are used to calculate the net upward infrared radiative fluxes at the surface. In the model's equilibrium climate, the principal processes balancing the solar radiation absorbed at the surface are evaporation in the tropical zone and net infrared radiation in the extratropical zone. The stability of small perturbations about the equilibrium is studied using a linearized form of the ocean energy equations. Ice-albedo and cloud feedbacks are omitted and attention is focussed on the competing effects of the water vapour/infrared radiative feedback and the turbulent surface flux and oceanic heat transport feedbacks associated with the angular momentum cycle. The perturbation equations involve inter-zone coupling and have coefficients dependent on the values of the equilibrium fluxes and the sensitivity of the angular momentum transport. Analytical solutions for the perturbations are obtained. These provide criteria for the stability of the equilibrium climate. If the evaporative feedback on SST perturbations is omitted, the equilibrium climate is unstable due to the influence of the water vapour/infrared radiative feedback, which dominates over the effects of the sensible heat and ocean heat transport feedbacks. The inclusion of evaporation gives a negative feedback which is of sufficient strength to stabilize the system. The stabilizing mechanism involves wind and humidity factors in the evaporative fluxes that are of comparable magnitude. Both factors involve the angular momentum transport. In including angular momentum and calculating the surface fluxes explicitly, the model presented here differs from the many simple climate models based on the Budyko Sellers formulation. In that formulation, an atmospheric energy balance equation is used to eliminate surface fluxes in favour of top-of-the-atmosphere radiative fluxes and meridional atmospheric energy transports. In the resulting models, infrared radiation appears as a stabilizing influence on SST perturbations and the dynamical stabilizing mechanism found here cannot be identified.

  12. How does non-linear dynamics affect the baryon acoustic oscillation?

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

    Sugiyama, Naonori S.; Spergel, David N., E-mail: nao.s.sugiyama@gmail.com, E-mail: dns@astro.princeton.edu

    2014-02-01

    We study the non-linear behavior of the baryon acoustic oscillation in the power spectrum and the correlation function by decomposing the dark matter perturbations into the short- and long-wavelength modes. The evolution of the dark matter fluctuations can be described as a global coordinate transformation caused by the long-wavelength displacement vector acting on short-wavelength matter perturbation undergoing non-linear growth. Using this feature, we investigate the well known cancellation of the high-k solutions in the standard perturbation theory. While the standard perturbation theory naturally satisfies the cancellation of the high-k solutions, some of the recently proposed improved perturbation theories do notmore » guarantee the cancellation. We show that this cancellation clarifies the success of the standard perturbation theory at the 2-loop order in describing the amplitude of the non-linear power spectrum even at high-k regions. We propose an extension of the standard 2-loop level perturbation theory model of the non-linear power spectrum that more accurately models the non-linear evolution of the baryon acoustic oscillation than the standard perturbation theory. The model consists of simple and intuitive parts: the non-linear evolution of the smoothed power spectrum without the baryon acoustic oscillations and the non-linear evolution of the baryon acoustic oscillations due to the large-scale velocity of dark matter and due to the gravitational attraction between dark matter particles. Our extended model predicts the smoothing parameter of the baryon acoustic oscillation peak at z = 0.35 as ∼ 7.7Mpc/h and describes the small non-linear shift in the peak position due to the galaxy random motions.« less

  13. Stability of barotropic vortex strip on a rotating sphere

    PubMed Central

    Sohn, Sung-Ik; Kim, Sun-Chul

    2018-01-01

    We study the stability of a barotropic vortex strip on a rotating sphere, as a simple model of jet streams. The flow is approximated by a piecewise-continuous vorticity distribution by zonal bands of uniform vorticity. The linear stability analysis shows that the vortex strip becomes stable as the strip widens or the rotation speed increases. When the vorticity constants in the upper and the lower regions of the vortex strip have the same positive value, the inner flow region of the vortex strip becomes the most unstable. However, when the upper and the lower vorticity constants in the polar regions have different signs, a complex pattern of instability is found, depending on the wavenumber of perturbations, and interestingly, a boundary far away from the vortex strip can be unstable. We also compute the nonlinear evolution of the vortex strip on the rotating sphere and compare with the linear stability analysis. When the width of the vortex strip is small, we observe a good agreement in the growth rate of perturbation at an early time, and the eigenvector corresponding to the unstable eigenvalue coincides with the most unstable part of the flow. We demonstrate that a large structure of rolling-up vortex cores appears in the vortex strip after a long-time evolution. Furthermore, the geophysical relevance of the model to jet streams of Jupiter, Saturn and Earth is examined. PMID:29507524

  14. Stability of barotropic vortex strip on a rotating sphere.

    PubMed

    Sohn, Sung-Ik; Sakajo, Takashi; Kim, Sun-Chul

    2018-02-01

    We study the stability of a barotropic vortex strip on a rotating sphere, as a simple model of jet streams. The flow is approximated by a piecewise-continuous vorticity distribution by zonal bands of uniform vorticity. The linear stability analysis shows that the vortex strip becomes stable as the strip widens or the rotation speed increases. When the vorticity constants in the upper and the lower regions of the vortex strip have the same positive value, the inner flow region of the vortex strip becomes the most unstable. However, when the upper and the lower vorticity constants in the polar regions have different signs, a complex pattern of instability is found, depending on the wavenumber of perturbations, and interestingly, a boundary far away from the vortex strip can be unstable. We also compute the nonlinear evolution of the vortex strip on the rotating sphere and compare with the linear stability analysis. When the width of the vortex strip is small, we observe a good agreement in the growth rate of perturbation at an early time, and the eigenvector corresponding to the unstable eigenvalue coincides with the most unstable part of the flow. We demonstrate that a large structure of rolling-up vortex cores appears in the vortex strip after a long-time evolution. Furthermore, the geophysical relevance of the model to jet streams of Jupiter, Saturn and Earth is examined.

  15. Integration of the Rotation of an Earth-like Body as a Perturbed Spherical Rotor

    NASA Astrophysics Data System (ADS)

    Ferrer, Sebastián; Lara, Martin

    2010-05-01

    For rigid bodies close to a sphere, we propose an analytical solution that is free from elliptic integrals and functions, and can be fundamental for application to perturbed problems. After reordering the Hamiltonian as a perturbed spherical rotor, the Lie-series solution is generated up to an arbitrary order. Using the inertia parameters of different solar system bodies, the comparison of the approximate series solution with the exact analytical one shows that the precision reached with relatively low orders is at the same level of the observational accuracy for the Earth and Mars. Thus, for instance, the periodic errors of the mathematical solution are confined to the microarcsecond level with a simple second-order truncation for the Earth. On the contrary, higher orders are required for the mathematical solution to reach a precision at the expected level of accuracy of proposed new theories for the rotational dynamics of the Moon.

  16. A higher-order Skyrme model

    NASA Astrophysics Data System (ADS)

    Gudnason, Sven Bjarke; Nitta, Muneto

    2017-09-01

    We propose a higher-order Skyrme model with derivative terms of eighth, tenth and twelfth order. Our construction yields simple and easy-to-interpret higher-order Lagrangians. We first show that a Skyrmion with higher-order terms proposed by Marleau has an instability in the form of a baby-Skyrmion string, while the static energies of our construction are positive definite, implying stability against time-independent perturbations. However, we also find that the Hamiltonians of our construction possess two kinds of dynamical instabilities, which may indicate the instability with respect to time-dependent perturbations. Different from the well-known Ostrogradsky instability, the instabilities that we find are intrinsically of nonlinear nature and also due to the fact that even powers of the inverse metric gives a ghost-like higher-order kinetic-like term. The vacuum state is, however, stable. Finally, we show that at sufficiently low energies, our Hamiltonians in the simplest cases, are stable against time-dependent perturbations.

  17. 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).

  18. Examining the Crossover from the Hadronic to Partonic Phase in QCD

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

    Xu Mingmei; Yu Meiling; Liu Lianshou

    2008-03-07

    A mechanism, consistent with color confinement, for the transition between perturbative and physical vacua during the gradual crossover from the hadronic to partonic phase is proposed. The essence of this mechanism is the appearance and growing up of a kind of grape-shape perturbative vacuum inside the physical one. A percolation model based on simple dynamics for parton delocalization is constructed to exhibit this mechanism. The crossover from hadronic matter to sQGP (strongly coupled quark-gluon plasma) as well as the transition from sQGP to weakly coupled quark-gluon plasma with increasing temperature is successfully described by using this model.

  19. Perturbation propagation in random and evolved Boolean networks

    NASA Astrophysics Data System (ADS)

    Fretter, Christoph; Szejka, Agnes; Drossel, Barbara

    2009-03-01

    In this paper, we investigate the propagation of perturbations in Boolean networks by evaluating the Derrida plot and its modifications. We show that even small random Boolean networks agree well with the predictions of the annealed approximation, but nonrandom networks show a very different behaviour. We focus on networks that were evolved for high dynamical robustness. The most important conclusion is that the simple distinction between frozen, critical and chaotic networks is no longer useful, since such evolved networks can display the properties of all three types of networks. Furthermore, we evaluate a simplified empirical network and show how its specific state space properties are reflected in the modified Derrida plots.

  20. The influence of a high pressure gradient on unsteady velocity perturbations in the case of a turbulent supersonic flow

    NASA Technical Reports Server (NTRS)

    Dussauge, J. P.; Debieve, J. F.

    1980-01-01

    The amplification or reduction of unsteady velocity perturbations under the influence of strong flow acceleration or deceleration was studied. Supersonic flows with large velocity, pressure gradients, and the conditions in which the velocity fluctuations depend on the action of the average gradients of pressure and velocity rather than turbulence, are described. Results are analyzed statistically and interpreted as a return to laminar process. It is shown that this return to laminar implies negative values in the turbulence production terms for kinetic energy. A simple geometrical representation of the Reynolds stress production is given.

  1. The Helium Atom and Isoelectronic Ions in Two Dimensions

    ERIC Educational Resources Information Center

    Patil, S. H.

    2008-01-01

    The energy levels of the helium atom and isoelectronic ions in two dimensions are considered. The difficulties encountered in the analytical evaluation of the perturbative and variational expressions for the ground state, promote an interesting factorization of the inter-electronic interaction, leading to simple expressions for the energy. This…

  2. Constraining higher derivative supergravity with scattering amplitudes

    DOE PAGES

    Wang, Yifan; Yin, Xi

    2015-08-31

    We study supersymmetry constraints on higher derivative deformations of type IIB supergravity by consideration of superamplitudes. Thus, combining constraints of on-shell supervertices and basic results from string perturbation theory, we give a simple argument for the non-renormalization theorem of Green and Sethi, and some of its generalizations.

  3. Self-organized criticality in forest-landscape evolution

    Treesearch

    J.C. Sprott; Janine Bolliger; David J. Mladenoff

    2002-01-01

    A simple cellular automaton replicates the fractal pattern of a natural forest landscape and predicts its evolution. Spatial distributions and temporal fluctuations in global quantities show power-law spectra, implying scale-invariance, characteristic of self-organized criticality. The evolution toward the SOC state and the robustness of that state to perturbations...

  4. Planetary period modulations of Saturn's magnetotail current sheet: A simple illustrative mathematical model

    NASA Astrophysics Data System (ADS)

    Cowley, S. W. H.; Provan, G.; Hunt, G. J.; Jackman, C. M.

    2017-01-01

    We mathematically model the modulation effects on Saturn's equatorial magnetotail and magnetodisk current sheet produced by the combined magnetic field perturbations of the northern and southern planetary period oscillation (PPO) systems, specifically north-south displacements associated with the radial perturbation field and thickness modulations associated with the colatitudinal perturbation field. Since the phasing of the two PPO systems is taken to be related to the radial field perturbations, while the relative phasing of the colatitudinal perturbations is opposite for the two systems, the north-south oscillations reinforce when the two PPO systems are in phase, while the thickening-thinning effects reinforce when they are in antiphase. For intermediate relative phases we show that when the northern PPO system leads the southern the sheet is thicker when moving south to north than when moving north to south, while when the northern PPO system lags the southern the sheet is thicker when moving north to south than when moving south to north, thus leading to sawtooth profiles in the radial field for near-equatorial observers, of opposite senses in the two cases. Given empirically determined modulation amplitudes, the maximum sawtooth effect is found to be small when one system dominates the other, but becomes clear when the amplitude of one system lies within a factor of 2 of the other.

  5. Formation of free round jets with long laminar regions at large Reynolds numbers

    NASA Astrophysics Data System (ADS)

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

    2018-04-01

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

  6. Structures, Energetics, and IR Spectra of Monohydrated Inorganic Acids: Ab initio and DFT Study.

    PubMed

    Kołaski, Maciej; Zakharenko, Aleksey A; Karthikeyan, S; Kim, Kwang S

    2011-10-11

    We carried out extensive calculations of diverse inorganic acids interacting with a single water molecule, through a detailed analysis of many possible conformations. The optimized structures were obtained by using density functional theory (DFT) and the second order Møller-Plesset perturbation theory (MP2). For the most stable conformers, we calculated the interaction energies at the complete basis set (CBS) limit using coupled cluster theory with single, double, and perturbative triple excitations [CCSD(T)]. The -OH stretching harmonic and anharmonic frequencies are provided as fingerprints of characteristic conformers. The zero-point energy (ZPE) uncorrected/corrected (ΔEe/ΔE0) interaction energies and the enthalpies/free energies (ΔHr/ΔGr at room temperature and 1 bar) are reported. Various comparisons are made between many diverse inorganic acids (HmXOn where X = B/N/P/Cl/Br/I, m = 1-3, and n = 0-4) as well as other simple inorganic acids. In many cases, we find that the dispersion-driven van der Waals interactions between X in inorganic acid molecules and O in water molecules as well as the X(+)···O(-) electrostatic interactions are important.

  7. 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

  8. 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.

  9. Vesicle electrohydrodynamics.

    PubMed

    Schwalbe, Jonathan T; Vlahovska, Petia M; Miksis, Michael J

    2011-04-01

    A small amplitude perturbation analysis is developed to describe the effect of a uniform electric field on the dynamics of a lipid bilayer vesicle in a simple shear flow. All media are treated as leaky dielectrics and fluid motion is described by the Stokes equations. The instantaneous vesicle shape is obtained by balancing electric, hydrodynamic, bending, and tension stresses exerted on the membrane. We find that in the absence of ambient shear flow, it is possible that an applied stepwise uniform dc electric field could cause the vesicle shape to evolve from oblate to prolate over time if the encapsulated fluid is less conducting than the suspending fluid. For a vesicle in ambient shear flow, the electric field damps the tumbling motion, leading to a stable tank-treading state.

  10. EXCITATION OF A BURIED MAGMATIC PIPE: A SEISMIC SOURCE MODEL FOR VOLCANIC TREMOR.

    USGS Publications Warehouse

    Chouet, Bernard

    1985-01-01

    A model of volcanic tremor is presented in which the modes of vibration of a volcanic pipe are excited by the motion of the fluid within the pipe in response to a short-term perturbation in pressure. The model shows the relative importance of the various parts constituting this composite source in the radiated elastic field at near and intermediate distances. The paper starts with the presentation of the elastic field radiated by the source, and proceeds with an analysis of the energy balance between hydraulic and elastic motions. Next, the hydraulic excitation of the source is addressed and, finally, the ground response to this excitation is analyzed in the simple case of a pipe buried in a homogeneous half space.

  11. Self-regulating galaxy formation. Part 1: HII disk and Lyman alpha pressure

    NASA Technical Reports Server (NTRS)

    Cox, D. P.

    1983-01-01

    Assuming a simple but physically based prototype for behavior of interstellar material during formation of a disk galaxy, coupled with the lowest order description of infall, a scenario is developed for self-regulated disk galaxy formation. Radiation pressure, particularly that of Lyman depha (from fluorescence conversion Lyman continuum), is an essential component, maintaining an inflated disk and stopping infall when only a small fraction of the overall perturbation has joined the disk. The resulting galaxies consist of a two dimensional family whose typical scales and surface density are expressable in terms of fundamental constants. The model leads naturally to galaxies with a rich circumgalactic environment and flat rotation curves (but is weak in its analysis of the subsequent evolution of halo material).

  12. Performance Analysis of Blind Subspace-Based Signature Estimation Algorithms for DS-CDMA Systems with Unknown Correlated Noise

    NASA Astrophysics Data System (ADS)

    Zarifi, Keyvan; Gershman, Alex B.

    2006-12-01

    We analyze the performance of two popular blind subspace-based signature waveform estimation techniques proposed by Wang and Poor and Buzzi and Poor for direct-sequence code division multiple-access (DS-CDMA) systems with unknown correlated noise. Using the first-order perturbation theory, analytical expressions for the mean-square error (MSE) of these algorithms are derived. We also obtain simple high SNR approximations of the MSE expressions which explicitly clarify how the performance of these techniques depends on the environmental parameters and how it is related to that of the conventional techniques that are based on the standard white noise assumption. Numerical examples further verify the consistency of the obtained analytical results with simulation results.

  13. Simulation and analysis of chemical release in the ionosphere

    NASA Astrophysics Data System (ADS)

    Gao, Jing-Fan; Guo, Li-Xin; Xu, Zheng-Wen; Zhao, Hai-Sheng; Feng, Jie

    2018-05-01

    Ionospheric inhomogeneous plasma produced by single point chemical release has simple space-time structure, and cannot impact radio wave frequencies higher than Very High Frequency (VHF) band. In order to produce more complicated ionospheric plasma perturbation structure and trigger instabilities phenomena, multiple-point chemical release scheme is presented in this paper. The effects of chemical release on low latitude ionospheric plasma are estimated by linear instability growth rate theory that high growth rate represents high irregularities, ionospheric scintillation occurrence probability and high scintillation intension in scintillation duration. The amplitude scintillations and the phase scintillations of 150 MHz, 400 MHz, and 1000 MHz are calculated based on the theory of multiple phase screen (MPS), when they propagate through the disturbed area.

  14. Winnerless competition principle and prediction of the transient dynamics in a Lotka-Volterra model

    NASA Astrophysics Data System (ADS)

    Afraimovich, Valentin; Tristan, Irma; Huerta, Ramon; Rabinovich, Mikhail I.

    2008-12-01

    Predicting the evolution of multispecies ecological systems is an intriguing problem. A sufficiently complex model with the necessary predicting power requires solutions that are structurally stable. Small variations of the system parameters should not qualitatively perturb its solutions. When one is interested in just asymptotic results of evolution (as time goes to infinity), then the problem has a straightforward mathematical image involving simple attractors (fixed points or limit cycles) of a dynamical system. However, for an accurate prediction of evolution, the analysis of transient solutions is critical. In this paper, in the framework of the traditional Lotka-Volterra model (generalized in some sense), we show that the transient solution representing multispecies sequential competition can be reproducible and predictable with high probability.

  15. Winnerless competition principle and prediction of the transient dynamics in a Lotka-Volterra model.

    PubMed

    Afraimovich, Valentin; Tristan, Irma; Huerta, Ramon; Rabinovich, Mikhail I

    2008-12-01

    Predicting the evolution of multispecies ecological systems is an intriguing problem. A sufficiently complex model with the necessary predicting power requires solutions that are structurally stable. Small variations of the system parameters should not qualitatively perturb its solutions. When one is interested in just asymptotic results of evolution (as time goes to infinity), then the problem has a straightforward mathematical image involving simple attractors (fixed points or limit cycles) of a dynamical system. However, for an accurate prediction of evolution, the analysis of transient solutions is critical. In this paper, in the framework of the traditional Lotka-Volterra model (generalized in some sense), we show that the transient solution representing multispecies sequential competition can be reproducible and predictable with high probability.

  16. An analysis of the extension of a ZnO piezoelectric semiconductor nanofiber under an axial force

    NASA Astrophysics Data System (ADS)

    Zhang, Chunli; Wang, Xiaoyuan; Chen, Weiqiu; Yang, Jiashi

    2017-02-01

    This paper presents a theoretical analysis on the axial extension of an n-type ZnO piezoelectric semiconductor nanofiber under an axial force. The phenomenological theory of piezoelectric semiconductors consisting of Newton’s second law of motion, the charge equation of electrostatics and the conservation of charge was used. The equations were linearized for small axial force and hence small electron concentration perturbation, and were reduced to one-dimensional equations for thin fibers. Simple and analytical expressions for the electromechanical fields and electron concentration in the fiber were obtained. The fields are either totally or partially described by hyperbolic functions relatively large near the ends of the fiber and change rapidly there. The behavior of the fields is sensitive to the initial electron concentration and the applied axial force. For higher initial electron concentrations the fields are larger near the ends and change more rapidly there.

  17. Nuclear quadrupole resonance lineshape analysis for different motional models: Stochastic Liouville approach

    NASA Astrophysics Data System (ADS)

    Kruk, D.; Earle, K. A.; Mielczarek, A.; Kubica, A.; Milewska, A.; Moscicki, J.

    2011-12-01

    A general theory of lineshapes in nuclear quadrupole resonance (NQR), based on the stochastic Liouville equation, is presented. The description is valid for arbitrary motional conditions (particularly beyond the valid range of perturbation approaches) and interaction strengths. It can be applied to the computation of NQR spectra for any spin quantum number and for any applied magnetic field. The treatment presented here is an adaptation of the "Swedish slow motion theory," [T. Nilsson and J. Kowalewski, J. Magn. Reson. 146, 345 (2000), 10.1006/jmre.2000.2125] originally formulated for paramagnetic systems, to NQR spectral analysis. The description is formulated for simple (Brownian) diffusion, free diffusion, and jump diffusion models. The two latter models account for molecular cooperativity effects in dense systems (such as liquids of high viscosity or molecular glasses). The sensitivity of NQR slow motion spectra to the mechanism of the motional processes modulating the nuclear quadrupole interaction is discussed.

  18. Nonlinear ideal magnetohydrodynamics instabilities

    NASA Astrophysics Data System (ADS)

    Pfirsch, D.; Sudan, R. N.

    1993-07-01

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

  19. 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

  20. Systems Perturbation Analysis of a Large-Scale Signal Transduction Model Reveals Potentially Influential Candidates for Cancer Therapeutics

    PubMed Central

    Puniya, Bhanwar Lal; Allen, Laura; Hochfelder, Colleen; Majumder, Mahbubul; Helikar, Tomáš

    2016-01-01

    Dysregulation in signal transduction pathways can lead to a variety of complex disorders, including cancer. Computational approaches such as network analysis are important tools to understand system dynamics as well as to identify critical components that could be further explored as therapeutic targets. Here, we performed perturbation analysis of a large-scale signal transduction model in extracellular environments that stimulate cell death, growth, motility, and quiescence. Each of the model’s components was perturbed under both loss-of-function and gain-of-function mutations. Using 1,300 simulations under both types of perturbations across various extracellular conditions, we identified the most and least influential components based on the magnitude of their influence on the rest of the system. Based on the premise that the most influential components might serve as better drug targets, we characterized them for biological functions, housekeeping genes, essential genes, and druggable proteins. The most influential components under all environmental conditions were enriched with several biological processes. The inositol pathway was found as most influential under inactivating perturbations, whereas the kinase and small lung cancer pathways were identified as the most influential under activating perturbations. The most influential components were enriched with essential genes and druggable proteins. Moreover, known cancer drug targets were also classified in influential components based on the affected components in the network. Additionally, the systemic perturbation analysis of the model revealed a network motif of most influential components which affect each other. Furthermore, our analysis predicted novel combinations of cancer drug targets with various effects on other most influential components. We found that the combinatorial perturbation consisting of PI3K inactivation and overactivation of IP3R1 can lead to increased activity levels of apoptosis-related components and tumor-suppressor genes, suggesting that this combinatorial perturbation may lead to a better target for decreasing cell proliferation and inducing apoptosis. Finally, our approach shows a potential to identify and prioritize therapeutic targets through systemic perturbation analysis of large-scale computational models of signal transduction. Although some components of the presented computational results have been validated against independent gene expression data sets, more laboratory experiments are warranted to more comprehensively validate the presented results. PMID:26904540

  1. High-Content Analysis of CRISPR-Cas9 Gene-Edited Human Embryonic Stem Cells.

    PubMed

    Carlson-Stevermer, Jared; Goedland, Madelyn; Steyer, Benjamin; Movaghar, Arezoo; Lou, Meng; Kohlenberg, Lucille; Prestil, Ryan; Saha, Krishanu

    2016-01-12

    CRISPR-Cas9 gene editing of human cells and tissues holds much promise to advance medicine and biology, but standard editing methods require weeks to months of reagent preparation and selection where much or all of the initial edited samples are destroyed during analysis. ArrayEdit, a simple approach utilizing surface-modified multiwell plates containing one-pot transcribed single-guide RNAs, separates thousands of edited cell populations for automated, live, high-content imaging and analysis. The approach lowers the time and cost of gene editing and produces edited human embryonic stem cells at high efficiencies. Edited genes can be expressed in both pluripotent stem cells and differentiated cells. This preclinical platform adds important capabilities to observe editing and selection in situ within complex structures generated by human cells, ultimately enabling optical and other molecular perturbations in the editing workflow that could refine the specificity and versatility of gene editing. Copyright © 2016 The Authors. Published by Elsevier Inc. All rights reserved.

  2. Stability analysis of ultrasound thick-shell contrast agents

    PubMed Central

    Lu, Xiaozhen; Chahine, Georges L.; Hsiao, Chao-Tsung

    2012-01-01

    The stability of thick shell encapsulated bubbles is studied analytically. 3-D small perturbations are introduced to the spherical oscillations of a contrast agent bubble in response to a sinusoidal acoustic field with different amplitudes of excitation. The equations of the perturbation amplitudes are derived using asymptotic expansions and linear stability analysis is then applied to the resulting differential equations. The stability of the encapsulated microbubbles to nonspherical small perturbations is examined by solving an eigenvalue problem. The approach then identifies the fastest growing perturbations which could lead to the breakup of the encapsulated microbubble or contrast agent. PMID:22280568

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

    PubMed Central

    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. PMID:29326496

  4. A Saturnian cam current system driven by asymmetric thermospheric heating

    NASA Astrophysics Data System (ADS)

    Smith, C. G. A.

    2011-02-01

    We show that asymmetric heating of Saturn's thermosphere can drive a current system consistent with the magnetospheric ‘cam’ proposed by Espinosa, Southwood & Dougherty. A geometrically simple heating distribution is imposed on the Northern hemisphere of a simplified three-dimensional global circulation model of Saturn's thermosphere. Currents driven by the resulting winds are calculated using a globally averaged ionosphere model. Using a simple assumption about how divergences in these currents close by flowing along dipolar field lines between the Northern and Southern hemispheres, we estimate the magnetic field perturbations in the equatorial plane and show that they are broadly consistent with the proposed cam fields, showing a roughly uniform field implying radial and azimuthal components in quadrature. We also identify a small longitudinal phase drift in the cam current with radial distance as a characteristic of a thermosphere-driven current system. However, at present our model does not produce magnetic field perturbations of the required magnitude, falling short by a factor of ˜100, a discrepancy that may be a consequence of an incomplete model of the ionospheric conductance.

  5. Solving regularly and singularly perturbed reaction-diffusion equations in three space dimensions

    NASA Astrophysics Data System (ADS)

    Moore, Peter K.

    2007-06-01

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

  6. Classical and quantum stability in putative landscapes

    DOE PAGES

    Dine, Michael

    2017-01-18

    Landscape analyses often assume the existence of large numbers of fields, N, with all of the many couplings among these fields (subject to constraints such as local supersymmetry) selected independently and randomly from simple (say Gaussian) distributions. We point out that unitarity and perturbativity place significant constraints on behavior of couplings with N, eliminating otherwise puzzling results. In would-be flux compactifications of string theory, we point out that in order that there be large numbers of light fields, the compactification radii must scale as a positive power of N; scaling of couplings with N may also be necessary for perturbativity.more » We show that in some simple string theory settings with large numbers of fields, for fixed R and string coupling, one can bound certain sums of squares of couplings by order one numbers. This may argue for strong correlations, possibly calling into question the assumption of uncorrelated distributions. Finally, we consider implications of these considerations for classical and quantum stability of states without supersymmetry, with low energy supersymmetry arising from tuning of parameters, and with dynamical breaking of supersymmetry.« less

  7. On the Origin of Chaos in the Asteroid Belt

    NASA Technical Reports Server (NTRS)

    Murray, N.; Holman, M.; Potter, M.

    1998-01-01

    We consider the effect of gravitational perturbations from Jupiter on the dynamics of asteroids, when Jupiter is itself perturbed by Saturn. The presence of Saturn introduces a number of additional frequencies into Jupiters orbit. These frequencies in turn produce chaos in narrow regions on either side of the chaotic zones associated with the mean motion resonances between the asteroids and Jupiter. The resonant arguments of these three-body resonances contain the longitudes of Jupiter and the asteroid together with either the secular frequency 9-6, or the longitude of Saturn. Resonances involving the longitude of Saturn are analogs of the Laplace resonance in the Jovian satellite system. We show that many three-body resonances involving the longitude of Saturn are chaotic. We give simple expressions for the width of the chaotic region and the associated Lyapunov time. In some cases the chaos can produce a diffusive growth in the 4 eccentricity of the asteroid that leads to ejection of the asteroid on times shorter than the age of the solar system. We give simple estimates for the diffusion time. Finally, we present the results of numerical integrations testing the theory.

  8. Le Châtelier reciprocal relations and the mechanical analog

    NASA Astrophysics Data System (ADS)

    Gilmore, Robert

    1983-08-01

    Le Châtelier's principle is discussed carefully in terms of two sets of simple thermodynamic examples. The principle is then formulated quantitatively for general thermodynamic systems. The formulation is in terms of a perturbation-response matrix, the Le Châtelier matrix [L]. Le Châtelier's principle is contained in the diagonal elements of this matrix, all of which exceed one. These matrix elements describe the response of a system to a perturbation of either its extensive or intensive variables. These response ratios are inverses of each other. The Le Châtelier matrix is symmetric, so that a new set of thermodynamic reciprocal relations is derived. This quantitative formulation is illustrated by a single simple example which includes the original examples and shows the reciprocities among them. The assumptions underlying this new quantitative formulation of Le Châtelier's principle are general and applicable to a wide variety of nonthermodynamic systems. Le Châtelier's principle is formulated quantitatively for mechanical systems in static equilibrium, and mechanical examples of this formulation are given.

  9. Classical and quantum stability in putative landscapes

    NASA Astrophysics Data System (ADS)

    Dine, Michael

    2017-01-01

    Landscape analyses often assume the existence of large numbers of fields, N , with all of the many couplings among these fields (subject to constraints such as local supersymmetry) selected independently and randomly from simple (say Gaussian) distributions. We point out that unitarity and perturbativity place significant constraints on behavior of couplings with N , eliminating otherwise puzzling results. In would-be flux compactifications of string theory, we point out that in order that there be large numbers of light fields, the compactification radii must scale as a positive power of N ; scaling of couplings with N may also be necessary for perturbativity. We show that in some simple string theory settings with large numbers of fields, for fixed R and string coupling, one can bound certain sums of squares of couplings by order one numbers. This may argue for strong correlations, possibly calling into question the assumption of uncorrelated distributions. We consider implications of these considerations for classical and quantum stability of states without supersymmetry, with low energy supersymmetry arising from tuning of parameters, and with dynamical breaking of supersymmetry.

  10. Orbits in elementary, power-law galaxy bars - 1. Occurrence and role of single loops

    NASA Astrophysics Data System (ADS)

    Struck, Curtis

    2018-05-01

    Orbits in galaxy bars are generally complex, but simple closed loop orbits play an important role in our conceptual understanding of bars. Such orbits are found in some well-studied potentials, provide a simple model of the bar in themselves, and may generate complex orbit families. The precessing, power ellipse (p-ellipse) orbit approximation provides accurate analytic orbit fits in symmetric galaxy potentials. It remains useful for finding and fitting simple loop orbits in the frame of a rotating bar with bar-like and symmetric power-law potentials. Second-order perturbation theory yields two or fewer simple loop solutions in these potentials. Numerical integrations in the parameter space neighbourhood of perturbation solutions reveal zero or one actual loops in a range of such potentials with rising rotation curves. These loops are embedded in a small parameter region of similar, but librating orbits, which have a subharmonic frequency superimposed on the basic loop. These loops and their librating companions support annular bars. Solid bars can be produced in more complex potentials, as shown by an example with power-law indices varying with radius. The power-law potentials can be viewed as the elementary constituents of more complex potentials. Numerical integrations also reveal interesting classes of orbits with multiple loops. In two-dimensional, self-gravitating bars, with power-law potentials, single-loop orbits are very rare. This result suggests that gas bars or oval distortions are unlikely to be long-lived, and that complex orbits or three-dimensional structure must support self-gravitating stellar bars.

  11. Adiabatic perturbation theory for atoms and molecules in the low-frequency regime

    NASA Astrophysics Data System (ADS)

    Martiskainen, Hanna; Moiseyev, Nimrod

    2017-12-01

    There is an increasing interest in the photoinduced dynamics in the low frequency, ω, regime. The multiphoton absorptions by molecules in strong laser fields depend on the polarization of the laser and on the molecular structure. The unique properties of the interaction of atoms and molecules with lasers in the low-frequency regime imply new concepts and directions in strong-field light-matter interactions. Here we represent a perturbational approach for the calculations of the quasi-energy spectrum in the low-frequency regime, which avoids the construction of the Floquet operator with extremely large number of Floquet channels. The zero-order Hamiltonian in our perturbational approach is the adiabatic Hamiltonian where the atoms/molecules are exposed to a dc electric field rather than to ac-field. This is in the spirit of the first step in the Corkum three-step model. The second-order perturbation correction terms are obtained when i ℏ ω ∂/∂ τ serves as a perturbation and τ is a dimensionless variable. The second-order adiabatic perturbation scheme is found to be an excellent approach for calculating the ac-field Floquet solutions in our test case studies of a simple one-dimensional time-periodic model Hamiltonian. It is straightforward to implement the perturbation approach presented here for calculating atomic and molecular energy shifts (positions) due to the interaction with low-frequency ac-fields using high-level electronic structure methods. This is enabled since standard quantum chemistry packages allow the calculations of atomic and molecular energy shifts due to the interaction with dc-fields. In addition to the shift of the energy positions, the energy widths (inverse lifetimes) can be obtained at the same level of theory. These energy shifts are functions of the laser parameters (low frequency, intensity, and polarization).

  12. Experimental study of complex mixed-mode oscillations generated in a Bonhoeffer-van der Pol oscillator under weak periodic perturbation

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

    Shimizu, Kuniyasu, E-mail: kuniyasu.shimizu@it-chiba.ac.jp; Sekikawa, Munehisa; Inaba, Naohiko

    2015-02-15

    Bifurcations of complex mixed-mode oscillations denoted as mixed-mode oscillation-incrementing bifurcations (MMOIBs) have frequently been observed in chemical experiments. In a previous study [K. Shimizu et al., Physica D 241, 1518 (2012)], we discovered an extremely simple dynamical circuit that exhibits MMOIBs. Our model was represented by a slow/fast Bonhoeffer-van der Pol circuit under weak periodic perturbation near a subcritical Andronov-Hopf bifurcation point. In this study, we experimentally and numerically verify that our dynamical circuit captures the essence of the underlying mechanism causing MMOIBs, and we observe MMOIBs and chaos with distinctive waveforms in real circuit experiments.

  13. Optimal Detection of a Localized Perturbation in Random Networks of Integrate-and-Fire Neurons.

    PubMed

    Bernardi, Davide; Lindner, Benjamin

    2017-06-30

    Experimental and theoretical studies suggest that cortical networks are chaotic and coding relies on averages over large populations. However, there is evidence that rats can respond to the short stimulation of a single cortical cell, a theoretically unexplained fact. We study effects of single-cell stimulation on a large recurrent network of integrate-and-fire neurons and propose a simple way to detect the perturbation. Detection rates obtained from simulations and analytical estimates are similar to experimental response rates if the readout is slightly biased towards specific neurons. Near-optimal detection is attained for a broad range of intermediate values of the mean coupling between neurons.

  14. Optimal Detection of a Localized Perturbation in Random Networks of Integrate-and-Fire Neurons

    NASA Astrophysics Data System (ADS)

    Bernardi, Davide; Lindner, Benjamin

    2017-06-01

    Experimental and theoretical studies suggest that cortical networks are chaotic and coding relies on averages over large populations. However, there is evidence that rats can respond to the short stimulation of a single cortical cell, a theoretically unexplained fact. We study effects of single-cell stimulation on a large recurrent network of integrate-and-fire neurons and propose a simple way to detect the perturbation. Detection rates obtained from simulations and analytical estimates are similar to experimental response rates if the readout is slightly biased towards specific neurons. Near-optimal detection is attained for a broad range of intermediate values of the mean coupling between neurons.

  15. Vibroacoustic response of structures and perturbation Reynolds stress near structure-turbulence interface

    NASA Technical Reports Server (NTRS)

    Maekawa, S.; Lin, Y. K.

    1977-01-01

    The interaction between a turbulent flow and certain types of structures which respond to its excitation is investigated. One-dimensional models were used to develop the basic ideas applied to a second model resembling the fuselage construction of an aircraft. In the two-dimensional case a simple membrane, with a small random variation in the membrane tension, was used. A decaying turbulence was constructed by superposing infinitely many components, each of which is convected as a frozen pattern at a different velocity. Structure-turbulence interaction results are presented in terms of the spectral densities of the structural response and the perturbation Reynolds stress in the fluid at the vicinity of the interface.

