Time-Reversal Generation of Rogue Waves

NASA Astrophysics Data System (ADS)

Chabchoub, Amin; Fink, Mathias

2014-03-01

The formation of extreme localizations in nonlinear dispersive media can be explained and described within the framework of nonlinear evolution equations, such as the nonlinear Schrödinger equation (NLS). Within the class of exact NLS breather solutions on a finite background, which describe the modulational instability of monochromatic wave trains, the hierarchy of rational solutions localized in both time and space is considered to provide appropriate prototypes to model rogue wave dynamics. Here, we use the time-reversal invariance of the NLS to propose and experimentally demonstrate a new approach to constructing strongly nonlinear localized waves focused in both time and space. The potential applications of this time-reversal approach include remote sensing and motivated analogous experimental analysis in other nonlinear dispersive media, such as optics, Bose-Einstein condensates, and plasma, where the wave motion dynamics is governed by the NLS.

The soliton transform and a possible application to nonlinear Alfven waves in space

NASA Technical Reports Server (NTRS)

Hada, T.; Hamilton, R. L.; Kennel, C. F.

1993-01-01

The inverse scattering transform (IST) based on the derivative nonlinear Schroedinger (DNLS) equation is applied to a complex time series of nonlinear Alfven wave data generated by numerical simulation. The IST describes the long-time evolution of quasi-parallel Alfven waves more efficiently than the Fourier transform, which is adapted to linear rather than nonlinear problems. When dissipation is added, so the conditions for the validity of the DNLS are not strictly satisfied, the IST continues to provide a compact description of the wavefield in terms of a small number of decaying envelope solitons.

Topics Associated with Nonlinear Evolution Equations and Inverse Scattering in Multidimensions,

DTIC Science & Technology

1987-03-01

significant that these concepts can be generalized to 2 spatial plus one time dimension. Here the prototype equation is the Kadomtsev - Petviashvili (K-P...O-193 32 ? T TOPICS ASSOCIATED WITH NONLINEAR E VOLUTION EQUATIONS / AND INVERSE SCATTER! .(U) CLARKSON UNIV POTSDAM NY INST...8217 - Evolution Equations and L Inverse Scattering in Multi- dimensions by _i A ,’I Mark J. Ablowi ClrsnUiest PosaNwYr/37 LaRMFOMON* .F-5 Anwo~~~d kr /ua

Time-dependent nonlinear Jaynes-Cummings dynamics of a trapped ion

NASA Astrophysics Data System (ADS)

Krumm, F.; Vogel, W.

2018-04-01

In quantum interaction problems with explicitly time-dependent interaction Hamiltonians, the time ordering plays a crucial role for describing the quantum evolution of the system under consideration. In such complex scenarios, exact solutions of the dynamics are rarely available. Here we study the nonlinear vibronic dynamics of a trapped ion, driven in the resolved sideband regime with some small frequency mismatch. By describing the pump field in a quantized manner, we are able to derive exact solutions for the dynamics of the system. This eventually allows us to provide analytical solutions for various types of time-dependent quantities. In particular, we study in some detail the electronic and the motional quantum dynamics of the ion, as well as the time evolution of the nonclassicality of the motional quantum state.

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

NASA Astrophysics Data System (ADS)

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

2018-07-01

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

Universality in the nonlinear leveling of capillary films

NASA Astrophysics Data System (ADS)

Zheng, Zhong; Fontelos, Marco A.; Shin, Sangwoo; Stone, Howard A.

2018-03-01

Many material science, coating, and manufacturing problems involve liquid films where defects that span the film thickness must be removed. Here, we study the surface-tension-driven leveling dynamics of a thin viscous film following closure of an initial hole. The dynamics of the film shape is described by a nonlinear evolution equation, for which we obtain a self-similar solution. The analytical results are verified using time-dependent numerical and experimental results for the profile shapes and the minimum film thickness at the center. The universal behavior we identify can be useful for characterizing the time evolution of the leveling process and estimating material properties from experiments.

Nondestructive distributed measurement of supercontinuum generation along highly nonlinear optical fibers.

PubMed

Hontinfinde, Régis; Coulibaly, Saliya; Megret, Patrice; Taki, Majid; Wuilpart, Marc

2017-05-01

Supercontinuum generation (SCG) in optical fibers arises from the spectral broadening of an intense light, which results from the interplay of both linear and nonlinear optical effects. In this Letter, a nondestructive optical time domain reflectometry method is proposed for the first time, to the best of our knowledge, to measure the spatial (longitudinal) evolution of the SC induced along an optical fiber. The method was experimentally tested on highly nonlinear fibers. The experimental results are in a good agreement with the optical spectra measured at the fiber outputs.

Dynamical evolution of topology of large-scale structure. [in distribution of galaxies

NASA Technical Reports Server (NTRS)

Park, Changbom; Gott, J. R., III

1991-01-01

The nonlinear effects of statistical biasing and gravitational evolution on the genus are studied. The biased galaxy subset is picked for the first time by actually identifying galaxy-sized peaks above a fixed threshold in the initial conditions, and their subsequent evolution is followed. It is found that in the standard cold dark matter (CDM) model the statistical biasing in the locations of galaxies produces asymmetry in the genus curve and coupling with gravitational evolution gives rise to a shift in the genus curve to the left in moderately nonlinear regimes. Gravitational evolution alone reduces the amplitude of the genus curve due to strong phase correlations in the density field and also produces asymmetry in the curve. Results on the genus of the mass density field for both CDM and hot dark matter models are consistent with previous work by Melott, Weinberg, and Gott (1987).

Evolution of lower hybrid turbulence in the ionosphere

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

Ganguli, G.; Crabtree, C.; Mithaiwala, M.

2015-11-15

Three-dimensional evolution of the lower hybrid turbulence driven by a spatially localized ion ring beam perpendicular to the ambient magnetic field in space plasmas is analyzed. It is shown that the quasi-linear saturation model breaks down when the nonlinear rate of scattering by thermal electron is larger than linear damping rates, which can occur even for low wave amplitudes. The evolution is found to be essentially a three-dimensional phenomenon, which cannot be accurately explained by two-dimensional simulations. An important feature missed in previous studies of this phenomenon is the nonlinear conversion of electrostatic lower hybrid waves into electromagnetic whistler andmore » magnetosonic waves and the consequent energy loss due to radiation from the source region. This can result in unique low-amplitude saturation with extended saturation time. It is shown that when the nonlinear effects are considered the net energy that can be permanently extracted from the ring beam is larger. The results are applied to anticipate the outcome of a planned experiment that will seed lower hybrid turbulence in the ionosphere and monitor its evolution.« less

Observation of ion acoustic multi-Peregrine solitons in multicomponent plasma with negative ions

NASA Astrophysics Data System (ADS)

Pathak, Pallabi; Sharma, Sumita K.; Nakamura, Y.; Bailung, H.

2017-12-01

The evolution of the multi-Peregrine soliton is investigated in a multicomponent plasma and found to be critically dependent on the initial bound state. Formation and splitting of Peregrine soliton, broadening of the frequency spectra provide clear evidence of nonlinear-dispersive focusing due to modulational instability, a generic mechanism for rogue wave formation in which amplitude and phase modulation grow as a result of interplay between nonlinearity and anomalous dispersion. We have shown that initial perturbation parameters (amplitude & temporal length) critically determine the number of solitons evolution. It is also found that a sufficiently long wavelength perturbation of high amplitude invoke strong nonlinearity to generate a supercontinuum state. Continuous Wavelet Transform (CWT) and Fast Fourier Transform (FFT) analysis of the experimental time series data clearly indicate the spatio-temporal localization and spectral broadening. We consider a model based on the frame work of Nonlinear Schrodinger equation (NLSE) to explain the experimental observations.

Modulation instability, Fermi-Pasta-Ulam recurrence, rogue waves, nonlinear phase shift, and exact solutions of the Ablowitz-Ladik equation.

PubMed

Akhmediev, Nail; Ankiewicz, Adrian

2011-04-01

We study modulation instability (MI) of the discrete constant-background wave of the Ablowitz-Ladik (A-L) equation. We derive exact solutions of the A-L equation which are nonlinear continuations of MI at longer times. These periodic solutions comprise a family of two-parameter solutions with an arbitrary background field and a frequency of initial perturbation. The solutions are recurrent, since they return the field state to the original constant background solution after the process of nonlinear evolution has passed. These solutions can be considered as a complete resolution of the Fermi-Pasta-Ulam paradox for the A-L system. One remarkable consequence of the recurrent evolution is the nonlinear phase shift gained by the constant background wave after the process. A particular case of this family is the rational solution of the first-order or fundamental rogue wave.

Loss of Energy Concentration in Nonlinear Evolution Beam Equations

NASA Astrophysics Data System (ADS)

Garrione, Maurizio; Gazzola, Filippo

2017-12-01

Motivated by the oscillations that were seen at the Tacoma Narrows Bridge, we introduce the notion of solutions with a prevailing mode for the nonlinear evolution beam equation u_{tt} + u_{xxxx} + f(u)= g(x, t) in bounded space-time intervals. We give a new definition of instability for these particular solutions, based on the loss of energy concentration on their prevailing mode. We distinguish between two different forms of energy transfer, one physiological (unavoidable and depending on the nonlinearity) and one due to the insurgence of instability. We then prove a theoretical result allowing to reduce the study of this kind of infinite-dimensional stability to that of a finite-dimensional approximation. With this background, we study the occurrence of instability for three different kinds of nonlinearities f and for some forcing terms g, highlighting some of their structural properties and performing some numerical simulations.

Non-equilibrium condensation process in holographic superconductor with nonlinear electrodynamics

NASA Astrophysics Data System (ADS)

Liu, Yunqi; Gong, Yungui; Wang, Bin

2016-02-01

We study the non-equilibrium condensation process in a holographic superconductor with nonlinear corrections to the U (1) gauge field. We start with an asymptotic Anti-de-Sitter (AdS) black hole against a complex scalar perturbation at the initial time, and solve the dynamics of the gravitational systems in the bulk. When the black hole temperature T is smaller than a critical value T c , the scalar perturbation grows exponentially till saturation, the final state of spacetime approaches to a hairy black hole. In the bulk theory, we find the clue of the influence of nonlinear corrections in the gauge filed on the process of the scalar field condensation. We show that the bulk dynamics in the non-equilibrium process is completely consistent with the observations on the boundary order parameter. Furthermore we examine the time evolution of horizons in the bulk non-equilibrium transformation process from the bald AdS black hole to the AdS hairy hole. Both the evolution of apparent and event horizons show that the original AdS black hole configuration requires more time to finish the transformation to become a hairy black hole if there is nonlinear correction to the electromagnetic field. We generalize our non-equilibrium discussions to the holographic entanglement entropy and find that the holographic entanglement entropy can give us further understanding of the influence of the nonlinearity in the gauge field on the scalar condensation.

Nonlinear Image Denoising Methodologies

DTIC Science & Technology

2002-05-01

53 5.3 A Multiscale Approach to Scale-Space Analysis . . . . . . . . . . . . . . . . 53 5.4...etc. In this thesis, Our approach to denoising is first based on a controlled nonlinear stochastic random walk to achieve a scale space analysis ( as in... stochastic treatment or interpretation of the diffusion. In addition, unless a specific stopping time is known to be adequate, the resulting evolution

Exact traveling wave solutions for system of nonlinear evolution equations.

PubMed

Khan, Kamruzzaman; Akbar, M Ali; Arnous, Ahmed H

2016-01-01

In this work, recently deduced generalized Kudryashov method is applied to the variant Boussinesq equations, and the (2 + 1)-dimensional breaking soliton equations. As a result a range of qualitative explicit exact traveling wave solutions are deduced for these equations, which motivates us to develop, in the near future, a new approach to obtain unsteady solutions of autonomous nonlinear evolution equations those arise in mathematical physics and engineering fields. It is uncomplicated to extend this method to higher-order nonlinear evolution equations in mathematical physics. And it should be possible to apply the same method to nonlinear evolution equations having more general forms of nonlinearities by utilizing the traveling wave hypothesis.

The periodic structure of the natural record, and nonlinear dynamics.

USGS Publications Warehouse

Shaw, H.R.

1987-01-01

This paper addresses how nonlinear dynamics can contribute to interpretations of the geologic record and evolutionary processes. Background is given to explain why nonlinear concepts are important. A resume of personal research is offered to illustrate why I think nonlinear processes fit with observations on geological and cosmological time series data. The fabric of universal periodicity arrays generated by nonlinear processes is illustrated by means of a simple computer mode. I conclude with implications concerning patterns of evolution, stratigraphic boundary events, and close correlations of major geologically instantaneous events (such as impacts or massive volcanic episodes) with any sharply defined boundary in the geologic column. - from Author

Numerical study of bandwidth effect on stimulated Raman backscattering in nonlinear regime

NASA Astrophysics Data System (ADS)

Zhou, H. Y.; Xiao, C. Z.; Zou, D. B.; Li, X. Z.; Yin, Y.; Shao, F. Q.; Zhuo, H. B.

2018-06-01

Nonlinear behaviors of stimulated Raman scattering driven by finite bandwidth pumps are studied by one dimensional particle-in-cell simulations. The broad spectral feature of plasma waves and backscattered light reveals the different coupling and growth mechanisms, which lead to the suppression effect before the deep nonlinear stage. It causes nonperiodic plasma wave packets and reduces packet and etching velocities. Based on the negative frequency shift and electron energy distribution, the long-time evolution of instability can be divided into two stages by the relaxation time. It is a critical time after which the alleviation effects of nonlinear frequency shift and hot electrons are replaced by enhancement. Thus, the broadband pump suppresses instability at early time. However, it aggravates in the deep nonlinear stage by lifting the saturation level due to the coupling of the incident pump with each frequency shifted plasma wave. Our simulation results show that the nonlinear effects are valid in a bandwidth range from 2.25% to 3.0%, and the physics are similar within a nearby parameter space.

Gene family evolution: an in-depth theoretical and simulation analysis of non-linear birth-death-innovation models.

PubMed

Karev, Georgy P; Wolf, Yuri I; Berezovskaya, Faina S; Koonin, Eugene V

2004-09-09

The size distribution of gene families in a broad range of genomes is well approximated by a generalized Pareto function. Evolution of ensembles of gene families can be described with Birth, Death, and Innovation Models (BDIMs). Analysis of the properties of different versions of BDIMs has the potential of revealing important features of genome evolution. In this work, we extend our previous analysis of stochastic BDIMs. In addition to the previously examined rational BDIMs, we introduce potentially more realistic logistic BDIMs, in which birth/death rates are limited for the largest families, and show that their properties are similar to those of models that include no such limitation. We show that the mean time required for the formation of the largest gene families detected in eukaryotic genomes is limited by the mean number of duplications per gene and does not increase indefinitely with the model degree. Instead, this time reaches a minimum value, which corresponds to a non-linear rational BDIM with the degree of approximately 2.7. Even for this BDIM, the mean time of the largest family formation is orders of magnitude greater than any realistic estimates based on the timescale of life's evolution. We employed the embedding chains technique to estimate the expected number of elementary evolutionary events (gene duplications and deletions) preceding the formation of gene families of the observed size and found that the mean number of events exceeds the family size by orders of magnitude, suggesting a highly dynamic process of genome evolution. The variance of the time required for the formation of the largest families was found to be extremely large, with the coefficient of variation > 1. This indicates that some gene families might grow much faster than the mean rate such that the minimal time required for family formation is more relevant for a realistic representation of genome evolution than the mean time. We determined this minimal time using Monte Carlo simulations of family growth from an ensemble of simultaneously evolving singletons. In these simulations, the time elapsed before the formation of the largest family was much shorter than the estimated mean time and was compatible with the timescale of evolution of eukaryotes. The analysis of stochastic BDIMs presented here shows that non-linear versions of such models can well approximate not only the size distribution of gene families but also the dynamics of their formation during genome evolution. The fact that only higher degree BDIMs are compatible with the observed characteristics of genome evolution suggests that the growth of gene families is self-accelerating, which might reflect differential selective pressure acting on different genes.

The Nonlinear Jaynes-Cummings Model for the Multiphoton Transition

NASA Astrophysics Data System (ADS)

Liu, Xiao-Jing; Lu, Jing-Bin; Zhang, Si-Qi; Liu, Ji-Ping; Li, Hong; Liang, Yu; Ma, Ji; Weng, Yi-Jiao; Zhang, Qi-Rui; Liu, Han; Zhang, Xiao-Ru; Wu, Xiang-Yao

2018-01-01

With the nonlinear Jaynes-Cummings model, we have studied the atom and light field quantum entanglement of multiphoton transition in nonlinear medium, and researched the effect of the transition photon number N and the nonlinear coefficient χ on the quantum entanglement degrees. We have given the quantum entanglement degrees curves with time evolution, we find when the transition photon number N increases, the entanglement degrees oscillation get faster. When the nonlinear coefficient α > 0, the entanglement degrees oscillation get quickly, the nonlinear term is disadvantage of the atom and light field entanglement, and when the nonlinear coefficient α < 0, the entanglement degrees oscillation get slow, the nonlinear term is advantage of the atom and light field entanglement. These results will have been used in the quantum communication and quantum information.

Extremely broadband, on-chip optical nonreciprocity enabled by mimicking nonlinear anti-adiabatic quantum jumps near exceptional points

NASA Astrophysics Data System (ADS)

Choi, Youngsun; Hahn, Choloong; Yoon, Jae Woong; Song, Seok Ho; Berini, Pierre

2017-01-01

Time-asymmetric state-evolution properties while encircling an exceptional point are presently of great interest in search of new principles for controlling atomic and optical systems. Here, we show that encircling-an-exceptional-point interactions that are essentially reciprocal in the linear interaction regime make a plausible nonlinear integrated optical device architecture highly nonreciprocal over an extremely broad spectrum. In the proposed strategy, we describe an experimentally realizable coupled-waveguide structure that supports an encircling-an-exceptional-point parametric evolution under the influence of a gain saturation nonlinearity. Using an intuitive time-dependent Hamiltonian and rigorous numerical computations, we demonstrate strictly nonreciprocal optical transmission with a forward-to-backward transmission ratio exceeding 10 dB and high forward transmission efficiency (~100%) persisting over an extremely broad bandwidth approaching 100 THz. This predicted performance strongly encourages experimental realization of the proposed concept to establish a practical on-chip optical nonreciprocal element for ultra-short laser pulses and broadband high-density optical signal processing.

Hyperextended Cosmological Perturbation Theory: Predicting Nonlinear Clustering Amplitudes

NASA Astrophysics Data System (ADS)

Scoccimarro, Román; Frieman, Joshua A.

1999-07-01

We consider the long-standing problem of predicting the hierarchical clustering amplitudes Sp in the strongly nonlinear regime of gravitational evolution. N-body results for the nonlinear evolution of the bispectrum (the Fourier transform of the three-point density correlation function) suggest a physically motivated Ansatz that yields the strongly nonlinear behavior of the skewness, S3, starting from leading-order perturbation theory. When generalized to higher order (p>3) polyspectra or correlation functions, this Ansatz leads to a good description of nonlinear amplitudes in the strongly nonlinear regime for both scale-free and cold dark matter models. Furthermore, these results allow us to provide a general fitting formula for the nonlinear evolution of the bispectrum that interpolates between the weakly and strongly nonlinear regimes, analogous to previous expressions for the power spectrum.

Two-dimensional solitons in conservative and parity-time-symmetric triple-core waveguides with cubic-quintic nonlinearity

NASA Astrophysics Data System (ADS)

Feijoo, David; Zezyulin, Dmitry A.; Konotop, Vladimir V.

2015-12-01

We analyze a system of three two-dimensional nonlinear Schrödinger equations coupled by linear terms and with the cubic-quintic (focusing-defocusing) nonlinearity. We consider two versions of the model: conservative and parity-time (PT ) symmetric. These models describe triple-core nonlinear optical waveguides, with balanced gain and losses in the PT -symmetric case. We obtain families of soliton solutions and discuss their stability. The latter study is performed using a linear stability analysis and checked with direct numerical simulations of the evolutional system of equations. Stable solitons are found in the conservative and PT -symmetric cases. Interactions and collisions between the conservative and PT -symmetric solitons are briefly investigated, as well.

Construction of Optimally Reduced Empirical Model by Spatially Distributed Climate Data

NASA Astrophysics Data System (ADS)

Gavrilov, A.; Mukhin, D.; Loskutov, E.; Feigin, A.

2016-12-01

We present an approach to empirical reconstruction of the evolution operator in stochastic form by space-distributed time series. The main problem in empirical modeling consists in choosing appropriate phase variables which can efficiently reduce the dimension of the model at minimal loss of information about system's dynamics which consequently leads to more robust model and better quality of the reconstruction. For this purpose we incorporate in the model two key steps. The first step is standard preliminary reduction of observed time series dimension by decomposition via certain empirical basis (e. g. empirical orthogonal function basis or its nonlinear or spatio-temporal generalizations). The second step is construction of an evolution operator by principal components (PCs) - the time series obtained by the decomposition. In this step we introduce a new way of reducing the dimension of the embedding in which the evolution operator is constructed. It is based on choosing proper combinations of delayed PCs to take into account the most significant spatio-temporal couplings. The evolution operator is sought as nonlinear random mapping parameterized using artificial neural networks (ANN). Bayesian approach is used to learn the model and to find optimal hyperparameters: the number of PCs, the dimension of the embedding, the degree of the nonlinearity of ANN. The results of application of the method to climate data (sea surface temperature, sea level pressure) and their comparing with the same method based on non-reduced embedding are presented. The study is supported by Government of Russian Federation (agreement #14.Z50.31.0033 with the Institute of Applied Physics of RAS).

Simulation of linear and nonlinear Landau damping of lower hybrid waves

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

Qi, Lei; Wang, X. Y.; Lin, Y.

2013-06-15

The linear physics of lower hybrid waves (LHWs) and their nonlinear interaction with particles through Landau damping are studied with the gyrokinetic electron and fully kinetic ion (GeFi) particle simulation model in the electrostatic limit. Unlike most other wave modes, the LHWs can resonantly interact with both electrons and ions, with the former being highly magnetized and latter nearly unmagnetized around the lower hybrid frequency. Direct interactions of LHWs with electrons and/or ions are investigated for cases with various k{sub ∥}/k,T{sub i}/T{sub e}, and wave amplitudes. In the linear electron Landau damping (ELD), the dispersion relation and the linear dampingmore » rate obtained from our simulation agree well with the analytical linear theory. As the wave amplitude increases, the nonlinear Landau effects are present, and a transition from strong decay at smaller amplitudes to weak decay at larger amplitudes is observed. In the nonlinear stage, the LHWs in the long time evolution finally exhibit a steady Bernstein-Greene-Kruskal mode, in which the wave amplitude is saturated above the noise level. While the resonant electrons are trapped in the wave field in the nonlinear ELD, the resonant ions are untrapped in the LHW time scales. The ion Landau damping is thus predominantly in a linear fashion, leading to a wave saturation level significantly lower than that in the ELD. On the long time scales, however, the ions are still weakly trapped. The results show a coupling between the LHW frequency and the ion cyclotron frequency during the long-time LHW evolution.« less

Evolution of statistical properties for a nonlinearly propagating sinusoid.

PubMed

Shepherd, Micah R; Gee, Kent L; Hanford, Amanda D

2011-07-01

The nonlinear propagation of a pure sinusoid is considered using time domain statistics. The probability density function, standard deviation, skewness, kurtosis, and crest factor are computed for both the amplitude and amplitude time derivatives as a function of distance. The amplitude statistics vary only in the postshock realm, while the amplitude derivative statistics vary rapidly in the preshock realm. The statistical analysis also suggests that the sawtooth onset distance can be considered to be earlier than previously realized. © 2011 Acoustical Society of America

Nonlinear techniques for forecasting solar activity directly from its time series

NASA Technical Reports Server (NTRS)

Ashrafi, S.; Roszman, L.; Cooley, J.

1992-01-01

Numerical techniques for constructing nonlinear predictive models to forecast solar flux directly from its time series are presented. This approach makes it possible to extract dynamical invariants of our system without reference to any underlying solar physics. We consider the dynamical evolution of solar activity in a reconstructed phase space that captures the attractor (strange), given a procedure for constructing a predictor of future solar activity, and discuss extraction of dynamical invariants such as Lyapunov exponents and attractor dimension.

Nonlinear techniques for forecasting solar activity directly from its time series

NASA Technical Reports Server (NTRS)

Ashrafi, S.; Roszman, L.; Cooley, J.

1993-01-01

This paper presents numerical techniques for constructing nonlinear predictive models to forecast solar flux directly from its time series. This approach makes it possible to extract dynamical in variants of our system without reference to any underlying solar physics. We consider the dynamical evolution of solar activity in a reconstructed phase space that captures the attractor (strange), give a procedure for constructing a predictor of future solar activity, and discuss extraction of dynamical invariants such as Lyapunov exponents and attractor dimension.

Ghost Dark Energy with Non-Linear Interaction Term

NASA Astrophysics Data System (ADS)

Ebrahimi, E.

2016-06-01

Here we investigate ghost dark energy (GDE) in the presence of a non-linear interaction term between dark matter and dark energy. To this end we take into account a general form for the interaction term. Then we discuss about different features of three choices of the non-linear interacting GDE. In all cases we obtain equation of state parameter, w D = p/ ρ, the deceleration parameter and evolution equation of the dark energy density parameter (Ω D ). We find that in one case, w D cross the phantom line ( w D < -1). However in two other classes w D can not cross the phantom divide. The coincidence problem can be solved in these models completely and there exist good agreement between the models and observational values of w D , q. We study squared sound speed {vs2}, and find that for one case of non-linear interaction term {vs2} can achieves positive values at late time of evolution.

Comparing nonlinear MHD simulations of low-aspect-ratio RFPs to RELAX experiments

NASA Astrophysics Data System (ADS)

McCollam, K. J.; den Hartog, D. J.; Jacobson, C. M.; Sovinec, C. R.; Masamune, S.; Sanpei, A.

2016-10-01

Standard reversed-field pinch (RFP) plasmas provide a nonlinear dynamical system as a validation domain for numerical MHD simulation codes, with applications in general toroidal confinement scenarios including tokamaks. Using the NIMROD code, we simulate the nonlinear evolution of RFP plasmas similar to those in the RELAX experiment. The experiment's modest Lundquist numbers S (as low as a few times 104) make closely matching MHD simulations tractable given present computing resources. Its low aspect ratio ( 2) motivates a comparison study using cylindrical and toroidal geometries in NIMROD. We present initial results from nonlinear single-fluid runs at S =104 for both geometries and a range of equilibrium parameters, which preliminarily show that the magnetic fluctuations are roughly similar between the two geometries and between simulation and experiment, though there appear to be some qualitative differences in their temporal evolution. Runs at higher S are planned. This work is supported by the U.S. DOE and by the Japan Society for the Promotion of Science.

Direct measurement of nonlinear dispersion relation for water surface waves

NASA Astrophysics Data System (ADS)

Magnus Arnesen Taklo, Tore; Trulsen, Karsten; Elias Krogstad, Harald; Gramstad, Odin; Nieto Borge, José Carlos; Jensen, Atle

2013-04-01

The linear dispersion relation for water surface waves is often taken for granted for the interpretation of wave measurements. High-resolution spatiotemporal measurements suitable for direct validation of the linear dispersion relation are on the other hand rarely available. While the imaging of the ocean surface with nautical radar does provide the desired spatiotemporal coverage, the interpretation of the radar images currently depends on the linear dispersion relation as a prerequisite, (Nieto Borge et al., 2004). Krogstad & Trulsen (2010) carried out numerical simulations with the nonlinear Schrödinger equation and its generalizations demonstrating that the nonlinear evolution of wave fields may render the linear dispersion relation inadequate for proper interpretation of observations, the reason being that the necessary domain of simultaneous coverage in space and time would allow significant nonlinear evolution. They found that components above the spectral peak can have larger phase and group velocities than anticipated by linear theory, and that the spectrum does not maintain a thin dispersion surface. We have run laboratory experiments and accurate numerical simulations designed to have sufficient resolution in space and time to deduce the dispersion relation directly. For a JONSWAP spectrum we find that the linear dispersion relation can be appropriate for the interpretation of spatiotemporal measurements. For a Gaussian spectrum with narrower bandwidth we find that the dynamic nonlinear evolution in space and time causes the directly measured dispersion relation to deviate from the linear dispersion surface in good agreement with our previous numerical predictions. This work has been supported by RCN grant 214556/F20. Krogstad, H. E. & Trulsen, K. (2010) Interpretations and observations of ocean wave spectra. Ocean Dynamics 60:973-991. Nieto Borge, J. C., Rodríguez, G., Hessner, K., Izquierdo, P. (2004) Inversion of marine radar images for surface wave analysis. J. Atmos. Ocean. Tech. 21:1291-1300.

The hair-trigger effect for a class of nonlocal nonlinear equations

NASA Astrophysics Data System (ADS)

Finkelshtein, Dmitri; Tkachov, Pasha

2018-06-01

We prove the hair-trigger effect for a class of nonlocal nonlinear evolution equations on which have only two constant stationary solutions, 0 and . The effect consists in that the solution with an initial condition non identical to zero converges (when time goes to ) to θ locally uniformly in . We also find sufficient conditions for existence, uniqueness and comparison principle in the considered equations.

Extracting third order optical nonlinearities of Mn(III)-Phthalocyanine chloride using high repetition rate femtosecond pulses

NASA Astrophysics Data System (ADS)

Makhal, Krishnandu; Mathur, Paresh; Maurya, Sidharth; Goswami, Debabrata

2017-02-01

Third order nonlinearities of Mn(III)-Phthalocyanine chloride in dimethyl-sulphoxide under 50 fs pulses, operating at 94 MHz, by eliminating cumulative thermal effects have been investigated and reported by us. Modifications were done in data acquisition during Z-scan experiment, which included recording of time evolution waveform traces in an oscilloscope and not collection of Z versus transmission and utilization of a chopper of a suitable duty cycle. Time evolution traces were further processed analytically through MatLab® programming, which yielded Z-scan traces similar to what was obtained with single shot 50 fs pulse. We observed reverse saturable absorption at 800 nm owing to excited state absorption. We show that the nonlinear refractive index (γ) and nonlinear absorption coefficient (β) are over estimated almost 100 times, when MHz pulses are used compared to a situation, where thermo-optical nonlinearities are accounted. Illumination and dark periods are carefully set in a way, so that the sample is able to completely recover its initial temperature before arrival of the next pulse. Magnitudes of γ and β were found to be -(6.5-4.9) × 10-16 m2/W and (5.4-6.2) × 10-10 m/W under the MHz condition, whereas they were -(0.18-2.2) × 10-18 m2/W and (9.5-15) × 10-12 m/W under the thermally managed condition, respectively. To reveal the associated fast nonlinearity, femtosecond transient absorption experiment was performed, which inferred excited state absorption and ground state bleaching across the 450-780 nm region. Dynamics associated with these processes are reported along with fluorescence lifetime obtained through the TCSPC technique. Structure optimization using TDDFT calculations and HOMO-LUMO gaps with orbital pictures are also shown.

Study of nonlinear electron-acoustic solitary and shock waves in a dissipative, nonplanar space plasma with superthermal hot electrons

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

Han, Jiu-Ning, E-mail: hanjiuning@126.com; He, Yong-Lin; Luo, Jun-Hua

2014-01-15

With the consideration of the superthermal electron distribution, we present a theoretical investigation about the nonlinear propagation of electron-acoustic solitary and shock waves in a dissipative, nonplanar non-Maxwellian plasma comprised of cold electrons, superthermal hot electrons, and stationary ions. The reductive perturbation technique is used to obtain a modified Korteweg-de Vries Burgers equation for nonlinear waves in this plasma. We discuss the effects of various plasma parameters on the time evolution of nonplanar solitary waves, the profile of shock waves, and the nonlinear structure induced by the collision between planar solitary waves. It is found that these parameters have significantmore » effects on the properties of nonlinear waves and collision-induced nonlinear structure.« less

The effects of stimulated star formation on the evolution of the galaxy. III - The chemical evolution of nonlinear systems

NASA Technical Reports Server (NTRS)

Shore, Steven N.; Ferrini, Federico; Palla, Francesco

1987-01-01

The evolution of models for star formation in galaxies with disk and halo components is discussed. Two phases for the halo (gas and stars) and three for the disk (including clouds) are used in these calculations. The star-formation history is followed using nonlinear phase-coupling models which completely determine the populations of the phases as a function of time. It is shown that for a wide range of parameters, including the effects of both spontaneous and stimulated star formation and mass exchange between the spatial components of the system, the observed chemical history of the galaxy can easily be obtained. The most sensitive parameter in the detailed metallicity and star-formation history for the system is the rate of return of gas to the diffuse phase upon stellar death.

Monotonic entropy growth for a nonlinear model of random exchanges.

PubMed

Apenko, S M

2013-02-01

We present a proof of the monotonic entropy growth for a nonlinear discrete-time model of a random market. This model, based on binary collisions, also may be viewed as a particular case of Ulam's redistribution of energy problem. We represent each step of this dynamics as a combination of two processes. The first one is a linear energy-conserving evolution of the two-particle distribution, for which the entropy growth can be easily verified. The original nonlinear process is actually a result of a specific "coarse graining" of this linear evolution, when after the collision one variable is integrated away. This coarse graining is of the same type as the real space renormalization group transformation and leads to an additional entropy growth. The combination of these two factors produces the required result which is obtained only by means of information theory inequalities.

A nonlinear control scheme based on dynamic evolution path theory for improved dynamic performance of boost PFC converter working on nonlinear features.

PubMed

Mohanty, Pratap Ranjan; Panda, Anup Kumar

2016-11-01

This paper is concerned to performance improvement of boost PFC converter under large random load fluctuation, ensuring unity power factor (UPF) at source end and regulated voltage at load side. To obtain such performance, a nonlinear controller based on dynamic evolution path theory is designed and its robustness is examined under both heavy and light loading condition. In this paper, %THD and zero-cross-over dead-zone of input current is significantly reduced. Also, very less response time of input current and output voltage to that of load and reference variation is remarked. A simulation model of proposed system is designed and it is realized using dSPACE 1104 signal processor for a 390V DC , 500W prototype. The relevant experimental and simulation waveforms are presented. Copyright © 2016 ISA. Published by Elsevier Ltd. All rights reserved.

Monotonic entropy growth for a nonlinear model of random exchanges

NASA Astrophysics Data System (ADS)

Apenko, S. M.

2013-02-01

We present a proof of the monotonic entropy growth for a nonlinear discrete-time model of a random market. This model, based on binary collisions, also may be viewed as a particular case of Ulam's redistribution of energy problem. We represent each step of this dynamics as a combination of two processes. The first one is a linear energy-conserving evolution of the two-particle distribution, for which the entropy growth can be easily verified. The original nonlinear process is actually a result of a specific “coarse graining” of this linear evolution, when after the collision one variable is integrated away. This coarse graining is of the same type as the real space renormalization group transformation and leads to an additional entropy growth. The combination of these two factors produces the required result which is obtained only by means of information theory inequalities.

Lipschitz regularity results for nonlinear strictly elliptic equations and applications

NASA Astrophysics Data System (ADS)

Ley, Olivier; Nguyen, Vinh Duc

2017-10-01

Most of Lipschitz regularity results for nonlinear strictly elliptic equations are obtained for a suitable growth power of the nonlinearity with respect to the gradient variable (subquadratic for instance). For equations with superquadratic growth power in gradient, one usually uses weak Bernstein-type arguments which require regularity and/or convex-type assumptions on the gradient nonlinearity. In this article, we obtain new Lipschitz regularity results for a large class of nonlinear strictly elliptic equations with possibly arbitrary growth power of the Hamiltonian with respect to the gradient variable using some ideas coming from Ishii-Lions' method. We use these bounds to solve an ergodic problem and to study the regularity and the large time behavior of the solution of the evolution equation.

Diffeomorphism groups and nonlinear quantum mechanics

NASA Astrophysics Data System (ADS)

Goldin, Gerald A.

2012-02-01

This talk is dedicated to my friend and collaborator, Prof. Dr. Heinz-Dietrich Doebner, on the occasion of his 80th birthday. I shall review some highlights of the approach we have taken in deriving and interpreting an interesting class of nonlinear time-evolution equations for quantum-mechanical wave functions, with few equations; more detail may be found in the references. Then I shall comment on the corresponding hydrodynamical description.

Nonlinear critical-layer evolution of a forced gravity wave packet

NASA Astrophysics Data System (ADS)

Campbell, L. J.; Maslowe, S. A.

2003-10-01

In this paper, numerical simulations are presented of the nonlinear critical-layer evolution of a forced gravity wave packet in a stratified shear flow. The wave packet, localized in the horizontal direction, is forced at the lower boundary of a two-dimensional domain and propagates vertically towards the critical layer. The wave mean-flow interactions in the critical layer are investigated numerically and contrasted with the results obtained using a spatially periodic monochromatic forcing. With the horizontally localized forcing, the net absorption of the disturbance at the critical layer continues for large time and the onset of the nonlinear breakdown is delayed compared with the case of monochromatic forcing. There is an outward flux of momentum in the horizontal direction so that the horizontal extent of the packet increases with time. The extent to which this happens depends on a number of factors including the amplitude and horizontal length of the forcing. It is also seen that the prolonged absorption of the disturbance stabilizes the solution to the extent that it is always convectively stable; the local Richardson number remains positive well into the nonlinear regime. In this respect, our results for the localized forcing differ from those in the case of monochromatic forcing where significant regions with negative Richardson number appear.

A non-linear 4-wave resonant model for non-perturbative fast ion interactions with Alfv'enic modes in burning plasmas

NASA Astrophysics Data System (ADS)

Zonca, Fulvio; Chen, Liu

2007-11-01

We adopt the 4-wave modulation interaction model, introduced by Chen et al [1] for analyzing modulational instabilities of the radial envelope of Ion Temperature Gradient driven modes in toroidal geometry, extending it to the modulations on the fast particle distribution function due to nonlinear Alfv'enic mode dynamics, as proposed in Ref. [2]. In the case where the wave-particle interactions are non-perturbative and strongly influence the mode evolution, as in the case of Energetic Particle Modes (EPM) [3], radial distortions (redistributions) of the fast ion source dominate the mode nonlinear dynamics. In this work, we show that the resonant particle motion is secular with a time-scale inversely proportional to the mode amplitude [4] and that the time evolution of the EPM radial envelope can be cast into the form of a nonlinear Schr"odinger equation a la Ginzburg-Landau [5]. [1] L. Chen et al, Phys. Plasmas 7 3129 (2000) [2] F. Zonca et al, Theory of Fusion Plasmas (Bologna: SIF) 17 (2000) [3] L. Chen, Phys. Plasmas 1, 1519 (1994).[4] F. Zonca et al, Nucl. Fusion 45 477 (2005) [5] F. Zonca et al, Plasma Phys. Contr. Fusion 48 B15 (2006)

Self-excitation of a nonlinear scalar field in a random medium

PubMed Central

Zeldovich, Ya. B.; Molchanov, S. A.; Ruzmaikin, A. A.; Sokoloff, D. D.

1987-01-01

We discuss the evolution in time of a scalar field under the influence of a random potential and diffusion. The cases of a short-correlation in time and of stationary potentials are considered. In a linear approximation and for sufficiently weak diffusion, the statistical moments of the field grow exponentially in time at growth rates that progressively increase with the order of the moment; this indicates the intermittent nature of the field. Nonlinearity halts this growth and in some cases can destroy the intermittency. However, in many nonlinear situations the intermittency is preserved: high, persistent peaks of the field exist against the background of a smooth field distribution. These widely spaced peaks may make a major contribution to the average characteristics of the field. PMID:16593872

Generation and propagation of nonlinear internal waves in Massachusetts Bay

USGS Publications Warehouse

Scotti, A.; Beardsley, R.C.; Butman, B.

2007-01-01

During the summer, nonlinear internal waves (NLIWs) are commonly observed propagating in Massachusetts Bay. The topography of the area is unique in the sense that the generation area (over Stellwagen Bank) is only 25 km away from the shoaling area, and thus it represents an excellent natural laboratory to study the life cycle of NLIWs. To assist in the interpretation of the data collected during the 1998 Massachusetts Bay Internal Wave Experiment (MBIWE98), a fully nonlinear and nonhydrostatic model covering the generation/shoaling region was developed, to investigate the response of the system to the range of background and driving conditions observed. Simplified models were also used to elucidate the role of nonlinearity and dispersion in shaping the NLIW field. This paper concentrates on the generation process and the subsequent evolution in the basin. The model was found to reproduce well the range of propagation characteristics observed (arrival time, propagation speed, amplitude), and provided a coherent framework to interpret the observations. Comparison with a fully nonlinear hydrostatic model shows that during the generation and initial evolution of the waves as they move away from Stellwagen Bank, dispersive effects play a negligible role. Thus the problem can be well understood considering the geometry of the characteristics along which the Riemann invariants of the hydrostatic problem propagate. Dispersion plays a role only during the evolution of the undular bore in the middle of Stellwagen Basin. The consequences for modeling NLIWs within hydrostatic models are briefly discussed at the end.

Rosenzweig instability in a thin layer of a magnetic fluid

NASA Astrophysics Data System (ADS)

Korovin, V. M.

2013-12-01

A simple mathematical model of the initial stage of nonlinear evolution of the Rosenzweig instability in a thin layer of a nonlinearly magnetized viscous ferrofluid coating a horizontal nonmagnetizable plate is constructed on the basis of the system of equations and boundary conditions of ferrofluid dynamics. A dispersion relation is derived and analyzed using the linearized equations of this model. The critical magnetization of the initial layer with a flat free surface, the threshold wavenumber, and the characteristic time of evolution of the most rapidly growing mode are determined. The equation for the neutral stability curve, which is applicable for any physically admissible law of magnetization of a ferrofluid, is derived analytically.

A low-altitude mechanism for mesoscale dynamics, structure, and current filamentation in the discrete aurora

NASA Technical Reports Server (NTRS)

Keskinen, M. J.; Chaturvedi, P. K.; Ossakow, S. L.

1992-01-01

The 2D nonlinear evolution of the ionization-driven adiabatic auroral arc instability is studied. We find: (1) the adiabatic auroral arc instability can fully develop on time scales of tens to hundreds of seconds and on spatial scales of tens to hundreds of kilometers; (2) the evolution of this instability leads to nonlinear 'hook-shaped' conductivity structures: (3) this instability can lead to parallel current filamentation over a wide range of scale sizes; and (4) the k-spectra of the density, electric field, and parallel current develop into inverse power laws in agreement with satellite observations. Comparison with mesoscale auroral phenomenology and current filamentation structures is made.

A comparison/validation of a fractional derivative model with an empirical model of non-linear shock waves in swelling shales

NASA Astrophysics Data System (ADS)

Droghei, Riccardo; Salusti, Ettore

2013-04-01

Control of drilling parameters, as fluid pressure, mud weight, salt concentration is essential to avoid instabilities when drilling through shale sections. To investigate shale deformation, fundamental for deep oil drilling and hydraulic fracturing for gas extraction ("fracking"), a non-linear model of mechanic and chemo-poroelastic interactions among fluid, solute and the solid matrix is here discussed. The two equations of this model describe the isothermal evolution of fluid pressure and solute density in a fluid saturated porous rock. Their solutions are quick non-linear Burger's solitary waves, potentially destructive for deep operations. In such analysis the effect of diffusion, that can play a particular role in fracking, is investigated. Then, following Civan (1998), both diffusive and shock waves are applied to fine particles filtration due to such quick transients , their effect on the adjacent rocks and the resulting time-delayed evolution. Notice how time delays in simple porous media dynamics have recently been analyzed using a fractional derivative approach. To make a tentative comparison of these two deeply different methods,in our model we insert fractional time derivatives, i.e. a kind of time-average of the fluid-rocks interactions. Then the delaying effects of fine particles filtration is compared with fractional model time delays. All this can be seen as an empirical check of these fractional models.

Hidden symmetry and nonlinear paraxial atom optics

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

Impens, Francois

2009-12-15

A hidden symmetry of the nonlinear wave equation is exploited to analyze the propagation of paraxial and uniform atom-laser beams in time-independent and quadratic transverse potentials with cylindrical symmetry. The quality factor and the paraxial ABCD formalism are generalized to account exactly for mean-field interaction effects in such beams. Using an approach based on moments, these theoretical tools provide a simple yet exact picture of the interacting beam profile evolution. Guided atom laser experiments are discussed. This treatment addresses simultaneously optical and atomic beams in a unified manner, exploiting the formal analogy between nonlinear optics, nonlinear paraxial atom optics, andmore » the physics of two-dimensional Bose-Einstein condensates.« less

A lattice Boltzmann model with an amending function for simulating nonlinear partial differential equations

NASA Astrophysics Data System (ADS)

Chen, Lin-Jie; Ma, Chang-Feng

2010-01-01

This paper proposes a lattice Boltzmann model with an amending function for one-dimensional nonlinear partial differential equations (NPDEs) in the form ut + αuux + βunux + γuxx + δuxxx + ζuxxxx = 0. This model is different from existing models because it lets the time step be equivalent to the square of the space step and derives higher accuracy and nonlinear terms in NPDEs. With the Chapman-Enskog expansion, the governing evolution equation is recovered correctly from the continuous Boltzmann equation. The numerical results agree well with the analytical solutions.

Evolution of diffraction and self-diffraction phenomena in thin films of Gelite Bloom/Hibiscus Sabdariffa

NASA Astrophysics Data System (ADS)

Cano-Lara, Miroslava; Severiano-Carrillo, Israel; Trejo-Durán, Mónica; Alvarado-Méndez, Edgar

2017-09-01

In this work, we present a study of non-linear optical response in thin films elaborated with Gelite Bloom and extract of Hibiscus Sabdariffa. Non-linear refraction and absorption effects were studied experimentally (Z-scan technique) and numerically, by considering the transmittance as non-linear absorption and refraction contribution. We observe large phase shifts to far field, and diffraction due to self-phase modulation of the sample. Diffraction and self-diffraction effects were observed as time function. The aim of studying non-linear optical properties in thin films is to eliminate thermal vortex effects that occur in liquids. This is desirable in applications such as non-linear phase contrast, optical limiting, optics switches, etc. Finally, we find good agreement between experimental and theoretical results.

Compressive Spectral Method for the Simulation of the Nonlinear Gravity Waves

PubMed Central

Bayındır, Cihan

2016-01-01

In this paper an approach for decreasing the computational effort required for the spectral simulations of the fully nonlinear ocean waves is introduced. The proposed approach utilizes the compressive sampling algorithm and depends on the idea of using a smaller number of spectral components compared to the classical spectral method. After performing the time integration with a smaller number of spectral components and using the compressive sampling technique, it is shown that the ocean wave field can be reconstructed with a significantly better efficiency compared to the classical spectral method. For the sparse ocean wave model in the frequency domain the fully nonlinear ocean waves with Jonswap spectrum is considered. By implementation of a high-order spectral method it is shown that the proposed methodology can simulate the linear and the fully nonlinear ocean waves with negligible difference in the accuracy and with a great efficiency by reducing the computation time significantly especially for large time evolutions. PMID:26911357

Experimental study of linear and nonlinear regimes of density-driven instabilities induced by CO{sub 2} dissolution in water

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

Outeda, R.; D'Onofrio, A.; El Hasi, C.

Density driven instabilities produced by CO{sub 2} (gas) dissolution in water containing a color indicator were studied in a Hele Shaw cell. The images were analyzed and instability patterns were characterized by mixing zone temporal evolution, dispersion curves, and the growth rate for different CO{sub 2} pressures and different color indicator concentrations. The results obtained from an exhaustive analysis of experimental data show that this system has a different behaviour in the linear regime of the instabilities (when the growth rate has a linear dependence with time), from the nonlinear regime at longer times. At short times using a colormore » indicator to see the evolution of the pattern, the images show that the effects of both the color indicator and CO{sub 2} pressure are of the same order of magnitude: The growth rates are similar and the wave numbers are in the same range (0–30 cm{sup −1}) when the system is unstable. Although in the linear regime the dynamics is affected similarly by the presence of the indicator and CO{sub 2} pressure, in the nonlinear regime, the influence of the latter is clearly more pronounced than the effects of the color indicator.« less

Nonlinear Evolution of Counter-Propagating Whistler Mode Waves Excited by Anisotropic Electrons Within the Equatorial Source Region: 1-D PIC Simulations

NASA Astrophysics Data System (ADS)

Chen, Huayue; Gao, Xinliang; Lu, Quanming; Sun, Jicheng; Wang, Shui

2018-02-01

Nonlinear physical processes related to whistler mode waves are attracting more and more attention for their significant role in reshaping whistler mode spectra in the Earth's magnetosphere. Using a 1-D particle-in-cell simulation model, we have investigated the nonlinear evolution of parallel counter-propagating whistler mode waves excited by anisotropic electrons within the equatorial source region. In our simulations, after the linear phase of whistler mode instability, the strong electrostatic standing structures along the background magnetic field will be formed, resulting from the coupling between excited counter-propagating whistler mode waves. The wave numbers of electrostatic standing structures are about twice those of whistler mode waves generated by anisotropic hot electrons. Moreover, these electrostatic standing structures can further be coupled with either parallel or antiparallel propagating whistler mode waves to excite high-k modes in this plasma system. Compared with excited whistler mode waves, these high-k modes typically have 3 times wave number, same frequency, and about 2 orders of magnitude smaller amplitude. Our study may provide a fresh view on the evolution of whistler mode waves within their equatorial source regions in the Earth's magnetosphere.

Systematic derivation of reaction-diffusion equations with distributed delays and relations to fractional reaction-diffusion equations and hyperbolic transport equations: application to the theory of Neolithic transition.

PubMed

Vlad, Marcel Ovidiu; Ross, John

2002-12-01

We introduce a general method for the systematic derivation of nonlinear reaction-diffusion equations with distributed delays. We study the interactions among different types of moving individuals (atoms, molecules, quasiparticles, biological organisms, etc). The motion of each species is described by the continuous time random walk theory, analyzed in the literature for transport problems, whereas the interactions among the species are described by a set of transformation rates, which are nonlinear functions of the local concentrations of the different types of individuals. We use the time interval between two jumps (the transition time) as an additional state variable and obtain a set of evolution equations, which are local in time. In order to make a connection with the transport models used in the literature, we make transformations which eliminate the transition time and derive a set of nonlocal equations which are nonlinear generalizations of the so-called generalized master equations. The method leads under different specified conditions to various types of nonlocal transport equations including a nonlinear generalization of fractional diffusion equations, hyperbolic reaction-diffusion equations, and delay-differential reaction-diffusion equations. Thus in the analysis of a given problem we can fit to the data the type of reaction-diffusion equation and the corresponding physical and kinetic parameters. The method is illustrated, as a test case, by the study of the neolithic transition. We introduce a set of assumptions which makes it possible to describe the transition from hunting and gathering to agriculture economics by a differential delay reaction-diffusion equation for the population density. We derive a delay evolution equation for the rate of advance of agriculture, which illustrates an application of our analysis.

Single evolution equation in a light-matter pairing system

NASA Astrophysics Data System (ADS)

Bugaychuk, S.; Tobisch, E.

2018-03-01

The coupled system including wave mixing and nonlinear dynamics of a nonlocal optical medium is usually studied (1) numerically, with the medium being regarded as a black box, or (2) experimentally, making use of some empirical assumptions. In this paper we deduce for the first time a single evolution equation describing the dynamics of the pairing system as a holistic complex. For a non-degenerate set of parameters, we obtain the nonlinear Schrödinger equation with coefficients being written out explicitly. Analytical solutions of this equation can be experimentally realized in any photorefractive medium, e.g. in photorefractive, liquid or photonic crystals. For instance, a soliton-like solution can be used in dynamical holography for designing an artificial grating with maximal amplification of an image.