  16. Notes on wall crossing and instanton in compactified gauge theory with matter

    NASA Astrophysics Data System (ADS)

    Chen, Heng-Yu; Petunin, Kirill

    2010-10-01

    We study the quantum effects on the Coulomb branch of mathcal{N} = 2 SU(2) super-symmetric Yang-Mills with fundamental matters compactified on {mathbb{R}^3} × {S^1} , and extract the explicit perturbative and leading non-perturbative corrections to the moduli space metric predicted from the recent work of Gaiotto, Moore and Neitzke on wall-crossing [1]. We verify the predicted metric by computing the leading weak coupling instanton contribution to the four fermion correlation using standard field theory techniques, and demonstrate perfect agreement. We also demonstrate how previously known three dimensional quantities can be recovered in appropriate small radius limit, and provide a simple geometric picture from brane construction.

  17. Numerical optimization of perturbative coils for tokamaks

    NASA Astrophysics Data System (ADS)

    Lazerson, Samuel; Park, Jong-Kyu; Logan, Nikolas; Boozer, Allen; NSTX-U Research Team

    2014-10-01

    Numerical optimization of coils which apply three dimensional (3D) perturbative fields to tokamaks is presented. The application of perturbative 3D magnetic fields in tokamaks is now commonplace for control of error fields, resistive wall modes, resonant field drive, and neoclassical toroidal viscosity (NTV) torques. The design of such systems has focused on control of toroidal mode number, with coil shapes based on simple window-pane designs. In this work, a numerical optimization suite based on the STELLOPT 3D equilibrium optimization code is presented. The new code, IPECOPT, replaces the VMEC equilibrium code with the IPEC perturbed equilibrium code, and targets NTV torque by coupling to the PENT code. Fixed boundary optimizations of the 3D fields for the NSTX-U experiment are underway. Initial results suggest NTV torques can be driven by normal field spectrums which are not pitch-resonant with the magnetic field lines. Work has focused on driving core torque with n = 1 and edge torques with n = 3 fields. Optimizations of the coil currents for the planned NSTX-U NCC coils highlight the code's free boundary capability. This manuscript has been authored by Princeton University under Contract Number DE-AC02-09CH11466 with the U.S. Department of Energy.

  18. Applying the new HIT results to tokamak and solar plasmas

    NASA Astrophysics Data System (ADS)

    Jarboe, Thomas; Sutherland, Derek; Hossack, Aaron; Nelson, Brian; Morgan, Kyle; Chris, Hansen; Benedett, Thomas; Everson, Chris; Penna, James

    2016-10-01

    Understanding sustainment of stable equilibria with helicity injection in HIT-SI has led to a simple picture of several tokamak features. Perturbations cause a viscous-like force on the current that flattens the λ profile, which sustains and stabilizes the equilibrium. An explanation of the mechanism is based on two properties of stable, ideal, two-fluid, magnetized plasma. First, the electron fluid is frozen to magnetic fields and, therefore, current flow is also magnetic field flow. Second, for a stable equilibrium the structure perpendicular to the flux surface resists deformation. Thus toroidal current is from electrons frozen in nested, rotating resilient flux surfaces. Only symmetric flux surfaces allow free differential current flow. Perturbations cause interference of the flux surfaces. Thus, perturbations cause forces that oppose differential electron rotation and forced differential flow produces a symmetrizing force against perturbations and instability. This mechanism can explain the level of field error that spoils tokamak performance and the rate of poloidal flux loss in argon-induced disruptions in DIII-D. This new understanding has led to an explanation of the source of the solar magnetic fields and the power source for the chromosphere, solar wind and corona. Please place in spheromak and FRC section with other HIT posters.

  19. Supernatural inflation: inflation from supersymmetry with no (very) small parameters

    NASA Astrophysics Data System (ADS)

    Randall, Lisa; SoljačiĆ, Marin; Guth, Alan H.

    1996-02-01

    Most models of inflation have small parameters, either to guarantee sufficient inflation or the correct magnitude of the density perturbations. In this paper we show that, in supersymmetric theories with weak-scale supersymmetry breaking, one can construct viable inflationary models in which the requisite parameters appear naturally in the form of the ratio of mass scales that are already present in the theory. Successful inflationary models can be constructed from the flat-direction fields of a renormalizable supersymmetric potential, and such models can be realized even in the context of a simple GUT extension of the MSSM. We evade naive ``naturalness'' arguments by allowing for more than one field to be relevant to inflation, as in ``hybrid inflation'' models, and we argue that this is the most natural possibility if inflation fields are to be associated with flat direction fields of a supersymmetric theory. Such models predict a very low Hubble constant during inflation, of order 103-104 GeV, a scalar density perturbation index n which is very close to or greater than unity, and negligible tensor perturbations. In addition, these models lead to a large spike in the density perturbation spectrum at short wavelengths.

  20. Projector Augmented-Wave formulation of response to strain and electric field perturbation within the density-functional perturbation theory

    NASA Astrophysics Data System (ADS)

    Martin, Alexandre; Torrent, Marc; Caracas, Razvan

    2015-03-01

    A formulation of the response of a system to strain and electric field perturbations in the pseudopotential-based density functional perturbation theory (DFPT) has been proposed by D.R Hamman and co-workers. It uses an elegant formalism based on the expression of DFT total energy in reduced coordinates, the key quantity being the metric tensor and its first and second derivatives. We propose to extend this formulation to the Projector Augmented-Wave approach (PAW). In this context, we express the full elastic tensor including the clamped-atom tensor, the atomic-relaxation contributions (internal stresses) and the response to electric field change (piezoelectric tensor and effective charges). With this we are able to compute the elastic tensor for all materials (metals and insulators) within a fully analytical formulation. The comparison with finite differences calculations on simple systems shows an excellent agreement. This formalism has been implemented in the plane-wave based DFT ABINIT code. We apply it to the computation of elastic properties and seismic-wave velocities of iron with impurity elements. By analogy with the materials contained in meteorites, tested impurities are light elements (H, O, C, S, Si).

  1. Quantum geometry of resurgent perturbative/nonperturbative relations

    NASA Astrophysics Data System (ADS)

    Basar, Gökçe; Dunne, Gerald V.; Ünsal, Mithat

    2017-05-01

    For a wide variety of quantum potentials, including the textbook `instanton' examples of the periodic cosine and symmetric double-well potentials, the perturbative data coming from fluctuations about the vacuum saddle encodes all non-perturbative data in all higher non-perturbative sectors. Here we unify these examples in geometric terms, arguing that the all-orders quantum action determines the all-orders quantum dual action for quantum spectral problems associated with a classical genus one elliptic curve. Furthermore, for a special class of genus one potentials this relation is particularly simple: this class includes the cubic oscillator, symmetric double-well, symmetric degenerate triple-well, and periodic cosine potential. These are related to the Chebyshev potentials, which are in turn related to certain \\mathcal{N} = 2 supersymmetric quantum field theories, to mirror maps for hypersurfaces in projective spaces, and also to topological c = 3 Landau-Ginzburg models and `special geometry'. These systems inherit a natural modular structure corresponding to Ramanujan's theory of elliptic functions in alternative bases, which is especially important for the quantization. Insights from supersymmetric quantum field theory suggest similar structures for more complicated potentials, corresponding to higher genus. Our approach is very elementary, using basic classical geometry combined with all-orders WKB.

  2. Secular dynamics of hierarchical multiple systems composed of nested binaries, with an arbitrary number of bodies and arbitrary hierarchical structure - II. External perturbations: flybys and supernovae

    NASA Astrophysics Data System (ADS)

    Hamers, Adrian S.

    2018-05-01

    We extend the formalism of a previous paper to include the effects of flybys and instantaneous perturbations such as supernovae on the long-term secular evolution of hierarchical multiple systems with an arbitrary number of bodies and hierarchy, provided that the system is composed of nested binary orbits. To model secular encounters, we expand the Hamiltonian in terms of the ratio of the separation of the perturber with respect to the barycentre of the multiple system, to the separation of the widest orbit. Subsequently, we integrate over the perturber orbit numerically or analytically. We verify our method for secular encounters and illustrate it with an example. Furthermore, we describe a method to compute instantaneous orbital changes to multiple systems, such as asymmetric supernovae and impulsive encounters. The secular code, with implementation of the extensions described in this paper, is publicly available within AMUSE, and we provide a number of simple example scripts to illustrate its usage for secular and impulsive encounters and asymmetric supernovae. The extensions presented in this paper are a next step towards efficiently modelling the evolution of complex multiple systems embedded in star clusters.

  3. From star-disc encounters to numerical solutions for a subset of the restricted three-body problem

    NASA Astrophysics Data System (ADS)

    Breslau, Andreas; Vincke, Kirsten; Pfalzner, Susanne

    2017-03-01

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

  4. Effect of neoclassical poloidal viscosity and resonant magnetic perturbation on the response of the m/n=1/1 magnetic island in LHD

    NASA Astrophysics Data System (ADS)

    Botsz, Huang; Satake, Shinsuke; Kanno, Ryutaro; Narushima, Yoshiro; Sakakibara, Satoru; Ohdachi, Satoshi

    2014-10-01

    In the LHD experiments in which m/n = 1/1 resonant magnetic perturbation (RMP) amplitude is ramped up, it is observed that the perturbed field is initially shielded, and when the amplitude exceeds a threshold value, the field penetrates into the plasma and m/n/ = 1/1 magnetic island appears. It is also found that the threshold amplitude depends on the magnetic field configuration of LHD, that is, on the magnetic axis position. It is expected that the poloidal force balance between the electromagnetic force and the drug force from poloidal rotation determines the threshold of island formation. Since neoclassical poloidal viscosity (NPV) in LHD strongly depends on the magnetic axis position, we investigate the relationship between NPV and the threshold amplitude of m/n = 1/1 RMP to penetrate by using drift-kinetic simulation code FORTEC-3D. ExB poloidal rotation determined from the ambipolar radial flux condition is taken into account in the evaluation of NPV. We mainly focus on the situation that the external magnetic perturbation is compensated by the plasma response and therefore the effect of RMP on the total NPV is shielded. However, by using a simple model to express the penetrated magnetic perturbation, we will also study the dependence of NPV on the RMP amplitude.

  5. 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.

  6. Comprehensive analysis of the simplest curvaton model

    NASA Astrophysics Data System (ADS)

    Byrnes, Christian T.; Cortês, Marina; Liddle, Andrew R.

    2014-07-01

    We carry out a comprehensive analysis of the simplest curvaton model, which is based on two noninteracting massive fields. Our analysis encompasses cases where the inflaton and curvaton both contribute to observable perturbations, and where the curvaton itself drives a second period of inflation. We consider both power spectrum and non-Gaussianity observables, and focus on presenting constraints in model parameter space. The fully curvaton-dominated regime is in some tension with observational data, while an admixture of inflaton-generated perturbations improves the fit. The inflating curvaton regime mimics the predictions of Nflation. Some parts of parameter space permitted by power spectrum data are excluded by non-Gaussianity constraints. The recent BICEP2 results [P. A. R. Ade et al. (BICEP2 Collaboration), Phys. Rev. Lett. 112, 241101 (2014)], if confirmed as of predominantly primordial origin, require that the inflaton perturbations provide a significant fraction of the total perturbation, ruling out the usual curvaton scenario in which the inflaton perturbations are negligible, though not the admixture regime where both inflaton and curvaton contribute to the spectrum.

  7. 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.

  8. Perturbations of the Richardson number field by gravity waves

    NASA Technical Reports Server (NTRS)

    Wurtele, M. G.; Sharman, R. D.

    1985-01-01

    An analytic solution is presented for a stratified fluid of arbitrary constant Richardson number. By computer aided analysis the perturbation fields, including that of the Richardson number can be calculated. The results of the linear analytic model were compared with nonlinear simulations, leading to the following conclusions: (1) the perturbations in the Richardson number field, when small, are produced primarily by the perturbations of the shear; (2) perturbations of in the Richardson number field, even when small, are not symmetric, the increase being significantly larger than the decrease (the linear analytic solution and the nonlinear simulations both confirm this result); (3) as the perturbations grow, this asymmetry increases, but more so in the nonlinear simulations than in the linear analysis; (4) for large perturbations of the shear flow, the static stability, as represented by N2, is the dominating mechanism, becoming zero or negative, and producing convective overturning; and (5) the convectional measure of linearity in lee wave theory, NH/U, is no longer the critical parameter (it is suggested that (H/u sub 0) (du sub 0/dz) takes on this role in a shearing flow).

  9. Stability analysis of ultrasound thick-shell contrast agents.

    PubMed

    Lu, Xiaozhen; Chahine, Georges L; Hsiao, Chao-Tsung

    2012-01-01

    The stability of thick shell encapsulated bubbles is studied analytically. 3-D small perturbations are introduced to the spherical oscillations of a contrast agent bubble in response to a sinusoidal acoustic field with different amplitudes of excitation. The equations of the perturbation amplitudes are derived using asymptotic expansions and linear stability analysis is then applied to the resulting differential equations. The stability of the encapsulated microbubbles to nonspherical small perturbations is examined by solving an eigenvalue problem. The approach then identifies the fastest growing perturbations which could lead to the breakup of the encapsulated microbubble or contrast agent. © 2012 Acoustical Society of America.

  10. Trajectory optimization and guidance law development for national aerospace plane applications

    NASA Technical Reports Server (NTRS)

    Calise, A. J.; Flandro, G. A.; Corban, J. E.

    1988-01-01

    The work completed to date is comprised of the following: a simple vehicle model representative of the aerospace plane concept in the hypersonic flight regime, fuel-optimal climb profiles for the unconstrained and dynamic pressure constrained cases generated using a reduced order dynamic model, an analytic switching condition for transition to rocket powered flight as orbital velocity is approached, simple feedback guidance laws for both the unconstrained and dynamic pressure constrained cases derived via singular perturbation theory and a nonlinear transformation technique, and numerical simulation results for ascent to orbit in the dynamic pressure constrained case.

  11. Understanding the effects of strain on morphological instabilities of a nanoscale island during heteroepitaxial growth

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

    Feng, Lu; Wang, Jing; Wang, Shibin

    A comprehensive morphological stability analysis of a nanoscale circular island during heteroepitaxial growth is presented based on continuum elasticity theory. The interplay between kinetic and thermodynamic mechanisms is revealed by including strain-related kinetic processes. In the kinetic regime, the Burton-Cabrera-Frank model is adopted to describe the growth front of the island. Together with kinetic boundary conditions, various kinetic processes including deposition flow, adatom diffusion, attachment-detachment kinetics, and the Ehrlich-Schwoebel barrier can be taken into account at the same time. In the thermodynamic regime, line tension, surface energy, and elastic energy are considered. As the strain relief in the early stagesmore » of heteroepitaxy is more complicated than commonly suggested by simple consideration of lattice mismatch, we also investigate the effects of external applied strain and elastic response due to perturbations on the island shape evolution. The analytical expressions for elastic fields induced by mismatch strain, external applied strain, and relaxation strain are presented. A systematic approach is developed to solve the system via a perturbation analysis which yields the conditions of film morphological instabilities. Consistent with previous experimental and theoretical work, parametric studies show the kinetic evolution of elastic relaxation, island morphology, and film composition under various conditions. Our present work offers an effective theoretical approach to get a comprehensive understanding of the interplay between different growth mechanisms and how to tailor the growth mode by controlling the nature of the crucial factors.« less

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

    NASA Astrophysics Data System (ADS)

    Mon, K. K.

    2001-06-01

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

  13. Renormalization of minimally doubled fermions

    NASA Astrophysics Data System (ADS)

    Capitani, Stefano; Creutz, Michael; Weber, Johannes; Wittig, Hartmut

    2010-09-01

    We investigate the renormalization properties of minimally doubled fermions, at one loop in perturbation theory. Our study is based on the two particular realizations of Boriçi-Creutz and Karsten-Wilczek. A common feature of both formulations is the breaking of hyper-cubic symmetry, which requires that the lattice actions are supplemented by suitable counterterms. We show that three counterterms are required in each case and determine their coefficients to one loop in perturbation theory. For both actions we compute the vacuum polarization of the gluon. It is shown that no power divergences appear and that all contributions which arise from the breaking of Lorentz symmetry are cancelled by the counterterms. We also derive the conserved vector and axial-vector currents for Karsten-Wilczek fermions. Like in the case of the previously studied Boriçi-Creutz action, one obtains simple expressions, involving only nearest-neighbour sites. We suggest methods how to fix the coefficients of the counterterms non-perturbatively and discuss the implications of our findings for practical simulations.

  14. Dynamics of anisotropies close to a cosmological bounce in quantum gravity

    NASA Astrophysics Data System (ADS)

    de Cesare, Marco; Oriti, Daniele; Pithis, Andreas G. A.; Sakellariadou, Mairi

    2018-01-01

    We study the dynamics of perturbations representing deviations from perfect isotropy in the context of the emergent cosmology obtained from the group field theory formalism for quantum gravity. Working in the mean field approximation of the group field theory formulation of the Lorentzian EPRL model, we derive the equations of motion for such perturbations to first order. We then study these equations around a specific simple isotropic background, characterised by the fundamental representation of SU(2) , and in the regime of the effective cosmological dynamics corresponding to the bouncing region replacing the classical singularity, well approximated by the free GFT dynamics. In this particular example, we identify a region in the parameter space of the model such that perturbations can be large at the bounce but become negligible away from it, i.e. when the background enters the non-linear regime. We also study the departures from perfect isotropy by introducing specific quantities, such as the surface-area-to-volume ratio and the effective volume per quantum, which make them quantitative.

  15. Adiabatic perturbation theory of electronic stopping in insulators

    DOE PAGES

    Horsfield, Andrew P.; Lim, Anthony; Foulkes, W. M. C.; ...

    2016-06-02

    A model able to explain the complicated structure of electronic stopping at low velocities in insulating materials is presented. It is shown to be in good agreement with results obtained from time-dependent density-functional theory for the stopping of a channeling Si atom in a Si crystal. If we define the repeat frequency f=v/λ, where λ is the periodic repeat length of the crystal along the direction the channeling atom is traveling, and v is the velocity of the channeling atom, we find that electrons experience a perturbing force that varies in time at integer multiples l of f. This enablesmore » electronic excitations at low atom velocity, but their contributions diminish rapidly with increasing values of l. The expressions for stopping power are derived using adiabatic perturbation theory for many-electron systems, and they are then specialized to the case of independent electrons. Lastly, a simple model for the nonadiabatic matrix elements is described, along with the procedure for determining its parameters.« less

  16. A quantum perturbative pair distribution for determining interatomic potentials from extended x-ray absorption spectroscopy

    NASA Astrophysics Data System (ADS)

    Piazza, F.

    2002-11-01

    In this paper we develop a technique for determining interatomic potentials in materials in the quantum regime from single-shell extended x-ray absorption spectroscopy (EXAFS) spectra. We introduce a pair distribution function, based on ordinary quantum time-independent perturbation theory. In the proposed scheme, the model potential parameters enter the distribution through a fourth-order Taylor expansion of the potential, and are directly refined in the fit of the model signal to the experimental spectrum. We discuss in general the validity of our theoretical framework, namely the quantum regime and perturbative treatment, and work out a simple tool for monitoring the sensitivity of our theory in determining lattice anharmonicities based on the statistical F-test. As an example, we apply our formalism to an EXAFS spectrum at the Ag K edge of AgI at T = 77 K. We determine the Ag-I potential parameters and find good agreement with previous studies.

  17. Nonlinear ideal magnetohydrodynamics instabilities

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

    Pfirsch, D.; Sudan, R.N.

    1993-07-01

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

  18. 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...

  19. Thermophysical properties of simple liquid metals: A brief review of theory

    NASA Technical Reports Server (NTRS)

    Stroud, David

    1993-01-01

    In this paper, we review the current theory of the thermophysical properties of simple liquid metals. The emphasis is on thermodynamic properties, but we also briefly discuss the nonequilibrium properties of liquid metals. We begin by defining a 'simple liquid metal' as one in which the valence electrons interact only weakly with the ionic cores, so that the interaction can be treated by perturbation theory. We then write down the equilibrium Hamiltonian of a liquid metal as a sum of five terms: the bare ion-ion interaction, the electron-electron interaction, the bare electron-ion interaction, and the kinetic energies of electrons and ions. Since the electron-ion interaction can be treated by perturbation, the electronic part contributes in two ways to the Helmholtz free energy: it gives a density-dependent term which is independent of the arrangement of ions, and it acts to screen the ion-ion interaction, giving rise to effective ion-ion pair potentials which are density-dependent, in general. After sketching the form of a typical pair potential, we briefly enumerate some methods for calculating the ionic distribution function and hence the Helmholtz free energy of the liquid: monte Carlo simulations, molecular dynamics simulations, and thermodynamic perturbation theory. The final result is a general expression for the Helmholtz free energy of the liquid metal. It can be used to calculate a wide range of thermodynamic properties of simple metal liquids, which we enumerate. They include not only a range of thermodynamic coefficients of both metals and alloys, but also many aspects of the phase diagram, including freezing curves of pure elements and phase diagrams of liquid alloys (including liquidus and solidus curves). We briefly mention some key discoveries resulting from previous applications of this method, and point out that the same methods work for other materials not normally considered to be liquid metals (such as colloidal suspensions, in which the suspended microspheres behave like ions screened by the salt solution in which they are suspended). We conclude with a brief discussion of some non-equilibrium (i.e., transport) properties which can be treated by an extension of these methods. These include electrical resistivity, thermal conductivity, viscosity, atomic self-diffusion coefficients, concentration diffusion coefficients in alloys, surface tension and thermal emissivity. Finally, we briefly mention two methods by which the theory might be extended to non-simple liquid metals: these are empirical techniques (i.e., empirical two- and three-body potentials), and numerical many-body approaches. Both may be potentially applicable to extremely complex systems, such as nonstoichiometric liquid semiconductor alloys.

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

    Emami, Razieh; Mukohyama, Shinji; Namba, Ryo

    Many models of inflation driven by vector fields alone have been known to be plagued by pathological behaviors, namely ghost and/or gradient instabilities. In this work, we seek a new class of vector-driven inflationary models that evade all of the mentioned instabilities. We build our analysis on the Generalized Proca Theory with an extension to three vector fields to realize isotropic expansion. We obtain the conditions required for quasi de-Sitter solutions to be an attractor analogous to the standard slow-roll one and those for their stability at the level of linearized perturbations. Identifying the remedy to the existing unstable models,more » we provide a simple example and explicitly show its stability. This significantly broadens our knowledge on vector inflationary scenarios, reviving potential phenomenological interests for this class of models.« less

  1. Nonlocal Galileons and self-acceleration

    NASA Astrophysics Data System (ADS)

    Gabadadze, Gregory; Yu, Siqing

    2017-05-01

    A certain class of nonlocal theories eliminates an arbitrary cosmological constant (CC) from a universe that can be perceived as our world. Dark energy then cannot be explained by a CC; it could however be due to massive gravity. We calculate the new corrections, which originate from the nonlocal terms that eliminate the CC, to the decoupling limit Lagrangian of massive gravity. The new nonlocal terms also have internal field space Galilean symmetry and are referred here as ;nonlocal Galileons.; We then study a self-accelerated solution and show that the new nonlocal terms change the perturbative stability analysis. In particular, small fluctuations are now stable and non-superluminal for some simple parameter choices, whereas for the same choices the pure massive gravity fluctuations are unstable. We also study stable spherically symmetric solutions on this background.

  2. Stable solutions of inflation driven by vector fields

    NASA Astrophysics Data System (ADS)

    Emami, Razieh; Mukohyama, Shinji; Namba, Ryo; Zhang, Ying-li

    2017-03-01

    Many models of inflation driven by vector fields alone have been known to be plagued by pathological behaviors, namely ghost and/or gradient instabilities. In this work, we seek a new class of vector-driven inflationary models that evade all of the mentioned instabilities. We build our analysis on the Generalized Proca Theory with an extension to three vector fields to realize isotropic expansion. We obtain the conditions required for quasi de-Sitter solutions to be an attractor analogous to the standard slow-roll one and those for their stability at the level of linearized perturbations. Identifying the remedy to the existing unstable models, we provide a simple example and explicitly show its stability. This significantly broadens our knowledge on vector inflationary scenarios, reviving potential phenomenological interests for this class of models.

  3. Perturbations from strings don't look like strings!

    NASA Technical Reports Server (NTRS)

    Albrecht, Andreas; Stebbins, Albert

    1991-01-01

    A systematic analysis is challenging popular ideas about perturbation from cosmic strings. One way in which the picture has changed is reviewed. It is concluded that, while the scaling properties of cosmic strings figure significantly in the analysis, care must be taken when thinking in terms of single time snapshots. The process of seeding density perturbations is not fundamentally localized in time, and this fact can wash out many of the details which appear in a single snapshot.

  4. Interactions between globular proteins and F-actin in isotonic saline solution.

    PubMed

    Lakatos, S; Minton, A P

    1991-10-05

    Solutions of each of three different globular proteins (cytochrome c, chromophorically labeled serum albumin, and chromophorically labeled aldolase), mixed with another unlabeled globular protein or with fibrous actin, were prepared in pH 8.0 Tris-HCl buffer containing 0.15 M NaCl. Each solution was centrifuged at low speed, at 5 degrees C, until unassociated globular protein in solution achieved sedimentation equilibrium. Individual absorbance gradients of both macrosolutes in the mixtures subsequent to centrifugation were obtained via optical scans of the centrifuge tubes at two wavelengths. The gradients of each macrosolute in mixtures of two globular proteins revealed no association of globular proteins under the conditions of these experiments, but perturbation of the gradients of serum albumin, aldolase, and cytochrome c in the presence of F-actin indicated association of all three globular proteins with F-actin. Perturbation of actin gradients in the presence of serum albumin and aldolase suggested partial depolymerization of the F-actin by the globular protein. Analysis of the data with a simple phenomenological model relating free globular protein, bound globular protein, and total actin concentration provided estimates of the respective equilibrium constants for association of serum albumin and aldolase with F-actin, under the conditions of these experiments, of the order of 0.1 microM-1.

  5. Non-Gaussianity from self-ordering scalar fields

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

    Figueroa, Daniel G.; Instituto de Fisica Teorica UAM/CSIC, Universidad Autonoma de Madrid, 28049 Madrid; Caldwell, Robert R.

    The Universe may harbor relics of the post-inflationary epoch in the form of a network of self-ordered scalar fields. Such fossils, while consistent with current cosmological data at trace levels, may leave too weak an imprint on the cosmic microwave background and the large-scale distribution of matter to allow for direct detection. The non-Gaussian statistics of the density perturbations induced by these fields, however, permit a direct means to probe for these relics. Here we calculate the bispectrum that arises in models of self-ordered scalar fields. We find a compact analytic expression for the bispectrum, evaluate it numerically, and providemore » a simple approximation that may be useful for data analysis. The bispectrum is largest for triangles that are aligned (have edges k{sub 1{approx_equal}}2k{sub 2{approx_equal}}2k{sub 3}) as opposed to the local-model bispectrum, which peaks for squeezed triangles (k{sub 1{approx_equal}}k{sub 2}>>k{sub 3}), and the equilateral bispectrum, which peaks at k{sub 1{approx_equal}}k{sub 2{approx_equal}}k{sub 3}. We estimate that this non-Gaussianity should be detectable by the Planck satellite if the contribution from self-ordering scalar fields to primordial perturbations is near the current upper limit.« less

  6. Viscoelastic and elastomeric active matter: Linear instability and nonlinear dynamics.

    PubMed

    Hemingway, E J; Cates, M E; Fielding, S M

    2016-03-01

    We consider a continuum model of active viscoelastic matter, whereby an active nematic liquid crystal is coupled to a minimal model of polymer dynamics with a viscoelastic relaxation time τ(C). To explore the resulting interplay between active and polymeric dynamics, we first generalize a linear stability analysis (from earlier studies without polymer) to derive criteria for the onset of spontaneous heterogeneous flows (strain rate) and/or deformations (strain). We find two modes of instability. The first is a viscous mode, associated with strain rate perturbations. It dominates for relatively small values of τ(C) and is a simple generalization of the instability known previously without polymer. The second is an elastomeric mode, associated with strain perturbations, which dominates at large τ(C) and persists even as τ(C)→∞. We explore the dynamical states to which these instabilities lead by means of direct numerical simulations. These reveal oscillatory shear-banded states in one dimension and activity-driven turbulence in two dimensions even in the elastomeric limit τ(C)→∞. Adding polymer can also have calming effects, increasing the net throughput of spontaneous flow along a channel in a type of drag reduction. The effect of including strong antagonistic coupling between the nematic and polymer is examined numerically, revealing a rich array of spontaneously flowing states.

  7. Viscoelastic and elastomeric active matter: Linear instability and nonlinear dynamics

    NASA Astrophysics Data System (ADS)

    Hemingway, E. J.; Cates, M. E.; Fielding, S. M.

    2016-03-01

    We consider a continuum model of active viscoelastic matter, whereby an active nematic liquid crystal is coupled to a minimal model of polymer dynamics with a viscoelastic relaxation time τC. To explore the resulting interplay between active and polymeric dynamics, we first generalize a linear stability analysis (from earlier studies without polymer) to derive criteria for the onset of spontaneous heterogeneous flows (strain rate) and/or deformations (strain). We find two modes of instability. The first is a viscous mode, associated with strain rate perturbations. It dominates for relatively small values of τC and is a simple generalization of the instability known previously without polymer. The second is an elastomeric mode, associated with strain perturbations, which dominates at large τC and persists even as τC→∞ . We explore the dynamical states to which these instabilities lead by means of direct numerical simulations. These reveal oscillatory shear-banded states in one dimension and activity-driven turbulence in two dimensions even in the elastomeric limit τC→∞ . Adding polymer can also have calming effects, increasing the net throughput of spontaneous flow along a channel in a type of drag reduction. The effect of including strong antagonistic coupling between the nematic and polymer is examined numerically, revealing a rich array of spontaneously flowing states.

  8. Nucleation type instabilities in partially wetting nanoscale nematic liquid films

    NASA Astrophysics Data System (ADS)

    Lam, Michael; Cummings, Linda; Kondic, Lou

    2016-11-01

    Nucleation type instabilities are studied in nematic liquid crystal (NLC) films with thicknesses less than a micrometer. Within the framework of the long wave approximation, a 4th order nonlinear partial differential equation is proposed for the free surface height. Unlike simple fluids, NLC molecules have a dipole moment which induces an elastic response due to deformation in the bulk of the fluid. The model includes the balance between the bulk elasticity energy and the anchoring (boundary) energy at the substrate and free surface, and van der Waals' intermolecular forces, by means of a structural disjoining pressure. In this presentation, we focus on two-dimensional flow and present simulation results for a flat film with a localized perturbation. We are interested in the morphology of the dewetted film as a function of the initial film thickness. We will show that there exists a range of film thicknesses within the linearly unstable flat film regime where stability analysis does not explain the morphology of the dewetted film. Marginal stability criterion (MSC) is used to derive an analytical expression for the velocity at which a perturbation propagates into the unstable flat film. Finally, we discuss the degree to which MSC can be used to explain the observed morphology.

  9. The multidimensional perturbation value: a single metric to measure similarity and activity of treatments in high-throughput multidimensional screens.

    PubMed

    Hutz, Janna E; Nelson, Thomas; Wu, Hua; McAllister, Gregory; Moutsatsos, Ioannis; Jaeger, Savina A; Bandyopadhyay, Somnath; Nigsch, Florian; Cornett, Ben; Jenkins, Jeremy L; Selinger, Douglas W

    2013-04-01

    Screens using high-throughput, information-rich technologies such as microarrays, high-content screening (HCS), and next-generation sequencing (NGS) have become increasingly widespread. Compared with single-readout assays, these methods produce a more comprehensive picture of the effects of screened treatments. However, interpreting such multidimensional readouts is challenging. Univariate statistics such as t-tests and Z-factors cannot easily be applied to multidimensional profiles, leaving no obvious way to answer common screening questions such as "Is treatment X active in this assay?" and "Is treatment X different from (or equivalent to) treatment Y?" We have developed a simple, straightforward metric, the multidimensional perturbation value (mp-value), which can be used to answer these questions. Here, we demonstrate application of the mp-value to three data sets: a multiplexed gene expression screen of compounds and genomic reagents, a microarray-based gene expression screen of compounds, and an HCS compound screen. In all data sets, active treatments were successfully identified using the mp-value, and simulations and follow-up analyses supported the mp-value's statistical and biological validity. We believe the mp-value represents a promising way to simplify the analysis of multidimensional data while taking full advantage of its richness.

  10. Simplification and its consequences in biological modelling: conclusions from a study of calcium oscillations in hepatocytes.

    PubMed

    Hetherington, James P J; Warner, Anne; Seymour, Robert M

    2006-04-22

    Systems Biology requires that biological modelling is scaled up from small components to system level. This can produce exceedingly complex models, which obscure understanding rather than facilitate it. The successful use of highly simplified models would resolve many of the current problems faced in Systems Biology. This paper questions whether the conclusions of simple mathematical models of biological systems are trustworthy. The simplification of a specific model of calcium oscillations in hepatocytes is examined in detail, and the conclusions drawn from this scrutiny generalized. We formalize our choice of simplification approach through the use of functional 'building blocks'. A collection of models is constructed, each a progressively more simplified version of a well-understood model. The limiting model is a piecewise linear model that can be solved analytically. We find that, as expected, in many cases the simpler models produce incorrect results. However, when we make a sensitivity analysis, examining which aspects of the behaviour of the system are controlled by which parameters, the conclusions of the simple model often agree with those of the richer model. The hypothesis that the simplified model retains no information about the real sensitivities of the unsimplified model can be very strongly ruled out by treating the simplification process as a pseudo-random perturbation on the true sensitivity data. We conclude that sensitivity analysis is, therefore, of great importance to the analysis of simple mathematical models in biology. Our comparisons reveal which results of the sensitivity analysis regarding calcium oscillations in hepatocytes are robust to the simplifications necessarily involved in mathematical modelling. For example, we find that if a treatment is observed to strongly decrease the period of the oscillations while increasing the proportion of the cycle during which cellular calcium concentrations are rising, without affecting the inter-spike or maximum calcium concentrations, then it is likely that the treatment is acting on the plasma membrane calcium pump.

  11. The Geometry of Resonant Signatures in Debris Disks with Planets

    NASA Astrophysics Data System (ADS)

    Kuchner, M. J.; Holman, M. J.

    2002-09-01

    Using simple geometrical arguments, we paint an overview of the variety of resonant structures a single planet with moderate eccentricity (e < 0.6) can create in a dynamically cold, optically thin dust disk. This overview may serve as a key for interpreting images of perturbed debris disks and inferring the dynamical properties of the planets responsible for the perturbations. We compare the resonant structures found in the solar system with observations of planetary systems around Vega and other stars and we offer a new model for the asymmetries in the Epsilon Eridani disk. This work was performed in part under contract with the Jet Propulsion Laboratory (JPL) through the Michelson Fellowship program funded by NASA as an element of the Planet Finder Program.

  12. Diffusion in randomly perturbed dissipative dynamics

    NASA Astrophysics Data System (ADS)

    Rodrigues, Christian S.; Chechkin, Aleksei V.; de Moura, Alessandro P. S.; Grebogi, Celso; Klages, Rainer

    2014-11-01

    Dynamical systems having many coexisting attractors present interesting properties from both fundamental theoretical and modelling points of view. When such dynamics is under bounded random perturbations, the basins of attraction are no longer invariant and there is the possibility of transport among them. Here we introduce a basic theoretical setting which enables us to study this hopping process from the perspective of anomalous transport using the concept of a random dynamical system with holes. We apply it to a simple model by investigating the role of hyperbolicity for the transport among basins. We show numerically that our system exhibits non-Gaussian position distributions, power-law escape times, and subdiffusion. Our simulation results are reproduced consistently from stochastic continuous time random walk theory.

  13. A simple molecular orbital treatment of current distributions in quantum transport through molecular junctions

    NASA Astrophysics Data System (ADS)

    Jhan, Sin-Mu; Jin, Bih-Yaw

    2017-11-01

    A simple molecular orbital treatment of local current distributions inside single molecular junctions is developed in this paper. Using the first-order perturbation theory and nonequilibrium Green's function techniques in the framework of Hückel theory, we show that the leading contributions to local current distributions are directly proportional to the off-diagonal elements of transition density matrices. Under the orbital approximation, the major contributions to local currents come from a few dominant molecular orbital pairs which are mixed by the interactions between the molecule and electrodes. A few simple molecular junctions consisting of single- and multi-ring conjugated systems are used to demonstrate that local current distributions inside molecular junctions can be decomposed by partial sums of a few leading contributing transition density matrices.

  14. Perturbation Effects on a Supercritical C7H16/N2 Mixing Layer

    NASA Technical Reports Server (NTRS)

    Okongo'o, Nora; Bellan, Josette

    2008-01-01

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

  15. Comparative evaluation of differential laser-induced perturbation spectroscopy as a technique to discriminate emerging skin pathology

    NASA Astrophysics Data System (ADS)

    Kozikowski, Raymond T.; Smith, Sarah E.; Lee, Jennifer A.; Castleman, William L.; Sorg, Brian S.; Hahn, David W.