Ultrafast Non-thermal Response of Plasmonic Resonance in Gold Nanoantennas

NASA Astrophysics Data System (ADS)

Soavi, Giancarlo; Valle, Giuseppe Della; Biagioni, Paolo; Cattoni, Andrea; Longhi, Stefano; Cerullo, Giulio; Brida, Daniele

Ultrafast thermalization of electrons in metal nanostructures is studied by means of pump-probe spectroscopy. We track in real-time the plasmon resonance evolution, providing a tool for understanding and controlling gold nanoantennas non-linear optical response.

Convergence of Galerkin approximations for operator Riccati equations: A nonlinear evolution equation approach

NASA Technical Reports Server (NTRS)

Rosen, I. G.

1988-01-01

An approximation and convergence theory was developed for Galerkin approximations to infinite dimensional operator Riccati differential equations formulated in the space of Hilbert-Schmidt operators on a separable Hilbert space. The Riccati equation was treated as a nonlinear evolution equation with dynamics described by a nonlinear monotone perturbation of a strongly coercive linear operator. A generic approximation result was proven for quasi-autonomous nonlinear evolution system involving accretive operators which was then used to demonstrate the Hilbert-Schmidt norm convergence of Galerkin approximations to the solution of the Riccati equation. The application of the results was illustrated in the context of a linear quadratic optimal control problem for a one dimensional heat equation.

Richtmyer-Meshkov instability of a sinusoidal interface driven by a cylindrical shock

NASA Astrophysics Data System (ADS)

Liu, L.; Ding, J.; Zhai, Z.; Luo, X.

2018-04-01

Evolution of a single-mode interface triggered by a cylindrically converging shock in a V-shaped geometry is investigated numerically using an adaptive multi-phase solver. Several physical mechanisms, including the Bell-Plesset (BP) effect, the Rayleigh-Taylor (RT) effect, the nonlinearity, and the compressibility are found to be pronounced in the converging environment. Generally, the BP and nonlinear effects play an important role at early stages, while the RT effect and the compressibility dominate the late-stage evolution. Four sinusoidal interfaces with different initial amplitudes (a_0 ) and wavelengths (λ ) are found to evolve differently in the converging geometry. For the very small a_0 /λ interfaces, nonlinearity is negligible at the early stages and the sole presence of the BP effect results in an increasing growth rate, confining the linear growth of the instability to a relatively small amount of time. For the moderately small a_0 /λ cases, the BP and nonlinear effects, which, respectively, promote and inhibit the perturbation development, coexist in the early stage. The counterbalancing effects between them produce a very long period of growth that is linear in time, even to a moment when the amplitude over wavelength ratio approaches 0.6. The RT stabilization effect at late stages due to the interface deceleration significantly inhibits the perturbation growth, which can be reasonably predicted by a modified Bell model.

Super-rogue waves in simulations based on weakly nonlinear and fully nonlinear hydrodynamic equations.

PubMed

Slunyaev, A; Pelinovsky, E; Sergeeva, A; Chabchoub, A; Hoffmann, N; Onorato, M; Akhmediev, N

2013-07-01

The rogue wave solutions (rational multibreathers) of the nonlinear Schrödinger equation (NLS) are tested in numerical simulations of weakly nonlinear and fully nonlinear hydrodynamic equations. Only the lowest order solutions from 1 to 5 are considered. A higher accuracy of wave propagation in space is reached using the modified NLS equation, also known as the Dysthe equation. This numerical modeling allowed us to directly compare simulations with recent results of laboratory measurements in Chabchoub et al. [Phys. Rev. E 86, 056601 (2012)]. In order to achieve even higher physical accuracy, we employed fully nonlinear simulations of potential Euler equations. These simulations provided us with basic characteristics of long time evolution of rational solutions of the NLS equation in the case of near-breaking conditions. The analytic NLS solutions are found to describe the actual wave dynamics of steep waves reasonably well.

Optical Quasi-Soliton Solutions for the Cubic-Quintic Nonlinear SCHRÖDINGER Equation with Variable Coefficients

NASA Astrophysics Data System (ADS)

Yang, Qin; Zhang, Jie-Fang

Optical quasi-soliton solutions for the cubic-quintic nonlinear Schrödinger equation (CQNLSE) with variable coefficients are considered. Based on the extended tanh-function method, we not only successfully obtained bright and dark quasi-soliton solutions, but also obtained the kink quasi-soliton solutions under certain parametric conditions. We conclude that the quasi-solitons induced by the combined effects of the group velocity dispersion (GVD) distribution, the nonlinearity distribution, higher-order nonlinearity distribution, and the amplification or absorption coefficient are quite different from those of the solitons induced only by the combined effects of the GVD, the nonlinearity distribution, and the amplification or absorption coefficient without considering the higher-order nonlinearity distribution (i.e. α(z)=0). Furthermore, we choose appropriate optical fiber parameters D(z) and R(z) to control the velocity of quasi-soliton and time shift, and discuss the evolution behavior of the special quasi-soliton.

Influence of heating rate on the condensational instability. [in outer layers of solar atmosphere

NASA Technical Reports Server (NTRS)

Dahlburg, R. B.; Mariska, J. T.

1988-01-01

Analysis and numerical simulation are used to determine the effect that various heating rates have on the linear and nonlinear evolution of a typical plasma within a solar magnetic flux tube subject to the condensational instability. It is found that linear stability depends strongly on the heating rate. The results of numerical simulations of the nonlinear evolution of the condensational instability in a solar magnetic flux tube are presented. Different heating rates lead to quite different nonlinear evolutions, as evidenced by the behavior of the global internal energy.

Nonlinear dynamics and quantum entanglement in optomechanical systems.

PubMed

Wang, Guanglei; Huang, Liang; Lai, Ying-Cheng; Grebogi, Celso

2014-03-21

To search for and exploit quantum manifestations of classical nonlinear dynamics is one of the most fundamental problems in physics. Using optomechanical systems as a paradigm, we address this problem from the perspective of quantum entanglement. We uncover strong fingerprints in the quantum entanglement of two common types of classical nonlinear dynamical behaviors: periodic oscillations and quasiperiodic motion. There is a transition from the former to the latter as an experimentally adjustable parameter is changed through a critical value. Accompanying this process, except for a small region about the critical value, the degree of quantum entanglement shows a trend of continuous increase. The time evolution of the entanglement measure, e.g., logarithmic negativity, exhibits a strong dependence on the nature of classical nonlinear dynamics, constituting its signature.

The simulation of electromagnetically driven strong Langmuir turbulence effect on the backscatter radiation from ionosphere

NASA Astrophysics Data System (ADS)

Kochetov, Andrey

2016-07-01

Numerical simulations of the dynamics of electromagnetic fields in a smoothly inhomogeneous nonlinear plasma layer in frameworks of the nonlinear Schrödinger equation with boundary conditions responsible for the pumping of the field in the layer by an incident wave and the inverse radiation losses supplemented the volume field dissipation due to the electromagnetic excitation of Langmuir turbulence are carried out. The effects of the threshold of non-linearity and it's evolution, of the threshold and saturation levels of dissipation in the vicinity of the wave reflection point on the features of the dynamics of reflection and absorption indexes are investigated. We consider the hard drive damping depending on the local field amplitude and hysteresis losses with different in several times "on" and "off" absorption thresholds as well. The dependence of the thresholds of the steady-state, periodic and chaotic regimes of plasma-wave interaction on the scenario of turbulence evolution is demonstrated. The results are compared with the experimental observations of Langmuir stage ionospheric modification.

The limitation and applicability of Musher-Sturman equation to two dimensional lower hybrid wave collapse

NASA Technical Reports Server (NTRS)

Tam, Sunny W. Y.; Chang, Tom

1995-01-01

The existence of localized regions of intense lower hybrid waves in the auroral ionosphere recently observed by rocket and satellite experiments can be understood by the study of a non-linear two-timescale coupling process. In this Letter, we demonstrate that the leading non-linear term in the standard Musher-Sturman equation vanishes identically in strict two-dimensions (normal to the magnetic field). Instead, the new two-dimensional equation is characterized by a much weaker non-linear term which arises from the ponderomotive force perpendicular to the magnetic field, particularly that due to the ions. The old and new equations are compared by means of time-evolution calculations of wave fields. The results exhibit a remarkable difference in the evolution of the waves as governed by the two equations. Such dissimilar outcomes motivate our investigation of the limitation of Musher-Sturman equation in quasi-two-dimensions. Only within all these limits can Musher-Sturman equation adequately describe the collapse of lower hybrid waves.

Modeling of the spectral evolution in a narrow-linewidth fiber amplifier

NASA Astrophysics Data System (ADS)

Liu, Wei; Kuang, Wenjun; Jiang, Man; Xu, Jiangming; Zhou, Pu; Liu, Zejin

2016-03-01

Efficient numerical modeling of the spectral evolution in a narrow-linewidth fiber amplifier is presented. By describing the seeds using a statistical model and simulating the amplification process through power balanced equations combined with the nonlinear Schrödinger equations, the spectral evolution of different seeds in the fiber amplifier can be evaluated accurately. The simulation results show that the output spectra are affected by the temporal stability of the seeds and the seeds with constant amplitude in time are beneficial to maintain the linewidth of the seed in the fiber amplifier.

Parametric resonant triad interactions in a free shear layer

NASA Technical Reports Server (NTRS)

Mallier, R.; Maslowe, S. A.

1993-01-01

We investigate the weakly nonlinear evolution of a triad of nearly-neutral modes superimposed on a mixing layer with velocity profile u bar equals Um + tanh y. The perturbation consists of a plane wave and a pair of oblique waves each inclined at approximately 60 degrees to the mean flow direction. Because the evolution occurs on a relatively fast time scale, the critical layer dynamics dominate the process and the amplitude evolution of the oblique waves is governed by an integro-differential equation. The long-time solution of this equation predicts very rapid (exponential of an exponential) amplification and we discuss the pertinence of this result to vortex pairing phenomena in mixing layers.

Nonlinear viscosity in brane-world cosmology with a Gauss–Bonnet term

NASA Astrophysics Data System (ADS)

Debnath, P. S.; Beesham, A.; Paul, B. C.

2018-06-01

Cosmological solutions are obtained with nonlinear bulk viscous cosmological fluid in the Randall–Sundrum type II (RS) brane-world model with or without Gauss–Bonnet (GB) terms. To describe such a viscous fluid, we consider the nonlinear transport equation which may be used far from equilibrium during inflation or reheating. Cosmological models are explored for both (i) power law and (ii) exponential evolution of the early universe in the presence of an imperfect fluid described by the non-linear Israel and Stewart theory (nIS). We obtain analytic solutions and the complex field equations are also analyzed numerically to study the evolution of the universe. The stability analysis of the equilibrium points of the dynamical system associated with the evolution of the nonlinear bulk viscous fluid in the RS Brane in the presence (or absence) of a GB term are also studied.

Empirical Investigation of Critical Transitions in Paleoclimate

NASA Astrophysics Data System (ADS)

Loskutov, E. M.; Mukhin, D.; Gavrilov, A.; Feigin, A.

2016-12-01

In this work we apply a new empirical method for the analysis of complex spatially distributed systems to the analysis of paleoclimate data. The method consists of two general parts: (i) revealing the optimal phase-space variables and (ii) construction the empirical prognostic model by observed time series. The method of phase space variables construction based on the data decomposition into nonlinear dynamical modes which was successfully applied to global SST field and allowed clearly separate time scales and reveal climate shift in the observed data interval [1]. The second part, the Bayesian approach to optimal evolution operator reconstruction by time series is based on representation of evolution operator in the form of nonlinear stochastic function represented by artificial neural networks [2,3]. In this work we are focused on the investigation of critical transitions - the abrupt changes in climate dynamics - in match longer time scale process. It is well known that there were number of critical transitions on different time scales in the past. In this work, we demonstrate the first results of applying our empirical methods to analysis of paleoclimate variability. In particular, we discuss the possibility of detecting, identifying and prediction such critical transitions by means of nonlinear empirical modeling using the paleoclimate record time series. The study is supported by Government of Russian Federation (agreement #14.Z50.31.0033 with the Institute of Applied Physics of RAS). 1. Mukhin, D., Gavrilov, A., Feigin, A., Loskutov, E., & Kurths, J. (2015). Principal nonlinear dynamical modes of climate variability. Scientific Reports, 5, 15510. http://doi.org/10.1038/srep155102. Ya. I. Molkov, D. N. Mukhin, E. M. Loskutov, A.M. Feigin, (2012) : Random dynamical models from time series. Phys. Rev. E, Vol. 85, n.3.3. Mukhin, D., Kondrashov, D., Loskutov, E., Gavrilov, A., Feigin, A., & Ghil, M. (2015). Predicting Critical Transitions in ENSO models. Part II: Spatially Dependent Models. Journal of Climate, 28(5), 1962-1976. http://doi.org/10.1175/JCLI-D-14-00240.1

Evolution of association between renal and liver functions while awaiting heart transplant: An application using a bivariate multiphase nonlinear mixed effects model.

PubMed

Rajeswaran, Jeevanantham; Blackstone, Eugene H; Barnard, John

2018-07-01

In many longitudinal follow-up studies, we observe more than one longitudinal outcome. Impaired renal and liver functions are indicators of poor clinical outcomes for patients who are on mechanical circulatory support and awaiting heart transplant. Hence, monitoring organ functions while waiting for heart transplant is an integral part of patient management. Longitudinal measurements of bilirubin can be used as a marker for liver function and glomerular filtration rate for renal function. We derive an approximation to evolution of association between these two organ functions using a bivariate nonlinear mixed effects model for continuous longitudinal measurements, where the two submodels are linked by a common distribution of time-dependent latent variables and a common distribution of measurement errors.

MURI: Adaptive Waveform Design for Full Spectral Dominance

DTIC Science & Technology

2011-03-11

a three- dimensional urban tracking model, based on the nonlinear measurement model (that uses the urban multipath geometry with different types of ... the time evolution of the scattering function with a high dimensional dynamic system; a multiple particle filter technique is used to sequentially...integration of space -time coding with a fixed set of beams. It complements the

The Dynamics of Small-Scale Turbulence Driven Flows

NASA Astrophysics Data System (ADS)

Beer, M. A.; Hammett, G. W.

1997-11-01

The dynamics of small-scale fluctuation driven flows are of great interest for micro-instability driven turbulence, since nonlinear toroidal simulations have shown that these flows play an important role in the regulation of the turbulence and transport levels. The gyrofluid treatment of these flows was shown to be accurate for times shorter than a bounce time.(Beer, M. A., Ph. D. thesis, Princeton University (1995).) Since the decorrelation times of the turbulence are generally shorter than a bounce time, our original hypothesis was that this description was adequate. Recent work(Hinton, F. L., Rosenbluth, M. N., and Waltz, R. E., International Sherwood Fusion Theory Conference (1997).) pointed out possible problems with this hypothesis, emphasizing the existence of a linearly undamped component of the flow which could build up in time and lower the final turbulence level. While our original gyrofluid model reproduces some aspects of the linear flow, there are differences between the long time gyrofluid and kinetic linear results in some cases. On the other hand, if the long time behavior of these flows is dominated by nonlinear damping (which seems reasonable), then the existing nonlinear gyrofluid simulations may be sufficiently accurate. We test these possibilities by modifying the gyrofluid description of these flows and diagnosing the flow evolution in nonlinear simulations.

New exact solutions of the Tzitzéica-type equations in non-linear optics using the expa function method

NASA Astrophysics Data System (ADS)

Hosseini, K.; Ayati, Z.; Ansari, R.

2018-04-01

One specific class of non-linear evolution equations, known as the Tzitzéica-type equations, has received great attention from a group of researchers involved in non-linear science. In this article, new exact solutions of the Tzitzéica-type equations arising in non-linear optics, including the Tzitzéica, Dodd-Bullough-Mikhailov and Tzitzéica-Dodd-Bullough equations, are obtained using the expa function method. The integration technique actually suggests a useful and reliable method to extract new exact solutions of a wide range of non-linear evolution equations.

Quantum simulation from the bottom up: the case of rebits

NASA Astrophysics Data System (ADS)

Enshan Koh, Dax; Yuezhen Niu, Murphy; Yoder, Theodore J.

2018-05-01

Typically, quantum mechanics is thought of as a linear theory with unitary evolution governed by the Schrödinger equation. While this is technically true and useful for a physicist, with regards to computation it is an unfortunately narrow point of view. Just as a classical computer can simulate highly nonlinear functions of classical states, so too can the more general quantum computer simulate nonlinear evolutions of quantum states. We detail one particular simulation of nonlinearity on a quantum computer, showing how the entire class of -unitary evolutions (on n qubits) can be simulated using a unitary, real-amplitude quantum computer (consisting of n  +  1 qubits in total). These operators can be represented as the sum of a linear and antilinear operator, and add an intriguing new set of nonlinear quantum gates to the toolbox of the quantum algorithm designer. Furthermore, a subgroup of these nonlinear evolutions, called the -Cliffords, can be efficiently classically simulated, by making use of the fact that Clifford operators can simulate non-Clifford (in fact, non-linear) operators. This perspective of using the physical operators that we have to simulate non-physical ones that we do not is what we call bottom-up simulation, and we give some examples of its broader implications.

Adaptive Finite Element Methods for Continuum Damage Modeling

NASA Technical Reports Server (NTRS)

Min, J. B.; Tworzydlo, W. W.; Xiques, K. E.

1995-01-01

The paper presents an application of adaptive finite element methods to the modeling of low-cycle continuum damage and life prediction of high-temperature components. The major objective is to provide automated and accurate modeling of damaged zones through adaptive mesh refinement and adaptive time-stepping methods. The damage modeling methodology is implemented in an usual way by embedding damage evolution in the transient nonlinear solution of elasto-viscoplastic deformation problems. This nonlinear boundary-value problem is discretized by adaptive finite element methods. The automated h-adaptive mesh refinements are driven by error indicators, based on selected principal variables in the problem (stresses, non-elastic strains, damage, etc.). In the time domain, adaptive time-stepping is used, combined with a predictor-corrector time marching algorithm. The time selection is controlled by required time accuracy. In order to take into account strong temperature dependency of material parameters, the nonlinear structural solution a coupled with thermal analyses (one-way coupling). Several test examples illustrate the importance and benefits of adaptive mesh refinements in accurate prediction of damage levels and failure time.

Transverse instabilities of stripe domains in magnetic thin films with perpendicular magnetic anisotropy

NASA Astrophysics Data System (ADS)

Ruth, Max E.; Iacocca, Ezio; Kevrekidis, Panayotis G.; Hoefer, Mark A.

2018-03-01

Stripe domains are narrow, elongated, reversed regions that exist in magnetic materials with perpendicular magnetic anisotropy. They appear as a pair of domain walls that can exhibit topology with a nonzero chirality. Recent experimental and numerical investigations identify an instability of stripe domains along the long direction as a means of nucleating isolated magnetic skyrmions. Here, the onset and nonlinear evolution of transverse instabilities for a dynamic stripe domain known as the bion stripe are investigated. Both nontopological and topological variants of the bion stripe are shown to exhibit a long-wavelength transverse instability with different characteristic features. In the former, small transverse variations in the stripe's width lead to a neck instability that eventually pinches the nontopological stripe into a chain of two-dimensional breathers composed of droplet soliton pairs. In the latter case, small variations in the stripe's center result in a snake instability whose topological structure leads to the nucleation of dynamic magnetic skyrmions and antiskyrmions as well as perimeter-modulated droplets. Quantitative, analytical predictions for both the early, linear evolution and the long-time, nonlinear evolution are achieved using an averaged Lagrangian approach that incorporates both exchange (dispersion) and anisotropy (nonlinearity). The method of analysis is general and can be applied to other filamentary structures.

Nonlinear calculations of the time evolution of black hole accretion disks

NASA Technical Reports Server (NTRS)

Luo, C.

1994-01-01

Based on previous works on black hole accretion disks, I continue to explore the disk dynamics using the finite difference method to solve the highly nonlinear problem of time-dependent alpha disk equations. Here a radially zoned model is used to develop a computational scheme in order to accommodate functional dependence of the viscosity parameter alpha on the disk scale height and/or surface density. This work is based on the author's previous work on the steady disk structure and the linear analysis of disk dynamics to try to apply to x-ray emissions from black candidates (i.e., multiple-state spectra, instabilities, QPO's, etc.).

Phantom solution in a non-linear Israel-Stewart theory

NASA Astrophysics Data System (ADS)

Cruz, Miguel; Cruz, Norman; Lepe, Samuel

2017-06-01

In this paper we present a phantom solution with a big rip singularity in a non-linear regime of the Israel-Stewart formalism. In this framework it is possible to extend this causal formalism in order to describe accelerated expansion, where assumption of near equilibrium is no longer valid. We assume a flat universe filled with a single viscous fluid ruled by a barotropic EoS, p = ωρ, which can represent a late time accelerated phase of the cosmic evolution. The solution allows to cross the phantom divide without evoking an exotic matter fluid and the effective EoS parameter is always lesser than -1 and constant in time.

NLO evolution of color dipole

DOE PAGES

Balitsky, Ian; Chirilli, Giovanni A.

2008-09-01

The small-x deep inelastic scattering in the saturation region is governed by the non-linear evolution of Wilson-line operators. In the leading logarithmic approximation it is given by the BK equation for the evolution of color dipoles. In the next-to-leading order the BK equation gets contributions from quark and gluon loops as well as from the tree gluon diagrams with quadratic and cubic nonlinearities.

Allowing for Slow Evolution of Background Plasma in the 3D FDTD Plasma, Sheath, and Antenna Model

NASA Astrophysics Data System (ADS)

Smithe, David; Jenkins, Thomas; King, Jake

2015-11-01

We are working to include a slow-time evolution capability for what has previously been the static background plasma parameters, in the 3D finite-difference time-domain (FDTD) plasma and sheath model used to model ICRF antennas in fusion plasmas. A key aspect of this is SOL-density time-evolution driven by ponderomotive rarefaction from the strong fields in the vicinity of the antenna. We demonstrate and benchmark a Scalar Ponderomotive Potential method, based on local field amplitudes, which is included in the 3D simulation. And present a more advanced Tensor Ponderomotive Potential approach, which we hope to employ in the future, which should improve the physical fidelity in the highly anisotropic environment of the SOL. Finally, we demonstrate and benchmark slow time (non-linear) evolution of the RF sheath, and include realistic collisional effects from the neutral gas. Support from US DOE Grants DE-FC02-08ER54953, DE-FG02-09ER55006.

Holographic dark energy in higher derivative gravity with time varying model parameter c2

NASA Astrophysics Data System (ADS)

Borah, B.; Ansari, M.

2015-01-01

Purpose of this paper is to study holographic dark energy in higher derivative gravity assuming the model parameter c2 as a slowly time varying function. Since dark energy emerges as combined effect of linear as well as non-linear terms of curvature, therefore it is important to see holographic dark energy at higher derivative gravity, where action contains both linear as well as non-linear terms of Ricci curvature R. We consider non-interacting scenario of the holographic dark energy with dark matter in spatially flat universe and obtain evolution of the equation of state parameter. Also, we determine deceleration parameter as well as the evolution of dark energy density to explain expansion of the universe. Further, we investigate validity of generalized second law of thermodynamics in this scenario. Finally, we find out a cosmological application of our work by evaluating a relation for the equation of state of holographic dark energy for low red-shifts containing c2 correction.

Generation of localized patterns in anharmonic lattices with cubic-quintic nonlinearities and fourth-order dispersion via a variational approach

NASA Astrophysics Data System (ADS)

Wamba, Etienne; Tchakoutio Nguetcho, Aurélien S.

2018-05-01

We use the time-dependent variational method to examine the formation of localized patterns in dynamically unstable anharmonic lattices with cubic-quintic nonlinearities and fourth-order dispersion. The governing equation is an extended nonlinear Schrödinger equation known for modified Frankel-Kontorova models of atomic lattices and here derived from an extended Bose-Hubbard model of bosonic lattices with local three-body interactions. In presence of modulated waves, we derive and investigate the ordinary differential equations for the time evolution of the amplitude and phase of dynamical perturbation. Through an effective potential, we find the modulationally unstable domains of the lattice and discuss the effect of the fourth-order dispersion in the dynamics. Direct numerical simulations are performed to support our analytical results, and a good agreement is found. Various types of localized patterns, including breathers and solitonic chirped-like pulses, form in the system as a result of interplay between the cubic-quintic nonlinearities and the second- and fourth-order dispersions.

Peculiarities of evolutions of elastic-plastic shock compression waves in different materials

NASA Astrophysics Data System (ADS)

Kanel, G. I.; Savinykh, A. S.; Garkushin, G. V.; Razorenov, S. V.; Ashitkov, S. I.; Zaretsky, E. B.

2016-11-01

In the paper, we discuss such unexpected features in the wave evolution in solids as strongly nonlinear uniaxial elastic compression in a picosecond time range, a departure from self-similar development of the wave process which is accompanied with apparent sub-sonic wave propagation, changes of shape of elastic precursor wave as a result of variations in the material structure and the temperature, unexpected peculiarities of reflection of elastic-plastic waves from free surface.

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

Bifurcation-based adiabatic quantum computation with a nonlinear oscillator network.

PubMed

Goto, Hayato

2016-02-22

The dynamics of nonlinear systems qualitatively change depending on their parameters, which is called bifurcation. A quantum-mechanical nonlinear oscillator can yield a quantum superposition of two oscillation states, known as a Schrödinger cat state, via quantum adiabatic evolution through its bifurcation point. Here we propose a quantum computer comprising such quantum nonlinear oscillators, instead of quantum bits, to solve hard combinatorial optimization problems. The nonlinear oscillator network finds optimal solutions via quantum adiabatic evolution, where nonlinear terms are increased slowly, in contrast to conventional adiabatic quantum computation or quantum annealing, where quantum fluctuation terms are decreased slowly. As a result of numerical simulations, it is concluded that quantum superposition and quantum fluctuation work effectively to find optimal solutions. It is also notable that the present computer is analogous to neural computers, which are also networks of nonlinear components. Thus, the present scheme will open new possibilities for quantum computation, nonlinear science, and artificial intelligence.

Bifurcation-based adiabatic quantum computation with a nonlinear oscillator network

NASA Astrophysics Data System (ADS)

Goto, Hayato

2016-02-01

The dynamics of nonlinear systems qualitatively change depending on their parameters, which is called bifurcation. A quantum-mechanical nonlinear oscillator can yield a quantum superposition of two oscillation states, known as a Schrödinger cat state, via quantum adiabatic evolution through its bifurcation point. Here we propose a quantum computer comprising such quantum nonlinear oscillators, instead of quantum bits, to solve hard combinatorial optimization problems. The nonlinear oscillator network finds optimal solutions via quantum adiabatic evolution, where nonlinear terms are increased slowly, in contrast to conventional adiabatic quantum computation or quantum annealing, where quantum fluctuation terms are decreased slowly. As a result of numerical simulations, it is concluded that quantum superposition and quantum fluctuation work effectively to find optimal solutions. It is also notable that the present computer is analogous to neural computers, which are also networks of nonlinear components. Thus, the present scheme will open new possibilities for quantum computation, nonlinear science, and artificial intelligence.

Progress in Modeling Nonlinear Dendritic Evolution in Two and Three Dimensions, and Its Mathematical Justification

NASA Technical Reports Server (NTRS)

Tanveer, S.; Foster, M. R.

2002-01-01

We report progress in three areas of investigation related to dendritic crystal growth. Those items include: 1. Selection of tip features dendritic crystal growth; 2) Investigation of nonlinear evolution for two-sided model; and 3) Rigorous mathematical justification.

Nonlinear second order evolution inclusions with noncoercive viscosity term

NASA Astrophysics Data System (ADS)

Papageorgiou, Nikolaos S.; Rădulescu, Vicenţiu D.; Repovš, Dušan D.

2018-04-01

In this paper we deal with a second order nonlinear evolution inclusion, with a nonmonotone, noncoercive viscosity term. Using a parabolic regularization (approximation) of the problem and a priori bounds that permit passing to the limit, we prove that the problem has a solution.

On a hierarchy of nonlinearly dispersive generalized Korteweg - de Vries evolution equations

DOE PAGES

Christov, Ivan C.

2015-08-20

We propose a hierarchy of nonlinearly dispersive generalized Korteweg–de Vries (KdV) evolution equations based on a modification of the Lagrangian density whose induced action functional the KdV equation extremizes. Two recent nonlinear evolution equations describing wave propagation in certain generalized continua with an inherent material length scale are members of the proposed hierarchy. Like KdV, the equations from the proposed hierarchy possess Hamiltonian structure. Unlike KdV, the solutions to these equations can be compact (i.e., they vanish outside of some open interval) and, in addition, peaked. Implicit solutions for these peaked, compact traveling waves (“peakompactons”) are presented.

Detectability of the impacts of ozone-depleting substances and greenhouse gases upon stratospheric ozone accounting for nonlinearities in historical forcings

NASA Astrophysics Data System (ADS)

Bandoro, Justin; Solomon, Susan; Santer, Benjamin D.; Kinnison, Douglas E.; Mills, Michael J.

2018-01-01

We perform a formal attribution study of upper- and lower-stratospheric ozone changes using observations together with simulations from the Whole Atmosphere Community Climate Model. Historical model simulations were used to estimate the zonal-mean response patterns (fingerprints) to combined forcing by ozone-depleting substances (ODSs) and well-mixed greenhouse gases (GHGs), as well as to the individual forcing by each factor. Trends in the similarity between the searched-for fingerprints and homogenized observations of stratospheric ozone were compared to trends in pattern similarity between the fingerprints and the internally and naturally generated variability inferred from long control runs. This yields estimated signal-to-noise (S/N) ratios for each of the three fingerprints (ODS, GHG, and ODS + GHG). In both the upper stratosphere (defined in this paper as 1 to 10 hPa) and lower stratosphere (40 to 100 hPa), the spatial fingerprints of the ODS + GHG and ODS-only patterns were consistently detectable not only during the era of maximum ozone depletion but also throughout the observational record (1984-2016). We also develop a fingerprint attribution method to account for forcings whose time evolutions are markedly nonlinear over the observational record. When the nonlinearity of the time evolution of the ODS and ODS + GHG signals is accounted for, we find that the S/N ratios obtained with the stratospheric ODS and ODS + GHG fingerprints are enhanced relative to standard linear trend analysis. Use of the nonlinear signal detection method also reduces the detection time - the estimate of the date at which ODS and GHG impacts on ozone can be formally identified. Furthermore, by explicitly considering nonlinear signal evolution, the complete observational record can be used in the S/N analysis, without applying piecewise linear regression and introducing arbitrary break points. The GHG-driven fingerprint of ozone changes was not statistically identifiable in either the upper- or lower-stratospheric SWOOSH data, irrespective of the signal detection method used. In the WACCM simulations of future climate change, the GHG signal is statistically identifiable between 2020 and 2030. Our findings demonstrate the importance of continued stratospheric ozone monitoring to improve estimates of the contributions of ODS and GHG forcing to global changes in stratospheric ozone.

Evolution and End Point of the Black String Instability: Large D Solution.

PubMed

Emparan, Roberto; Suzuki, Ryotaku; Tanabe, Kentaro

2015-08-28

We derive a simple set of nonlinear, (1+1)-dimensional partial differential equations that describe the dynamical evolution of black strings and branes to leading order in the expansion in the inverse of the number of dimensions D. These equations are easily solved numerically. Their solution shows that thin enough black strings are unstable to developing inhomogeneities along their length, and at late times they asymptote to stable nonuniform black strings. This proves an earlier conjecture about the end point of the instability of black strings in a large enough number of dimensions. If the initial black string is very thin, the final configuration is highly nonuniform and resembles a periodic array of localized black holes joined by short necks. We also present the equations that describe the nonlinear dynamics of anti-de Sitter black branes at large D.

Reaction-diffusion-like formalism for plastic neural networks reveals dissipative solitons at criticality

NASA Astrophysics Data System (ADS)

Grytskyy, Dmytro; Diesmann, Markus; Helias, Moritz

2016-06-01

Self-organized structures in networks with spike-timing dependent synaptic plasticity (STDP) are likely to play a central role for information processing in the brain. In the present study we derive a reaction-diffusion-like formalism for plastic feed-forward networks of nonlinear rate-based model neurons with a correlation sensitive learning rule inspired by and being qualitatively similar to STDP. After obtaining equations that describe the change of the spatial shape of the signal from layer to layer, we derive a criterion for the nonlinearity necessary to obtain stable dynamics for arbitrary input. We classify the possible scenarios of signal evolution and find that close to the transition to the unstable regime metastable solutions appear. The form of these dissipative solitons is determined analytically and the evolution and interaction of several such coexistent objects is investigated.

Nonlinear evolution of Benjamin-Feir wave group based on third order solution of Benjamin-Bona-Mahony equation

NASA Astrophysics Data System (ADS)

Zahnur; Halfiani, Vera; Salmawaty; Tulus; Ramli, Marwan

2018-01-01

This study concerns on the evolution of trichromatic wave group. It has been known that the trichromatic wave group undergoes an instability during its propagation, which results wave deformation and amplification on the waves amplitude. The previous results on the KdV wave group showed that the nonlinear effect will deform the wave and lead to large wave whose amplitude is higher than the initial input. In this study we consider the Benjamin-Bona-Mahony equation and the theory of third order side band approximation to investigate the peaking and splitting phenomena of the wave groups which is initially in trichromatic signal. The wave amplitude amplification and the maximum position will be observed through a quantity called Maximal Temporal Amplitude (MTA) which measures the maximum amplitude of the waves over time.

Fast and local non-linear evolution of steep wave-groups on deep water: A comparison of approximate models to fully non-linear simulations

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

Adcock, T. A. A.; Taylor, P. H.

2016-01-15

The non-linear Schrödinger equation and its higher order extensions are routinely used for analysis of extreme ocean waves. This paper compares the evolution of individual wave-packets modelled using non-linear Schrödinger type equations with packets modelled using fully non-linear potential flow models. The modified non-linear Schrödinger Equation accurately models the relatively large scale non-linear changes to the shape of wave-groups, with a dramatic contraction of the group along the mean propagation direction and a corresponding extension of the width of the wave-crests. In addition, as extreme wave form, there is a local non-linear contraction of the wave-group around the crest whichmore » leads to a localised broadening of the wave spectrum which the bandwidth limited non-linear Schrödinger Equations struggle to capture. This limitation occurs for waves of moderate steepness and a narrow underlying spectrum.« less

Study of travelling wave solutions for some special-type nonlinear evolution equations

NASA Astrophysics Data System (ADS)

Song, Junquan; Hu, Lan; Shen, Shoufeng; Ma, Wen-Xiu

2018-07-01

The tanh-function expansion method has been improved and used to construct travelling wave solutions of the form U={\\sum }j=0n{a}j{\\tanh }jξ for some special-type nonlinear evolution equations, which have a variety of physical applications. The positive integer n can be determined by balancing the highest order linear term with the nonlinear term in the evolution equations. We improve the tanh-function expansion method with n = 0 by introducing a new transform U=-W\\prime (ξ )/{W}2. A nonlinear wave equation with source terms, and mKdV-type equations, are considered in order to show the effectiveness of the improved scheme. We also propose the tanh-function expansion method of implicit function form, and apply it to a Harry Dym-type equation as an example.

A Nonlinear Dynamical Systems based Model for Stochastic Simulation of Streamflow

NASA Astrophysics Data System (ADS)

Erkyihun, S. T.; Rajagopalan, B.; Zagona, E. A.

2014-12-01

Traditional time series methods model the evolution of the underlying process as a linear or nonlinear function of the autocorrelation. These methods capture the distributional statistics but are incapable of providing insights into the dynamics of the process, the potential regimes, and predictability. This work develops a nonlinear dynamical model for stochastic simulation of streamflows. In this, first a wavelet spectral analysis is employed on the flow series to isolate dominant orthogonal quasi periodic timeseries components. The periodic bands are added denoting the 'signal' component of the time series and the residual being the 'noise' component. Next, the underlying nonlinear dynamics of this combined band time series is recovered. For this the univariate time series is embedded in a d-dimensional space with an appropriate lag T to recover the state space in which the dynamics unfolds. Predictability is assessed by quantifying the divergence of trajectories in the state space with time, as Lyapunov exponents. The nonlinear dynamics in conjunction with a K-nearest neighbor time resampling is used to simulate the combined band, to which the noise component is added to simulate the timeseries. We demonstrate this method by applying it to the data at Lees Ferry that comprises of both the paleo reconstructed and naturalized historic annual flow spanning 1490-2010. We identify interesting dynamics of the signal in the flow series and epochal behavior of predictability. These will be of immense use for water resources planning and management.

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

Zhang, Hailong; Vibration Control Lab, School of Electrical and Automation Engineering, Nanjing Normal University, Nanjing 210042; Zhang, Ning

Magneto-rheological (MR) damper possesses inherent hysteretic characteristics. We investigate the resulting nonlinear behaviors of a two degree-of-freedom (2-DoF) MR vibration isolation system under harmonic external excitation. A MR damper is identified by employing the modified Bouc-wen hysteresis model. By numerical simulation, we characterize the nonlinear dynamic evolution of period-doubling, saddle node bifurcating and inverse period-doubling using bifurcation diagrams of variations in frequency with a fixed amplitude of the harmonic excitation. The strength of chaos is determined by the Lyapunov exponent (LE) spectrum. Semi-physical experiment on the 2-DoF MR vibration isolation system is proposed. We trace the time history and phasemore » trajectory under certain values of frequency of the harmonic excitation to verify the nonlinear dynamical evolution of period-doubling bifurcations to chaos. The largest LEs computed with the experimental data are also presented, confirming the chaotic motion in the experiment. We validate the chaotic motion caused by the hysteresis of the MR damper, and show the transitions between distinct regimes of stable motion and chaotic motion of the 2-DoF MR vibration isolation system for variations in frequency of external excitation.« less

Nonlinear Modeling of Forced Magnetic Reconnection with Transient Perturbations

NASA Astrophysics Data System (ADS)

Beidler, Matthew T.; Callen, James D.; Hegna, Chris C.; Sovinec, Carl R.

2017-10-01

Externally applied 3D magnetic fields in tokamaks can penetrate into the plasma and lead to forced magnetic reconnection, and hence magnetic islands, on resonant surfaces. Analytic theory has been reasonably successful in describing many aspects of this paradigm with regard to describing the time asymptotic-steady state. However, understanding the nonlinear evolution into a low-slip, field-penetrated state, especially how MHD events such as sawteeth and ELMs precipitate this transition, is in its early development. We present nonlinear computations employing the extended-MHD code NIMROD, building on previous work by incorporating a temporally varying external perturbation as a simple model for an MHD event that produces resonant magnetic signals. A parametric series of proof-of-principle computations and accompanying analytical theory characterize the transition into a mode-locked state with an emphasis on detailing the temporal evolution properties. Supported by DOE OFES Grants DE-FG02-92ER54139, DE-FG02-86ER53218, and the U.S. DOE FES Postdoctoral Research program administered by ORISE and managed by ORAU under DOE contract DE-SC0014664.

Symmetry reduction and exact solutions of two higher-dimensional nonlinear evolution equations.

PubMed

Gu, Yongyi; Qi, Jianming

2017-01-01

In this paper, symmetries and symmetry reduction of two higher-dimensional nonlinear evolution equations (NLEEs) are obtained by Lie group method. These NLEEs play an important role in nonlinear sciences. We derive exact solutions to these NLEEs via the [Formula: see text]-expansion method and complex method. Five types of explicit function solutions are constructed, which are rational, exponential, trigonometric, hyperbolic and elliptic function solutions of the variables in the considered equations.

Nonlinear inhomogeneous Fokker-Planck equations: Entropy and free-energy time evolution.

PubMed

Sicuro, Gabriele; Rapčan, Peter; Tsallis, Constantino

2016-12-01

We extend a recently introduced free-energy formalism for homogeneous Fokker-Planck equations to a wide, and physically appealing, class of inhomogeneous nonlinear Fokker-Planck equations. In our approach, the free-energy functional is expressed in terms of an entropic functional and an auxiliary potential, both derived from the coefficients of the equation. With reference to the introduced entropic functional, we discuss the entropy production in a relaxation process towards equilibrium. The properties of the stationary solutions of the considered Fokker-Planck equations are also discussed.

A nonlinear wave equation in nonadiabatic flame propagation

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

Booty, M.R.; Matalon, M.; Matkowsky, B.J.

1988-06-01

The authors derive a nonlinear wave equation from the diffusional thermal model of gaseous combustion to describe the evolution of a flame front. The equation arises as a long wave theory, for values of the volumeric heat loss in a neighborhood of the extinction point (beyond which planar uniformly propagating flames cease to exist), and for Lewis numbers near the critical value beyond which uniformly propagating planar flames lose stability via a degenerate Hopf bifurcation. Analysis of the equation suggests the possibility of a singularity developing in finite time.

Linear and non-linear perturbations in dark energy models

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

Escamilla-Rivera, Celia; Casarini, Luciano; Fabris, Júlio C.

2016-11-01

In this work we discuss observational aspects of three time-dependent parameterisations of the dark energy equation of state w ( z ). In order to determine the dynamics associated with these models, we calculate their background evolution and perturbations in a scalar field representation. After performing a complete treatment of linear perturbations, we also show that the non-linear contribution of the selected w ( z ) parameterisations to the matter power spectra is almost the same for all scales, with no significant difference from the predictions of the standard ΛCDM model.

Power-induced evolution and increased dimensionality of nonlinear modes in reorientational soft matter.

PubMed

Laudyn, Urszula A; Jung, Paweł S; Zegadło, Krzysztof B; Karpierz, Miroslaw A; Assanto, Gaetano

2014-11-15

We demonstrate the evolution of higher order one-dimensional guided modes into two-dimensional solitary waves in a reorientational medium. The observations, carried out at two different wavelengths in chiral nematic liquid crystals, are in good agreement with a simple nonlocal nonlinear model.

Multidimensional discrete compactons in nonlinear Schrödinger lattices with strong nonlinearity management

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

D'Ambroise, J.; Salerno, M.; Kevrekidis, P. G.

The existence of multidimensional lattice compactons in the discrete nonlinear Schrödinger equation in the presence of fast periodic time modulations of the nonlinearity is demonstrated. By averaging over the period of the fast modulations, an effective averaged dynamical equation arises with coupling constants involving Bessel functions of the first and zeroth kinds. We show that these terms allow one to solve, at this averaged level, for exact discrete compacton solution configurations in the corresponding stationary equation. We focus on seven types of compacton solutions. Single-site and vortex solutions are found to be always stable in the parametric regimes we examined.more » We also found that other solutions such as double-site in- and out-of-phase, four-site symmetric and antisymmetric, and a five-site compacton solution are found to have regions of stability and instability in two-dimensional parametric planes, involving variations of the strength of the coupling and of the nonlinearity. We also explore the time evolution of the solutions and compare the dynamics according to the averaged equations with those of the original dynamical system. Finally, the possible observation of compactons in Bose-Einstein condensates loaded in a deep two-dimensional optical lattice with interactions modulated periodically in time is also discussed.« less

Multidimensional discrete compactons in nonlinear Schrödinger lattices with strong nonlinearity management

DOE PAGES

D'Ambroise, J.; Salerno, M.; Kevrekidis, P. G.; ...

2015-11-19

The existence of multidimensional lattice compactons in the discrete nonlinear Schrödinger equation in the presence of fast periodic time modulations of the nonlinearity is demonstrated. By averaging over the period of the fast modulations, an effective averaged dynamical equation arises with coupling constants involving Bessel functions of the first and zeroth kinds. We show that these terms allow one to solve, at this averaged level, for exact discrete compacton solution configurations in the corresponding stationary equation. We focus on seven types of compacton solutions. Single-site and vortex solutions are found to be always stable in the parametric regimes we examined.more » We also found that other solutions such as double-site in- and out-of-phase, four-site symmetric and antisymmetric, and a five-site compacton solution are found to have regions of stability and instability in two-dimensional parametric planes, involving variations of the strength of the coupling and of the nonlinearity. We also explore the time evolution of the solutions and compare the dynamics according to the averaged equations with those of the original dynamical system. Finally, the possible observation of compactons in Bose-Einstein condensates loaded in a deep two-dimensional optical lattice with interactions modulated periodically in time is also discussed.« less

Model Predictive Control of the Current Profile and the Internal Energy of DIII-D Plasmas

NASA Astrophysics Data System (ADS)

Lauret, M.; Wehner, W.; Schuster, E.

2015-11-01

For efficient and stable operation of tokamak plasmas it is important that the current density profile and the internal energy are jointly controlled by using the available heating and current-drive (H&CD) sources. The proposed approach is a version of nonlinear model predictive control in which the input set is restricted in size by the possible combinations of the H&CD on/off states. The controller uses real-time predictions over a receding-time horizon of both the current density profile (nonlinear partial differential equation) and the internal energy (nonlinear ordinary differential equation) evolutions. At every time instant the effect of every possible combination of H&CD sources on the current profile and internal energy is evaluated over the chosen time horizon. The combination that leads to the best result, which is assessed by a user-defined cost function, is then applied up until the next time instant. Simulations results based on a control-oriented transport code illustrate the effectiveness of the proposed control method. Supported by the US DOE under DE-FC02-04ER54698 & DE-SC0010661.

Identifying the Flow Physics and Modeling Transient Forces on Two-Dimensional Wings

DTIC Science & Technology

2016-09-02

MODELS USING EDMD (a) ( b ) (c) (d) ( e ) (f) (g) (h... Model EDMD Model , β = 0.5 EDMD Model , optimal β ( b ) Model order 5 10 15 20 25 L im it c y c le f re q u e n c y 0.12 0.125 0.13 0.135 0.14 0.145...GP and EDMD nonlinear models in predicting the evolution of POD coefficients for transitional flow past a cylinder, showing (a) time evolution and ( b

Nonlinearity Role in Long-Term Interaction of the Ocean Gravity Waves

DTIC Science & Technology

2012-09-30

3 4 =s We found that in the fetch-limited case the wind forcing index s is similar to the time domain situation, and the wind forcing is given by...of its evolution. Fig.5 gives a graphical summary of four reference cases of self-similar evolution of wind-driven waves. These cases are shown as...different R, tangents of one-parametric dependencies H~TR height-to-period in logarithmic axes. Reference cases of growing wind sea are shown as

Gas evolution from spheres

NASA Astrophysics Data System (ADS)

Longhurst, G. R.

1991-04-01

Gas evolution from spherical solids or liquids where no convective processes are active is analyzed. Three problem classes are considered: (1) constant concentration boundary, (2) Henry's law (first order) boundary, and (3) Sieverts' law (second order) boundary. General expressions are derived for dimensionless times and transport parameters appropriate to each of the classes considered. However, in the second order case, the non-linearities of the problem require the presence of explicit dimensional variables in the solution. Sample problems are solved to illustrate the method.

Transit-time and age distributions for nonlinear time-dependent compartmental systems.

PubMed

Metzler, Holger; Müller, Markus; Sierra, Carlos A

2018-02-06

Many processes in nature are modeled using compartmental systems (reservoir/pool/box systems). Usually, they are expressed as a set of first-order differential equations describing the transfer of matter across a network of compartments. The concepts of age of matter in compartments and the time required for particles to transit the system are important diagnostics of these models with applications to a wide range of scientific questions. Until now, explicit formulas for transit-time and age distributions of nonlinear time-dependent compartmental systems were not available. We compute densities for these types of systems under the assumption of well-mixed compartments. Assuming that a solution of the nonlinear system is available at least numerically, we show how to construct a linear time-dependent system with the same solution trajectory. We demonstrate how to exploit this solution to compute transit-time and age distributions in dependence on given start values and initial age distributions. Furthermore, we derive equations for the time evolution of quantiles and moments of the age distributions. Our results generalize available density formulas for the linear time-independent case and mean-age formulas for the linear time-dependent case. As an example, we apply our formulas to a nonlinear and a linear version of a simple global carbon cycle model driven by a time-dependent input signal which represents fossil fuel additions. We derive time-dependent age distributions for all compartments and calculate the time it takes to remove fossil carbon in a business-as-usual scenario.

Nonlinear interaction of kinetic Alfven wave and whistler: Turbulent spectra and anisotropic scaling

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

Kumar Dwivedi, Navin; Sharma, R. P.

2013-04-15

In this work, we are presenting the excitation of oblique propagating whistler wave as a consequence of nonlinear interaction between whistler wave and kinetic Alfven wave (KAW) in intermediate beta plasmas. Numerical simulation has been done to study the transient evolution of magnetic field structures of KAW when the nonlinearity arises due to ponderomotive effects by taking the adiabatic response of the background density. Weak oblique propagating whistler signals in these nonlinear plasma density filaments (produced by KAW localization) get amplified. The spectral indices of the power spectrum at different times are calculated with given initial conditions of the simulations.more » Anisotropic scaling laws for KAW and whistlers are presented. The relevance of the present investigation to solar wind turbulence and its acceleration is also pointed out.« less

Multiple re-encounter approach to radical pair reactions and the role of nonlinear master equations.

PubMed

Clausen, Jens; Guerreschi, Gian Giacomo; Tiersch, Markus; Briegel, Hans J

2014-08-07

We formulate a multiple-encounter model of the radical pair mechanism that is based on a random coupling of the radical pair to a minimal model environment. These occasional pulse-like couplings correspond to the radical encounters and give rise to both dephasing and recombination. While this is in agreement with the original model of Haberkorn and its extensions that assume additional dephasing, we show how a nonlinear master equation may be constructed to describe the conditional evolution of the radical pairs prior to the detection of their recombination. We propose a nonlinear master equation for the evolution of an ensemble of independently evolving radical pairs whose nonlinearity depends on the record of the fluorescence signal. We also reformulate Haberkorn's original argument on the physicality of reaction operators using the terminology of quantum optics/open quantum systems. Our model allows one to describe multiple encounters within the exponential model and connects this with the master equation approach. We include hitherto neglected effects of the encounters, such as a separate dephasing in the triplet subspace, and predict potential new effects, such as Grover reflections of radical spins, that may be observed if the strength and time of the encounters can be experimentally controlled.

Effect of control-beam polarization and power on optical time-domain demultiplexing in a new nonlinear optical loop mirror design

NASA Astrophysics Data System (ADS)

Grendár, Drahomír; Pottiez, Olivier; Dado, Milan; Müllerová, Jarmila; Dubovan, Jozef

2009-05-01

A new scheme of a control-beam-driven nonlinear optical loop mirror (NOLM) with a birefringent twisted fiber and a symmetrical coupler designed for optical time division demultiplexing (OTDM) is analyzed. The theoretical model of the proposed NOLM scheme considers the evolution of polarization states of data and control beams and the mutual interactions of the data and control beams due to the cross-phase modulation (XPM). Attention is given to the optical switching commanded by the control-beam power and by the manipulation of nonlinear polarization rotation of the data and control beam. The simulations of NOLM transmissions demonstrate that the cross talk between demultiplexed and nondemultiplexed beams as an important parameter for optical switching by the presented NOLM can be significantly reduced. The results show that the device can be of interest for all-optical signal manipulations in optical communication networks.

Nonlinear power spectrum from resummed perturbation theory: a leap beyond the BAO scale

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

Anselmi, Stefano; Pietroni, Massimo, E-mail: anselmi@ieec.uab.es, E-mail: massimo.pietroni@pd.infn.it

2012-12-01

A new computational scheme for the nonlinear cosmological matter power spectrum (PS) is presented. Our method is based on evolution equations in time, which can be cast in a form extremely convenient for fast numerical evaluations. A nonlinear PS is obtained in a time comparable to that needed for a simple 1-loop computation, and the numerical implementation is very simple. Our results agree with N-body simulations at the percent level in the BAO range of scales, and at the few-percent level up to k ≅ 1 h/Mpc at z∼>0.5, thereby opening the possibility of applying this tool to scales interestingmore » for weak lensing. We clarify the approximations inherent to this approach as well as its relations to previous ones, such as the Time Renormalization Group, and the multi-point propagator expansion. We discuss possible lines of improvements of the method and its intrinsic limitations by multi streaming at small scales and low redshifts.« less

Nonlinear dynamics analysis of the spur gear system for railway locomotive

NASA Astrophysics Data System (ADS)

Wang, Junguo; He, Guangyue; Zhang, Jie; Zhao, Yongxiang; Yao, Yuan

2017-02-01

Considering the factors such as the nonlinearity backlash, static transmission error and time-varying meshing stiffness, a three-degree-of-freedom torsional vibration model of spur gear transmission system for a typical locomotive is developed, in which the wheel/rail adhesion torque is considered as uncertain but bounded parameter. Meantime, the Ishikawa method is used for analysis and calculation of the time-varying mesh stiffness of the gear pair in meshing process. With the help of bifurcation diagrams, phase plane diagrams, Poincaré maps, time domain response diagrams and amplitude-frequency spectrums, the effects of the pinion speed and stiffness on the dynamic behavior of gear transmission system for locomotive are investigated in detail by using the numerical integration method. Numerical examples reveal various types of nonlinear phenomena and dynamic evolution mechanism involving one-period responses, multi-periodic responses, bifurcation and chaotic responses. Some research results present useful information to dynamic design and vibration control of the gear transmission system for railway locomotive.

Asymptotics of the evolution semigroup associated with a scalar field in the presence of a non-linear electromagnetic field

NASA Astrophysics Data System (ADS)

Albeverio, Sergio; Tamura, Hiroshi

2018-04-01

We consider a model describing the coupling of a vector-valued and a scalar homogeneous Markovian random field over R4, interpreted as expressing the interaction between a charged scalar quantum field coupled with a nonlinear quantized electromagnetic field. Expectations of functionals of the random fields are expressed by Brownian bridges. Using this, together with Feynman-Kac-Itô type formulae and estimates on the small time and large time behaviour of Brownian functionals, we prove asymptotic upper and lower bounds on the kernel of the transition semigroup for our model. The upper bound gives faster than exponential decay for large distances of the corresponding resolvent (propagator).

Early time evolution of a chemically produced electron depletion

NASA Technical Reports Server (NTRS)

Scales, W. A.; Bernhardt, P. A.; Ganguli, G.

1995-01-01

The early time evolution of an ionospheric electron depletion produced by a radially expanding electron attachment chemical release is studied with a two-dimensional simulation model. The model includes electron attachment chemistry, incorporates fluid electrons, particle ions and neutrals, and considers the evolution in a plane perpendicular to the geomagnetic field for a low beta plasma. Timescales considered are of the order of or less than the cyclotron period of the negative ions that result as a by-product of the electron attacment reaction. This corresponds to time periods of tenths of seconds during recent experiemts. Simulation results show that a highly sheared azimuthal electron flow velocity develops in the radially expanding depletion boundary. This sheared electron flow velocity and the steep density gradients in the boundary give rise to small-scale irregulatities in the form of electron density cavities and spikes. The nonlinear evolution of these irregularities results in trapping and ultimately turbulent heating of the negative ions.

The emphasis given to evolution in state science standards: A lever for change in evolution education?

NASA Astrophysics Data System (ADS)

Skoog, Gerald; Bilica, Kimberly

2002-07-01

This study analyzed the science frameworks of 49 states and the District of Colombia to determine the emphasis given to evolution in these documents at the middle and secondary levels. These concepts were species evolve over time, speciation, diversity of life, descent with modification from common ancestry, evidence of evolution, natural selection, pace and direction of evolution, and human evolution. Collectively, the 50 science frameworks emphasized evolution in a manner that suggests that if the public's support for standards-based curricula is a reality, the study of evolution will be emphasized in an unprecedented manner in the nation's schools in the near future. However, all concepts were not emphasized equally in these documents. For example, human evolution was included in only seven documents. The word evolution is absent from some standards. Despite these negatives, recent actions to improve existing standards or to adopt new standards that emphasize evolution have occurred. The metaphor lever of change is often used in the context of school reform. This metaphor suggests a simple system where one change can result in a desired outcome. However, in classrooms where curriculum decisions evolve constantly, multiple factors interact and reinforce one another in response to both internal and external contingencies that emerge. Educational change can not be reduced to a simple linear cause/effect situation. The change process involved is nonlinear where what goes in is not proportional to what comes out because of feedback loops and other factors that complicate results. This nonlinearity is reflected in the varied responses of teachers to specific contingencies. Yet, systems can be changed and nudged towards a structure where desired outcomes will emerge. Judicial rulings indicating that the teaching of evolution cannot be prohibited or equal time for creationism mandated, improved coverage of evolution in secondary school biology textbooks, the negative response of many leaders, scientists, organizations, and editorial writers to the 1999 decision of the Kansas State Board of Education to deemphasize and misrepresent evolution in the state's science standards, and the emphasis given to evolution in the standards reviewed for this study, all coalesce to provide needed support for administrators and teachers who are striving to create science curricula that emphasize evolution in a manner commensurate with its importance in understanding the natural world and our place within it.

Real-time Monitoring Of Damage Evolution In Aerospace Materials Using Nonlinear Acoustics

NASA Astrophysics Data System (ADS)

Matikas, T. E.; Paipetis, A.; Kostopoulos, V.

2008-06-01

This work deals with the development of a novel non-destructive technique based on nonlinear acoustics, enabling real-time monitoring of material degradation in aerospace structures. When a sinusoidal ultrasonic wave of a given frequency and of sufficient amplitude is introduced into a nonlinear or an-harmonic solid, the fundamental wave distorts as it propagates, so that the second and higher harmonics of the fundamental frequency are generated. The measurement of the amplitude of these harmonics provides information on the coefficient of the second and higher order terms of the stress-strain relation for a nonlinear solid. It is demonstrated here that the material bulk nonlinear parameter for titanium alloy samples at different fatigue levels exhibits large changes compared to linear ultrasonic parameters such as velocity and attenuation. However, the use of bulk ultrasonic waves has serious disadvantages for the health monitoring of aerospace structures since it requires the placement of ultrasonic transducers on two, perfectly parallel, opposite sides of the samples. Such a setup is hardly feasible in real field conditions. For this reason, surface acoustic waves (SAW) were used in this study enabling the in-situ characterization of fatigue damage. The experimental setup for measuring the material nonlinear parameter using SAW was realised and the feasibility of the technique for health monitoring of aerospace structures was evaluated.

Bifurcation-based adiabatic quantum computation with a nonlinear oscillator network

PubMed Central

Goto, Hayato

2016-01-01

The dynamics of nonlinear systems qualitatively change depending on their parameters, which is called bifurcation. A quantum-mechanical nonlinear oscillator can yield a quantum superposition of two oscillation states, known as a Schrödinger cat state, via quantum adiabatic evolution through its bifurcation point. Here we propose a quantum computer comprising such quantum nonlinear oscillators, instead of quantum bits, to solve hard combinatorial optimization problems. The nonlinear oscillator network finds optimal solutions via quantum adiabatic evolution, where nonlinear terms are increased slowly, in contrast to conventional adiabatic quantum computation or quantum annealing, where quantum fluctuation terms are decreased slowly. As a result of numerical simulations, it is concluded that quantum superposition and quantum fluctuation work effectively to find optimal solutions. It is also notable that the present computer is analogous to neural computers, which are also networks of nonlinear components. Thus, the present scheme will open new possibilities for quantum computation, nonlinear science, and artificial intelligence. PMID:26899997

A Bivariate Chebyshev Spectral Collocation Quasilinearization Method for Nonlinear Evolution Parabolic Equations

PubMed Central

Motsa, S. S.; Magagula, V. M.; Sibanda, P.

2014-01-01

This paper presents a new method for solving higher order nonlinear evolution partial differential equations (NPDEs). The method combines quasilinearisation, the Chebyshev spectral collocation method, and bivariate Lagrange interpolation. In this paper, we use the method to solve several nonlinear evolution equations, such as the modified KdV-Burgers equation, highly nonlinear modified KdV equation, Fisher's equation, Burgers-Fisher equation, Burgers-Huxley equation, and the Fitzhugh-Nagumo equation. The results are compared with known exact analytical solutions from literature to confirm accuracy, convergence, and effectiveness of the method. There is congruence between the numerical results and the exact solutions to a high order of accuracy. Tables were generated to present the order of accuracy of the method; convergence graphs to verify convergence of the method and error graphs are presented to show the excellent agreement between the results from this study and the known results from literature. PMID:25254252

A bivariate Chebyshev spectral collocation quasilinearization method for nonlinear evolution parabolic equations.

PubMed

Motsa, S S; Magagula, V M; Sibanda, P

2014-01-01

This paper presents a new method for solving higher order nonlinear evolution partial differential equations (NPDEs). The method combines quasilinearisation, the Chebyshev spectral collocation method, and bivariate Lagrange interpolation. In this paper, we use the method to solve several nonlinear evolution equations, such as the modified KdV-Burgers equation, highly nonlinear modified KdV equation, Fisher's equation, Burgers-Fisher equation, Burgers-Huxley equation, and the Fitzhugh-Nagumo equation. The results are compared with known exact analytical solutions from literature to confirm accuracy, convergence, and effectiveness of the method. There is congruence between the numerical results and the exact solutions to a high order of accuracy. Tables were generated to present the order of accuracy of the method; convergence graphs to verify convergence of the method and error graphs are presented to show the excellent agreement between the results from this study and the known results from literature.

Cylindrical and spherical solitary waves in an electron-acoustic plasma with vortex electron distribution

NASA Astrophysics Data System (ADS)

Demiray, Hilmi; El-Zahar, Essam R.

2018-04-01

We consider the nonlinear propagation of electron-acoustic waves in a plasma composed of a cold electron fluid, hot electrons obeying a trapped/vortex-like distribution, and stationary ions. The basic nonlinear equations of the above described plasma are re-examined in the cylindrical (spherical) coordinates by employing the reductive perturbation technique. The modified cylindrical (spherical) KdV equation with fractional power nonlinearity is obtained as the evolution equation. Due to the nature of nonlinearity, this evolution equation cannot be reduced to the conventional KdV equation. A new family of closed form analytical approximate solution to the evolution equation and a comparison with numerical solution are presented and the results are depicted in some 2D and 3D figures. The results reveal that both solutions are in good agreement and the method can be used to obtain a new progressive wave solution for such evolution equations. Moreover, the resulting closed form analytical solution allows us to carry out a parametric study to investigate the effect of the physical parameters on the solution behavior of the modified cylindrical (spherical) KdV equation.

On the nonlinear three dimensional instability of Stokes layers and other shear layers to pairs of oblique waves

NASA Technical Reports Server (NTRS)

Wu, Xuesong; Lee, Sang Soo; Cowley, Stephen J.

1992-01-01

The nonlinear evolution of a pair of initially oblique waves in a high Reynolds Number Stokes layer is studied. Attention is focused on times when disturbances of amplitude epsilon have O(epsilon(exp 1/3)R) growth rates, where R is the Reynolds number. The development of a pair of oblique waves is then controlled by nonlinear critical-layer effects. Viscous effects are included by studying the distinguished scaling epsilon = O(R(exp -1)). This leads to a complicated modification of the kernel function in the integro-differential amplitude equation. When viscosity is not too large, solutions to the amplitude equation develop a finite-time singularity, indicating that an explosive growth can be introduced by nonlinear effects; we suggest that such explosive growth can lead to the bursts observed in experiments. Increasing the importance of viscosity generally delays the occurrence of the finite-time singularity, and sufficiently large viscosity may lead to the disturbance decaying exponentially. For the special case when the streamwise and spanwise wavenumbers are equal, the solution can evolve into a periodic oscillation. A link between the unsteady critical-layer approach to high-Reynolds-number flow instability, and the wave vortex approach is identified.

Spectral decomposition of nonlinear systems with memory

NASA Astrophysics Data System (ADS)

Svenkeson, Adam; Glaz, Bryan; Stanton, Samuel; West, Bruce J.

2016-02-01

We present an alternative approach to the analysis of nonlinear systems with long-term memory that is based on the Koopman operator and a Lévy transformation in time. Memory effects are considered to be the result of interactions between a system and its surrounding environment. The analysis leads to the decomposition of a nonlinear system with memory into modes whose temporal behavior is anomalous and lacks a characteristic scale. On average, the time evolution of a mode follows a Mittag-Leffler function, and the system can be described using the fractional calculus. The general theory is demonstrated on the fractional linear harmonic oscillator and the fractional nonlinear logistic equation. When analyzing data from an ill-defined (black-box) system, the spectral decomposition in terms of Mittag-Leffler functions that we propose may uncover inherent memory effects through identification of a small set of dynamically relevant structures that would otherwise be obscured by conventional spectral methods. Consequently, the theoretical concepts we present may be useful for developing more general methods for numerical modeling that are able to determine whether observables of a dynamical system are better represented by memoryless operators, or operators with long-term memory in time, when model details are unknown.

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

NASA Astrophysics Data System (ADS)

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

2000-04-01

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

Room-temperature ultrafast nonlinear spectroscopy of a single molecule

NASA Astrophysics Data System (ADS)

Liebel, Matz; Toninelli, Costanza; van Hulst, Niek F.

2018-01-01

Single-molecule spectroscopy aims to unveil often hidden but potentially very important contributions of single entities to a system's ensemble response. Albeit contributing tremendously to our ever growing understanding of molecular processes, the fundamental question of temporal evolution, or change, has thus far been inaccessible, thus painting a static picture of a dynamic world. Here, we finally resolve this dilemma by performing ultrafast time-resolved transient spectroscopy on a single molecule. By tracing the femtosecond evolution of excited electronic state spectra of single molecules over hundreds of nanometres of bandwidth at room temperature, we reveal their nonlinear ultrafast response in an effective three-pulse scheme with fluorescence detection. A first excitation pulse is followed by a phase-locked de-excitation pulse pair, providing spectral encoding with 25 fs temporal resolution. This experimental realization of true single-molecule transient spectroscopy demonstrates that two-dimensional electronic spectroscopy of single molecules is experimentally within reach.

A Generalized National Planning Approach for Admission Capacity in Higher Education: A Nonlinear Integer Goal Programming Model with a Novel Differential Evolution Algorithm

PubMed Central

El-Qulity, Said Ali; Mohamed, Ali Wagdy

2016-01-01

This paper proposes a nonlinear integer goal programming model (NIGPM) for solving the general problem of admission capacity planning in a country as a whole. The work aims to satisfy most of the required key objectives of a country related to the enrollment problem for higher education. The system general outlines are developed along with the solution methodology for application to the time horizon in a given plan. The up-to-date data for Saudi Arabia is used as a case study and a novel evolutionary algorithm based on modified differential evolution (DE) algorithm is used to solve the complexity of the NIGPM generated for different goal priorities. The experimental results presented in this paper show their effectiveness in solving the admission capacity for higher education in terms of final solution quality and robustness. PMID:26819583

A Generalized National Planning Approach for Admission Capacity in Higher Education: A Nonlinear Integer Goal Programming Model with a Novel Differential Evolution Algorithm.

PubMed

El-Qulity, Said Ali; Mohamed, Ali Wagdy

2016-01-01

This paper proposes a nonlinear integer goal programming model (NIGPM) for solving the general problem of admission capacity planning in a country as a whole. The work aims to satisfy most of the required key objectives of a country related to the enrollment problem for higher education. The system general outlines are developed along with the solution methodology for application to the time horizon in a given plan. The up-to-date data for Saudi Arabia is used as a case study and a novel evolutionary algorithm based on modified differential evolution (DE) algorithm is used to solve the complexity of the NIGPM generated for different goal priorities. The experimental results presented in this paper show their effectiveness in solving the admission capacity for higher education in terms of final solution quality and robustness.

New solitary wave and multiple soliton solutions for fifth order nonlinear evolution equation with time variable coefficients

NASA Astrophysics Data System (ADS)

Jaradat, H. M.; Syam, Muhammed; Jaradat, M. M. M.; Mustafa, Zead; Moman, S.

2018-03-01

In this paper, we investigate the multiple soliton solutions and multiple singular soliton solutions of a class of the fifth order nonlinear evolution equation with variable coefficients of t using the simplified bilinear method based on a transformation method combined with the Hirota's bilinear sense. In addition, we present analysis for some parameters such as the soliton amplitude and the characteristic line. Several equation in the literature are special cases of the class which we discuss such as Caudrey-Dodd-Gibbon equation and Sawada-Kotera. Comparison with several methods in the literature, such as Helmholtz solution of the inverse variational problem, rational exponential function method, tanh method, homotopy perturbation method, exp-function method, and coth method, are made. From these comparisons, we conclude that the proposed method is efficient and our solutions are correct. It is worth mention that the proposed solution can solve many physical problems.

Asymptotic Analysis of Time-Dependent Neutron Transport Coupled with Isotopic Depletion and Radioactive Decay

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

Brantley, P S

2006-09-27

We describe an asymptotic analysis of the coupled nonlinear system of equations describing time-dependent three-dimensional monoenergetic neutron transport and isotopic depletion and radioactive decay. The classic asymptotic diffusion scaling of Larsen and Keller [1], along with a consistent small scaling of the terms describing the radioactive decay of isotopes, is applied to this coupled nonlinear system of equations in a medium of specified initial isotopic composition. The analysis demonstrates that to leading order the neutron transport equation limits to the standard time-dependent neutron diffusion equation with macroscopic cross sections whose number densities are determined by the standard system of ordinarymore » differential equations, the so-called Bateman equations, describing the temporal evolution of the nuclide number densities.« less

Temporal evolution of age data under transient pumping conditions

NASA Astrophysics Data System (ADS)

Leray, S.; De Dreuzy, J.; Aquilina, L.; Vergnaud, V.; Labasque, T.; Bour, O.; Le Borgne, T.

2013-12-01

While most age data derived from tracers have been analyzed in steady-state flow conditions, we determine their temporal evolution under transient pumping conditions. Starting pumping in a well modifies the natural flow patterns induced by the topographical gradient to a mainly convergent flow to the well. Our study is based on a set of models made up of a shallowly dipping aquifer overlain by a less permeable aquitard. These settings are characteristic of the crystalline aquifer of Plœmeur (Brittany, France) located in a highly fractured zone at the contact between a granite and micaschists. Under a pseudo steady-state flow assumption (instantaneous shift between two steady-state flow fields), we solve the transport equation with a backward particle-tracking method and determine the temporal evolution of the concentrations at the pumping well of the four atmospheric tracers CFC 11, CFC 12, CFC 113 and SF6. We show that apparent ages deduced from these concentrations evolve both because of the flow patterns modifications and because of the non-linear evolution of the atmospheric tracer concentrations. Flow patterns modifications only intervene just after the start of pumping, when the initially piston-like residence time distribution is transformed to a broader distribution mixing residence times from a wide variety of flow lines. Later, while flow patterns and the supplying volume of the pumping well still evolve, the residence time distributions are hardly modified and apparent ages are solely altered by the non-linear atmospheric tracer concentrations that progressively modifies the weighting of the residence time distribution. These results are confirmed by the observations at the site of Plœmeur in the pumping area. First, long term chloride observations confirm the quick evolution of the flow patterns after the start of pumping. Second, posterior and more recent evolutions of apparent ages derived from CFCs are consistent with the modeling results revealing in turn the marginal effect of the 20-year pumping on the first 70 years of the residence time distribution. We conclude that the temporal evolution of apparent ages should be used with great care for identifying the temporal evolution of the flow patterns as the apparent age evolution can have two sources - the transient flow patterns and transient tracer atmospheric concentrations. We argue that both evolutions either controlled by transient flow patterns or by transient tracer atmospheric concentrations provide key information that can be further used for the characterization of the hydrogeological system. This study illustrates that the temporal evolution of apparent ages could be used for models segregation and slightly compensate for the small number of tracers.

Dam break problem for the focusing nonlinear Schrödinger equation and the generation of rogue waves

NASA Astrophysics Data System (ADS)

El, G. A.; Khamis, E. G.; Tovbis, A.

2016-09-01

We propose a novel, analytically tractable, scenario of the rogue wave formation in the framework of the small-dispersion focusing nonlinear Schrödinger (NLS) equation with the initial condition in the form of a rectangular barrier (a ‘box’). We use the Whitham modulation theory combined with the nonlinear steepest descent for the semi-classical inverse scattering transform, to describe the evolution and interaction of two counter-propagating nonlinear wave trains—the dispersive dam break flows—generated in the NLS box problem. We show that the interaction dynamics results in the emergence of modulated large-amplitude quasi-periodic breather lattices whose amplitude profiles are closely approximated by the Akhmediev and Peregrine breathers within certain space-time domain. Our semi-classical analytical results are shown to be in excellent agreement with the results of direct numerical simulations of the small-dispersion focusing NLS equation.

From the nonlinear Fokker-Planck equation to the Vlasov description and back: Confined interacting particles with drag

NASA Astrophysics Data System (ADS)

Plastino, A. R.; Curado, E. M. F.; Nobre, F. D.; Tsallis, C.

2018-02-01

Nonlinear Fokker-Planck equations endowed with power-law diffusion terms have proven to be valuable tools for the study of diverse complex systems in physics, biology, and other fields. The nonlinearity appearing in these evolution equations can be interpreted as providing an effective description of a system of particles interacting via short-range forces while performing overdamped motion under the effect of an external confining potential. This point of view has been recently applied to the study of thermodynamical features of interacting vortices in type II superconductors. In the present work we explore an embedding of the nonlinear Fokker-Planck equation within a Vlasov equation, thus incorporating inertial effects to the concomitant particle dynamics. Exact time-dependent solutions of the q -Gaussian form (with compact support) are obtained for the Vlasov equation in the case of quadratic confining potentials.

Evolution of basic equations for nearshore wave field

PubMed Central

ISOBE, Masahiko

2013-01-01

In this paper, a systematic, overall view of theories for periodic waves of permanent form, such as Stokes and cnoidal waves, is described first with their validity ranges. To deal with random waves, a method for estimating directional spectra is given. Then, various wave equations are introduced according to the assumptions included in their derivations. The mild-slope equation is derived for combined refraction and diffraction of linear periodic waves. Various parabolic approximations and time-dependent forms are proposed to include randomness and nonlinearity of waves as well as to simplify numerical calculation. Boussinesq equations are the equations developed for calculating nonlinear wave transformations in shallow water. Nonlinear mild-slope equations are derived as a set of wave equations to predict transformation of nonlinear random waves in the nearshore region. Finally, wave equations are classified systematically for a clear theoretical understanding and appropriate selection for specific applications. PMID:23318680

An inverse problem for a semilinear parabolic equation arising from cardiac electrophysiology

NASA Astrophysics Data System (ADS)

Beretta, Elena; Cavaterra, Cecilia; Cerutti, M. Cristina; Manzoni, Andrea; Ratti, Luca

2017-10-01

In this paper we develop theoretical analysis and numerical reconstruction techniques for the solution of an inverse boundary value problem dealing with the nonlinear, time-dependent monodomain equation, which models the evolution of the electric potential in the myocardial tissue. The goal is the detection of an inhomogeneity \

Nonlinear dynamics of Aeolian sand ripples.

PubMed

Prigozhin, L

1999-07-01

We study the initial instability of flat sand surface and further nonlinear dynamics of wind ripples. The proposed continuous model of ripple formation allowed us to simulate the development of a typical asymmetric ripple shape and the evolution of a sand ripple pattern. We suggest that this evolution occurs via ripple merger preceded by several soliton-like interaction of ripples.

Universal and integrable nonlinear evolution systems of equations in 2+1 dimensions

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

Maccari, A.

1997-08-01

Integrable systems of nonlinear partial differential equations (PDEs) are obtained from integrable equations in 2+1 dimensions, by means of a reduction method of broad applicability based on Fourier expansion and spatio{endash}temporal rescalings, which is asymptotically exact in the limit of weak nonlinearity. The integrability by the spectral transform is explicitly demonstrated, because the corresponding Lax pairs have been derived, applying the same reduction method to the Lax pair of the initial equation. These systems of nonlinear PDEs are likely to be of applicative relevance and have a {open_quotes}universal{close_quotes} character, inasmuch as they may be derived from a very large classmore » of nonlinear evolution equations with a linear dispersive part. {copyright} {ital 1997 American Institute of Physics.}« less

Nonlinear Waves in the Terrestrial Quasiparallel Foreshock.

PubMed

Hnat, B; Kolotkov, D Y; O'Connell, D; Nakariakov, V M; Rowlands, G

2016-12-02

We provide strongly conclusive evidence that the cubic nonlinearity plays an important part in the evolution of the large amplitude magnetic structures in the terrestrial foreshock. Large amplitude nonlinear wave trains at frequencies above the proton cyclotron frequency are identified after nonharmonic slow variations are filtered out by applying the empirical mode decomposition. Numerical solutions of the derivative nonlinear Schrödinger equation, predicted analytically by the use of a pseudopotential approach, are found to be consistent with the observed wave forms. The approximate phase speed of these nonlinear waves, indicated by the parameters of numerical solutions, is of the order of the local Alfvén speed. We suggest that the feedback of the large amplitude fluctuations on background plasma is reflected in the evolution of the pseudopotential.

Nonlinear evolution dynamics of holographic superconductor model with scalar self-interaction

NASA Astrophysics Data System (ADS)

Li, Ran; Zi, Tieguang; Zhang, Hongbao

2018-04-01

We investigate the holographic superconductor model that is described by the Einstein-Maxwell theory with the self-interaction term λ |Ψ |4 of complex scalar field in asymptotic anti-de Sitter (AdS) spacetime. Below critical temperature Tc, the planar Reissner-Nordström-AdS black hole is unstable due to the near-horizon scalar condensation instability. We study the full nonlinear development of this instability by numerically solving the gravitational dynamics in the asymptotic AdS spacetime, and observe a dynamical process from the perturbed Reissner-Nordström-AdS black hole to a hairy black hole when the initial black hole temperature T

Nonlinear spatial evolution of inviscid instabilities on hypersonic boundary layers

NASA Technical Reports Server (NTRS)

Wundrow, David W.

1996-01-01

The spatial development of an initially linear vorticity-mode instability on a compressible flat-plate boundary layer is considered. The analysis is done in the framework of the hypersonic limit where the free-stream Mach number M approaches infinity. Nonlinearity is shown to become important locally, in a thin critical layer, when sigma, the deviation of the phase speed from unity, becomes o(M(exp -8/7)) and the magnitude of the pressure fluctuations becomes 0(sigma(exp 5/2)M(exp 2)). The unsteady flow outside the critical layer takes the form of a linear instability wave but with its amplitude completely determined by the nonlinear flow within the critical layer. The coupled set of equations which govern the critical-layer dynamics reflect a balance between spatial-evolution, (linear and nonlinear) convection and nonlinear vorticity-generation terms. The numerical solution to these equations shows that nonlinear effects produce a dramatic reduction in the instability-wave amplitude.

Extracting Leading Nonlinear Modes of Changing Climate From Global SST Time Series

NASA Astrophysics Data System (ADS)

Mukhin, D.; Gavrilov, A.; Loskutov, E. M.; Feigin, A. M.; Kurths, J.

2017-12-01

Data-driven modeling of climate requires adequate principal variables extracted from observed high-dimensional data. For constructing such variables it is needed to find spatial-temporal patterns explaining a substantial part of the variability and comprising all dynamically related time series from the data. The difficulties of this task rise from the nonlinearity and non-stationarity of the climate dynamical system. The nonlinearity leads to insufficiency of linear methods of data decomposition for separating different processes entangled in the observed time series. On the other hand, various forcings, both anthropogenic and natural, make the dynamics non-stationary, and we should be able to describe the response of the system to such forcings in order to separate the modes explaining the internal variability. The method we present is aimed to overcome both these problems. The method is based on the Nonlinear Dynamical Mode (NDM) decomposition [1,2], but takes into account external forcing signals. An each mode depends on hidden, unknown a priori, time series which, together with external forcing time series, are mapped onto data space. Finding both the hidden signals and the mapping allows us to study the evolution of the modes' structure in changing external conditions and to compare the roles of the internal variability and forcing in the observed behavior. The method is used for extracting of the principal modes of SST variability on inter-annual and multidecadal time scales accounting the external forcings such as CO2, variations of the solar activity and volcanic activity. The structure of the revealed teleconnection patterns as well as their forecast under different CO2 emission scenarios are discussed.[1] Mukhin, D., Gavrilov, A., Feigin, A., Loskutov, E., & Kurths, J. (2015). Principal nonlinear dynamical modes of climate variability. Scientific Reports, 5, 15510. [2] Gavrilov, A., Mukhin, D., Loskutov, E., Volodin, E., Feigin, A., & Kurths, J. (2016). Method for reconstructing nonlinear modes with adaptive structure from multidimensional data. Chaos: An Interdisciplinary Journal of Nonlinear Science, 26(12), 123101.

Monitoring microstructural evolution of alloy 617 with non-linear acoustics for remaining useful life prediction; multiaxial creep-fatigue and creep-ratcheting

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

Lissenden, Cliff; Hassan, Tasnin; Rangari, Vijaya

The research built upon a prior investigation to develop a unified constitutive model for design-­by-­analysis of the intermediate heat exchanger (IHX) for a very high temperature reactor (VHTR) design of next generation nuclear plants (NGNPs). Model development requires a set of failure data from complex mechanical experiments to characterize the material behavior. Therefore uniaxial and multiaxial creep-­fatigue and creep-­ratcheting tests were conducted on the nickel-­base Alloy 617 at 850 and 950°C. The time dependence of material behavior, and the interaction of time dependent behavior (e.g., creep) with ratcheting, which is an increase in the cyclic mean strain under load-­controlled cycling,more » are major concerns for NGNP design. This research project aimed at characterizing the microstructure evolution mechanisms activated in Alloy 617 by mechanical loading and dwell times at elevated temperature. The acoustic harmonic generation method was researched for microstructural characterization. It is a nonlinear acoustics method with excellent potential for nondestructive evaluation, and even online continuous monitoring once high temperature sensors become available. It is unique because it has the ability to quantitatively characterize microstructural features well before macroscale defects (e.g., cracks) form. The nonlinear acoustics beta parameter was shown to correlate with microstructural evolution using a systematic approach to handle the complexity of multiaxial creep-­fatigue and creep-­ratcheting deformation. Mechanical testing was conducted to provide a full spectrum of data for: thermal aging, tensile creep, uniaxial fatigue, uniaxial creep-­fatigue, uniaxial creep-ratcheting, multiaxial creep-fatigue, and multiaxial creep-­ratcheting. Transmission Electron Microscopy (TEM), Scanning Electron Microscopy (SEM), and Optical Microscopy were conducted to correlate the beta parameter with individual microstructure mechanisms. We researched application of the harmonic generation method to tubular mechanical test specimens and pipes for nondestructive evaluation. Tubular specimens and pipes act as waveguides, thus we applied the acoustic harmonic generation method to guided waves in both plates and shells. Magnetostrictive transducers were used to generate and receive guided wave modes in the shell sample and the received signals were processed to show the sensitivity of higher harmonic generation to microstructure evolution. Modeling was initiated to correlate higher harmonic generation with the microstructure that will lead to development of a life prediction model that is informed by the nonlinear acoustics measurements.« less

Temporal evolution of age data under transient pumping conditions

NASA Astrophysics Data System (ADS)

Leray, S.; de Dreuzy, J.-R.; Aquilina, L.; Vergnaud-Ayraud, V.; Labasque, T.; Bour, O.; Le Borgne, T.

2014-04-01

While most age data derived from tracers have been analyzed in steady-state flow conditions, we determine their temporal evolution when starting a pumping. Our study is based on a model made up of a shallowly dipping aquifer overlain by a less permeable aquitard characteristic of the crystalline aquifer of Plœmeur (Brittany, France). Under a pseudo transient flow assumption (instantaneous shift between two steady-state flow fields), we solve the transport equation with a backward particle-tracking method and determine the temporal evolution of the concentrations at the pumping well of CFC-11, CFC-12, CFC-113 and SF6. Apparent ages evolve because of the modifications of the flow pattern and because of the non-linear evolution of the tracer atmospheric concentrations. To identify the respective role of these two causes, we propose two successive analyses. We first convolute residence time distributions initially arising at different times at the same sampling time. We secondly convolute one residence time distribution at various sampling times. We show that flow pattern modifications control the apparent ages evolution in the first pumping year when the residence time distribution is modified from a piston-like distribution to a much broader distribution. In the first pumping year, the apparent age evolution contains transient information that can be used to better constrain hydrogeological systems and slightly compensate for the small number of tracers. Later, the residence time distribution hardly evolves and apparent ages only evolve because of the tracer atmospheric concentrations. In this phase, apparent age time-series do not reflect any evolution in the flow pattern.

Time dependence of breakdown in a global fiber-bundle model with continuous damage.

PubMed

Moral, L; Moreno, Y; Gómez, J B; Pacheco, A F

2001-06-01

A time-dependent global fiber-bundle model of fracture with continuous damage is formulated in terms of a set of coupled nonlinear differential equations. A first integral of this set is analytically obtained. The time evolution of the system is studied by applying a discrete probabilistic method. Several results are discussed emphasizing their differences with the standard time-dependent model. The results obtained show that with this simple model a variety of experimental observations can be qualitatively reproduced.

Constraining modified theories of gravity with the galaxy bispectrum

NASA Astrophysics Data System (ADS)

Yamauchi, Daisuke; Yokoyama, Shuichiro; Tashiro, Hiroyuki

2017-12-01

We explore the use of the galaxy bispectrum induced by the nonlinear gravitational evolution as a possible probe to test general scalar-tensor theories with second-order equations of motion. We find that time dependence of the leading second-order kernel is approximately characterized by one parameter, the second-order index, which is expected to trace the higher-order growth history of the Universe. We show that our new parameter can significantly carry new information about the nonlinear growth of structure. We forecast future constraints on the second-order index as well as the equation-of-state parameter and the growth index.

TRIADS: A phase-resolving model for nonlinear shoaling of directional wave spectra

NASA Astrophysics Data System (ADS)

Sheremet, Alex; Davis, Justin R.; Tian, Miao; Hanson, Jeffrey L.; Hathaway, Kent K.

2016-03-01

We investigate the performance of TRIADS, a numerical implementation of a phase-resolving, nonlinear, spectral model describing directional wave evolution in intermediate and shallow water. TRIADS simulations of shoaling waves generated by Hurricane Bill, 2009 are compared to directional spectral estimates based on observations collected at the Field Research Facility of the US Army Corps Of Engineers, at Duck, NC. Both the ability of the model to capture the processes essential to the nonlinear wave evolution, and the efficiency of the numerical implementations are analyzed and discussed.

Nonlinear Waves In A Stenosed Elastic Tube Filled With Viscous Fluid: Forced Perturbed Korteweg-De Vries Equation

NASA Astrophysics Data System (ADS)

Gaik*, Tay Kim; Demiray, Hilmi; Tiong, Ong Chee

In the present work, treating the artery as a prestressed thin-walled and long circularly cylindrical elastic tube with a mild symmetrical stenosis and the blood as an incompressible Newtonian fluid, we have studied the pro pagation of weakly nonlinear waves in such a composite medium, in the long wave approximation, by use of the reductive perturbation method. By intro ducing a set of stretched coordinates suitable for the boundary value type of problems and expanding the field variables into asymptotic series of the small-ness parameter of nonlinearity and dispersion, we obtained a set of nonlinear differential equations governing the terms at various order. By solving these nonlinear differential equations, we obtained the forced perturbed Korteweg-de Vries equation with variable coefficient as the nonlinear evolution equation. By use of the coordinate transformation, it is shown that this type of nonlinear evolution equation admits a progressive wave solution with variable wave speed.

Approximation and Numerical Analysis of Nonlinear Equations of Evolution.

DTIC Science & Technology

1980-01-31

dominant convective terms, or Stefan type problems such as the flow of fluids through porous media or the melting and freezing of ice. Such problems...means of formulating time-dependent Stefan problems was initiated. Classes of problems considered here include the one-phase and two-phase Stefan ...some new numerical methods were 2 developed for two dimensional, two-phase Stefan problems with time dependent boundary conditions. A variety of example

Consistent nonlinear deterministic and stochastic evolution equations for deep to shallow water wave shoaling

NASA Astrophysics Data System (ADS)

Vrecica, Teodor; Toledo, Yaron

2015-04-01

One-dimensional deterministic and stochastic evolution equations are derived for the dispersive nonlinear waves while taking dissipation of energy into account. The deterministic nonlinear evolution equations are formulated using operational calculus by following the approach of Bredmose et al. (2005). Their formulation is extended to include the linear and nonlinear effects of wave dissipation due to friction and breaking. The resulting equation set describes the linear evolution of the velocity potential for each wave harmonic coupled by quadratic nonlinear terms. These terms describe the nonlinear interactions between triads of waves, which represent the leading-order nonlinear effects in the near-shore region. The equations are translated to the amplitudes of the surface elevation by using the approach of Agnon and Sheremet (1997) with the correction of Eldeberky and Madsen (1999). The only current possibility for calculating the surface gravity wave field over large domains is by using stochastic wave evolution models. Hence, the above deterministic model is formulated as a stochastic one using the method of Agnon and Sheremet (1997) with two types of stochastic closure relations (Benney and Saffman's, 1966, and Hollway's, 1980). These formulations cannot be applied to the common wave forecasting models without further manipulation, as they include a non-local wave shoaling coefficients (i.e., ones that require integration along the wave rays). Therefore, a localization method was applied (see Stiassnie and Drimer, 2006, and Toledo and Agnon, 2012). This process essentially extracts the local terms that constitute the mean nonlinear energy transfer while discarding the remaining oscillatory terms, which transfer energy back and forth. One of the main findings of this work is the understanding that the approximated non-local coefficients behave in two essentially different manners. In intermediate water depths these coefficients indeed consist of rapidly oscillating terms, but as the water depth becomes shallow they change to an exponential growth (or decay) behavior. Hence, the formerly used localization technique cannot be justified for the shallow water region. A new formulation is devised for the localization in shallow water, it approximates the nonlinear non-local shoaling coefficient in shallow water and matches it to the one fitting to the intermediate water region. This allows the model behavior to be consistent from deep water to intermediate depths and up to the shallow water regime. Various simulations of the model were performed for the cases of intermediate, and shallow water, overall the model was found to give good results in both shallow and intermediate water depths. The essential difference between the shallow and intermediate nonlinear shoaling physics is explained via the dominating class III Bragg resonances phenomenon. By inspecting the resonance conditions and the nature of the dispersion relation, it is shown that unlike in the intermediate water regime, in shallow water depths the formation of resonant interactions is possible without taking into account bottom components. References Agnon, Y. & Sheremet, A. 1997 Stochastic nonlinear shoaling of directional spectra. J. Fluid Mech. 345, 79-99. Benney, D. J. & Saffman, P. G. 1966 Nonlinear interactions of random waves. Proc. R. Soc. Lond. A 289, 301-321. Bredmose, H., Agnon, Y., Madsen, P.A. & Schaffer, H.A. 2005 Wave transformation models with exact second-order transfer. European J. of Mech. - B/Fluids 24 (6), 659-682. Eldeberky, Y. & Madsen, P. A. 1999 Deterministic and stochastic evolution equations for fully dispersive and weakly nonlinear waves. Coastal Engineering 38, 1-24. Kaihatu, J. M. & Kirby, J. T. 1995 Nonlinear transformation of waves in infinite water depth. Phys. Fluids 8, 175-188. Holloway, G. 1980 Oceanic internal waves are not weak waves. J. Phys. Oceanogr. 10, 906-914. Stiassnie, M. & Drimer, N. 2006 Prediction of long forcing waves for harbor agitation studies. J. of waterways, port, coastal and ocean engineering 132(3), 166-171. Toledo, Y. & Agnon, Y. 2012 Stochastic evolution equations with localized nonlinear shoaling coefficients. European J. of Mech. - B/Fluids 34, 13-18.

Chaotic universe model.

PubMed

Aydiner, Ekrem

2018-01-15

In this study, we consider nonlinear interactions between components such as dark energy, dark matter, matter and radiation in the framework of the Friedman-Robertson-Walker space-time and propose a simple interaction model based on the time evolution of the densities of these components. By using this model we show that these interactions can be given by Lotka-Volterra type equations. We numerically solve these coupling equations and show that interaction dynamics between dark energy-dark matter-matter or dark energy-dark matter-matter-radiation has a strange attractor for 0 > w de  >-1, w dm  ≥ 0, w m  ≥ 0 and w r  ≥ 0 values. These strange attractors with the positive Lyapunov exponent clearly show that chaotic dynamics appears in the time evolution of the densities. These results provide that the time evolution of the universe is chaotic. The present model may have potential to solve some of the cosmological problems such as the singularity, cosmic coincidence, big crunch, big rip, horizon, oscillation, the emergence of the galaxies, matter distribution and large-scale organization of the universe. The model also connects between dynamics of the competing species in biological systems and dynamics of the time evolution of the universe and offers a new perspective and a new different scenario for the universe evolution.

Simulations of particle and heat fluxes in an ELMy H-mode discharge on EAST using BOUT++ code

NASA Astrophysics Data System (ADS)

Wu, Y. B.; Xia, T. Y.; Zhong, F. C.; Zheng, Z.; Liu, J. B.; team3, EAST

2018-05-01

In order to study the distribution and evolution of the transient particle and heat fluxes during edge-localized mode (ELM) bursts on the Experimental Advanced Superconducting Tokamak (EAST), the BOUT++ six-field two-fluid model is used to simulate the pedestal collapse. The profiles from the EAST H-mode discharge #56129 are used as the initial conditions. Linear analysis shows that the resistive ballooning mode and drift-Alfven wave are two dominant instabilities for the equilibrium, and play important roles in driving ELMs. The evolution of the density profile and the growing process of the heat flux at divertor targets during the burst of ELMs are reproduced. The time evolution of the poloidal structures of T e is well simulated, and the dominant mode in each stage of the ELM crash process is found. The studies show that during the nonlinear phase, the dominant mode is 5, and it changes to 0 when the nonlinear phase goes to saturation after the ELM crash. The time evolution of the radial electron heat flux, ion heat flux, and particle density flux at the outer midplane (OMP) are obtained, and the corresponding transport coefficients D r, χ ir, and χ er reach maximum around 0.3 ∼ 0.5 m2 s‑1 at ΨN = 0.9. The heat fluxes at outer target plates are several times larger than that at inner target plates, which is consistent with the experimental observations. The simulated profiles of ion saturation current density (j s) at the lower outboard (LO) divertor target are compared to those of experiments by Langmuir probes. The profiles near the strike point are similar, and the peak values of j s from simulation are very close to the measurements.

Inferring internal properties of Earth's core dynamics and their evolution from surface observations and a numerical geodynamo model

NASA Astrophysics Data System (ADS)

Aubert, J.; Fournier, A.

2011-10-01

Over the past decades, direct three-dimensional numerical modelling has been successfully used to reproduce the main features of the geodynamo. Here we report on efforts to solve the associated inverse problem, aiming at inferring the underlying properties of the system from the sole knowledge of surface observations and the first principle dynamical equations describing the convective dynamo. To this end we rely on twin experiments. A reference model time sequence is first produced and used to generate synthetic data, restricted here to the large-scale component of the magnetic field and its rate of change at the outer boundary. Starting from a different initial condition, a second sequence is next run and attempts are made to recover the internal magnetic, velocity and buoyancy anomaly fields from the sparse surficial data. In order to reduce the vast underdetermination of this problem, we use stochastic inversion, a linear estimation method determining the most likely internal state compatible with the observations and some prior knowledge, and we also implement a sequential evolution algorithm in order to invert time-dependent surface observations. The prior is the multivariate statistics of the numerical model, which are directly computed from a large number of snapshots stored during a preliminary direct run. The statistics display strong correlation between different harmonic degrees of the surface observations and internal fields, provided they share the same harmonic order, a natural consequence of the linear coupling of the governing dynamical equations and of the leading influence of the Coriolis force. Synthetic experiments performed with a weakly nonlinear model yield an excellent quantitative retrieval of the internal structure. In contrast, the use of a strongly nonlinear (and more realistic) model results in less accurate static estimations, which in turn fail to constrain the unobserved small scales in the time integration of the evolution scheme. Evaluating the quality of forecasts of the system evolution against the reference solution, we show that our scheme can improve predictions based on linear extrapolations on forecast horizons shorter than the system e-folding time. Still, in the perspective of forthcoming data assimilation activities, our study underlines the need of advanced estimation techniques able to cope with the moderate to strong nonlinearities present in the geodynamo.

Electron precipitation in solar flares - Collisionless effects

NASA Technical Reports Server (NTRS)

Vlahos, L.; Rowland, H. L.

1984-01-01

A large fraction of the electrons which are accelerated during the impulsive phase of solar flares stream towards the chromosphere and are unstable to the growth of plasma waves. The linear and nonlinear evolution of plasma waves as a function of time is analyzed with a set of rate equations that follows, in time, the nonlinearly coupled system of plasma waves-ion fluctuations. As an outcome of the fast transfer of wave energy from the beam to the ambient plasma, nonthermal electron tails are formed which can stabilize the anomalous Doppler resonance instability responsible for the pitch angle scattering of the beam electrons. The non-collisional losses of the precipitating electrons are estimated, and the observational implication of these results are discussed.

Simulation of Alfvén eigenmode bursts using a hybrid code for nonlinear magnetohydrodynamics and energetic particles

NASA Astrophysics Data System (ADS)

Todo, Y.; Berk, H. L.; Breizman, B. N.

2012-03-01

A hybrid simulation code for nonlinear magnetohydrodynamics (MHD) and energetic-particle dynamics has been extended to simulate recurrent bursts of Alfvén eigenmodes by implementing the energetic-particle source, collisions and losses. The Alfvén eigenmode bursts with synchronization of multiple modes and beam ion losses at each burst are successfully simulated with nonlinear MHD effects for the physics condition similar to a reduced simulation for a TFTR experiment (Wong et al 1991 Phys. Rev. Lett. 66 1874, Todo et al 2003 Phys. Plasmas 10 2888). It is demonstrated with a comparison between nonlinear MHD and linear MHD simulation results that the nonlinear MHD effects significantly reduce both the saturation amplitude of the Alfvén eigenmodes and the beam ion losses. Two types of time evolution are found depending on the MHD dissipation coefficients, namely viscosity, resistivity and diffusivity. The Alfvén eigenmode bursts take place for higher dissipation coefficients with roughly 10% drop in stored beam energy and the maximum amplitude of the dominant magnetic fluctuation harmonic δBm/n/B ~ 5 × 10-3 at the mode peak location inside the plasma. Quadratic dependence of beam ion loss rate on magnetic fluctuation amplitude is found for the bursting evolution in the nonlinear MHD simulation. For lower dissipation coefficients, the amplitude of the Alfvén eigenmodes is at steady levels δBm/n/B ~ 2 × 10-3 and the beam ion losses take place continuously. The beam ion pressure profiles are similar among the different dissipation coefficients, and the stored beam energy is higher for higher dissipation coefficients.

Evolution of cooperation on complex networks with synergistic and discounted group interactions

NASA Astrophysics Data System (ADS)

Zhou, Lei; Li, Aming; Wang, Long

2015-06-01

In the real world individuals often engage in group interactions and their payoffs are determined by many factors, including the typical nonlinear interactions, i.e., synergy and discounting. Previous literatures assume that individual payoffs are either synergistically enhanced or discounted with the additional cooperators. Such settings ignore the interplay of these two factors, which is in sharp contrast with the fact that they ubiquitously coexist. Here we investigate how the coexistence and periodical switching of synergistic and discounted group interactions affect the evolution of cooperation on various complex networks. We show that scale-free networks facilitate the emergence of cooperation in terms of fixation probability for group interactions. With nonlinear interactions the heterogeneity of the degree acts as a double-edged sword: below the neutral drift it is the best for cooperation while above the neutral drift it instead provides the least opportunity for cooperators to be fixed. The advantages of the heterogeneity fade as interactive attributes switch between synergy and discounting, which suggests that the heterogeneity of population structures cannot favor cooperators in group interactions even with simple nonlinear interactions. Nonetheless, scale-free networks always guarantee cooperators the fastest rate of fixation. Our work implies that even very simple nonlinear group interactions could greatly shape the fixation probability and fixation time of cooperators in structured populations indicated by complex networks.

Nonlinear Plasma Response to Resonant Magnetic Perturbation in Rutherford Regime

NASA Astrophysics Data System (ADS)

Zhu, Ping; Yan, Xingting; Huang, Wenlong

2017-10-01

Recently a common analytic relation for both the locked mode and the nonlinear plasma response in the Rutherford regime has been developed based on the steady-state solution to the coupled dynamic system of magnetic island evolution and torque balance equations. The analytic relation predicts the threshold and the island size for the full penetration of resonant magnetic perturbation (RMP). It also rigorously proves a screening effect of the equilibrium toroidal flow. In this work, we test the theory by solving for the nonlinear plasma response to a single-helicity RMP of a circular-shaped limiter tokamak equilibrium with a constant toroidal flow, using the initial-value, full MHD simulation code NIMROD. Time evolution of the parallel flow or ``slip frequency'' profile and its asymptotic approach to steady state obtained from the NIMROD simulations qualitatively agree with the theory predictions. Further comparisons are carried out for the saturated island size, the threshold for full mode penetration, as well as the screening effects of equilibrium toroidal flow in order to understand the physics of nonlinear plasma response in the Rutherford regime. Supported by National Magnetic Confinement Fusion Science Program of China Grants 2014GB124002 and 2015GB101004, the 100 Talent Program of the Chinese Academy of Sciences, and U.S. Department of Energy Grants DE-FG02-86ER53218 and DE-FC02-08ER54975.