    2012-06-01

    Fluorescence spectroscopy has been widely investigated as a technique for identifying pathological tissue; however, unrelated subject-to-subject variations in spectra complicate data analysis and interpretation. We describe and evaluate a new biosensing technique, differential laser-induced perturbation spectroscopy (DLIPS), based on deep ultraviolet (UV) photochemical perturbation in combination with difference spectroscopy. This technique combines sequential fluorescence probing (pre- and post-perturbation) with sub-ablative UV perturbation and difference spectroscopy to provide a new spectral dimension, facilitating two improvements over fluorescence spectroscopy. First, the differential technique eliminates significant variations in absolute fluorescence response within subject populations. Second, UV perturbations alter the extracellular matrix (ECM), directly coupling the DLIPS response to the biological structure. Improved biosensing with DLIPS is demonstrated in vivo in a murine model of chemically induced skin lesion development. Component loading analysis of the data indicates that the DLIPS technique couples to structural proteins in the ECM. Analysis of variance shows that DLIPS has a significant response to emerging pathology as opposed to other population differences. An optimal likelihood ratio classifier for the DLIPS dataset shows that this technique holds promise for improved diagnosis of epithelial pathology. Results further indicate that DLIPS may improve diagnosis of tissue by augmenting fluorescence spectra (i.e. orthogonal sensing).

  16. SHORT-WAVELENGTH MAGNETIC BUOYANCY INSTABILITY

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

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

    2013-04-01

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

  17. Flap-lag-torsional dynamics of helicopter rotor blades in forward flight

    NASA Technical Reports Server (NTRS)

    Crespodasilva, M. R. M.

    1986-01-01

    A perturbation/numerical methodology to analyze the flap-lead/lag motion of a centrally hinged spring restrained rotor blade that is valid for both hover and for forward flight was developed. The derivation of the nonlinear differential equations of motion and the analysis of the stability of the steady state response of the blade were conducted entirely in a Symbolics 3670 Machine using MACSYMA to perform all the lengthy symbolic manipulations. It also includes generation of the fortran codes and plots of the results. The Floquet theory was also applied to the differential equations of motion in order to compare results with those obtained from the perturbation analysis. The results obtained from the perturbation methodology and from Floquet theory were found to be very close to each other, which demonstrates the usefullness of the perturbation methodology. Another problem under study consisted in the analysis of the influence of higher order terms in the response and stability of a flexible rotor blade in forward flight using Computerized Symbolic Manipulation and a perturbation technique to bypass the Floquet theory. The derivation of the partial differential equations of motion is presented.

  18. Cosmic Star Formation: A Simple Model of the SFRD(z)

    NASA Astrophysics Data System (ADS)

    Chiosi, Cesare; Sciarratta, Mauro; D’Onofrio, Mauro; Chiosi, Emanuela; Brotto, Francesca; De Michele, Rosaria; Politino, Valeria

    2017-12-01

    We investigate the evolution of the cosmic star formation rate density (SFRD) from redshift z = 20 to z = 0 and compare it with the observational one by Madau and Dickinson derived from recent compilations of ultraviolet (UV) and infrared (IR) data. The theoretical SFRD(z) and its evolution are obtained using a simple model that folds together the star formation histories of prototype galaxies that are designed to represent real objects of different morphological type along the Hubble sequence and the hierarchical growing of structures under the action of gravity from small perturbations to large-scale objects in Λ-CDM cosmogony, i.e., the number density of dark matter halos N(M,z). Although the overall model is very simple and easy to set up, it provides results that mimic results obtained from highly complex large-scale N-body simulations well. The simplicity of our approach allows us to test different assumptions for the star formation law in galaxies, the effects of energy feedback from stars to interstellar gas, the efficiency of galactic winds, and also the effect of N(M,z). The result of our analysis is that in the framework of the hierarchical assembly of galaxies, the so-called time-delayed star formation under plain assumptions mainly for the energy feedback and galactic winds can reproduce the observational SFRD(z).

  19. Substructure Versus Property-Level Dispersed Modes Calculation

    NASA Technical Reports Server (NTRS)

    Stewart, Eric C.; Peck, Jeff A.; Bush, T. Jason; Fulcher, Clay W.

    2016-01-01

    This paper calculates the effect of perturbed finite element mass and stiffness values on the eigenvectors and eigenvalues of the finite element model. The structure is perturbed in two ways: at the "subelement" level and at the material property level. In the subelement eigenvalue uncertainty analysis the mass and stiffness of each subelement is perturbed by a factor before being assembled into the global matrices. In the property-level eigenvalue uncertainty analysis all material density and stiffness parameters of the structure are perturbed modified prior to the eigenvalue analysis. The eigenvalue and eigenvector dispersions of each analysis (subelement and property-level) are also calculated using an analytical sensitivity approximation. Two structural models are used to compare these methods: a cantilevered beam model, and a model of the Space Launch System. For each structural model it is shown how well the analytical sensitivity modes approximate the exact modes when the uncertainties are applied at the subelement level and at the property level.

  20. Biomechanical influences on balance recovery by stepping.

    PubMed

    Hsiao, E T; Robinovitch, S N

    1999-10-01

    Stepping represents a common means for balance recovery after a perturbation to upright posture. Yet little is known regarding the biomechanical factors which determine whether a step succeeds in preventing a fall. In the present study, we developed a simple pendulum-spring model of balance recovery by stepping, and used this to assess how step length and step contact time influence the effort (leg contact force) and feasibility of balance recovery by stepping. We then compared model predictions of step characteristics which minimize leg contact force to experimentally observed values over a range of perturbation strengths. At all perturbation levels, experimentally observed step execution times were higher than optimal, and step lengths were smaller than optimal. However, the predicted increase in leg contact force associated with these deviations was substantial only for large perturbations. Furthermore, increases in the strength of the perturbation caused subjects to take larger, quicker steps, which reduced their predicted leg contact force. We interpret these data to reflect young subjects' desire to minimize recovery effort, subject to neuromuscular constraints on step execution time and step length. Finally, our model predicts that successful balance recovery by stepping is governed by a coupling between step length, step execution time, and leg strength, so that the feasibility of balance recovery decreases unless declines in one capacity are offset by enhancements in the others. This suggests that one's risk for falls may be affected more by small but diffuse neuromuscular impairments than by larger impairment in a single motor capacity.

  1. Theory and practice of solving ordinary differential equations (ODEs). [Runge-Kutta method; lectures in Spanish

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

    Shampine, L.F.

    1978-04-01

    Between January 23 and 27, 1978, several lectures were presented at the Instituto de Investigaciones en Matematicas Aplicadas y en Sistemas, National University of Mexico, Mexico City. The author concentrated on the Runge--Kutta method of solving differential equations because its details are simple and it is illustrative of classical perturbation and asymptotic methods.

  2. Science support for the Earth radiation budget sensor on the Nimbus-7 spacecraft

    NASA Technical Reports Server (NTRS)

    Ingersoll, A. P.

    1982-01-01

    Experimental data supporting the Earth radiation budget sensor on the Nimbus 7 Satellite is given. The data deals with the empirical relations between radiative flux, cloudiness, and other meteorological parameters; response of a zonal climate ice sheet model to the orbital perturbations during the quaternary ice ages; and a simple parameterization for ice sheet ablation rate.

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

    NASA Astrophysics Data System (ADS)

    Huang, Xingguo; Sun, Jianguo; Greenhalgh, Stewart

    2018-04-01

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

  4. Robust control with structured perturbations

    NASA Technical Reports Server (NTRS)

    Keel, Leehyun

    1988-01-01

    Two important problems in the area of control systems design and analysis are discussed. The first is the robust stability using characteristic polynomial, which is treated first in characteristic polynomial coefficient space with respect to perturbations in the coefficients of the characteristic polynomial, and then for a control system containing perturbed parameters in the transfer function description of the plant. In coefficient space, a simple expression is first given for the l(sup 2) stability margin for both monic and non-monic cases. Following this, a method is extended to reveal much larger stability region. This result has been extended to the parameter space so that one can determine the stability margin, in terms of ranges of parameter variations, of the closed loop system when the nominal stabilizing controller is given. The stability margin can be enlarged by a choice of better stabilizing controller. The second problem describes the lower order stabilization problem, the motivation of the problem is as follows. Even though the wide range of stabilizing controller design methodologies is available in both the state space and transfer function domains, all of these methods produce unnecessarily high order controllers. In practice, the stabilization is only one of many requirements to be satisfied. Therefore, if the order of a stabilizing controller is excessively high, one can normally expect to have a even higher order controller on the completion of design such as inclusion of dynamic response requirements, etc. Therefore, it is reasonable to have a lowest possible order stabilizing controller first and then adjust the controller to meet additional requirements. The algorithm for designing a lower order stabilizing controller is given. The algorithm does not necessarily produce the minimum order controller; however, the algorithm is theoretically logical and some simulation results show that the algorithm works in general.

  5. Orbital theory in terms of KS elements with luni-solar perturbations

    NASA Astrophysics Data System (ADS)

    Sellamuthu, Harishkumar; Sharma, Ram

    2016-07-01

    Precise orbit computation of Earth orbiting satellites is essential for efficient mission planning of planetary exploration, navigation and satellite geodesy. The third-body perturbations of the Sun and the Moon predominantly affect the satellite motion in the high altitude and elliptical orbits, where the effect of atmospheric drag is negligible. The physics of the luni-solar gravity effect on Earth satellites have been studied extensively over the years. The combined luni-solar gravitational attraction will induce a cumulative effect on the dynamics of satellite orbits, which mainly oscillates the perigee altitude. Though accurate orbital parameters are computed by numerical integration with respect to complex force models, analytical theories are highly valued for the manifold of solutions restricted to relatively simple force models. During close approach, the classical equations of motion in celestial mechanics are almost singular and they are unstable for long-term orbit propagation. A new singularity-free analytical theory in terms of KS (Kustaanheimo and Stiefel) regular elements with respect to luni-solar perturbation is developed. These equations are regular everywhere and eccentric anomaly is the independent variable. Plataforma Solar de Almería (PSA) algorithm and a Fourier series algorithm are used to compute the accurate positions of the Sun and the Moon, respectively. Numerical studies are carried out for wide range of initial parameters and the analytical solutions are found to be satisfactory when compared with numerically integrated values. The symmetrical nature of the equations allows only two of the nine equations to be solved for computing the state vectors and the time. Only a change in the initial conditions is required to solve the other equations. This theory will find multiple applications including on-board software packages and for mission analysis purposes.

  6. Quantum geometry of resurgent perturbative/nonperturbative relations

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

    Basar, Gokce; Dunne, Gerald V.; Unsal, Mithat

    For a wide variety of quantum potentials, including the textbook ‘instanton’ examples of the periodic cosine and symmetric double-well potentials, the perturbative data coming from fluctuations about the vacuum saddle encodes all non-perturbative data in all higher non-perturbative sectors. Here we unify these examples in geometric terms, arguing that the all-orders quantum action determines the all-orders quantum dual action for quantum spectral problems associated with a classical genus one elliptic curve. Furthermore, for a special class of genus one potentials this relation is particularly simple: this class includes the cubic oscillator, symmetric double-well, symmetric degenerate triple-well, and periodic cosine potential.more » These are related to the Chebyshev potentials, which are in turn related to certain N = 2 supersymmetric quantum field theories, to mirror maps for hypersurfaces in projective spaces, and also to topological c = 3 Landau-Ginzburg models and ‘special geometry’. These systems inherit a natural modular structure corresponding to Ramanujan’s theory of elliptic functions in alternative bases, which is especially important for the quantization. Insights from supersymmetric quantum field theory suggest similar structures for more complicated potentials, corresponding to higher genus. Lastly, our approach is very elementary, using basic classical geometry combined with all-orders WKB.« less

  7. Quantum geometry of resurgent perturbative/nonperturbative relations

    DOE PAGES

    Basar, Gokce; Dunne, Gerald V.; Unsal, Mithat

    2017-05-16

    For a wide variety of quantum potentials, including the textbook ‘instanton’ examples of the periodic cosine and symmetric double-well potentials, the perturbative data coming from fluctuations about the vacuum saddle encodes all non-perturbative data in all higher non-perturbative sectors. Here we unify these examples in geometric terms, arguing that the all-orders quantum action determines the all-orders quantum dual action for quantum spectral problems associated with a classical genus one elliptic curve. Furthermore, for a special class of genus one potentials this relation is particularly simple: this class includes the cubic oscillator, symmetric double-well, symmetric degenerate triple-well, and periodic cosine potential.more » These are related to the Chebyshev potentials, which are in turn related to certain N = 2 supersymmetric quantum field theories, to mirror maps for hypersurfaces in projective spaces, and also to topological c = 3 Landau-Ginzburg models and ‘special geometry’. These systems inherit a natural modular structure corresponding to Ramanujan’s theory of elliptic functions in alternative bases, which is especially important for the quantization. Insights from supersymmetric quantum field theory suggest similar structures for more complicated potentials, corresponding to higher genus. Lastly, our approach is very elementary, using basic classical geometry combined with all-orders WKB.« less

  8. 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

  9. Effects of Low MN Perturbation on Last Good Surface

    NASA Astrophysics Data System (ADS)

    Casas, Micaela; Ali, Halima; Punjabi, Alkesh

    2003-10-01

    This project explores the effects of low MN perturbation on last good magnetic surface (LGS) in single-null divertor tokamak. Punjabi and Boozer developed Simple Map (SM)/1/to represent cross-sections of field line trajectories in phase space. SM with low MN perturbation is given by: X_n+1=X_n-kY_n(1-δ_LowMNs(frac2π nN_p)-Y_n) and Y_n+1=Y_n-k(1-δ_LowMNs(frac2π nN_p))X_n+1 /2/ where δ_LowMN is amplitude of perturbation and Np is fixed at 10. We fix map parameter k at 0.6. By varying δ_LowMN we determine when and how LGS breaks up and becomes chaotic. We begin graphs with small increments in δ_LowMN. We observe no significant changes in LGS until δ_LowMN is more than 4.9x10-9, then it progresses to chaos in five stages. The paper will present these LGS results in depth. This research is done under mentorship of Drs. H. Ali and A. Punjabi. NASA SHARP and US DOE grant number DE-FG02-02ER54673 support the project. 1. Punjabi A. et al, Phys. Rev. Lett., 69, 3322 (1992) 2. Punjabi A. et al, Phys Plasmas, 4, 337 (1997)

  10. Effect of Dipole Perturbation on a Good Confining Surface Near X Point

    NASA Astrophysics Data System (ADS)

    Prakash, Sushant; Witmer, Lisa; Punjabi, Alkesh; Ali, Halima

    2002-11-01

    We analyze effects of dipole perturbation on a good magnetic surface of a single null divertor tokamak using the method of maps developed by Punjabi and Boozer /1/. Unperturbed fields are represented by the Symmetric Simple Map /2/. Effects of high MN perturbation are represented by the Dipole Map (DM) /2/ given by: x_n+1 = x_n+2δ s^3x_n[(y_n-y_s+s) / [x_n+1^2+(y_n-y_s+s)^2]^2], y_n+1 = y_n+δ s^3x_n[[(y_n-y_s+s)^2-x_n+1^2] / [x_n+1^2+(y_n-y_s+s)^2]^2] The good surface is x_0=0 and y_0=0.952873. We start with the strength of perturbation, δ=0, increase it slowly, and observe how the surface changes. The results will be presented. This project is supported by the QEM network NASA Sharp Plus program and by DE-FG02-02ER54673. The work is done on the FUSION1 server under Profs. Ali and Punjabi 1. Punjabi A., Verma A. and Boozer A., Phys. Rev. Lett., 69, 3322 (1992) 2. Ali H., Punjabi A. and Boozer A., Dipole Map for Single-null Divertor Tokamak, 2002 International Congress on Plasma Physics, Manly, Australia.

  11. Implications of Secondary Aftershocks for Failure Processes

    NASA Astrophysics Data System (ADS)

    Gross, S. J.

    2001-12-01

    When a seismic sequence with more than one mainshock or an unusually large aftershock occurs, there is a compound aftershock sequence. The secondary aftershocks need not have exactly the same decay as the primary sequence, with the differences having implications for the failure process. When the stress step from the secondary mainshock is positive but not large enough to cause immediate failure of all the remaining primary aftershocks, failure processes which involve accelerating slip will produce secondary aftershocks that decay more rapidly than primary aftershocks. This is because the primary aftershocks are an accelerated version of the background seismicity, and secondary aftershocks are an accelerated version of the primary aftershocks. Real stress perturbations may be negative, and heterogeneities in mainshock stress fields mean that the real world situation is quite complicated. I will first describe and verify my picture of secondary aftershock decay with reference to a simple numerical model of slipping faults which obeys rate and state dependent friction and lacks stress heterogeneity. With such a model, it is possible to generate secondary aftershock sequences with perturbed decay patterns, quantify those patterns, and develop an analysis technique capable of correcting for the effect in real data. The secondary aftershocks are defined in terms of frequency linearized time s(T), which is equal to the number of primary aftershocks expected by a time T, $ s ≡ ∫ t=0T n(t) dt, where the start time t=0 is the time of the primary aftershock, and the primary aftershock decay function n(t) is extrapolated forward to the times of the secondary aftershocks. In the absence of secondary sequences the function s(T)$ re-scales the time so that approximately one event occurs per new time unit; the aftershock sequence is gone. If this rescaling is applied in the presence of a secondary sequence, the secondary sequence is shaped like a primary aftershock sequence, and can be fit by the same modeling techniques applied to simple sequences. The later part of the presentation will concern the decay of Hector Mine aftershocks as influenced by the Landers aftershocks. Although attempts to predict the abundance of Hector aftershocks based on stress overlap analysis are not very successful, the analysis does do a good job fitting the decay of secondary sequences.

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

    PubMed

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

    2016-01-25

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

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

    PubMed Central

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

    2016-01-01

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

  14. An Analytical State Transition Matrix for Orbits Perturbed by an Oblate Spheroid

    NASA Technical Reports Server (NTRS)

    Mueller, A. C.

    1977-01-01

    An analytical state transition matrix and its inverse, which include the short period and secular effects of the second zonal harmonic, were developed from the nonsingular PS satellite theory. The fact that the independent variable in the PS theory is not time is in no respect disadvantageous, since any explicit analytical solution must be expressed in the true or eccentric anomaly. This is shown to be the case for the simple conic matrix. The PS theory allows for a concise, accurate, and algorithmically simple state transition matrix. The improvement over the conic matrix ranges from 2 to 4 digits accuracy.

  15. Dressed tunneling approximation for electronic transport through molecular transistors

    NASA Astrophysics Data System (ADS)

    Seoane Souto, R.; Yeyati, A. Levy; Martín-Rodero, A.; Monreal, R. C.

    2014-02-01

    A theoretical approach for the nonequilibrium transport properties of nanoscale systems coupled to metallic electrodes with strong electron-phonon interactions is presented. It consists of a resummation of the dominant Feynman diagrams from the perturbative expansion in the coupling to the leads. We show that this scheme eliminates the main pathologies found in previous simple analytical approaches for the polaronic regime. The results for the spectral and transport properties are compared with those from several other approaches for a wide range of parameters. The method can be formulated in a simple way to obtain the full counting statistics. Results for the shot and thermal noise are presented.

  16. How proteins modify water dynamics

    NASA Astrophysics Data System (ADS)

    Persson, Filip; Söderhjelm, Pär; Halle, Bertil

    2018-06-01

    Much of biology happens at the protein-water interface, so all dynamical processes in this region are of fundamental importance. Local structural fluctuations in the hydration layer can be probed by 17O magnetic relaxation dispersion (MRD), which, at high frequencies, measures the integral of a biaxial rotational time correlation function (TCF)—the integral rotational correlation time. Numerous 17O MRD studies have demonstrated that this correlation time, when averaged over the first hydration shell, is longer than in bulk water by a factor 3-5. This rotational perturbation factor (RPF) has been corroborated by molecular dynamics simulations, which can also reveal the underlying molecular mechanisms. Here, we address several outstanding problems in this area by analyzing an extensive set of molecular dynamics data, including four globular proteins and three water models. The vexed issue of polarity versus topography as the primary determinant of hydration water dynamics is resolved by establishing a protein-invariant exponential dependence of the RPF on a simple confinement index. We conclude that the previously observed correlation of the RPF with surface polarity is a secondary effect of the correlation between polarity and confinement. Water rotation interpolates between a perturbed but bulk-like collective mechanism at low confinement and an exchange-mediated orientational randomization (EMOR) mechanism at high confinement. The EMOR process, which accounts for about half of the RPF, was not recognized in previous simulation studies, where only the early part of the TCF was examined. Based on the analysis of the experimentally relevant TCF over its full time course, we compare simulated and measured RPFs, finding a 30% discrepancy attributable to force field imperfections. We also compute the full 17O MRD profile, including the low-frequency dispersion produced by buried water molecules. Computing a local RPF for each hydration shell, we find that the perturbation decays exponentially with a decay "length" of 0.3 shells and that the second and higher shells account for a mere 3% of the total perturbation measured by 17O MRD. The only long-range effect is a weak water alignment in the electric field produced by an electroneutral protein (not screened by counterions), but this effect is negligibly small for 17O MRD. By contrast, we find that the 17O TCF is significantly more sensitive to the important short-range perturbations than the other two TCFs examined here.

  17. Simple analytical model reveals the functional role of embodied sensorimotor interaction in hexapod gaits

    PubMed Central

    Aoi, Shinya; Nachstedt, Timo; Manoonpong, Poramate; Wörgötter, Florentin; Matsuno, Fumitoshi

    2018-01-01

    Insects have various gaits with specific characteristics and can change their gaits smoothly in accordance with their speed. These gaits emerge from the embodied sensorimotor interactions that occur between the insect’s neural control and body dynamic systems through sensory feedback. Sensory feedback plays a critical role in coordinated movements such as locomotion, particularly in stick insects. While many previously developed insect models can generate different insect gaits, the functional role of embodied sensorimotor interactions in the interlimb coordination of insects remains unclear because of their complexity. In this study, we propose a simple physical model that is amenable to mathematical analysis to explain the functional role of these interactions clearly. We focus on a foot contact sensory feedback called phase resetting, which regulates leg retraction timing based on touchdown information. First, we used a hexapod robot to determine whether the distributed decoupled oscillators used for legs with the sensory feedback generate insect-like gaits through embodied sensorimotor interactions. The robot generated two different gaits and one had similar characteristics to insect gaits. Next, we proposed the simple model as a minimal model that allowed us to analyze and explain the gait mechanism through the embodied sensorimotor interactions. The simple model consists of a rigid body with massless springs acting as legs, where the legs are controlled using oscillator phases with phase resetting, and the governed equations are reduced such that they can be explained using only the oscillator phases with some approximations. This simplicity leads to analytical solutions for the hexapod gaits via perturbation analysis, despite the complexity of the embodied sensorimotor interactions. This is the first study to provide an analytical model for insect gaits under these interaction conditions. Our results clarified how this specific foot contact sensory feedback contributes to generation of insect-like ipsilateral interlimb coordination during hexapod locomotion. PMID:29489831

  18. Development of a universal measure of quadrupedal forelimb-hindlimb coordination using digital motion capture and computerised analysis.

    PubMed

    Hamilton, Lindsay; Franklin, Robin J M; Jeffery, Nick D

    2007-09-18

    Clinical spinal cord injury in domestic dogs provides a model population in which to test the efficacy of putative therapeutic interventions for human spinal cord injury. To achieve this potential a robust method of functional analysis is required so that statistical comparison of numerical data derived from treated and control animals can be achieved. In this study we describe the use of digital motion capture equipment combined with mathematical analysis to derive a simple quantitative parameter - 'the mean diagonal coupling interval' - to describe coordination between forelimb and hindlimb movement. In normal dogs this parameter is independent of size, conformation, speed of walking or gait pattern. We show here that mean diagonal coupling interval is highly sensitive to alterations in forelimb-hindlimb coordination in dogs that have suffered spinal cord injury, and can be accurately quantified, but is unaffected by orthopaedic perturbations of gait. Mean diagonal coupling interval is an easily derived, highly robust measurement that provides an ideal method to compare the functional effect of therapeutic interventions after spinal cord injury in quadrupeds.

  19. Theory of finite disturbances in a centrifugal compression system with a vaneless radial diffuser

    NASA Technical Reports Server (NTRS)

    Moore, F. K.

    1990-01-01

    A previous small perturbation analysis of circumferential waves in circumferential compression systems, assuming inviscid flow, is shown to be consistent with observations that narrow diffusers are more stable than wide ones, when boundary layer displacement effect is included. The Moore-Greitzer analysis for finite strength transients containing both surge and rotating stall in axial machines is adapted for a centrifugal compression system. Under certain assumptions, and except for a new second order swirl, the diffuser velocity field, including resonant singularities, can be carried over from the previous inviscid linear analysis. Nonlinear transient equations are derived and applied in a simple example to show that throttling through a resonant value of flow coefficient must occur in a sudden surge-like drop, accompanied by a transient rotating wave. This inner solution is superseded by an outer surge response on a longer time scale. Surge may occur purely as result of circumferential wave resonance. Numerical results are shown for various parametric choices relating to throttle schedule and the characteristic slope. A number of circumferential modes considered simultaneously is briefly discussed.

  20. Dalitz plot analysis of the D+→K-π+π+ decay in the FOCUS experiment

    NASA Astrophysics Data System (ADS)

    Link, J. M.; Yager, P. M.; Anjos, J. C.; Bediaga, I.; Castromonte, C.; Machado, A. A.; Magnin, J.; Massafferri, A.; de Miranda, J. M.; Pepe, I. M.; Polycarpo, E.; Dos Reis, A. C.; Carrillo, S.; Casimiro, E.; Cuautle, E.; Sánchez-Hernández, A.; Uribe, C.; Vázquez, F.; Agostino, L.; Cinquini, L.; Cumalat, J. P.; Frisullo, V.; O'Reilly, B.; Segoni, I.; Stenson, K.; Butler, J. N.; Cheung, H. W. K.; Chiodini, G.; Gaines, I.; Garbincius, P. H.; Garren, L. A.; Gottschalk, E.; Kasper, P. H.; Kreymer, A. E.; Kutschke, R.; Wang, M.; Benussi, L.; Bianco, S.; Fabbri, F. L.; Zallo, A.; Reyes, M.; Cawlfield, C.; Kim, D. Y.; Rahimi, A.; Wiss, J.; Gardner, R.; Kryemadhi, A.; Chung, Y. S.; Kang, J. S.; Ko, B. R.; Kwak, J. W.; Lee, K. B.; Cho, K.; Park, H.; Alimonti, G.; Barberis, S.; Boschini, M.; Cerutti, A.; D'Angelo, P.; Dicorato, M.; Dini, P.; Edera, L.; Erba, S.; Inzani, P.; Leveraro, F.; Malvezzi, S.; Menasce, D.; Mezzadri, M.; Moroni, L.; Pedrini, D.; Pontoglio, C.; Prelz, F.; Rovere, M.; Sala, S.; Davenport, T. F.; Arena, V.; Boca, G.; Bonomi, G.; Gianini, G.; Liguori, G.; Lopes Pegna, D.; Merlo, M. M.; Pantea, D.; Ratti, S. P.; Riccardi, C.; Vitulo, P.; Göbel, C.; Otalora, J.; Hernandez, H.; Lopez, A. M.; Mendez, H.; Paris, A.; Quinones, J.; Ramirez, J. E.; Zhang, Y.; Wilson, J. R.; Handler, T.; Mitchell, R.; Engh, D.; Hosack, M.; Johns, W. E.; Luiggi, E.; Nehring, M.; Sheldon, P. D.; Vaandering, E. W.; Webster, M.; Sheaff, M.; Pennington, M. R.; Focus Collaboration

    2007-09-01

    Using data collected by the high-energy photoproduction experiment FOCUS at Fermilab we performed a Dalitz plot analysis of the Cabibbo favored decay D+ →K-π+π+. This study uses 53653 Dalitz-plot events with a signal fraction of ∼ 97%, and represents the highest statistics, most complete Dalitz plot analysis for this channel. Results are presented and discussed using two different formalisms. The first is a simple sum of Breit-Wigner functions with freely fitted masses and widths. It is the model traditionally adopted and serves as comparison with the already published analyses. The second uses a K-matrix approach for the dominant S-wave, in which the parameters are fixed by first fitting Kπ scattering data and continued to threshold by Chiral Perturbation Theory. We show that the Dalitz plot distribution for this decay is consistent with the assumption of two-body dominance of the final state interactions and the description of these interactions is in agreement with other data on the Kπ final state.

  1. Examining the accuracy of the infinite order sudden approximation using sensitivity analysis

    NASA Astrophysics Data System (ADS)

    Eno, Larry; Rabitz, Herschel

    1981-08-01

    A method is developed for assessing the accuracy of scattering observables calculated within the framework of the infinite order sudden (IOS) approximation. In particular, we focus on the energy sudden assumption of the IOS method and our approach involves the determination of the sensitivity of the IOS scattering matrix SIOS with respect to a parameter which reintroduces the internal energy operator ?0 into the IOS Hamiltonian. This procedure is an example of sensitivity analysis of missing model components (?0 in this case) in the reference Hamiltonian. In contrast to simple first-order perturbation theory a finite result is obtained for the effect of ?0 on SIOS. As an illustration, our method of analysis is applied to integral state-to-state cross sections for the scattering of an atom and rigid rotor. Results are generated within the He+H2 system and a comparison is made between IOS and coupled states cross sections and the corresponding IOS sensitivities. It is found that the sensitivity coefficients are very useful indicators of the accuracy of the IOS results. Finally, further developments and applications are discussed.

  2. A comparison of Lorentz, planetary gravitational, and satellite gravitational resonances

    NASA Technical Reports Server (NTRS)

    Hamilton, Douglas P.

    1994-01-01

    We consider a charged dust grain whose orbital motion is dominated by a planet's point-source gravity, but perturbed by higher-order terms in the planet's gravity field as well as by the Lorentz force arising from an asymmetric planetary magnetic field. Perturbations to Keplerian orbits due to a nonspherical gravity field are expressed in the traditional way: in terms of a disturbing function which can be expanded in a series of spherical harmonics (W. M. Kaula, 1966). In order to calculate the electromagnetic perturbation, we first write the Lorentz force in terms of the orbital elements and then substitute it into Gauss' perturbation equations. We use our result to derive strengths of Lorentz resonances and elucidate their properties. In particular, we compare Lorentz resonances to two types of gravitational resonances: those arising from periodic tugs of a satellite and those due to the attraction of an arbitrarily shaped planet. We find that Lorentz resonances share numerous properties with their gravitational counterparts and show, using simple physical arguments, that several of these patterns are fundamental, applying not only to our expansions, but to all quantities expressed in terms of orbital elements. Some of these patterns have been previously called 'd'Alembert rules' for satellite resonances. Other similarities arise because, to first-order in the perturbing force, the three problems share an integral of the motion. Yet there are also differences; for example, first-order inclination resonances exist for perturbations arising from planetary gravity and from the Lorentz force, but not for those due to an orbiting satellite. Finally, we provide a heuristic treatment of a particle's orbital evolution under the influence of drag and resonant forces. Particles brought into mean-motion resonances experience either trapping or resonant 'jumps,' depending on the direction from which the resonance is approached. We show that this behavior does not depend on the details of the perturbing force but rather is fundamental to all mean-motion resonances.

  3. 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'.

  4. SU-E-T-115: Dose Perturbation Study of Self-Expandable Metal and Polyester Esophageal Stents in Proton Therapy Beams

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

    Lee, S; Li, Z; Jalaj, S

    2014-06-01

    Purpose: This work investigates dose perturbations due to Self-expandable metal and polyester esophageal stents undergoing proton radiotherapy for esophageal cancer. Methods: Five commercially available esophageal stents made of nitinol (Evolution, Wallflex and Ultraflex), stainless steel (Z-Stent) and polyester (Polyflex) were tested. Radiochromic film (GafChromic EBT3 film, Ashland, Covington, KY) wrapped around a stent and a 12cc syringe was irradiated with 2CGE (Cobalt Gray Equivalent) of proton beam in a custom fabricated acrylic phantom. An air-hollow syringe simulates the esophagus. Results: The Z-stent created the largest dose perturbations ranges from -14.5% to 6.1% due to the steel composition. The WallFlex, Evolutionmore » and Ultraflex stents produced the dose perturbation ranges of (−9.2%∼8.6%), (−6.8%∼5.7%) and (−6.2%∼6.2%), respectively. The PolyFlex stent contains the radiopaque tungsten markers located top, middle and bottom portions. When the focal cold spots induced by the markers were excluded in the analysis, the dose perturbation range was changed from (−11.6%∼6.4%) to (−0.6%∼5.0%). Conclusion: The magnitude of dose perturbation is related to material of a metallic stent. The non-metallic stent such as PolyFlex shows relatively lower dose perturbation than metallic stents except a radiopaque marker region. Overall Evolution and Ultraflex stent appear to be less dose perturbations. The largest dose perturbations (cold spots) were located at both edges of stents in distal area for the single proton beam irradiation study. The analysis of more than two proton beam which is more typical clinical beam arrangement would be necessary to minimize the doe perturbation effect in proton ratiotherapy.« less

  5. Pre- and post-flight-test models versus measured skyship-500 control responses

    NASA Technical Reports Server (NTRS)

    Jex, Henry R.; Magdaleno, Raymond E.; Gelhausen, Paul; Tischler, Mark B.

    1987-01-01

    The dynamical equations-of-motion (EOM) for cruising airships require nonconventional terms to account for buoyancy and apparent-mass-effects, but systematic validation of these equations against flight data is not available. Using a candidate set of EOM, three comparisons are made with carefully-measured describing functions derived from frequency-sweep flight tests on the Skyship-500 airship. The first compares the pre-flight predictions to the data; the second compares the 'best-fit' equations to data at each of two airspeeds and the third compared the ability to extrapolate from one condition to another via airship-specific scaling laws. Two transient responses are also compared. The generally good results demonstrate that fairly simple, perturbation equation models are adequate for many types of flight-control analysis and flying quality evaluations of cruising airships.

  6. Equation of state and critical point behavior of hard-core double-Yukawa fluids.

    PubMed

    Montes, J; Robles, M; López de Haro, M

    2016-02-28

    A theoretical study on the equation of state and the critical point behavior of hard-core double-Yukawa fluids is presented. Thermodynamic perturbation theory, restricted to first order in the inverse temperature and having the hard-sphere fluid as the reference system, is used to derive a relatively simple analytical equation of state of hard-core multi-Yukawa fluids. Using such an equation of state, the compressibility factor and phase behavior of six representative hard-core double-Yukawa fluids are examined and compared with available simulation results. The effect of varying the parameters of the hard-core double-Yukawa intermolecular potential on the location of the critical point is also analyzed using different perspectives. The relevance of this analysis for fluids whose molecules interact with realistic potentials is also pointed out.

  7. Renormalization group analysis of the Reynolds stress transport equation

    NASA Technical Reports Server (NTRS)

    Rubinstein, R.; Barton, J. M.

    1992-01-01

    The pressure velocity correlation and return to isotropy term in the Reynolds stress transport equation are analyzed using the Yakhot-Orszag renormalization group. The perturbation series for the relevant correlations, evaluated to lowest order in the epsilon-expansion of the Yakhot-Orszag theory, are infinite series in tensor product powers of the mean velocity gradient and its transpose. Formal lowest order Pade approximations to the sums of these series produce a fast pressure strain model of the form proposed by Launder, Reece, and Rodi, and a return to isotropy model of the form proposed by Rotta. In both cases, the model constant are computed theoretically. The predicted Reynolds stress ratios in simple shear flows are evaluated and compared with experimental data. The possibility is discussed of driving higher order nonlinear models by approximating the sums more accurately.

  8. N-point statistics of large-scale structure in the Zel'dovich approximation

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

    Tassev, Svetlin, E-mail: tassev@astro.princeton.edu

    2014-06-01

    Motivated by the results presented in a companion paper, here we give a simple analytical expression for the matter n-point functions in the Zel'dovich approximation (ZA) both in real and in redshift space (including the angular case). We present numerical results for the 2-dimensional redshift-space correlation function, as well as for the equilateral configuration for the real-space 3-point function. We compare those to the tree-level results. Our analysis is easily extendable to include Lagrangian bias, as well as higher-order perturbative corrections to the ZA. The results should be especially useful for modelling probes of large-scale structure in the linear regime,more » such as the Baryon Acoustic Oscillations. We make the numerical code used in this paper freely available.« less

  9. Stability analysis of BWR nuclear-coupled thermal-hyraulics using a simple model

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

    Karve, A.A.; Rizwan-uddin; Dorning, J.J.