Nonlinear evolution of f(R) cosmologies. II. Power spectrum

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

Oyaizu, Hiroaki; Hu, Wayne; Department of Astronomy and Astrophysics, University of Chicago, Chicago Illinois 60637

2008-12-15

We carry out a suite of cosmological simulations of modified action f(R) models where cosmic acceleration arises from an alteration of gravity instead of dark energy. These models introduce an extra scalar degree of freedom which enhances the force of gravity below the inverse mass or Compton scale of the scalar. The simulations exhibit the so-called chameleon mechanism, necessary for satisfying local constraints on gravity, where this scale depends on environment, in particular, the depth of the local gravitational potential. We find that the chameleon mechanism can substantially suppress the enhancement of power spectrum in the nonlinear regime if themore » background field value is comparable to or smaller than the depth of the gravitational potentials of typical structures. Nonetheless power spectrum enhancements at intermediate scales remain at a measurable level for models even when the expansion history is indistinguishable from a cosmological constant, cold dark matter model. Simple scaling relations that take the linear power spectrum into a nonlinear spectrum fail to capture the modifications of f(R) due to the change in collapsed structures, the chameleon mechanism, and the time evolution of the modifications.« less

Cosmic bubble and domain wall instabilities II: fracturing of colliding walls

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

Braden, Jonathan; Bond, J. Richard; Mersini-Houghton, Laura, E-mail: j.braden@ucl.ac.uk, E-mail: bond@cita.utoronto.ca, E-mail: mersini@physics.unc.edu

2015-08-01

We study collisions between nearly planar domain walls including the effects of small initial nonplanar fluctuations. These perturbations represent the small fluctuations that must exist in a quantum treatment of the problem. In a previous paper, we demonstrated that at the linear level a subset of these fluctuations experience parametric amplification as a result of their coupling to the planar symmetric background. Here we study the full three-dimensional nonlinear dynamics using lattice simulations, including both the early time regime when the fluctuations are well described by linear perturbation theory as well as the subsequent stage of fully nonlinear evolution. Wemore » find that the nonplanar fluctuations have a dramatic effect on the overall evolution of the system. Specifically, once these fluctuations begin to interact nonlinearly the split into a planar symmetric part of the field and the nonplanar fluctuations loses its utility. At this point the colliding domain walls dissolve, with the endpoint of this being the creation of a population of oscillons in the collision region. The original (nearly) planar symmetry has been completely destroyed at this point and an accurate study of the system requires the full three-dimensional simulation.« less

Cosmic bubble and domain wall instabilities II: fracturing of colliding walls

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

Braden, Jonathan; Department of Physics, University of Toronto,60 St. George Street, Toronto, ON, M5S 3H8; Department of Physics and Astronomy, University College London,Gower Street, London, WC1E 6BT

2015-08-26

We study collisions between nearly planar domain walls including the effects of small initial nonplanar fluctuations. These perturbations represent the small fluctuations that must exist in a quantum treatment of the problem. In a previous paper, we demonstrated that at the linear level a subset of these fluctuations experience parametric amplification as a result of their coupling to the planar symmetric background. Here we study the full three-dimensional nonlinear dynamics using lattice simulations, including both the early time regime when the fluctuations are well described by linear perturbation theory as well as the subsequent stage of fully nonlinear evolution. Wemore » find that the nonplanar fluctuations have a dramatic effect on the overall evolution of the system. Specifically, once these fluctuations begin to interact nonlinearly the split into a planar symmetric part of the field and the nonplanar fluctuations loses its utility. At this point the colliding domain walls dissolve, with the endpoint of this being the creation of a population of oscillons in the collision region. The original (nearly) planar symmetry has been completely destroyed at this point and an accurate study of the system requires the full three-dimensional simulation.« less

On a generalized Ablowitz-Kaup-Newell-Segur hierarchy in inhomogeneities of media: soliton solutions and wave propagation influenced from coefficient functions and scattering data

NASA Astrophysics Data System (ADS)

Zhang, Sheng; Hong, Siyu

2018-07-01

In this paper, a generalized Ablowitz-Kaup-Newell-Segur (AKNS) hierarchy in inhomogeneities of media described by variable coefficients is investigated, which includes some important nonlinear evolution equations as special cases, for example, the celebrated Korteweg-de Vries equation modeling waves on shallow water surfaces. To be specific, the known AKNS spectral problem and its time evolution equation are first generalized by embedding a finite number of differentiable and time-dependent functions. Starting from the generalized AKNS spectral problem and its generalized time evolution equation, a generalized AKNS hierarchy with variable coefficients is then derived. Furthermore, based on a systematic analysis on the time dependence of related scattering data of the generalized AKNS spectral problem, exact solutions of the generalized AKNS hierarchy are formulated through the inverse scattering transform method. In the case of reflectionless potentials, the obtained exact solutions are reduced to n-soliton solutions. It is graphically shown that the dynamical evolutions of such soliton solutions are influenced by not only the time-dependent coefficients but also the related scattering data in the process of propagations.

Nonlinear stability of Halley comethosheath with transverse plasma motion

NASA Technical Reports Server (NTRS)

Srivastava, Krishna M.; Tsurutani, Bruce T.

1994-01-01

Weakly nonlinear Magneto Hydrodynamic (MHD) stability of the Halley cometosheath determined by the balance between the outward ion-neutral drag force and the inward Lorentz force is investigated including the transverse plasma motion as observed in the flanks with the help of the method of multiple scales. The eigenvalues and the eigenfunctions are obtained for the linear problem and the time evolution of the amplitude is obtained using the solvability condition for the solution of the second order problem. The diamagnetic cavity boundary and the adjacent layer of about 100 km thickness is found unstable for the travelling waves of certain wave numbers. Halley ionopause has been observed to have strong ripples with a wavelength of several hundred kilometers. It is found that nonlinear effects have stabilizing effect.

Nonlinear acoustics experimental characterization of microstructure evolution in Inconel 617

NASA Astrophysics Data System (ADS)

Yao, Xiaochu; Liu, Yang; Lissenden, Cliff J.

2014-02-01

Inconel 617 is a candidate material for the intermediate heat exchanger in a very high temperature reactor for the next generation nuclear power plant. This application will require the material to withstand fatigue-ratcheting interaction at temperatures up to 950°C. Therefore nondestructive evaluation and structural health monitoring are important capabilities. Acoustic nonlinearity (which is quantified in terms of a material parameter, the acoustic nonlinearity parameter, β) has been proven to be sensitive to microstructural changes in material. This research develops a robust experimental procedure to track the evolution of damage precursors in laboratory tested Inconel 617 specimens using ultrasonic bulk waves. The results from the acoustic non-linear tests are compared with stereoscope surface damage results. Therefore, the relationship between acoustic nonlinearity and microstructural evaluation can be clearly demonstrated for the specimens tested.

Relations between nonlinear Riccati equations and other equations in fundamental physics

NASA Astrophysics Data System (ADS)

Schuch, Dieter

2014-10-01

Many phenomena in the observable macroscopic world obey nonlinear evolution equations while the microscopic world is governed by quantum mechanics, a fundamental theory that is supposedly linear. In order to combine these two worlds in a common formalism, at least one of them must sacrifice one of its dogmas. Linearizing nonlinear dynamics would destroy the fundamental property of this theory, however, it can be shown that quantum mechanics can be reformulated in terms of nonlinear Riccati equations. In a first step, it will be shown that the information about the dynamics of quantum systems with analytical solutions can not only be obtainable from the time-dependent Schrödinger equation but equally-well from a complex Riccati equation. Comparison with supersymmetric quantum mechanics shows that even additional information can be obtained from the nonlinear formulation. Furthermore, the time-independent Schrödinger equation can also be rewritten as a complex Riccati equation for any potential. Extension of the Riccati formulation to include irreversible dissipative effects is straightforward. Via (real and complex) Riccati equations, other fields of physics can also be treated within the same formalism, e.g., statistical thermodynamics, nonlinear dynamical systems like those obeying a logistic equation as well as wave equations in classical optics, Bose- Einstein condensates and cosmological models. Finally, the link to abstract "quantizations" such as the Pythagorean triples and Riccati equations connected with trigonometric and hyperbolic functions will be shown.

Rapidity evolution of gluon TMD from low to moderate x

DOE PAGES

Balitsky, Ian; Tarasov, A.

2015-10-05

In this article, we study how the rapidity evolution of gluon transverse momentum dependent distribution changes from nonlinear evolution at smallmore » $$x \\ll 1$$ to linear evolution at moderate $$x \\sim 1$$.« less

Detecting time-specific differences between temporal nonlinear curves: Analyzing data from the visual world paradigm

PubMed Central

Oleson, Jacob J; Cavanaugh, Joseph E; McMurray, Bob; Brown, Grant

2015-01-01

In multiple fields of study, time series measured at high frequencies are used to estimate population curves that describe the temporal evolution of some characteristic of interest. These curves are typically nonlinear, and the deviations of each series from the corresponding curve are highly autocorrelated. In this scenario, we propose a procedure to compare the response curves for different groups at specific points in time. The method involves fitting the curves, performing potentially hundreds of serially correlated tests, and appropriately adjusting the overall alpha level of the tests. Our motivating application comes from psycholinguistics and the visual world paradigm. We describe how the proposed technique can be adapted to compare fixation curves within subjects as well as between groups. Our results lead to conclusions beyond the scope of previous analyses. PMID:26400088

Elliptic-type soliton combs in optical ring microresonators

NASA Astrophysics Data System (ADS)

Dikandé Bitha, Rodrigues D.; Dikandé, Alain M.

2018-03-01

Soliton crystals are periodic patterns of multispot optical fields formed from either time or space entanglements of equally separated identical high-intensity pulses. These specific nonlinear optical structures have gained interest in recent years with the advent and progress in nonlinear optical fibers and fiber lasers, photonic crystals, wave-guided wave systems, and most recently optical ring microresonator devices. In this work an extensive analysis of characteristic features of soliton crystals is carried out, with an emphasis on their one-to-one correspondence with elliptic solitons. With this purpose in mind, we examine their formation, their stability, and their dynamics in ring-shaped nonlinear optical media within the framework of the Lugiato-Lefever equation. The stability analysis deals with internal modes of the system via a 2 ×2 -matrix Lamé-type eigenvalue problem, the spectrum of which is shown to possess a rich set of bound states consisting of stable zero-fequency modes and unstable decaying as well as growing modes. Turning towards the dynamics of elliptic solitons in ring-shaped fiber resonators with Kerr nonlinearity, we first propose a collective-coordinate approach, based on a Lagrangian formalism suitable for elliptic-soliton solutions to the nonlinear Schrödinger equation with an arbitrary perturbation. Next we derive time evolutions of elliptic-soliton parameters in the specific context of ring-shaped optical fiber resonators, where the optical field evolution is thought to be governed by the Lugiato-Lefever equation. By solving numerically the collective-coordinate equations an analysis of the amplitude, the position, the phase of internal oscillations, the phase velocity, the energy, and phase portraits of the amplitude is carried out and reveals a complex dynamics of the elliptic soliton in ring-shaped optical microresonators. Direct numerical simulations of the Lugiato-Lefever equation are also carried out seeking for stationary-wave solutions, and the numerical results are in very good agreement with the collective-coordinate approach.

A string of Peregrine rogue waves in the nonlocal nonlinear Schrödinger equation with parity-time symmetric self-induced potential

NASA Astrophysics Data System (ADS)

Gupta, Samit Kumar

2018-03-01

Dynamic wave localization phenomena draw fundamental and technological interests in optics and photonics. Based on the recently proposed (Ablowitz and Musslimani, 2013) continuous nonlocal nonlinear Schrödinger system with parity-time symmetric Kerr nonlinearity (PTNLSE), a numerical investigation has been carried out for two first order Peregrine solitons as the initial ansatz. Peregrine soliton, as an exact solution to the PTNLSE, evokes a very potent question: what effects does the interaction of two first order Peregrine solitons have on the overall optical field dynamics. Upon numerical computation, we observe the appearance of Kuznetsov-Ma (KM) soliton trains in the unbroken PT-phase when the initial Peregrine solitons are in phase. In the out of phase condition, it shows repulsive nonlinear waves. Quite interestingly, our study shows that within a specific range of the interval factor in the transverse co-ordinate there exists a string of high intensity well-localized Peregrine rogue waves in the PT unbroken phase. We note that the interval factor as well as the transverse shift parameter play important roles in the nonlinear interaction and evolution dynamics of the optical fields. This could be important in developing fundamental understanding of nonlocal non-Hermitian NLSE systems and dynamic wave localization behaviors.

Nonlinear gyrotropic motion of skyrmion in a magnetic nanodisk

NASA Astrophysics Data System (ADS)

Chen, Yi-fu; Li, Zhi-xiong; Zhou, Zhen-wei; Xia, Qing-lin; Nie, Yao-zhuang; Guo, Guang-hua

2018-07-01

We study the nonlinear gyrotropic motion of a magnetic skyrmion in a nanodisk by means of micromagnetic simulations. The skyrmion is driven by a linearly polarized harmonic field with the frequency of counterclockwise gyrotropic mode. It is found that the motion of the skyrmion displays different patterns with increasing field amplitude. In the linear regime of weak driving field, the skyrmion performs a single counterclockwise gyrotropic motion. The guiding center of the skyrmion moves along a helical line from the centre of the nanodisk to a stable circular orbit. The stable orbital radius increases linearly with the field amplitude. When the driving field is larger than a critical value, the skyrmion exhibits complex nonlinear motion. With the advance of time, the motion trajectory of the skyrmion goes through a series of evolution process, from a single circular motion to a bird nest-like and a flower-like trajectory and finally, to a gear-like steady-state motion. The frequency spectra show that except the counterclockwise gyrotropic mode, the clockwise gyrotropic mode is also nonlinearly excited and its amplitude increases with time. The complex motion trajectory of the skyrmion is the result of superposition of the two gyrotropic motions with changing amplitude. Both the linear and nonlinear gyrotropic motions of the skyrmion can be well described by a generalized Thiele's equation of motion.

Mechanical energy fluctuations in granular chains: the possibility of rogue fluctuations or waves.

PubMed

Han, Ding; Westley, Matthew; Sen, Surajit

2014-09-01

The existence of rogue or freak waves in the ocean has been known for some time. They have been reported in the context of optical lattices and the financial market. We ask whether such waves are generic to late time behavior in nonlinear systems. In that vein, we examine the dynamics of an alignment of spherical elastic beads held within fixed, rigid walls at zero precompression when they are subjected to sufficiently rich initial conditions. Here we define such waves generically as unusually large energy fluctuations that sustain for short periods of time. Our simulations suggest that such unusually large fluctuations ("hot spots") and occasional series of such fluctuations through space and time ("rogue fluctuations") are likely to exist in the late time dynamics of the granular chain system at zero dissipation. We show that while hot spots are common in late time evolution, rogue fluctuations are seen in purely nonlinear systems (i.e., no precompression) at late enough times. We next show that the number of such fluctuations grows exponentially with increasing nonlinearity whereas rogue fluctuations decrease superexponentially with increasing precompression. Dissipation-free granular alignment systems may be possible to realize as integrated circuits and hence our observations may potentially be testable in the laboratory.

A nonlinear dynamical analogue model of geomagnetic activity

NASA Technical Reports Server (NTRS)

Klimas, A. J.; Baker, D. N.; Roberts, D. A.; Fairfield, D. H.; Buechner, J.

1992-01-01

Consideration is given to the solar wind-magnetosphere interaction within the framework of deterministic nonlinear dynamics. An earlier dripping faucet analog model of the low-dimensional solar wind-magnetosphere system is reviewed, and a plasma physical counterpart to that model is constructed. A Faraday loop in the magnetotail is considered, and the relationship of electric potentials on the loop to changes in the magnetic flux threading the loop is developed. This approach leads to a model of geomagnetic activity which is similar to the earlier mechanical model but described in terms of the geometry and plasma contents of the magnetotail. The model is characterized as an elementary time-dependent global convection model. The convection evolves within a magnetotail shape that varies in a prescribed manner in response to the dynamical evolution of the convection. The result is a nonlinear model capable of exhibiting a transition from regular to chaotic loading and unloading. The model's behavior under steady loading and also some elementary forms of time-dependent loading is discussed.

Nonlinear Riccati equations as a unifying link between linear quantum mechanics and other fields of physics

NASA Astrophysics Data System (ADS)

Schuch, Dieter

2014-04-01

Theoretical physics seems to be in a kind of schizophrenic state. Many phenomena in the observable macroscopic world obey nonlinear evolution equations, whereas the microscopic world is governed by quantum mechanics, a fundamental theory that is supposedly linear. In order to combine these two worlds in a common formalism, at least one of them must sacrifice one of its dogmas. I claim that linearity in quantum mechanics is not as essential as it apparently seems since quantum mechanics can be reformulated in terms of nonlinear Riccati equations. In a first step, it will be shown where complex Riccati equations appear in time-dependent quantum mechanics and how they can be treated and compared with similar space-dependent Riccati equations in supersymmetric quantum mechanics. Furthermore, the time-independent Schrödinger equation can also be rewritten as a complex Riccati equation. Finally, it will be shown that (real and complex) Riccati equations also appear in many other fields of physics, like statistical thermodynamics and cosmology.

Nonlinear Evolution of Observed Fast Streams in the Solar Wind - Micro-instabilities and Energy Exchange between Protons and Alpha Particles

NASA Astrophysics Data System (ADS)

Maneva, Y. G.; Poedts, S.

2017-12-01

Non-thermal kinetic components such as deformed velocity distributions, temperature anisotropies and relative drifts between the multiple ion populations are frequently observed features in the collisionless fast solar wind streams near the Earth whose origin is still to be better understood. Some of the traditional models consider the formation of the temperature anisotropies through the effect of the solar wind expansion, while others assume in situ heating and particle acceleration by local fluctuations, such as plasma waves, or by spacial structures, such as advected or locally generated current sheets. In this study we consider the evolution of initial ion temperature anisotropies and relative drifts in the presence of plasma oscillations, such as ion-cyclotron and kinetic Alfven waves. We perform 2.5D hybrid simulations to study the evolution of observed fast solar wind plasma parcels, including the development of the plasma micro-instabilities, the field-particle correlations and the energy transfer between the multiple ion species. We consider two distinct cases of highly anisotropic and quickly drifting protons which excite ion-cyclotron waves and of moderately anisotropic slower protons, which co-exist with kinetic Alfven waves. The alpha particles for both cases are slightly anisotropic in the beginning and remain anisotropic throughout the simulation time. Both the imposed magnetic fluctuations and the initial differential streaming decrease in time for both cases, while the minor ions are getting heated. Finally we study the effects of the solar wind expansion and discuss its implications for the nonlinear evolution of the system.

A numerical and experimental study on the nonlinear evolution of long-crested irregular waves

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

Goullet, Arnaud; Choi, Wooyoung; Division of Ocean Systems Engineering, Korea Advanced Institute of Science and Technology, Daejeon 305-701

2011-01-15

The spatial evolution of nonlinear long-crested irregular waves characterized by the JONSWAP spectrum is studied numerically using a nonlinear wave model based on a pseudospectral (PS) method and the modified nonlinear Schroedinger (MNLS) equation. In addition, new laboratory experiments with two different spectral bandwidths are carried out and a number of wave probe measurements are made to validate these two wave models. Strongly nonlinear wave groups are observed experimentally and their propagation and interaction are studied in detail. For the comparison with experimental measurements, the two models need to be initialized with care and the initialization procedures are described. Themore » MNLS equation is found to approximate reasonably well for the wave fields with a relatively smaller Benjamin-Feir index, but the phase error increases as the propagation distance increases. The PS model with different orders of nonlinear approximation is solved numerically, and it is shown that the fifth-order model agrees well with our measurements prior to wave breaking for both spectral bandwidths.« less

Theory of Aging, Rejuvenation, and the Nonequilibrium Steady State in Deformed Polymer Glasses

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

Chen, Kang

The nonlinear Langevin equation theory of segmental relaxation, elasticity, and mechanical response of polymer glasses is extended to describe the coupled effects of physical aging, mechanical rejuvenation, and thermal history. The key structural variable is the amplitude of density fluctuations, and segmental dynamics proceeds via stress-modified activated barrier hopping on a dynamic free-energy profile. Mechanically generated disorder rejuvenation is quantified by a dissipative work argument and increases the amplitude of density fluctuations, thereby speeding up relaxation beyond that induced by the landscape tilting mechanism. The theory makes testable predictions for the time evolution and nonequilibrium steady state of the alphamore » relaxation time, density fluctuation amplitude, elastic modulus, and other properties. Model calculations reveal a rich dependence of these quantities on preaging time, applied stress, and temperature that reflects the highly nonlinear competition between physical aging and mechanical disordering. Thermal history is erased in the long-time limit, although the nonequilibrium steady state is not the literal fully rejuvenated freshly quenched glass. The present work provides the conceptual foundation for a quantitative treatment of the nonlinear mechanical response of polymer glasses under a variety of deformation protocols.« less

Initial-value problem for the Gardner equation applied to nonlinear internal waves

NASA Astrophysics Data System (ADS)

Rouvinskaya, Ekaterina; Kurkina, Oxana; Kurkin, Andrey; Talipova, Tatiana; Pelinovsky, Efim

2017-04-01

The Gardner equation is a fundamental mathematical model for the description of weakly nonlinear weakly dispersive internal waves, when cubic nonlinearity cannot be neglected. Within this model coefficients of quadratic and cubic nonlinearity can both be positive as well as negative, depending on background conditions of the medium, where waves propagate (sea water density stratification, shear flow profile) [Rouvinskaya et al., 2014, Kurkina et al., 2011, 2015]. For the investigation of weakly dispersive behavior in the framework of nondimensional Gardner equation with fixed (positive) sign of quadratic nonlinearity and positive or negative cubic nonlinearity {eq1} partial η/partial t+6η( {1± η} )partial η/partial x+partial ^3η/partial x^3=0, } the series of numerical experiments of initial-value problem was carried out for evolution of a bell-shaped impulse of negative polarity (opposite to the sign of quadratic nonlinear coefficient): {eq2} η(x,t=0)=-asech2 ( {x/x0 } ), for which amplitude a and width x0 was varied. Similar initial-value problem was considered in the paper [Trillo et al., 2016] for the Korteweg - de Vries equation. For the Gardner equation with different signs of cubic nonlinearity the initial-value problem for piece-wise constant initial condition was considered in detail in [Grimshaw et al., 2002, 2010]. It is widely known, for example, [Pelinovsky et al., 2007], that the Gardner equation (1) with negative cubic nonlinearity has a family of classic solitary wave solutions with only positive polarity,and with limiting amplitude equal to 1. Therefore evolution of impulses (2) of negative polarity (whose amplitudes a were varied from 0.1 to 3, and widths at the level of a/2 were equal to triple width of solitons with the same amplitude for a 1) was going on a universal scenario with the generation of nonlinear Airy wave. For the Gardner equation (1) with the positive cubic nonlinearity coefficient there exist two one-parametric families of solitons (family with positive polarity, and family with negative polarity bounded below by the amplitude of 2) and two-parametric family of breathers (oscillatory wave packets). In this case varying amplitude and width of bell-shaped initial impulse leads to plenty of different evolutionary scenarios with the generation of solitary waves, breathers, solibores and nonlinear Airy wave in their various combinations. Statistical analysis of the wave field in time shows almost permanent substantial exceedance of the level of the significant wave height in some position in spatial coordinate. Evolution of Fourier spectrum of the wave field is also analyzed, and its behavior after a long time of initial wave evolution demonstrates the power asymptotic for small wave numbers and exponential asymptotic for large wave numbers. The presented results of research are obtained with the support of the grant of the President of the Russian Federation for state support of the young Russian scientists - Candidates of Sciences (MK-5208.2016.5) and Russian Foundation for Basic Research grant 16-05-00049. References: Grimshaw R., Pelinovsky D., Pelinovsky E and Slunyaev A. Generation of large-amplitude solitons in the extended Korteweg-de Vries equation // Chaos, 2002. - V.12. - No 4. - 1070-1076. Grimshaw, R., Slunyaev, A., and Pelinovsky, E. Generation of solitons and breathers in the extended Korteweg-de Vries equation with positive cubic nonlinearity //Chaos, 2010. - vol. 20.-013102. Kurkina O.E., Kurkin A.A., Soomere T., Pelinovsky E.N., Rouvinskaya E.A. Higher-order (2+4) Korteweg-de Vries - like equation for interfacial waves in a symmetric three-layer fluid // Physics of Fluids, 2011. - Volume 23. - Issue 11. - p.116602--1--13. Kurkina O., Rouvinskaya E., Talipova T., Kurkin A., Pelinovsky E. Nonlinear disintegration of sine wave in the framework of the Gardner equation // Physica D: Nonlinear Phenomena, 2015. - doi:10.1016/j.physd.2015.12.007. Pelinovsky E., Polukhina O., Slunyaev A., Talipova T. Internal solitary waves // Chapter 4 in the book ``Solitary Waves in Fluids''. WIT Press. Southampton, Boston. 2007. P. 85 - 110. Rouvinskaya E., Kurkina O., Kurkin A. Dynamics of nonlinear internal gravity waves in layered fluids // NNSTU n.a. R.E. Alekseev Press - Nizhny Novgorod, 2014 - 160 p. [In Russian] Trillo S., Klein M., Clauss G., Onorato M. Observation of dispersive shock waves developing from initial depressions in shallow water // Physica D, 2016. - http://dx.doi.org/10.1016/j.physd.2016.01.007.

Bioconvection in spatially extended domains

NASA Astrophysics Data System (ADS)

Karimi, A.; Paul, M. R.

2013-05-01

We numerically explore gyrotactic bioconvection in large spatially extended domains of finite depth using parameter values from available experiments with the unicellular alga Chlamydomonas nivalis. We numerically integrate the three-dimensional, time-dependent continuum model of Pedley [J. Fluid Mech.10.1017/S0022112088002393 195, 223 (1988)] using a high-order, parallel, spectral-element approach. We explore the long-time nonlinear patterns and dynamics found for layers with an aspect ratio of 10 over a range of Rayleigh numbers. Our results yield the pattern wavelength and pattern dynamics which we compare with available theory and experimental measurement. There is good agreement for the pattern wavelength at short times between numerics, experiment, and a linear stability analysis. At long times we find that the general sequence of patterns given by the nonlinear evolution of the governing equations correspond qualitatively to what has been described experimentally. However, at long times the patterns in numerics grow to larger wavelengths, in contrast to what is observed in experiment where the wavelength is found to decrease with time.

Going virtual with quicktime VR: new methods and standardized tools for interactive dynamic visualization of anatomical structures.

PubMed

Trelease, R B; Nieder, G L; Dørup, J; Hansen, M S

2000-04-15

Continuing evolution of computer-based multimedia technologies has produced QuickTime, a multiplatform digital media standard that is supported by stand-alone commercial programs and World Wide Web browsers. While its core functions might be most commonly employed for production and delivery of conventional video programs (e.g., lecture videos), additional QuickTime VR "virtual reality" features can be used to produce photorealistic, interactive "non-linear movies" of anatomical structures ranging in size from microscopic through gross anatomic. But what is really included in QuickTime VR and how can it be easily used to produce novel and innovative visualizations for education and research? This tutorial introduces the QuickTime multimedia environment, its QuickTime VR extensions, basic linear and non-linear digital video technologies, image acquisition, and other specialized QuickTime VR production methods. Four separate practical applications are presented for light and electron microscopy, dissectable preserved specimens, and explorable functional anatomy in magnetic resonance cinegrams.

Variational Bayesian identification and prediction of stochastic nonlinear dynamic causal models.

PubMed

Daunizeau, J; Friston, K J; Kiebel, S J

2009-11-01

In this paper, we describe a general variational Bayesian approach for approximate inference on nonlinear stochastic dynamic models. This scheme extends established approximate inference on hidden-states to cover: (i) nonlinear evolution and observation functions, (ii) unknown parameters and (precision) hyperparameters and (iii) model comparison and prediction under uncertainty. Model identification or inversion entails the estimation of the marginal likelihood or evidence of a model. This difficult integration problem can be finessed by optimising a free-energy bound on the evidence using results from variational calculus. This yields a deterministic update scheme that optimises an approximation to the posterior density on the unknown model variables. We derive such a variational Bayesian scheme in the context of nonlinear stochastic dynamic hierarchical models, for both model identification and time-series prediction. The computational complexity of the scheme is comparable to that of an extended Kalman filter, which is critical when inverting high dimensional models or long time-series. Using Monte-Carlo simulations, we assess the estimation efficiency of this variational Bayesian approach using three stochastic variants of chaotic dynamic systems. We also demonstrate the model comparison capabilities of the method, its self-consistency and its predictive power.

Preserving Lagrangian Structure in Nonlinear Model Reduction with Application to Structural Dynamics

DOE PAGES

Carlberg, Kevin; Tuminaro, Ray; Boggs, Paul

2015-03-11

Our work proposes a model-reduction methodology that preserves Lagrangian structure and achieves computational efficiency in the presence of high-order nonlinearities and arbitrary parameter dependence. As such, the resulting reduced-order model retains key properties such as energy conservation and symplectic time-evolution maps. We focus on parameterized simple mechanical systems subjected to Rayleigh damping and external forces, and consider an application to nonlinear structural dynamics. To preserve structure, the method first approximates the system's “Lagrangian ingredients''---the Riemannian metric, the potential-energy function, the dissipation function, and the external force---and subsequently derives reduced-order equations of motion by applying the (forced) Euler--Lagrange equation with thesemore » quantities. Moreover, from the algebraic perspective, key contributions include two efficient techniques for approximating parameterized reduced matrices while preserving symmetry and positive definiteness: matrix gappy proper orthogonal decomposition and reduced-basis sparsification. Our results for a parameterized truss-structure problem demonstrate the practical importance of preserving Lagrangian structure and illustrate the proposed method's merits: it reduces computation time while maintaining high accuracy and stability, in contrast to existing nonlinear model-reduction techniques that do not preserve structure.« less

Preserving Lagrangian Structure in Nonlinear Model Reduction with Application to Structural Dynamics

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

Carlberg, Kevin; Tuminaro, Ray; Boggs, Paul

Our work proposes a model-reduction methodology that preserves Lagrangian structure and achieves computational efficiency in the presence of high-order nonlinearities and arbitrary parameter dependence. As such, the resulting reduced-order model retains key properties such as energy conservation and symplectic time-evolution maps. We focus on parameterized simple mechanical systems subjected to Rayleigh damping and external forces, and consider an application to nonlinear structural dynamics. To preserve structure, the method first approximates the system's “Lagrangian ingredients''---the Riemannian metric, the potential-energy function, the dissipation function, and the external force---and subsequently derives reduced-order equations of motion by applying the (forced) Euler--Lagrange equation with thesemore » quantities. Moreover, from the algebraic perspective, key contributions include two efficient techniques for approximating parameterized reduced matrices while preserving symmetry and positive definiteness: matrix gappy proper orthogonal decomposition and reduced-basis sparsification. Our results for a parameterized truss-structure problem demonstrate the practical importance of preserving Lagrangian structure and illustrate the proposed method's merits: it reduces computation time while maintaining high accuracy and stability, in contrast to existing nonlinear model-reduction techniques that do not preserve structure.« less

Influence of helical external driven current on nonlinear resistive tearing mode evolution and saturation in tokamaks

NASA Astrophysics Data System (ADS)

Zhang, W.; Wang, S.; Ma, Z. W.

2017-06-01

The influences of helical driven currents on nonlinear resistive tearing mode evolution and saturation are studied by using a three-dimensional toroidal resistive magnetohydrodynamic code (CLT). We carried out three types of helical driven currents: stationary, time-dependent amplitude, and thickness. It is found that the helical driven current is much more efficient than the Gaussian driven current used in our previous study [S. Wang et al., Phys. Plasmas 23(5), 052503 (2016)]. The stationary helical driven current cannot persistently control tearing mode instabilities. For the time-dependent helical driven current with f c d = 0.01 and δ c d < 0.04 , the island size can be reduced to its saturated level that is about one third of the initial island size. However, if the total driven current increases to about 7% of the total plasma current, tearing mode instabilities will rebound again due to the excitation of the triple tearing mode. For the helical driven current with time dependent strength and thickness, the reduction speed of the radial perturbation component of the magnetic field increases with an increase in the driven current and then saturates at a quite low level. The tearing mode is always controlled even for a large driven current.

The Nonlinear Magnetosphere: Expressions in MHD and in Kinetic Models

NASA Technical Reports Server (NTRS)

Hesse, Michael; Birn, Joachim

2011-01-01

Like most plasma systems, the magnetosphere of the Earth is governed by nonlinear dynamic evolution equations. The impact of nonlinearities ranges from large scales, where overall dynamics features are exhibiting nonlinear behavior, to small scale, kinetic, processes, where nonlinear behavior governs, among others, energy conversion and dissipation. In this talk we present a select set of examples of such behavior, with a specific emphasis on how nonlinear effects manifest themselves in MHD and in kinetic models of magnetospheric plasma dynamics.

Exact solutions of unsteady Korteweg-de Vries and time regularized long wave equations.

PubMed

Islam, S M Rayhanul; Khan, Kamruzzaman; Akbar, M Ali

2015-01-01

In this paper, we implement the exp(-Φ(ξ))-expansion method to construct the exact traveling wave solutions for nonlinear evolution equations (NLEEs). Here we consider two model equations, namely the Korteweg-de Vries (KdV) equation and the time regularized long wave (TRLW) equation. These equations play significant role in nonlinear sciences. We obtained four types of explicit function solutions, namely hyperbolic, trigonometric, exponential and rational function solutions of the variables in the considered equations. It has shown that the applied method is quite efficient and is practically well suited for the aforementioned problems and so for the other NLEEs those arise in mathematical physics and engineering fields. PACS numbers: 02.30.Jr, 02.70.Wz, 05.45.Yv, 94.05.Fq.

Nonlinear nature of composite structure induced by the interaction of nonplanar solitons in a nonextensive plasma

NASA Astrophysics Data System (ADS)

Han, Jiu-Ning; Luo, Jun-Hua; Liu, Zhen-Lai; Shi, Jun; Xiang, Gen-Xiang; Li, Jun-Xiu

2015-06-01

The nonlinear properties of composite structure induced by the head-on collision of electron-acoustic solitons in a general plasma composed of cold fluid electrons, hot nonextensive distributed electron, and stationary ions are studied. We have made a detailed investigation on the time-evolution process of this merged wave structure. It is found that the structure survives during some time interval, and there are obviously different for the properties of the composite structures which are induced in cylindrical and spherical geometries. Moreover, it is shown that there are both positive and negative phase shifts for each colliding soliton after the interaction. For fixed plasma parameters, the soliton received the largest phase shift in spherical geometry, followed by the cylindrical and one-dimensional planar geometries.

Nonlinear and Dissipation Characteristics of Ocean Surface Waves in Estuarine Environments

DTIC Science & Technology

2014-09-30

transformation and evolution . In addition these modules would allow for feedback between the surface wave and the energy dissipating feature. OBJECTIVES...dissipation on wave processes. 3) Develop and test low-dimension, reduced representations of estuarine effects for inclusion into operational wave models...Sheremet (PI), Miao Tian and Cihan Sahin (Ph.D. students) who are working on modeling nonlinear wave evolution in dissipative environments (mud), and

Interspecific competition alters nonlinear selection on offspring size in the field.

PubMed

Marshall, Dustin J; Monro, Keyne

2013-02-01

Offspring size is one of the most important life-history traits with consequences for both the ecology and evolution of most organisms. Surprisingly, formal estimates of selection on offspring size are rare, and the degree to which selection (particularly nonlinear selection) varies among environments remains poorly explored. We estimate linear and nonlinear selection on offspring size, module size, and senescence rate for a sessile marine invertebrate in the field under three different intensities of interspecific competition. The intensity of competition strongly modified the strength and form of selection acting on offspring size. We found evidence for differences in nonlinear selection across the three environments. Our results suggest that the fitness returns of a given offspring size depend simultaneously on their environmental context, and on the context of other offspring traits. Offspring size effects can be more pervasive with regards to their influence on the fitness returns of other traits than previously recognized, and we suggest that the evolution of offspring size cannot be understood in isolation from other traits. Overall, variability in the form and strength of selection on offspring size in nature may reduce the efficacy of selection on offspring size and maintain variation in this trait. © 2012 The Author(s). Evolution© 2012 The Society for the Study of Evolution.

An efficient nonlinear Feshbach engine

NASA Astrophysics Data System (ADS)

Li, Jing; Fogarty, Thomás; Campbell, Steve; Chen, Xi; Busch, Thomas

2018-01-01

We investigate a thermodynamic cycle using a Bose-Einstein condensate (BEC) with nonlinear interactions as the working medium. Exploiting Feshbach resonances to change the interaction strength of the BEC allows us to produce work by expanding and compressing the gas. To ensure a large power output from this engine these strokes must be performed on a short timescale, however such non-adiabatic strokes can create irreversible work which degrades the engine’s efficiency. To combat this, we design a shortcut to adiabaticity which can achieve an adiabatic-like evolution within a finite time, therefore significantly reducing the out-of-equilibrium excitations in the BEC. We investigate the effect of the shortcut to adiabaticity on the efficiency and power output of the engine and show that the tunable nonlinearity strength, modulated by Feshbach resonances, serves as a useful tool to enhance the system’s performance.

Ion hole formation and nonlinear generation of electromagnetic ion cyclotron waves: THEMIS observations

NASA Astrophysics Data System (ADS)

Shoji, Masafumi; Miyoshi, Yoshizumi; Katoh, Yuto; Keika, Kunihiro; Angelopoulos, Vassilis; Kasahara, Satoshi; Asamura, Kazushi; Nakamura, Satoko; Omura, Yoshiharu

2017-09-01

Electromagnetic plasma waves are thought to be responsible for energy exchange between charged particles in space plasmas. Such an energy exchange process is evidenced by phase space holes identified in the ion distribution function and measurements of the dot product of the plasma wave electric field and the ion velocity. We develop a method to identify ion hole formation, taking into consideration the phase differences between the gyromotion of ions and the electromagnetic ion cyclotron (EMIC) waves. Using this method, we identify ion holes in the distribution function and the resulting nonlinear EMIC wave evolution from Time History of Events and Macroscale Interactions during Substorms (THEMIS) observations. These ion holes are key to wave growth and frequency drift by the ion currents through nonlinear wave-particle interactions, which are identified by a computer simulation in this study.

Curl forces and the nonlinear Fokker-Planck equation.

PubMed

Wedemann, R S; Plastino, A R; Tsallis, C

2016-12-01

Nonlinear Fokker-Planck equations endowed with curl drift forces are investigated. The conditions under which these evolution equations admit stationary solutions, which are q exponentials of an appropriate potential function, are determined. It is proved that when these stationary solutions exist, the nonlinear Fokker-Planck equations satisfy an H theorem in terms of a free-energy-like quantity involving the S_{q} entropy. A particular two-dimensional model admitting analytical, time-dependent q-Gaussian solutions is discussed in detail. This model describes a system of particles with short-range interactions, performing overdamped motion under drag effects due to a rotating resisting medium. It is related to models that have been recently applied to the study of type-II superconductors. The relevance of the present developments to the study of complex systems in physics, astronomy, and biology is discussed.

The method of projected characteristics for the evolution of magnetic arches

NASA Technical Reports Server (NTRS)

Nakagawa, Y.; Hu, Y. Q.; Wu, S. T.

1987-01-01

A numerical method of solving fully nonlinear MHD equation is described. In particular, the formulation based on the newly developed method of projected characteristics (Nakagawa, 1981) suitable to study the evolution of magnetic arches due to motions of their foot-points is presented. The final formulation is given in the form of difference equations; therefore, the analysis of numerical stability is also presented. Further, the most important derivation of physically self-consistent, time-dependent boundary conditions (i.e. the evolving boundary equations) is given in detail, and some results obtained with such boundary equations are reported.

A mathematical model of the structure and evolution of small-scale discrete auroral arcs

NASA Technical Reports Server (NTRS)

Seyler, Charles E.

1990-01-01

A three-dimensional fluid model for the structure and evolution of small-scale discrete auroral arcs originating from Alfven waves is developed and used to study the nonlinear macroscopic plasma dynamics of these auroral arcs. The results of simulations show that stationary auroral arcs can be unstable to a collisionless tearing mode which may be responsible for the observed transverse structuring in the form of folds and curls. At late times, the plasma becomes turbulent having transverse electric field power spectra that tend toward a universal k exp -5/3 spectral form.

Turbulence closure for mixing length theories

NASA Astrophysics Data System (ADS)

Jermyn, Adam S.; Lesaffre, Pierre; Tout, Christopher A.; Chitre, Shashikumar M.

2018-05-01

We present an approach to turbulence closure based on mixing length theory with three-dimensional fluctuations against a two-dimensional background. This model is intended to be rapidly computable for implementation in stellar evolution software and to capture a wide range of relevant phenomena with just a single free parameter, namely the mixing length. We incorporate magnetic, rotational, baroclinic, and buoyancy effects exactly within the formalism of linear growth theories with non-linear decay. We treat differential rotation effects perturbatively in the corotating frame using a novel controlled approximation, which matches the time evolution of the reference frame to arbitrary order. We then implement this model in an efficient open source code and discuss the resulting turbulent stresses and transport coefficients. We demonstrate that this model exhibits convective, baroclinic, and shear instabilities as well as the magnetorotational instability. It also exhibits non-linear saturation behaviour, and we use this to extract the asymptotic scaling of various transport coefficients in physically interesting limits.

WAKES: Wavelet Adaptive Kinetic Evolution Solvers

NASA Astrophysics Data System (ADS)

Mardirian, Marine; Afeyan, Bedros; Larson, David

2016-10-01

We are developing a general capability to adaptively solve phase space evolution equations mixing particle and continuum techniques in an adaptive manner. The multi-scale approach is achieved using wavelet decompositions which allow phase space density estimation to occur with scale dependent increased accuracy and variable time stepping. Possible improvements on the SFK method of Larson are discussed, including the use of multiresolution analysis based Richardson-Lucy Iteration, adaptive step size control in explicit vs implicit approaches. Examples will be shown with KEEN waves and KEEPN (Kinetic Electrostatic Electron Positron Nonlinear) waves, which are the pair plasma generalization of the former, and have a much richer span of dynamical behavior. WAKES techniques are well suited for the study of driven and released nonlinear, non-stationary, self-organized structures in phase space which have no fluid, limit nor a linear limit, and yet remain undamped and coherent well past the drive period. The work reported here is based on the Vlasov-Poisson model of plasma dynamics. Work supported by a Grant from the AFOSR.

Delayed collapses of Bose-Einstein condensates in relation to anti-de Sitter gravity.

PubMed

Biasi, Anxo F; Mas, Javier; Paredes, Angel

2017-03-01

We numerically investigate spherically symmetric collapses in the Gross-Pitaevskii equation with attractive nonlinearity in a harmonic potential. Even below threshold for direct collapse, the wave function bounces off from the origin and may eventually become singular after a number of oscillations in the trapping potential. This is reminiscent of the evolution of Einstein gravity sourced by a scalar field in anti de Sitter space where collapse corresponds to black-hole formation. We carefully examine the long time evolution of the wave function for continuous families of initial states in order to sharpen out this qualitative coincidence which may bring new insights in both directions. On the one hand, we comment on possible implications for the so-called Bosenova collapses in cold atom Bose-Einstein condensates. On the other hand, Gross-Pitaevskii provides a toy model to study the relevance of either the resonance conditions or the nonlinearity for the problem of anti de Sitter instability.

Exact Solutions of Atmospheric (2+1)-Dimensional Nonlinear Incompressible Non-hydrostatic Boussinesq Equations

NASA Astrophysics Data System (ADS)

Liu, Ping; Wang, Ya-Xiong; Ren, Bo; Li, Jin-Hua

2016-12-01

Exact solutions of the atmospheric (2+1)-dimensional nonlinear incompressible non-hydrostatic Boussinesq (INHB) equations are researched by Combining function expansion and symmetry method. By function expansion, several expansion coefficient equations are derived. Symmetries and similarity solutions are researched in order to obtain exact solutions of the INHB equations. Three types of symmetry reduction equations and similarity solutions for the expansion coefficient equations are proposed. Non-traveling wave solutions for the INHB equations are obtained by symmetries of the expansion coefficient equations. Making traveling wave transformations on expansion coefficient equations, we demonstrate some traveling wave solutions of the INHB equations. The evolutions on the wind velocities, temperature perturbation and pressure perturbation are demonstrated by figures, which demonstrate the periodic evolutions with time and space. Supported by the National Natural Science Foundation of China under Grant Nos. 11305031 and 11305106, and Training Programme Foundation for Outstanding Young Teachers in Higher Education Institutions of Guangdong Province under Grant No. Yq2013205

Dynamical Signatures of Living Systems

NASA Technical Reports Server (NTRS)

Zak, M.

1999-01-01

One of the main challenges in modeling living systems is to distinguish a random walk of physical origin (for instance, Brownian motions) from those of biological origin and that will constitute the starting point of the proposed approach. As conjectured, the biological random walk must be nonlinear. Indeed, any stochastic Markov process can be described by linear Fokker-Planck equation (or its discretized version), only that type of process has been observed in the inanimate world. However, all such processes always converge to a stable (ergodic or periodic) state, i.e., to the states of a lower complexity and high entropy. At the same time, the evolution of living systems directed toward a higher level of complexity if complexity is associated with a number of structural variations. The simplest way to mimic such a tendency is to incorporate a nonlinearity into the random walk; then the probability evolution will attain the features of diffusion equation: the formation and dissipation of shock waves initiated by small shallow wave disturbances. As a result, the evolution never "dies:" it produces new different configurations which are accompanied by an increase or decrease of entropy (the decrease takes place during formation of shock waves, the increase-during their dissipation). In other words, the evolution can be directed "against the second law of thermodynamics" by forming patterns outside of equilibrium in the probability space. Due to that, a specie is not locked up in a certain pattern of behavior: it still can perform a variety of motions, and only the statistics of these motions is constrained by this pattern. It should be emphasized that such a "twist" is based upon the concept of reflection, i.e., the existence of the self-image (adopted from psychology). The model consists of a generator of stochastic processes which represents the motor dynamics in the form of nonlinear random walks, and a simulator of the nonlinear version of the diffusion equation which represents the mental dynamics. It has been demonstrated that coupled mental-motor dynamics can simulate emerging self-organization, prey-predator games, collaboration and competition, "collective brain," etc.

An interactive approach based on a discrete differential evolution algorithm for a class of integer bilevel programming problems

NASA Astrophysics Data System (ADS)

Li, Hong; Zhang, Li; Jiao, Yong-Chang

2016-07-01

This paper presents an interactive approach based on a discrete differential evolution algorithm to solve a class of integer bilevel programming problems, in which integer decision variables are controlled by an upper-level decision maker and real-value or continuous decision variables are controlled by a lower-level decision maker. Using the Karush--Kuhn-Tucker optimality conditions in the lower-level programming, the original discrete bilevel formulation can be converted into a discrete single-level nonlinear programming problem with the complementarity constraints, and then the smoothing technique is applied to deal with the complementarity constraints. Finally, a discrete single-level nonlinear programming problem is obtained, and solved by an interactive approach. In each iteration, for each given upper-level discrete variable, a system of nonlinear equations including the lower-level variables and Lagrange multipliers is solved first, and then a discrete nonlinear programming problem only with inequality constraints is handled by using a discrete differential evolution algorithm. Simulation results show the effectiveness of the proposed approach.

Nonlinear chiral plasma transport in rotating coordinates

NASA Astrophysics Data System (ADS)

Dayi, Ömer F.; Kilinçarslan, Eda

2017-08-01

The nonlinear transport features of inhomogeneous chiral plasma in the presence of electromagnetic fields, in rotating coordinates are studied within the relaxation time approach. The chiral distribution functions up to second order in the electric field in rotating coordinates and the derivatives of chemical potentials are established by solving the Boltzmann transport equation. First, the vector and axial current densities in the weakly ionized chiral plasma for vanishing magnetic field are calculated. They involve the rotational analogues of the Hall effect as well as several new terms arising from the Coriolis and fictitious centrifugal forces. Then in the short relaxation time regime the angular velocity and electromagnetic fields are treated as perturbations. The current densities are obtained by retaining the terms up to second order in perturbations. The time evolution equations of the inhomogeneous chemical potentials are derived by demanding that collisions conserve the particle number densities.

Hybrid grammar-based approach to nonlinear dynamical system identification from biological time series

NASA Astrophysics Data System (ADS)

McKinney, B. A.; Crowe, J. E., Jr.; Voss, H. U.; Crooke, P. S.; Barney, N.; Moore, J. H.

2006-02-01

We introduce a grammar-based hybrid approach to reverse engineering nonlinear ordinary differential equation models from observed time series. This hybrid approach combines a genetic algorithm to search the space of model architectures with a Kalman filter to estimate the model parameters. Domain-specific knowledge is used in a context-free grammar to restrict the search space for the functional form of the target model. We find that the hybrid approach outperforms a pure evolutionary algorithm method, and we observe features in the evolution of the dynamical models that correspond with the emergence of favorable model components. We apply the hybrid method to both artificially generated time series and experimentally observed protein levels from subjects who received the smallpox vaccine. From the observed data, we infer a cytokine protein interaction network for an individual’s response to the smallpox vaccine.

New extended (G'/G)-expansion method to solve nonlinear evolution equation: the (3 + 1)-dimensional potential-YTSF equation.

PubMed

Roshid, Harun-Or-; Akbar, M Ali; Alam, Md Nur; Hoque, Md Fazlul; Rahman, Nizhum

2014-01-01

In this article, a new extended (G'/G) -expansion method has been proposed for constructing more general exact traveling wave solutions of nonlinear evolution equations with the aid of symbolic computation. In order to illustrate the validity and effectiveness of the method, we pick the (3 + 1)-dimensional potential-YTSF equation. As a result, abundant new and more general exact solutions have been achieved of this equation. It has been shown that the proposed method provides a powerful mathematical tool for solving nonlinear wave equations in applied mathematics, engineering and mathematical physics.

Study of diffusion of wave packets in a square lattice under external fields along the discrete nonlinear Schrödinger equation

NASA Astrophysics Data System (ADS)

de Brito, P. E.; Nazareno, H. N.

2012-09-01

The object of the present work is to analyze the effect of nonlinearity on wave packet propagation in a square lattice subject to a magnetic and an electric field in the Hall configuration, by using the Discrete Nonlinear Schrödinger Equation (DNLSE). In previous works we have shown that without the nonlinear term, the presence of the magnetic field induces the formation of vortices that remain stationary, while a wave packet is introduced in the system. As for the effect of an applied electric field, it was shown that the vortices propagate in a direction perpendicular to the electric field, similar behavior as presented in the classical treatment, we provide a quantum mechanics explanation for that. We have performed the calculations considering first the action of the magnetic field as well as the nonlinearity. The results indicate that for low values of the nonlinear parameter U the vortices remain stationary while preserving the form. For greater values of the parameter the picture gets distorted, the more so, the greater the nonlinearity. As for the inclusion of the electric field, we note that for small U, the wave packet propagates perpendicular to the applied field, until for greater values of U the wave gets partially localized in a definite region of the lattice. That is, for strong nonlinearity the wave packet gets partially trapped, while the tail of it can propagate through the lattice. Note that this tail propagation is responsible for the over-diffusion for long times of the wave packet under the action of an electric field. We have produced short films that show clearly the time evolution of the wave packet, which can add to the understanding of the dynamics.

Classical evolution of fractal measures on the lattice

NASA Astrophysics Data System (ADS)

Antoniou, N. G.; Diakonos, F. K.; Saridakis, E. N.; Tsolias, G. A.

2007-04-01

We consider the classical evolution of a lattice of nonlinear coupled oscillators for a special case of initial conditions resembling the equilibrium state of a macroscopic thermal system at the critical point. The displacements of the oscillators define initially a fractal measure on the lattice associated with the scaling properties of the order parameter fluctuations in the corresponding critical system. Assuming a sudden symmetry breaking (quench), leading to a change in the equilibrium position of each oscillator, we investigate in some detail the deformation of the initial fractal geometry as time evolves. In particular, we show that traces of the critical fractal measure can be sustained for large times, and we extract the properties of the chain that determine the associated time scales. Our analysis applies generally to critical systems for which, after a slow developing phase where equilibrium conditions are justified, a rapid evolution, induced by a sudden symmetry breaking, emerges on time scales much shorter than the corresponding relaxation or observation time. In particular, it can be used in the fireball evolution in a heavy-ion collision experiment, where the QCD critical point emerges, or in the study of evolving fractals of astrophysical and cosmological scales, and may lead to determination of the initial critical properties of the Universe through observations in the symmetry-broken phase.

Nonlinear-optical activity owing to anisotropy of ultrafast nonlinear refraction in cubic materials.

PubMed

Hutchings, D C

1995-08-01

The evolution of the polarization state in a cubic material with an anisotropic Kerr nonlinearity is examined. It is shown that in certain cases this provides a mechanism for nonlinear-optical activity, leaving the state of the polarization unchanged but causing a signif icant rotation in its major axis. The use of the anisotropic ultrafast nonlinear refraction that exists just beneath the half-gap in semiconductors to demonstrate these effects is discussed.

Symmetries and exact solutions of a class of nonlocal nonlinear Schrödinger equations with self-induced parity-time-symmetric potential.

PubMed

Sinha, Debdeep; Ghosh, Pijush K

2015-04-01

A class of nonlocal nonlinear Schrödinger equations (NLSEs) is considered in an external potential with a space-time modulated coefficient of the nonlinear interaction term as well as confining and/or loss-gain terms. This is a generalization of a recently introduced integrable nonlocal NLSE with self-induced potential that is parity-time-symmetric in the corresponding stationary problem. Exact soliton solutions are obtained for the inhomogeneous and/or nonautonomous nonlocal NLSE by using similarity transformation, and the method is illustrated with a few examples. It is found that only those transformations are allowed for which the transformed spatial coordinate is odd under the parity transformation of the original one. It is shown that the nonlocal NLSE without the external potential and a (d+1)-dimensional generalization of it admits all the symmetries of the (d+1)-dimensional Schrödinger group. The conserved Noether charges associated with the time translation, dilatation, and special conformal transformation are shown to be real-valued in spite of being non-Hermitian. Finally, the dynamics of different moments are studied with an exact description of the time evolution of the "pseudowidth" of the wave packet for the special case in which the system admits a O(2,1) conformal symmetry.

Numerical simulation of stability and stability control of high speed compressible rotating couette flow

NASA Technical Reports Server (NTRS)

Biringen, Sedat; Hatay, Ferhat F.

1993-01-01

The nonlinear temporal evolution of disturbances in compressible flow between infinitely long, concentric cylinders is investigated through direct numerical simulations of the full, three-dimensional Navier-Stokes and energy equations. Counter-rotating cylinders separated by wide gaps are considered with supersonic velocities of the inner cylinder. Initially, the primary disturbance grows exponentially in accordance with linear stability theory. As the disturbances evolve, higher harmonics and subharmonics are generated in a cascading order eventually reaching a saturation state. Subsequent highly nonlinear stages of the evolution are governed by the interaction of the disturbance modes, particularly the axial subharmonics. Nonlinear evolution of the disturbance field is characterized by the formation of high-shear layers extending from the inner cylinder towards the center of the gap in the form of jets similar to the ejection events in transitional and turbulent wall-bounded shear flows.

A Finite-Difference Time-Domain Model of Artificial Ionospheric Modification

NASA Astrophysics Data System (ADS)

Cannon, Patrick; Honary, Farideh; Borisov, Nikolay

Experiments in the artificial modification of the ionosphere via a radio frequency pump wave have observed a wide range of non-linear phenomena near the reflection height of an O-mode wave. These effects exhibit a strong aspect-angle dependence thought to be associated with the process by which, for a narrow range of off-vertical launch angles, the O-mode pump wave can propagate beyond the standard reflection height at X=1 as a Z-mode wave and excite additional plasma activity. A numerical model based on Finite-Difference Time-Domain method has been developed to simulate the interaction of the pump wave with an ionospheric plasma and investigate different non-linear processes involved in modification experiments. The effects on wave propagation due to plasma inhomogeneity and anisotropy are introduced through coupling of the Lorentz equation of motion for electrons and ions to Maxwell’s wave equations in the FDTD formulation, leading to a model that is capable of exciting a variety of plasma waves including Langmuir and upper-hybrid waves. Additionally, discretized equations describing the time-dependent evolution of the plasma fluid temperature and density are included in the FDTD update scheme. This model is used to calculate the aspect angle dependence and angular size of the radio window for which Z-mode excitation occurs, and the results compared favourably with both theoretical predictions and experimental observations. The simulation results are found to reproduce the angular dependence on electron density and temperature enhancement observed experimentally. The model is used to investigate the effect of different initial plasma density conditions on the evolution of non-linear effects, and demonstrates that the inclusion of features such as small field-aligned density perturbations can have a significant influence on wave propagation and the magnitude of temperature and density enhancements.

Effects of time ordering in quantum nonlinear optics

NASA Astrophysics Data System (ADS)

Quesada, Nicolás; Sipe, J. E.

2014-12-01

We study time-ordering corrections to the description of spontaneous parametric down-conversion (SPDC), four-wave mixing (SFWM), and frequency conversion using the Magnus expansion. Analytic approximations to the evolution operator that are unitary are obtained. They are Gaussian preserving, and allow us to understand order-by-order the effects of time ordering. We show that the corrections due to time ordering vanish exactly if the phase-matching function is sufficiently broad. The calculation of the effects of time ordering on the joint spectral amplitude of the photons generated in SPDC and SFWM are reduced to quadrature.

A non-linear theory of the parallel firehose and gyrothermal instabilities in a weakly collisional plasma

NASA Astrophysics Data System (ADS)

Rosin, M. S.; Schekochihin, A. A.; Rincon, F.; Cowley, S. C.

2011-05-01

Weakly collisional magnetized cosmic plasmas have a dynamical tendency to develop pressure anisotropies with respect to the local direction of the magnetic field. These anisotropies trigger plasma instabilities at scales just above the ion Larmor radius ρi and much below the mean free path λmfp. They have growth rates of a fraction of the ion cyclotron frequency, which is much faster than either the global dynamics or even local turbulence. Despite their microscopic nature, these instabilities dramatically modify the transport properties and, therefore, the macroscopic dynamics of the plasma. The non-linear evolution of these instabilities is expected to drive pressure anisotropies towards marginal stability values, controlled by the plasma beta βi. Here this non-linear evolution is worked out in an ab initio kinetic calculation for the simplest analytically tractable example - the parallel (k⊥= 0) firehose instability in a high-beta plasma. An asymptotic theory is constructed, based on a particular physical ordering and leading to a closed non-linear equation for the firehose turbulence. In the non-linear regime, both the analytical theory and the numerical solution predict secular (∝t) growth of magnetic fluctuations. The fluctuations develop a k-3∥ spectrum, extending from scales somewhat larger than ρi to the maximum scale that grows secularly with time (∝t1/2); the relative pressure anisotropy (p⊥-p∥)/p∥ tends to the marginal value -2/βi. The marginal state is achieved via changes in the magnetic field, not particle scattering. When a parallel ion heat flux is present, the parallel firehose mutates into the new gyrothermal instability (GTI), which continues to exist up to firehose-stable values of pressure anisotropy, which can be positive and are limited by the magnitude of the ion heat flux. The non-linear evolution of the GTI also features secular growth of magnetic fluctuations, but the fluctuation spectrum is eventually dominated by modes around a maximal scale ˜ρilT/λmfp, where lT is the scale of the parallel temperature variation. Implications for momentum and heat transport are speculated about. This study is motivated by our interest in the dynamics of galaxy cluster plasmas (which are used as the main astrophysical example), but its relevance to solar wind and accretion flow plasmas is also briefly discussed.

An idealised study for the long term evolution of crescentic bars

NASA Astrophysics Data System (ADS)

Chen, W. L.; Dodd, N.; Tiessen, M. C. H.; Calvete, D.

2018-01-01

An idealised study that identifies the mechanisms in the long term evolution of crescentic bar systems in nature is presented. Growth to finite amplitude (i.e., equilibration, sometimes referred to as saturation) and higher harmonic interaction are hypothesised to be the leading nonlinear effects in long-term evolution of these systems. These nonlinear effects are added to a linear stability model and used to predict crescentic bar development along a beach in Duck, North Carolina (USA) over a 2-month period. The equilibration prolongs the development of bed patterns, thus allowing the long term evolution. Higher harmonic interaction enables the amplitude to be transferred from longer to shorter lengthscales, which leads to the dominance of shorter lengthscales in latter post-storm stages, as observed at Duck. The comparison with observations indicates the importance of higher harmonic interaction in the development of nearshore crescentic bar systems in nature. Additionally, it is concluded that these nonlinear effects should be included in models simulating the development of different bed patterns, and that this points a way forward for long-term morphodynamical modelling in general.

Evolution model with a cumulative feedback coupling

NASA Astrophysics Data System (ADS)

Trimper, Steffen; Zabrocki, Knud; Schulz, Michael

2002-05-01

The paper is concerned with a toy model that generalizes the standard Lotka-Volterra equation for a certain population by introducing a competition between instantaneous and accumulative, history-dependent nonlinear feedback the origin of which could be a contribution from any kind of mismanagement in the past. The results depend on the sign of that additional cumulative loss or gain term of strength λ. In case of a positive coupling the system offers a maximum gain achieved after a finite time but the population will die out in the long time limit. In this case the instantaneous loss term of strength u is irrelevant and the model exhibits an exact solution. In the opposite case λ<0 the time evolution of the system is terminated in a crash after ts provided u=0. This singularity after a finite time can be avoided if u≠0. The approach may well be of relevance for the qualitative understanding of more realistic descriptions.

Observation of ultrafast temporal evolution of symmetry in short-pulsed laser induced transient states of matter (Conference Presentation)

NASA Astrophysics Data System (ADS)

Garnett, Joy; Krzyzanowska, Halina; Baydin, Andrey; Tolk, Norman H.

2017-02-01

In condensed matter physics, ultrafast photoexcitation has been shown to result in modification of macroscopic material properties, sometimes involving phase changes, on a subpicosecond time scale. In semiconductors, irreversible non-thermal solid-to-liquid structural transitions have been demonstrated at high laser fluences. In the pump-probe experiments reported here, we observe a striking continuously varying low-fluence pump-induced time-dependent structural symmetry modification in intrinsic gallium arsenide (GaAs) using a probe that produces femtosecond polarization-resolved second harmonic generation (f-PRSHG) data. SHG spectroscopy is particularly suited to monitor symmetry changes since its magnitude is governed by the nonlinear optical susceptibility tensor whose elements are determined by the underlying material symmetry. Conceptually, these experiments seek to provide insight into the details of the time evolution of symmetry arising from laser induced transient states of matter in GaAs. Overall, the basic explanation of these experimental observations is that as a result of the photoinduced electronic excitation, many electrons, including bond electrons are excited to higher states. This results in subpicosecond changes in the local anharmonic potential and produces a changing nonlinear polarization response thus accounting for the nonthermal time dependent symmetry changes. Clearly, our approach may be easily extended to many different crystalline materials with different levels of defects, dopants and stresses to fully characterize the time dependent behavior of laser induced transient states in material systems.

Near-equilibrium desorption of helium films

NASA Astrophysics Data System (ADS)

Weimer, M.; Housley, R. M.; Goodstein, D. L.

1987-10-01

The thermal desorption of helium films in the presence of their equilibrium vapor is studied experimentally for small but rapid departures from ambient temperature. The results are analyzed within the framework of a quasithermodynamic phenomenological model based on detailed balance. Under the usual experimental conditions, isothermal desorption at the temperature of the substrate is a general prediction of the model which seems to be substantiated. For realistic adsorption isotherms the time evolution of the net desorption flux nevertheless appears to be governed by a highly nonlinear equation. In such circumstances, a number of characteristic relaxation times may be identified. These time scales are distinct from, and in general unrelated to, the coverage-dependent mean lifetime of an atom on the surface. To characterize the overall nonlinear evolution towards steady state, a global time scale, defined in terms of both initial- and steady-state properties, is introduced to summarize the experimental data. Internal evidence suggests a criterion for judging when collisions among desorbed atoms are unimportant. When this condition is satisfied, data for near-equilibrium desorption agree well with the predictions of the model. Combining our results with earlier data at higher substrate temperatures and different ambient conditions, the overall picture is consistent with scaling properties implied by the theory. We show that the values of the parameters deduced from a Frenkel-Arrhenius parametrization of the global relaxation times, as well as a variety of other aspects of desorption kinetics, are actually consequences of the shape of the equilibrium adsorption isotherm.

Mode locking with a compensated space--time astigmatism

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

Christov, I.P.; Stoev, V.D.; Murnane, M.M.

1995-10-15

We present what is to our knowledge the first full spatial plus temporal model of a self-mode-locked titanium-doped sapphire laser. The self-consistent evolution of the pulse toward steady state imposes strong space--time focusing in the crystal, where both the space and time foci are located. This combined focusing significantly improves the discrimination properties of the nonlinear resonator for shorter pulses and reduces the transient stage of pulse formation. Our theoretical results are in very good agreement with experiment. {copyright} {ital 1995} {ital Optical} {ital Society} {ital of} {ital America}.

Nonlinear Instability of Hypersonic Flow past a Wedge

NASA Technical Reports Server (NTRS)

Seddougui, Sharon O.; Bassom, Andrew P.

1991-01-01

The nonlinear stability of a compressible flow past a wedge is investigated in the hypersonic limit. The analysis follows the ideas of a weakly nonlinear approach. Interest is focussed on Tollmien-Schlichting waves governed by a triple deck structure and it is found that the attached shock can profoundly affect the stability characteristics of the flow. In particular, it is shown that nonlinearity tends to have a stabilizing influence. The nonlinear evolution of the Tollmien-Schlichting mode is described in a number of asymptotic limits.

Tidal Response of Europa's Subsurface Ocean

NASA Astrophysics Data System (ADS)

Karatekin, O.; Comblen, R.; Deleersnijder, E.; Dehant, V. M.

2010-12-01

Time-variable tides in the subsurface oceans of icy satellites cause large periodic surface displacements and tidal dissipation can become a major energy source that can affect long-term orbital and internal evolution. In the present study, we investigate the response of the subsurface ocean of Europa to a time-varibale tidal potential. Two-dimensional nonlinear shallow water equations are solved on a sphere by means of a finite element code. The resulting ocean tidal flow velocities,dissipation and surface displacements will be presented.

Free-carrier-induced soliton fission unveiled by in situ measurements in nanophotonic waveguides

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

Husko, Chad; Wulf, Matthias; Lefrancois, Simon

Solitons are localized waves formed by a balance of focusing and defocusing effects. These nonlinear waves exist in diverse forms of matter yet exhibit similar properties including stability, periodic recurrence and particle-like trajectories. One important property is soliton fission, a process by which an energetic higher-order soliton breaks apart due to dispersive or nonlinear perturbations. Here we demonstrate through both experiment and theory that nonlinear photocarrier generation can induce soliton fission. Using near-field measurements, we directly observe the nonlinear spatial and temporal evolution of optical pulses in situ in a nanophotonic semiconductor waveguide. We develop an analytic formalism describing themore » free-carrier dispersion (FCD) perturbation and show the experiment exceeds the minimum threshold by an order of magnitude. We confirm these observations with a numerical nonlinear Schrodinger equation model. Finally, these results provide a fundamental explanation and physical scaling of optical pulse evolution in free-carrier media and could enable improved supercontinuum sources in gas based and integrated semiconductor waveguides.« less

Free-carrier-induced soliton fission unveiled by in situ measurements in nanophotonic waveguides

DOE PAGES

Husko, Chad; Wulf, Matthias; Lefrancois, Simon; ...

2016-04-15

Solitons are localized waves formed by a balance of focusing and defocusing effects. These nonlinear waves exist in diverse forms of matter yet exhibit similar properties including stability, periodic recurrence and particle-like trajectories. One important property is soliton fission, a process by which an energetic higher-order soliton breaks apart due to dispersive or nonlinear perturbations. Here we demonstrate through both experiment and theory that nonlinear photocarrier generation can induce soliton fission. Using near-field measurements, we directly observe the nonlinear spatial and temporal evolution of optical pulses in situ in a nanophotonic semiconductor waveguide. We develop an analytic formalism describing themore » free-carrier dispersion (FCD) perturbation and show the experiment exceeds the minimum threshold by an order of magnitude. We confirm these observations with a numerical nonlinear Schrodinger equation model. Finally, these results provide a fundamental explanation and physical scaling of optical pulse evolution in free-carrier media and could enable improved supercontinuum sources in gas based and integrated semiconductor waveguides.« less

New Perspectives: Wave Mechanical Interpretations of Dark Matter, Baryon and Dark Energy

NASA Astrophysics Data System (ADS)

Russell, Esra

We model the cosmic components: dark matter, dark energy and baryon distributions in the Cosmic Web by means of highly nonlinear Schrodinger type and reaction diffusion type wave mechanical descriptions. The construction of these wave mechanical models of the structure formation is achieved by introducing the Fisher information measure and its comparison with highly nonlinear term which has dynamical analogy to infamous quantum potential in the wave equations. Strikingly, the comparison of this nonlinear term and the Fisher information measure provides a dynamical distinction between lack of self-organization and self-organization in the dynamical evolution of the cosmic components. Mathematically equivalent to the standard cosmic fluid equations, these approaches make it possible to follow the evolution of the matter distribution even into the highly nonlinear regime by circumventing singularities. Also, numerical realizations of the emerging web-like patterns are presented from the nonlinear dynamics of the baryon component while dark energy component shows Gaussian type dynamics corresponding to soliton-like solutions.

OBSERVING LYAPUNOV EXPONENTS OF INFINITE-DIMENSIONAL DYNAMICAL SYSTEMS

PubMed Central

OTT, WILLIAM; RIVAS, MAURICIO A.; WEST, JAMES

2016-01-01

Can Lyapunov exponents of infinite-dimensional dynamical systems be observed by projecting the dynamics into ℝN using a ‘typical’ nonlinear projection map? We answer this question affirmatively by developing embedding theorems for compact invariant sets associated with C1 maps on Hilbert spaces. Examples of such discrete-time dynamical systems include time-T maps and Poincaré return maps generated by the solution semigroups of evolution partial differential equations. We make every effort to place hypotheses on the projected dynamics rather than on the underlying infinite-dimensional dynamical system. In so doing, we adopt an empirical approach and formulate checkable conditions under which a Lyapunov exponent computed from experimental data will be a Lyapunov exponent of the infinite-dimensional dynamical system under study (provided the nonlinear projection map producing the data is typical in the sense of prevalence). PMID:28066028

OBSERVING LYAPUNOV EXPONENTS OF INFINITE-DIMENSIONAL DYNAMICAL SYSTEMS.

PubMed

Ott, William; Rivas, Mauricio A; West, James

2015-12-01

Can Lyapunov exponents of infinite-dimensional dynamical systems be observed by projecting the dynamics into ℝ N using a 'typical' nonlinear projection map? We answer this question affirmatively by developing embedding theorems for compact invariant sets associated with C 1 maps on Hilbert spaces. Examples of such discrete-time dynamical systems include time- T maps and Poincaré return maps generated by the solution semigroups of evolution partial differential equations. We make every effort to place hypotheses on the projected dynamics rather than on the underlying infinite-dimensional dynamical system. In so doing, we adopt an empirical approach and formulate checkable conditions under which a Lyapunov exponent computed from experimental data will be a Lyapunov exponent of the infinite-dimensional dynamical system under study (provided the nonlinear projection map producing the data is typical in the sense of prevalence).

Composite nonlinear structure within the magnetosonic soliton interactions in a spin-1/2 degenerate quantum plasma

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

Han, Jiu-Ning, E-mail: hanjiuning@126.com; Luo, Jun-Hua; Li, Jun-Xiu

2015-06-15

We study the basic physical properties of composite nonlinear structure induced by the head-on collision of magnetosonic solitons. Solitary waves are assumed to propagate in a quantum electron-ion magnetoplasma with spin-1/2 degenerate electrons. The main interest of the present work is to investigate the time evolution of the merged composite structure during a specific time interval of the wave interaction process. We consider three cases of colliding-situation, namely, compressive-rarefactive solitons interaction, compressive-compressive solitons interaction, and rarefactive-rarefactive solitons interaction, respectively. Compared with the last two colliding cases, the changing process of the composite structure is more complex for the first situation.more » Moreover, it is found that they are obviously different for the last two colliding cases.« less

Nonlinear Ocean Waves

DTIC Science & Technology

1994-01-06

for all of this work is the fact that the Kadomtsev - Petviashvili equation , a1(atu + ui)xU + a.3u) + ay2u = 0, (KP) describes approximately the evolution...the contents of these two papers. (a) Numerically induced chaos The cubic-nonlinear Schrtdinger equation in one dimension, iatA +,2V + 21i,1 =0, (NLS...arises in several physical contexts, including the evolution of nearly monochromatic, one-dimensional waves in deep water. The equation is known to be

Linear analysis of auto-organization in Hebbian neural networks.

PubMed

Carlos Letelier, J; Mpodozis, J

1995-01-01

The self-organization of neurotopies where neural connections follow Hebbian dynamics is framed in terms of linear operator theory. A general and exact equation describing the time evolution of the overall synaptic strength connecting two neural laminae is derived. This linear matricial equation, which is similar to the equations used to describe oscillating systems in physics, is modified by the introduction of non-linear terms, in order to capture self-organizing (or auto-organizing) processes. The behavior of a simple and small system, that contains a non-linearity that mimics a metabolic constraint, is analyzed by computer simulations. The emergence of a simple "order" (or degree of organization) in this low-dimensionality model system is discussed.

Characterization of Perovskite Oxide/Semiconductor Heterostructures

NASA Astrophysics Data System (ADS)

Walker, Phillip

The tools developed for the use of investigating dynamical systems have provided critical understanding to a wide range of physical phenomena. Here these tools are used to gain further insight into scalar transport, and how it is affected by mixing. The aim of this research is to investigate the efficiency of several different partitioning methods which demarcate flow fields into dynamically distinct regions, and the correlation of finite-time statistics from the advection-diffusion equation to these regions. For autonomous systems, invariant manifold theory can be used to separate the system into dynamically distinct regions. Despite there being no equivalent method for nonautonomous systems, a similar analysis can be done. Systems with general time dependencies must resort to using finite-time transport barriers for partitioning; these barriers are the edges of Lagrangian coherent structures (LCS), the analog to the stable and unstable manifolds of invariant manifold theory. Using the coherent structures of a flow to analyze the statistics of trapping, flight, and residence times, the signature of anomalous diffusion are obtained. This research also investigates the use of linear models for approximating the elements of the covariance matrix of nonlinear flows, and then applying the covariance matrix approximation over coherent regions. The first and second-order moments can be used to fully describe an ensemble evolution in linear systems, however there is no direct method for nonlinear systems. The problem is only compounded by the fact that the moments for nonlinear flows typically don't have analytic representations, therefore direct numerical simulations would be needed to obtain the moments throughout the domain. To circumvent these many computations, the nonlinear system is approximated as many linear systems for which analytic expressions for the moments exist. The parameters introduced in the linear models are obtained locally from the nonlinear deformation tensor.

Nonlinear evolution of three-dimensional instabilities of thin and thick electron scale current sheets: Plasmoid formation and current filamentation

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

Jain, Neeraj; Büchner, Jörg; Max Planck Institute for Solar System Research, Justus-Von-Liebig-Weg-3, Göttingen

Nonlinear evolution of three dimensional electron shear flow instabilities of an electron current sheet (ECS) is studied using electron-magnetohydrodynamic simulations. The dependence of the evolution on current sheet thickness is examined. For thin current sheets (half thickness =d{sub e}=c/ω{sub pe}), tearing mode instability dominates. In its nonlinear evolution, it leads to the formation of oblique current channels. Magnetic field lines form 3-D magnetic spirals. Even in the absence of initial guide field, the out-of-reconnection-plane magnetic field generated by the tearing instability itself may play the role of guide field in the growth of secondary finite-guide-field instabilities. For thicker current sheetsmore » (half thickness ∼5 d{sub e}), both tearing and non-tearing modes grow. Due to the non-tearing mode, current sheet becomes corrugated in the beginning of the evolution. In this case, tearing mode lets the magnetic field reconnect in the corrugated ECS. Later thick ECS develops filamentary structures and turbulence in which reconnection occurs. This evolution of thick ECS provides an example of reconnection in self-generated turbulence. The power spectra for both the thin and thick current sheets are anisotropic with respect to the electron flow direction. The cascade towards shorter scales occurs preferentially in the direction perpendicular to the electron flow.« less

Cosmological perturbation theory for baryons and dark matter: One-loop corrections in the renormalized perturbation theory framework

NASA Astrophysics Data System (ADS)

Somogyi, Gábor; Smith, Robert E.

2010-01-01

We generalize the renormalized perturbation theory (RPT) formalism of Crocce and Scoccimarro [M. Crocce and R. Scoccimarro, Phys. Rev. DPRVDAQ1550-7998 73, 063519 (2006)10.1103/PhysRevD.73.063519] to deal with multiple fluids in the Universe and here we present the complete calculations up to the one-loop level in the RPT. We apply this approach to the problem of following the nonlinear evolution of baryon and cold dark matter (CDM) perturbations, evolving from the distinct sets of initial conditions, from the high redshift post-recombination Universe right through to the present day. In current theoretical and numerical models of structure formation, it is standard practice to treat baryons and CDM as an effective single matter fluid—the so-called dark matter only modeling. In this approximation, one uses a weighed sum of late-time baryon and CDM transfer functions to set initial mass fluctuations. In this paper we explore whether this approach can be employed for high precision modeling of structure formation. We show that, even if we only follow the linear evolution, there is a large-scale scale-dependent bias between baryons and CDM for the currently favored WMAP5 ΛCDM model. This time evolving bias is significant (>1%) until the present day, when it is driven towards unity through gravitational relaxation processes. Using the RPT formalism we test this approximation in the nonlinear regime. We show that the nonlinear CDM power spectrum in the two-component fluid differs from that obtained from an effective mean-mass one-component fluid by ˜3% on scales of order k˜0.05hMpc-1 at z=10, and by ˜0.5% at z=0. However, for the case of the nonlinear evolution of the baryons the situation is worse and we find that the power spectrum is suppressed, relative to the total matter, by ˜15% on scales k˜0.05hMpc-1 at z=10, and by ˜3%-5% at z=0. Importantly, besides the suppression of the spectrum, the baryonic acoustic oscillation (BAO) features are amplified for baryon and slightly damped for CDM spectra. If we compare the total matter power spectra in the two- and one-component fluid approaches, then we find excellent agreement, with deviations being <0.5% throughout the evolution. Consequences: high precision modeling of the large-scale distribution of baryons in the Universe cannot be achieved through an effective mean-mass one-component fluid approximation; detection significance of BAO will be amplified in probes that study baryonic matter, relative to probes that study the CDM or total mass only. The CDM distribution can be modeled accurately at late times and the total matter at all times. This is good news for probes that are sensitive to the total mass, such as gravitational weak lensing as existing modeling techniques are good enough. Lastly, we identify an analytic approximation that greatly simplifies the evaluation of the full PT expressions, and it is better than <1% over the full range of scales and times considered.

A note on improved F-expansion method combined with Riccati equation applied to nonlinear evolution equations.

PubMed

Islam, Md Shafiqul; Khan, Kamruzzaman; Akbar, M Ali; Mastroberardino, Antonio

2014-10-01

The purpose of this article is to present an analytical method, namely the improved F-expansion method combined with the Riccati equation, for finding exact solutions of nonlinear evolution equations. The present method is capable of calculating all branches of solutions simultaneously, even if multiple solutions are very close and thus difficult to distinguish with numerical techniques. To verify the computational efficiency, we consider the modified Benjamin-Bona-Mahony equation and the modified Korteweg-de Vries equation. Our results reveal that the method is a very effective and straightforward way of formulating the exact travelling wave solutions of nonlinear wave equations arising in mathematical physics and engineering.

A note on improved F-expansion method combined with Riccati equation applied to nonlinear evolution equations

PubMed Central

Islam, Md. Shafiqul; Khan, Kamruzzaman; Akbar, M. Ali; Mastroberardino, Antonio

2014-01-01

The purpose of this article is to present an analytical method, namely the improved F-expansion method combined with the Riccati equation, for finding exact solutions of nonlinear evolution equations. The present method is capable of calculating all branches of solutions simultaneously, even if multiple solutions are very close and thus difficult to distinguish with numerical techniques. To verify the computational efficiency, we consider the modified Benjamin–Bona–Mahony equation and the modified Korteweg-de Vries equation. Our results reveal that the method is a very effective and straightforward way of formulating the exact travelling wave solutions of nonlinear wave equations arising in mathematical physics and engineering. PMID:26064530

Traveling wave solutions and conservation laws for nonlinear evolution equation

NASA Astrophysics Data System (ADS)

Baleanu, Dumitru; Inc, Mustafa; Yusuf, Abdullahi; Aliyu, Aliyu Isa

2018-02-01

In this work, the Riccati-Bernoulli sub-ordinary differential equation and modified tanh-coth methods are used to reach soliton solutions of the nonlinear evolution equation. We acquire new types of traveling wave solutions for the governing equation. We show that the equation is nonlinear self-adjoint by obtaining suitable substitution. Therefore, we construct conservation laws for the equation using new conservation theorem. The obtained solutions in this work may be used to explain and understand the physical nature of the wave spreads in the most dispersive medium. The constraint condition for the existence of solitons is stated. Some three dimensional figures for some of the acquired results are illustrated.

Information-theoretic decomposition of embodied and situated systems.

PubMed

Da Rold, Federico

2018-07-01

The embodied and situated view of cognition stresses the importance of real-time and nonlinear bodily interaction with the environment for developing concepts and structuring knowledge. In this article, populations of robots controlled by an artificial neural network learn a wall-following task through artificial evolution. At the end of the evolutionary process, time series are recorded from perceptual and motor neurons of selected robots. Information-theoretic measures are estimated on pairings of variables to unveil nonlinear interactions that structure the agent-environment system. Specifically, the mutual information is utilized to quantify the degree of dependence and the transfer entropy to detect the direction of the information flow. Furthermore, the system is analyzed with the local form of such measures, thus capturing the underlying dynamics of information. Results show that different measures are interdependent and complementary in uncovering aspects of the robots' interaction with the environment, as well as characteristics of the functional neural structure. Therefore, the set of information-theoretic measures provides a decomposition of the system, capturing the intricacy of nonlinear relationships that characterize robots' behavior and neural dynamics. Copyright © 2018 Elsevier Ltd. All rights reserved.

NIMROD: A computational laboratory for studying nonlinear fusion magnetohydrodynamics

NASA Astrophysics Data System (ADS)

Sovinec, C. R.; Gianakon, T. A.; Held, E. D.; Kruger, S. E.; Schnack, D. D.

2003-05-01

Nonlinear numerical studies of macroscopic modes in a variety of magnetic fusion experiments are made possible by the flexible high-order accurate spatial representation and semi-implicit time advance in the NIMROD simulation code [A. H. Glasser et al., Plasma Phys. Controlled Fusion 41, A747 (1999)]. Simulation of a resistive magnetohydrodynamics mode in a shaped toroidal tokamak equilibrium demonstrates computation with disparate time scales, simulations of discharge 87009 in the DIII-D tokamak [J. L. Luxon et al., Plasma Physics and Controlled Nuclear Fusion Research 1986 (International Atomic Energy Agency, Vienna, 1987), Vol. I, p. 159] confirm an analytic scaling for the temporal evolution of an ideal mode subject to plasma-β increasing beyond marginality, and a spherical torus simulation demonstrates nonlinear free-boundary capabilities. A comparison of numerical results on magnetic relaxation finds the n=1 mode and flux amplification in spheromaks to be very closely related to the m=1 dynamo modes and magnetic reversal in reversed-field pinch configurations. Advances in local and nonlocal closure relations developed for modeling kinetic effects in fluid simulation are also described.

Nonlinear propagation analysis of few-optical-cycle pulses for subfemtosecond compression and carrier envelope phase effect

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

Mizuta, Yo; Nagasawa, Minoru; Ohtani, Morimasa

2005-12-15

A numerical approach called Fourier direct method (FDM) is applied to nonlinear propagation of optical pulses with the central wavelength 800 nm, the width 2.67-12.00 fs, and the peak power 25-6870 kW in a fused-silica fiber. Bidirectional propagation, delayed Raman response, nonlinear dispersion (self-steepening, core dispersion), as well as correct linear dispersion are incorporated into 'bidirectional propagation equations' which are derived directly from Maxwell's equations. These equations are solved for forward and backward waves, instead of the electric-field envelope as in the nonlinear Schroedinger equation (NLSE). They are integrated as multidimensional simultaneous evolution equations evolved in space. We investigate, bothmore » theoretically and numerically, the validity and the limitation of assumptions and approximations used for deriving the NLSE. Also, the accuracy and the efficiency of the FDM are compared quantitatively with those of the finite-difference time-domain numerical approach. The time-domain size 500 fs and the number of grid points in time 2048 are chosen to investigate numerically intensity spectra, spectral phases, and temporal electric-field profiles up to the propagation distance 1.0 mm. On the intensity spectrum of a few-optical-cycle pulses, the self-steepening, core dispersion, and the delayed Raman response appear as dominant, middle, and slight effects, respectively. The delayed Raman response and the core dispersion reduce the effective nonlinearity. Correct linear dispersion is important since it affects the intensity spectrum sensitively. For the compression of femtosecond optical pulses by the complete phase compensation, the shortness and the pulse quality of compressed pulses are remarkably improved by the intense initial peak power rather than by the short initial pulse width or by the propagation distance longer than 0.1 mm. They will be compressed as short as 0.3 fs below the damage threshold of fused-silica fiber 6 MW. It is demonstrated that the carrier envelope phase (CEP) causes the difference on the temporal electric-field profile and the intensity spectrum for the initial peak power of the order of megawatts. At the propagation distance longer than the coherence length for third-order harmonics, the difference grows in the spectral components around the third-order and higher-order harmonics. The CEP can be a sensitive marker to monitor the evolution of nonlinear optical process by a few-optical-cycle electric-field wave-packet source.« less

Surface plasmon polariton Akhmediev Breather in a dielectric-metal-dielectric geometry with subwavelength thickness

NASA Astrophysics Data System (ADS)

Devi, Koijam Monika; Porsezian, K.; Sarma, Amarendra K.

2018-05-01

We report Akhmediev Breather solutions in a nonlinear multilayer structure comprising of a metal sandwiched between two semi-infinite dielectric layers with subwavelength thickness. These nonlinear solutions inherit the properties of Surface plasmon polaritons and its dynamics is governed by the Nonlinear Schrodinger equation. The breather evolution is studied for specific values of nonlinear and dispersion parameters. An experimental scheme to observe these breathers is also proposed.

Environmental Noise Could Promote Stochastic Local Stability of Behavioral Diversity Evolution

NASA Astrophysics Data System (ADS)

Zheng, Xiu-Deng; Li, Cong; Lessard, Sabin; Tao, Yi

2018-05-01

In this Letter, we investigate stochastic stability in a two-phenotype evolutionary game model for an infinite, well-mixed population undergoing discrete, nonoverlapping generations. We assume that the fitness of a phenotype is an exponential function of its expected payoff following random pairwise interactions whose outcomes randomly fluctuate with time. We show that the stochastic local stability of a constant interior equilibrium can be promoted by the random environmental noise even if the system may display a complicated nonlinear dynamics. This result provides a new perspective for a better understanding of how environmental fluctuations may contribute to the evolution of behavioral diversity.

Evolution of rogue waves in dusty plasmas

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

Tolba, R. E., E-mail: tolba-math@yahoo.com; El-Bedwehy, N. A., E-mail: nab-elbedwehy@yahoo.com; Moslem, W. M., E-mail: wmmoslem@hotmail.com

2015-04-15

The evolution of rogue waves associated with the dynamics of positively charged dust grains that interact with streaming electrons and ions is investigated. Using a perturbation method, the basic set of fluid equations is reduced to a nonlinear Schrödinger equation (NLSE). The rational solution of the NLSE is presented, which proposed as an effective tool for studying the rogue waves in Jupiter. It is found that the existence region of rogue waves depends on the dust-acoustic speed and the streaming densities of the ions and electrons. Furthermore, the supersonic rogue waves are much taller than the subsonic rogue waves bymore » ∼25 times.« less

A connection between the maximum displacements of rogue waves and the dynamics of poles in the complex plane.

PubMed

Liu, T Y; Chiu, T L; Clarkson, P A; Chow, K W

2017-09-01

Rogue waves of evolution systems are displacements which are localized in both space and time. The locations of the points of maximum displacements of the wave profiles may correlate with the trajectories of the poles of the exact solutions from the perspective of complex variables through analytic continuation. More precisely, the location of the maximum height of the rogue wave in laboratory coordinates (real space and time) is conjectured to be equal to the real part of the pole of the exact solution, if the spatial coordinate is allowed to be complex. This feature can be verified readily for the Peregrine breather (lowest order rogue wave) of the nonlinear Schrödinger equation. This connection is further demonstrated numerically here for more complicated scenarios, namely the second order rogue wave of the Boussinesq equation (for bidirectional long waves in shallow water), an asymmetric second order rogue wave for the nonlinear Schrödinger equation (as evolution system for slowly varying wave packets), and a symmetric second order rogue wave of coupled Schrödinger systems. Furthermore, the maximum displacements in physical space occur at a time instant where the trajectories of the poles in the complex plane reverse directions. This property is conjectured to hold for many other systems, and will help to determine the maximum amplitudes of rogue waves.

A connection between the maximum displacements of rogue waves and the dynamics of poles in the complex plane

NASA Astrophysics Data System (ADS)

Liu, T. Y.; Chiu, T. L.; Clarkson, P. A.; Chow, K. W.

2017-09-01

Rogue waves of evolution systems are displacements which are localized in both space and time. The locations of the points of maximum displacements of the wave profiles may correlate with the trajectories of the poles of the exact solutions from the perspective of complex variables through analytic continuation. More precisely, the location of the maximum height of the rogue wave in laboratory coordinates (real space and time) is conjectured to be equal to the real part of the pole of the exact solution, if the spatial coordinate is allowed to be complex. This feature can be verified readily for the Peregrine breather (lowest order rogue wave) of the nonlinear Schrödinger equation. This connection is further demonstrated numerically here for more complicated scenarios, namely the second order rogue wave of the Boussinesq equation (for bidirectional long waves in shallow water), an asymmetric second order rogue wave for the nonlinear Schrödinger equation (as evolution system for slowly varying wave packets), and a symmetric second order rogue wave of coupled Schrödinger systems. Furthermore, the maximum displacements in physical space occur at a time instant where the trajectories of the poles in the complex plane reverse directions. This property is conjectured to hold for many other systems, and will help to determine the maximum amplitudes of rogue waves.

Nonlinear amplification of coherent waves in media with soliton-type refractive index pattern.

PubMed

Bugaychuk, S; Conte, R

2012-08-01

We derive the complex Ginzburg-Landau equation for the dynamical self-diffraction of optical waves in a nonlinear cavity. The case of the reflection geometry of wave interaction as well as a medium that possesses the cubic nonlinearity (including a local and a nonlocal nonlinear responses) and the relaxation is considered. A stable localized spatial structure in the form of a "dark" dissipative soliton is formed in the cavity in the steady state. The envelope of the intensity pattern, as well as of the dynamical grating amplitude, takes the shape of a tanh function. The obtained complex Ginzburg-Landau equation describes the dynamics of this envelope; at the same time, the evolution of this spatial structure changes the parameters of the output waves. New effects are predicted in this system due to the transformation of the dissipative soliton which takes place during the interaction of a pulse with a continuous wave, such as retention of the pulse shape during the transmission of impulses in a long nonlinear cavity, and giant amplification of a seed pulse, which takes energy due to redistribution of the pump continuous energy into the signal.

Falling films on flexible inclines

NASA Astrophysics Data System (ADS)

Matar, O. K.; Craster, R. V.; Kumar, S.

2007-11-01

The nonlinear stability and dynamic behavior of falling fluid films is studied for flow over a flexible substrate. We use asymptotic methods to deduce governing equations valid in various limits. Long-wave theory is used to derive Benney-like coupled equations for the film thickness and substrate deflection. Weakly nonlinear equations are then derived from these equations that, in the limit of large wall damping and/or large wall tension, reduce to the Kuramoto-Sivashinsky equation. These models break down when inertia becomes more significant, so we also use a long-wave approximation in conjunction with integral theory to derive three strongly coupled nonlinear evolution equations for the film thickness, substrate deflection, and film volumetric flow rate valid at higher Reynolds numbers. These equations, accounting for inertia, capillary, viscous, wall tension, and damping effects, are solved over a wide range of parameters. Our results suggest that decreasing wall damping and/or wall tension can promote the development of chaos in the weakly nonlinear regime and lead to severe substrate deformations in the strongly nonlinear regime; these can give rise to situations in which the free surface and underlying substrate come into contact in finite time.

Black-hole universe: time evolution.

PubMed

Yoo, Chul-Moon; Okawa, Hirotada; Nakao, Ken-ichi

2013-10-18

Time evolution of a black hole lattice toy model universe is simulated. The vacuum Einstein equations in a cubic box with a black hole at the origin are numerically solved with periodic boundary conditions on all pairs of faces opposite to each other. Defining effective scale factors by using the area of a surface and the length of an edge of the cubic box, we compare them with that in the Einstein-de Sitter universe. It is found that the behavior of the effective scale factors is well approximated by that in the Einstein-de Sitter universe. In our model, if the box size is sufficiently larger than the horizon radius, local inhomogeneities do not significantly affect the global expansion law of the Universe even though the inhomogeneity is extremely nonlinear.

Time series analysis for minority game simulations of financial markets

NASA Astrophysics Data System (ADS)

Ferreira, Fernando F.; Francisco, Gerson; Machado, Birajara S.; Muruganandam, Paulsamy

2003-04-01

The minority game (MG) model introduced recently provides promising insights into the understanding of the evolution of prices, indices and rates in the financial markets. In this paper we perform a time series analysis of the model employing tools from statistics, dynamical systems theory and stochastic processes. Using benchmark systems and a financial index for comparison, several conclusions are obtained about the generating mechanism for this kind of evolution. The motion is deterministic, driven by occasional random external perturbation. When the interval between two successive perturbations is sufficiently large, one can find low dimensional chaos in this regime. However, the full motion of the MG model is found to be similar to that of the first differences of the SP500 index: stochastic, nonlinear and (unit root) stationary.

Wave kinetics of random fibre lasers

PubMed Central

Churkin, D V.; Kolokolov, I V.; Podivilov, E V.; Vatnik, I D.; Nikulin, M A.; Vergeles, S S.; Terekhov, I S.; Lebedev, V V.; Falkovich, G.; Babin, S A.; Turitsyn, S K.

2015-01-01

Traditional wave kinetics describes the slow evolution of systems with many degrees of freedom to equilibrium via numerous weak non-linear interactions and fails for very important class of dissipative (active) optical systems with cyclic gain and losses, such as lasers with non-linear intracavity dynamics. Here we introduce a conceptually new class of cyclic wave systems, characterized by non-uniform double-scale dynamics with strong periodic changes of the energy spectrum and slow evolution from cycle to cycle to a statistically steady state. Taking a practically important example—random fibre laser—we show that a model describing such a system is close to integrable non-linear Schrödinger equation and needs a new formalism of wave kinetics, developed here. We derive a non-linear kinetic theory of the laser spectrum, generalizing the seminal linear model of Schawlow and Townes. Experimental results agree with our theory. The work has implications for describing kinetics of cyclical systems beyond photonics. PMID:25645177

Wave packet dynamics for a non-linear Schrödinger equation describing continuous position measurements

NASA Astrophysics Data System (ADS)

Zander, C.; Plastino, A. R.; Díaz-Alonso, J.

2015-11-01

We investigate time-dependent solutions for a non-linear Schrödinger equation recently proposed by Nassar and Miret-Artés (NM) to describe the continuous measurement of the position of a quantum particle (Nassar, 2013; Nassar and Miret-Artés, 2013). Here we extend these previous studies in two different directions. On the one hand, we incorporate a potential energy term in the NM equation and explore the corresponding wave packet dynamics, while in the previous works the analysis was restricted to the free-particle case. On the other hand, we investigate time-dependent solutions while previous studies focused on a stationary one. We obtain exact wave packet solutions for linear and quadratic potentials, and approximate solutions for the Morse potential. The free-particle case is also revisited from a time-dependent point of view. Our analysis of time-dependent solutions allows us to determine the stability properties of the stationary solution considered in Nassar (2013), Nassar and Miret-Artés (2013). On the basis of these results we reconsider the Bohmian approach to the NM equation, taking into account the fact that the evolution equation for the probability density ρ =| ψ | 2 is not a continuity equation. We show that the effect of the source term appearing in the evolution equation for ρ has to be explicitly taken into account when interpreting the NM equation from a Bohmian point of view.

Mathematical problems arising in interfacial electrohydrodynamics

NASA Astrophysics Data System (ADS)

Tseluiko, Dmitri

In this work we consider the nonlinear stability of thin films in the presence of electric fields. We study a perfectly conducting thin film flow down an inclined plane in the presence of an electric field which is uniform in its undisturbed state, and normal to the plate at infinity. In addition, the effect of normal electric fields on films lying above, or hanging from, horizontal substrates is considered. Systematic asymptotic expansions are used to derive fully nonlinear long wave model equations for the scaled interface motion and corresponding flow fields. For the case of an inclined plane, higher order terms are need to be retained to regularize the problem in the sense that the long wave approximation remains valid for long times. For the case of a horizontal plane the fully nonlinear evolution equation which is derived at the leading order, is asymptotically correct and no regularization procedure is required. In both physical situations, the effect of the electric field is to introduce a non-local term which arises from the potential region above the liquid film, and enters through the electric Maxwell stresses at the interface. This term is always linearly destabilizing and produces growth rates proportional to the cubic power of the wavenumber - surface tension is included and provides a short wavelength cut-off, that is, all sufficiently short waves are linearly stable. For the case of film flow down an inclined plane, the fully nonlinear equation can produce singular solutions (for certain parameter values) after a finite time, even in the absence of an electric field. This difficulty is avoided at smaller amplitudes where the weakly nonlinear evolution is governed by an extension of the Kuramoto-Sivashinsky (KS) equation. Global existence and uniqueness results are proved, and refined estimates of the radius of the absorbing ball in L2 are obtained in terms of the parameters of the equations for a generalized class of modified KS equations. The established estimates are compared with numerical solutions of the equations which in turn suggest an optimal upper bound for the radius of the absorbing ball. A scaling argument is used to explain this, and a general conjecture is made based on extensive computations. We also carry out a complete study of the nonlinear behavior of competing physical mechanisms: long wave instability above a critical Reynolds number, short wave damping due to surface tension and intermediate growth due to the electric field. Through a combination of analysis and extensive numerical experiments, we elucidate parameter regimes that support non-uniform travelling waves, time-periodic travelling waves and complex nonlinear dynamics including chaotic interfacial oscillations. It is established that a sufficiently high electric field will drive the system to chaotic oscillations, even when the Reynolds number is smaller than the critical value below which the non-electrified problem is linearly stable. A particular case of this is Stokes flow, which is known to be stable for this class of problems (an analogous statement holds for horizontally supported films also). Our theoretical results indicate that such highly stable flows can be rendered unstable by using electric fields. This opens the way for possible heat and mass transfer applications which can benefit significantly from interfacial oscillations and interfacial turbulence. For the case of a horizontal plane, a weakly nonlinear theory is not possible due to the absence of the shear flow generated by the gravitational force along the plate when the latter is inclined. We study the fully nonlinear equation, which in this case is asymptotically correct and is obtained at the leading order. The model equation describes both overlying and hanging films - in the former case gravity is stabilizing while in the latter it is destabilizing. The numerical and theoretical analysis of the fully nonlinear evolution is complicated by the fact that the coefficients of the highest order terms (surface tension in this instance) are nonlinear. We implement a fully implicit two level numerical scheme and perform numerical experiments. We also prove global boundedness of positive periodic smooth solutions, using an appropriate energy functional. This global boundedness result is seen in all our numerical results. Through a combination of analysis and extensive numerical experiments we present evidence for global existence of positive smooth solutions. This means, in turn, that the film does not touch the wall in finite time but asymptotically at infinite time. Numerical solutions are presented to support such phenomena.

Two-fluid and finite Larmor radius effects on helicity evolution in a plasma pinch

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

Sauppe, J. P., E-mail: jpsauppe@gmail.com; Department of Physics, University of Wisconsin-Madison, 1150 University Avenue, Madison, Wisconsin 53706; Sovinec, C. R., E-mail: csovinec@wisc.edu

2016-03-15

The evolution of magnetic energy, helicity, and hybrid helicity during nonlinear relaxation of a driven-damped plasma pinch is compared in visco-resistive magnetohydrodynamics and two-fluid models with and without the ion gyroviscous stress tensor. Magnetic energy and helicity are supplied via a boundary electric field which initially balances the resistive dissipation, and the plasma undergoes multiple relaxation events during the nonlinear evolution. The magnetic helicity is well conserved relative to the magnetic energy over each event, which is short compared with the global resistive diffusion time. The magnetic energy decreases by roughly 1.5% of its initial value over a relaxation event,more » while the magnetic helicity changes by at most 0.2% of the initial value. The hybrid helicity is dominated by magnetic helicity in low-β pinch conditions and is also well conserved. Differences of less than 1% between magnetic helicity and hybrid helicity are observed with two-fluid modeling and result from cross helicity evolution. The cross helicity is found to change appreciably due to the first-order finite Larmor radius effects which have not been included in contemporary relaxation theories. The plasma current evolves towards the flat parallel current state predicted by Taylor relaxation theory but does not achieve it. Plasma flow develops significant structure for two-fluid models, and the flow perpendicular to the magnetic field is much more substantial than the flow along it.« less

Widening Disparity and its Suppression in a Stochastic Replicator Model

NASA Astrophysics Data System (ADS)

Sakaguchi, Hidetsugu

2016-04-01

Winner-take-all phenomena are observed in various competitive systems. We find similar phenomena in replicator models with randomly fluctuating growth rates. The disparity between winners and losers increases indefinitely, even if all elements are statistically equivalent. A lognormal distribution describes well the nonstationary time evolution. If a nonlinear load corresponding to progressive taxation is introduced, a stationary distribution is obtained and disparity widening is suppressed.

Science and Technology Text Mining: Nonlinear Dynamics

DTIC Science & Technology

2004-02-01

journal/ institution publication and citation data. 15. SUBJECT TERMS 16. SECURITY CLASSIFICATION OF: 17. LIMITATION OF ABSTRACT 18. NUMBER OF PAGES...systems whose time evolution has a sensitive dependence on initial conditions. An approximately 100 term query was developed for accessing records from the...SCI papers by a factor of ~ 2. Appendix 4 contains a co-occurrence matrix of the top 15 countries. In terms of absolute numbers of co-authored papers

Separation of irradiance and reflectance from observed color images by logarithmical nonlinear diffusion process

NASA Astrophysics Data System (ADS)

Saito, Takahiro; Takahashi, Hiromi; Komatsu, Takashi

2006-02-01

The Retinex theory was first proposed by Land, and deals with separation of irradiance from reflectance in an observed image. The separation problem is an ill-posed problem. Land and others proposed various Retinex separation algorithms. Recently, Kimmel and others proposed a variational framework that unifies the previous Retinex algorithms such as the Poisson-equation-type Retinex algorithms developed by Horn and others, and presented a Retinex separation algorithm with the time-evolution of a linear diffusion process. However, the Kimmel's separation algorithm cannot achieve physically rational separation, if true irradiance varies among color channels. To cope with this problem, we introduce a nonlinear diffusion process into the time-evolution. Moreover, as to its extension to color images, we present two approaches to treat color channels: the independent approach to treat each color channel separately and the collective approach to treat all color channels collectively. The latter approach outperforms the former. Furthermore, we apply our separation algorithm to a high quality chroma key in which before combining a foreground frame and a background frame into an output image a color of each pixel in the foreground frame are spatially adaptively corrected through transformation of the separated irradiance. Experiments demonstrate superiority of our separation algorithm over the Kimmel's separation algorithm.

Constrained multi-objective optimization of storage ring lattices

NASA Astrophysics Data System (ADS)

Husain, Riyasat; Ghodke, A. D.

2018-03-01

The storage ring lattice optimization is a class of constrained multi-objective optimization problem, where in addition to low beam emittance, a large dynamic aperture for good injection efficiency and improved beam lifetime are also desirable. The convergence and computation times are of great concern for the optimization algorithms, as various objectives are to be optimized and a number of accelerator parameters to be varied over a large span with several constraints. In this paper, a study of storage ring lattice optimization using differential evolution is presented. The optimization results are compared with two most widely used optimization techniques in accelerators-genetic algorithm and particle swarm optimization. It is found that the differential evolution produces a better Pareto optimal front in reasonable computation time between two conflicting objectives-beam emittance and dispersion function in the straight section. The differential evolution was used, extensively, for the optimization of linear and nonlinear lattices of Indus-2 for exploring various operational modes within the magnet power supply capabilities.