    1995-09-01

    A simple mathematical model is developed to describe the dynamics of the nuclear-coupled thermal-hydraulics in a boiling water reactor (BWR) core. The model, which incorporates the essential features of neutron kinetics, and single-phase and two-phase thermal-hydraulics, leads to simple dynamical system comprised of a set of nonlinear ordinary differential equations (ODEs). The stability boundary is determined and plotted in the inlet-subcooling-number (enthalpy)/external-reactivity operating parameter plane. The eigenvalues of the Jacobian matrix of the dynamical system also are calculated at various steady-states (fixed points); the results are consistent with those of the direct stability analysis and indicate that a Hopf bifurcationmore » occurs as the stability boundary in the operating parameter plane is crossed. Numerical simulations of the time-dependent, nonlinear ODEs are carried out for selected points in the operating parameter plane to obtain the actual damped and growing oscillations in the neutron number density, the channel inlet flow velocity, and the other phase variables. These indicate that the Hopf bifurcation is subcritical, hence, density wave oscillations with growing amplitude could result from a finite perturbation of the system even where the steady-state is stable. The power-flow map, frequently used by reactor operators during start-up and shut-down operation of a BWR, is mapped to the inlet-subcooling-number/neutron-density (operating-parameter/phase-variable) plane, and then related to the stability boundaries for different fixed inlet velocities corresponding to selected points on the flow-control line. The stability boundaries for different fixed inlet subcooling numbers corresponding to those selected points, are plotted in the neutron-density/inlet-velocity phase variable plane and then the points on the flow-control line are related to their respective stability boundaries in this plane.« less

  10. PeTTSy: a computational tool for perturbation analysis of complex systems biology models.

    PubMed

    Domijan, Mirela; Brown, Paul E; Shulgin, Boris V; Rand, David A

    2016-03-10

    Over the last decade sensitivity analysis techniques have been shown to be very useful to analyse complex and high dimensional Systems Biology models. However, many of the currently available toolboxes have either used parameter sampling, been focused on a restricted set of model observables of interest, studied optimisation of a objective function, or have not dealt with multiple simultaneous model parameter changes where the changes can be permanent or temporary. Here we introduce our new, freely downloadable toolbox, PeTTSy (Perturbation Theory Toolbox for Systems). PeTTSy is a package for MATLAB which implements a wide array of techniques for the perturbation theory and sensitivity analysis of large and complex ordinary differential equation (ODE) based models. PeTTSy is a comprehensive modelling framework that introduces a number of new approaches and that fully addresses analysis of oscillatory systems. It examines sensitivity analysis of the models to perturbations of parameters, where the perturbation timing, strength, length and overall shape can be controlled by the user. This can be done in a system-global setting, namely, the user can determine how many parameters to perturb, by how much and for how long. PeTTSy also offers the user the ability to explore the effect of the parameter perturbations on many different types of outputs: period, phase (timing of peak) and model solutions. PeTTSy can be employed on a wide range of mathematical models including free-running and forced oscillators and signalling systems. To enable experimental optimisation using the Fisher Information Matrix it efficiently allows one to combine multiple variants of a model (i.e. a model with multiple experimental conditions) in order to determine the value of new experiments. It is especially useful in the analysis of large and complex models involving many variables and parameters. PeTTSy is a comprehensive tool for analysing large and complex models of regulatory and signalling systems. It allows for simulation and analysis of models under a variety of environmental conditions and for experimental optimisation of complex combined experiments. With its unique set of tools it makes a valuable addition to the current library of sensitivity analysis toolboxes. We believe that this software will be of great use to the wider biological, systems biology and modelling communities.

  11. Ghost-Free APT Analysis of Perturbative QCD Observables

    NASA Astrophysics Data System (ADS)

    Shirkov, Dmitry V.

    The review of the essence and of application of recently devised ghost-free Analytic Perturbation Theory (APT) is presented. First, we discuss the main intrinsic problem of perturbative QCD - ghost singularities and with the resume of its resolving within the APT. By examples for diverse energy and momentum transfer values we show the property of better convergence for the APT modified QCD expansion. It is shown that in the APT analysis the three-loop contribution (sim alpha_s^3) is numerically inessential. This gives raise a hope for practical solution of the well-known problem of non-satisfactory convergence of QFT perturbation series due to its asymptotic nature. Our next result is that a usual perturbative analysis of time-like events is not adequate at sleq 2 GeV2. In particular, this relates to tau decay. Then, for the "high" (f=5) region it is shown that the common NLO, NLLA perturbation approximation widely used there (at 10 GeV lesssimsqrt{s}lesssim 170 GeV) yields a systematic theoretic negative error of a couple per cent level for the bar {alpha}_s^2 values. This results in a conclusion that the bar α_s(M^2_Z) value averaged over the f=5 data appreciably differs < bar {alpha}_s(M^2_Z)rangle_{f=5} simeq 0.124 from the currently popular "world average" (=0.118 ).

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

    Bukh, Boris; Lund, Steven M.

    We present an analysis of envelope perturbations evolving in the limit of a fully space-charge depressed (zero emittance) beam in periodic, thin-lens focusing channels. Both periodic solenoidal and FODO quadrupole focusing channels are analyzed. The phase advance and growth rate of normal mode perturbations are analytically calculated as a function of the undepressed particle phase advance to characterize the evolution of envelope perturbations.

  13. Simple and accurate sum rules for highly relativistic systems

    NASA Astrophysics Data System (ADS)

    Cohen, Scott M.

    2005-03-01

    In this paper, I consider the Bethe and Thomas-Reiche-Kuhn sum rules, which together form the foundation of Bethe's theory of energy loss from fast charged particles to matter. For nonrelativistic target systems, the use of closure leads directly to simple expressions for these quantities. In the case of relativistic systems, on the other hand, the calculation of sum rules is fraught with difficulties. Various perturbative approaches have been used over the years to obtain relativistic corrections, but these methods fail badly when the system in question is very strongly bound. Here, I present an approach that leads to relatively simple expressions yielding accurate sums, even for highly relativistic many-electron systems. I also offer an explanation for the difference between relativistic and nonrelativistic sum rules in terms of the Zitterbewegung of the electrons.

  14. Some finite terms from ladder diagrams in three and four loop maximal supergravity

    NASA Astrophysics Data System (ADS)

    Basu, Anirban

    2015-10-01

    We consider the finite part of the leading local interactions in the low energy expansion of the four graviton amplitude from the ladder skeleton diagrams in maximal supergravity on T 2, at three and four loops. At three loops, we express the {D}8{{R}}4 and {D}10{{R}}4 amplitudes as integrals over the moduli space of an underlying auxiliary geometry. These amplitudes are evaluated exactly for special values of the the moduli of the auxiliary geometry, where the integrand simplifies. We also perform a similar analysis for the {D}8{{R}}4 amplitude at four loops that arise from the ladder skeleton diagrams for a special value of a parameter in the moduli space of the auxiliary geometry. While the dependence of the amplitudes on the volume of the T 2 is very simple, the dependence on the complex structure of the T 2 is quite intricate. In some of the cases, the amplitude consists of terms each of which factorizes into a product of two {SL}(2,{{Z}}) invariant modular forms. While one of the factors is a non-holomorphic Eisenstein series, the other factor splits into a sum of modular forms each of which satisfies a Poisson equation on moduli space with source terms that are bilinear in the Eisenstein series. This leads to several possible perturbative contributions unto genus 5 in type II string theory on S1. Unlike the one and two loop supergravity analysis, these amplitudes also receive non-perturbative contributions from bound states of three D-(anti)instantons in the IIB theory.

  15. Torsional Splitting in the Degenerate Vibrational States of (70)Ge(2)H(6): Rotation-Torsion Analysis of the nu(7) and nu(9) Fundamentals.

    PubMed

    Lattanzi; di Lauro C; Bürger; Mkadmi

    2000-09-01

    The rotational and torsional structure of the nu(7) and nu(9) degenerate fundamentals of (70)Ge(2)H(6) has been analyzed under high resolution. The torsional structure of both v(7) = 1 and v(9) = 1 states can be fitted by a simple one-parameter formula. The x,y-Coriolis interaction with the parallel nu(5) fundamental was accounted for in the analysis of nu(7). A strong perturbation of the J structure of the E(3s) torsional component of the KDeltaK = -2 subbranches of nu(9) can be explained by the resonance with an E(3s) excited level of the pure torsional manifold. The perturber is centered at 361.58 cm(-1), very close to the value estimated with a barrier height of 285 cm(-1). This confirms that the fundamental torsional wavenumber is close to 103 cm(-1), in good agreement with the "ab initio" prediction. The torsional splittings of all the infrared active degenerate fundamentals, nu(7), nu(8), and nu(9), follow the trend predicted by theory, and have been fitted by exploratory calculations accounting only for the torsional Coriolis-coupling mechanism of all degenerate vibrational fundamentals in several torsional states. This confirms that torsional Coriolis coupling is the dominant mechanism responsible for the decrease of the torsional splitting in the degenerate vibrational states. A higher value of the barrier had to be used for the nu(9) mode. Copyright 2000 Academic Press.

  16. Characterizing species interactions to understand press perturbations: What is the community matrix?

    USGS Publications Warehouse

    Novak, Mark; Yeakel, Justin D.; Noble, Andrew E.; Doak, Daniel F.; Emmerson, Mark; Estes, James A.; Jacob, Ute; Tinker, M. Tim; Wootton, J. Timothy

    2016-01-01

    The community matrix is among ecology's most important mathematical abstractions, formally encapsulating the interconnected network of effects that species have on one another's populations. Despite its importance, the term `community matrix' has been applied to matrices having differing interpretations. This has hindered the application of theory for understanding community structure and perturbation responses, particularly in the contexts of ecosystem-based management and conservation. Here we clarify the correspondence and distinctions between the Interaction matrix, the Alpha matrix and the Jacobian matrix, terms which are frequently used interchangeably and have numerous synonyms, including the term Community matrix. We illustrate how these matrices correspond to different ways of characterizing interaction strengths, how they permit insights regarding different types of press perturbations of species growth rates or abundances, and how these are related by a simple scaling relationship. Connections to additional interaction strength characterizations encapsulated by the Beta matrix, the Gamma matrix, and the Removal matrix are also discussed. Our synthesis highlights the empirical challenges that remain in using these mathematical tools to understand actual communities.

  17. Infrared emission and tidal interactions of spiral galaxies

    NASA Technical Reports Server (NTRS)

    Byrd, Gene G.

    1987-01-01

    Computer simulations of tidal interactions of spiral galaxies are used to attempt to understand recent discoveries about infrared (IR) emitting galaxies. It is found that the stronger tidal perturbation by a companion the more disk gas clouds are thrown into nucleus crossing orbits and the greater the velocity jumps crossing spiral arms. Both these tidally created characteristics would create more IR emission by high speed cloud collisions and more IR via effects of recently formed stars. This expectation at greater tidal perturbation matches the observation of greater IR emission for spiral galaxies with closer and/or more massive companions. The greater collision velocities found at stronger perturbations on the models will also result in higher dust temperature in the colliding clouds. In the IR pairs examined, most have only one member, the larger, detected and when both are detected, the larger is always the more luminous. In simulations and in a simple analytic description of the strong distance dependence of the tidal force, it is found that the big galaxy of a pair is more strongly affected than the small.

  18. Renormalizing a viscous fluid model for large scale structure formation

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

    Führer, Florian; Rigopoulos, Gerasimos, E-mail: fuhrer@thphys.uni-heidelberg.de, E-mail: gerasimos.rigopoulos@ncl.ac.uk

    2016-02-01

    Using the Stochastic Adhesion Model (SAM) as a simple toy model for cosmic structure formation, we study renormalization and the removal of the cutoff dependence from loop integrals in perturbative calculations. SAM shares the same symmetry with the full system of continuity+Euler equations and includes a viscosity term and a stochastic noise term, similar to the effective theories recently put forward to model CDM clustering. We show in this context that if the viscosity and noise terms are treated as perturbative corrections to the standard eulerian perturbation theory, they are necessarily non-local in time. To ensure Galilean Invariance higher ordermore » vertices related to the viscosity and the noise must then be added and we explicitly show at one-loop that these terms act as counter terms for vertex diagrams. The Ward Identities ensure that the non-local-in-time theory can be renormalized consistently. Another possibility is to include the viscosity in the linear propagator, resulting in exponential damping at high wavenumber. The resulting local-in-time theory is then renormalizable to one loop, requiring less free parameters for its renormalization.« less

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

    PubMed

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

    2015-07-01

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

  20. Local ion direction of motion and electron flow in a magnetically insulated diode

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

    Maron, Y.; Litwin, C.

    Ion motion in the acceleration region of a magnetically insulated ion diode and electron flux to the anode are studied locally. Two classes of slowly growing ion deflections are observed, indicating the presence of transverse electric fields in the diode gap. A simple model, which treates the diode as an emitting surface perturbed away from planarity, is offered to infer profiles of the electric field. These profiles are consistent with the observation that one of the ion-deflection classes is associated with a significant fraction of the increases of the electron flux to the anode. The inferred growth rates of themore » perturbations suggest that the observed ion deflections are caused by a nonuniform expansion of the anode plasma. The transverse electric fields associated with the perturbations constitute a significant (as much as 20%) fraction of the diode accelerating field. Short duration ion deflections accompanied by intense electron bursts to the anode are also observed. The data suggest that these deflections and the electron bursts originate at processes in the cathode plasma.« less

  1. Effect of Random Circuit Fabrication Errors on Small Signal Gain and Phase in Helix Traveling Wave Tubes

    NASA Astrophysics Data System (ADS)

    Pengvanich, P.; Chernin, D. P.; Lau, Y. Y.; Luginsland, J. W.; Gilgenbach, R. M.

    2007-11-01

    Motivated by the current interest in mm-wave and THz sources, which use miniature, difficult-to-fabricate circuit components, we evaluate the statistical effects of random fabrication errors on a helix traveling wave tube amplifier's small signal characteristics. The small signal theory is treated in a continuum model in which the electron beam is assumed to be monoenergetic, and axially symmetric about the helix axis. Perturbations that vary randomly along the beam axis are introduced in the dimensionless Pierce parameters b, the beam-wave velocity mismatch, C, the gain parameter, and d, the cold tube circuit loss. Our study shows, as expected, that perturbation in b dominates the other two. The extensive numerical data have been confirmed by our analytic theory. They show in particular that the standard deviation of the output phase is linearly proportional to standard deviation of the individual perturbations in b, C, and d. Simple formulas have been derived which yield the output phase variations in terms of the statistical random manufacturing errors. This work was supported by AFOSR and by ONR.

  2. The influence of super-horizon scales on cosmological observables generated during inflation

    NASA Astrophysics Data System (ADS)

    Matarrese, Sabino; Musso, Marcello A.; Riotto, Antonio

    2004-05-01

    Using the techniques of out-of-equilibrium field theory, we study the influence on properties of cosmological perturbations generated during inflation on observable scales coming from fluctuations corresponding today to scales much bigger than the present Hubble radius. We write the effective action for the coarse grained inflaton perturbations, integrating out the sub-horizon modes, which manifest themselves as a coloured noise and lead to memory effects. Using the simple model of a scalar field with cubic self-interactions evolving in a fixed de Sitter background, we evaluate the two- and three-point correlation function on observable scales. Our basic procedure shows that perturbations do preserve some memory of the super-horizon scale dynamics, in the form of scale dependent imprints in the statistical moments. In particular, we find a blue tilt of the power spectrum on large scales, in agreement with the recent results of the WMAP collaboration which show a suppression of the lower multipoles in the cosmic microwave background anisotropies, and a substantial enhancement of the intrinsic non-Gaussianity on large scales.

  3. From data towards knowledge: revealing the architecture of signaling systems by unifying knowledge mining and data mining of systematic perturbation data.

    PubMed

    Lu, Songjian; Jin, Bo; Cowart, L Ashley; Lu, Xinghua

    2013-01-01

    Genetic and pharmacological perturbation experiments, such as deleting a gene and monitoring gene expression responses, are powerful tools for studying cellular signal transduction pathways. However, it remains a challenge to automatically derive knowledge of a cellular signaling system at a conceptual level from systematic perturbation-response data. In this study, we explored a framework that unifies knowledge mining and data mining towards the goal. The framework consists of the following automated processes: 1) applying an ontology-driven knowledge mining approach to identify functional modules among the genes responding to a perturbation in order to reveal potential signals affected by the perturbation; 2) applying a graph-based data mining approach to search for perturbations that affect a common signal; and 3) revealing the architecture of a signaling system by organizing signaling units into a hierarchy based on their relationships. Applying this framework to a compendium of yeast perturbation-response data, we have successfully recovered many well-known signal transduction pathways; in addition, our analysis has led to many new hypotheses regarding the yeast signal transduction system; finally, our analysis automatically organized perturbed genes as a graph reflecting the architecture of the yeast signaling system. Importantly, this framework transformed molecular findings from a gene level to a conceptual level, which can be readily translated into computable knowledge in the form of rules regarding the yeast signaling system, such as "if genes involved in the MAPK signaling are perturbed, genes involved in pheromone responses will be differentially expressed."

  4. The link between tidal interaction and nuclear activity in galaxies

    NASA Technical Reports Server (NTRS)

    Lin, D. N. C.; Pringle, J. E.; Rees, M. J.

    1988-01-01

    It is considered how nuclear activity in galaxies may be induced by the tidal perturbation of companion galaxies. It is suggested that if the central regions of the galaxies contain marginally self-gravitating disks of gas, trailing spiral density waves, triggered by nonaxisymmetric gravitational instability, lead to efficient angular momentum transport. If the net effect of the external perturbation is to increase the effect of self-gravity in the gas, then the result is to induce a considerable increase in the mass accretion rate into the central region on a relatively short time scale. With a simple prescription, the evolution of self-gravitating accretion disks is examined in this context. These results are discussed in the context of the frequent occurrence of nuclear activity in interacting galaxies.

  5. Hierarchically Superstructured Metal Sulfides: Facile Perturbation-Assisted Nanofusion Synthesis and Visible Light Photocatalytic Characterizations

    DOE PAGES

    Yue, Yanfeng; Li, Yunchao; Bridges, Craig A.; ...

    2016-11-29

    A novel and simple perturbation-assisted nanofusion (PNF) synthetic strategy was developed for the fabrication of stable hierarchically superstructured metal sulfides. This promising approach, based on a kinetically controlled precipitation to simultaneously condense and re-dissolve polymorphic nanocrystallites, provides the resultant samples with a unique mesoporous framework. This PNF approach is environmentally friendly, produces gram-scale products in a matter of hours, and is complimentary to traditional hard or soft templating methods for the construction of mesoporous metal sulfides. PNF derived hierarchical porous CdS exhibited a vastly improved photocatalytic performance over its commercial bulk counterpart under visible light irradiation, demonstrating the advantage ofmore » the porous morphology for photocatalysis resulting from the enlarged surface area and the easy accessibility of the mesopores.« less

  6. Optimal control of singularly perturbed nonlinear systems with state-variable inequality constraints

    NASA Technical Reports Server (NTRS)

    Calise, A. J.; Corban, J. E.

    1990-01-01

    The established necessary conditions for optimality in nonlinear control problems that involve state-variable inequality constraints are applied to a class of singularly perturbed systems. The distinguishing feature of this class of two-time-scale systems is a transformation of the state-variable inequality constraint, present in the full order problem, to a constraint involving states and controls in the reduced problem. It is shown that, when a state constraint is active in the reduced problem, the boundary layer problem can be of finite time in the stretched time variable. Thus, the usual requirement for asymptotic stability of the boundary layer system is not applicable, and cannot be used to construct approximate boundary layer solutions. Several alternative solution methods are explored and illustrated with simple examples.

  7. Linear analysis of the Richtmyer-Meshkov instability in shock-flame interactions

    NASA Astrophysics Data System (ADS)

    Massa, L.; Jha, P.

    2012-05-01

    Shock-flame interactions enhance supersonic mixing and detonation formation. Therefore, their analysis is important to explosion safety, internal combustion engine performance, and supersonic combustor design. The fundamental process at the basis of the interaction is the Richtmyer-Meshkov instability supported by the density difference between burnt and fresh mixtures. In the present study we analyze the effect of reactivity on the Richtmyer-Meshkov instability with particular emphasis on combustion lengths that typify the scaling between perturbation growth and induction. The results of the present linear analysis study show that reactivity changes the perturbation growth rate by developing a pressure gradient at the flame surface. The baroclinic torque based on the density gradient across the flame acts to slow down the instability growth of high wave-number perturbations. A gasdynamic flame representation leads to the definition of a Peclet number representing the scaling between perturbation and thermal diffusion lengths within the flame. Peclet number effects on perturbation growth are observed to be marginal. The gasdynamic model also considers a finite flame Mach number that supports a separation between flame and contact discontinuity. Such a separation destabilizes the interface growth by augmenting the tangential shear.

  8. Destruction of Invariant Surfaces and Magnetic Coordinates for Perturbed Magnetic Fields

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

    S.R. Hudson

    2003-11-20

    Straight-field-line coordinates are constructed for nearly integrable magnetic fields. The coordinates are based on the robust, noble-irrational rotational-transform surfaces, whose existence is determined by an application of Greene's residue criterion. A simple method to locate these surfaces is described. Sequences of surfaces with rotational-transform converging to low order rationals maximize the region of straight-field-line coordinates.

  9. Thermodynamics of Thomas-Fermi screened Coulomb systems

    NASA Technical Reports Server (NTRS)

    Firey, B.; Ashcroft, N. W.

    1977-01-01

    We obtain in closed analytic form, estimates for the thermodynamic properties of classical fluids with pair potentials of Yukawa type, with special reference to dense fully ionized plasmas with Thomas-Fermi or Debye-Hueckel screening. We further generalize the hard-sphere perturbative approach used for similarly screened two-component mixtures, and demonstrate phase separation in this simple model of a liquid mixture of metallic helium and hydrogen.

  10. 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.

  11. 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.

  12. An Examination of Environment Perturbation Effects on Single Event Upset Rates

    NASA Technical Reports Server (NTRS)

    Gates, Michele M.; Leidecker, Henning W.; Lewis, Mark J.

    1997-01-01

    This paper presents an analysis of the sensitivity of single event upset (SEU) rate predictions to changes in the direct ionization-inducing environment. An examination based on the nature of the SEU rate equation is presented for the case in which the perturbation is constant across varying particle linear energy transfer (LET). It is shown that the relative variation in SEU rate is equal to the relative perturbation in flux. Results are also presented for the case in which the environment perturbations exist in small LET bins. Through this analysis it is shown that the relative variation in expected SEU rate is equal to that in flux only for the LET regime in which the product of the cross section and differential flux is maximum.

  13. A perturbation approach for assessing trends in precipitation extremes across Iran

    NASA Astrophysics Data System (ADS)

    Tabari, Hossein; AghaKouchak, Amir; Willems, Patrick

    2014-11-01

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

  14. Notes on hyperscaling violating Lifshitz and shear diffusion

    NASA Astrophysics Data System (ADS)

    Kolekar, Kedar S.; Mukherjee, Debangshu; Narayan, K.

    2017-07-01

    We explore in greater detail our investigations of shear diffusion in hyperscaling violating Lifshitz theories in Phys. Lett. B 760, 86 (2016), 10.1016/j.physletb.2016.06.046. This adapts and generalizes the membrane-paradigm-like analysis of Kovtun, Son, and Starinets for shear gravitational perturbations in the near horizon region given certain self-consistent approximations, leading to the shear diffusion constant on an appropriately defined stretched horizon. In theories containing a gauge field, some of the metric perturbations mix with some of the gauge field perturbations and the above analysis is somewhat more complicated. We find a similar near-horizon analysis can be obtained in terms of new field variables involving a linear combination of the metric and the gauge field perturbation resulting in a corresponding diffusion equation. Thereby as before, for theories with Lifshitz and hyperscaling violating exponents z , θ satisfying z <4 -θ in four bulk dimensions, our analysis here results in a similar expression for the shear diffusion constant with power-law scaling with temperature suggesting universal behavior in relation to the viscosity bound. For z =4 -θ , we find logarithmic behavior.

  15. Modification of response functions of cat visual cortical cells by spatially congruent perturbing stimuli.

    PubMed

    Kabara, J F; Bonds, A B

    2001-12-01

    Responses of cat striate cortical cells to a drifting sinusoidal grating were modified by the superimposition of a second, perturbing grating (PG) that did not excite the cell when presented alone. One consequence of the presence of a PG was a shift in the tuning curves. The orientation tuning of all 41 cells exposed to a PG and the spatial frequency tuning of 83% of the 23 cells exposed to a PG showed statistically significant dislocations of both the response function peak and center of mass from their single grating values. As found in earlier reports, the presence of PGs suppressed responsiveness. However, reductions measured at the single grating optimum orientation or spatial frequency were on average 1.3 times greater than the suppression found at the peak of the response function modified by the presence of the PG. Much of the loss in response seen at the single grating optimum is thus a result of a shift in the tuning function rather than outright suppression. On average orientation shifts were repulsive and proportional (approximately 0.10 deg/deg) to the angle between the perturbing stimulus and the optimum single grating orientation. Shifts in the spatial frequency response function were both attractive and repulsive, resulting in an overall average of zero. For both simple and complex cells, PGs generally broadened orientation response function bandwidths. Similarly, complex cell spatial frequency response function bandwidths broadened. Simple cell spatial frequency response functions usually did not change, and those that did broadened only 4% on average. These data support the hypothesis that additional sinusoidal components in compound stimuli retune cells' response functions for orientation and spatial frequency.

  16. Examination of multi-model ensemble seasonal prediction methods using a simple climate system

    NASA Astrophysics Data System (ADS)

    Kang, In-Sik; Yoo, Jin Ho

    2006-02-01

    A simple climate model was designed as a proxy for the real climate system, and a number of prediction models were generated by slightly perturbing the physical parameters of the simple model. A set of long (240 years) historical hindcast predictions were performed with various prediction models, which are used to examine various issues of multi-model ensemble seasonal prediction, such as the best ways of blending multi-models and the selection of models. Based on these results, we suggest a feasible way of maximizing the benefit of using multi models in seasonal prediction. In particular, three types of multi-model ensemble prediction systems, i.e., the simple composite, superensemble, and the composite after statistically correcting individual predictions (corrected composite), are examined and compared to each other. The superensemble has more of an overfitting problem than the others, especially for the case of small training samples and/or weak external forcing, and the corrected composite produces the best prediction skill among the multi-model systems.

  17. Simultaneous determination of 13 carotenoids by a simple C18 column-based ultra-high-pressure liquid chromatography method for carotenoid profiling in the astaxanthin-accumulating Haematococcus pluvialis.

    PubMed

    Jin, Hui; Lao, Yong Min; Zhou, Jin; Zhang, Huai Jin; Cai, Zhong Hua

    2017-03-10

    A simple ultra-high-pressure liquid chromatography (UHPLC) method for rapidly and simultaneously identifying thirteen carotenoids in Haematococcus pluvialis was developed in this study. The method is capable of effectively separating two astaxanthin isomers, two ζ-carotene isomers, and three phytoene isomers on two simple C18 columns within 9 and 12min only by using methanol and acetonitrile, respectively. To our best knowledge, this is the rapidest method for these carotenoid isomers, currently. Using this method, carotenoid profiling in the astaxanthin-accumulating H. pluvialis under environmental stresses was successfully carried out. Results indicated that carotenoid biosynthesis was differentially perturbed by environmental stresses, indicating that this simple and rapid method is suitable to not only bacterial but also algal samples, with potential applications for a wide range of samples from plant to animal. Finally, possible reasons for the elution order of carotenoids were studied. Copyright © 2017 Elsevier B.V. All rights reserved.

  18. 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

  19. Numerical Analysis of Orbital Perturbation Effects on Inclined Geosynchronous SAR

    PubMed Central

    Dong, Xichao; Hu, Cheng; Long, Teng; Li, Yuanhao

    2016-01-01

    The geosynchronous synthetic aperture radar (GEO SAR) is susceptible to orbit perturbations, leading to orbit drifts and variations. The influences behave very differently from those in low Earth orbit (LEO) SAR. In this paper, the impacts of perturbations on GEO SAR orbital elements are modelled based on the perturbed dynamic equations, and then, the focusing is analyzed theoretically and numerically by using the Systems Tool Kit (STK) software. The accurate GEO SAR slant range histories can be calculated according to the perturbed orbit positions in STK. The perturbed slant range errors are mainly the first and second derivatives, leading to image drifts and defocusing. Simulations of the point target imaging are performed to validate the aforementioned analysis. In the GEO SAR with an inclination of 53° and an argument of perigee of 90°, the Doppler parameters and the integration time are different and dependent on the geometry configurations. Thus, the influences are varying at different orbit positions: at the equator, the first-order phase errors should be mainly considered; at the perigee and apogee, the second-order phase errors should be mainly considered; at other positions, first-order and second-order exist simultaneously. PMID:27598168

  20. Flexible, task-dependent use of sensory feedback to control hand movements

    PubMed Central

    Knill, David C.; Bondada, Amulya; Chhabra, Manu

    2011-01-01

    We tested whether changing accuracy demands for simple pointing movements leads humans to adjust the feedback control laws that map sensory signals from the moving hand to motor commands. Subjects made repeated pointing movements in a virtual environment to touch a button whose shape varied randomly from trial-to-trial – between squares, rectangles oriented perpendicular to the movement path and rectangles oriented parallel to the movement path. Subjects performed the task on a horizontal table, but saw the target configuration and a virtual rendering of their pointing finger through a mirror mounted between a monitor and the table. On a one-third of trials, the position of the virtual finger was perturbed by ±1 cm either in the movement direction or perpendicular to the movement direction when the finger passed behind an occluder. Subjects corrected quickly for the perturbations despite not consciously noticing them; however, they corrected almost twice as much for perturbations aligned with the narrow dimension of a target than for perturbations aligned with the long dimension. These changes in apparent feedback gain appeared in the kinematic trajectories soon after the time of the perturbations, indicating that they reflect differences in the feedback control law used throughout the duration of movements. The results indicate that the brain adjusts its feedback control law for individual movements “on-demand” to fit task demands. Simulations of optimal control laws for a two-joint arm show that accuracy demands alone, coupled with signal dependent noise lead to qualitatively the same behavior. PMID:21273407

  1. Perturbation and Nonlinear Dynamic Analysis of Different Singing Styles

    PubMed Central

    Butte, Caitlin J.; Zhang, Yu; Song, Huangqiang; Jiang, Jack J.

    2012-01-01

    Summary Previous research has used perturbation analysis methods to study the singing voice. Using perturbation and nonlinear dynamic analysis (NDA) methods in conjunction may provide more accurate information on the singing voice and may distinguish vocal usage in different styles. Acoustic samples from different styles of singing were compared using nonlinear dynamic and perturbation measures. Twenty-six songs from different musical styles were obtained from an online music database (Rhapsody, RealNetworks, Inc., Seattle, WA). One-second samples were selected from each song for analysis. Perturbation analyses of jitter, shimmer, and signal-to-noise ratio and NDA of correlation dimension (D2) were performed on samples from each singing style. Percent jitter and shimmer median values were low normal for country (0.32% and 3.82%), musical theater (MT) (0.280% and 2.80%), jazz (0.440% and 2.34%), and soul (0.430% and 6.42%). The popular style had slightly higher median jitter and shimmer values (1.13% and 6.78%) than other singing styles, although this was not statistically significant. The opera singing style had median jitter of 0.520%, and yielded significantly high shimmer (P = 0.001) of 7.72%. All six singing styles were measured reliably using NDA, indicating that operatic singing is notably more chaotic than other singing styles. Median correlation dimension values were low to normal, compared to healthy voices, in country (median D2 = 2.14), jazz (median D2 = 2.24), pop (median D2 = 2.60), MT (median D2 = 2.73), and soul (mean D2 = 3.26). Correlation dimension was significantly higher in opera (P < 0.001) with median D2 = 6.19. In this study, acoustic analysis in opera singing gave significantly high values for shimmer and D2, suggesting that it is more irregular than other singing styles; a previously unknown quality of opera singing. Perturbation analysis also suggested significant differences in vocal output in different singing styles. This preliminary study using acoustic analysis with nonlinear dynamic measures and perturbation measures may represent a valuable procedure in quantitatively describing the properties of the singing voice. Further research with human test subjects may allow us to characterize singing styles and diagnose vocal dysfunction in the singing voice. PMID:18504114

  2. Unsteady locomotion: integrating muscle function with whole body dynamics and neuromuscular control

    PubMed Central

    Biewener, Andrew A.; Daley, Monica A.

    2009-01-01

    Summary By integrating studies of muscle function with analysis of whole body and limb dynamics, broader appreciation of neuromuscular function can be achieved. Ultimately, such studies need to address non-steady locomotor behaviors relevant to animals in their natural environments. When animals move slowly they likely rely on voluntary coordination of movement involving higher brain centers. However, when moving fast, their movements depend more strongly on responses controlled at more local levels. Our focus here is on control of fast-running locomotion. A key observation emerging from studies of steady level locomotion is that simple spring-mass dynamics, which help to economize energy expenditure, also apply to stabilization of unsteady running. Spring-mass dynamics apply to conditions that involve lateral impulsive perturbations, sudden changes in terrain height, and sudden changes in substrate stiffness or damping. Experimental investigation of unsteady locomotion is challenging, however, due to the variability inherent in such behaviors. Another emerging principle is that initial conditions associated with postural changes following a perturbation define different context-dependent stabilization responses. Distinct stabilization modes following a perturbation likely result from proximo-distal differences in limb muscle architecture, function and control strategy. Proximal muscles may be less sensitive to sudden perturbations and appear to operate, in such circumstances, under feed-forward control. In contrast, multiarticular distal muscles operate, via their tendons, to distribute energy among limb joints in a manner that also depends on the initial conditions of limb contact with the ground. Intrinsic properties of these distal muscle–tendon elements, in combination with limb and body dynamics, appear to provide rapid initial stabilizing mechanisms that are often consistent with spring-mass dynamics. These intrinsic mechanisms likely help to simplify the neural control task, in addition to compensating for delays inherent to subsequent force- and length-dependent neural feedback. Future work will benefit from integrative biomechanical approaches that employ a combination of modeling and experimental techniques to understand how the elegant interplay of intrinsic muscle properties, body dynamics and neural control allows animals to achieve stability and agility over a variety of conditions. PMID:17704070

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

    PubMed

    Su, Jimmy Li-Shin; Dingwell, Jonathan B

    2007-12-01

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

  4. Can the second order multireference perturbation theory be considered a reliable tool to study mixed-valence compounds?

    PubMed

    Pastore, Mariachiara; Helal, Wissam; Evangelisti, Stefano; Leininger, Thierry; Malrieu, Jean-Paul; Maynau, Daniel; Angeli, Celestino; Cimiraglia, Renzo

    2008-05-07

    In this paper, the problem of the calculation of the electronic structure of mixed-valence compounds is addressed in the frame of multireference perturbation theory (MRPT). Using a simple mixed-valence compound (the 5,5(') (4H,4H('))-spirobi[ciclopenta[c]pyrrole] 2,2('),6,6(') tetrahydro cation), and the n-electron valence state perturbation theory (NEVPT2) and CASPT2 approaches, it is shown that the ground state (GS) energy curve presents an unphysical "well" for nuclear coordinates close to the symmetric case, where a maximum is expected. For NEVPT, the correct shape of the energy curve is retrieved by applying the MPRT at the (computationally expensive) third order. This behavior is rationalized using a simple model (the ionized GS of two weakly interacting identical systems, each neutral system being described by two electrons in two orbitals), showing that the unphysical well is due to the canonical orbital energies which at the symmetric (delocalized) conformation lead to a sudden modification of the denominators in the perturbation expansion. In this model, the bias introduced in the second order correction to the energy is almost entirely removed going to the third order. With the results of the model in mind, one can predict that all MRPT methods in which the zero order Hamiltonian is based on canonical orbital energies are prone to present unreasonable energy profiles close to the symmetric situation. However, the model allows a strategy to be devised which can give a correct behavior even at the second order, by simply averaging the orbital energies of the two charge-localized electronic states. Such a strategy is adopted in a NEVPT2 scheme obtaining a good agreement with the third order results based on the canonical orbital energies. The answer to the question reported in the title (is this theoretical approach a reliable tool for a correct description of these systems?) is therefore positive, but care must be exercised, either in defining the orbital energies or by resorting to the third order using for them the standard definition.

  5. Photoionization of N 2X ¹Σ g⁺, v"=0 and 1 near threshold. Preionization of the Worley–Jenkins Rydberg series.

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

    Dehmer, Patricia M.; Miller, P. J.; Chupka, W. A.

    The high resolution relative photoionization cross section for N 2 is reported in the wavelength region from the ionization threshold to 650 Â, with particular attention given to the region between the N₂⁺ X ²Σ g⁺, v'=0 and 1 ionization limits. Cross sections from both the X ¹Σ g⁺, v''=0 and 1 vibrational levels were determined in this region, and preionized members of the n ρπ u ¹Π u Worley–Jenkins Rydberg series converging to N₂⁺ X ²Σ g⁺, v' = 1 are observed in both spectra. In the spectrum excited from v'' = 1, the Worley–Jenkins series appears prominently asmore » a result of good Franck–Condon overlap between the N₂⁺ X ¹Σ g, v"=1 and the N₂⁺ X ²Σ g⁺, v'=1 levels; the intensities of the series members decrease approximately as 1/n³, in accord with simple theoretical predictions. However, in the spectrum excited from v''=0, the Worley–Jenkins series converging to N₂⁺ X ²Σ g⁺, v'=1 is weak as a result of a poor Franck–Condon overlap with the ground vibrational level; the intensities of the series members show large deviations from the simple theory as a result of channel interactions with Rydberg states converging to N₂ ⁺A ²Π u. These perturbing Rydberg states have low photoabsorptionoscillator strengths for excitation from v"=1 (in contrast to excitation from v"=0) and hence have only a small effect on the cross section from the excited vibrational level. Just as in the case of photoionization of H₂, the results demonstrate that channel interaction can redistribute the oscillator strength of a perturbing Rydberg state of low principal quantum number over a number of members of an interacting Rydberg series and that the spectral range affected by the perturber can be much greater than the width of the perturbing level.« less

  6. The Damping Rates of Embedded Oscillating Starless Cores

    NASA Astrophysics Data System (ADS)

    Broderick, Avery E.; Narayan, Ramesh; Keto, Eric; Lada, Charles J.