Role of nonlinear refraction in the generation of terahertz field pulses by light fields

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

Zabolotskii, A. A., E-mail: zabolotskii@iae.nsk.su

2013-07-15

The generation of microwave (terahertz) pulses without any envelope in a four-level quasi-resonant medium is considered. Two intense quasi-monochromatic laser fields lead to a partial upper-level population. Microwave field pulses cause the transition between these levels. For appropriately chosen scales, the evolution of the fields is shown to be described by the pseudo-spin evolution equations in a microwave field with the inclusion of nonlinear refraction caused by an adiabatic upper-level population. The evolution of terahertz field pulses is described outside the scope of the slow-envelope approximation. When a number of standard approximations are taken into account, this system of equationsmore » is shown to be equivalent to an integrable version of the generalized reduced Maxwell-Bloch equations or to the generalized three-wave mixing equations. The soliton solution found by the inverse scattering transform method is used as an example to show that nonlinear refraction leads to a strong compression of the microwave (terahertz) field soliton.« less

Dynamics of vector dark solitons propagation and tunneling effect in the variable coefficient coupled nonlinear Schrödinger equation.

PubMed

Musammil, N M; Porsezian, K; Subha, P A; Nithyanandan, K

2017-02-01

We investigate the dynamics of vector dark solitons propagation using variable coefficient coupled nonlinear Schrödinger (Vc-CNLS) equation. The dark soliton propagation and evolution dynamics in the inhomogeneous system are studied analytically by employing the Hirota bilinear method. It is apparent from our asymptotic analysis that the collision between the dark solitons is elastic in nature. The various inhomogeneous effects on the evolution and interaction between dark solitons are explored, with a particular emphasis on nonlinear tunneling. It is found that the tunneling of the soliton depends on a condition related to the height of the barrier and the amplitude of the soliton. The intensity of the tunneling soliton either forms a peak or a valley, thus retaining its shape after tunneling. For the case of exponential background, the soliton tends to compress after tunneling through the barrier/well. Thus, a comprehensive study of dark soliton pulse evolution and propagation dynamics in Vc-CNLS equation is presented in the paper.

Nonlinear Diamagnetic Stabilization of Double Tearing Modes in Cylindrical MHD Simulations

NASA Astrophysics Data System (ADS)

Abbott, Stephen; Germaschewski, Kai

2014-10-01

Double tearing modes (DTMs) may occur in reversed-shear tokamak configurations if two nearby rational surfaces couple and begin reconnecting. During the DTM's nonlinear evolution it can enter an ``explosive'' growth phase leading to complete reconnection, making it a possible driver for off-axis sawtooth crashes. Motivated by similarities between this behavior and that of the m = 1 kink-tearing mode in conventional tokamaks we investigate diamagnetic drifts as a possible DTM stabilization mechanism. We extend our previous linear studies of an m = 2 , n = 1 DTM in cylindrical geometry to the fully nonlinear regime using the MHD code MRC-3D. A pressure gradient similar to observed ITB profiles is used, together with Hall physics, to introduce ω* effects. We find the diamagnetic drifts can have a stabilizing effect on the nonlinear DTM through a combination of large scale differential rotation and mechanisms local to the reconnection layer. MRC-3D is an extended MHD code based on the libMRC computational framework. It supports nonuniform grids in curvilinear coordinates with parallel implicit and explicit time integration.

Ultrafast Plasmonic Control of Second Harmonic Generation

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

Davidson, Roderick B.; Yanchenko, Anna; Ziegler, Jed I.

Efficient frequency conversion techniques are crucial to the development of plasmonic metasurfaces for information processing and signal modulation. In principle, nanoscale electric-field confinement in nonlinear materials enables higher harmonic conversion efficiencies per unit volume than those attainable in bulk materials. Here we demonstrate efficient second-harmonic generation (SHG) in a serrated nanogap plasmonic geometry that generates steep electric field gradients on a dielectric metasurface. An ultrafast control pulse is used to control plasmon-induced electric fields in a thin-film material with inversion symmetry that, without plasmonic enhancement, does not exhibit an even-order nonlinear optical response. The temporal evolution of the plasmonic near-fieldmore » is characterized with ~100 as resolution using a novel nonlinear interferometric technique. The serrated nanogap is a unique platform in which to investigate optically controlled, plasmonically enhanced harmonic generation in dielectric materials on an ultrafast time scale. Lastly, this metamaterial geometry can also be readily extended to all-optical control of other nonlinear phenomena, such as four-wave mixing and sum- and difference-frequency generation, in a wide variety of dielectric materials.« less

Ultrafast Plasmonic Control of Second Harmonic Generation

DOE PAGES

Davidson, Roderick B.; Yanchenko, Anna; Ziegler, Jed I.; ...

2016-06-01

Efficient frequency conversion techniques are crucial to the development of plasmonic metasurfaces for information processing and signal modulation. In principle, nanoscale electric-field confinement in nonlinear materials enables higher harmonic conversion efficiencies per unit volume than those attainable in bulk materials. Here we demonstrate efficient second-harmonic generation (SHG) in a serrated nanogap plasmonic geometry that generates steep electric field gradients on a dielectric metasurface. An ultrafast control pulse is used to control plasmon-induced electric fields in a thin-film material with inversion symmetry that, without plasmonic enhancement, does not exhibit an even-order nonlinear optical response. The temporal evolution of the plasmonic near-fieldmore » is characterized with ~100 as resolution using a novel nonlinear interferometric technique. The serrated nanogap is a unique platform in which to investigate optically controlled, plasmonically enhanced harmonic generation in dielectric materials on an ultrafast time scale. Lastly, this metamaterial geometry can also be readily extended to all-optical control of other nonlinear phenomena, such as four-wave mixing and sum- and difference-frequency generation, in a wide variety of dielectric materials.« less

Spatio-temporal instabilities for counterpropagating waves in periodic media.

PubMed

Haus, Joseph; Soon, Boon Yi; Scalora, Michael; Bloemer, Mark; Bowden, Charles; Sibilia, Concita; Zheltikov, Alexei

2002-01-28

Nonlinear evolution of coupled forward and backward fields in a multi-layered film is numerically investigated. We examine the role of longitudinal and transverse modulation instabilities in media of finite length with a homogeneous nonlinear susceptibility c((3)). The numerical solution of the nonlinear equations by a beam-propagation method that handles backward waves is described.

Gyrofluid turbulence models with kinetic effects

NASA Astrophysics Data System (ADS)

Dorland, W.; Hammett, G. W.

1993-03-01

Nonlinear gyrofluid equations are derived by taking moments of the nonlinear, electrostatic gyrokinetic equation. The principal model presented includes evolution equations for the guiding center n, u∥, T∥, and T⊥ along with an equation expressing the quasineutrality constraint. Additional evolution equations for higher moments are derived that may be used if greater accuracy is desired. The moment hierarchy is closed with a Landau damping model [G. W. Hammett and F. W. Perkins, Phys. Rev. Lett. 64, 3019 (1990)], which is equivalent to a multipole approximation to the plasma dispersion function, extended to include finite Larmor radius effects (FLR). In particular, new dissipative, nonlinear terms are found that model the perpendicular phase mixing of the distribution function along contours of constant electrostatic potential. These ``FLR phase-mixing'' terms introduce a hyperviscositylike damping ∝k⊥2‖Φkk×k'‖, which should provide a physics-based damping mechanism at high k⊥ρ which is potentially as important as the usual polarization drift nonlinearity. The moments are taken in guiding center space to pick up the correct nonlinear FLR terms and the gyroaveraging of the shear. The equations are solved with a nonlinear, three-dimensional initial value code. Linear results are presented, showing excellent agreement with linear gyrokinetic theory.

Higher-order modulation instability in nonlinear fiber optics.

PubMed

Erkintalo, Miro; Hammani, Kamal; Kibler, Bertrand; Finot, Christophe; Akhmediev, Nail; Dudley, John M; Genty, Goëry

2011-12-16

We report theoretical, numerical, and experimental studies of higher-order modulation instability in the focusing nonlinear Schrödinger equation. This higher-order instability arises from the nonlinear superposition of elementary instabilities, associated with initial single breather evolution followed by a regime of complex, yet deterministic, pulse splitting. We analytically describe the process using the Darboux transformation and compare with experiments in optical fiber. We show how a suitably low frequency modulation on a continuous wave field induces higher-order modulation instability splitting with the pulse characteristics at different phases of evolution related by a simple scaling relationship. We anticipate that similar processes are likely to be observed in many other systems including plasmas, Bose-Einstein condensates, and deep water waves. © 2011 American Physical Society

Ultrasonic Monitoring of the Interaction between Cement Matrix and Alkaline Silicate Solution in Self-Healing Systems.

PubMed

Ait Ouarabi, Mohand; Antonaci, Paola; Boubenider, Fouad; Gliozzi, Antonio S; Scalerandi, Marco

2017-01-07

Alkaline solutions, such as sodium, potassium or lithium silicates, appear to be very promising as healing agents for the development of encapsulated self-healing concretes. However, the evolution of their mechanical and acoustic properties in time has not yet been completely clarified, especially regarding their behavior and related kinetics when they are used in the form of a thin layer in contact with a hardened cement matrix. This study aims to monitor, using linear and nonlinear ultrasonic methods, the evolution of a sodium silicate solution interacting with a cement matrix in the presence of localized cracks. The ultrasonic inspection via linear methods revealed that an almost complete recovery of the elastic and acoustic properties occurred within a few days of healing. The nonlinear ultrasonic measurements contributed to provide further insight into the kinetics of the recovery due to the presence of the healing agent. A good regain of mechanical performance was ascertained through flexural tests at the end of the healing process, confirming the suitability of sodium silicate as a healing agent for self-healing cementitious systems.

Nonlinear Dynamical Analysis of Fibrillation

NASA Astrophysics Data System (ADS)

Kerin, John A.; Sporrer, Justin M.; Egolf, David A.

2013-03-01

The development of spatiotemporal chaotic behavior in heart tissue, termed fibrillation, is a devastating, life-threatening condition. The chaotic behavior of electrochemical signals, in the form of spiral waves, causes the muscles of the heart to contract in an incoherent manner, hindering the heart's ability to pump blood. We have applied the mathematical tools of nonlinear dynamics to large-scale simulations of a model of fibrillating heart tissue to uncover the dynamical modes driving this chaos. By studying the evolution of Lyapunov vectors and exponents over short times, we have found that the fibrillating tissue is sensitive to electrical perturbations only in narrow regions immediately in front of the leading edges of spiral waves, especially when these waves collide, break apart, or hit the edges of the tissue sample. Using this knowledge, we have applied small stimuli to areas of varying sensitivity. By studying the evolution of the effects of these perturbations, we have made progress toward controlling the electrochemical patterns associated with heart fibrillation. This work was supported by the U.S. National Science Foundation (DMR-0094178) and Research Corporation.

Nonlinear evolution of Mack modes in a hypersonic boundary layer

NASA Astrophysics Data System (ADS)

Chokani, Ndaona

2005-01-01

In hypersonic boundary layer flows the nonlinear disturbance evolution occurs relatively slowly over a very long length scale and has a profound effect on boundary layer transition. In the case of low-level freestream disturbances and negligible surface roughness, the transition is due to the modal growth of exponentially growing Mack modes that are destabilized by wall cooling. Cross-bicoherence measurements, derived from hot-wire data acquired in a quiet hypersonic tunnel, are used to identify and quantify phase-locked, quadratic sum and difference interactions involving the Mack modes. In the early stages of the nonlinear disturbance evolution, cross-bicoherence measurements indicate that the energy exchange between the Mack mode and the mean flow first occurs to broaden the sidebands; this is immediately followed by a sum interaction of the Mack mode to generate the first harmonic. In the next stages of the nonlinear disturbance evolution, there is a difference interaction of the first harmonic, which is also thought to contribute to the mean flow distortion. This difference interaction, in the latter stages, is also accompanied by a difference interaction between Mack mode and first harmonic, and a sum interaction, which forces the second harmonic. Analysis using the digital complex demodulation technique, shows that the low-frequency, phase-locked interaction that is identified in the cross bicoherence when the Mack mode and first harmonic have large amplitudes, arises due to the amplitude modulation of Mack mode and first harmonic.

Linear dynamical modes as new variables for data-driven ENSO forecast

NASA Astrophysics Data System (ADS)

Gavrilov, Andrey; Seleznev, Aleksei; Mukhin, Dmitry; Loskutov, Evgeny; Feigin, Alexander; Kurths, Juergen

2018-05-01

A new data-driven model for analysis and prediction of spatially distributed time series is proposed. The model is based on a linear dynamical mode (LDM) decomposition of the observed data which is derived from a recently developed nonlinear dimensionality reduction approach. The key point of this approach is its ability to take into account simple dynamical properties of the observed system by means of revealing the system's dominant time scales. The LDMs are used as new variables for empirical construction of a nonlinear stochastic evolution operator. The method is applied to the sea surface temperature anomaly field in the tropical belt where the El Nino Southern Oscillation (ENSO) is the main mode of variability. The advantage of LDMs versus traditionally used empirical orthogonal function decomposition is demonstrated for this data. Specifically, it is shown that the new model has a competitive ENSO forecast skill in comparison with the other existing ENSO models.

Multirate Particle-in-Cell Time Integration Techniques of Vlasov-Maxwell Equations for Collisionless Kinetic Plasma Simulations

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

Chen, Guangye; Chacon, Luis; Knoll, Dana Alan

2015-07-31

A multi-rate PIC formulation was developed that employs large timesteps for slow field evolution, and small (adaptive) timesteps for particle orbit integrations. Implementation is based on a JFNK solver with nonlinear elimination and moment preconditioning. The approach is free of numerical instabilities (ω peΔt >>1, and Δx >> λ D), and requires many fewer dofs (vs. explicit PIC) for comparable accuracy in challenging problems. Significant gains (vs. conventional explicit PIC) may be possible for large scale simulations. The paper is organized as follows: Vlasov-Maxwell Particle-in-cell (PIC) methods for plasmas; Explicit, semi-implicit, and implicit time integrations; Implicit PIC formulation (Jacobian-Free Newton-Krylovmore » (JFNK) with nonlinear elimination allows different treatments of disparate scales, discrete conservation properties (energy, charge, canonical momentum, etc.)); Some numerical examples; and Summary.« less

Early time evolution of a localized nonlinear excitation in the β-FPUT chain

NASA Astrophysics Data System (ADS)

Kashyap, Rahul; Westley, Alexandra; Datta, Amitava; Sen, Surajit

2017-04-01

We present the detailed dynamics of the particles in the β-Fermi-Pasta-Ulam-Tsingou (FPUT) chain after the initiation of a localized nonlinear excitation (LNE) by squeezing a central bond in the monodispersed chain at time t = 0 while all other particles remain in their original relaxed positions. In the absence of phonons in the system, the LNE appears to initiate its relaxation process by symmetrically emitting two very weak solitary waves. The next stage involves the spreading of the LNE and the formation of nonsolitary wave-like objects to broaden the excitation region until a stage is reached when many weak solitary wave-like objects can be emitted as the system begins its journey to quasi-equilibrium and then to equilibrium. In addition to being of fundamental interest, these systems may be realized using cantilever systems and could well hold the key to constructing the next generation of broadband energy harvesting systems.

Scaling Laws of Nonlinear Rayleigh-Taylor and Richtmyer-Meshkov Instabilities in Two and Three Dimensions (IFSA 1999)

NASA Astrophysics Data System (ADS)

Shvarts, D.; Oron, D.; Kartoon, D.; Rikanati, A.; Sadot, O.; Srebro, Y.; Yedvab, Y.; Ofer, D.; Levin, A.; Sarid, E.; Ben-Dor, G.; Erez, L.; Erez, G.; Yosef-Hai, A.; Alon, U.; Arazi, L.

2016-10-01

The late-time nonlinear evolution of the Rayleigh-Taylor (RT) and Richtmyer-Meshkov (RM) instabilities for random initial perturbations is investigated using a statistical mechanics model based on single-mode and bubble-competition physics at all Atwood numbers (A) and full numerical simulations in two and three dimensions. It is shown that the RT mixing zone bubble and spike fronts evolve as h ~ α · A · gt2 with different values of a for the bubble and spike fronts. The RM mixing zone fronts evolve as h ~ tθ with different values of θ for bubbles and spikes. Similar analysis yields a linear growth with time of the Kelvin-Helmholtz mixing zone. The dependence of the RT and RM scaling parameters on A and the dimensionality will be discussed. The 3D predictions are found to be in good agreement with recent Linear Electric Motor (LEM) experiments.

Alfven wave transport effects in the time evolution of parallel cosmic-ray modified shocks

NASA Technical Reports Server (NTRS)

Jones, T. W.

1993-01-01

Some of the issues associated with a more complete treatment of Alfven transport in cosmic ray shocks are explored qualitatively. The treatment is simplified in some important respects, but some new issues are examined and for the first time a nonlinear, time dependent study of plane cosmic ray mediated shocks with both the entropy producing effects of wave dissipation and effects due to the Alfven wave advection of the cosmic ray relative to the gas is included. Examination of the direct consequences of including the pressure and energy of the Alfven waves in the formalism began.

Comparing TCV experimental VDE responses with DINA code simulations

NASA Astrophysics Data System (ADS)

Favez, J.-Y.; Khayrutdinov, R. R.; Lister, J. B.; Lukash, V. E.

2002-02-01

The DINA free-boundary equilibrium simulation code has been implemented for TCV, including the full TCV feedback and diagnostic systems. First results showed good agreement with control coil perturbations and correctly reproduced certain non-linear features in the experimental measurements. The latest DINA code simulations, presented in this paper, exploit discharges with different cross-sectional shapes and different vertical instability growth rates which were subjected to controlled vertical displacement events (VDEs), extending previous work with the DINA code on the DIII-D tokamak. The height of the TCV vessel allows observation of the non-linear evolution of the VDE growth rate as regions of different vertical field decay index are crossed. The vertical movement of the plasma is found to be well modelled. For most experiments, DINA reproduces the S-shape of the vertical displacement in TCV with excellent precision. This behaviour cannot be modelled using linear time-independent models because of the predominant exponential shape due to the unstable pole of any linear time-independent model. The other most common equilibrium parameters like the plasma current Ip, the elongation κ, the triangularity δ, the safety factor q, the ratio between the averaged plasma kinetic pressure and the pressure of the poloidal magnetic field at the edge of the plasma βp, and the internal self inductance li also show acceptable agreement. The evolution of the growth rate γ is estimated and compared with the evolution of the closed-loop growth rate calculated with the RZIP linear model, confirming the origin of the observed behaviour.

Nonlinear evolution of the first mode supersonic oblique waves in compressible boundary layers. Part 1: Heated/cooled walls

NASA Technical Reports Server (NTRS)

Gajjar, J. S. B.

1993-01-01

The nonlinear stability of an oblique mode propagating in a two-dimensional compressible boundary layer is considered under the long wave-length approximation. The growth rate of the wave is assumed to be small so that the concept of unsteady nonlinear critical layers can be used. It is shown that the spatial/temporal evolution of the mode is governed by a pair of coupled unsteady nonlinear equations for the disturbance vorticity and density. Expressions for the linear growth rate show clearly the effects of wall heating and cooling and in particular how heating destabilizes the boundary layer for these long wavelength inviscid modes at O(1) Mach numbers. A generalized expression for the linear growth rate is obtained and is shown to compare very well for a range of frequencies and wave-angles at moderate Mach numbers with full numerical solutions of the linear stability problem. The numerical solution of the nonlinear unsteady critical layer problem using a novel method based on Fourier decomposition and Chebychev collocation is discussed and some results are presented.

Discharging dynamics in an electrolytic cell

NASA Astrophysics Data System (ADS)

Feicht, Sarah E.; Frankel, Alexandra E.; Khair, Aditya S.

2016-07-01

We analyze the dynamics of a discharging electrolytic cell comprised of a binary symmetric electrolyte between two planar, parallel blocking electrodes. When a voltage is initially applied, ions in the electrolyte migrate towards the electrodes, forming electrical double layers. After the system reaches steady state and the external current decays to zero, the applied voltage is switched off and the cell discharges, with the ions eventually returning to a uniform spatial concentration. At voltages on the order of the thermal voltage VT=kBT /q ≃25 mV, where kB is Boltzmann's constant, T is temperature, and q is the charge of a proton, experiments on surfactant-doped nonpolar fluids observe that the temporal evolution of the external current during charging and discharging is not symmetric [V. Novotny and M. A. Hopper, J. Electrochem. Soc. 126, 925 (1979), 10.1149/1.2129195; P. Kornilovitch and Y. Jeon, J. Appl. Phys. 109, 064509 (2011), 10.1063/1.3554445]. In fact, at sufficiently large voltages (several VT), the current during discharging is no longer monotonic: it displays a "reverse peak" before decaying in magnitude to zero. We analyze the dynamics of discharging by solving the Poisson-Nernst-Planck equations governing ion transport via asymptotic and numerical techniques in three regimes. First, in the "linear regime" when the applied voltage V is formally much less than VT, the charging and discharging currents are antisymmetric in time; however, the potential and charge density profiles during charging and discharging are asymmetric. The current evolution is on the R C timescale of the cell, λDL /D , where L is the width of the cell, D is the diffusivity of ions, and λD is the Debye length. Second, in the (experimentally relevant) thin-double-layer limit ɛ =λD/L ≪1 , there is a "weakly nonlinear" regime defined by VT≲V ≲VTln(1 /ɛ ) , where the bulk salt concentration is uniform; thus the R C timescale of the evolution of the current magnitude persists. However, nonlinear, voltage-dependent, capacitance of the double layer is responsible for a break in temporal antisymmetry of the charging and discharging currents. Third, the reverse peak in the discharging current develops in a "strongly nonlinear" regime V ≳VTln(1 /ɛ ) , driven by neutral salt adsorption into the double layers and consequent bulk depletion during charging. The strongly nonlinear regime features current evolution over three timescales. The current decays in magnitude on the double layer relaxation timescale, λD2/D ; then grows exponentially in time towards the reverse peak on the diffusion timescale, L2/D , indicating that the reverse peak is the results of fast diffusion of ions from the double layer layer to the bulk. Following the reverse peak, the current decays exponentially to zero on the R C timescale. Notably, the current at the reverse peak and the time of the reverse peak saturate at large voltages V ≫VTln(1 /ɛ ) . We provide semi-analytic expressions for the saturated reverse peak time and current, which can be used to infer charge carrier diffusivity and concentration from experiments.

Single-shot spectroscopy of broadband Yb fiber laser

NASA Astrophysics Data System (ADS)

Suzuki, Masayuki; Yoneya, Shin; Kuroda, Hiroto

2017-02-01

We have experimentally reported on a real-time single-shot spectroscopy of a broadband Yb-doped fiber (YDF) laser which based on a nonlinear polarization evolution by using a time-stretched dispersive Fourier transformation technique. We have measured an 8000 consecutive single-shot spectra of mode locking and noise-like pulse (NLP), because our developed broadband YDF oscillator can individually operate the mode locking and NLP by controlling a pump LD power and angle of waveplates. A shot-to-shot spectral fluctuation was observed in NLP. For the investigation of pulse formation dynamics, we have measured the spectral evolution in an initial fluctuations of mode locked broadband YDF laser at an intracavity dispersion of 1500 and 6200 fs2 for the first time. In both case, a build-up time between cw and steady-state mode locking was estimated to be 50 us, the dynamics of spectral evolution between cw and mode locking, however, was completely different. A shot-to-shot strong spectral fluctuation, as can be seen in NLP spectra, was observed in the initial timescale of 20 us at the intracavity dispersion of 1500 fs2. These new findings would impact on understanding the birth of the broadband spectral formation in fiber laser oscillator.

Strong nonlinear rupture theory of thin free liquid films

NASA Astrophysics Data System (ADS)

Chi-Chuan, Hwang; Jun-Liang, Chen; Li-Fu, Shen; Cheng-I, Weng

1996-02-01

A simplified governing equation with high-order effects is formulated after a procedure of evaluating the order of magnitude. Furthermore, the nonlinear evolution equations are derived by the Kármán-Polhausen integral method with a specified velocity profile. Particularly, the effects of surface tension, van der Waals potential, inertia and high-order viscous dissipation are taken into consideration in these equation. The numerical results reveal that the rupture time of free film is much shorter than that of a film on a flat plate. It is shown that because of a more complete high-order viscous dissipation effect discussed in the present study, the rupture process of present model is slower than is predicted by the high-order long wave theory.

Turbomachinery Airfoil Design Optimization Using Differential Evolution

NASA Technical Reports Server (NTRS)

Madavan, Nateri K.; Biegel, Bryan A. (Technical Monitor)

2002-01-01

An aerodynamic design optimization procedure that is based on a evolutionary algorithm known at Differential Evolution is described. Differential Evolution is a simple, fast, and robust evolutionary strategy that has been proven effective in determining the global optimum for several difficult optimization problems, including highly nonlinear systems with discontinuities and multiple local optima. The method is combined with a Navier-Stokes solver that evaluates the various intermediate designs and provides inputs to the optimization procedure. An efficient constraint handling mechanism is also incorporated. Results are presented for the inverse design of a turbine airfoil from a modern jet engine. The capability of the method to search large design spaces and obtain the optimal airfoils in an automatic fashion is demonstrated. Substantial reductions in the overall computing time requirements are achieved by using the algorithm in conjunction with neural networks.

Probabilistic density function method for nonlinear dynamical systems driven by colored noise.

PubMed

Barajas-Solano, David A; Tartakovsky, Alexandre M

2016-05-01

We present a probability density function (PDF) method for a system of nonlinear stochastic ordinary differential equations driven by colored noise. The method provides an integrodifferential equation for the temporal evolution of the joint PDF of the system's state, which we close by means of a modified large-eddy-diffusivity (LED) closure. In contrast to the classical LED closure, the proposed closure accounts for advective transport of the PDF in the approximate temporal deconvolution of the integrodifferential equation. In addition, we introduce the generalized local linearization approximation for deriving a computable PDF equation in the form of a second-order partial differential equation. We demonstrate that the proposed closure and localization accurately describe the dynamics of the PDF in phase space for systems driven by noise with arbitrary autocorrelation time. We apply the proposed PDF method to analyze a set of Kramers equations driven by exponentially autocorrelated Gaussian colored noise to study nonlinear oscillators and the dynamics and stability of a power grid. Numerical experiments show the PDF method is accurate when the noise autocorrelation time is either much shorter or longer than the system's relaxation time, while the accuracy decreases as the ratio of the two timescales approaches unity. Similarly, the PDF method accuracy decreases with increasing standard deviation of the noise.

Frequency sweep rates of rising tone electromagnetic ion cyclotron waves: Comparison between nonlinear theory and Cluster observation

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

He, Zhaoguo; University of Chinese Academy of Sciences, Beijing 100049; Zong, Qiugang, E-mail: qgzong@gmail.com

2014-12-15

Resonant pitch angle scattering by electromagnetic ion cyclotron (EMIC) waves has been suggested to account for the rapid loss of ring current ions and radiation belt electrons. For the rising tone EMIC wave (classified as triggered EMIC emission), its frequency sweep rate strongly affects the efficiency of pitch-angle scattering. Based on the Cluster observations, we analyze three typical cases of rising tone EMIC waves. Two cases locate at the nightside (22.3 and 22.6 magnetic local time (MLT)) equatorial region and one case locates at the duskside (18MLT) higher magnetic latitude (λ = –9.3°) region. For the three cases, the time-dependent wave amplitude,more » cold electron density, and cold ion density ratio are derived from satellite data; while the ambient magnetic field, thermal proton perpendicular temperature, and the wave spectral can be directly provided by observation. These parameters are input into the nonlinear wave growth model to simulate the time-frequency evolutions of the rising tones. The simulated results show good agreements with the observations of the rising tones, providing further support for the previous finding that the rising tone EMIC wave is excited through the nonlinear wave growth process.« less

New nonlinear evolution equations from surface theory

NASA Astrophysics Data System (ADS)

Gürses, Metin; Nutku, Yavuz

1981-07-01

We point out that the connection between surfaces in three-dimensional flat space and the inverse scattering problem provides a systematic way for constructing new nonlinear evolution equations. In particular we study the imbedding for Guichard surfaces which gives rise to the Calapso-Guichard equations generalizing the sine-Gordon (SG) equation. Further, we investigate the geometry of surfaces and their imbedding which results in the Korteweg-deVries (KdV) equation. Then by constructing a family of applicable surfaces we obtain a generalization of the KdV equation to a compressible fluid.

Nonlocal Sediment Transport on Steep Lateral Moraines, Eastern Sierra Nevada, California, USA

NASA Astrophysics Data System (ADS)

Doane, Tyler H.; Furbish, David Jon; Roering, Joshua J.; Schumer, Rina; Morgan, Daniel J.

2018-01-01

Recent work has highlighted the significance of long-distance particle motions in hillslope sediment transport. Such motions imply that the flux at a given hillslope position is appropriately described as a weighted function of surrounding conditions that influence motions reaching the given position. Although the idea of nonlocal sediment transport is well grounded in theory, limited field evidence has been provided. We test local and nonlocal formulations of the flux and compare their ability to reproduce land surface profiles of steep moraines in California. We show that nonlocal and nonlinear models better reproduce evolved land surface profiles, notably the amount of lowering and concavity near the moraine crest and the lengthening and straightening of the depositional apron. The analysis provides the first estimates of key parameters that set sediment entrainment rates and travel distances in nonlocal formulations and highlights the importance of correctly specifying the entrainment rate when modeling land surface evolution. Moraine evolution associated with nonlocal and nonlinear transport formulations, when described in terms of the evolution of the Fourier transform of the moraine surface, displays a distinct behavior involving growth of certain wave numbers, in contrast to the decay of all wave numbers associated with linear transport. Nonlinear and nonlocal formulations share key mathematical elements yielding a nonlinear relation between the flux and the land surface slope.

Multidimensional Time-Resolved Spectroscopy of Vibrational Coherence in Biopolyenes

NASA Astrophysics Data System (ADS)

Buckup, Tiago; Motzkus, Marcus

2014-04-01

Multidimensional femtosecond time-resolved vibrational coherence spectroscopy allows one to investigate the evolution of vibrational coherence in electronic excited states. Methods such as pump-degenerate four-wave mixing and pump-impulsive vibrational spectroscopy combine an initial ultrashort laser pulse with a nonlinear probing sequence to reinduce vibrational coherence exclusively in the excited states. By carefully exploiting specific electronic resonances, one can detect vibrational coherence from 0 cm-1 to over 2,000 cm-1 and map its evolution. This review focuses on the observation and mapping of high-frequency vibrational coherence for all-trans biological polyenes such as β-carotene, lycopene, retinal, and retinal Schiff base. We discuss the role of molecular symmetry in vibrational coherence activity in the S1 electronic state and the interplay of coupling between electronic states and vibrational coherence.

Modelling of NSTX hot vertical displacement events using M 3 D -C 1

NASA Astrophysics Data System (ADS)

Pfefferlé, D.; Ferraro, N.; Jardin, S. C.; Krebs, I.; Bhattacharjee, A.

2018-05-01

The main results of an intense vertical displacement event (VDE) modelling activity using the implicit 3D extended MHD code M3D-C1 are presented. A pair of nonlinear 3D simulations are performed using realistic transport coefficients based on the reconstruction of a so-called NSTX frozen VDE where the feedback control was purposely switched off to trigger a vertical instability. The vertical drift phase is solved assuming axisymmetry until the plasma contacts the first wall, at which point the intricate evolution of the plasma, decaying to large extent in force-balance with induced halo/wall currents, is carefully resolved via 3D nonlinear simulations. The faster 2D nonlinear runs allow to assess the sensitivity of the simulations to parameter changes. In the limit of perfectly conducting wall, the expected linear relation between vertical growth rate and wall resistivity is recovered. For intermediate wall resistivities, the halo region contributes to slowing the plasma down, and the characteristic VDE time depends on the choice of halo temperature. The evolution of the current quench and the onset of 3D halo/eddy currents are diagnosed in detail. The 3D simulations highlight a rich structure of toroidal modes, penetrating inwards from edge to core and cascading from high-n to low-n mode numbers. The break-up of flux-surfaces results in a progressive stochastisation of field-lines precipitating the thermalisation of the plasma with the wall. The plasma current then decays rapidly, inducing large currents in the halo region and the wall. Analysis of normal currents flowing in and out of the divertor plate reveals rich time-varying patterns.

Combining in silico evolution and nonlinear dimensionality reduction to redesign responses of signaling networks

NASA Astrophysics Data System (ADS)

Prescott, Aaron M.; Abel, Steven M.

2016-12-01

The rational design of network behavior is a central goal of synthetic biology. Here, we combine in silico evolution with nonlinear dimensionality reduction to redesign the responses of fixed-topology signaling networks and to characterize sets of kinetic parameters that underlie various input-output relations. We first consider the earliest part of the T cell receptor (TCR) signaling network and demonstrate that it can produce a variety of input-output relations (quantified as the level of TCR phosphorylation as a function of the characteristic TCR binding time). We utilize an evolutionary algorithm (EA) to identify sets of kinetic parameters that give rise to: (i) sigmoidal responses with the activation threshold varied over 6 orders of magnitude, (ii) a graded response, and (iii) an inverted response in which short TCR binding times lead to activation. We also consider a network with both positive and negative feedback and use the EA to evolve oscillatory responses with different periods in response to a change in input. For each targeted input-output relation, we conduct many independent runs of the EA and use nonlinear dimensionality reduction to embed the resulting data for each network in two dimensions. We then partition the results into groups and characterize constraints placed on the parameters by the different targeted response curves. Our approach provides a way (i) to guide the design of kinetic parameters of fixed-topology networks to generate novel input-output relations and (ii) to constrain ranges of biological parameters using experimental data. In the cases considered, the network topologies exhibit significant flexibility in generating alternative responses, with distinct patterns of kinetic rates emerging for different targeted responses.

Plasma Waves Associated with Mass-Loaded Comets

NASA Technical Reports Server (NTRS)

Tsurutani, Bruce; Glassmeier, Karl-Heinz

2015-01-01

Plasma waves and instabilities are integrally involved with the plasma "pickup" process and the mass loading of the solar wind (thus the formation of ion tails and the magnetic tails). Anisotropic plasmas generated by solar wind-comet interactions (the bow shock, magnetic field pileup) cause the generation of plasma waves which in turn "smooth out" these discontinuities. The plasma waves evolve and form plasma turbulence. Comets are perhaps the best "laboratories" to study waves and turbulence because over time (and distance) one can identify the waves and their evolution. We will argue that comets in some ways are better laboratories than magnetospheres, interplanetary space and fusion devices to study nonlinear waves and their evolution.

Real-time full-field characterization of transient dissipative soliton dynamics in a mode-locked laser

NASA Astrophysics Data System (ADS)

Ryczkowski, P.; Närhi, M.; Billet, C.; Merolla, J.-M.; Genty, G.; Dudley, J. M.

2018-04-01

Dissipative solitons are remarkably localized states of a physical system that arise from the dynamical balance between nonlinearity, dispersion and environmental energy exchange. They are the most universal form of soliton that can exist, and are seen in far-from-equilibrium systems in many fields, including chemistry, biology and physics. There has been particular interest in studying their properties in mode-locked lasers, but experiments have been limited by the inability to track the dynamical soliton evolution in real time. Here, we use simultaneous dispersive Fourier transform and time-lens measurements to completely characterize the spectral and temporal evolution of ultrashort dissipative solitons as their dynamics pass through a transient unstable regime with complex break-up and collisions before stabilization. Further insight is obtained from reconstruction of the soliton amplitude and phase and calculation of the corresponding complex-valued eigenvalue spectrum. These findings show how real-time measurements provide new insights into ultrafast transient dynamics in optics.

Space-time-modulated stochastic processes

NASA Astrophysics Data System (ADS)

Giona, Massimiliano

2017-10-01

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

Wave-Kinetic Simulations of the Nonlinear Generation of Electromagnetic VLF Waves through Velocity Ring Instabilities

NASA Astrophysics Data System (ADS)

Ganguli, G.; Crabtree, C. E.; Rudakov, L.; Mithaiwala, M.

2014-12-01

Velocity ring instabilities are a common naturally occuring magnetospheric phenomenon that can also be generated by man made ionospheric experiments. These instabilities are known to generate lower-hybrid waves, which generally cannot propagte out of the source region. However, nonlinear wave physics can convert these linearly driven electrostatic lower-hybrid waves into electromagnetic waves that can escape the source region. These nonlinearly generated waves can be an important source of VLF turbulence that controls the trapped electron lifetime in the radiation belts. We develop numerical solutions to the wave-kinetic equation in a periodic box including the effects of nonlinear (NL) scattering (nonlinear Landau damping) of Lower-hybrid waves giving the evolution of the wave-spectra in wavenumber space. Simultaneously we solve the particle diffusion equation of both the background plasma particles and the ring ions, due to both linear and nonlinear Landau resonances. At initial times for cold ring ions, an electrostatic beam mode is excited, while the kinetic mode is stable. As the instability progresses the ring ions heat, the beam mode is stabilized, and the kinetic mode destabilizes. When the amplitude of the waves becomes sufficient the lower-hybrid waves are scattered (by either nearly unmagnetized ions or magnetized electrons) into electromagnetic magnetosonic waves [Ganguli et al 2010]. The effect of NL scattering is to limit the amplitude of the waves, slowing down the quasilinear relaxation time and ultimately allowing more energy from the ring to be liberated into waves [Mithaiwala et al. 2011]. The effects of convection out of the instability region are modeled, additionally limiting the amplitude of the waves, allowing further energy to be liberated from the ring [Scales et al., 2012]. Results are compared to recent 3D PIC simulations [Winske and Duaghton 2012].

Flow regimes for fluid injection into a confined porous medium

DOE PAGES

Zheng, Zhong; Guo, Bo; Christov, Ivan C.; ...

2015-02-24

We report theoretical and numerical studies of the flow behaviour when a fluid is injected into a confined porous medium saturated with another fluid of different density and viscosity. For a two-dimensional configuration with point source injection, a nonlinear convection–diffusion equation is derived to describe the time evolution of the fluid–fluid interface. In the early time period, the fluid motion is mainly driven by the buoyancy force and the governing equation is reduced to a nonlinear diffusion equation with a well-known self-similar solution. In the late time period, the fluid flow is mainly driven by the injection, and the governingmore » equation is approximated by a nonlinear hyperbolic equation that determines the global spreading rate; a shock solution is obtained when the injected fluid is more viscous than the displaced fluid, whereas a rarefaction wave solution is found when the injected fluid is less viscous. In the late time period, we also obtain analytical solutions including the diffusive term associated with the buoyancy effects (for an injected fluid with a viscosity higher than or equal to that of the displaced fluid), which provide the structure of the moving front. Numerical simulations of the convection–diffusion equation are performed; the various analytical solutions are verified as appropriate asymptotic limits, and the transition processes between the individual limits are demonstrated.« less

Spectral evolution of weakly nonlinear random waves: kinetic description vs direct numerical simulations

NASA Astrophysics Data System (ADS)

Annenkov, Sergei; Shrira, Victor

2016-04-01

We study numerically the long-term evolution of water wave spectra without wind forcing, using three different models, aiming at understanding the role of different sets of assumptions. The first model is the classical Hasselmann kinetic equation (KE). We employ the WRT code kindly provided by G. van Vledder. Two other models are new. As the second model, we use the generalised kinetic equation (gKE), derived without the assumption of quasi-stationarity. Thus, unlike the KE, the gKE is valid in the cases when a wave spectrum is changing rapidly (e.g. at the initial stage of evolution of a narrow spectrum). However, the gKE employs the same statistical closure as the KE. The third model is based on the Zakharov integrodifferential equation for water waves and does not depend on any statistical assumptions. Since the Zakharov equation plays the role of the primitive equation of the theory of wave turbulence, we refer to this model as direct numerical simulation of spectral evolution (DNS-ZE). For initial conditions, we choose two narrow-banded spectra with the same frequency distribution (a JONSWAP spectrum with high peakedness γ = 6) and different degrees of directionality. These spectra are from the set of observations collected in a directional wave tank by Onorato et al (2009). Spectrum A is very narrow in angle (corresponding to N = 840 in the cosN directional model). Spectrum B is initially wider in angle (corresponds to N = 24). Short-term evolution of both spectra (O(102) wave periods) has been studied numerically by Xiao et al (2013) using two other approaches (broad-band modified nonlinear Schrödinger equation and direct numerical simulation based on the high-order spectral method). We use these results to verify the initial stage of our DNS-ZE simulations. However, the advantage of the DNS-ZE method is that it allows to study long-term spectral evolution (up to O(104) periods), which was previously possible only with the KE. In the short-term evolution, we find a good agreement between our DNS-ZE results and simulations by Xiao et al (2013), both for the evolution of frequency spectra and for the directional spreading. In the long term, all three approaches demonstrate very close evolution of integral characteristics of spectra, approaching for large time the theoretical asymptotes of the self-similar stage of evolution. However, the detailed comparison of the spectral evolution shows certain notable differences. Both kinetic equations give virtually identical evolution of spectrum B, but in the case of initially nearly one-dimensional spectrum A the KE overestimates the amplitude of the spectral peak. Meanwhile, the DNS-ZE results show considerably wider spectra with less pronounced peak. There is a striking difference for the rate of spectral broadening, which is much larger for the gKE and especially for the KE, than for the DNS-ZE. We show that the rates of change of the spectra obtained with the DNS-ZE are proportional to the fourth power of nonlinearity, corresponding to the dynamical timescale of evolution, rather than the statistical timescale of both kinetic equations.

Weak Nonlinearity Effects in TG and EAW Modes

NASA Astrophysics Data System (ADS)

Ashourvan, Arash; Dubin, Daniel H. E.

2013-10-01

We have studied the nonlinear coupling of Trivelpiece-Gould modes as well as EAW modes, in a cylindrically symmetric plasma with average density n0 and periodic boundary conditions at the axial ends of plasma. For Trivelpiece-Gould modes, the cold fluid formalism gives the slow time evolution of mode amplitudes due to nonlinear couplings. For EAW modes, the Vlasov-Poisson formalism is required. We analyze the coupling between mode mz = 2 with frequency ω2 and mode mz = 1 with frequency ω1, with initial density perturbations n2 (0) >>n1 (0) . For small detuning Δω ≡ 2ω1 -ω2 <<ω1n2 (0) /n0 , mode amplitude n1 grows exponentially in time due to resonant parametric interaction with mode mz = 2 , at a rate Γ which is linearly propotional to n2 (0) . For Δω >>ω1n2 (0) /n0 , mode amplitude n1 oscillates about its initial value, with frequency Δω and amplitude n1(2) ~n2 (0) n1 (0) . In both cases the theory is consistent with experiments. Work supported by PHY-0903877, DE-SC0002451, DE-SC0008693.

Nonlinear simulation of the fishbone instability

NASA Astrophysics Data System (ADS)

Idouakass, Malik; Faganello, Matteo; Berk, Herbert; Garbet, Xavier; Benkadda, Sadruddin; PIIM Team; IFS Team; IRFM Team

2014-10-01

We propose to extend the Odblom-Breizman precessional fishbone model to account for both the MagnetoHydroDynamic (MHD) nonlinearity at the q = 1 surface and the nonlinear response of the energetic particles contained within the q = 1 surface. This electromagnetic mode, whose excitation, damping and frequency chirping are determined by the self-consistent interaction between an energetic trapped particle population and the bulk plasma evolution, can induce effective transport and losses for the energetic particles, being them alpha-particles in next-future fusion devices or heated particles in present Tokamaks. The model is reduced to its simplest form, assuming a reduced MHD description for the bulk plasma and a two-dimensional phase-space evolution (gyro and bounce averaged) for deeply trapped energetic particles. Numerical simulations have been performed in order to characterize the mode chirping and saturation, in particular looking at the interplay between the development of phase-space structures and the system dissipation associated to the MHD non-linearities at the resonance locations.

Nonlinear evolution of magnetic flux ropes. I - Low-beta limit

NASA Technical Reports Server (NTRS)

Osherovich, V. A.; Farrugia, C. J.; Burlaga, L. F.

1993-01-01

We study the nonlinear self-similar evolution of a cylindrical magnetic flux tube with two components of the magnetic field, axial and azimuthal. We restrict ourselves to the case of a plasma of low beta. Introducing a special class of configurations we call 'separable fields', we reduce the problem to an ordinary differential equation. Two cases are to be distinguished: (1) when the total field minimizes on the symmetry axis, the magnetic configuration inexorably collapses, and (2) when, on the other hand, the total field maximizes on the symmetry axis, the magnetic configuration behaves analogously to a nonlinear oscillator. Here we focus on the latter case. The effective potential of the motion contains two terms: a strong repulsive term and a weak restoring term associated with the pinch. We solve the nonlinear differential equation of motion numerically and find that the period of oscillations grows exponentially with the energy of the oscillator. Our treatment emphasizes the role of the force-free configuration as the lowest potential energy state about which the system oscillates.

Families of stable solitons and excitations in the PT-symmetric nonlinear Schrödinger equations with position-dependent effective masses.

PubMed

Chen, Yong; Yan, Zhenya; Mihalache, Dumitru; Malomed, Boris A

2017-04-28

Since the parity-time-([Formula: see text]-) symmetric quantum mechanics was put forward, fundamental properties of some linear and nonlinear models with [Formula: see text]-symmetric potentials have been investigated. However, previous studies of [Formula: see text]-symmetric waves were limited to constant diffraction coefficients in the ambient medium. Here we address effects of variable diffraction coefficient on the beam dynamics in nonlinear media with generalized [Formula: see text]-symmetric Scarf-II potentials. The broken linear [Formula: see text] symmetry phase may enjoy a restoration with the growing diffraction parameter. Continuous families of one- and two-dimensional solitons are found to be stable. Particularly, some stable solitons are analytically found. The existence range and propagation dynamics of the solitons are identified. Transformation of the solitons by means of adiabatically varying parameters, and collisions between solitons are studied too. We also explore the evolution of constant-intensity waves in a model combining the variable diffraction coefficient and complex potentials with globally balanced gain and loss, which are more general than [Formula: see text]-symmetric ones, but feature similar properties. Our results may suggest new experiments for [Formula: see text]-symmetric nonlinear waves in nonlinear nonuniform optical media.

Nonlinear waveform distortion and shock formation in the near field of a continuous wave piston source

NASA Astrophysics Data System (ADS)

Sapozhnikov, Oleg A.; Khokhlova, Vera A.; Cathignol, Dominique

2004-05-01

A classical effect of nonlinear acoustics is that a plane sinusoidal acoustic wave propagating in a nonlinear medium transforms to a sawtooth wave with one shock per cycle. However, the waveform evolution can be quite different in the near field of a plane source due to diffraction. Previous numerical simulations of nonlinear acoustic waves in the near field of a circular piston source predict the development of two shocks per wave cycle [Khokhlova et al., J. Acoust. Soc. Am. 110, 95-108 (2001)]. Moreover, at some locations the peak pressure may be up to 4 times the source amplitude. The motivation of this work was to experimentally verify and further explain the phenomena of the nonlinear waveform distortion. Measurements were conducted in water with a 47-mm-diameter unfocused transducer, working at 1-MHz frequency. For pressure amplitudes higher than 0.5 MPa, two shocks per cycle were observed in the waveform beyond the last minimum of the fundamental harmonic amplitude. With the increase of the observation distance, these two shocks collided and formed one shock (per cycle), i.e., the waveform developed into the classical sawtooth wave. The experimental results were in a very good agreement with the modeling based on the Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation.

Time-local equation for exact time-dependent optimized effective potential in time-dependent density functional theory

NASA Astrophysics Data System (ADS)

Liao, Sheng-Lun; Ho, Tak-San; Rabitz, Herschel; Chu, Shih-I.

2017-04-01

Solving and analyzing the exact time-dependent optimized effective potential (TDOEP) integral equation has been a longstanding challenge due to its highly nonlinear and nonlocal nature. To meet the challenge, we derive an exact time-local TDOEP equation that admits a unique real-time solution in terms of time-dependent Kohn-Sham orbitals and effective memory orbitals. For illustration, the dipole evolution dynamics of a one-dimension-model chain of hydrogen atoms is numerically evaluated and examined to demonstrate the utility of the proposed time-local formulation. Importantly, it is shown that the zero-force theorem, violated by the time-dependent Krieger-Li-Iafrate approximation, is fulfilled in the current TDOEP framework. This work was partially supported by DOE.

Study of dispersive and nonlinear effects of coastal wave dynamics with a fully nonlinear potential flow model

NASA Astrophysics Data System (ADS)

Benoit, Michel; Yates, Marissa L.; Raoult, Cécile

2017-04-01

Efficient and accurate numerical models simulating wave propagation are required for a variety of engineering projects including the evaluation of coastal risks, the design of protective coastal structures, and the estimation of the potential for marine renewable energy devices. Nonlinear and dispersive effects are particularly significant in the coastal zone where waves interact with the bottom, the shoreline, and coastal structures. The main challenge in developing a numerical models is finding a compromise between computational efficiency and the required accuracy of the simulated wave field. Here, a potential approach is selected and the (fully nonlinear) water wave problem is formulated using the Euler-Zakharov equations (Zakharov, 1968) describing the temporal evolution of the free surface elevation and velocity potential. The proposed model (Yates and Benoit, 2015) uses a spectral approach in the vertical (i.e. the vertical variation of the potential is approximated by a linear combination of the first NT+1 Chebyshev polynomials, following the work of Tian and Sato (2008)). The Zakharov equations are integrated in time using a fourth-order Runge-Kutta scheme with a constant time step. At each sub-timestep, the Laplace Boundary Value Problem (BVP) is solved to estimate the free surface vertical velocity using the spectral approach, with typical values of NT between 5 to 8 for practical applications. The 1DH version of the code is validated with comparisons to the experimental data set of Becq-Girard et al. (1999), which studied the propagation of irregular waves over a beach profile with a submerged bar. The nonlinear and dispersive capacities of the model are verified with the correct representation of wave-wave interactions, in particular the transfer of energy between different harmonic components during wave propagation (analysis of the transformation of the variance spectrum along the channel). Evolution of wave skewness, asymmetry and kurtosis along the bathymetric profile also compare well with the measured values. The statistical distributions of the free surface elevation and wave height, calculated from the simulated time series, are compared to those of the measurements, with particular attention paid to the extreme waves. To use this model for realistic cases with complex bathymetric variations and multidirectional wave fields, the model has been extended to two horizontal dimensions (2DH). The spectral approach in the vertical dimension is retained, while the horizontal plane is discretized with scattered nodes to maintain the model's flexibility. The horizontal derivatives are estimated with finite-difference type formulas using Radial Basis Functions (Wright and Fornberg, 2006). The 2DH version of the code is applied to simulate the propagation of regular waves over a semi-circular step, which acts as a focusing lens. The simulation results are compared to the experimental data set of Whalin (1971). The evolution of the higher harmonic amplitudes in the shallow-water zone demonstrates the ability of the model to simulate wave propagation over complex 2DH coastal bathymetries. References: Becq-Girard F., Forget P., Benoit M. (1999) Non-linear propagation of unidirectional wave fields over varying topography. Coastal Eng., 38, 91-113. Tian Y., Sato S. (2008) A numerical model on the interaction between nearshore nonlinear waves and strong currents. Coast. Eng. Journal, 50(4), 369-395. Whalin R.W. (1971) The limit of applicability of linear wave refraction theory in a convergence zone. Technical report, DTIC Documents. Wright G.B., Fornberg B. (2006) Scattered node compact finite difference-type formulas generated from radial basis functions. J. Comp. Phys., 212, 99-123. Yates M.L., Benoit M. (2015) Accuracy and efficiency of two numerical methods of solving the potential flow problem for highly nonlinear and dispersive water waves. Int. J. Numer. Meth. Fluids, 77, 616-640. Zakharov V.E. (1968) Stability of periodic waves of finite amplitude on the surface of a deep fluid. J. Appl. Mech. Tech. Phys., 9(2), 190-194.

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

PubMed

Venturi, D; Karniadakis, G E

2014-06-08

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

Nonlinear electrodynamics and CMB polarization

NASA Astrophysics Data System (ADS)

Mosquera Cuesta, Herman J.; Lambiase, G.

2011-03-01

Recently WMAP and BOOMERanG experiments have set stringent constraints on the polarization angle of photons propagating in an expanding universe: Δα = (-2.4±1.9)°. The polarization of the Cosmic Microwave Background radiation (CMB) is reviewed in the context of nonlinear electrodynamics (NLED). We compute the polarization angle of photons propagating in a cosmological background with planar symmetry. For this purpose, we use the Pagels-Tomboulis (PT) Lagrangian density describing NLED, which has the form L ~ (X/Λ4)δ-1 X, where X = ¼FαβFαβ, and δ the parameter featuring the non-Maxwellian character of the PT nonlinear description of the electromagnetic interaction. After looking at the polarization components in the plane orthogonal to the (x)-direction of propagation of the CMB photons, the polarization angle is defined in terms of the eccentricity of the universe, a geometrical property whose evolution on cosmic time (from the last scattering surface to the present) is constrained by the strength of magnetic fields over extragalactic distances.

Nonlinear Large Scale Flow in a Precessing Cylinder and Its Ability To Drive Dynamo Action

NASA Astrophysics Data System (ADS)

Giesecke, André; Vogt, Tobias; Gundrum, Thomas; Stefani, Frank

2018-01-01

We have conducted experimental measurements and numerical simulations of a precession-driven flow in a cylindrical cavity. The study is dedicated to the precession dynamo experiment currently under construction at Helmholtz-Zentrum Dresden-Rossendorf and aims at the evaluation of the hydrodynamic flow with respect to its ability to drive a dynamo. We focus on the strongly nonlinear regime in which the flow is essentially composed of the directly forced primary Kelvin mode and higher modes in terms of standing inertial waves arising from nonlinear self-interactions. We obtain an excellent agreement between experiment and simulation with regard to both flow amplitudes and flow geometry. A peculiarity is the resonance-like emergence of an axisymmetric mode that represents a double roll structure in the meridional plane. Kinematic simulations of the magnetic field evolution induced by the time-averaged flow yield dynamo action at critical magnetic Reynolds numbers around Rmc≈430 , which is well within the range of the planned liquid sodium experiment.

Analytic study of solutions for a (3 + 1) -dimensional generalized KP equation

NASA Astrophysics Data System (ADS)

Gao, Hui; Cheng, Wenguang; Xu, Tianzhou; Wang, Gangwei

2018-03-01

The (3 + 1) -dimensional generalized KP (gKP) equation is an important nonlinear partial differential equation in theoretical and mathematical physics which can be used to describe nonlinear wave motion. Through the Hirota bilinear method, one-solition, two-solition and N-solition solutions are derived via symbolic computation. Two classes of lump solutions, rationally localized in all directions in space, to the dimensionally reduced cases in (2 + 1)-dimensions, are constructed by using a direct method based on the Hirota bilinear form of the equation. It implies that we can derive the lump solutions of the reduced gKP equation from positive quadratic function solutions to the aforementioned bilinear equation. Meanwhile, we get interaction solutions between a lump and a kink of the gKP equation. The lump appears from a kink and is swallowed by it with the change of time. This work offers a possibility which can enrich the variety of the dynamical features of solutions for higher-dimensional nonlinear evolution equations.

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

PubMed Central

Venturi, D.; Karniadakis, G. E.

2014-01-01

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

Nonlinear Large Scale Flow in a Precessing Cylinder and Its Ability To Drive Dynamo Action.

PubMed

Giesecke, André; Vogt, Tobias; Gundrum, Thomas; Stefani, Frank

2018-01-12

We have conducted experimental measurements and numerical simulations of a precession-driven flow in a cylindrical cavity. The study is dedicated to the precession dynamo experiment currently under construction at Helmholtz-Zentrum Dresden-Rossendorf and aims at the evaluation of the hydrodynamic flow with respect to its ability to drive a dynamo. We focus on the strongly nonlinear regime in which the flow is essentially composed of the directly forced primary Kelvin mode and higher modes in terms of standing inertial waves arising from nonlinear self-interactions. We obtain an excellent agreement between experiment and simulation with regard to both flow amplitudes and flow geometry. A peculiarity is the resonance-like emergence of an axisymmetric mode that represents a double roll structure in the meridional plane. Kinematic simulations of the magnetic field evolution induced by the time-averaged flow yield dynamo action at critical magnetic Reynolds numbers around Rm^{c}≈430, which is well within the range of the planned liquid sodium experiment.

Laboratory tests of short intense envelope solitons

NASA Astrophysics Data System (ADS)

Slunyaev, A.; Clauss, G. F.; Klein, M.; Onorato, M.

2012-04-01

Stability of short intense nonlinear wave groups propagating over deep water is tested in laboratory runs which are performed in the facility of the Technical University of Berlin. The strongly nonlinear simulation of quasi-steady nonlinear wave groups within the framework of the Euler equations is used to generate the surface elevation time series at a border of the water tank. Besides, the exact analytic solution of the nonlinear Schrodinger equation is used for this purpose. The time series is then transformed to a wave maker signal with use of a designed transfer algorithm. Wave group propagation along the tank was recorded by 4 distant gauges and by an array of 6 densely situated gauges. This setup allows to consider the wave evolution from 10 to 85 m from the wave maker, and to obtain the wave envelope shape directly from the instrumental data. In the experiments wave groups were characterized by the steepness values up to kAcr < 0.32 and kAtr < 0.24, where k is the mean wavenumber, Acr is the crest amplitude, and Atr is the trough amplitude; and the maximum local wave slope was up to 0.34. Wave breaking phenomenon was not observed in the experiments. Different mean wave numbers and wave groups of different intensities were considered. In some cases the wave groups exhibit noticeable radiation in the course of propagation, though the groups are not dispersed fully. The effect of finite water depth is found to be significant on the wave group stability. Intense wave groups have shorter time of adjustment, what in some sense may help them to manifest their individuality clearer. The experimental tests confirm recent numerical simulations of fully nonlinear equations, where very steep stable single and interacting nonlinear wave groups were reported [1-3]. The quasi-stationary wave groups observed in numerical and laboratory experiments are strongly nonlinear analogues of the nonlinear Schrodinger envelope solitons. The results emphasize the importance of long-living nonlinear wave groups in dynamics of intense sea waves. [1] V.E. Zakharov, A.I. Dyachenko, A.O. Prokofiev, Eur. J. Mech. B / Fluids 25, 677 (2006). [2] A.I. Dyachenko, V.E. Zakharov, JETP Lett. 88, 307 (2008). [3] A.V. Slunyaev, JETP 109, 676 (2009).

The Evolution of Finite Amplitude Wavetrains in Plane Channel Flow

NASA Technical Reports Server (NTRS)

Hewitt, R. E.; Hall, P.

1996-01-01

We consider a viscous incompressible fluid flow driven between two parallel plates by a constant pressure gradient. The flow is at a finite Reynolds number, with an 0(l) disturbance in the form of a traveling wave. A phase equation approach is used to discuss the evolution of slowly varying fully nonlinear two dimensional wavetrains. We consider uniform wavetrains in detail, showing that the development of a wavenumber perturbation is governed by Burgers equation in most cases. The wavenumber perturbation theory, constructed using the phase equation approach for a uniform wavetrain, is shown to be distinct from an amplitude perturbation expansion about the periodic flow. In fact we show that the amplitude equation contains only linear terms and is simply the heat equation. We review, briefly, the well known dynamics of Burgers equation, which imply that both shock structures and finite time singularities of the wavenumber perturbation can occur with respect to the slow scales. Numerical computations have been performed to identify areas of the (wavenumber, Reynolds number, energy) neutral surface for which each of these possibilities can occur. We note that the evolution equations will breakdown under certain circumstances, in particular for a weakly nonlinear secondary flow. Finally we extend the theory to three dimensions and discuss the limit of a weak spanwise dependence for uniform wavetrains, showing that two functions are required to describe the evolution. These unknowns are a phase and a pressure function which satisfy a pair of linearly coupled partial differential equations. The results obtained from applying the same analysis to the fully three dimensional problem are included as an appendix.

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

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

Blas, Diego; Garny, Mathias; Sibiryakov, Sergey

2016-07-01

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

Open problems of magnetic island control by electron cyclotron current drive

DOE PAGES

Grasso, Daniela; Lazzaro, E.; Borgogno, D.; ...

2016-11-17

This study reviews key aspects of the problem of magnetic islands control by electron cyclotron current drive in fusion devices. On the basis of the ordering of the basic spatial and time scales of the magnetic reconnection physics, we present the established results, highlighting some of the open issues posed by the small-scale structures that typically accompany the nonlinear evolution of the magnetic islands and constrain the effect of the control action.

Widely-pulsewidth-tunable ultrashort pulse generation from a birefringent carbon nanotube mode-locked fiber laser.

PubMed

Liu, Ya; Zhao, Xin; Liu, Jiansheng; Hu, Guoqing; Gong, Zheng; Zheng, Zheng

2014-08-25

We demonstrate the generation of soliton pulses covering a nearly one order-of-magnitude pulsewidth range from a simple carbon nanotube (CNT) mode-locked fiber laser with birefringence. A polarization-maintaining-fiber-pigtailed, inline polarization beam splitter and its associated birefringence is leveraged to either enable additional nonlinear polarization evolution (NPE) mode-locking effect or result in a bandwidth-tunable Lyot filter, through adjusting the intracavity polarization settings. The large pulsewidth tuning range is achieved by exploiting both the nonlinear CNT-NPE hybrid mode-locking mechanism that narrows the pulses and the linear filtering effect that broadens them. Induced vector soliton pulses with pulsewidth from 360 fs to 3 ps can be generated, and their time-bandwidth products indicate they are close to transform-limited.

Nonlinear density wave investigation for an extended car-following model considering driver’s memory and jerk

NASA Astrophysics Data System (ADS)

Jin, Zhizhan; Li, Zhipeng; Cheng, Rongjun; Ge, Hongxia

2018-01-01

Based on the two velocity difference model (TVDM), an extended car-following model is developed to investigate the effect of driver’s memory and jerk on traffic flow in this paper. By using linear stability analysis, the stability conditions are derived. And through nonlinear analysis, the time-dependent Ginzburg-Landau (TDGL) equation and the modified Korteweg-de Vries (mKdV) equation are obtained, respectively. The mKdV equation is constructed to describe the traffic behavior near the critical point. The evolution of traffic congestion and the corresponding energy consumption are discussed. Numerical simulations show that the improved model is found not only to enhance the stability of traffic flow, but also to depress the energy consumption, which are consistent with the theoretical analysis.

Nonlinear solar cycle forecasting: theory and perspectives

NASA Astrophysics Data System (ADS)

Baranovski, A. L.; Clette, F.; Nollau, V.

2008-02-01

In this paper we develop a modern approach to solar cycle forecasting, based on the mathematical theory of nonlinear dynamics. We start from the design of a static curve fitting model for the experimental yearly sunspot number series, over a time scale of 306 years, starting from year 1700 and we establish a least-squares optimal pulse shape of a solar cycle. The cycle-to-cycle evolution of the parameters of the cycle shape displays different patterns, such as a Gleissberg cycle and a strong anomaly in the cycle evolution during the Dalton minimum. In a second step, we extract a chaotic mapping for the successive values of one of the key model parameters - the rate of the exponential growth-decrease of the solar activity during the n-th cycle. We examine piece-wise linear techniques for the approximation of the derived mapping and we provide its probabilistic analysis: calculation of the invariant distribution and autocorrelation function. We find analytical relationships for the sunspot maxima and minima, as well as their occurrence times, as functions of chaotic values of the above parameter. Based on a Lyapunov spectrum analysis of the embedded mapping, we finally establish a horizon of predictability for the method, which allows us to give the most probable forecasting of the upcoming solar cycle 24, with an expected peak height of 93±21 occurring in 2011/2012.

On a quantum mechanical system theory of the origin of life: from the Stapp-model to the origin of natural symbols

NASA Astrophysics Data System (ADS)

Balázs, András

2016-01-01

The Heisenberg-James-Stapp (quantum mechanical) mind model is surveyed and criticized briefly. The criticism points out that the model, while being essentially consistent concerning (human) consciousness, fundamentally lacks the evolutional point of view both onto- and phylogenetically. Ethology and other than Jamesian psychology is quoted and a quantum mechanical theoretical scheme is suggested to essentially extend Stapp's frame in an evolutionary context. It is proposed that its central supposition, spontaneous quantum measurement can be better utilized in an investigation of the origin of the "subjective" process, having come about concomitantly with the chemistry of the origin of life. We dwell on its applicability at this latter process, at its heart standing, it is supposed, the endophysical nonlinear "self-measurement" of (quantum mechanically describable) matter, and so our investigation is extended to this primeval phenomenon. It is suggested that the life phenomenon is an indirect C* → (W*) → C* quantum algebraic process transition, where the (W*) system would represent the living state. Summarized also are our previous results on an internalized, "reversed", time process, introduced originally by Gunji, which is subordinated to the external "forwards" time evolution, driving towards symmetry by gradual space-mappings, where the original splitting-up must have come about in a spontaneous symmetry breaking nonlinear "self-measurement" of matter in an endophysical World.

Radio Evolution of Supernova Remnants Including Nonlinear Particle Acceleration: Insights from Hydrodynamic Simulations

NASA Astrophysics Data System (ADS)

Pavlović, Marko Z.; Urošević, Dejan; Arbutina, Bojan; Orlando, Salvatore; Maxted, Nigel; Filipović, Miroslav D.

2018-01-01

We present a model for the radio evolution of supernova remnants (SNRs) obtained by using three-dimensional hydrodynamic simulations coupled with nonlinear kinetic theory of cosmic-ray (CR) acceleration in SNRs. We model the radio evolution of SNRs on a global level by performing simulations for a wide range of the relevant physical parameters, such as the ambient density, supernova (SN) explosion energy, acceleration efficiency, and magnetic field amplification (MFA) efficiency. We attribute the observed spread of radio surface brightnesses for corresponding SNR diameters to the spread of these parameters. In addition to our simulations of Type Ia SNRs, we also considered SNR radio evolution in denser, nonuniform circumstellar environments modified by the progenitor star wind. These simulations start with the mass of the ejecta substantially higher than in the case of a Type Ia SN and presumably lower shock speed. The magnetic field is understandably seen as very important for the radio evolution of SNRs. In terms of MFA, we include both resonant and nonresonant modes in our large-scale simulations by implementing models obtained from first-principles, particle-in-cell simulations and nonlinear magnetohydrodynamical simulations. We test the quality and reliability of our models on a sample consisting of Galactic and extragalactic SNRs. Our simulations give Σ ‑ D slopes between ‑4 and ‑6 for the full Sedov regime. Recent empirical slopes obtained for the Galactic samples are around ‑5, while those for the extragalactic samples are around ‑4.

Thermodynamic output of single-atom quantum optical amplifiers and their phase-space fingerprint

NASA Astrophysics Data System (ADS)

Perl, Y.; Band, Y. B.; Boukobza, E.

2017-05-01

We analyze a resonant single-atom two-photon quantum optical amplifier both dynamically and thermodynamically. A detailed thermodynamic analysis shows that the nonlinear amplifier is thermodynamically equivalent to the linear amplifier. However, by calculating the Wigner quasiprobability distribution for various initial field states, we show that unique quantum features in optical phase space, absent in the linear amplifier, are retained for extended times, despite the fact that dissipation tends to wash out dynamical features observed at early evolution times. These features are related to the discrete nature of the two-photon matter-field interaction and fingerprint the initial field state at thermodynamic times.

Spectrum Evolution of Accelerating or Slowing down Soliton at its Propagation in a Medium with Gold Nanorods

NASA Astrophysics Data System (ADS)

Trofimov, Vyacheslav A.; Lysak, Tatiana M.

2018-04-01

We investigate both numerically and analytically the spectrum evolution of a novel type soliton - nonlinear chirped accelerating or decelerating soliton - at a femtosecond pulse propagation in a medium containing noble nanoparticles. In our consideration, we take into account one- or two-photon absorption of laser radiation by nanorods, and time-dependent nanorod aspect ratio changing due to their melting or reshaping because of laser energy absorption. The chirped solitons are formed due to the trapping of laser radiation by the nanorods reshaping fronts, if a positive or negative phase-amplitude grating is induced by laser radiation. Accelerating or slowing down chirped soliton formation is accompanied by the soliton spectrum blue or red shift. To prove our numerical results, we derived the approximate analytical law for the spectrum maximum intensity evolution along the propagation coordinate, based on earlier developed approximate analytical solutions for accelerating and decelerating solitons.

Electron acceleration via magnetic island coalescence

NASA Astrophysics Data System (ADS)

Shinohara, I.; Yumura, T.; Tanaka, K. G.; Fujimoto, M.

2009-06-01

Electron acceleration via fast magnetic island coalescence that happens as quick magnetic reconnection triggering (QMRT) proceeds has been studied. We have carried out a three-dimensional full kinetic simulation of the Harris current sheet with a large enough simulation run for two magnetic islands coalescence. Due to the strong inductive electric field associated with the non-linear evolution of the lower-hybrid-drift instability and the magnetic island coalescence process observed in the non-linear stage of the collisionless tearing mode, electrons are significantly accelerated at around the neutral sheet and the subsequent X-line. The accelerated meandering electrons generated by the non-linear evolution of the lower-hybrid-drift instability are resulted in QMRT, and QMRT leads to fast magnetic island coalescence. As a whole, the reconnection triggering and its transition to large-scale structure work as an effective electron accelerator.

A note on a nonlinear equation arising in discussions of the steady fall of a resistive, viscous, isothermal fluid across a magnetic field

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

Tautz, R. C., E-mail: robert.c.tautz@gmail.com; Lerche, I., E-mail: lercheian@yahoo.com

2015-11-15

This note considers the evolution of steady isothermal flow across a uniform magnetic field from an analytic standpoint. This problem is of concern in developments of magnetic fields in the solar corona and for prominence dynamics. Limiting behaviors are obtained to the nonlinear equation describing the flow depending on the value of a single parameter. For the situation where the viscous drag is a small correction to the inviscid flow limiting structures are also outlined. The purpose of the note is to show how one can evaluate some of the analytic properties of the highly nonlinear equation that are ofmore » use in considering the numerical evolution as done in Low and Egan [Phys. Plasmas 21, 062105 (2014)].« less

Emergence, reductionism and landscape response to climate change

NASA Astrophysics Data System (ADS)

Harrison, Stephan; Mighall, Tim

2010-05-01

Predicting landscape response to external forcing is hampered by the non-linear, stochastic and contingent (ie dominated by historical accidents) forcings inherent in landscape evolution. Using examples from research carried out in southwest Ireland we suggest that non-linearity in landform evolution is likely to be a strong control making regional predictions of landscape response to climate change very difficult. While uncertainties in GCM projections have been widely explored in climate science much less attention has been directed by geomorphologists to the uncertainties in landform evolution under conditions of climate change and this problem may be viewed within the context of philosophical approaches to reductionsim and emergence. Understanding the present and future trajectory of landform change may also guide us to provide an enhanced appreciation of how landforms evolved in the past.

On the nonlinear stability of the unsteady, viscous flow of an incompressible fluid in a curved pipe

NASA Technical Reports Server (NTRS)

Shortis, Trudi A.; Hall, Philip

1995-01-01

The stability of the flow of an incompressible, viscous fluid through a pipe of circular cross-section curved about a central axis is investigated in a weakly nonlinear regime. A sinusoidal pressure gradient with zero mean is imposed, acting along the pipe. A WKBJ perturbation solution is constructed, taking into account the need for an inner solution in the vicinity of the outer bend, which is obtained by identifying the saddle point of the Taylor number in the complex plane of the cross-sectional angle co-ordinate. The equation governing the nonlinear evolution of the leading order vortex amplitude is thus determined. The stability analysis of this flow to periodic disturbances leads to a partial differential system dependent on three variables, and since the differential operators in this system are periodic in time, Floquet theory may be applied to reduce this system to a coupled infinite system of ordinary differential equations, together with homogeneous uncoupled boundary conditions. The eigenvalues of this system are calculated numerically to predict a critical Taylor number consistent with the analysis of Papageorgiou. A discussion of how nonlinear effects alter the linear stability analysis is also given, and the nature of the instability determined.

Nonlinearity without superluminality

NASA Astrophysics Data System (ADS)

Kent, Adrian

2005-07-01

Quantum theory is compatible with special relativity. In particular, though measurements on entangled systems are correlated in a way that cannot be reproduced by local hidden variables, they cannot be used for superluminal signaling. As Czachor, Gisin, and Polchinski pointed out, this is not generally true of general nonlinear modifications of the Schrödinger equation. Excluding superluminal signaling has thus been taken to rule out most nonlinear versions of quantum theory. The no-superluminal-signaling constraint has also been used for alternative derivations of the optimal fidelities attainable for imperfect quantum cloning and other operations. These results apply to theories satisfying the rule that their predictions for widely separated and slowly moving entangled systems can be approximated by nonrelativistic equations of motion with respect to a preferred time coordinate. This paper describes a natural way in which this rule might fail to hold. In particular, it is shown that quantum readout devices which display the values of localized pure states need not allow superluminal signaling, provided that the devices display the values of the states of entangled subsystems as defined in a nonstandard, although natural, way. It follows that any locally defined nonlinear evolution of pure states can be made consistent with Minkowski causality.

A Multiscale Nested Modeling Framework to Simulate the Interaction of Surface Gravity Waves with Nonlinear Internal Gravity Waves

DTIC Science & Technology

2015-09-30

We aim at understanding the impact of tidal , seasonal, and mesoscale variability of the internal wave field and how it influences the surface waves ...Interaction of Surface Gravity Waves with Nonlinear Internal Gravity Waves Lian Shen St. Anthony Falls Laboratory and Department of Mechanical...on studying surface gravity wave evolution and spectrum in the presence of surface currents caused by strongly nonlinear internal solitary waves

Self-accelerating parabolic beams in quadratic nonlinear media

NASA Astrophysics Data System (ADS)

Dolev, Ido; Libster, Ana; Arie, Ady

2012-09-01

We present experimental observation of self-accelerating parabolic beams in quadratic nonlinear media. We show that the intensity peaks of the first and second harmonics are asynchronous with respect to one another in the two transverse coordinates. In addition, the two coupled harmonics have the same acceleration within and after the nonlinear medium. We also study the evolution of second harmonic accelerating beams inside the quadratic media and their correlation with theoretical beams.

Analysis of wheezes using wavelet higher order spectral features.

PubMed

Taplidou, Styliani A; Hadjileontiadis, Leontios J

2010-07-01

Wheezes are musical breath sounds, which usually imply an existing pulmonary obstruction, such as asthma and chronic obstructive pulmonary disease (COPD). Although many studies have addressed the problem of wheeze detection, a limited number of scientific works has focused in the analysis of wheeze characteristics, and in particular, their time-varying nonlinear characteristics. In this study, an effort is made to reveal and statistically analyze the nonlinear characteristics of wheezes and their evolution over time, as they are reflected in the quadratic phase coupling of their harmonics. To this end, the continuous wavelet transform (CWT) is used in combination with third-order spectra to define the analysis domain, where the nonlinear interactions of the harmonics of wheezes and their time variations are revealed by incorporating instantaneous wavelet bispectrum and bicoherence, which provide with the instantaneous biamplitude and biphase curves. Based on this nonlinear information pool, a set of 23 features is proposed for the nonlinear analysis of wheezes. Two complementary perspectives, i.e., general and detailed, related to average performance and to localities, respectively, were used in the construction of the feature set, in order to embed trends and local behaviors, respectively, seen in the nonlinear interaction of the harmonic elements of wheezes over time. The proposed feature set was evaluated on a dataset of wheezes, acquired from adult patients with diagnosed asthma and COPD from a lung sound database. The statistical evaluation of the feature set revealed discrimination ability between the two pathologies for all data subgroupings. In particular, when the total breathing cycle was examined, all 23 features, but one, showed statistically significant difference between the COPD and asthma pathologies, whereas for the subgroupings of inspiratory and expiratory phases, 18 out of 23 and 22 out of 23 features exhibited discrimination power, respectively. This paves the way for the use of the wavelet higher order spectral features as an input vector to an efficient classifier. Apparently, this would integrate the intrinsic characteristics of wheezes within computerized diagnostic tools toward their more efficient evaluation.

The Emergence of Temporal Structures in Dynamical Systems

NASA Astrophysics Data System (ADS)

Mainzer, Klaus

2010-10-01

Dynamical systems in classical, relativistic and quantum physics are ruled by laws with time reversibility. Complex dynamical systems with time-irreversibility are known from thermodynamics, biological evolution, growth of organisms, brain research, aging of people, and historical processes in social sciences. Complex systems are systems that compromise many interacting parts with the ability to generate a new quality of macroscopic collective behavior the manifestations of which are the spontaneous emergence of distinctive temporal, spatial or functional structures. But, emergence is no mystery. In a general meaning, the emergence of macroscopic features results from the nonlinear interactions of the elements in a complex system. Mathematically, the emergence of irreversible structures is modelled by phase transitions in non-equilibrium dynamics of complex systems. These methods have been modified even for chemical, biological, economic and societal applications (e.g., econophysics). Emergence of irreversible structures can also be simulated by computational systems. The question arises how the emergence of irreversible structures is compatible with the reversibility of fundamental physical laws. It is argued that, according to quantum cosmology, cosmic evolution leads from symmetry to complexity of irreversible structures by symmetry breaking and phase transitions. Thus, arrows of time and aging processes are not only subjective experiences or even contradictions to natural laws, but they can be explained by quantum cosmology and the nonlinear dynamics of complex systems. Human experiences and religious concepts of arrows of time are considered in a modern scientific framework. Platonic ideas of eternity are at least understandable with respect to mathematical invariance and symmetry of physical laws. Heraclit’s world of change and dynamics can be mapped onto our daily real-life experiences of arrows of time.

Models of fold-related hysteresis

NASA Astrophysics Data System (ADS)

Shtern, Vladimir

2018-05-01

Hysteresis is a strongly nonlinear physics phenomenon observed in many fluid mechanics flows. This paper composes evolution equations of the minimal nonlinearity and dimension which describe three hysteresis kinds related to a fold catastrophe formed by (i) two fold bifurcations, (ii) fold and transcritical bifurcations, and (iii) fold and subcritical bifurcations.

Nonlinear Evolution of Short-wavelength Torsional Alfvén Waves

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

Shestov, S. V.; Nakariakov, V. M.; Ulyanov, A. S.

2017-05-10

We analyze nonlinear evolution of torsional Alfvén waves in a straight magnetic flux tube filled in with a low- β plasma, and surrounded with a plasma of lower density. Such magnetic tubes model, in particular, a segment of a coronal loop or a polar plume. The wavelength is taken comparable to the tube radius. We perform a numerical simulation of the wave propagation using ideal magnetohydrodynamics. We find that a torsional wave nonlinearly induces three kinds of compressive flows: the parallel flow at the Alfvén speed, which constitutes a bulk plasma motion along the magnetic field, the tube wave, andmore » also transverse flows in the radial direction, associated with sausage fast magnetoacoustic modes. In addition, the nonlinear torsional wave steepens and its propagation speed increases. The latter effect leads to the progressive distortion of the torsional wave front, i.e., nonlinear phase mixing. Because of the intrinsic non-uniformity of the torsional wave amplitude across the tube radius, the nonlinear effects are more pronounced in regions with higher wave amplitudes. They are always absent at the axes of the flux tube. In the case of a linear radial profile of the wave amplitude, the nonlinear effects are localized in an annulus region near the tube boundary. Thus, the parallel compressive flows driven by torsional Alfvén waves in the solar and stellar coronae, are essentially non-uniform in the perpendicular direction. The presence of additional sinks for the wave energy reduces the efficiency of the nonlinear parallel cascade in torsional Alfvén waves.« less

Nonlinear Evolution of Short-wavelength Torsional Alfvén Waves

NASA Astrophysics Data System (ADS)

Shestov, S. V.; Nakariakov, V. M.; Ulyanov, A. S.; Reva, A. A.; Kuzin, S. V.

2017-05-01

We analyze nonlinear evolution of torsional Alfvén waves in a straight magnetic flux tube filled in with a low-β plasma, and surrounded with a plasma of lower density. Such magnetic tubes model, in particular, a segment of a coronal loop or a polar plume. The wavelength is taken comparable to the tube radius. We perform a numerical simulation of the wave propagation using ideal magnetohydrodynamics. We find that a torsional wave nonlinearly induces three kinds of compressive flows: the parallel flow at the Alfvén speed, which constitutes a bulk plasma motion along the magnetic field, the tube wave, and also transverse flows in the radial direction, associated with sausage fast magnetoacoustic modes. In addition, the nonlinear torsional wave steepens and its propagation speed increases. The latter effect leads to the progressive distortion of the torsional wave front, I.e., nonlinear phase mixing. Because of the intrinsic non-uniformity of the torsional wave amplitude across the tube radius, the nonlinear effects are more pronounced in regions with higher wave amplitudes. They are always absent at the axes of the flux tube. In the case of a linear radial profile of the wave amplitude, the nonlinear effects are localized in an annulus region near the tube boundary. Thus, the parallel compressive flows driven by torsional Alfvén waves in the solar and stellar coronae, are essentially non-uniform in the perpendicular direction. The presence of additional sinks for the wave energy reduces the efficiency of the nonlinear parallel cascade in torsional Alfvén waves.

The cooling time scales of growing sunspots

NASA Technical Reports Server (NTRS)

Chou, Dean-Yi

1987-01-01

The evolution of brightness and magnetic fields of growing sunspots is studied. Growing sunspots are found to be brighter (or less dark) than stable sunspots with the same magnetic field strength. From comparison of brightness and magnetic fields of a growing sunspot with those of stable sunspots, a dynamical parameter, the cooling time, of the growing sunspot is obtained. Ten growing sunspots are studied, and cooling times of 0.5 to 9 hr are found. Two models, the inhibition model and the Alfven wave model, give cooling times of about 0.05 hr, based on linear theory. The discrepancy between theory and observation may be due to the fact that the observed sunspots are in the nonlinear regime.

Feedback coupling in dynamical systems

NASA Astrophysics Data System (ADS)

Trimper, Steffen; Zabrocki, Knud

2003-05-01

Different evolution models are considered with feedback-couplings. In particular, we study the Lotka-Volterra system under the influence of a cumulative term, the Ginzburg-Landau model with a convolution memory term and chemical rate equations with time delay. The memory leads to a modified dynamical behavior. In case of a positive coupling the generalized Lotka-Volterra system exhibits a maximum gain achieved after a finite time, but the population will die out in the long time limit. In the opposite case, the time evolution is terminated in a crash. Due to the nonlinear feedback coupling the two branches of a bistable model are controlled by the the strength and the sign of the memory. For a negative coupling the system is able to switch over between both branches of the stationary solution. The dynamics of the system is further controlled by the initial condition. The diffusion-limited reaction is likewise studied in case the reacting entities are not available simultaneously. Whereas for an external feedback the dynamics is altered, but the stationary solution remain unchanged, a self-organized internal feedback leads to a time persistent solution.

Use of recurrence plot and recurrence quantification analysis in Taiwan unemployment rate time series

NASA Astrophysics Data System (ADS)

Chen, Wei-Shing

2011-04-01

The aim of the article is to answer the question if the Taiwan unemployment rate dynamics is generated by a non-linear deterministic dynamic process. This paper applies a recurrence plot and recurrence quantification approach based on the analysis of non-stationary hidden transition patterns of the unemployment rate of Taiwan. The case study uses the time series data of the Taiwan’s unemployment rate during the period from 1978/01 to 2010/06. The results show that recurrence techniques are able to identify various phases in the evolution of unemployment transition in Taiwan.

Propagation of large-amplitude waves on dielectric liquid sheets in a tangential electric field: exact solutions in three-dimensional geometry.

PubMed

Zubarev, Nikolay M; Zubareva, Olga V

2010-10-01

Nonlinear waves on sheets of dielectric liquid in the presence of an external tangential electric field are studied theoretically. It is shown that waves of arbitrary shape in three-dimensional geometry can propagate along (or against) the electric field direction without distortion, i.e., the equations of motion admit a wide class of exact traveling wave solutions. This unusual situation occurs for nonconducting ideal liquids with high dielectric constants in the case of a sufficiently strong field strength. Governing equations for evolution of plane symmetric waves on fluid sheets are derived using conformal variables. A dispersion relation for the evolution of small perturbations of the traveling wave solutions is obtained. It follows from this relation that, regardless of the wave shape, the amplitudes of small-scale perturbations do not increase with time and, hence, the traveling waves are stable. We also study the interaction of counterpropagating symmetric waves with small but finite amplitudes. The corresponding solution of the equations of motion describes the nonlinear superposition of the oppositely directed waves. The results obtained are applicable for the description of long waves on fluid sheets in a horizontal magnetic field.

Fitness consequences of larval traits persist across the metamorphic boundary.

PubMed

Crean, Angela J; Monro, Keyne; Marshall, Dustin J

2011-11-01

Metamorphosis is thought to provide an adaptive decoupling between traits specialized for each life-history stage in species with complex life cycles. However, an increasing number of studies are finding that larval traits can carry-over to influence postmetamorphic performance, suggesting that these life-history stages may not be free to evolve independently of each other. We used a phenotypic selection framework to compare the relative and interactive effects of larval size, time to hatching, and time to settlement on postmetamorphic survival and growth in a marine invertebrate, Styela plicata. Time to hatching was the only larval trait found to be under directional selection, individuals that took more time to hatch into larvae survived better after metamorphosis but grew more slowly. Nonlinear selection was found to act on multivariate trait combinations, once again acting in opposite directions for selection acting via survival and growth. Individuals with above average values of larval traits were most likely to survive, but surviving individuals with intermediate larval traits grew to the largest size. These results demonstrate that larval traits can have multiple, complex fitness consequences that persist across the metamorphic boundary; and thus postmetamorphic selection pressures may constrain the evolution of larval traits. © 2011 The Author(s). Evolution© 2011 The Society for the Study of Evolution.

The temporal evolution of 3-m striations in the modified ionosphere

NASA Technical Reports Server (NTRS)

Coster, A. J.; Djuth, F. T.; Jost, R. J.; Gordon, W. E.

1985-01-01

Experiments were performed at Arecibo, Puerto Rico, to investigate the evolution times of 3-m field-aligned striations produced in the ionosphere by powerful high-frequency (HF) radio waves. The results of this investigation are now summarized. First, the striations' rise times are dependent on the HF electric field. The E region data suggest that this dependence is nonlinear. Second, the threshold value of the HF electric field required to produce detectable striations was experimentally determined. At threshold the component of the HF electric field perpendicular to the geomagnetic field is calculated to be 0.09 V/m in the F region and 0.37 V/m in the E region. Third, both the E and the F region data verify theoretical predictions that the striations' decay times are directly proportional to the electron diffusion across B. Finally, a one-to-one correspondence between the growth of the 3-m striations and the decline of the HF-enhanced plasma line during overshoot is sometimes observed.

On a model of electromagnetic field propagation in ferroelectric media

NASA Astrophysics Data System (ADS)

Picard, Rainer

2007-04-01

The Maxwell system in an anisotropic, inhomogeneous medium with non-linear memory effect produced by a Maxwell type system for the polarization is investigated under low regularity assumptions on data and domain. The particular form of memory in the system is motivated by a model for electromagnetic wave propagation in ferromagnetic materials suggested by Greenberg, MacCamy and Coffman [J.M. Greenberg, R.C. MacCamy, C.V. Coffman, On the long-time behavior of ferroelectric systems, Phys. D 134 (1999) 362-383]. To avoid unnecessary regularity requirements the problem is approached as a system of space-time operator equation in the framework of extrapolation spaces (Sobolev lattices), a theoretical framework developed in [R. Picard, Evolution equations as space-time operator equations, Math. Anal. Appl. 173 (2) (1993) 436-458; R. Picard, Evolution equations as operator equations in lattices of Hilbert spaces, Glasnik Mat. 35 (2000) 111-136]. A solution theory for a large class of ferromagnetic materials confined to an arbitrary open set (with suitably generalized boundary conditions) is obtained.

Amplification of nonlinear surface waves by wind

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

Leblanc, Stephane

2007-10-15

A weakly nonlinear analysis is conducted to study the evolution of slowly varying wavepackets with small but finite amplitudes, that evolve at the interface between air and water under the effect of wind. In the inviscid assumption, wave envelopes are governed by cubic nonlinear Schroedinger or Davey-Stewartson equations forced by a linear term corresponding to Miles' mechanism of wave generation. Under fair wind, it is shown that Stokes waves grow exponentially and that Benjamin-Feir instability becomes explosive.

Nonlinear energy transfer and current sheet development in localized Alfvén wavepacket collisions in the strong turbulence limit

NASA Astrophysics Data System (ADS)

Verniero, J. L.; Howes, G. G.; Klein, K. G.

2018-02-01

In space and astrophysical plasmas, turbulence is responsible for transferring energy from large scales driven by violent events or instabilities, to smaller scales where turbulent energy is ultimately converted into plasma heat by dissipative mechanisms. The nonlinear interaction between counterpropagating Alfvén waves, denoted Alfvén wave collisions, drives this turbulent energy cascade, as recognized by early work with incompressible magnetohydrodynamic (MHD) equations. Recent work employing analytical calculations and nonlinear gyrokinetic simulations of Alfvén wave collisions in an idealized periodic initial state have demonstrated the key properties that strong Alfvén wave collisions mediate effectively the transfer of energy to smaller perpendicular scales and self-consistently generate current sheets. For the more realistic case of the collision between two initially separated Alfvén wavepackets, we use a nonlinear gyrokinetic simulation to show here that these key properties persist: strong Alfvén wavepacket collisions indeed facilitate the perpendicular cascade of energy and give rise to current sheets. Furthermore, the evolution shows that nonlinear interactions occur only while the wavepackets overlap, followed by a clean separation of the wavepackets with straight uniform magnetic fields and the cessation of nonlinear evolution in between collisions, even in the gyrokinetic simulation presented here which resolves dispersive and kinetic effects beyond the reach of the MHD theory.

Probing and exploiting the chaotic dynamics of a hydrodynamic photochemical oscillator to implement all the basic binary logic functions

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

Hayashi, Kenta; Department of Chemistry, Biology, and Biotechnology, University of Perugia, 06123 Perugia; Gotoda, Hiroshi

2016-05-15

The convective motions within a solution of a photochromic spiro-oxazine being irradiated by UV only on the bottom part of its volume, give rise to aperiodic spectrophotometric dynamics. In this paper, we study three nonlinear properties of the aperiodic time series: permutation entropy, short-term predictability and long-term unpredictability, and degree distribution of the visibility graph networks. After ascertaining the extracted chaotic features, we show how the aperiodic time series can be exploited to implement all the fundamental two-inputs binary logic functions (AND, OR, NAND, NOR, XOR, and XNOR) and some basic arithmetic operations (half-adder, full-adder, half-subtractor). This is possible duemore » to the wide range of states a nonlinear system accesses in the course of its evolution. Therefore, the solution of the convective photochemical oscillator results in hardware for chaos-computing alternative to conventional complementary metal-oxide semiconductor-based integrated circuits.« less

Skewness in large-scale structure and non-Gaussian initial conditions

NASA Technical Reports Server (NTRS)

Fry, J. N.; Scherrer, Robert J.

1994-01-01

We compute the skewness of the galaxy distribution arising from the nonlinear evolution of arbitrary non-Gaussian intial conditions to second order in perturbation theory including the effects of nonlinear biasing. The result contains a term identical to that for a Gaussian initial distribution plus terms which depend on the skewness and kurtosis of the initial conditions. The results are model dependent; we present calculations for several toy models. At late times, the leading contribution from the initial skewness decays away relative to the other terms and becomes increasingly unimportant, but the contribution from initial kurtosis, previously overlooked, has the same time dependence as the Gaussian terms. Observations of a linear dependence of the normalized skewness on the rms density fluctuation therefore do not necessarily rule out initially non-Gaussian models. We also show that with non-Gaussian initial conditions the first correction to linear theory for the mean square density fluctuation is larger than for Gaussian models.

A combined averaging and frequency mixing approach for force identification in weakly nonlinear high-Q oscillators: Atomic force microscope

NASA Astrophysics Data System (ADS)

Sah, Si Mohamed; Forchheimer, Daniel; Borgani, Riccardo; Haviland, David

2018-02-01

We present a polynomial force reconstruction of the tip-sample interaction force in Atomic Force Microscopy. The method uses analytical expressions for the slow-time amplitude and phase evolution, obtained from time-averaging over the rapidly oscillating part of the cantilever dynamics. The slow-time behavior can be easily obtained in either the numerical simulations or the experiment in which a high-Q resonator is perturbed by a weak nonlinearity and a periodic driving force. A direct fit of the theoretical expressions to the simulated and experimental data gives the best-fit parameters for the force model. The method combines and complements previous works (Platz et al., 2013; Forchheimer et al., 2012 [2]) and it allows for computationally more efficient parameter mapping with AFM. Results for the simulated asymmetric piecewise linear force and VdW-DMT force models are compared with the reconstructed polynomial force and show a good agreement. It is also shown that the analytical amplitude and phase modulation equations fit well with the experimental data.

An approximation theory for the identification of nonlinear distributed parameter systems

NASA Technical Reports Server (NTRS)

Banks, H. T.; Reich, Simeon; Rosen, I. G.

1988-01-01

An abstract approximation framework for the identification of nonlinear distributed parameter systems is developed. Inverse problems for nonlinear systems governed by strongly maximal monotone operators (satisfying a mild continuous dependence condition with respect to the unknown parameters to be identified) are treated. Convergence of Galerkin approximations and the corresponding solutions of finite dimensional approximating identification problems to a solution of the original finite dimensional identification problem is demonstrated using the theory of nonlinear evolution systems and a nonlinear analog of the Trotter-Kato approximation result for semigroups of bounded linear operators. The nonlinear theory developed here is shown to subsume an existing linear theory as a special case. It is also shown to be applicable to a broad class of nonlinear elliptic operators and the corresponding nonlinear parabolic partial differential equations to which they lead. An application of the theory to a quasilinear model for heat conduction or mass transfer is discussed.

Femtosecond Kerr index of cyclic olefin co/polymers for THz nonlinear optics

NASA Astrophysics Data System (ADS)

Noskovicova, E.; Lorenc, D.; Slusna, L.; Velic, D.

2016-10-01

The second-order nonlinear refractive index n2 (Kerr index) of cyclic olefin copolymer (TOPAS) and cyclic olefin polymers (ZEONEX, ZEONOR) was determined at the wavelength of 800 nm within this work. Bulk samples of ZEONEX, ZEONOR and TOPAS were measured using the single-beam Z-scan technique and the values of their nonlinear refractive index were determined to be approximately 2 × 10-20 m2W-1 for all cases. The obtained values of n2 play a vital role for ultrafast pulse evolution and corresponding phenomena such as nonlinear spectral transformation.

Analysis of Some Properties of the Nonlinear Schrödinger Equation Used for Filamentation Modeling

NASA Astrophysics Data System (ADS)

Zemlyanov, A. A.; Bulygin, A. D.

2018-06-01

Properties of the integral of motion and evolution of the effective light beam radius are analyzed for the stationary model of the nonlinear Schrödinger equation describing the filamentation. It is demonstrated that within the limits of such model, filamentation is limited only by the dissipation mechanisms.

Counting defects in an instantaneous quench.

PubMed

Ibaceta, D; Calzetta, E

1999-09-01

We consider the formation of defects in a nonequilibrium second-order phase transition induced by an instantaneous quench to zero temperature in a type II superconductor. We perform a full nonlinear simulation where we follow the evolution in time of the local order parameter field. We determine how far into the phase transition theoretical estimates of the defect density based on the Gaussian approximation yield a reliable prediction for the actual density. We also characterize quantitatively some aspects of the out of equilibrium phase transition.

Construction of even and odd combinations of Morse-like coherent states

NASA Astrophysics Data System (ADS)

Récamier, José; Jáuregui, Rocio

2003-06-01

In this work we construct approximate coherent states for the Morse potential using a method inspired by the f-oscillator formalism (Man'ko et al 1996 Proc. 4th Wigner Symp. ed M Natig, Atakishiyev, T H Seligman and K B Wolf (Singapore: World Scientific) p 421). We make even and odd combinations of these states and evaluate the temporal evolution of the position operator and its dispersion as a function of time when the states evolve under a nonlinear Morse Hamiltonian.

Widely tunable Tm-doped mode-locked all-fiber laser

PubMed Central

Yan, Zhiyu; Sun, Biao; Li, Xiaohui; Luo, Jiaqi; Shum, Perry Ping; Yu, Xia; Zhang, Ying; Wang, Qi Jie

2016-01-01

We demonstrated a widely tunable Tm-doped mode-locked all-fiber laser, with the widest tunable range of 136 nm, from 1842 to 1978 nm. Nonlinear polarization evolution (NPE) technique is employed to enable mode-locking and the wavelength-tunable operation. The widely tunable range attributes to the NPE-induced transmission modulation and bidirectional pumping mechanism. Such kind of tunable mode-locked laser can find various applications in optical communications, spectroscopy, time-resolved measurement, and among others. PMID:27263655

Non-linear Internal Wave Evolution in the South China Sea: 2005 Field Program

DTIC Science & Technology

2009-05-01

Revelle in SCS05 (right). Soliton sightings from late April ( dark blue), early May (light blue) and mid May (yellow orange) are shown geographically...focus areas was the South China Sea (SCS). At that time, large-scale solitary waves were known to shoal on the western shelves of the SCS. Solitons ...we were gambling that solitons would indeed be traversing the central SCS and that they would already be well formed before reaching our approved

Shear Banding in a Partially Molten Mantle

NASA Astrophysics Data System (ADS)

Alisic, L.; Rudge, J. F.; Wells, G.; Katz, R. F.; Rhebergen, S.

2013-12-01

We investigate the nonlinear behaviour of partially molten mantle material under shear. Numerical models of compaction and advection-diffusion of a porous matrix with a spherical inclusion are built using the automated code generation package FEniCS. The time evolution of melt distribution with increasing shear in these models is compared to laboratory experiments that show high-porosity shear banding in the medium and pressure shadows around the inclusion. We focus on understanding the interaction between these shear bands and pressure shadows as a function of rheological parameters.

Nonlinear penetration of whistler pulses into collisional plasmas via conductivity modifications

NASA Technical Reports Server (NTRS)

Urrutia, J. M.; Stenzel, R. L.

1991-01-01

A strong electromagnetic impulse (about 0.2 microsec) with central frequency in the whistler-wave regime is applied to a large laboratory plasma dominated by Coulomb collisions. Local electron heating at the antenna and transport along B0 create a channel of high conductivity along which the whistler pulse penetrates with little damping. Because of its rapid temporal evolution, this new form of modulational instability does not involve ducting by density gradients which require ion time scales to develop.

Conference on Operator Theory, Wavelet Theory and Control Theory

DTIC Science & Technology

1993-09-30

UNCC and TAMU Wavelet collocation method for nonlinear time evolution - PDE’s 4 : 00 - 4: 20 A in Li, the University of Nevada - Las Vagas Wav slet...operator-valued functions. Inspired by Robinson’s characterization, we havc found a similar mninimum deliy characterization for the central... Midi -Pyr{\\ ’e)n{\\’e)les de l’Universit{\\e) Paul SabatierO, ADDRESS=*Toulouse, France’, NOTE=’ISBN 2-86332-130-7’, MONTH=08--13 June’, YEAR=�

Directional Ocean Wave Spectra

DTIC Science & Technology

1991-01-01

between the wave height time series from the different LEWEX." Data Report Programa de Clima iarnimo. Madrid (l9L8i. 84 AIR AND SPACE MEASUREMENTS IN... inclusion of the nonlinear azimuthal Summation over the velocity-bunching index m for cutoff factor, remains a valid approximation for the en - fixed...buoy observations. ’Guillaurne, A., "VAG-Modele de PT[iSJon de rFEtif de [a Mer en F’au However, an analysis of the evolution of the direc- Proflonde

Evolution of large amplitude Alfven waves in solar wind plasmas: Kinetic-fluid models

NASA Astrophysics Data System (ADS)

Nariyuki, Y.

2014-12-01

Large amplitude Alfven waves are ubiquitously observed in solar wind plasmas. Mjolhus(JPP, 1976) and Mio et al(JPSJ, 1976) found that nonlinear evolution of the uni-directional, parallel propagating Alfven waves can be described by the derivative nonlinear Schrodinger equation (DNLS). Later, the multi-dimensional extension (Mjolhus and Wyller, JPP, 1988; Passot and Sulem, POP, 1993; Gazol et al, POP, 1999) and ion kinetic modification (Mjolhus and Wyller, JPP, 1988; Spangler, POP, 1989; Medvedev and Diamond, POP, 1996; Nariyuki et al, POP, 2013) of DNLS have been reported. Recently, Nariyuki derived multi-dimensional DNLS from an expanding box model of the Hall-MHD system (Nariyuki, submitted). The set of equations including the nonlinear evolution of compressional wave modes (TDNLS) was derived by Hada(GRL, 1993). DNLS can be derived from TDNLS by rescaling of the variables (Mjolhus, Phys. Scr., 2006). Nariyuki and Hada(JPSJ, 2007) derived a kinetically modified TDNLS by using a simple Landau closure (Hammet and Perkins, PRL, 1990; Medvedev and Diamond, POP, 1996). In the present study, we revisit the ion kinetic modification of multi-dimensional TDNLS through more rigorous derivations, which is consistent with the past kinetic modification of DNLS. Although the original TDNLS was derived in the multi-dimensional form, the evolution of waves with finite propagation angles in TDNLS has not been paid much attention. Applicability of the resultant models to solar wind turbulence is discussed.

When linear stability does not exclude nonlinear instability

DOE PAGES

Kevrekidis, P. G.; Pelinovsky, D. E.; Saxena, A.

2015-05-29

We describe a mechanism that results in the nonlinear instability of stationary states even in the case where the stationary states are linearly stable. In this study, this instability is due to the nonlinearity-induced coupling of the linearization’s internal modes of negative energy with the continuous spectrum. In a broad class of nonlinear Schrödinger equations considered, the presence of such internal modes guarantees the nonlinear instability of the stationary states in the evolution dynamics. To corroborate this idea, we explore three prototypical case examples: (a) an antisymmetric soliton in a double-well potential, (b) a twisted localized mode in a one-dimensionalmore » lattice with cubic nonlinearity, and (c) a discrete vortex in a two-dimensional saturable lattice. In all cases, we observe a weak nonlinear instability, despite the linear stability of the respective states.« less

Nonlinear rocket motor stability prediction: Limit amplitude, triggering, and mean pressure shifta)

NASA Astrophysics Data System (ADS)

Flandro, Gary A.; Fischbach, Sean R.; Majdalani, Joseph

2007-09-01

High-amplitude pressure oscillations in solid propellant rocket motor combustion chambers display nonlinear effects including: (1) limit cycle behavior in which the fluctuations may dwell for a considerable period of time near their peak amplitude, (2) elevated mean chamber pressure (DC shift), and (3) a triggering amplitude above which pulsing will cause an apparently stable system to transition to violent oscillations. Along with the obvious undesirable vibrations, these features constitute the most damaging impact of combustion instability on system reliability and structural integrity. The physical mechanisms behind these phenomena and their relationship to motor geometry and physical parameters must, therefore, be fully understood if instability is to be avoided in the design process, or if effective corrective measures must be devised during system development. Predictive algorithms now in use have limited ability to characterize the actual time evolution of the oscillations, and they do not supply the motor designer with information regarding peak amplitudes or the associated critical triggering amplitudes. A pivotal missing element is the ability to predict the mean pressure shift; clearly, the designer requires information regarding the maximum chamber pressure that might be experienced during motor operation. In this paper, a comprehensive nonlinear combustion instability model is described that supplies vital information. The central role played by steep-fronted waves is emphasized. The resulting algorithm provides both detailed physical models of nonlinear instability phenomena and the critically needed predictive capability. In particular, the origin of the DC shift is revealed.