    2008-08-01

    In a previous paper we demonstrated that nonradial hydrodynamic oscillations of a thermally supported (Bonnor-Ebert) sphere embedded in a low-density, high-temperature medium persist for many periods. The predicted column density variations and molecular spectral line profiles are similar to those observed in the Bok globule B68, suggesting that the motions in some starless cores may be oscillating perturbations on a thermally supported equilibrium structure. Such oscillations can produce molecular line maps which mimic rotation, collapse, or expansion and, thus, could make determining the dynamical state from such observations alone difficult. However, while B68 is embedded in a very hot, low-density medium, many starless cores are not, having interior/exterior density contrasts closer to unity. In this paper we investigate the oscillation damping rate as a function of the exterior density. For concreteness we use the same interior model employed by Broderick et al., with varying models for the exterior gas. We also develop a simple analytical formalism, based on the linear perturbation analysis of the oscillations, which predicts the contribution to the damping rates due to the excitation of sound waves in the external medium. We find that the damping rate of oscillations on globules in dense molecular environments is always many periods, corresponding to hundreds of thousands of years and persisting over the inferred lifetimes of the globules.

  7. Refined elasticity sampling for Monte Carlo-based identification of stabilizing network patterns.

    PubMed

    Childs, Dorothee; Grimbs, Sergio; Selbig, Joachim

    2015-06-15

    Structural kinetic modelling (SKM) is a framework to analyse whether a metabolic steady state remains stable under perturbation, without requiring detailed knowledge about individual rate equations. It provides a representation of the system's Jacobian matrix that depends solely on the network structure, steady state measurements, and the elasticities at the steady state. For a measured steady state, stability criteria can be derived by generating a large number of SKMs with randomly sampled elasticities and evaluating the resulting Jacobian matrices. The elasticity space can be analysed statistically in order to detect network positions that contribute significantly to the perturbation response. Here, we extend this approach by examining the kinetic feasibility of the elasticity combinations created during Monte Carlo sampling. Using a set of small example systems, we show that the majority of sampled SKMs would yield negative kinetic parameters if they were translated back into kinetic models. To overcome this problem, a simple criterion is formulated that mitigates such infeasible models. After evaluating the small example pathways, the methodology was used to study two steady states of the neuronal TCA cycle and the intrinsic mechanisms responsible for their stability or instability. The findings of the statistical elasticity analysis confirm that several elasticities are jointly coordinated to control stability and that the main source for potential instabilities are mutations in the enzyme alpha-ketoglutarate dehydrogenase. © The Author 2015. Published by Oxford University Press.

  8. MULTICOMPONENT THEORY OF BUOYANCY INSTABILITIES IN ASTROPHYSICAL PLASMA OBJECTS: THE CASE OF MAGNETIC FIELD PERPENDICULAR TO GRAVITY

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

    Nekrasov, Anatoly K.; Shadmehri, Mohsen, E-mail: anatoli.nekrassov@t-online.d, E-mail: mshadmehri@thphys.nuim.i

    2010-12-01

    We develop a general theory of buoyancy instabilities in the electron-ion plasma with the electron heat flux based not upon magnetohydrodynamic (MHD) equations, but using a multicomponent plasma approach in which the momentum equation is solved for each species. We investigate the geometry in which the background magnetic field is perpendicular to the gravity and stratification. General expressions for the perturbed velocities are given without any simplifications. Collisions between electrons and ions are taken into account in the momentum equations in a general form, permitting us to consider both weakly and strongly collisional objects. However, the electron heat flux ismore » assumed to be directed along the magnetic field, which implies a weakly collisional case. Using simplifications justified for an investigation of buoyancy instabilities with electron thermal flux, we derive simple dispersion relations for both collisionless and collisional cases for arbitrary directions of the wave vector. Our dispersion relations considerably differ from that obtained in the MHD framework and conditions of instability are similar to Schwarzschild's criterion. This difference is connected with simplified assumptions used in the MHD analysis of buoyancy instabilities and with the role of the longitudinal electric field perturbation which is not captured by the ideal MHD equations. The results obtained can be applied to clusters of galaxies and other astrophysical objects.« less

  9. Some Results Relevant to Statistical Closures for Compressible Turbulence

    NASA Technical Reports Server (NTRS)

    Ristorcelli, J. R.

    1998-01-01

    For weakly compressible turbulent fluctuations there exists a small parameter, the square of the fluctuating Mach number, that allows an investigation using a perturbative treatment. The consequences of such a perturbative analysis in three different subject areas are described: 1) initial conditions in direct numerical simulations, 2) an explanation for the oscillations seen in the compressible pressure in the direct numerical simulations of homogeneous shear, and 3) for turbulence closures accounting for the compressibility of velocity fluctuations. Initial conditions consistent with small turbulent Mach number asymptotics are constructed. The importance of consistent initial conditions in the direct numerical simulation of compressible turbulence is dramatically illustrated: spurious oscillations associated with inconsistent initial conditions are avoided, and the fluctuating dilatational field is some two orders of magnitude smaller for a compressible isotropic turbulence. For the isotropic decay it is shown that the choice of initial conditions can change the scaling law for the compressible dissipation. A two-time expansion of the Navier-Stokes equations is used to distinguish compressible acoustic and compressible advective modes. A simple conceptual model for weakly compressible turbulence - a forced linear oscillator is described. It is shown that the evolution equations for the compressible portions of turbulence can be understood as a forced wave equation with refraction. Acoustic modes of the flow can be amplified by refraction and are able to manifest themselves in large fluctuations of the compressible pressure.

  10. Natural descriptions of motor behavior: examples from E. coli and C. elegans.

    NASA Astrophysics Data System (ADS)

    Ryu, William

    2007-03-01

    E. coli has a natural behavioral variable - the direction of rotation of its flagellar rotorary motor. Monitoring this one-dimensional behavioral response in reaction to chemical perturbation has been instrumental in the understanding of how E. coli performs chemotaxis at the genetic, physiological, and computational level. Here we apply this experimental strategy to the study of bacterial thermotaxis - a sensory mode that is less well understood. We investigate bacterial thermosensation by studying the motor response of single cells subjected to impulses of heat produced by an IR laser. A simple temperature dependent modification to an existing chemotaxis model can explain the observed temperature response. Higher organisms may have a more complicated behavioral response due to the simple fact that their motions have more degrees of freedom. Here we provide a principled analysis of motor behavior of such an organism -- the roundworm C. elegans. Using tracking video-microscopy we capture a worm's image and extract the skeleton of the shape as a head-to-tail ordered collection of tangent angles sampled along the curve. Applying principal components analysis we show that the space of shapes is remarkably low dimensional, with four dimensions accounting for > 95% of the shape variance. We also show that these dimensions align with behaviorally relevant states. As an application of this analysis we study the thermal response of worms stimulated by laser heating. Our quantitative description of C. elegans movement should prove useful in a wide variety of contexts, from the linking of motor output with neural circuitry to the genetic basis of adaptive behavior.

  11. Identification of authentic and adulterated Aquilariae Lignum Resinatum by Fourier transform infrared (FT-IR) spectroscopy and two-dimensional correlation analysis

    NASA Astrophysics Data System (ADS)

    Qu, Lei; Chen, Jian-bo; Zhou, Qun; Zhang, Gui-jun; Sun, Su-qin; Guo, Yi-zhen

    2016-11-01

    As a kind of expensive perfume and valuable herb, the commercial Aquilariae Lignum Resinatum (ALR) is often adulterated for economic motivations. In this research, Fourier transform infrared (FT-IR) spectroscopy and two-dimensional (2D) correlation analysis are employed to establish a simple and quick identification method for the authentic and adulterated ALR. In the conventional infrared spectra, the standard ALR has a strong peak at 1658 cm-1 referring to the conjugated carbonyl of resin, while this peak is absent in the adulterated samples. The position, intensity, and shape of the auto-peaks and cross-peaks of the authentic and adulterated ALR are much different in the synchronous 2D correlation spectra with thermal perturbation. In the range of 1700-1500 cm-1, the standard ALR has four obvious auto-peaks, while the strongest one is at 1659 cm-1. The adulterated sample w-1 has three obvious auto-peaks and the strongest one is at 1647 cm-1. The adulterated sample w-2 has three obvious auto-peaks and the strongest one is at 1519 cm-1. The adulterated sample w-3 has four obvious auto-peaks and the strongest one is at 1690 cm-1. The above auto-peaks confirm that the standard ALR contains a certain content of resin compounds, while the three counterfeits contain little or different resins. The results show the potential of FT-IR spectroscopy and 2D correlation analysis in the simple and quick identification of authentic and adulterated ALR.

  12. A simple miniature device for wireless stimulation of neural circuits in small behaving animals.

    PubMed

    Zhang, Yisi; Langford, Bruce; Kozhevnikov, Alexay

    2011-10-30

    The use of wireless neural stimulation devices offers significant advantages for neural stimulation experiments in behaving animals. We demonstrate a simple, low-cost and extremely lightweight wireless neural stimulation device which is made from off-the-shelf components. The device has low power consumption and does not require a high-power RF preamplifier. Neural stimulation can be carried out in either a voltage source mode or a current source mode. Using the device, we carry out wireless stimulation in the premotor brain area HVC of a songbird and demonstrate that such stimulation causes rapid perturbations of the acoustic structure of the song. Published by Elsevier B.V.

  13. Stochastic Ocean Eddy Perturbations in a Coupled General Circulation Model.

    NASA Astrophysics Data System (ADS)

    Howe, N.; Williams, P. D.; Gregory, J. M.; Smith, R. S.

    2014-12-01

    High-resolution ocean models, which are eddy permitting and resolving, require large computing resources to produce centuries worth of data. Also, some previous studies have suggested that increasing resolution does not necessarily solve the problem of unresolved scales, because it simply introduces a new set of unresolved scales. Applying stochastic parameterisations to ocean models is one solution that is expected to improve the representation of small-scale (eddy) effects without increasing run-time. Stochastic parameterisation has been shown to have an impact in atmosphere-only models and idealised ocean models, but has not previously been studied in ocean general circulation models. Here we apply simple stochastic perturbations to the ocean temperature and salinity tendencies in the low-resolution coupled climate model, FAMOUS. The stochastic perturbations are implemented according to T(t) = T(t-1) + (ΔT(t) + ξ(t)), where T is temperature or salinity, ΔT is the corresponding deterministic increment in one time step, and ξ(t) is Gaussian noise. We use high-resolution HiGEM data coarse-grained to the FAMOUS grid to provide information about the magnitude and spatio-temporal correlation structure of the noise to be added to the lower resolution model. Here we present results of adding white and red noise, showing the impacts of an additive stochastic perturbation on mean climate state and variability in an AOGCM.

  14. Generalized hydromechanical model for stomatal responses to hydraulic perturbations.

    PubMed

    Kwon, H W; Choi, M Y

    2014-01-07

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

  15. Integrated structural and optical modeling of the orbiting stellar interferometer

    NASA Astrophysics Data System (ADS)

    Shaklan, Stuart B.; Yu, Jeffrey W.; Briggs, Hugh C.

    1993-11-01

    The Integrated Modeling of Optical Systems (IMOS) Integration Workbench at JPL has been used to model the effects of structural perturbations on the optics in the proposed Orbiting Stellar Interferometer (OSI). OSI consists of 3 pairs of interferometers and delay lines attached to a 7.5 meter truss. They are interferometrically monitored from a separate boom by a laser metrology system. The spatially distributed nature of the science instrument calls for a high level of integration between the optics and support structure. Because OSI is designed to achieve micro-arcsecond astrometry, many of its alignment, stability, and knowledge tolerances are in the submicron regime. The spacecraft will be subject to vibrations caused by reaction wheels and on-board equipment, as well as thermal strain due to solar and terrestrial heating. These perturbations affect optical parameters such as optical path differences and beam co-parallelism which are critical to instrument performance. IMOS provides an environment that allows one to design and perturb the structure, attach optics to structural or non-structural nodes, trace rays, and analyze the impact of mechanical perturbations on optical performance. This tool makes it simple to change the structure and immediately see performance enhancement/degradation. We have employed IMOS to analyze the effect of reaction wheel disturbances on the optical path difference in both the science and metrology interferometers.

  16. Phosphoenolpyruvate Transporter Enables Targeted Perturbation During Metabolic Analysis of L-Phenylalanine Production With Escherichia coli.

    PubMed

    Tröndle, Julia; Albermann, Christoph; Weiner, Michael; Sprenger, Georg A; Weuster-Botz, Dirk

    2018-05-01

    Usually perturbation of the metabolism of cells by addition of substrates is applied for metabolic analysis of production organisms, but perturbation studies are restricted to the endogenous substrates of the cells under study. The goal of this study is to overcome this limitation by making phosphoenolpyruvate (PEP) available for perturbation studies with Escherichia coli producing L-phenylalanine. A production strain overexpressing a PEP-transporter variant (UhpT-D388C) is applied in a standardized fed-batch production-process on a 42 L-scale. Four parallel short-term perturbation experiments of 20 min are performed with glucose and glycerol as fed-batch carbon sources after rapid media transition of cells from the production-process. PEP is added after 9 min and is immediately consumed by the cells with up to 1.5 mmol g CDW -1  h -1 . L-phenylalanine production rates increased by up to 200% after addition of PEP. This clearly indicates an intracellular PEP-limitation in the L-phenylalanine production strain under study. Thus, it is shown that overexpressing specific transporters for analytical reasons makes exogenous substrates available as perturbation substrates for metabolic analyses of cells sampled from production-processes and thereby allows a very targeted perturbation of whole-cell metabolism. © 2017 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

  17. Constrained Perturbation Regularization Approach for Signal Estimation Using Random Matrix Theory

    NASA Astrophysics Data System (ADS)

    Suliman, Mohamed; Ballal, Tarig; Kammoun, Abla; Al-Naffouri, Tareq Y.

    2016-12-01

    In this supplementary appendix we provide proofs and additional extensive simulations that complement the analysis of the main paper (constrained perturbation regularization approach for signal estimation using random matrix theory).

  18. Rapid distortion analysis of high speed homogeneous turbulence subject to periodic shear

    DOE PAGES

    Bertsch, Rebecca L.; Girimaji, Sharath S.

    2015-12-30

    The effect of unsteady shear forcing on small perturbation growth in compressible flow is investigated. In particular, flow-thermodynamic field interaction and the resulting effect on the phase-lag between applied shear and Reynolds stress are examined. Simplified linear analysis of the perturbation pressure equation reveals crucial differences between steady and unsteady shear effects. The analytical findings are validated with numerical simulations of inviscid rapid distortion theory (RDT) equations. In contrast to steadily sheared compressible flows, perturbations in the unsteady (periodic) forcing case do not experience an asymptotic growth phase. Further, the resonance growth phenomenon found in incompressible unsteady shear turbulence ismore » absent in the compressible case. Overall, the stabilizing influence of both unsteadiness and compressibility is compounded leading to suppression of all small perturbations. As a result, the underlying mechanisms are explained.« less

  19. Rapid distortion analysis of high speed homogeneous turbulence subject to periodic shear

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

    Bertsch, Rebecca L., E-mail: rlb@lanl.gov; Girimaji, Sharath S., E-mail: girimaji@aero.tamu.edu

    2015-12-15

    The effect of unsteady shear forcing on small perturbation growth in compressible flow is investigated. In particular, flow-thermodynamic field interaction and the resulting effect on the phase-lag between applied shear and Reynolds stress are examined. Simplified linear analysis of the perturbation pressure equation reveals crucial differences between steady and unsteady shear effects. The analytical findings are validated with numerical simulations of inviscid rapid distortion theory (RDT) equations. In contrast to steadily sheared compressible flows, perturbations in the unsteady (periodic) forcing case do not experience an asymptotic growth phase. Further, the resonance growth phenomenon found in incompressible unsteady shear turbulence ismore » absent in the compressible case. Overall, the stabilizing influence of both unsteadiness and compressibility is compounded leading to suppression of all small perturbations. The underlying mechanisms are explained.« less

  20. Stress fluctuations in fracture networks from theoretical and numerical models

    NASA Astrophysics Data System (ADS)

    Davy, P.; Darcel, C.; Mas Ivars, D.; Le Goc, R.

    2017-12-01

    We analyze the spatial fluctuations of stress in a simple tridimensional model constituted by a population of disc-shaped fractures embedded in an elastic matrix with uniform and isotropic properties. The fluctuations arise from the classical stress enhancement at fracture tips and stress shadowing around fracture centers that are amplified or decreased by the interactions between close-by fractures. The distribution of local stresses is calculated at the elementary mesh scale with the 3DEC numerical program based on the distinct element method. As expected, the stress distributions vary with fracture density, the larger is the density, the wider is the distribution. For freely slipping fractures, it is mainly controlled by the percolation parameter p (i.e., the total volume of spheres surrounding fractures). For stresses smaller than the remote deviatoric stress, the distribution depends only on for the range of density that has been studied. For large stresses, the distribution decreases exponentially when increasing stress, with a characteristic stress that increases with entailing a widening of the stress distribution. We extend the analysis to fractures with plane resistance defined by an elastic shear stiffness ks and a slip Coulomb threshold. A consequence of the fracture plane resistance is to lower the stress perturbation in the surrounding matrix by a factor that depends on the ratio between ks and a fracture-matrix stiffness km mainly dependent on the ratio between Young modulus and fracture size. km is also the ratio between the remote shear stress and the displacement across the fracture plane in the case of freely slipping fractures. A complete analytical derivation of the expressions of the stress perturbations and of the fracture displacements is obtained and checked with numerical simulations. In the limit ks >> km, the stress perturbation tends to 0 and the stress state is spatially uniform. The analysis allows us to quantify the intensity of the stress fluctuations in fractured rocks as a function of both the fracture network characteristics (density and size distribution), and the mechanical properties (fracture shear stiffness vs matrix elastic properties).

  1. A laboratory experiment simulating the dynamics of topographic relief: methodology and results

    NASA Astrophysics Data System (ADS)

    Crave, A.; Lague, D.; Davy, P.; Bonnet, S.; Laguionie, P.

    2002-12-01

    Theoretical analysis and numerical models of landscape evolution have advanced several scenarios for the long-term evolution of terrestrial topography. These scenarios require quantitative evaluation. Analyses of topography, sediment fluxes, and the physical mechanisms of erosion and sediment transport can provide some constraints on the range of plausible models. But in natural systems the boundary conditions (tectonic uplift, climate, base level) are often not well constrained and the spatial heterogeneity of substrate, climate, vegetation, and prevalent processes commonly confounds attempts at extrapolation of observations to longer timescales. In the laboratory, boundary conditions are known and heterogeneity and complexity can be controlled. An experimental approach can thus provide valuable constraints on the dynamics of geomorphic systems, provided that (1) the elementary processes are well calibrated and (2) the topography and sediment fluxes are sufficiently well documented. We have built an experimental setup of decimeter scale that is designed to develop a complete drainage network by the growth and propagation of erosion instabilities in response to tectonic and climatic perturbations. Uplift and precipitation rates can be changed over an order of magnitude. Telemetric lasers and 3D stereo-photography allow the precise quantification of the topographic evolution of the experimental surface. In order to calibrate the principal processes of erosion and transport we have used three approaches: (1) theoretical derivation of erosion laws deduced from the geometrical properties of experimental surfaces at steady-state under different rates of tectonic uplift; (2) comparison of the experimental transient dynamics with a numerical simulation model to test the validity of the predicted erosion laws; and (3) detailed analysis of particle detachment and transport in a millimeter sheet flow on a two-meter long flume under precisely controlled water discharge, slope and flow width. The analogy with real geomorphic systems is limited by the imperfect downscaling in both time and space of the experiments. However, these simple experiments have allowed us to probe (1) the importance of a threshold for particle mobilization to the relationship between steady-state elevation and uplift rate, (2) the role of initial drainage network organization in the transient dynamics of tectonically perturbed systems and (3) the sediment flux dynamics of climatically perturbed systems.

  2. Perturbing Hele-Shaw flow with a small gap gradient

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

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

    1992-02-15

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

  3. Compression-based distance (CBD): a simple, rapid, and accurate method for microbiota composition comparison

    PubMed Central

    2013-01-01

    Background Perturbations in intestinal microbiota composition have been associated with a variety of gastrointestinal tract-related diseases. The alleviation of symptoms has been achieved using treatments that alter the gastrointestinal tract microbiota toward that of healthy individuals. Identifying differences in microbiota composition through the use of 16S rRNA gene hypervariable tag sequencing has profound health implications. Current computational methods for comparing microbial communities are usually based on multiple alignments and phylogenetic inference, making them time consuming and requiring exceptional expertise and computational resources. As sequencing data rapidly grows in size, simpler analysis methods are needed to meet the growing computational burdens of microbiota comparisons. Thus, we have developed a simple, rapid, and accurate method, independent of multiple alignments and phylogenetic inference, to support microbiota comparisons. Results We create a metric, called compression-based distance (CBD) for quantifying the degree of similarity between microbial communities. CBD uses the repetitive nature of hypervariable tag datasets and well-established compression algorithms to approximate the total information shared between two datasets. Three published microbiota datasets were used as test cases for CBD as an applicable tool. Our study revealed that CBD recaptured 100% of the statistically significant conclusions reported in the previous studies, while achieving a decrease in computational time required when compared to similar tools without expert user intervention. Conclusion CBD provides a simple, rapid, and accurate method for assessing distances between gastrointestinal tract microbiota 16S hypervariable tag datasets. PMID:23617892

  4. Compression-based distance (CBD): a simple, rapid, and accurate method for microbiota composition comparison.

    PubMed

    Yang, Fang; Chia, Nicholas; White, Bryan A; Schook, Lawrence B

    2013-04-23

    Perturbations in intestinal microbiota composition have been associated with a variety of gastrointestinal tract-related diseases. The alleviation of symptoms has been achieved using treatments that alter the gastrointestinal tract microbiota toward that of healthy individuals. Identifying differences in microbiota composition through the use of 16S rRNA gene hypervariable tag sequencing has profound health implications. Current computational methods for comparing microbial communities are usually based on multiple alignments and phylogenetic inference, making them time consuming and requiring exceptional expertise and computational resources. As sequencing data rapidly grows in size, simpler analysis methods are needed to meet the growing computational burdens of microbiota comparisons. Thus, we have developed a simple, rapid, and accurate method, independent of multiple alignments and phylogenetic inference, to support microbiota comparisons. We create a metric, called compression-based distance (CBD) for quantifying the degree of similarity between microbial communities. CBD uses the repetitive nature of hypervariable tag datasets and well-established compression algorithms to approximate the total information shared between two datasets. Three published microbiota datasets were used as test cases for CBD as an applicable tool. Our study revealed that CBD recaptured 100% of the statistically significant conclusions reported in the previous studies, while achieving a decrease in computational time required when compared to similar tools without expert user intervention. CBD provides a simple, rapid, and accurate method for assessing distances between gastrointestinal tract microbiota 16S hypervariable tag datasets.

  5. Perturbations from cosmic strings in cold dark matter

    NASA Technical Reports Server (NTRS)

    Albrecht, Andreas; Stebbins, Albert

    1992-01-01

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

  6. Perturbations from cosmic strings in cold dark matter

    NASA Technical Reports Server (NTRS)

    Albrecht, Andreas; Stebbins, Albert

    1991-01-01

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

  7. Impacts of invasive earthworms on soil mercury cycling: Two mass balance approaches to an earthworm invasion in a northern Minnesota forest

    Treesearch

    Sona Psarska; Edward A. Nater; Randy Kolka

    2016-01-01

    Invasive earthworms perturb natural forest ecosystems that initially developed without them, mainly by consuming the forest floor (an organic rich surficial soil horizon) and by mixing the upper parts of the soil. The fate of mercury (Hg) formerly contained in the forest floor is largely unknown. We used two mass balance approaches (simple mass balance and geochemical...

  8. Swinging Atwood's Machine

    NASA Astrophysics Data System (ADS)

    Tufillaro, Nicholas B.; Abbott, Tyler A.; Griffiths, David J.

    1984-10-01

    We examine the motion of an Atwood's Machine in which one of the masses is allowed to swing in a plane. Computer studies reveal a rich variety of trajectories. The orbits are classified (bounded, periodic, singular, and terminating), and formulas for the critical mass ratios are developed. Perturbative techniques yield good approximations to the computer-generated trajectories. The model constitutes a simple example of a nonlinear dynamical system with two degrees of freedom.

  9. Mechanical Characterization of Microengineered Epithelial Cysts by Using Atomic Force Microscopy.

    PubMed

    Shen, Yusheng; Guan, Dongshi; Serien, Daniela; Takeuchi, Shoji; Tong, Penger; Yobas, Levent; Huang, Pingbo

    2017-01-24

    Most organs contain interconnected tubular tissues that are one-cell-thick, polarized epithelial monolayers enclosing a fluid-filled lumen. Such tissue organization plays crucial roles in developmental and normal physiology, and the proper functioning of these tissues depends on their regulation by complex biochemical perturbations and equally important, but poorly understood, mechanical perturbations. In this study, by combining micropatterning techniques and atomic force microscopy, we developed a simple in vitro experimental platform for characterizing the mechanical properties of the MDCK II cyst, the simplest model of lumen-enclosing epithelial monolayers. By using this platform, we estimated the elasticity of the cyst monolayer and showed that the presence of a luminal space influences cyst mechanics substantially, which could be attributed to polarization and tissue-level coordination. More interestingly, the results from force-relaxation experiments showed that the cysts also displayed tissue-level poroelastic characteristics that differed slightly from those of single cells. Our study provides the first quantitative findings, to our knowledge, on the tissue-level mechanics of well-polarized epithelial cysts and offers new insights into the interplay between cyst mechanics and cyst physiology. Moreover, our simple platform is a potentially useful tool for enhancing the current understanding of cyst mechanics in health and disease. Copyright © 2017 Biophysical Society. Published by Elsevier Inc. All rights reserved.

  10. Mechanically Assisted Self-Healing of Ultrathin Gold Nanowires.

    PubMed

    Wang, Binjun; Han, Ying; Xu, Shang; Qiu, Lu; Ding, Feng; Lou, Jun; Lu, Yang

    2018-04-17

    As the critical feature sizes of integrated circuits approaching sub-10 nm, ultrathin gold nanowires (diameter <10 nm) have emerged as one of the most promising candidates for next-generation interconnects in nanoelectronics. Also due to their ultrasmall dimensions, however, the structures and morphologies of ultrathin gold nanowires are more prone to be damaged during practical services, for example, Rayleigh instability can significantly alter their morphologies upon Joule heating, hindering their applications as interconnects. Here, it is shown that upon mechanical perturbations, predamaged, nonuniform ultrathin gold nanowires can quickly recover into uniform diameters and restore their smooth surfaces, via a simple mechanically assisted self-healing process. By examining the local self-healing process through in situ high-resolution transmission electron microscopy, the underlying mechanism is believed to be associated with surface atomic diffusion as evidenced by molecular dynamics simulations. In addition, mechanical manipulation can assist the atoms to overcome the diffusion barriers, as suggested by ab initio calculations, to activate more surface adatoms to diffuse and consequently speed up the self-healing process. This result can provide a facile method to repair ultrathin metallic nanowires directly in functional devices, and quickly restore their microstructures and morphologies by simple global mechanical perturbations. © 2018 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

  11. Oscillator strengths of the optical transitions in a semiconductor superlattice under an electric field

    NASA Astrophysics Data System (ADS)

    Tronc, P.

    1992-04-01

    The oscillator strengths of the optical transitions in a semiconductor superlattice under an electric field parallel to the growth axis can be calculated using a perturbative model with Bloch envelope functions. The applied electric field and the electron-hole interaction inducing formation of indirect excitons both induce strength asymmetry between the oblique +p and -p transitions of the Wannier-Stark ladder. Features of the photocurrent spectra recorded at low temperature can be accounted for by the present model in a very simple manner. Les forces d'oscillateur des transitions optiques dans un superréseau semiconducteur soumis à un champ électrique parallèle à la direction de croissance, peuvent être calculées à l'aide d'un modèle de perturbation avec des fonctions enveloppes de Bloch. Le champ électrique appliqué ainsi que l'interaction électron-trou, qui induit la formation d'excitons indirects, entraînent une asymétrie entre les forces d'oscillateur des transitions +p et -p dans l'échelle de Wannier-Stark. Certaines caractéristiques des spectres de photocourant enregistrés à basse température peuvent être prévues d'une manière très simple.

  12. A movable mass control system to detumble a disabled space vehicle

    NASA Technical Reports Server (NTRS)

    Edwards, T. L.

    1973-01-01

    An internal autonomous control system to either completely detumble a spacecraft or lessen the tumbling motions until the rescue craft arrives is discussed. Such a device would become active upon loss of control. The development of a movable mass control system to convert the tumbling motions of a disabled vehicle into simple spin is presented. A simple spin state would greatly facilitate crew evacuation and final despinning by an external means. The system moves a control mass, according to a selected control law, in the acceleration environment created by the tumbling motion. By moving the mass properly, the rotational kinetic energy of the system may be increased or decreased creating simple spin states about the minimum or maximum moment of inertia axis, respectively. The control system is designed for the latter case due to its associated stability in the presence of perturbing forces.

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

    Ade, P. A. R.; Aghanim, N.; Arnaud, M.

    In this paper, we present the implications for cosmic inflation of the Planck measurements of the cosmic microwave background (CMB) anisotropies in both temperature and polarization based on the full Planck survey, which includes more than twice the integration time of the nominal survey used for the 2013 release papers. The Planck full mission temperature data and a first release of polarization data on large angular scales measure the spectral index of curvature perturbations to be n s = 0.968 ± 0.006 and tightly constrain its scale dependence to dn s/ dlnk = -0.003 ± 0.007 when combined with themore » Planck lensing likelihood. When the Planck high-ℓ polarization data are included, the results are consistent and uncertainties are further reduced. The upper bound on the tensor-to-scalar ratio is r 0.002< 0.11 (95% CL). This upper limit is consistent with the B-mode polarization constraint r< 0.12 (95% CL) obtained from a joint analysis of the BICEP2/Keck Array and Planck data. These results imply that V(φ) ∝ φ 2 and natural inflation are now disfavoured compared to models predicting a smaller tensor-to-scalar ratio, such as R 2 inflation. We search for several physically motivated deviations from a simple power-law spectrum of curvature perturbations, including those motivated by a reconstruction of the inflaton potential not relying on the slow-roll approximation. We find that such models are not preferred, either according to a Bayesian model comparison or according to a frequentist simulation-based analysis. Three independent methods reconstructing the primordial power spectrum consistently recover a featureless and smooth P R(k)over the range of scales 0.008 Mpc -1 ≲ k ≲ 0.1 Mpc -1. At large scales, each method finds deviations from a power law, connected to a deficit at multipoles ℓ ≈ 20-40 in the temperature power spectrum, but at an uncompelling statistical significance owing to the large cosmic variance present at these multipoles. By combining power spectrum and non-Gaussianity bounds, we constrain models with generalized Lagrangians, including Galileon models and axion monodromy models. The Planck data are consistent with adiabatic primordial perturbations, and the estimated values for the parameters of the base Λ cold dark matter (ΛCDM) model are not significantly altered when more general initial conditions are admitted. In correlated mixed adiabatic and isocurvature models, the 95% CL upper bound for the non-adiabatic contribution to the observed CMB temperature variance is | α non - adi | < 1.9%, 4.0%, and 2.9% for CDM, neutrino density, and neutrino velocity isocurvature modes, respectively. We have tested inflationary models producing an anisotropic modulation of the primordial curvature power spectrum finding that the dipolar modulation in the CMB temperature field induced by a CDM isocurvature perturbation is not preferred at a statistically significant level. We also establish tight constraints on a possible quadrupolar modulation of the curvature perturbation. Lastly, these results are consistent with the Planck 2013 analysis based on the nominal mission data and further constrain slow-roll single-field inflationary models, as expected from the increased precision of Planck data using the full set of observations.« less

  14. Planck 2015 results. XX. Constraints on inflation

    NASA Astrophysics Data System (ADS)

    Planck Collaboration; Ade, P. A. R.; Aghanim, N.; Arnaud, M.; Arroja, F.; Ashdown, M.; Aumont, J.; Baccigalupi, C.; Ballardini, M.; Banday, A. J.; Barreiro, R. B.; Bartolo, N.; Battaner, E.; Benabed, K.; Benoît, A.; Benoit-Lévy, A.; Bernard, J.-P.; Bersanelli, M.; Bielewicz, P.; Bock, J. J.; Bonaldi, A.; Bonavera, L.; Bond, J. R.; Borrill, J.; Bouchet, F. R.; Boulanger, F.; Bucher, M.; Burigana, C.; Butler, R. C.; Calabrese, E.; Cardoso, J.-F.; Catalano, A.; Challinor, A.; Chamballu, A.; Chary, R.-R.; Chiang, H. C.; Christensen, P. R.; Church, S.; Clements, D. L.; Colombi, S.; Colombo, L. P. L.; Combet, C.; Contreras, D.; Couchot, F.; Coulais, A.; Crill, B. P.; Curto, A.; Cuttaia, F.; Danese, L.; Davies, R. D.; Davis, R. J.; de Bernardis, P.; de Rosa, A.; de Zotti, G.; Delabrouille, J.; Désert, F.-X.; Diego, J. M.; Dole, H.; Donzelli, S.; Doré, O.; Douspis, M.; Ducout, A.; Dupac, X.; Efstathiou, G.; Elsner, F.; Enßlin, T. A.; Eriksen, H. K.; Fergusson, J.; Finelli, F.; Forni, O.; Frailis, M.; Fraisse, A. A.; Franceschi, E.; Frejsel, A.; Frolov, A.; Galeotta, S.; Galli, S.; Ganga, K.; Gauthier, C.; Giard, M.; Giraud-Héraud, Y.; Gjerløw, E.; González-Nuevo, J.; Górski, K. M.; Gratton, S.; Gregorio, A.; Gruppuso, A.; Gudmundsson, J. E.; Hamann, J.; Handley, W.; Hansen, F. K.; Hanson, D.; Harrison, D. L.; Henrot-Versillé, S.; Hernández-Monteagudo, C.; Herranz, D.; Hildebrandt, S. R.; Hivon, E.; Hobson, M.; Holmes, W. A.; Hornstrup, A.; Hovest, W.; Huang, Z.; Huffenberger, K. M.; Hurier, G.; Jaffe, A. H.; Jaffe, T. R.; Jones, W. C.; Juvela, M.; Keihänen, E.; Keskitalo, R.; Kim, J.; Kisner, T. S.; Kneissl, R.; Knoche, J.; Kunz, M.; Kurki-Suonio, H.; Lagache, G.; Lähteenmäki, A.; Lamarre, J.-M.; Lasenby, A.; Lattanzi, M.; Lawrence, C. R.; Leonardi, R.; Lesgourgues, J.; Levrier, F.; Lewis, A.; Liguori, M.; Lilje, P. B.; Linden-Vørnle, M.; López-Caniego, M.; Lubin, P. M.; Ma, Y.-Z.; Macías-Pérez, J. F.; Maggio, G.; Maino, D.; Mandolesi, N.; Mangilli, A.; Maris, M.; Martin, P. G.; Martínez-González, E.; Masi, S.; Matarrese, S.; McGehee, P.; Meinhold, P. R.; Melchiorri, A.; Mendes, L.; Mennella, A.; Migliaccio, M.; Mitra, S.; Miville-Deschênes, M.-A.; Molinari, D.; Moneti, A.; Montier, L.; Morgante, G.; Mortlock, D.; Moss, A.; Münchmeyer, M.; Munshi, D.; Murphy, J. A.; Naselsky, P.; Nati, F.; Natoli, P.; Netterfield, C. B.; Nørgaard-Nielsen, H. U.; Noviello, F.; Novikov, D.; Novikov, I.; Oxborrow, C. A.; Paci, F.; Pagano, L.; Pajot, F.; Paladini, R.; Pandolfi, S.; Paoletti, D.; Pasian, F.; Patanchon, G.; Pearson, T. J.; Peiris, H. V.; Perdereau, O.; Perotto, L.; Perrotta, F.; Pettorino, V.; Piacentini, F.; Piat, M.; Pierpaoli, E.; Pietrobon, D.; Plaszczynski, S.; Pointecouteau, E.; Polenta, G.; Popa, L.; Pratt, G. W.; Prézeau, G.; Prunet, S.; Puget, J.-L.; Rachen, J. P.; Reach, W. T.; Rebolo, R.; Reinecke, M.; Remazeilles, M.; Renault, C.; Renzi, A.; Ristorcelli, I.; Rocha, G.; Rosset, C.; Rossetti, M.; Roudier, G.; Rowan-Robinson, M.; Rubiño-Martín, J. A.; Rusholme, B.; Sandri, M.; Santos, D.; Savelainen, M.; Savini, G.; Scott, D.; Seiffert, M. D.; Shellard, E. P. S.; Shiraishi, M.; Spencer, L. D.; Stolyarov, V.; Stompor, R.; Sudiwala, R.; Sunyaev, R.; Sutton, D.; Suur-Uski, A.-S.; Sygnet, J.-F.; Tauber, J. A.; Terenzi, L.; Toffolatti, L.; Tomasi, M.; Tristram, M.; Trombetti, T.; Tucci, M.; Tuovinen, J.; Valenziano, L.; Valiviita, J.; Van Tent, B.; Vielva, P.; Villa, F.; Wade, L. A.; Wandelt, B. D.; Wehus, I. K.; White, M.; Yvon, D.; Zacchei, A.; Zibin, J. P.; Zonca, A.

    2016-09-01

    We present the implications for cosmic inflation of the Planck measurements of the cosmic microwave background (CMB) anisotropies in both temperature and polarization based on the full Planck survey, which includes more than twice the integration time of the nominal survey used for the 2013 release papers. The Planck full mission temperature data and a first release of polarization data on large angular scales measure the spectral index of curvature perturbations to be ns = 0.968 ± 0.006 and tightly constrain its scale dependence to dns/ dlnk = -0.003 ± 0.007 when combined with the Planck lensing likelihood. When the Planck high-ℓ polarization data are included, the results are consistent and uncertainties are further reduced. The upper bound on the tensor-to-scalar ratio is r0.002< 0.11 (95% CL). This upper limit is consistent with the B-mode polarization constraint r< 0.12 (95% CL) obtained from a joint analysis of the BICEP2/Keck Array and Planck data. These results imply that V(φ) ∝ φ2 and natural inflation are now disfavoured compared to models predicting a smaller tensor-to-scalar ratio, such as R2 inflation. We search for several physically motivated deviations from a simple power-law spectrum of curvature perturbations, including those motivated by a reconstruction of the inflaton potential not relying on the slow-roll approximation. We find that such models are not preferred, either according to a Bayesian model comparison or according to a frequentist simulation-based analysis. Three independent methods reconstructing the primordial power spectrum consistently recover a featureless and smooth PR(k) over the range of scales 0.008 Mpc-1 ≲ k ≲ 0.1 Mpc-1. At large scales, each method finds deviations from a power law, connected to a deficit at multipoles ℓ ≈ 20-40 in the temperature power spectrum, but at an uncompelling statistical significance owing to the large cosmic variance present at these multipoles. By combining power spectrum and non-Gaussianity bounds, we constrain models with generalized Lagrangians, including Galileon models and axion monodromy models. The Planck data are consistent with adiabatic primordial perturbations, and the estimated values for the parameters of the base Λ cold dark matter (ΛCDM) model are not significantly altered when more general initial conditions are admitted. In correlated mixed adiabatic and isocurvature models, the 95% CL upper bound for the non-adiabatic contribution to the observed CMB temperature variance is | αnon - adi | < 1.9%, 4.0%, and 2.9% for CDM, neutrino density, and neutrino velocity isocurvature modes, respectively. We have tested inflationary models producing an anisotropic modulation of the primordial curvature power spectrum findingthat the dipolar modulation in the CMB temperature field induced by a CDM isocurvature perturbation is not preferred at a statistically significant level. We also establish tight constraints on a possible quadrupolar modulation of the curvature perturbation. These results are consistent with the Planck 2013 analysis based on the nominal mission data and further constrain slow-roll single-field inflationary models, as expected from the increased precision of Planck data using the full set of observations.

  15. 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.

  16. Kinematid Parameters of Corrective Postural Responses Differ between Upper and Lower Body Perturbations

    NASA Technical Reports Server (NTRS)

    Sayenko, G.

    2004-01-01

    Balance control is disrupted following prolonged microgravity exposure, and to better understand this, both upper and lower body perturbations have been used to study postural control in space flight crewmembers. However, differences between several postural response indicators observed using the two techniques suggest that different sensory systems may be involved in organizing responses to these different perturbation approaches. The present study sought to compare differences in parameters of corrective postural responses between upper body perturbations (pushes to the chest) and forward translations of the support surface. Nine subjects participated in this study. Forward translations were performed using a NeuroCom EquiTest(TM) CDP system, which was synchronized with a Northern Digital OptoTrak motion tracking system (3 subjects). Chest pushes were applied using a hand-held force transducer device and were performed using a stabilometric system (6 subjects). Analysis of EMG has shown that: i) the earliest response of the leg muscles was registered significantly later during forward translation of the support surface than during chest pushes, and ii) there was a tendency for the different order of leg muscles activation during the translation tests. Analysis of the kinematic data showed a significant difference in the subject's body segments inclinations during corrective postural responses to upper and lower body perturbations. It appears that upper body perturbations likely engage the vestibular system more rapidly, while lower body perturbations likely engage somatosensory systems more rapidly. These differences must be taken into account when choosing the type of perturbation for testing postural function.

  17. 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.

  18. Precision Control of the Electron Longitudinal Bunch Shape Using an Emittance-Exchange Beam Line

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

    Ha, Gwanghui; Cho, Moo -Hyun; Namkung, W.

    2017-03-09

    Here, we report on the experimental generation of relativistic electron bunches with a tunable longitudinal bunch shape. A longitudinal bunch-shaping (LBS) beam line, consisting of a transverse mask followed by a transverse-to-longitudinal emittance exchange (EEX) beam line, is used to tailor the longitudinal bunch shape (or current profile) of the electron bunch. The mask shapes the bunch’s horizontal profile, and the EEX beam line converts it to a corresponding longitudinal profile. The Argonne wakefield accelerator rf photoinjector delivers electron bunches into a LBS beam line to generate a variety of longitudinal bunch shapes. The quality of the longitudinal bunch shapemore » is limited by various perturbations in the exchange process. We develop a simple method, based on the incident slope of the bunch, to significantly suppress the perturbations.« less

  19. The formation of sharp edges in planetary rings by nearby satellites

    NASA Astrophysics Data System (ADS)

    Borderies, N.; Goldreich, P.; Tremaine, S.

    1989-08-01

    Equations are derived which govern the shapes of the perturbed streamlines near the 'sharp edge' boundaries between regions of high and low planetary ring optical depth; these are maintained by the shepherd satellites, which transfer angular momentum to and from ring particles. The results obtained by these equations' solution with a simple numerical model, whose parameters resemble those of the Encke division, are found to faithfully reproduce the sharp edges bounding the division; they imply that the ring thickness in the unperturbed regions far from the edges is of the order of 10 m, and that the angle-averaged surface density varies on a much shorter radial length scale than that over which the satellite torque is applied. This feature's relationship to the local reversal of angular momentum viscous transport, in the most strongly perturbed regions, is demonstrated.

  20. The formation of sharp edges in planetary rings by nearby satellites

    NASA Technical Reports Server (NTRS)

    Borderies, Nicole; Goldreich, Peter; Tremaine, Scott

    1989-01-01

    Equations are derived which govern the shapes of the perturbed streamlines near the 'sharp edge' boundaries between regions of high and low planetary ring optical depth; these are maintained by the shepherd satellites, which transfer angular momentum to and from ring particles. The results obtained by these equations' solution with a simple numerical model, whose parameters resemble those of the Encke division, are found to faithfully reproduce the sharp edges bounding the division; they imply that the ring thickness in the unperturbed regions far from the edges is of the order of 10 m, and that the angle-averaged surface density varies on a much shorter radial length scale than that over which the satellite torque is applied. This feature's relationship to the local reversal of angular momentum viscous transport, in the most strongly perturbed regions, is demonstrated.

  1. Aging does not affect the intralimb coordination elicited by slip-like perturbation of different intensities.

    PubMed

    Aprigliano, Federica; Martelli, Dario; Tropea, Peppino; Pasquini, Guido; Micera, Silvestro; Monaco, Vito

    2017-09-01

    This study was aimed at verifying whether aging modifies intralimb coordination strategy during corrective responses elicited by unexpected slip-like perturbations delivered during steady walking on a treadmill. To this end, 10 young and 10 elderly subjects were asked to manage unexpected slippages of different intensities. We analyzed the planar covariation law of the lower limb segments, using the principal component analysis, to verify whether elevation angles of older subjects covaried along a plan before and after the perturbation. Results showed that segments related to the perturbed limbs of both younger and older people do not covary after all perturbations. Conversely, the planar covariation law of the unperturbed limb was systematically held for younger and older subjects. These results occurred despite differences in spatio-temporal and kinematic parameters being observed among groups and perturbation intensities. Overall, our analysis revealed that aging does not affect intralimb coordination during corrective responses induced by slip-like perturbation, suggesting that both younger and older subjects adopt this control strategy while managing sudden and unexpected postural transitions of increasing intensities. Accordingly, results corroborate the hypothesis that balance control emerges from a governing set of biomechanical invariants, that is, suitable control schemes (e.g., planar covariation law) shared across voluntary and corrective motor behaviors, and across different sensory contexts due to different perturbation intensities, in both younger and older subjects. In this respect, our findings provide further support to investigate the effects of specific task training programs to counteract the risk of fall. NEW & NOTEWORTHY This study was aimed at investigating how aging affects the intralimb coordination of lower limb segments, described by the planar covariation law, during unexpected slip-like perturbations of increasing intensity. Results revealed that neither the aging nor the perturbation intensity affects this coordination strategy. Accordingly, we proposed that the balance control emerges from an invariant set of control schemes shared across different sensory motor contexts and despite age-related neuromuscular adaptations. Copyright © 2017 the American Physiological Society.

  2. A simple low cost latent fingerprint sensor based on deflectometry and WFT analysis

    NASA Astrophysics Data System (ADS)

    Dhanotia, Jitendra; Chatterjee, Amit; Bhatia, Vimal; Prakash, Shashi

    2018-02-01

    In criminal investigations, latent fingerprints are one of the most significant forms of evidence and most commonly used forensic investigation tool worldwide. The existing non-contact latent fingerprint detection systems are bulky, expensive and require environment which is shock and vibration resistant, thereby limiting their usability outside the laboratory. In this article, a compact, full field, low cost technique for profiling of fingerprints using deflectometry is proposed. Using inexpensive mobile phone screen based structured illumination, and windowed Fourier transform (WFT) based phase retrieval mechanism, the 2D and 3D phase plots reconstruct the profile information of the fingerprint. The phase information is also used to confirm a match between two fingerprints in real time. Since the proposed technique is non-interferometric, the measurements are least affected by environmental perturbations. Using the proposed technique, a portable sensor capable of field deployment has been realized.

  3. Conformal manifolds: ODEs from OPEs

    NASA Astrophysics Data System (ADS)

    Behan, Connor

    2018-03-01

    The existence of an exactly marginal deformation in a conformal field theory is very special, but it is not well understood how this is reflected in the allowed dimensions and OPE coefficients of local operators. To shed light on this question, we compute perturbative corrections to several observables in an abstract CFT, starting with the beta function. This yields a sum rule that the theory must obey in order to be part of a conformal manifold. The set of constraints relating CFT data at different values of the coupling can in principle be written as a dynamical system that allows one to flow arbitrarily far. We begin the analysis of it by finding a simple form for the differential equations when the spacetime and theory space are both one-dimensional. A useful feature we can immediately observe is that our system makes it very difficult for level crossing to occur.

  4. Analysis of Mathematical Modelling on Potentiometric Biosensors

    PubMed Central

    Mehala, N.; Rajendran, L.

    2014-01-01

    A mathematical model of potentiometric enzyme electrodes for a nonsteady condition has been developed. The model is based on the system of two coupled nonlinear time-dependent reaction diffusion equations for Michaelis-Menten formalism that describes the concentrations of substrate and product within the enzymatic layer. Analytical expressions for the concentration of substrate and product and the corresponding flux response have been derived for all values of parameters using the new homotopy perturbation method. Furthermore, the complex inversion formula is employed in this work to solve the boundary value problem. The analytical solutions obtained allow a full description of the response curves for only two kinetic parameters (unsaturation/saturation parameter and reaction/diffusion parameter). Theoretical descriptions are given for the two limiting cases (zero and first order kinetics) and relatively simple approaches for general cases are presented. All the analytical results are compared with simulation results using Scilab/Matlab program. The numerical results agree with the appropriate theories. PMID:25969765

  5. Analysis of mathematical modelling on potentiometric biosensors.

    PubMed

    Mehala, N; Rajendran, L

    2014-01-01

    A mathematical model of potentiometric enzyme electrodes for a nonsteady condition has been developed. The model is based on the system of two coupled nonlinear time-dependent reaction diffusion equations for Michaelis-Menten formalism that describes the concentrations of substrate and product within the enzymatic layer. Analytical expressions for the concentration of substrate and product and the corresponding flux response have been derived for all values of parameters using the new homotopy perturbation method. Furthermore, the complex inversion formula is employed in this work to solve the boundary value problem. The analytical solutions obtained allow a full description of the response curves for only two kinetic parameters (unsaturation/saturation parameter and reaction/diffusion parameter). Theoretical descriptions are given for the two limiting cases (zero and first order kinetics) and relatively simple approaches for general cases are presented. All the analytical results are compared with simulation results using Scilab/Matlab program. The numerical results agree with the appropriate theories.

  6. Predicting excitonic gaps of semiconducting single-walled carbon nanotubes from a field theoretic analysis

    DOE PAGES

    Konik, Robert M.; Sfeir, Matthew Y.; Misewich, James A.

    2015-02-17

    We demonstrate that a non-perturbative framework for the treatment of the excitations of single walled carbon nanotubes based upon a field theoretic reduction is able to accurately describe experiment observations of the absolute values of excitonic energies. This theoretical framework yields a simple scaling function from which the excitonic energies can be read off. This scaling function is primarily determined by a single parameter, the charge Luttinger parameter of the tube, which is in turn a function of the tube chirality, dielectric environment, and the tube's dimensions, thus expressing disparate influences on the excitonic energies in a unified fashion. Asmore » a result, we test this theory explicitly on the data reported in [NanoLetters 5, 2314 (2005)] and [Phys. Rev. B 82, 195424 (2010)] and so demonstrate the method works over a wide range of reported excitonic spectra.« less

  7. Vertical-probe-induced asymmetric dust oscillation in complex plasma.

    PubMed

    Harris, B J; Matthews, L S; Hyde, T W

    2013-05-01

    A complex plasma vertical oscillation experiment which modifies the bulk is presented. Spherical, micron-sized particles within a Coulomb crystal levitated in the sheath above the powered lower electrode in a GEC reference cell are perturbed using a probe attached to a Zyvex S100 Nanomanipulator. By oscillating the probe potential sinusoidally, particle motion is found to be asymmetric, exhibiting superharmonic response in one case. Using a simple electric field model for the plasma sheath, including a nonzero electric field at the sheath edge, dust particle charges are found by employing a balance of relevant forces and emission analysis. Adjusting the parameters of the electric field model allowed the change predicted in the levitation height to be compared with experiment. A discrete oscillator Green's function is applied using the derived force, which accurately predicts the particle's motion and allows the determination of the electric field at the sheath edge.

  8. Analytical expression for Risken-Nummedal-Graham-Haken instability threshold in quantum cascade lasers.

    PubMed

    Vukovic, N; Radovanovic, J; Milanovic, V; Boiko, D L

    2016-11-14

    We have obtained a closed-form expression for the threshold of Risken-Nummedal-Graham-Haken (RNGH) multimode instability in a Fabry-Pérot (FP) cavity quantum cascade laser (QCL). This simple analytical expression is a versatile tool that can easily be applied in practical situations which require analysis of QCL dynamic behavior and estimation of its RNGH multimode instability threshold. Our model for a FP cavity laser accounts for the carrier coherence grating and carrier population grating as well as their relaxation due to carrier diffusion. In the model, the RNGH instability threshold is analyzed using a second-order bi-orthogonal perturbation theory and we confirm our analytical solution by a comparison with the numerical simulations. In particular, the model predicts a low RNGH instability threshold in QCLs. This agrees very well with experimental data available in the literature.

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

    Kirchner, F.; Benninghoven, A.

    Investigations on the applicability of double-focusing counter-tube mass spectrometers with iodine vapor counters for determination of mass spectra and trace analysis are reported. An ionizing electron current of several 10/sup -10/ amp is generally sufficient for taking normal mass spectra with counter tube and recorder. The effect of the iodine vapor can be kept so low through simple cutin of a condenser cooled with liquid air that the 127 mass of the iodine atom is scarcely noticeable. In the determination of the minimum gas mass that could be detected and quantitatively measured, it was surprisingly proved that in the usemore » of He as the test gas in the unheated mass spectrometer at a gas pressure of 5 x 10/sup -6/ Torr of the residual gas, there is a perturbation maximum at mass 4. This could significantly affect the sensitivity of helium detection. (tr-auth)« less

  10. Pockmarks: self-scouring seep features?

    USGS Publications Warehouse

    Brothers, Laura L.; Kelley, Joseph T.; Belknap, Daniel F.; Barnhardt, Walter A.; Koons, Peter O.

    2011-01-01

    Pockmarks, or seafloor craters, occur worldwide in a variety of geologic settings and are often associated with fluid discharge. The mechanisms responsible for pockmark preservation, and pockmarks? relation to active methane venting are not well constrained. Simple numerical simulations run in 2-and 3-dimensions, and corroborated by flume tank experiments, indicate turbulence may play a role in pockmark maintenance, and, potentially, in pockmark excavation. Morphological analysis of the pockmarks indicates an abundance of flat-bottomed and/or elongated pockmarks. Pockmarks transition into furrows as the bay narrows and tidal flow is enhanced, providing unmistakable evidence of post-formation evolution. We hypothesize that some pockmarks formed from seafloor perturbations (e.g., gas or methane discharge), are1 maintained and gradually modified by vortical flow. This hypothesis provides a mechanism for pockmark preservation and enlargement without active fluid venting, which has implications for the interpretation of seafloor seep features in gas hydrates areas.

  11. Swelling-induced wrinkling in layered gel beams

    NASA Astrophysics Data System (ADS)

    Nardinocchi, P.; Puntel, E.

    2017-11-01

    Gels are widely employed in smart mechanical devices and biomedical applications. Swelling-induced bending actuation can be obtained by means of a simple bilayer gel beam. We show that this system can also exhibit wrinkling patterns of potential interest for structural morphing and sensing. We study swelling-induced wrinkling at the extrados of a bilayer gel beam with the softer layer on top. The bent configuration at finite strain is recovered first and, starting from it, a linear perturbation analysis is performed. We delimit the zone corresponding to wrinkling modes in a parameter plane encompassing a mechanical stiffness ratio and a geometric top layer to total height ratio. Interestingly, we observe that surface instability precedes and envelopes wrinkling modes of finite wavelength. Finally, we discuss the effect of changes in stiffness and of the Flory-Huggins parameters χ on the size of the wrinkling domain.

  12. Mass spectra of the particle-antiparticle system with a Dirac oscillator interaction

    NASA Technical Reports Server (NTRS)

    Moshinsky, M.; Loyola, G.

    1993-01-01

    The present view about the structure of mesons is that they are a quark-antiquark system. The mass spectrum corresponding to this system should, in principle, be given by chromodynamics, but this turns out to be a complex affair. Thus it is of some interest to consider relativistic systems of particle-antiparticle, with a simple type of interaction, which could give some insight on the spectra we can expect for mesons. This analysis is carried out when the interaction is of the Dirac oscillator type. It is shown that the Dirac equation of the antiparticle can be obtained from that of the particle by just changing the frequency omega into -omega. Following a procedure suggested by Barut, the equation for the particle-antiparticle system is derived and it is solved by a perturbation procedure. Thus, explicit expressions for the square of the mass spectra are obtained and its implications in the meson case is discussed.

  13. Scaling Phenomenology in Meson Photoproduction from CLAS

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

    Biplab Dey, Curtis A. Meyer

    2010-08-01

    In the high energy limit, perturbative QCD predicts that hard scattering amplitudes should follow simple scaling laws. For hard scattering at 90°, we show that experiments support this prediction even in the “medium energy” regime of 2.3 GeV<=sqrt(s)<=2.84 GeV, as long as there are no s-channel resonances present. Our data consists of high statistics measurements for five different exclusive meson photoproduction channels (pomega, peta, peta[prime], K+Lambdaand K+[summation]0) recently obtained from CLAS at Jefferson Lab. The same power-law scaling also leads to “saturated” Regge trajectories at high energies. That is, at large -t and -u, Regge trajectories must approach constant negativemore » integers. We demonstrate the application of saturated Regge phenomenology by performing a partial wave analysis fit to the gammayp-->peta[prime]differential cross sections.« less

  14. GW quasiparticle bandgaps of anatase TiO2 starting from DFT + U.

    PubMed

    Patrick, Christopher E; Giustino, Feliciano

    2012-05-23

    We investigate the quasiparticle band structure of anatase TiO(2), a wide gap semiconductor widely employed in photovoltaics and photocatalysis. We obtain GW quasiparticle energies starting from density-functional theory (DFT) calculations including Hubbard U corrections. Using a simple iterative procedure we determine the value of the Hubbard parameter yielding a vanishing quasiparticle correction to the fundamental bandgap of anatase TiO(2). The bandgap (3.3 eV) calculated using this optimal Hubbard parameter is smaller than the value obtained by applying many-body perturbation theory to standard DFT eigenstates and eigenvalues (3.7 eV). We extend our analysis to the rutile polymorph of TiO(2) and reach similar conclusions. Our work highlights the role of the starting non-interacting Hamiltonian in the calculation of GW quasiparticle energies in TiO(2) and suggests an optimal Hubbard parameter for future calculations.

  15. On heart rate variability and autonomic activity in homeostasis and in systemic inflammation.

    PubMed

    Scheff, Jeremy D; Griffel, Benjamin; Corbett, Siobhan A; Calvano, Steve E; Androulakis, Ioannis P

    2014-06-01

    Analysis of heart rate variability (HRV) is a promising diagnostic technique due to the noninvasive nature of the measurements involved and established correlations with disease severity, particularly in inflammation-linked disorders. However, the complexities underlying the interpretation of HRV complicate understanding the mechanisms that cause variability. Despite this, such interpretations are often found in literature. In this paper we explored mathematical modeling of the relationship between the autonomic nervous system and the heart, incorporating basic mechanisms such as perturbing mean values of oscillating autonomic activities and saturating signal transduction pathways to explore their impacts on HRV. We focused our analysis on human endotoxemia, a well-established, controlled experimental model of systemic inflammation that provokes changes in HRV representative of acute stress. By contrasting modeling results with published experimental data and analyses, we found that even a simple model linking the autonomic nervous system and the heart confound the interpretation of HRV changes in human endotoxemia. Multiple plausible alternative hypotheses, encoded in a model-based framework, equally reconciled experimental results. In total, our work illustrates how conventional assumptions about the relationships between autonomic activity and frequency-domain HRV metrics break down, even in a simple model. This underscores the need for further experimental work towards unraveling the underlying mechanisms of autonomic dysfunction and HRV changes in systemic inflammation. Understanding the extent of information encoded in HRV signals is critical in appropriately analyzing prior and future studies. Copyright © 2014 Elsevier Inc. All rights reserved.

  16. On heart rate variability and autonomic activity in homeostasis and in systemic inflammation

    PubMed Central

    Scheff, Jeremy D.; Griffel, Benjamin; Corbett, Siobhan A.; Calvano, Steve E.; Androulakis, Ioannis P.

    2014-01-01

    Analysis of heart rate variability (HRV) is a promising diagnostic technique due to the noninvasive nature of the measurements involved and established correlations with disease severity, particularly in inflammation-linked disorders. However, the complexities underlying the interpretation of HRV complicate understanding the mechanisms that cause variability. Despite this, such interpretations are often found in literature. In this paper we explored mathematical modeling of the relationship between the autonomic nervous system and the heart, incorporating basic mechanisms such as perturbing mean values of oscillating autonomic activities and saturating signal transduction pathways to explore their impacts on HRV. We focused our analysis on human endotoxemia, a well-established, controlled experimental model of systemic inflammation that provokes changes in HRV representative of acute stress. By contrasting modeling results with published experimental data and analyses, we found that even a simple model linking the autonomic nervous system and the heart confound the interpretation of HRV changes in human endotoxemia. Multiple plausible alternative hypotheses, encoded in a model-based framework, equally reconciled experimental results. In total, our work illustrates how conventional assumptions about the relationships between autonomic activity and frequency-domain HRV metrics break down, even in a simple model. This underscores the need for further experimental work towards unraveling the underlying mechanisms of autonomic dysfunction and HRV changes in systemic inflammation. Understanding the extent of information encoded in HRV signals is critical in appropriately analyzing prior and future studies. PMID:24680646

  17. Implementation of the NMR CHEmical Shift Covariance Analysis (CHESCA): A Chemical Biologist's Approach to Allostery.

    PubMed

    Boulton, Stephen; Selvaratnam, Rajeevan; Ahmed, Rashik; Melacini, Giuseppe

    2018-01-01

    Mapping allosteric sites is emerging as one of the central challenges in physiology, pathology, and pharmacology. Nuclear Magnetic Resonance (NMR) spectroscopy is ideally suited to map allosteric sites, given its ability to sense at atomic resolution the dynamics underlying allostery. Here, we focus specifically on the NMR CHEmical Shift Covariance Analysis (CHESCA), in which allosteric systems are interrogated through a targeted library of perturbations (e.g., mutations and/or analogs of the allosteric effector ligand). The atomic resolution readout for the response to such perturbation library is provided by NMR chemical shifts. These are then subject to statistical correlation and covariance analyses resulting in clusters of allosterically coupled residues that exhibit concerted responses to the common set of perturbations. This chapter provides a description of how each step in the CHESCA is implemented, starting from the selection of the perturbation library and ending with an overview of different clustering options.

  18. Statistical analysis of effective singular values in matrix rank determination

    NASA Technical Reports Server (NTRS)

    Konstantinides, Konstantinos; Yao, Kung

    1988-01-01

    A major problem in using SVD (singular-value decomposition) as a tool in determining the effective rank of a perturbed matrix is that of distinguishing between significantly small and significantly large singular values to the end, conference regions are derived for the perturbed singular values of matrices with noisy observation data. The analysis is based on the theories of perturbations of singular values and statistical significance test. Threshold bounds for perturbation due to finite-precision and i.i.d. random models are evaluated. In random models, the threshold bounds depend on the dimension of the matrix, the noisy variance, and predefined statistical level of significance. Results applied to the problem of determining the effective order of a linear autoregressive system from the approximate rank of a sample autocorrelation matrix are considered. Various numerical examples illustrating the usefulness of these bounds and comparisons to other previously known approaches are given.

  19. Perturbative stability of SFT-based cosmological models

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

    Galli, Federico; Koshelev, Alexey S., E-mail: fgalli@tena4.vub.ac.be, E-mail: alexey.koshelev@vub.ac.be

    2011-05-01

    We review the appearance of multiple scalar fields in linearized SFT based cosmological models with a single non-local scalar field. Some of these local fields are canonical real scalar fields and some are complex fields with unusual coupling. These systems only admit numerical or approximate analysis. We introduce a modified potential for multiple scalar fields that makes the system exactly solvable in the cosmological context of Friedmann equations and at the same time preserves the asymptotic behavior expected from SFT. The main part of the paper consists of the analysis of inhomogeneous cosmological perturbations in this system. We show numericallymore » that perturbations corresponding to the new type of complex fields always vanish. As an example of application of this model we consider an explicit construction of the phantom divide crossing and prove the perturbative stability of this process at the linear order. The issue of ghosts and ways to resolve it are briefly discussed.« less

  20. Instability of black strings in the third-order Lovelock theory

    NASA Astrophysics Data System (ADS)

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

    2016-05-01

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

  1. Instabilities in mimetic matter perturbations

    NASA Astrophysics Data System (ADS)

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

    2017-07-01

    We study cosmological perturbations in mimetic matter scenario with a general higher derivative function. We calculate the quadratic action and show that both the kinetic term and the gradient term have the wrong sings. We perform the analysis in both comoving and Newtonian gauges and confirm that the Hamiltonians and the associated instabilities are consistent with each other in both gauges. The existence of instabilities is independent of the specific form of higher derivative function which generates gradients for mimetic field perturbations. It is verified that the ghost instability in mimetic perturbations is not associated with the higher derivative instabilities such as the Ostrogradsky ghost.

  2. The mechanism by which nonlinearity sustains turbulence in plane Couette flow

    NASA Astrophysics Data System (ADS)

    Nikolaidis, M.-A.; Farrell, B. F.; Ioannou, P. J.

    2018-04-01

    Turbulence in wall-bounded shear flow results from a synergistic interaction between linear non-normality and nonlinearity in which non-normal growth of a subset of perturbations configured to transfer energy from the externally forced component of the turbulent state to the perturbation component maintains the perturbation energy, while the subset of energy-transferring perturbations is replenished by nonlinearity. Although it is accepted that both linear non-normality mediated energy transfer from the forced component of the mean flow and nonlinear interactions among perturbations are required to maintain the turbulent state, the detailed physical mechanism by which these processes interact in maintaining turbulence has not been determined. In this work a statistical state dynamics based analysis is performed on turbulent Couette flow at R = 600 and a comparison to DNS is used to demonstrate that the perturbation component in Couette flow turbulence is replenished by a non-normality mediated parametric growth process in which the fluctuating streamwise mean flow has been adjusted to marginal Lyapunov stability. It is further shown that the alternative mechanism in which the subspace of non-normally growing perturbations is maintained directly by perturbation-perturbation nonlinearity does not contribute to maintaining the turbulent state. This work identifies parametric interaction between the fluctuating streamwise mean flow and the streamwise varying perturbations to be the mechanism of the nonlinear interaction maintaining the perturbation component of the turbulent state, and identifies the associated Lyapunov vectors with positive energetics as the structures of the perturbation subspace supporting the turbulence.

  3. 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.

  4. Specific sine-Gordon soliton dynamics in the presence of external driving forces

    NASA Astrophysics Data System (ADS)

    Reinisch, Gilbert; Fernandez, Jean Claude

    1981-07-01

    We consider the acceleration of a single sine-Gordon (SG) soliton kink wave by an external time-dependent force χ(t), first without any dissipation, and then in the presence of a weak damping effect. We use the method of Fogel, Trullinger, Bishop, and Krumhansl [FTBK,

    Phys. Rev. B 45, 1578 (1977)]
    which consists in perturbing the SG equation about its kink solution and solving the resulting linear inhomogeneous equation for the perturbation function by expanding it in the complete set of eigenfunctions of the Schrödinger operator with potential 1-2 2x. Our results concerning the accelerated soliton dynamics strongly disagree with the FTBK conclusion that the soliton should undergo an acceleration proportional to χ (this is the so-called Newtonian dynamical behavior of SG soliton, which is also predicted by all existing perturbation theories dealing with the perturbed SG equation). On the contrary, we find that this Newtonian acceleration is exactly balanced by a reaction effect of the continuous phonon spectrum excited by the external force χ, upon the moving kink, so that there is no soliton acceleration at all within the frame of this linear perturbation theory, i.e., for small time values. Actually, we show by the simple example of a static external force that the acceleration of an initially static kink is a higher-order effect (proportional to χt2, where t is the time, instead of being constant and proportional to χ). We emphasize that this last result has already been checked by numerical experiments and show, both by theory and by numerical simulations, that it does not qualitatively change when a small damping effect is taken into account.

  5. Adaptive strategies of remote systems operators exposed to perturbed camera-viewing conditions

    NASA Technical Reports Server (NTRS)

    Stuart, Mark A.; Manahan, Meera K.; Bierschwale, John M.; Sampaio, Carlos E.; Legendre, A. J.

    1991-01-01

    This report describes a preliminary investigation of the use of perturbed visual feedback during the performance of simulated space-based remote manipulation tasks. The primary objective of this NASA evaluation was to determine to what extent operators exhibit adaptive strategies which allow them to perform these specific types of remote manipulation tasks more efficiently while exposed to perturbed visual feedback. A secondary objective of this evaluation was to establish a set of preliminary guidelines for enhancing remote manipulation performance and reducing the adverse effects. These objectives were accomplished by studying the remote manipulator performance of test subjects exposed to various perturbed camera-viewing conditions while performing a simulated space-based remote manipulation task. Statistical analysis of performance and subjective data revealed that remote manipulation performance was adversely affected by the use of perturbed visual feedback and performance tended to improve with successive trials in most perturbed viewing conditions.

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

    PubMed

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

    2017-01-01

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

  7. Principal component analysis of chemical shift perturbation data of a multiple-ligand-binding system for elucidation of respective binding mechanism.

    PubMed

    Konuma, Tsuyoshi; Lee, Young-Ho; Goto, Yuji; Sakurai, Kazumasa

    2013-01-01

    Chemical shift perturbations (CSPs) in NMR spectra provide useful information about the interaction of a protein with its ligands. However, in a multiple-ligand-binding system, determining quantitative parameters such as a dissociation constant (K(d) ) is difficult. Here, we used a method we named CS-PCA, a principal component analysis (PCA) of chemical shift (CS) data, to analyze the interaction between bovine β-lactoglobulin (βLG) and 1-anilinonaphthalene-8-sulfonate (ANS), which is a multiple-ligand-binding system. The CSP on the binding of ANS involved contributions from two distinct binding sites. PCA of the titration data successfully separated the CSP pattern into contributions from each site. Docking simulations based on the separated CSP patterns provided the structures of βLG-ANS complexes for each binding site. In addition, we determined the K(d) values as 3.42 × 10⁻⁴ M² and 2.51 × 10⁻³ M for Sites 1 and 2, respectively. In contrast, it was difficult to obtain reliable K(d) values for respective sites from the isothermal titration calorimetry experiments. Two ANS molecules were found to bind at Site 1 simultaneously, suggesting that the binding occurs cooperatively with a partial unfolding of the βLG structure. On the other hand, the binding of ANS to Site 2 was a simple attachment without a significant conformational change. From the present results, CS-PCA was confirmed to provide not only the positions and the K(d) values of binding sites but also information about the binding mechanism. Thus, it is anticipated to be a general method to investigate protein-ligand interactions. Copyright © 2012 Wiley Periodicals, Inc.

  8. Lack of Critical Slowing Down Suggests that Financial Meltdowns Are Not Critical Transitions, yet Rising Variability Could Signal Systemic Risk.

    PubMed

    Guttal, Vishwesha; Raghavendra, Srinivas; Goel, Nikunj; Hoarau, Quentin

    2016-01-01

    Complex systems inspired analysis suggests a hypothesis that financial meltdowns are abrupt critical transitions that occur when the system reaches a tipping point. Theoretical and empirical studies on climatic and ecological dynamical systems have shown that approach to tipping points is preceded by a generic phenomenon called critical slowing down, i.e. an increasingly slow response of the system to perturbations. Therefore, it has been suggested that critical slowing down may be used as an early warning signal of imminent critical transitions. Whether financial markets exhibit critical slowing down prior to meltdowns remains unclear. Here, our analysis reveals that three major US (Dow Jones Index, S&P 500 and NASDAQ) and two European markets (DAX and FTSE) did not exhibit critical slowing down prior to major financial crashes over the last century. However, all markets showed strong trends of rising variability, quantified by time series variance and spectral function at low frequencies, prior to crashes. These results suggest that financial crashes are not critical transitions that occur in the vicinity of a tipping point. Using a simple model, we argue that financial crashes are likely to be stochastic transitions which can occur even when the system is far away from the tipping point. Specifically, we show that a gradually increasing strength of stochastic perturbations may have caused to abrupt transitions in the financial markets. Broadly, our results highlight the importance of stochastically driven abrupt transitions in real world scenarios. Our study offers rising variability as a precursor of financial meltdowns albeit with a limitation that they may signal false alarms.

  9. Lack of Critical Slowing Down Suggests that Financial Meltdowns Are Not Critical Transitions, yet Rising Variability Could Signal Systemic Risk

    PubMed Central

    Hoarau, Quentin

    2016-01-01

    Complex systems inspired analysis suggests a hypothesis that financial meltdowns are abrupt critical transitions that occur when the system reaches a tipping point. Theoretical and empirical studies on climatic and ecological dynamical systems have shown that approach to tipping points is preceded by a generic phenomenon called critical slowing down, i.e. an increasingly slow response of the system to perturbations. Therefore, it has been suggested that critical slowing down may be used as an early warning signal of imminent critical transitions. Whether financial markets exhibit critical slowing down prior to meltdowns remains unclear. Here, our analysis reveals that three major US (Dow Jones Index, S&P 500 and NASDAQ) and two European markets (DAX and FTSE) did not exhibit critical slowing down prior to major financial crashes over the last century. However, all markets showed strong trends of rising variability, quantified by time series variance and spectral function at low frequencies, prior to crashes. These results suggest that financial crashes are not critical transitions that occur in the vicinity of a tipping point. Using a simple model, we argue that financial crashes are likely to be stochastic transitions which can occur even when the system is far away from the tipping point. Specifically, we show that a gradually increasing strength of stochastic perturbations may have caused to abrupt transitions in the financial markets. Broadly, our results highlight the importance of stochastically driven abrupt transitions in real world scenarios. Our study offers rising variability as a precursor of financial meltdowns albeit with a limitation that they may signal false alarms. PMID:26761792

  10. Semilocal momentum-space regularized chiral two-nucleon potentials up to fifth order

    NASA Astrophysics Data System (ADS)

    Reinert, P.; Krebs, H.; Epelbaum, E.

    2018-05-01

    We introduce new semilocal two-nucleon potentials up to fifth order in the chiral expansion. We employ a simple regularization approach for the pion exchange contributions which i) maintains the long-range part of the interaction, ii) is implemented in momentum space and iii) can be straightforwardly applied to regularize many-body forces and current operators. We discuss in detail the two-nucleon contact interactions at fourth order and demonstrate that three terms out of fifteen used in previous calculations can be eliminated via suitably chosen unitary transformations. The removal of the redundant contact terms results in a drastic simplification of the fits to scattering data and leads to interactions which are much softer ( i.e., more perturbative) than our recent semilocal coordinate-space regularized potentials. Using the pion-nucleon low-energy constants from matching pion-nucleon Roy-Steiner equations to chiral perturbation theory, we perform a comprehensive analysis of nucleon-nucleon scattering and the deuteron properties up to fifth chiral order and study the impact of the leading F-wave two-nucleon contact interactions which appear at sixth order. The resulting chiral potentials at fifth order lead to an outstanding description of the proton-proton and neutron-proton scattering data from the self-consistent Granada-2013 database below the pion production threshold, which is significantly better than for any other chiral potential. For the first time, the chiral potentials match in precision and even outperform the available high-precision phenomenological potentials, while the number of adjustable parameters is, at the same time, reduced by about ˜ 40%. Last but not least, we perform a detailed error analysis and, in particular, quantify for the first time the statistical uncertainties of the fourth- and the considered sixth-order contact interactions.

  11. Nonlinear spherical perturbations in quintessence models of dark energy

    NASA Astrophysics Data System (ADS)

    Pratap Rajvanshi, Manvendra; Bagla, J. S.

    2018-06-01

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

  12. The time-resolved photoelectron spectrum of toluene using a perturbation theory approach

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

    Richings, Gareth W.; Worth, Graham A., E-mail: g.a.worth@bham.ac.uk

    A theoretical study of the intra-molecular vibrational-energy redistribution of toluene using time-resolved photo-electron spectra calculated using nuclear quantum dynamics and a simple, two-mode model is presented. Calculations have been carried out using the multi-configuration time-dependent Hartree method, using three levels of approximation for the calculation of the spectra. The first is a full quantum dynamics simulation with a discretisation of the continuum wavefunction of the ejected electron, whilst the second uses first-order perturbation theory to calculate the wavefunction of the ion. Both methods rely on the explicit inclusion of both the pump and probe laser pulses. The third method includesmore » only the pump pulse and generates the photo-electron spectrum by projection of the pumped wavepacket onto the ion potential energy surface, followed by evaluation of the Fourier transform of the autocorrelation function of the subsequently propagated wavepacket. The calculations performed have been used to study the periodic population flow between the 6a and 10b16b modes in the S{sub 1} excited state, and compared to recent experimental data. We obtain results in excellent agreement with the experiment and note the efficiency of the perturbation method.« less

  13. Assessment of the effects of azimuthal mode number perturbations upon the implosion processes of fluids in cylinders

    NASA Astrophysics Data System (ADS)

    Lindstrom, Michael

    2017-06-01

    Fluid instabilities arise in a variety of contexts and are often unwanted results of engineering imperfections. In one particular model for a magnetized target fusion reactor, a pressure wave is propagated in a cylindrical annulus comprised of a dense fluid before impinging upon a plasma and imploding it. Part of the success of the apparatus is a function of how axially-symmetric the final pressure pulse is upon impacting the plasma. We study a simple model for the implosion of the system to study how imperfections in the pressure imparted on the outer circumference grow due to geometric focusing. Our methodology entails linearizing the compressible Euler equations for mass and momentum conservation about a cylindrically symmetric problem and analysing the perturbed profiles at different mode numbers. The linearized system gives rise to singular shocks and through analysing the perturbation profiles at various times, we infer that high mode numbers are dampened through the propagation. We also study the Linear Klein-Gordon equation in the context of stability of linear cylindrical wave formation whereby highly oscillatory, bounded behaviour is observed in a far field solution.

  14. A model-based exploration of the role of pattern generating circuits during locomotor adaptation.

    PubMed

    Marjaninejad, Ali; Finley, James M

    2016-08-01

    In this study, we used a model-based approach to explore the potential contributions of central pattern generating circuits (CPGs) during adaptation to external perturbations during locomotion. We constructed a neuromechanical modeled of locomotion using a reduced-phase CPG controller and an inverted pendulum mechanical model. Two different forms of locomotor adaptation were examined in this study: split-belt treadmill adaptation and adaptation to a unilateral, elastic force field. For each simulation, we first examined the effects of phase resetting and varying the model's initial conditions on the resulting adaptation. After evaluating the effect of phase resetting on the adaptation of step length symmetry, we examined the extent to which the results from these simple models could explain previous experimental observations. We found that adaptation of step length symmetry during split-belt treadmill walking could be reproduced using our model, but this model failed to replicate patterns of adaptation observed in response to force field perturbations. Given that spinal animal models can adapt to both of these types of perturbations, our findings suggest that there may be distinct features of pattern generating circuits that mediate each form of adaptation.

  15. From "~" to Precision Science: Cosmology from 1995 to 2025

    NASA Astrophysics Data System (ADS)

    Kamionkowski, Marc; Spergel, David N.

    2016-01-01

    Over the past decade and a half, astronomical measurements, primarily of fluctuations in the cosmic microwave background, have transformed cosmology from an order-of-magnitude game into a paragon of precision science. From these measurements has emerged a 6-parameter cosmological "standard model": a flat universe filled with dark matter and dark energy and seeded by a nearly scale-invariant spectrum of Gaussian random-phase density perturbations. The striking resemblance between these perturbations and those expected from inflation motivates the search for a unique "B-mode" signature of inflation in the polarization of the cosmic microwave background. While the fluctuation spectrum is close to scale invariant, WMAP, Planck and ground-based CMB experiments now have strong evidence for a departure from scale invariance in primordial perturbations. This suggests, in simple models of inflation that these B modes should be within striking distance within the next 5-10 years. The advent of a new generation of galaxy surveys will, over similar timescales, shed additional light not only on the physics of inflation, but also the nature of the dark matter and dark energy required by the current cosmological standard model, and perhaps on the new physics that determines the baryon density.

  16. Error Field Assessment from Driven Mode Rotation: Results from Extrap-T2R Reversed-Field-Pinch and Perspectives for ITER

    NASA Astrophysics Data System (ADS)

    Volpe, F. A.; Frassinetti, L.; Brunsell, P. R.; Drake, J. R.; Olofsson, K. E. J.

    2012-10-01

    A new ITER-relevant non-disruptive error field (EF) assessment technique not restricted to low density and thus low beta was demonstrated at the Extrap-T2R reversed field pinch. Resistive Wall Modes (RWMs) were generated and their rotation sustained by rotating magnetic perturbations. In particular, stable modes of toroidal mode number n=8 and 10 and unstable modes of n=1 were used in this experiment. Due to finite EFs, and in spite of the applied perturbations rotating uniformly and having constant amplitude, the RWMs were observed to rotate non-uniformly and be modulated in amplitude (in the case of unstable modes, the observed oscillation was superimposed to the mode growth). This behavior was used to infer the amplitude and toroidal phase of n=1, 8 and 10 EFs. The method was first tested against known, deliberately applied EFs, and then against actual intrinsic EFs. Applying equal and opposite corrections resulted in longer discharges and more uniform mode rotation, indicating good EF compensation. The results agree with a simple theoretical model. Extensions to tearing modes, to the non-uniform plasma response to rotating perturbations, and to tokamaks, including ITER, will be discussed.

  17. Extended analytical formulas for the perturbed Keplerian motion under a constant control acceleration

    NASA Astrophysics Data System (ADS)

    Zuiani, Federico; Vasile, Massimiliano

    2015-03-01

    This paper presents a set of analytical formulae for the perturbed Keplerian motion of a spacecraft under the effect of a constant control acceleration. The proposed set of formulae can treat control accelerations that are fixed in either a rotating or inertial reference frame. Moreover, the contribution of the zonal harmonic is included in the analytical formulae. It will be shown that the proposed analytical theory allows for the fast computation of long, multi-revolution spirals while maintaining good accuracy. The combined effect of different perturbations and of the shadow regions due to solar eclipse is also included. Furthermore, a simplified control parameterisation is introduced to optimise thrusting patterns with two thrust arcs and two cost arcs per revolution. This simple parameterisation is shown to ensure enough flexibility to describe complex low thrust spirals. The accuracy and speed of the proposed analytical formulae are compared against a full numerical integration with different integration schemes. An averaging technique is then proposed as an application of the analytical formulae. Finally, the paper presents an example of design of an optimal low-thrust spiral to transfer a spacecraft from an elliptical to a circular orbit around the Earth.

  18. Numerical investigation of stability of breather-type solutions of the nonlinear Schrödinger equation

    NASA Astrophysics Data System (ADS)

    Calini, A.; Schober, C. M.

    2013-09-01

    In this article we present the results of a broad numerical investigation on the stability of breather-type solutions of the nonlinear Schrödinger (NLS) equation, specifically the one- and two-mode breathers for an unstable plane wave, which are frequently used to model rogue waves. The numerical experiments involve large ensembles of perturbed initial data for six typical random perturbations. Ensemble estimates of the "closeness", A(t), of the perturbed solution to an element of the respective unperturbed family indicate that the only neutrally stable breathers are the ones of maximal dimension, that is: given an unstable background with N unstable modes, the only neutrally stable breathers are the N-dimensional ones (obtained as a superimposition of N simple breathers via iterated Backlund transformations). Conversely, breathers which are not fully saturated are sensitive to noisy environments and are unstable. Interestingly, A(t) is smallest for the coalesced two-mode breather indicating the coalesced case may be the most robust two-mode breather in a laboratory setting. The numerical simulations confirm and provide a realistic realization of the stability behavior established analytically by the authors.

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

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

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

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

  20. Effects of Dipole Perturbation on Last Good Surface of a Single Null Divertor Tokomak

    NASA Astrophysics Data System (ADS)

    Sharma, Yogesh; Ali, Halima; Punjabi, Alkesh

    2003-10-01

    Using area preserving maps developed by Punjabi and Boozer /1,2/, one is able to investigate destruction of the last good surface (LGS) under dipole perturbation. Using simple map equations: X_n+1=X_n-KYn (1-Y_n) and Y_n+1=Y_n+KX_n+1, where X_0=0, Y_0=0.99692931261 and K=0.6 for LGS. These equations with dipole perturbation equations Y_n+1=Y_n+δ s^3 fracc-X^2_n+1(X^2_n+1 + c)^2 and sum_i=0^5c_iX_n+1^i=0 are used to study the destruction of the LGS. The surface transitions from a clean, smooth curve through a stage of embedded islands of high and low density and finally to chaos. This work is supported by NASA and DOE Grant Number DE-FG02-02ER54673. This work was done under mentorship of Drs. H. Ali and A. Punjabi. 1. A. Punjabi et al Phys. Rev. Letter 69, 3322 (1992) 2. Dipole Map for Single-Null Divertor Tokamaks, A. Punjabi et al, To Appear in Phys. of Plasma (2003)

  1. Terahertz field-induced ionization and perturbed free induction decay of excitons in bulk GaAs

    NASA Astrophysics Data System (ADS)

    Murotani, Yuta; Takayama, Masayuki; Sekiguchi, Fumiya; Kim, Changsu; Akiyama, Hidefumi; Shimano, Ryo

    2018-03-01

    We investigated the interaction between an intense terahertz (THz) pulse and excitons in bulk GaAs by using THz pump near-infrared (NIR) optical probe spectroscopy. We observed a clear spectral oscillation in the NIR transient absorption spectra at low temperature, which is interpreted as the THz pump-induced perturbed free induction decay (PFID) of the excitonic interband polarization. We performed a numerical simulation based on a microscopic theory and identified that the observed PFID signal originates from the THz field-induced ionization of excitons. Using a real-space representation of the excitonic wave function, we visualized how the ionization of an exciton proceeds under the intense single-cycle THz electric field. We also calculated the nonlinear susceptibility with the lowest-order perturbation theory assuming a weak THz pump, which showed a similar spectral feature with that obtained by the full treatment to field-induced ionization process. This coincidence is attributed to the fact that 1s-excitonic interband polarization is modified predominantly through interactions with the p-wave component of the excitonic wave function. A simple phenomenological expression of the PFID signal is presented to discuss effects of the THz pump pulse duration on the spectral oscillation.

  2. On the Minimal Length Uncertainty Relation and the Foundations of String Theory

    DOE PAGES

    Chang, Lay Nam; Lewis, Zachary; Minic, Djordje; ...

    2011-01-01

    We review our work on the minimal length uncertainty relation as suggested by perturbative string theory. We discuss simple phenomenological implications of the minimal length uncertainty relation and then argue that the combination of the principles of quantum theory and general relativity allow for a dynamical energy-momentum space. We discuss the implication of this for the problem of vacuum energy and the foundations of nonperturbative string theory.

  3. Equilibrium time correlation functions and the dynamics of fluctuations

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

    Luban, Marshall; Luscombe, James H.

    1999-12-01

    Equilibrium time correlation functions are of great importance because they probe the equilibrium dynamical response to external perturbations. We discuss the properties of time correlation functions for several systems that are simple enough to illustrate the calculational steps involved. The discussion underscores the need for avoiding language which misleadingly suggests that thermal equilibrium is associated with a quiescent or moribund state of the system. (c) 1999 American Association of Physics Teachers.

  4. Rayleigh-Bloch waves trapped by a periodic perturbation: exact solutions

    NASA Astrophysics Data System (ADS)

    Merzon, A.; Zhevandrov, P.; Romero Rodríguez, M. I.; De la Paz Méndez, J. E.

    2018-06-01

    Exact solutions describing the Rayleigh-Bloch waves for the two-dimensional Helmholtz equation are constructed in the case when the refractive index is a sum of a constant and a small amplitude function which is periodic in one direction and of finite support in the other. These solutions are quasiperiodic along the structure and exponentially decay in the orthogonal direction. A simple formula for the dispersion relation of these waves is obtained.

  5. High Angle-of-Attack Aerodynamics

    DTIC Science & Technology

    1982-12-01

    CONTRIBUTIONS DE TROIS MOUVEMENTS SIMPLES: UN MOUVEMENT DE BASE CONIQUE ET DES PERTURBATIONS OSCILLATOIRES DE CE MOUVEMENT DE BASE. RECOMMANDATIONS...Completes. Tome 1. 1879, p. CVI. 21. Poincari, H., "Les courbes d6finies par une 6quation dlffer~ntielle." Journal de Math6matigues 3 to 7, 1881, p...profila, ailes en flLche * corps fuselds, primes dWeir, aviona, complete, etc... im~ntrent que lee procidds adoptis aont en meaure de couvrir un domaine

  6. Modal analysis of untransposed bilateral three-phase lines -- a perturbation approach

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

    Faria, J.A.B.; Mendes, J.H.B.

    1997-01-01

    Model analysis of three-phase power lines exhibiting bilateral symmetry leads to modal transformation matrices that closely resemble Clarke`s transformation. The authors develop a perturbation theory approach to justify, interpret, and gain understanding of this well known fact. Further, the authors show how to find new frequency dependent correction terms that once added to Clarke`s transformation lead to improved accuracy.

  7. Sensitivity analysis of bi-layered ceramic dental restorations.

    PubMed

    Zhang, Zhongpu; Zhou, Shiwei; Li, Qing; Li, Wei; Swain, Michael V

    2012-02-01

    The reliability and longevity of ceramic prostheses have become a major concern. The existing studies have focused on some critical issues from clinical perspectives, but more researches are needed to address fundamental sciences and fabrication issues to ensure the longevity and durability of ceramic prostheses. The aim of this paper was to explore how "sensitive" the thermal and mechanical responses, in terms of changes in temperature and thermal residual stress of the bi-layered ceramic systems and crown models will be with respect to the perturbation of the design variables chosen (e.g. layer thickness and heat transfer coefficient) in a quantitative way. In this study, three bi-layered ceramic models with different geometries are considered: (i) a simple bi-layered plate, (ii) a simple bi-layer triangle, and (iii) an axisymmetric bi-layered crown. The layer thickness and convective heat transfer coefficient (or cooling rate) seem to be more sensitive for the porcelain fused on zirconia substrate models. The resultant sensitivities indicate a critical importance of the heat transfer coefficient and thickness ratio of core to veneer on the temperature distributions and residual stresses in each model. The findings provide a quantitative basis for assessing the effects of fabrication uncertainties and optimizing the design of ceramic prostheses. Copyright © 2011 Academy of Dental Materials. Published by Elsevier Ltd. All rights reserved.

  8. Rapid Microfluidic Mixers Utilizing Dispersion Effect and Interactively Time-Pulsed Injection

    NASA Astrophysics Data System (ADS)

    Leong, Jik-Chang; Tsai, Chien-Hsiung; Chang, Chin-Lung; Lin, Chiu-Feng; Fu, Lung-Ming

    2007-08-01

    In this paper, we present a novel active microfluidic mixer utilizing a dispersion effect in an expansion chamber and applying interactively time-pulsed driving voltages to the respective inlet fluid flows to induce electroosmotic flow velocity variations for developing a rapid mixing effect in a microchannel. Without using any additional equipment to induce flow perturbations, only a single high-voltage power source is required for simultaneously driving and mixing sample fluids, which results in a simple and low-cost system for mixing. The effects of the applied main electrical field, interactive frequency, and expansion ratio on the mixing performance are thoroughly examined experimentally and numerically. The mixing ratio can be as high as 95% within a mixing length of 3000 μm downstream from the secondary T-form when a driving electric field strength of 250 V/cm, a periodic switching frequency of 5 Hz, and the expansion ratio M=1:10 are applied. In addition, the optimization of the driving electric field, switching frequency, expansion ratio, expansion entry length, and expansion chamber length for achieving a maximum mixing ratio is also discussed in this study. The novel method proposed in this study can be used for solving the mixing problem in the field of micro-total-analysis systems in a simple manner.

  9. Vibronic spectra of the p-benzoquinone radical anion and cation: a matrix isolation and computational study.

    PubMed

    Piech, Krzysztof; Bally, Thomas; Ichino, Takatoshi; Stanton, John

    2014-02-07

    The electronic and vibrational absorption spectra of the radical anion and cation of p-benzoquinone (PBQ) in an Ar matrix between 500 and 40,000 cm(-1) are presented and discussed in detail. Of particular interest is the radical cation, which shows very unusual spectroscopic features that can be understood in terms of vibronic coupling between the ground and a very low-lying excited state. The infrared spectrum of PBQ˙(+) exhibits a very conspicuous and complicated pattern of features above 1900 cm(-1) that is due to this electronic transition, and offers an unusually vivid demonstration of the effects of vibronic coupling in what would usually be a relatively simple region of the electromagnetic spectrum associated only with vibrational transitions. As expected, the intensities of most of the IR transitions leading to levels that couple the ground to the very low-lying first excited state of PBQ˙(+) increase by large factors upon ionization, due to "intensity borrowing" from the D0 → D1 electronic transition. A notable exception is the antisymmetric C=O stretching vibration, which contributes significantly to the vibronic coupling, but has nevertheless quite small intensity in the cation spectrum. This surprising feature is rationalized on the basis of a simple perturbation analysis.

  10. Examining the accuracy of the infinite order sudden approximation using sensitivity analysis

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

    Eno, L.; Rabitz, H.

    1981-08-15

    A method is developed for assessing the accuracy of scattering observables calculated within the framework of the infinite order sudden (IOS) approximation. In particular, we focus on the energy sudden assumption of the IOS method and our approach involves the determination of the sensitivity of the IOS scattering matrix S/sup IOS/ with respect to a parameter which reintroduces the internal energy operator h/sub 0/ into the IOS Hamiltonian. This procedure is an example of sensitivity analysis of missing model components (h/sub 0/ in this case) in the reference Hamiltonian. In contrast to simple first-order perturbation theory a finite result ismore » obtained for the effect of h/sub 0/ on S/sup IOS/. As an illustration, our method of analysis is applied to integral state-to-state cross sections for the scattering of an atom and rigid rotor. Results are generated within the He+H/sub 2/ system and a comparison is made between IOS and coupled states cross sections and the corresponding IOS sensitivities. It is found that the sensitivity coefficients are very useful indicators of the accuracy of the IOS results. Finally, further developments and applications are discussed.« less

  11. Discontinuous non-equilibrium phase transition in a threshold Schloegl model for autocatalysis: Generic two-phase coexistence and metastability

    DOE PAGES

    Wang, Chi -Jen; Liu, Da -Jiang; Evans, James W.

    2015-04-28

    Threshold versions of Schloegl’s model on a lattice, which involve autocatalytic creation and spontaneous annihilation of particles, can provide a simple prototype for discontinuous non-equilibrium phase transitions. These models are equivalent to so-called threshold contact processes. A discontinuous transition between populated and vacuum states can occur selecting a threshold of N ≥ 2 for the minimum number, N, of neighboring particles enabling autocatalytic creation at an empty site. Fundamental open questions remain given the lack of a thermodynamic framework for analysis. For a square lattice with N = 2, we show that phase coexistence occurs not at a unique valuemore » but for a finite range of particle annihilation rate (the natural control parameter). This generic two-phase coexistence also persists when perturbing the model to allow spontaneous particle creation. Such behavior contrasts both the Gibbs phase rule for thermodynamic systems and also previous analysis for this model. We find metastability near the transition corresponding to a non-zero effective line tension, also contrasting previously suggested critical behavior. As a result, mean-field type analysis, extended to treat spatially heterogeneous states, further elucidates model behavior.« less

  12. Discontinuous non-equilibrium phase transition in a threshold Schloegl model for autocatalysis: Generic two-phase coexistence and metastability

    NASA Astrophysics Data System (ADS)

    Wang, Chi-Jen; Liu, Da-Jiang; Evans, James W.

    2015-04-01

    Threshold versions of Schloegl's model on a lattice, which involve autocatalytic creation and spontaneous annihilation of particles, can provide a simple prototype for discontinuous non-equilibrium phase transitions. These models are equivalent to so-called threshold contact processes. A discontinuous transition between populated and vacuum states can occur selecting a threshold of N ≥ 2 for the minimum number, N, of neighboring particles enabling autocatalytic creation at an empty site. Fundamental open questions remain given the lack of a thermodynamic framework for analysis. For a square lattice with N = 2, we show that phase coexistence occurs not at a unique value but for a finite range of particle annihilation rate (the natural control parameter). This generic two-phase coexistence also persists when perturbing the model to allow spontaneous particle creation. Such behavior contrasts both the Gibbs phase rule for thermodynamic systems and also previous analysis for this model. We find metastability near the transition corresponding to a non-zero effective line tension, also contrasting previously suggested critical behavior. Mean-field type analysis, extended to treat spatially heterogeneous states, further elucidates model behavior.

  13. Simple Emergent Power Spectra from Complex Inflationary Physics

    NASA Astrophysics Data System (ADS)

    Dias, Mafalda; Frazer, Jonathan; Marsh, M. C. David

    2016-09-01

    We construct ensembles of random scalar potentials for Nf-interacting scalar fields using nonequilibrium random matrix theory, and use these to study the generation of observables during small-field inflation. For Nf=O (few ), these heavily featured scalar potentials give rise to power spectra that are highly nonlinear, at odds with observations. For Nf≫1 , the superhorizon evolution of the perturbations is generically substantial, yet the power spectra simplify considerably and become more predictive, with most realizations being well approximated by a linear power spectrum. This provides proof of principle that complex inflationary physics can give rise to simple emergent power spectra. We explain how these results can be understood in terms of large Nf universality of random matrix theory.

  14. Simple Emergent Power Spectra from Complex Inflationary Physics.

    PubMed

    Dias, Mafalda; Frazer, Jonathan; Marsh, M C David

    2016-09-30

    We construct ensembles of random scalar potentials for N_{f}-interacting scalar fields using nonequilibrium random matrix theory, and use these to study the generation of observables during small-field inflation. For N_{f}=O(few), these heavily featured scalar potentials give rise to power spectra that are highly nonlinear, at odds with observations. For N_{f}≫1, the superhorizon evolution of the perturbations is generically substantial, yet the power spectra simplify considerably and become more predictive, with most realizations being well approximated by a linear power spectrum. This provides proof of principle that complex inflationary physics can give rise to simple emergent power spectra. We explain how these results can be understood in terms of large N_{f} universality of random matrix theory.

  15. A simple microgravity table for the Orbiter or Space Station

    NASA Technical Reports Server (NTRS)

    Garriott, O. K.; Debra, D. B.

    1985-01-01

    Methods of limiting perturbations in microgravity experiments are proposed. An acceleration level below 10 to the -4th m/s-squared is necessary to maintain an undisturbed microgravity environment. Machinery vibrations, crew motion, and the firing of vernier thrusters produce acceleration levels greate than 10 to the -4th m/s-squared. The use of a weak spring system or simple electromagnets to isolate an experimental table from these factors is described. The manners in which crew motion and vernier firing are countered by the springs are examined. The steady acceleration caused by atmospheric drag, gravity gradient force, and steady rotation can be maintained below 10 to the -th m/s-squared; however, the springs can protect the table from these accelerations if required.

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

    Williams, S.; Rohlfing, E.A.; Rahn, L.A.

    We present analytical signal expressions for each two-color resonant four-wave mixing (TC-RFWM) scheme that can be used for double-resonance molecular spectroscopy in the limit of weak fields (no saturation). The theoretical approach employs time-independent, diagrammatic perturbation theory and a spherical tensor analysis in an extension of recent treatments of degenerate four-wave mixing [S. Williams, R. N. Zare, and L. A. Rahn, J. Chem. Phys. {bold 101}, 1072 (1994)] and TC-RFWM for the specific case of stimulated emission pumping [S. Williams {ital et al.}, J. Chem. Phys. {bold 102}, 8342 (1995)]. Under the assumption that the relaxation of the population, themore » orientation, and the alignment are the same, simple analytic expressions are derived for commonly used experimental configurations. The TC-RFWM signal is found to be a product of a concentration term, a one-photon molecular term, a line shape function, and a laboratory-frame geometric factor. These expressions are intended to facilitate the practical analysis of TC-RFWM spectra by clarifying, for example, the dependence on beam polarizations and rotational branch combinations. {copyright} {ital 1997 American Institute of Physics.}« less

  17. Effects of sudden walking perturbations on neuromuscular reflex activity and three-dimensional motion of the trunk in healthy controls and back pain symptomatic subjects.

    PubMed

    Mueller, Juliane; Engel, Tilman; Mueller, Steffen; Stoll, Josefine; Baur, Heiner; Mayer, Frank

    2017-01-01

    Back pain patients (BPP) show delayed muscle onset, increased co-contractions, and variability as response to quasi-static sudden trunk loading in comparison to healthy controls (H). However, it is unclear whether these results can validly be transferred to suddenly applied walking perturbations, an automated but more functional and complex movement pattern. There is an evident need to develop research-based strategies for the rehabilitation of back pain. Therefore, the investigation of differences in trunk stability between H and BPP in functional movements is of primary interest in order to define suitable intervention regimes. The purpose of this study was to analyse neuromuscular reflex activity as well as three-dimensional trunk kinematics between H and BPP during walking perturbations. Eighty H (31m/49f;29±9yrs;174±10cm;71±13kg) and 14 BPP (6m/8f;30±8yrs;171±10cm;67±14kg) walked (1m/s) on a split-belt treadmill while 15 right-sided perturbations (belt decelerating, 40m/s2, 50ms duration; 200ms after heel contact) were randomly applied. Trunk muscle activity was assessed using a 12-lead EMG set-up. Trunk kinematics were measured using a 3-segment-model consisting of 12 markers (upper thoracic (UTA), lower thoracic (LTA), lumbar area (LA)). EMG-RMS ([%],0-200ms after perturbation) was calculated and normalized to the RMS of unperturbed gait. Latency (TON;ms) and time to maximum activity (TMAX;ms) were analysed. Total motion amplitude (ROM;[°]) and mean angle (Amean;[°]) for extension-flexion, lateral flexion and rotation were calculated (whole stride cycle; 0-200ms after perturbation) for each of the three segments during unperturbed and perturbed gait. For ROM only, perturbed was normalized to unperturbed step [%] for the whole stride as well as the 200ms after perturbation. Data were analysed descriptively followed by a student´s t-test to account for group differences. Co-contraction was analyzed between ventral and dorsal muscles (V:R) as well as side right:side left ratio (Sright:Sleft). The coefficient of variation (CV;%) was calculated (EMG-RMS;ROM) to evaluate variability between the 15 perturbations for all groups. With respect to unequal distribution of participants to groups, an additional matched-group analysis was conducted. Fourteen healthy controls out of group H were sex-, age- and anthropometrically matched (group Hmatched) to the BPP. No group differences were observed for EMG-RMS or CV analysis (EMG/ROM) (p>0.025). Co-contraction analysis revealed no differences for V:R and Srigth:Sleft between the groups (p>0.025). BPP showed an increased TON and TMAX, being significant for Mm. rectus abdominus (p = 0.019) and erector spinae T9/L3 (p = 0.005/p = 0.015). ROM analysis over the unperturbed stride cycle revealed no differences between groups (p>0.025). Normalization of perturbed to unperturbed step lead to significant differences for the lumbar segment (LA) in lateral flexion with BPP showing higher normalized ROM compared to Hmatched (p = 0.02). BPP showed a significant higher flexed posture (UTA (p = 0.02); LTA (p = 0.004)) during normal walking (Amean). Trunk posture (Amean) during perturbation showed higher trunk extension values in LTA segments for H/Hmatched compared to BPP (p = 0.003). Matched group (BPP vs. Hmatched) analysis did not show any systematic changes of all results between groups. BPP present impaired muscle response times and trunk posture, especially in the sagittal and transversal planes, compared to H. This could indicate reduced trunk stability and higher loading during gait perturbations.

  18. Effects of sudden walking perturbations on neuromuscular reflex activity and three-dimensional motion of the trunk in healthy controls and back pain symptomatic subjects

    PubMed Central

    Mueller, Juliane; Engel, Tilman; Mueller, Steffen; Stoll, Josefine; Baur, Heiner; Mayer, Frank

    2017-01-01

    Background Back pain patients (BPP) show delayed muscle onset, increased co-contractions, and variability as response to quasi-static sudden trunk loading in comparison to healthy controls (H). However, it is unclear whether these results can validly be transferred to suddenly applied walking perturbations, an automated but more functional and complex movement pattern. There is an evident need to develop research-based strategies for the rehabilitation of back pain. Therefore, the investigation of differences in trunk stability between H and BPP in functional movements is of primary interest in order to define suitable intervention regimes. The purpose of this study was to analyse neuromuscular reflex activity as well as three-dimensional trunk kinematics between H and BPP during walking perturbations. Methods Eighty H (31m/49f;29±9yrs;174±10cm;71±13kg) and 14 BPP (6m/8f;30±8yrs;171±10cm;67±14kg) walked (1m/s) on a split-belt treadmill while 15 right-sided perturbations (belt decelerating, 40m/s2, 50ms duration; 200ms after heel contact) were randomly applied. Trunk muscle activity was assessed using a 12-lead EMG set-up. Trunk kinematics were measured using a 3-segment-model consisting of 12 markers (upper thoracic (UTA), lower thoracic (LTA), lumbar area (LA)). EMG-RMS ([%],0-200ms after perturbation) was calculated and normalized to the RMS of unperturbed gait. Latency (TON;ms) and time to maximum activity (TMAX;ms) were analysed. Total motion amplitude (ROM;[°]) and mean angle (Amean;[°]) for extension-flexion, lateral flexion and rotation were calculated (whole stride cycle; 0-200ms after perturbation) for each of the three segments during unperturbed and perturbed gait. For ROM only, perturbed was normalized to unperturbed step [%] for the whole stride as well as the 200ms after perturbation. Data were analysed descriptively followed by a student´s t-test to account for group differences. Co-contraction was analyzed between ventral and dorsal muscles (V:R) as well as side right:side left ratio (Sright:Sleft). The coefficient of variation (CV;%) was calculated (EMG-RMS;ROM) to evaluate variability between the 15 perturbations for all groups. With respect to unequal distribution of participants to groups, an additional matched-group analysis was conducted. Fourteen healthy controls out of group H were sex-, age- and anthropometrically matched (group Hmatched) to the BPP. Results No group differences were observed for EMG-RMS or CV analysis (EMG/ROM) (p>0.025). Co-contraction analysis revealed no differences for V:R and Srigth:Sleft between the groups (p>0.025). BPP showed an increased TON and TMAX, being significant for Mm. rectus abdominus (p = 0.019) and erector spinae T9/L3 (p = 0.005/p = 0.015). ROM analysis over the unperturbed stride cycle revealed no differences between groups (p>0.025). Normalization of perturbed to unperturbed step lead to significant differences for the lumbar segment (LA) in lateral flexion with BPP showing higher normalized ROM compared to Hmatched (p = 0.02). BPP showed a significant higher flexed posture (UTA (p = 0.02); LTA (p = 0.004)) during normal walking (Amean). Trunk posture (Amean) during perturbation showed higher trunk extension values in LTA segments for H/Hmatched compared to BPP (p = 0.003). Matched group (BPP vs. Hmatched) analysis did not show any systematic changes of all results between groups. Conclusion BPP present impaired muscle response times and trunk posture, especially in the sagittal and transversal planes, compared to H. This could indicate reduced trunk stability and higher loading during gait perturbations. PMID:28319133

  19. Reduced conservatism in stability robustness bounds by state transformation

    NASA Technical Reports Server (NTRS)

    Yedavalli, R. K.; Liang, Z.

    1986-01-01

    This note addresses the issue of 'conservatism' in the time domain stability robustness bounds obtained by the Liapunov approach. A state transformation is employed to improve the upper bounds on the linear time-varying perturbation of an asymptotically stable linear time-invariant system for robust stability. This improvement is due to the variance of the conservatism of the Liapunov approach with respect to the basis of the vector space in which the Liapunov function is constructed. Improved bounds are obtained, using a transformation, on elemental and vector norms of perturbations (i.e., structured perturbations) as well as on a matrix norm of perturbations (i.e., unstructured perturbations). For the case of a diagonal transformation, an algorithm is proposed to find the 'optimal' transformation. Several examples are presented to illustrate the proposed analysis.

  20. Radiotherapy Dose Perturbation of Esophageal Stents Examined in an Experimental Model

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

    Atwood, Todd F.; Hsu, Annie; Ogara, Maydeen M.

    2012-04-01

    Purpose: To investigate the radiotherapy dose perturbations caused by esophageal stents in patients undergoing external beam treatments for esophageal cancer. Methods and Materials: Four esophageal stents were examined (three metallic stents: WallFlex, Ultraflex, and Alveolus; one nonmetallic stent with limited radiopaque markers for visualization: Polyflex). All experiments were performed in a liquid water phantom with a custom acrylic stent holder. Radiochromic film was used to measure the dose distributions adjacent to the stents at locations proximal and distal to the radiation source. The stents were placed in an air-filled cavity to simulate the esophagus. Treatment plans were created and deliveredmore » for photon energies of 6 and 15 MV, and data analysis was performed on uniform regions of interest, according to the size and geometric placement of the films, to quantify the dose perturbations. Results: The three metallic stents produced the largest dose perturbations with distinct patterns of 'hot' spots (increased dose) measured proximal to the radiation source (up to 15.4%) and both 'cold' (decreased dose) and hot spots measured distal to the radiation source (range, -6.1%-5.8%). The polymeric Polyflex stent produced similar dose perturbations when the radiopaque markers were examined (range, -7.6%-15.4%). However, when the radiopaque markers were excluded from the analysis, the Polyflex stent produced significantly smaller dose perturbations, with maximum hot spots of 7.3% and cold spots of -3.2%. Conclusions: The dose perturbations caused by esophageal stents during the treatment of esophageal cancer using external beam radiotherapy should be understood. These perturbations will result in hot and cold spots in the esophageal mucosa, with varying magnitudes depending on the stent. The nonmetallic Polyflex stent appears to be the most suitable for patients undergoing radiotherapy, but further studies are necessary to determine the clinical significance of the dose perturbations.« less

  1. Radiotherapy dose perturbation of esophageal stents examined in an experimental model.

    PubMed

    Atwood, Todd F; Hsu, Annie; Ogara, Maydeen M; Luba, Daniel G; Tamler, Bradley J; Disario, James A; Maxim, Peter G

    2012-04-01

    To investigate the radiotherapy dose perturbations caused by esophageal stents in patients undergoing external beam treatments for esophageal cancer. Four esophageal stents were examined (three metallic stents: WallFlex, Ultraflex, and Alveolus; one nonmetallic stent with limited radiopaque markers for visualization: Polyflex). All experiments were performed in a liquid water phantom with a custom acrylic stent holder. Radiochromic film was used to measure the dose distributions adjacent to the stents at locations proximal and distal to the radiation source. The stents were placed in an air-filled cavity to simulate the esophagus. Treatment plans were created and delivered for photon energies of 6 and 15 MV, and data analysis was performed on uniform regions of interest, according to the size and geometric placement of the films, to quantify the dose perturbations. The three metallic stents produced the largest dose perturbations with distinct patterns of "hot" spots (increased dose) measured proximal to the radiation source (up to 15.4%) and both "cold" (decreased dose) and hot spots measured distal to the radiation source (range, -6.1%-5.8%). The polymeric Polyflex stent produced similar dose perturbations when the radiopaque markers were examined (range, -7.6%-15.4%). However, when the radiopaque markers were excluded from the analysis, the Polyflex stent produced significantly smaller dose perturbations, with maximum hot spots of 7.3% and cold spots of -3.2%. The dose perturbations caused by esophageal stents during the treatment of esophageal cancer using external beam radiotherapy should be understood. These perturbations will result in hot and cold spots in the esophageal mucosa, with varying magnitudes depending on the stent. The nonmetallic Polyflex stent appears to be the most suitable for patients undergoing radiotherapy, but further studies are necessary to determine the clinical significance of the dose perturbations. Copyright © 2012 Elsevier Inc. All rights reserved.

  2. 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.

  3. Time-dependent generalized Gibbs ensembles in open quantum systems

    NASA Astrophysics Data System (ADS)

    Lange, Florian; Lenarčič, Zala; Rosch, Achim

    2018-04-01

    Generalized Gibbs ensembles have been used as powerful tools to describe the steady state of integrable many-particle quantum systems after a sudden change of the Hamiltonian. Here, we demonstrate numerically that they can be used for a much broader class of problems. We consider integrable systems in the presence of weak perturbations which break both integrability and drive the system to a state far from equilibrium. Under these conditions, we show that the steady state and the time evolution on long timescales can be accurately described by a (truncated) generalized Gibbs ensemble with time-dependent Lagrange parameters, determined from simple rate equations. We compare the numerically exact time evolutions of density matrices for small systems with a theory based on block-diagonal density matrices (diagonal ensemble) and a time-dependent generalized Gibbs ensemble containing only a small number of approximately conserved quantities, using the one-dimensional Heisenberg model with perturbations described by Lindblad operators as an example.

  4. Topological Hall Effect from Strong to Weak Coupling

    NASA Astrophysics Data System (ADS)

    Nakazawa, Kazuki; Bibes, Manuel; Kohno, Hiroshi

    2018-03-01

    The topological Hall effect (THE) of electrons coupled to a noncoplanar spin texture has been studied so far for the strong- and weak-coupling regimes separately; the former in terms of the Berry phase and the latter by perturbation theory. In this letter, we present a unified treatment in terms of spin gauge field by considering not only the adiabatic (Berry phase) component of the gauge field but also the nonadiabatic component. While only the adiabatic contribution is important in the strong-coupling regime, it is completely canceled by a part of the nonadiabatic contribution in the weak-coupling regime, where the THE is governed by the remaining nonadiabatic terms. We found a new weak-coupling region that cannot be accessed by a simple perturbation theory, where the Hall conductivity is proportional to M, with 2M being the exchange splitting of the electron spectrum.

  5. Toroidal momentum pinch velocity due to the coriolis drift effect on small scale instabilities in a toroidal plasma.

    PubMed

    Peeters, A G; Angioni, C; Strintzi, D

    2007-06-29

    In this Letter, the influence of the "Coriolis drift" on small scale instabilities in toroidal plasmas is shown to generate a toroidal momentum pinch velocity. Such a pinch results because the Coriolis drift generates a coupling between the density and temperature perturbations on the one hand and the perturbed parallel flow velocity on the other. A simple fluid model is used to highlight the physics mechanism and gyro-kinetic calculations are performed to accurately assess the magnitude of the pinch. The derived pinch velocity leads to a radial gradient of the toroidal velocity profile even in the absence of a torque on the plasma and is predicted to generate a peaking of the toroidal velocity profile similar to the peaking of the density profile. Finally, the pinch also affects the interpretation of current experiments.

  6. Toroidal Momentum Pinch Velocity due to the Coriolis Drift Effect on Small Scale Instabilities in a Toroidal Plasma

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

    Peeters, A. G.; Angioni, C.; Strintzi, D.

    In this Letter, the influence of the ''Coriolis drift'' on small scale instabilities in toroidal plasmas is shown to generate a toroidal momentum pinch velocity. Such a pinch results because the Coriolis drift generates a coupling between the density and temperature perturbations on the one hand and the perturbed parallel flow velocity on the other. A simple fluid model is used to highlight the physics mechanism and gyro-kinetic calculations are performed to accurately assess the magnitude of the pinch. The derived pinch velocity leads to a radial gradient of the toroidal velocity profile even in the absence of a torquemore » on the plasma and is predicted to generate a peaking of the toroidal velocity profile similar to the peaking of the density profile. Finally, the pinch also affects the interpretation of current experiment000.« less

  7. Stability of Lobed Balloons

    NASA Technical Reports Server (NTRS)

    Ball, Danny (Technical Monitor); Pagitz, M.; Pellegrino, Xu S.

    2004-01-01

    This paper presents a computational study of the stability of simple lobed balloon structures. Two approaches are presented, one based on a wrinkled material model and one based on a variable Poisson s ratio model that eliminates compressive stresses iteratively. The first approach is used to investigate the stability of both a single isotensoid and a stack of four isotensoids, for perturbations of in.nitesimally small amplitude. It is found that both structures are stable for global deformation modes, but unstable for local modes at su.ciently large pressure. Both structures are stable if an isotropic model is assumed. The second approach is used to investigate the stability of the isotensoid stack for large shape perturbations, taking into account contact between di.erent surfaces. For this structure a distorted, stable configuration is found. It is also found that the volume enclosed by this con.guration is smaller than that enclosed by the undistorted structure.

  8. Dynamical patterns and regime shifts in the nonlinear model of soil microorganisms growth

    NASA Astrophysics Data System (ADS)

    Zaitseva, Maria; Vladimirov, Artem; Winter, Anna-Marie; Vasilyeva, Nadezda

    2017-04-01

    Dynamical model of soil microorganisms growth and turnover is formulated as a system of nonlinear partial differential equations of reaction-diffusion type. We consider spatial distributions of concentrations of several substrates and microorganisms. Biochemical reactions are modelled by chemical kinetic equations. Transport is modelled by simple linear diffusion for all chemical substances, while for microorganisms we use different transport functions, e.g. some of them can actively move along gradient of substrate concentration, while others cannot move. We solve our model in two dimensions, starting from uniform state with small initial perturbations for various parameters and find parameter range, where small initial perturbations grow and evolve. We search for bifurcation points and critical regime shifts in our model and analyze time-space profile and phase portraits of these solutions approaching critical regime shifts in the system, exploring possibility to detect such shifts in advance. This work is supported by NordForsk, project #81513.

  9. Perihelion precession from power law central force and magnetic-like force

    NASA Astrophysics Data System (ADS)

    Xu, Feng

    2011-04-01

    By the Laplace-Runge-Lenz (LRL) vector, we analyzed perihelion precessions of orbit with arbitrary eccentricity from perturbations of 1) power law central force and 2) fThusmagnetic-like force. Exact and analytically closed expressions for the precession rate are derived in both cases. In the central force case, we give a further expansion expression of precession rate in orders of eccentricity, and a rule judging pro- or retrograde precession is also given. We applied the result of central force to precessions of a planet in 1) Schwarzschild space-time, for which the formula for the Mercury’s 43”/century is reproduced, and 2) spherically distributed dark matter, for which we find a formula that is a generalization of the result derived by others for circular orbit. In the magnetic case, the use of the LRL vector proves to be simple and efficient. An example of magnetic-like perturbation is also discussed.

  10. Perihelion precession from power law central force and magnetic-like force

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

    Xu Feng

    2011-04-15

    By the Laplace-Runge-Lenz (LRL) vector, we analyzed perihelion precessions of orbit with arbitrary eccentricity from perturbations of 1) power law central force and 2) fThusmagnetic-like force. Exact and analytically closed expressions for the precession rate are derived in both cases. In the central force case, we give a further expansion expression of precession rate in orders of eccentricity, and a rule judging pro- or retrograde precession is also given. We applied the result of central force to precessions of a planet in 1) Schwarzschild space-time, for which the formula for the Mercury's 43''/century is reproduced, and 2) spherically distributed darkmore » matter, for which we find a formula that is a generalization of the result derived by others for circular orbit. In the magnetic case, the use of the LRL vector proves to be simple and efficient. An example of magnetic-like perturbation is also discussed.« less

  11. 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.

  12. Non-perturbative reheating and Nnaturalness

    NASA Astrophysics Data System (ADS)

    Hardy, Edward

    2017-11-01

    We study models in which reheating happens only through non-perturbative processes. The energy transferred can be exponentially suppressed unless the inflaton is coupled to a particle with a parametrically small mass. Additionally, in some models a light scalar with a negative mass squared parameter leads to much more efficient reheating than one with a positive mass squared of the same magnitude. If a theory contains many sectors similar to the Standard Model coupled to the inflaton via their Higgses, such dynamics can realise the Nnaturalness solution to the hierarchy problem. A sector containing a light Higgs with a non-zero vacuum expectation value is dominantly reheated and there is little energy transferred to the other sectors, consistent with cosmological constraints. The inflaton must decouple from other particles and have a flat potential at large field values, in which case the visible sector UV cutoff can be raised to 10 TeV in a simple model.

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

    NASA Astrophysics Data System (ADS)

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

    2018-04-01

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

  14. Kinetic field theory: exact free evolution of Gaussian phase-space correlations

    NASA Astrophysics Data System (ADS)

    Fabis, Felix; Kozlikin, Elena; Lilow, Robert; Bartelmann, Matthias

    2018-04-01

    In recent work we developed a description of cosmic large-scale structure formation in terms of non-equilibrium ensembles of classical particles, with time evolution obtained in the framework of a statistical field theory. In these works, the initial correlations between particles sampled from random Gaussian density and velocity fields have so far been treated perturbatively or restricted to pure momentum correlations. Here we treat the correlations between all phase-space coordinates exactly by adopting a diagrammatic language for the different forms of correlations, directly inspired by the Mayer cluster expansion. We will demonstrate that explicit expressions for phase-space density cumulants of arbitrary n-point order, which fully capture the non-linear coupling of free streaming kinematics due to initial correlations, can be obtained from a simple set of Feynman rules. These cumulants will be the foundation for future investigations of perturbation theory in particle interactions.

  15. The Effect of Cement Dust Exposure on Haematological Parameters of Cement Factory workers in Nalagonda, Andhra Pradesh.

    NASA Astrophysics Data System (ADS)

    Guguloth, Mohan Rao.; Sambanaik, A.; srinivasnaik, L.; Mude, Jagadishnaik.

    2012-10-01

    This study was measured on haematological parameters in workers exposed to cement dust in order to test the the hypothesis and to identify a simple, readily available, cost effective screening test that could help in identifying the presence of disease, its severity, that Cement dust exposure may perturb these functions related to their workplace.Assesment of haematological parameters were performed in 100exposed workers occupationally exposed to cement dust and 50 matched unexposed controls with ages ranging from 20-35, 35-50, 50-65 years. The blood samples were taken from them and percentage of hemoglobin, Lymphocytes / monocytes count were analysed.The hemoglobin percentage of exposed workers were significantly lower(P<0.05).Lymphocytes/Monocytes counts of exposed workers was insignificant (P<0.05).These results suggest that long term occupational exposure to cement dust may perturb haemopoietic function.

  16. 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.

  17. Instabilities in mimetic matter perturbations

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

    Firouzjahi, Hassan; Gorji, Mohammad Ali; Mansoori, Seyed Ali Hosseini, E-mail: firouz@ipm.ir, E-mail: gorji@ipm.ir, E-mail: shosseini@shahroodut.ac.ir, E-mail: shossein@ipm.ir

    2017-07-01

    We study cosmological perturbations in mimetic matter scenario with a general higher derivative function. We calculate the quadratic action and show that both the kinetic term and the gradient term have the wrong sings. We perform the analysis in both comoving and Newtonian gauges and confirm that the Hamiltonians and the associated instabilities are consistent with each other in both gauges. The existence of instabilities is independent of the specific form of higher derivative function which generates gradients for mimetic field perturbations. It is verified that the ghost instability in mimetic perturbations is not associated with the higher derivative instabilitiesmore » such as the Ostrogradsky ghost.« less

  18. Distribution function approach to redshift space distortions. Part IV: perturbation theory applied to dark matter

    NASA Astrophysics Data System (ADS)

    Vlah, Zvonimir; Seljak, Uroš; McDonald, Patrick; Okumura, Teppei; Baldauf, Tobias

    2012-11-01

    We develop a perturbative approach to redshift space distortions (RSD) using the phase space distribution function approach and apply it to the dark matter redshift space power spectrum and its moments. RSD can be written as a sum over density weighted velocity moments correlators, with the lowest order being density, momentum density and stress energy density. We use standard and extended perturbation theory (PT) to determine their auto and cross correlators, comparing them to N-body simulations. We show which of the terms can be modeled well with the standard PT and which need additional terms that include higher order corrections which cannot be modeled in PT. Most of these additional terms are related to the small scale velocity dispersion effects, the so called finger of god (FoG) effects, which affect some, but not all, of the terms in this expansion, and which can be approximately modeled using a simple physically motivated ansatz such as the halo model. We point out that there are several velocity dispersions that enter into the detailed RSD analysis with very different amplitudes, which can be approximately predicted by the halo model. In contrast to previous models our approach systematically includes all of the terms at a given order in PT and provides a physical interpretation for the small scale dispersion values. We investigate RSD power spectrum as a function of μ, the cosine of the angle between the Fourier mode and line of sight, focusing on the lowest order powers of μ and multipole moments which dominate the observable RSD power spectrum. Overall we find considerable success in modeling many, but not all, of the terms in this expansion. This is similar to the situation in real space, but predicting power spectrum in redshift space is more difficult because of the explicit influence of small scale dispersion type effects in RSD, which extend to very large scales.

  19. A perturbation analysis of a mechanical model for stable spatial patterning in embryology

    NASA Astrophysics Data System (ADS)

    Bentil, D. E.; Murray, J. D.

    1992-12-01

    We investigate a mechanical cell-traction mechanism that generates stationary spatial patterns. A linear analysis highlights the model's potential for these heterogeneous solutions. We use multiple-scale perturbation techniques to study the evolution of these solutions and compare our solutions with numerical simulations of the model system. We discuss some potential biological applications among which are the formation of ridge patterns, dermatoglyphs, and wound healing.

  20. Analysis of orbit determination from Earth-based tracking for relay satellites in a perturbed areostationary orbit

    NASA Astrophysics Data System (ADS)

    Romero, P.; Pablos, B.; Barderas, G.

    2017-07-01

    Areostationary satellites are considered a high interest group of satellites to satisfy the telecommunications needs of the foreseen missions to Mars. An areostationary satellite, in an areoequatorial circular orbit with a period of 1 Martian sidereal day, would orbit Mars remaining at a fixed location over the Martian surface, analogous to a geostationary satellite around the Earth. This work addresses an analysis of the perturbed orbital motion of an areostationary satellite as well as a preliminary analysis of the aerostationary orbit estimation accuracy based on Earth tracking observations. First, the models for the perturbations due to the Mars gravitational field, the gravitational attraction of the Sun and the Martian moons, Phobos and Deimos, and solar radiation pressure are described. Then, the observability from Earth including possible occultations by Mars of an areostationary satellite in a perturbed areosynchronous motion is analyzed. The results show that continuous Earth-based tracking is achievable using observations from the three NASA Deep Space Network Complexes in Madrid, Goldstone and Canberra in an occultation-free scenario. Finally, an analysis of the orbit determination accuracy is addressed considering several scenarios including discontinuous tracking schedules for different epochs and different areoestationary satellites. Simulations also allow to quantify the aerostationary orbit estimation accuracy for various tracking series durations and observed orbit arc-lengths.

  1. Structure of a financial cross-correlation matrix under attack

    NASA Astrophysics Data System (ADS)

    Lim, Gyuchang; Kim, SooYong; Kim, Junghwan; Kim, Pyungsoo; Kang, Yoonjong; Park, Sanghoon; Park, Inho; Park, Sang-Bum; Kim, Kyungsik

    2009-09-01

    We investigate the structure of a perturbed stock market in terms of correlation matrices. For the purpose of perturbing a stock market, two distinct methods are used, namely local and global perturbation. The former involves replacing a correlation coefficient of the cross-correlation matrix with one calculated from two Gaussian-distributed time series while the latter reconstructs the cross-correlation matrix just after replacing the original return series with Gaussian-distributed time series. Concerning the local case, it is a technical study only and there is no attempt to model reality. The term ‘global’ means the overall effect of the replacement on other untouched returns. Through statistical analyses such as random matrix theory (RMT), network theory, and the correlation coefficient distributions, we show that the global structure of a stock market is vulnerable to perturbation. However, apart from in the analysis of inverse participation ratios (IPRs), the vulnerability becomes dull under a small-scale perturbation. This means that these analysis tools are inappropriate for monitoring the whole stock market due to the low sensitivity of a stock market to a small-scale perturbation. In contrast, when going down to the structure of business sectors, we confirm that correlation-based business sectors are regrouped in terms of IPRs. This result gives a clue about monitoring the effect of hidden intentions, which are revealed via portfolios taken mostly by large investors.

  2. Rayleigh-Taylor instability under curved substrates: An optimal transient growth analysis

    NASA Astrophysics Data System (ADS)

    Balestra, Gioele; Brun, P.-T.; Gallaire, François

    2016-12-01

    We investigate the stability of thin viscous films coated on the inside of a horizontal cylindrical substrate. In such a case, gravity acts both as a stabilizing force through the progressive drainage of the film and as a destabilizing force prone to form droplets via the Rayleigh-Taylor instability. The drainage solution, derived from lubrication equations, is found asymptotically stable with respect to infinitesimally small perturbations, although in reality, droplets often form. To resolve this paradox, we perform an optimal transient growth analysis for the first-order perturbations of the liquid's interface, generalizing the results of Trinh et al. [Phys. Fluids 26, 051704 (2014), 10.1063/1.4876476]. We find that the system displays a linear transient growth potential that gives rise to two different scenarios depending on the value of the Bond number (prescribing the relative importance of gravity and surface tension forces). At low Bond numbers, the optimal perturbation of the interface does not generate droplets. In contrast, for higher Bond numbers, perturbations on the upper hemicircle yield gains large enough to potentially form droplets. The gain increases exponentially with the Bond number. In particular, depending on the amplitude of the initial perturbation, we find a critical Bond number above which the short-time linear growth is sufficient to trigger the nonlinear effects required to form dripping droplets. We conclude that the transition to droplets detaching from the substrate is noise and perturbation dependent.

  3. Proteome analysis of the triton-insoluble erythrocyte membrane skeleton.

    PubMed

    Basu, Avik; Harper, Sandra; Pesciotta, Esther N; Speicher, Kaye D; Chakrabarti, Abhijit; Speicher, David W

    2015-10-14

    Erythrocyte shape and membrane integrity is imparted by the membrane skeleton, which can be isolated as a Triton X-100 insoluble structure that retains the biconcave shape of intact erythrocytes, indicating isolation of essentially intact membrane skeletons. These erythrocyte "Triton Skeletons" have been studied morphologically and biochemically, but unbiased proteome analysis of this substructure of the membrane has not been reported. In this study, different extraction buffers and in-depth proteome analyses were used to more fully define the protein composition of this functionally critical macromolecular complex. As expected, the major, well-characterized membrane skeleton proteins and their associated membrane anchors were recovered in good yield. But surprisingly, a substantial number of additional proteins that are not considered in erythrocyte membrane skeleton models were recovered in high yields, including myosin-9, lipid raft proteins (stomatin, flotillin1 and 2), multiple chaperone proteins (HSPs, protein disulfide isomerase and calnexin), and several other proteins. These results show that the membrane skeleton is substantially more complex than previous biochemical studies indicated, and it apparently has localized regions with unique protein compositions and functions. This comprehensive catalog of the membrane skeleton should lead to new insights into erythrocyte membrane biology and pathogenic mutations that perturb membrane stability. Biological significance Current models of erythrocyte membranes describe fairly simple homogenous structures that are incomplete. Proteome analysis of the erythrocyte membrane skeleton shows that it is quite complex and includes a substantial number of proteins whose roles and locations in the membrane are not well defined. Further elucidation of interactions involving these proteins and definition of microdomains in the membrane that contain these proteins should yield novel insights into how the membrane skeleton produces the normal biconcave erythrocyte shape and how it is perturbed in pathological conditions that destabilize the membrane. Copyright © 2015 Elsevier B.V. All rights reserved.

  4. Possibilities of Bragg filtering structures based on subwavelength grating guiding mechanism (Conference Presentation)

    NASA Astrophysics Data System (ADS)

    Kwiecien, Pavel; Litvik, Ján.; Richter, Ivan; Ctyroký, Jirí; Cheben, Pavel

    2017-05-01

    Silicon-on-insulator (SOI), as the most promising platform, for advanced photonic integrated structures, employs a high refractive index contrast between the silicon "core" and surrounding media. One of the recent new ideas within this field is based on the alternative formation of the subwavelength sized (quasi)periodic structures, manifesting as an effective medium with respect to propagating light. Such structures relay on Bloch wave propagation concept, in contrast to standard index guiding mechanism. Soon after the invention of such subwavelength grating (SWG) waveguides, the scientists concentrated on various functional elements such as couplers, crossings, mode transformers, convertors, MMI couplers, polarization converters, resonators, Bragg filters, and others. Our contribution is devoted to a detailed numerical analysis and design considerations of Bragg filtering structures based on SWG idea. Based on our previous studies where we have shown impossibility of application of various 2 and "2.5" dimensional methods for the proper numerical analysis, here we effectively use two independent but similar in-house approaches based on 3D Fourier modal methods, namely aperiodic rigorous coupled wave analysis (aRCWA) and bidirectional expansion and propagation method based on Fourier series (BEX) tools. As it was recently demonstrated, SWG Bragg filters are feasible. Based on this idea, we propose, simulate, and optimize spectral characteristics of such filters. In particular, we have investigated several possibilities of modifications of original SWG waveguides towards the Bragg filtering, including firstly - simple single-segment changes in position, thickness, and width, and secondly - several types of Si inclusions, in terms of perturbed width and thickness (and their combinations). The leading idea was to obtain required (e.g. sufficiently narrow) spectral characteristic while keeping the minimum size of Si features large enough. We have found that the second approach with the single element perturbations can provide promising designs. Furthermore, even more complex filtering SWG structures can be considered.

  5. Early universe with modified scalar-tensor theory of gravity

    NASA Astrophysics Data System (ADS)

    Mandal, Ranajit; Sarkar, Chandramouli; Sanyal, Abhik Kumar

    2018-05-01

    Scalar-tensor theory of gravity with non-minimal coupling is a fairly good candidate for dark energy, required to explain late-time cosmic evolution. Here we study the very early stage of evolution of the universe with a modified version of the theory, which includes scalar curvature squared term. One of the key aspects of the present study is that, the quantum dynamics of the action under consideration ends up generically with de-Sitter expansion under semiclassical approximation, rather than power-law. This justifies the analysis of inflationary regime with de-Sitter expansion. The other key aspect is that, while studying gravitational perturbation, the perturbed generalized scalar field equation obtained from the perturbed action, when matched with the perturbed form of the background scalar field equation, relates the coupling parameter and the potential exactly in the same manner as the solution of classical field equations does, assuming de-Sitter expansion. The study also reveals that the quantum theory is well behaved, inflationary parameters fall well within the observational limit and quantum perturbation analysis shows that the power-spectrum does not deviate considerably from the standard one obtained from minimally coupled theory.

  6. Speech waveform perturbation analysis: a perceptual-acoustical comparison of seven measures.

    PubMed

    Askenfelt, A G; Hammarberg, B

    1986-03-01

    The performance of seven acoustic measures of cycle-to-cycle variations (perturbations) in the speech waveform was compared. All measures were calculated automatically and applied on running speech. Three of the measures refer to the frequency of occurrence and severity of waveform perturbations in special selected parts of the speech, identified by means of the rate of change in the fundamental frequency. Three other measures refer to statistical properties of the distribution of the relative frequency differences between adjacent pitch periods. One perturbation measure refers to the percentage of consecutive pitch period differences with alternating signs. The acoustic measures were tested on tape recorded speech samples from 41 voice patients, before and after successful therapy. Scattergrams of acoustic waveform perturbation data versus an average of perceived deviant voice qualities, as rated by voice clinicians, are presented. The perturbation measures were compared with regard to the acoustic-perceptual correlation and their ability to discriminate between normal and pathological voice status. The standard deviation of the distribution of the relative frequency differences was suggested as the most useful acoustic measure of waveform perturbations for clinical applications.

  7. Behavior of a stochastic SIR epidemic model with saturated incidence and vaccination rules

    NASA Astrophysics Data System (ADS)

    Zhang, Yue; Li, Yang; Zhang, Qingling; Li, Aihua

    2018-07-01

    In this paper, the threshold behavior of a susceptible-infected-recovered (SIR) epidemic model with stochastic perturbation is investigated. Firstly, it is obtained that the system has a unique global positive solution with any positive initial value. Random effect may lead to disease extinction under a simple condition. Subsequently, sufficient condition for persistence has been established in the mean of the disease. Finally, some numerical simulations are carried out to confirm the analytical results.

  8. A Tester for Carbon Nanotube Mode Lockers

    NASA Astrophysics Data System (ADS)

    Song, Yong-Won; Yamashita, Shinji

    2007-05-01

    We propose and demonstrate a tester for laser pulsating operation of carbon nanotubes employing a circulator with the extra degree of freedom of the second port to access diversified nanotube samples. The nanotubes are deposited onto the end facet of a dummy optical fiber by spray method that guarantees simple sample loading along with the minimized perturbation of optimized laser cavity condition. Resultant optical spectra, autocorrelation traces and pulse train of the laser outputs with qualified samples are presented.

  9. Reconciling phase diffusion and Hartree-Fock approximation in condensate systems

    NASA Astrophysics Data System (ADS)

    Giorgi, Gian Luca; de Pasquale, Ferdinando

    2012-01-01

    Despite the weakly interacting regime, the physics of Bose-Einstein condensates is widely affected by particle-particle interactions. They determine quantum phase diffusion, which is known to be the main cause of loss of coherence. Studying a simple model of two interacting Bose systems, we show how to predict the appearance of phase diffusion beyond the Bogoliubov approximation, providing a self-consistent treatment in the framework of a generalized Hartree-Fock-Bogoliubov perturbation theory.

  10. On (in)stabilities of perturbations in mimetic models with higher derivatives

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

    Zheng, Yunlong; Shen, Liuyuan; Mou, Yicen

    2017-08-01

    Usually when applying the mimetic model to the early universe, higher derivative terms are needed to promote the mimetic field to be dynamical. However such models suffer from the ghost and/or the gradient instabilities and simple extensions cannot cure this pathology. We point out in this paper that it is possible to overcome this difficulty by considering the direct couplings of the higher derivatives of the mimetic field to the curvature of the spacetime.

  11. A Van der Waals-like theory of plasma double layers

    NASA Technical Reports Server (NTRS)

    Katz, Ira; Davis, V. A.

    1989-01-01

    A theory describing plasma double layers in terms of multiple roots of the charge density expression is presented. The theory presented uses the fact that equilibrium plasmas shield small potential perturbations linearly; for high potentials, the shielding decreases. The approach is analogous to Van der Waals' theory of simple fluids in which inclusion of approximate expressions for both excluded volume and long range attractive forces sufficiently describes the first-order liquid-gas phase transition.

  12. Choice of Bond Dissociation Enthalpies on which to Base the Stabilization Energies of Simple Radicals: DH(R-H)is Preferred because DH(R-Me) is Perturbed by Changes in Chain Branching

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

    Poutsma, Marvin L

    2008-01-01

    The relative stabilization energies of radicals, SE(R ), along the simple series methyl/ethyl/i-propyl/t-butyl are known to vary in spread and even direction dependent on which dissociation enthalpies, DH(R-X), they are based on. Using a highly electronegative X is recognized as unwise, but it is not clear whether a choice of X = Me or X = R might not be preferred over the almost universal use of R = H. The enthalpies of isomerization of C4 radical pairs that vary only in the substitution pattern at the radical center but not in carbon skeleton illustrate that R = H ismore » indeed the better choice. Comparisons in the context of recent predictive models for alkane and radical stability indicate that, while relative DH(R-H) values highlight the desired difference in substitution pattern at the radical center, relative DH(R-Me) values are perturbed by differences in skeletal branching or protobranching which are well-known to affect thermochemistry. As a result, SE(R ) values derived from relative DH(R-Me) values are consistently too small. The same pattern is illustrated for prim, sec, and tert allylic and benzylic radicals (larger SE(R )) and for the parent vinyl, phenyl, and ethynyl radicals (negative SE(R )).« less

  13. Parametrizing growth in dark energy and modified gravity models

    NASA Astrophysics Data System (ADS)

    Resco, Miguel Aparicio; Maroto, Antonio L.

    2018-02-01

    It is well known that an extremely accurate parametrization of the growth function of matter density perturbations in Λ CDM cosmology, with errors below 0.25%, is given by f (a )=Ωmγ(a ) with γ ≃0.55 . In this work, we show that a simple modification of this expression also provides a good description of growth in modified gravity theories. We consider the model-independent approach to modified gravity in terms of an effective Newton constant written as μ (a ,k )=Geff/G and show that f (a )=β (a )Ωmγ(a ) provides fits to the numerical solutions with similar accuracy to that of Λ CDM . In the time-independent case with μ =μ (k ), simple analytic expressions for β (μ ) and γ (μ ) are presented. In the time-dependent (but scale-independent) case μ =μ (a ), we show that β (a ) has the same time dependence as μ (a ). As an example, explicit formulas are provided in the Dvali-Gabadadze-Porrati (DGP) model. In the general case, for theories with μ (a ,k ), we obtain a perturbative expansion for β (μ ) around the general relativity case μ =1 which, for f (R ) theories, reaches an accuracy below 1%. Finally, as an example we apply the obtained fitting functions in order to forecast the precision with which future galaxy surveys will be able to measure the μ parameter.

  14. Rotating spiral waves in fertilized ascidian eggs.

    PubMed

    Ballarò, Benedetto; Reas, Pier Giorgio

    2002-01-01

    Excitable systems modelled by reaction-diffusion equation may be expected to produce quite complex spatial patterns. Winfree [1974] demonstrated experimentally, in the Belousov-Zhabotinskii reaction, the existence of particular waves called rotating spiral waves. Later Keener and Tyson [1986] presented a thorough analysis of these waves in excitable systems. Spiral waves can also be observed in brain tissue (Shibata and Bures [1974]), while it seems that the precursor to cardiac fibrillation is the appearance of rotating waves of electrical impulses (Winfree [1983]). In this work we suppose the appearance of Ca++ spiral waves in the vegetal pole of ascidian egg cells after the first ooplasmic segregation. Previously we observed that (Ballarò and Reas [2000a]), when the myoplasm is completely localized in the vegetal region (excitable stage) and the ascidian egg cell is perturbed by an increase of Ca++ concentration in the culture medium, the cell reacts by showing persistent mechanical waves of contraction which exist as long as the cell is perturbed. Experimentally we observed the production of a polar lobe located in the vegetal region and the change of the inclination of mitotic furrow, after the appearance of a myoplasmic spiral wave in the vegetal pole. So we suppose that the myoplasmic spiral wave is due to a Ca++ spiral wave, and the myoplasmic spiral wave then causes the changes in the shape of the cell (polar lobe, inclination of mitotic furrow, etc.). Moreover we give a simple geometrical description of a spiral wave.

  15. Yang-Mills condensate as dark energy: A nonperturbative approach

    NASA Astrophysics Data System (ADS)

    Donà, Pietro; Marcianò, Antonino; Zhang, Yang; Antolini, Claudia

    2016-02-01

    Models based on the Yang-Mills condensate (YMC) have been advocated for in the literature and claimed as successful candidates for explaining dark energy. Several variations on this simple idea have been considered, the most promising of which are reviewed here. Nevertheless, the previously attained results relied heavily on the perturbative approach to the analysis of the effective Yang-Mills action, which is only adequate in the asymptotically free limit, and were extended into a regime, the infrared limit, in which confinement is expected. We show that if a minimum of the effective Lagrangian in θ =-Fμν aFa μ ν/2 exists, a YMC forms that drives the Universe toward an accelerated de Sitter phase. The details of the models depend weakly on the specific form of the effective Yang-Mills Lagrangian. Using nonperturbative techniques mutated from the functional renormalization-group procedure, we finally show that the minimum in θ of the effective Lagrangian exists. Thus, a YMC can actually take place. The nonperturbative model has properties similar to the ones in the perturbative model. In the early stage of the Universe, the YMC equation of state has an evolution that resembles the radiation component, i.e., wy→1 /3 . However, in the late stage, wy naturally runs to the critical state with wy=-1 , and the Universe transitions from a matter-dominated into a dark energy dominated stage only at latest time, at a redshift whose value depends on the initial conditions that are chosen while solving the dynamical system.

  16. Stochastic uncertainty analysis for unconfined flow systems

    USGS Publications Warehouse

    Liu, Gaisheng; Zhang, Dongxiao; Lu, Zhiming

    2006-01-01

    A new stochastic approach proposed by Zhang and Lu (2004), called the Karhunen‐Loeve decomposition‐based moment equation (KLME), has been extended to solving nonlinear, unconfined flow problems in randomly heterogeneous aquifers. This approach is on the basis of an innovative combination of Karhunen‐Loeve decomposition, polynomial expansion, and perturbation methods. The random log‐transformed hydraulic conductivity field (lnKS) is first expanded into a series in terms of orthogonal Gaussian standard random variables with their coefficients obtained as the eigenvalues and eigenfunctions of the covariance function of lnKS. Next, head h is decomposed as a perturbation expansion series Σh(m), where h(m) represents the mth‐order head term with respect to the standard deviation of lnKS. Then h(m) is further expanded into a polynomial series of m products of orthogonal Gaussian standard random variables whose coefficients hi1,i2,...,im(m) are deterministic and solved sequentially from low to high expansion orders using MODFLOW‐2000. Finally, the statistics of head and flux are computed using simple algebraic operations on hi1,i2,...,im(m). A series of numerical test results in 2‐D and 3‐D unconfined flow systems indicated that the KLME approach is effective in estimating the mean and (co)variance of both heads and fluxes and requires much less computational effort as compared to the traditional Monte Carlo simulation technique.

  17. Solitary waves in morphogenesis: Determination fronts as strain-cued strain transformations among automatous cells

    NASA Astrophysics Data System (ADS)

    Cox, Brian N.; Landis, Chad M.

    2018-02-01

    We present a simple theory of a strain pulse propagating as a solitary wave through a continuous two-dimensional population of cells. A critical strain is assumed to trigger a strain transformation, while, simultaneously, cells move as automata to tend to restore a preferred cell density. We consider systems in which the strain transformation is a shape change, a burst of proliferation, or the commencement of growth (which changes the shape of the population sheet), and demonstrate isomorphism among these cases. Numerical and analytical solutions describe a strain pulse whose height does not depend on how the strain disturbance was first launched, or the rate at which the strain transformation is achieved, or the rate constant in the rule for the restorative cell motion. The strain pulse is therefore very stable, surviving the imposition of strong perturbations: it would serve well as a timing signal in development. The automatous wave formulation is simple, with few model parameters. A strong case exists for the presence of a strain pulse during amelogenesis. Quantitative analysis reveals a simple relationship between the velocity of the leading edge of the pulse in amelogenesis and the known speed of migration of ameloblast cells. This result and energy arguments support the depiction of wave motion as an automatous cell response to strain, rather than as a response to an elastic energy gradient. The theory may also contribute to understanding the determination front in somitogenesis, moving fronts of convergent-extension transformation, and mitotic wavefronts in the syncytial drosophila embryo.

  18. Shock wave viscosity measurements

    NASA Astrophysics Data System (ADS)

    Celliers, Peter

    2013-06-01

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

  19. Charged black rings at large D

    NASA Astrophysics Data System (ADS)

    Chen, Bin; Li, Peng-Cheng; Wang, Zi-zhi

    2017-04-01

    We study the charged slowly rotating black holes in the Einstein-Maxwell theory in the large dimensions ( D). By using the 1 /D expansion in the near regions of the black holes we obtain the effective equations for the charged slowly rotating black holes. The effective equations capture the dynamics of various stationary solutions, including the charged black ring, the charged slowly rotating Myers-Perry black hole and the charged slowly boosted black string. Via different embeddings we construct these stationary solutions explicitly. For the charged black ring at large D, we find that the charge lowers the angular momentum due to the regularity condition on the solution. By performing the perturbation analysis of the effective equations, we obtain the quasinormal modes of the charge perturbation and the gravitational perturbation analytically. Like the neutral case the charged thin black ring suffers from the Gregory-Laflamme-like instability under the non-axisymmetric perturbations, but the charge weakens the instability. Besides, we find that the large D analysis always respects the cosmic censorship.

  20. Revised Perturbation Statistics for the Global Scale Atmospheric Model

    NASA Technical Reports Server (NTRS)

    Justus, C. G.; Woodrum, A.

    1975-01-01

    Magnitudes and scales of atmospheric perturbations about the monthly mean for the thermodynamic variables and wind components are presented by month at various latitudes. These perturbation statistics are a revision of the random perturbation data required for the global scale atmospheric model program and are from meteorological rocket network statistical summaries in the 22 to 65 km height range and NASA grenade and pitot tube data summaries in the region up to 90 km. The observed perturbations in the thermodynamic variables were adjusted to make them consistent with constraints required by the perfect gas law and the hydrostatic equation. Vertical scales were evaluated by Buell's depth of pressure system equation and from vertical structure function analysis. Tables of magnitudes and vertical scales are presented for each month at latitude 10, 30, 50, 70, and 90 degrees.

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