Nature of short, high-amplitude compressive stress pulses in a periodic dissipative laminate.

PubMed

Franco Navarro, Pedro; Benson, David J; Nesterenko, Vitali F

2015-12-01

We study the evolution of high-amplitude stress pulses in periodic dissipative laminates taking into account the nonlinear constitutive equations of the components and their dissipative behavior. Aluminum-tungsten laminate was selected due to the large difference in acoustic impedances of components, the significant nonlinearity of the aluminum constitutive equation at the investigated range of stresses, and its possible practical applications. Laminates with different cell size, which controls the internal time scale, impacted by plates with different thicknesses that determine the incoming pulse duration, were investigated. It has been observed that the ratio of the duration of the incoming pulse to the internal characteristic time determines the nature of the high-amplitude dissipative propagating waves-a triangular oscillatory shock-like profile, a train of localized pulses, or a single localized pulse. These localized quasistationary waves resemble solitary waves even in the presence of dissipation: The similar pulses emerged from different initial conditions, indicating that they are inherent properties of the corresponding laminates; their characteristic length scale is determined by the scale of mesostructure, nonlinear properties of materials, and the stress amplitude; and a linear relationship exists between their speed and amplitude. They mostly recover their shapes after collision with phase shift. A theoretical description approximating the shape, length scale, and speed of these high-amplitude dissipative pulses was proposed based on the Korteweg-de Vries equation with a dispersive term determined by the mesostructure and a nonlinear term derived using Hugoniot curves of components.

Unambiguous demonstration of soliton evolution in slow-light silicon photonic crystal waveguides with SFG-XFROG.

PubMed

Li, Xiujian; Liao, Jiali; Nie, Yongming; Marko, Matthew; Jia, Hui; Liu, Ju; Wang, Xiaochun; Wong, Chee Wei

2015-04-20

We demonstrate the temporal and spectral evolution of picosecond soliton in the slow light silicon photonic crystal waveguides (PhCWs) by sum frequency generation cross-correlation frequency resolved optical grating (SFG-XFROG) and nonlinear Schrödinger equation (NLSE) modeling. The reference pulses for the SFG-XFROG measurements are unambiguously pre-characterized by the second harmonic generation frequency resolved optical gating (SHG-FROG) assisted with the combination of NLSE simulations and optical spectrum analyzer (OSA) measurements. Regardless of the inevitable nonlinear two photon absorption, high order soliton compressions have been observed remarkably owing to the slow light enhanced nonlinear effects in the silicon PhCWs. Both the measurements and the further numerical analyses of the pulse dynamics indicate that, the free carrier dispersion (FCD) enhanced by the slow light effects is mainly responsible for the compression, the acceleration, and the spectral blue shift of the soliton.

Nonlinear stability of non-stationary cross-flow vortices in compressible boundary layers

NASA Technical Reports Server (NTRS)

Gajjar, J. S. B.

1995-01-01

The nonlinear evolution of long wavelength non-stationary cross-flow vortices in a compressible boundary layer is investigated and the work extends that of Gajjar (1994) to flows involving multiple critical layers. The basic flow profile considered in this paper is that appropriate for a fully three-dimensional boundary layer with O(1) Mach number and with wall heating or cooling. The governing equations for the evolution of the cross-flow vortex are obtained and some special cases are discussed. One special case includes linear theory where exact analytic expressions for the growth rate of the vortices are obtained. Another special case is a generalization of the Bassom & Gajjar (1988) results for neutral waves to compressible flows. The viscous correction to the growth rate is derived and it is shown how the unsteady nonlinear critical layer structure merges with that for a Haberman type of viscous critical layer.

Simulating nonlinear neutrino flavor evolution

NASA Astrophysics Data System (ADS)

Duan, H.; Fuller, G. M.; Carlson, J.

2008-10-01

We discuss a new kind of astrophysical transport problem: the coherent evolution of neutrino flavor in core collapse supernovae. Solution of this problem requires a numerical approach which can simulate accurately the quantum mechanical coupling of intersecting neutrino trajectories and the associated nonlinearity which characterizes neutrino flavor conversion. We describe here the two codes developed to attack this problem. We also describe the surprising phenomena revealed by these numerical calculations. Chief among these is that the nonlinearities in the problem can engineer neutrino flavor transformation which is dramatically different to that in standard Mikheyev Smirnov Wolfenstein treatments. This happens even though the neutrino mass-squared differences are measured to be small, and even when neutrino self-coupling is sub-dominant. Our numerical work has revealed potential signatures which, if detected in the neutrino burst from a Galactic core collapse event, could reveal heretofore unmeasurable properties of the neutrinos, such as the mass hierarchy and vacuum mixing angle θ13.

Nonlinear Propagation of Planet-Generated Tidal Waves

NASA Technical Reports Server (NTRS)

Rafikov, R. R.

2002-01-01

The propagation and evolution of planet-generated density waves in protoplanetary disks is considered. The evolution of waves, leading to shock formation and wake dissipation, is followed in the weakly nonlinear regime. The 2001 local approach of Goodman and Rafikov is extended to include the effects of surface density and temperature variations in the disk as well as the disk cylindrical geometry and nonuniform shear. Wave damping due to shocks is demonstrated to be a nonlocal process spanning a significant fraction of the disk. Torques induced by the planet could be significant drivers of disk evolution on timescales of approx. 10(exp 6)-10(exp 7) yr, even in the absence of strong background viscosity. A global prescription for angular momentum deposition is developed that could be incorporated into the study of gap formation in a gaseous disk around the planet.

Data-Driven Modeling of Complex Systems by means of a Dynamical ANN

NASA Astrophysics Data System (ADS)

Seleznev, A.; Mukhin, D.; Gavrilov, A.; Loskutov, E.; Feigin, A.

2017-12-01

The data-driven methods for modeling and prognosis of complex dynamical systems become more and more popular in various fields due to growth of high-resolution data. We distinguish the two basic steps in such an approach: (i) determining the phase subspace of the system, or embedding, from available time series and (ii) constructing an evolution operator acting in this reduced subspace. In this work we suggest a novel approach combining these two steps by means of construction of an artificial neural network (ANN) with special topology. The proposed ANN-based model, on the one hand, projects the data onto a low-dimensional manifold, and, on the other hand, models a dynamical system on this manifold. Actually, this is a recurrent multilayer ANN which has internal dynamics and capable of generating time series. Very important point of the proposed methodology is the optimization of the model allowing us to avoid overfitting: we use Bayesian criterion to optimize the ANN structure and estimate both the degree of evolution operator nonlinearity and the complexity of nonlinear manifold which the data are projected on. The proposed modeling technique will be applied to the analysis of high-dimensional dynamical systems: Lorenz'96 model of atmospheric turbulence, producing high-dimensional space-time chaos, and quasi-geostrophic three-layer model of the Earth's atmosphere with the natural orography, describing the dynamics of synoptical vortexes as well as mesoscale blocking systems. The possibility of application of the proposed methodology to analyze real measured data is also discussed. The study was supported by the Russian Science Foundation (grant #16-12-10198).

F-Expansion Method and New Exact Solutions of the Schrödinger-KdV Equation

PubMed Central

Filiz, Ali; Ekici, Mehmet; Sonmezoglu, Abdullah

2014-01-01

F-expansion method is proposed to seek exact solutions of nonlinear evolution equations. With the aid of symbolic computation, we choose the Schrödinger-KdV equation with a source to illustrate the validity and advantages of the proposed method. A number of Jacobi-elliptic function solutions are obtained including the Weierstrass-elliptic function solutions. When the modulus m of Jacobi-elliptic function approaches to 1 and 0, soliton-like solutions and trigonometric-function solutions are also obtained, respectively. The proposed method is a straightforward, short, promising, and powerful method for the nonlinear evolution equations in mathematical physics. PMID:24672327

F-expansion method and new exact solutions of the Schrödinger-KdV equation.

PubMed

Filiz, Ali; Ekici, Mehmet; Sonmezoglu, Abdullah

2014-01-01

F-expansion method is proposed to seek exact solutions of nonlinear evolution equations. With the aid of symbolic computation, we choose the Schrödinger-KdV equation with a source to illustrate the validity and advantages of the proposed method. A number of Jacobi-elliptic function solutions are obtained including the Weierstrass-elliptic function solutions. When the modulus m of Jacobi-elliptic function approaches to 1 and 0, soliton-like solutions and trigonometric-function solutions are also obtained, respectively. The proposed method is a straightforward, short, promising, and powerful method for the nonlinear evolution equations in mathematical physics.

Pulse generation without gain-bandwidth limitation in a laser with self-similar evolution.

PubMed

Chong, A; Liu, H; Nie, B; Bale, B G; Wabnitz, S; Renninger, W H; Dantus, M; Wise, F W

2012-06-18

With existing techniques for mode-locking, the bandwidth of ultrashort pulses from a laser is determined primarily by the spectrum of the gain medium. Lasers with self-similar evolution of the pulse in the gain medium can tolerate strong spectral breathing, which is stabilized by nonlinear attraction to the parabolic self-similar pulse. Here we show that this property can be exploited in a fiber laser to eliminate the gain-bandwidth limitation to the pulse duration. Broad (∼200 nm) spectra are generated through passive nonlinear propagation in a normal-dispersion laser, and these can be dechirped to ∼20-fs duration.

Dynamic modification of optical nonlinearities related to femtosecond laser filamentation in gases

NASA Astrophysics Data System (ADS)

Romanov (1, 3), Dmitri; Tarazkar (2, 3), Maryam; Levis (2, 3), Robert

2017-04-01

During and immediately after the passing of a filamenting laser pulse through a gas-phase medium, the nonlinear optical characteristics of the emerging filament-wake channel undergo substantial transient modification, which stems from ionization and electronic excitation of constituent atoms/molecules. We calculate the related hyperpolarizability coefficients of individual ions, and we develop a theoretical model of filament channel evolution applicable to atmospheric-pressure and high-pressure gases. The evolution is mediated by energetic free-electron gas that results from the strong-field ionization and gains considerable energy via inverse Bremsstrahlung process. The ensuing impact ionization and excitation of the residual neutral atoms/molecules proceeds inhomogeneously both inside the channel and on its surface, being strongly influenced by the thermal conduction of the electron gas. The model shows critical importance of channel-surface effects, especially as regards the effective electron temperature. The calculated spatial-temporal evolution patterns ultimately determine the transient modifications of linear and nonlinear optical properties of filament wake channels. Medium-specific estimates are made for atmospheric- and high-pressure argon, as well as for molecular nitrogen gas. Support of Defense Threat Reduction Agency (Grant No. HDTRA1-12-1-0014) is gratefully acknowledged.

EVOLUTION OF FAST MAGNETOACOUSTIC PULSES IN RANDOMLY STRUCTURED CORONAL PLASMAS

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

Yuan, D.; Li, B.; Pascoe, D. J.

2015-02-01

We investigate the evolution of fast magnetoacoustic pulses in randomly structured plasmas, in the context of large-scale propagating waves in the solar atmosphere. We perform one-dimensional numerical simulations of fast wave pulses propagating perpendicular to a constant magnetic field in a low-β plasma with a random density profile across the field. Both linear and nonlinear regimes are considered. We study how the evolution of the pulse amplitude and width depends on their initial values and the parameters of the random structuring. Acting as a dispersive medium, a randomly structured plasma causes amplitude attenuation and width broadening of the fast wavemore » pulses. After the passage of the main pulse, secondary propagating and standing fast waves appear. Width evolution of both linear and nonlinear pulses can be well approximated by linear functions; however, narrow pulses may have zero or negative broadening. This arises because narrow pulses are prone to splitting, while broad pulses usually deviate less from their initial Gaussian shape and form ripple structures on top of the main pulse. Linear pulses decay at an almost constant rate, while nonlinear pulses decay exponentially. A pulse interacts most efficiently with a random medium with a correlation length of about half of the initial pulse width. This detailed model of fast wave pulses propagating in highly structured media substantiates the interpretation of EIT waves as fast magnetoacoustic waves. Evolution of a fast pulse provides us with a novel method to diagnose the sub-resolution filamentation of the solar atmosphere.« less

Glider Observations of Internal Tide Packets on the Australian Northwest Shelf

NASA Astrophysics Data System (ADS)

Book, J. W.; Steinberg, C. R.; Brinkman, R. M.; Jones, N. L.; Lowe, R.; Ivey, G. N.; Pattiaratchi, C. B.; Rice, A. E.

2016-02-01

The rapid profiling capabilities (less than 10 minutes per profile in 100 m of water excluding surfacing times) of autonomous gliders were utilized to study the structure of non-linear internal tide packets on the Australian Northwest Shelf. A total of five gliders were deployed on the shelf from 11 February - 21 April 2012 with more than 2900 glider CTD profiles collected during the final three weeks of this time period when the internal tide activity was intense. In general the internal tide packets showed high degrees of non-linearity, for example in one case a glider observed a 62 m rise of the 28° isotherm over 2.25 hours in a shelf location of 90 meters water depth. In addition to the glider measurements, moored strings of CTD sensors were used to measure the internal tide packets at fixed positions and the results show that the wave packets vary significantly with respect to their structure and arrival times from one tidal period to the next. This fact complicates interpretation of the glider data as wave packet spatial evolution is non-stationary and cannot be simply recovered from repeat glider visits to the same location. Furthermore, the packets were found to move at speeds near or greater (e.g., 0.55 m/s) than the speed that the gliders were moving. Despite these challenges, the gliders offer the only resource that can measure the spatial structure of the wave packets beyond the scope of our limited mooring positions. Therefore, we have implemented methods such as time-augmented empirical orthogonal functions to combine these glider measurements with the fixed mooring measurements in order to better understand the spatial and temporal patterns of the wave packet evolution over the slope and shelf of this region.

Parametric resonance in the early Universe—a fitting analysis

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

Figueroa, Daniel G.; Torrentí, Francisco, E-mail: daniel.figueroa@cern.ch, E-mail: f.torrenti@csic.es

Particle production via parametric resonance in the early Universe, is a non-perturbative, non-linear and out-of-equilibrium phenomenon. Although it is a well studied topic, whenever a new scenario exhibits parametric resonance, a full re-analysis is normally required. To avoid this tedious task, many works present often only a simplified linear treatment of the problem. In order to surpass this circumstance in the future, we provide a fitting analysis of parametric resonance through all its relevant stages: initial linear growth, non-linear evolution, and relaxation towards equilibrium. Using lattice simulations in an expanding grid in 3+1 dimensions, we parametrize the dynamics' outcome scanningmore » over the relevant ingredients: role of the oscillatory field, particle coupling strength, initial conditions, and background expansion rate. We emphasize the inaccuracy of the linear calculation of the decay time of the oscillatory field, and propose a more appropriate definition of this scale based on the subsequent non-linear dynamics. We provide simple fits to the relevant time scales and particle energy fractions at each stage. Our fits can be applied to post-inflationary preheating scenarios, where the oscillatory field is the inflaton, or to spectator-field scenarios, where the oscillatory field can be e.g. a curvaton, or the Standard Model Higgs.« less

Propagation of 3D internal gravity wave beams in a slowly varying stratification

NASA Astrophysics Data System (ADS)

Fan, Boyu; Akylas, T. R.

2017-11-01

The time-mean flows induced by internal gravity wave beams (IGWB) with 3D variations have been shown to have dramatic implications for long-term IGWB dynamics. While uniform stratifications are convenient both theoretically and in the laboratory, stratifications in the ocean can vary by more than an order of magnitude over the ocean depth. Here, in view of this fact, we study the propagation of a 3D IGWB in a slowly varying stratification. We assume that the stratification varies slowly relative to the local variations in the wave profile. In the 2D case, the IGWB bends in response to the changing stratification, but nonlinear effects are minor even in the finite amplitude regime. For a 3D IGWB, in addition to bending, we find that nonlinearity results in the transfer of energy from waves to a large-scale time-mean flow associated with the mean potential vorticity, similar to IGWB behavior in a uniform stratification. In a weakly nonlinear setting, we derive coupled evolution equations that govern this process. We also use these equations to determine the stability properties of 2D IGWB to 3D perturbations. These findings indicate that 3D effects may be relevant and possibly fundamental to IGWB dynamics in nature. Supported by NSF Grant DMS-1512925.

New envelope solitons for Gerdjikov-Ivanov model in nonlinear fiber optics

NASA Astrophysics Data System (ADS)

Triki, Houria; Alqahtani, Rubayyi T.; Zhou, Qin; Biswas, Anjan

2017-11-01

Exact soliton solutions in a class of derivative nonlinear Schrödinger equations including a pure quintic nonlinearity are investigated. By means of the coupled amplitude-phase formulation, we derive a nonlinear differential equation describing the evolution of the wave amplitude in the non-Kerr quintic media. The resulting amplitude equation is then solved to get exact analytical chirped bright, kink, antikink, and singular soliton solutions for the model. It is also shown that the nonlinear chirp associated with these solitons is crucially dependent on the wave intensity and related to self-steepening and group velocity dispersion parameters. Parametric conditions on physical parameters for the existence of chirped solitons are also presented. These localized structures exist due to a balance among quintic nonlinearity, group velocity dispersion, and self-steepening effects.

Hybrid simulation of fishbone instabilities in the EAST tokamak

DOE PAGES

Shen, Wei; Wang, Feng; Fu, G. Y.; ...

2017-08-11

Hybrid simulations with the global kinetic-magnetohydrodynamic (MHD) code M3D-K have been carried out to investigate the linear stability and nonlinear dynamics of beam-driven fishbone in the experimental advanced superconducting tokamak (EAST) experiment. Linear simulations show that a low frequency fishbone instability is excited at experimental value of beam ion pressure. The mode is mainly driven by low energy beam ions via precessional resonance. Our results are consistent with the experimental measurement with respect to mode frequency and mode structure. When the beam ion pressure is increased to exceed a critical value, the low frequency mode transits to a beta-induced Alfvenmore » eigenmode (BAE) with much higher frequency. This BAE is driven by higher energy beam ions. Nonlinear simulations show that the frequency of the low frequency fishbone chirps up and down with corresponding hole-clump structures in phase space, consistent with the Berk-Breizman theory. In addition to the low frequency mode, the high frequency BAE is excited during the nonlinear evolution. Furthermore, for the transient case of beam pressure fraction where the low and high frequency modes are simultaneously excited in the linear phase, only one dominant mode appears in the nonlinear phase with frequency jumps up and down during nonlinear evolution.« less

Long-term evolution of electron distribution function due to nonlinear resonant interaction with whistler mode waves

NASA Astrophysics Data System (ADS)

Artemyev, Anton V.; Neishtadt, Anatoly I.; Vasiliev, Alexei A.

2018-04-01

Accurately modelling and forecasting of the dynamics of the Earth's radiation belts with the available computer resources represents an important challenge that still requires significant advances in the theoretical plasma physics field of wave-particle resonant interaction. Energetic electron acceleration or scattering into the Earth's atmosphere are essentially controlled by their resonances with electromagnetic whistler mode waves. The quasi-linear diffusion equation describes well this resonant interaction for low intensity waves. During the last decade, however, spacecraft observations in the radiation belts have revealed a large number of whistler mode waves with sufficiently high intensity to interact with electrons in the nonlinear regime. A kinetic equation including such nonlinear wave-particle interactions and describing the long-term evolution of the electron distribution is the focus of the present paper. Using the Hamiltonian theory of resonant phenomena, we describe individual electron resonance with an intense coherent whistler mode wave. The derived characteristics of such a resonance are incorporated into a generalized kinetic equation which includes non-local transport in energy space. This transport is produced by resonant electron trapping and nonlinear acceleration. We describe the methods allowing the construction of nonlinear resonant terms in the kinetic equation and discuss possible applications of this equation.

Spillover, nonlinearity, and flexible structures

NASA Technical Reports Server (NTRS)

Bass, Robert W.; Zes, Dean

1991-01-01

Many systems whose evolution in time is governed by Partial Differential Equations (PDEs) are linearized around a known equilibrium before Computer Aided Control Engineering (CACE) is considered. In this case, there are infinitely many independent vibrational modes, and it is intuitively evident on physical grounds that infinitely many actuators would be needed in order to control all modes. A more precise, general formulation of this grave difficulty (spillover problem) is due to A.V. Balakrishnan. A possible route to circumvention of this difficulty lies in leaving the PDE in its original nonlinear form, and adding the essentially finite dimensional control action prior to linearization. One possibly applicable technique is the Liapunov Schmidt rigorous reduction of singular infinite dimensional implicit function problems to finite dimensional implicit function problems. Omitting details of Banach space rigor, the formalities of this approach are given.

Nonlinear evolution and final fate of (charged) superradiant instability

NASA Astrophysics Data System (ADS)

Green, Stephen; Bosch, Pablo; Lehner, Luis

2016-03-01

We describe the full nonlinear development of the superradiant instability for a charged massless scalar field, coupled to general relativity and electromagnetism, in the vicinity of a Reissner-Nordstrom-AdS black hole. The presence of the negative cosmological constant provides a natural context for considering perfectly reflecting boundary conditions and studying the dynamics as the scalar field interacts repeateadly with the black hole. At early times, small superradiant perturbations grow as expected from linearized studies. Backreaction then causes the black hole to lose charge and mass until the perturbation becomes nonsuperradiant, with the final state described by a stable hairy black hole. For large gauge coupling, the instability extracts a large amount of charge per unit mass, resulting in greater entropy increase. We discuss the implications of the observed behavior for the general problem of superradiance in black hole spacetimes.

Entanglement dynamics and position-momentum entropic uncertainty relation of a Λ-type three-level atom interacting with a two-mode cavity field in the presence of nonlinearities

NASA Astrophysics Data System (ADS)

Faghihi, M. J.; Tavassoly, M. K.; Hooshmandasl, M. R.

2013-05-01

In this paper, the interaction between a $\\Lambda$-type three-level atom and two-mode cavity field is discussed. The detuning parameters and cross-Kerr nonlinearity are taken into account and it is assumed that atom-field coupling and Kerr medium to be $f$-deformed. Even though the system seems to be complicated, the analytical form of the state vector of the entire system for considered model is exactly obtained. The time evolution of nonclassical properties such as quantum entanglement and position-momentum entropic uncertainty relation (entropy squeezing) of the field are investigated. In each case, the influences of the detuning parameters, generalized Kerr medium and intensity-dependent coupling on the latter nonclassicality signs are analyzed, in detail.

Numerical simulation of turbulence and terahertz magnetosonic waves generation in collisionless plasmas

NASA Astrophysics Data System (ADS)

Kumar, Narender; Singh, Ram Kishor; Sharma, Swati; Uma, R.; Sharma, R. P.

2018-01-01

This paper presents numerical simulations of laser beam (x-mode) coupling with a magnetosonic wave (MSW) in a collisionless plasma. The coupling arises through ponderomotive non-linearity. The pump beam has been perturbed by a periodic perturbation that leads to the nonlinear evolution of the laser beam. It is observed that the frequency spectra of the MSW have peaks at terahertz frequencies. The simulation results show quite complex localized structures that grow with time. The ensemble averaged power spectrum has also been studied which indicates that the spectral index follows an approximate scaling of the order of ˜ k-2.1 at large scales and scaling of the order of ˜ k-3.6 at smaller scales. The results indicate considerable randomness in the spatial structure of the magnetic field profile which gives sufficient indication of turbulence.

Nonlinear optical enhancement induced by synergistic effect of graphene nanosheets and CdS nanocrystals

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

Zhu, Baohua, E-mail: bhzhu@henu.edu.cn, E-mail: yzgu@henu.edu.cn; Cao, Yawan; Wang, Chong

2016-06-20

CdS nanocrystals are attached on graphene nanosheets and their nonlinear optical properties are investigated by picosecond Z-scan technique at 532 nm. We found that synergistic effect between the graphene and CdS makes a major enhancement on the nonlinear optical absorption of graphene/CdS nanohybrid in comparison with cooperative effect, and the synergistic improvement is restricted by nonradiative defects in hybrid. The synergistic mechanism involving the local field theory and charge transfer evolution is proposed.

Dynamics of electricity market correlations

NASA Astrophysics Data System (ADS)

Alvarez-Ramirez, J.; Escarela-Perez, R.; Espinosa-Perez, G.; Urrea, R.

2009-06-01

Electricity market participants rely on demand and price forecasts to decide their bidding strategies, allocate assets, negotiate bilateral contracts, hedge risks, and plan facility investments. However, forecasting is hampered by the non-linear and stochastic nature of price time series. Diverse modeling strategies, from neural networks to traditional transfer functions, have been explored. These approaches are based on the assumption that price series contain correlations that can be exploited for model-based prediction purposes. While many works have been devoted to the demand and price modeling, a limited number of reports on the nature and dynamics of electricity market correlations are available. This paper uses detrended fluctuation analysis to study correlations in the demand and price time series and takes the Australian market as a case study. The results show the existence of correlations in both demand and prices over three orders of magnitude in time ranging from hours to months. However, the Hurst exponent is not constant over time, and its time evolution was computed over a subsample moving window of 250 observations. The computations, also made for two Canadian markets, show that the correlations present important fluctuations over a seasonal one-year cycle. Interestingly, non-linearities (measured in terms of a multifractality index) and reduced price predictability are found for the June-July periods, while the converse behavior is displayed during the December-January period. In terms of forecasting models, our results suggest that non-linear recursive models should be considered for accurate day-ahead price estimation. On the other hand, linear models seem to suffice for demand forecasting purposes.

Sub-structure formation in starless cores

NASA Astrophysics Data System (ADS)

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

2018-02-01

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

Observing the dynamics of supermassive black hole binaries with pulsar timing arrays.

PubMed

Mingarelli, C M F; Grover, K; Sidery, T; Smith, R J E; Vecchio, A

2012-08-24

Pulsar timing arrays are a prime tool to study unexplored astrophysical regimes with gravitational waves. Here, we show that the detection of gravitational radiation from individually resolvable supermassive black hole binary systems can yield direct information about the masses and spins of the black holes, provided that the gravitational-wave-induced timing fluctuations both at the pulsar and at Earth are detected. This in turn provides a map of the nonlinear dynamics of the gravitational field and a new avenue to tackle open problems in astrophysics connected to the formation and evolution of supermassive black holes. We discuss the potential, the challenges, and the limitations of these observations.

Experimental and numerical investigations of temporally and spatially periodic modulated wave trains

NASA Astrophysics Data System (ADS)

Houtani, H.; Waseda, T.; Tanizawa, K.

2018-03-01

A number of studies on steep nonlinear waves were conducted experimentally with the temporally periodic and spatially evolving (TPSE) wave trains and numerically with the spatially periodic and temporally evolving (SPTE) ones. The present study revealed that, in the vicinity of their maximum crest height, the wave profiles of TPSE and SPTE modulated wave trains resemble each other. From the investigation of the Akhmediev-breather solution of the nonlinear Schrödinger equation (NLSE), it is revealed that the dispersion relation deviated from the quadratic dependence of frequency on wavenumber and became linearly dependent instead. Accordingly, the wave profiles of TPSE and SPTE breathers agree. The range of this agreement is within the order of one wave group of the maximum crest height and persists during the long-term evolution. The findings extend well beyond the NLSE regime and can be applied to modulated wave trains that are highly nonlinear and broad-banded. This was demonstrated from the numerical wave tank simulations with a fully nonlinear potential flow solver based on the boundary element method, in combination with the nonlinear wave generation method based on the prior simulation with the higher-order spectral model. The numerical wave tank results were confirmed experimentally in a physical wave tank. The findings of this study unravel the fundamental nature of the nonlinear wave evolution. The deviation of the dispersion relation of the modulated wave trains occurs because of the nonlinear phase variation due to quasi-resonant interaction, and consequently, the wave geometry of temporally and spatially periodic modulated wave trains coincides.

Petrological evidence for non-linear increase of magmatic intrusion rates before eruption at open vent mafic volcanoe

NASA Astrophysics Data System (ADS)

Ruth, D. C. S.; Costa Rodriguez, F.

2015-12-01

The most active volcanoes on earth erupt in a yearly to decadal time scales, typically erupt mafic magmas and are open-vent systems with prominent degassing plumes (e.g. Mayon, Arenal, Llaima, Etna). Here we investigate the plumbing systems, dynamics, and processes that drive eruptions at these systems. These are key questions for improving hazard evaluation, and better understanding the unrest associated with these types of volcanoes. The petrology and geochemistry from six historical eruptions (1947-2006) of Mayon volcano (Philippines) shows that all lavas are basaltic andesite with phenocrysts of plagioclase + orthopyroxene (Opx) + clinopyroxene. Opx crystals show a variety of compositions and zoning patterns (reverse, normal or complex) with Mg# (= 100 *Mg/[Mg+Fe]) varying from 67 to 81. The simplest interpretation is that the low Mg# parts of the crystals resided on an upper crustal and crystal rich reservoir that was intruded by more primitive magmas from which the high Mg# parts of the crystals grew. Modelling Mg-Fe diffusion in Opx shows that times since magma injection and eruption range from a few days up to 3.5 years in all of the investigated eruptions. The longest diffusion times are shorter than the repose times between the eruptions, which implies that crystal recycling between eruptive events is negligible. This is a surprising result that shows that for each eruption a different part of the evolved crystal-rich plumbing system is activated. This can be due to random intrusion location or an irreversibility of the plumbing system that prevents multiple eruptions from the same crystal-rich part. Moreover, we find that the number of intrusions markedly increases before each eruption in a non-linear manner. Such an increased rate of intrusions with time might reflect non-linear rheological properties of the crystal-rich system, of the enclosing rocks, or the non-linear evolution of crystal-melt reaction-dissolution fronts during magma intrusions.

A Large-Particle Monte Carlo Code for Simulating Non-Linear High-Energy Processes Near Compact Objects

NASA Technical Reports Server (NTRS)

Stern, Boris E.; Svensson, Roland; Begelman, Mitchell C.; Sikora, Marek

1995-01-01

High-energy radiation processes in compact cosmic objects are often expected to have a strongly non-linear behavior. Such behavior is shown, for example, by electron-positron pair cascades and the time evolution of relativistic proton distributions in dense radiation fields. Three independent techniques have been developed to simulate these non-linear problems: the kinetic equation approach; the phase-space density (PSD) Monte Carlo method; and the large-particle (LP) Monte Carlo method. In this paper, we present the latest version of the LP method and compare it with the other methods. The efficiency of the method in treating geometrically complex problems is illustrated by showing results of simulations of 1D, 2D and 3D systems. The method is shown to be powerful enough to treat non-spherical geometries, including such effects as bulk motion of the background plasma, reflection of radiation from cold matter, and anisotropic distributions of radiating particles. It can therefore be applied to simulate high-energy processes in such astrophysical systems as accretion discs with coronae, relativistic jets, pulsar magnetospheres and gamma-ray bursts.

Data dependence for the amplitude equation of surface waves

NASA Astrophysics Data System (ADS)

Secchi, Paolo

2016-04-01

We consider the amplitude equation for nonlinear surface wave solutions of hyperbolic conservation laws. This is an asymptotic nonlocal, Hamiltonian evolution equation with quadratic nonlinearity. For example, this equation describes the propagation of nonlinear Rayleigh waves (Hamilton et al. in J Acoust Soc Am 97:891-897, 1995), surface waves on current-vortex sheets in incompressible MHD (Alì and Hunter in Q Appl Math 61(3):451-474, 2003; Alì et al. in Stud Appl Math 108(3):305-321, 2002) and on the incompressible plasma-vacuum interface (Secchi in Q Appl Math 73(4):711-737, 2015). The local-in-time existence of smooth solutions to the Cauchy problem for the amplitude equation in noncanonical variables was shown in Hunter (J Hyperbolic Differ Equ 3(2):247-267, 2006), Secchi (Q Appl Math 73(4):711-737, 2015). In the present paper we prove the continuous dependence in strong norm of solutions on the initial data. This completes the proof of the well-posedness of the problem in the classical sense of Hadamard.

Vortex creep and the internal temperature of neutron stars - Linear and nonlinear response to a glitch

NASA Technical Reports Server (NTRS)

Alpar, M. A.; Cheng, K. S.; Pines, D.

1989-01-01

The dynamics of pinned superfluid in neutron stars is determined by the thermal 'creep' of vortices. Vortex creep can respond to changes in the rotation rate of the neutron star crust and provide the observed types of dynamical relaxation following pulsar glitches. It also gives rise to energy dissipation, which determines the thermal evolution of pulsars once the initial heat content has been radiated away. The different possible regimes of vortex creep are explored, and it is shown that the nature of the dynamical response of the pinned superfluid evolves with a pulsar's age. Younger pulsars display a linear regime, where the response is linear in the initial perturbation and is a simple exponential relaxation as a function of time. A nonliner response, with a characteristic nonlinear dependence on the initial perturbation, is responsible for energy dissipation and becomes the predominant mode of response as the pulsar ages. The transition from the linear to the nonlinear regime depends sensitively on the temperature of the neutron star interior. A preliminary review of existing postglitch observations is given within this general evolutionary framework.

Koopman decomposition of Burgers' equation: What can we learn?

NASA Astrophysics Data System (ADS)

Page, Jacob; Kerswell, Rich

2017-11-01

Burgers' equation is a well known 1D model of the Navier-Stokes equations and admits a selection of equilibria and travelling wave solutions. A series of Burgers' trajectories are examined with Dynamic Mode Decomposition (DMD) to probe the capability of the method to extract coherent structures from ``run-down'' simulations. The performance of the method depends critically on the choice of observable. We use the Cole-Hopf transformation to derive an observable which has linear, autonomous dynamics and for which the DMD modes overlap exactly with Koopman modes. This observable can accurately predict the flow evolution beyond the time window of the data used in the DMD, and in that sense outperforms other observables motivated by the nonlinearity in the governing equation. The linearizing observable also allows us to make informed decisions about often ambiguous choices in nonlinear problems, such as rank truncation and snapshot spacing. A number of rules of thumb for connecting DMD with the Koopman operator for nonlinear PDEs are distilled from the results. Related problems in low Reynolds number fluid turbulence are also discussed.

Evolution patterns and parameter regimes in edge localized modes on the National Spherical Torus Experiment

DOE Data Explorer

Smith, D. R. [Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States); Bell, R. E. [Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States); Podesta, M. [Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States); Smith, D. R. [Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States); Fonck, R. J. [Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States); McKee, G. R. [Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States); Diallo, A. [Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States); Kaye, S. M. [Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States); LeBlanc, B. P. [Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States); Sabbagh, S. A. [Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)

2015-09-01

We implement unsupervised machine learning techniques to identify characteristic evolution patterns and associated parameter regimes in edge localized mode (ELM) events observed on the National Spherical Torus Experiment. Multi-channel, localized measurements spanning the pedestal region capture the complex evolution patterns of ELM events on Alfven timescales. Some ELM events are active for less than 100~microsec, but others persist for up to 1~ms. Also, some ELM events exhibit a single dominant perturbation, but others are oscillatory. Clustering calculations with time-series similarity metrics indicate the ELM database contains at least two and possibly three groups of ELMs with similar evolution patterns. The identified ELM groups trigger similar stored energy loss, but the groups occupy distinct parameter regimes for ELM-relevant quantities like plasma current, triangularity, and pedestal height. Notably, the pedestal electron pressure gradient is not an effective parameter for distinguishing the ELM groups, but the ELM groups segregate in terms of electron density gradient and electron temperature gradient. The ELM evolution patterns and corresponding parameter regimes can shape the formulation or validation of nonlinear ELM models. Finally, the techniques and results demonstrate an application of unsupervised machine learning at a data-rich fusion facility.

A geomorphic process law for detachment-limited hillslopes

NASA Astrophysics Data System (ADS)

Turowski, Jens

2015-04-01

Geomorphic process laws are used to assess the shape evolution of structures at the Earth's surface over geological time scales, and are routinely used in landscape evolution models. There are two currently available concepts on which process laws for hillslope evolution rely. In the transport-limited concept, the evolution of a hillslope is described by a linear or a non-linear diffusion equation. In contrast, in the threshold slope concept, the hillslope is assumed to collapse to a slope equal to the internal friction angle of the material when the load due to the relief exists the material strength. Many mountains feature bedrock slopes, especially in the high mountains, and material transport along the slope is limited by the erosion of the material from the bedrock. Here, I suggest a process law for detachment-limited or threshold-dominated hillslopes, in which the erosion rate is a function of the applied stress minus the surface stress due to structural loading. The process law leads to the prediction of an equilibrium form that compares well to the shape of many mountain domes.

Emerging spectra of singular correlation matrices under small power-map deformations

NASA Astrophysics Data System (ADS)

Vinayak; Schäfer, Rudi; Seligman, Thomas H.

2013-09-01

Correlation matrices are a standard tool in the analysis of the time evolution of complex systems in general and financial markets in particular. Yet most analysis assume stationarity of the underlying time series. This tends to be an assumption of varying and often dubious validity. The validity of the assumption improves as shorter time series are used. If many time series are used, this implies an analysis of highly singular correlation matrices. We attack this problem by using the so-called power map, which was introduced to reduce noise. Its nonlinearity breaks the degeneracy of the zero eigenvalues and we analyze the sensitivity of the so-emerging spectra to correlations. This sensitivity will be demonstrated for uncorrelated and correlated Wishart ensembles.

Emerging spectra of singular correlation matrices under small power-map deformations.

PubMed

Vinayak; Schäfer, Rudi; Seligman, Thomas H

2013-09-01

Correlation matrices are a standard tool in the analysis of the time evolution of complex systems in general and financial markets in particular. Yet most analysis assume stationarity of the underlying time series. This tends to be an assumption of varying and often dubious validity. The validity of the assumption improves as shorter time series are used. If many time series are used, this implies an analysis of highly singular correlation matrices. We attack this problem by using the so-called power map, which was introduced to reduce noise. Its nonlinearity breaks the degeneracy of the zero eigenvalues and we analyze the sensitivity of the so-emerging spectra to correlations. This sensitivity will be demonstrated for uncorrelated and correlated Wishart ensembles.

Global, finite energy, weak solutions for the NLS with rough, time-dependent magnetic potentials

NASA Astrophysics Data System (ADS)

Antonelli, Paolo; Michelangeli, Alessandro; Scandone, Raffaele

2018-04-01

We prove the existence of weak solutions in the space of energy for a class of nonlinear Schrödinger equations in the presence of a external, rough, time-dependent magnetic potential. Under our assumptions, it is not possible to study the problem by means of usual arguments like resolvent techniques or Fourier integral operators, for example. We use a parabolic regularisation, and we solve the approximating Cauchy problem. This is achieved by obtaining suitable smoothing estimates for the dissipative evolution. The total mass and energy bounds allow to extend the solution globally in time. We then infer sufficient compactness properties in order to produce a global-in-time finite energy weak solution to our original problem.

On a Nonlinear Model for Tumor Growth: Global in Time Weak Solutions

NASA Astrophysics Data System (ADS)

Donatelli, Donatella; Trivisa, Konstantina

2014-07-01

We investigate the dynamics of a class of tumor growth models known as mixed models. The key characteristic of these type of tumor growth models is that the different populations of cells are continuously present everywhere in the tumor at all times. In this work we focus on the evolution of tumor growth in the presence of proliferating, quiescent and dead cells as well as a nutrient. The system is given by a multi-phase flow model and the tumor is described as a growing continuum Ω with boundary ∂Ω both of which evolve in time. Global-in-time weak solutions are obtained using an approach based on penalization of the boundary behavior, diffusion and viscosity in the weak formulation.

Non-linear macro evolution of a dc driven micro atmospheric glow discharge

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

Xu, S. F.; Zhong, X. X., E-mail: xxzhong@sjtu.edu.cn

2015-10-15

We studied the macro evolution of the micro atmospheric glow discharge generated between a micro argon jet into ambient air and static water. The micro discharge behaves similarly to a complex ecosystem. Non-linear behaviors are found for the micro discharge when the water acts as a cathode, different from the discharge when water behaves as an anode. Groups of snapshots of the micro discharge formed at different discharge currents are captured by an intensified charge-coupled device with controlled exposure time, and each group consisted of 256 images taken in succession. Edge detection methods are used to identify the water surfacemore » and then the total brightness is defined by adding up the signal counts over the area of the micro discharge. Motions of the water surface at different discharge currents show that the water surface lowers increasingly rapidly when the water acts as a cathode. In contrast, the water surface lowers at a constant speed when the water behaves as an anode. The light curves are similar to logistic growth curves, suggesting that a self-inhibition process occurs in the micro discharge. Meanwhile, the total brightness increases linearly during the same time when the water acts as an anode. Discharge-water interactions cause the micro discharge to evolve. The charged particle bomb process is probably responsible for the different behaviors of the micro discharges when the water acts as cathode and anode.« less

Research of large-amplitude waves evolution in the framework of shallow water equations and their implication for people's safety in extreme situations

NASA Astrophysics Data System (ADS)

Pelinovsky, Efim; Chaikovskaia, Natalya; Rodin, Artem

2015-04-01

The paper presents the analysis of the formation and evolution of shock wave in shallow water with no restrictions on its amplitude in the framework of the nonlinear shallow water equations. It is shown that in the case of large-amplitude waves appears a new nonlinear effect of reflection from the shock front of incident wave. These results are important for the assessment of coastal flooding by tsunami waves and storm surges. Very often the largest number of victims was observed on the coastline where the wave moved breaking. Many people, instead of running away, were just looking at the movement of the "raging wall" and lost time. This fact highlights the importance of researching the problem of security and optimal behavior of people in situations with increased risk. Usually there is uncertainty about the exact time, when rogue waves will impact. This fact limits the ability of people to adjust their behavior psychologically to the stressful situations. It concerns specialists, who are busy both in the field of flying activity and marine service as well as adults, young people and children, who live on the coastal zone. The rogue wave research is very important and it demands cooperation of different scientists - mathematicians and physicists, as well as sociologists and psychologists, because the final goal of efforts of all scientists is minimization of the harm, brought by rogue waves to humanity.

Frequency-Domain Streak Camera and Tomography for Ultrafast Imaging of Evolving and Channeled Plasma Accelerator Structures

NASA Astrophysics Data System (ADS)

Li, Zhengyan; Zgadzaj, Rafal; Wang, Xiaoming; Reed, Stephen; Dong, Peng; Downer, Michael C.

2010-11-01

We demonstrate a prototype Frequency Domain Streak Camera (FDSC) that can capture the picosecond time evolution of the plasma accelerator structure in a single shot. In our prototype Frequency-Domain Streak Camera, a probe pulse propagates obliquely to a sub-picosecond pump pulse that creates an evolving nonlinear index "bubble" in fused silica glass, supplementing a conventional Frequency Domain Holographic (FDH) probe-reference pair that co-propagates with the "bubble". Frequency Domain Tomography (FDT) generalizes Frequency-Domain Streak Camera by probing the "bubble" from multiple angles and reconstructing its morphology and evolution using algorithms similar to those used in medical CAT scans. Multiplexing methods (Temporal Multiplexing and Angular Multiplexing) improve data storage and processing capability, demonstrating a compact Frequency Domain Tomography system with a single spectrometer.

[Scale Relativity Theory in living beings morphogenesis: fratal, determinism and chance].

PubMed

Chaline, J

2012-10-01

The Scale Relativity Theory has many biological applications from linear to non-linear and, from classical mechanics to quantum mechanics. Self-similar laws have been used as model for the description of a huge number of biological systems. Theses laws may explain the origin of basal life structures. Log-periodic behaviors of acceleration or deceleration can be applied to branching macroevolution, to the time sequences of major evolutionary leaps. The existence of such a law does not mean that the role of chance in evolution is reduced, but instead that randomness and contingency may occur within a framework which may itself be structured in a partly statistical way. The scale relativity theory can open new perspectives in evolution. Copyright © 2012 Elsevier Masson SAS. All rights reserved.

High-energy evolution to three loops

NASA Astrophysics Data System (ADS)

Caron-Huot, Simon; Herranen, Matti

2018-02-01

The Balitsky-Kovchegov equation describes the high-energy growth of gauge theory scattering amplitudes as well as nonlinear saturation effects which stop it. We obtain the three-loop corrections to the equation in planar N = 4 super Yang-Mills theory. Our method exploits a recently established equivalence with the physics of soft wide-angle radiation, so-called non-global logarithms, and thus yields at the same time the threeloop evolution equation for non-global logarithms. As a by-product of our analysis, we develop a Lorentz-covariant method to subtract infrared and collinear divergences in crosssection calculations in the planar limit. We compare our result in the linear regime with a recent prediction for the so-called Pomeron trajectory, and compare its collinear limit with predictions from the spectrum of twist-two operators.

Fatigue damage evaluation of austenitic stainless steel using nonlinear ultrasonic waves in low cycle regime

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

Zhang, Jianfeng; Xuan, Fu-Zhen, E-mail: fzxuan@ecust.edu.cn

The interrupted low cycle fatigue test of austenitic stainless steel was conducted and the dislocation structure and fatigue damage was evaluated subsequently by using both transmission electron microscope and nonlinear ultrasonic wave techniques. A “mountain shape” correlation between the nonlinear acoustic parameter and the fatigue life fraction was achieved. This was ascribed to the generation and evolution of planar dislocation structure and nonplanar dislocation structure such as veins, walls, and cells. The “mountain shape” correlation was interpreted successfully by the combined contribution of dislocation monopole and dipole with an internal-stress dependent term of acoustic nonlinearity.

Effect of absorption on nonlinear propagation of short ultrasound pulses generated by rectangular transducers

NASA Astrophysics Data System (ADS)

Khokhlova, Vera A.; Ponomaryov, Anatoly E.; Averkiou, Michalakis A.; Crum, Lawrence A.

2002-11-01

A numerical solution of the KZK-type parabolic nonlinear evolution equation is presented for finite-amplitude sound beams radiated by rectangular sources. The initial acoustic waveform is a short tone burst, similar to those used in diagnostic ultrasound. The generation of higher harmonic components and their spatial structure are investigated for media similar to tissue with various frequency dependent absorption properties. Nonlinear propagation in a thermoviscous fluid with a quadratic frequency law of absorption is compared to that in tissue with a nearly linear frequency law of absorption. The algorithm is based on that originally developed by Lee and Hamilton [J. Acoust. Soc. Am. 97, 906-917 (1995)] to model circular sources. The algorithm is generalized for two-dimensional sources without axial symmetry. The diffraction integral is adapted in the time-domain for two dimensions with the implicit backward finite difference (IBFD) scheme in the nearfield and with the alternate direction implicit (ADI) method at longer distances. Arbitrary frequency dependence of absorption is included in this model and solved in the frequency-domain using the FFT technique. The results of simulation may be used to better understand the nonlinear beam structure for tissue harmonic imaging in modern medical diagnostic scanners. [Work supported by CRDF and RFBR.

Structural Evolutions of STOCK Markets Controlled by Generalized Entropy Principles of Complex Systems

NASA Astrophysics Data System (ADS)

Wang, Yi Jiao; Feng, Qing Yi; Chai, Li He

As one of the most important financial markets and one of the main parts of economic system, the stock market has become the research focus in economics. The stock market is a typical complex open system far from equilibrium. Many available models that make huge contribution to researches on market are strong in describing the market however, ignoring strong nonlinear interactions among active agents and weak in reveal underlying dynamic mechanisms of structural evolutions of market. From econophysical perspectives, this paper analyzes the complex interactions among agents and defines the generalized entropy in stock markets. Nonlinear evolutionary dynamic equation for the stock markets is then derived from Maximum Generalized Entropy Principle. Simulations are accordingly conducted for a typical case with the given data, by which the structural evolution of the stock market system is demonstrated. Some discussions and implications are finally provided.

A robust BAO extractor

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

Noda, Eugenio; Pietroni, Massimo; Peloso, Marco, E-mail: eugenio.noda@pr.infn.it, E-mail: peloso@physics.umn.edu, E-mail: massimo.pietroni@unipr.it

2017-08-01

We define a procedure to extract the oscillating part of a given nonlinear Power Spectrum, and derive an equation describing its evolution including the leading effects at all scales. The intermediate scales are taken into account by standard perturbation theory, the long range (IR) displacements are included by using consistency relations, and the effect of small (UV) scales is included via effective coefficients computed in simulations. We show that the UV effects are irrelevant in the evolution of the oscillating part, while they play a crucial role in reproducing the smooth component. Our 'extractor' operator can be applied to simulationsmore » and real data in order to extract the Baryonic Acoustic Oscillations (BAO) without any fitting function and nuisance parameter. We conclude that the nonlinear evolution of BAO can be accurately reproduced at all scales down to 0 z = by our fast analytical method, without any need of extra parameters fitted from simulations.« less

Driving the Oxygen Evolution Reaction by Nonlinear Cooperativity in Bimetallic Coordination Catalysts.

PubMed

Wurster, Benjamin; Grumelli, Doris; Hötger, Diana; Gutzler, Rico; Kern, Klaus

2016-03-23

Developing efficient catalysts for electrolysis, in particular for the oxygen evolution in the anodic half cell reaction, is an important challenge in energy conversion technologies. By taking inspiration from the catalytic properties of single-atom catalysts and metallo-proteins, we exploit the potential of metal-organic networks as electrocatalysts in the oxygen evolution reaction (OER). A dramatic enhancement of the catalytic activity toward the production of oxygen by nearly 2 orders of magnitude is demonstrated for novel heterobimetallic organic catalysts compared to metallo-porphyrins. Using a supramolecular approach we deliberately place single iron and cobalt atoms in either of two different coordination environments and observe a highly nonlinear increase in the catalytic activity depending on the coordination spheres of Fe and Co. Catalysis sets in at about 300 mV overpotential with high turnover frequencies that outperform other metal-organic catalysts like the prototypical hangman porphyrins.

Evolution of Lamb Vector as a Vortex Breaking into Turbulence.

NASA Astrophysics Data System (ADS)

Wu, J. Z.; Lu, X. Y.

1996-11-01

In an incompressible flow, either laminar or turbulent, the Lamb vector is solely responsible to nonlinear interactions. While its longitudinal part is balanced by stagnation enthalpy, its transverse part is the unique source (as an external forcing in spectral space) that causes the flow to evolve. Moreover, in Reynolds-averaged flows the turbulent force can be derived exclusively from the Lamb vector instead of the full Reynolds stress tensor. Therefore, studying the evolution of the Lamb vector itself (both longitudinal and transverse parts) is of great interest. We have numerically examined this problem, taking the nonlinear distabilization of a viscous vortex as an example. In the later stage of this evolution we introduced a forcing to keep a statistically steady state, and observed the Lamb vector behavior in the resulting fine turbulence. The result is presented in both physical and spectral spaces.

Artificial boundary conditions for certain evolution PDEs with cubic nonlinearity for non-compactly supported initial data

NASA Astrophysics Data System (ADS)

Vaibhav, V.

2011-04-01

The paper addresses the problem of constructing non-reflecting boundary conditions for two types of one dimensional evolution equations, namely, the cubic nonlinear Schrödinger (NLS) equation, ∂tu+Lu-iχ|u|2u=0 with L≡-i∂x2, and the equation obtained by letting L≡∂x3. The usual restriction of compact support of the initial data is relaxed by allowing it to have a constant amplitude along with a linear phase variation outside a compact domain. We adapt the pseudo-differential approach developed by Antoine et al. (2006) [5] for the NLS equation to the second type of evolution equation, and further, extend the scheme to the aforementioned class of initial data for both of the equations. In addition, we discuss efficient numerical implementation of our scheme and produce the results of several numerical experiments demonstrating its effectiveness.

Stochastic modeling of mode interactions via linear parabolized stability equations

NASA Astrophysics Data System (ADS)

Ran, Wei; Zare, Armin; Hack, M. J. Philipp; Jovanovic, Mihailo

2017-11-01

Low-complexity approximations of the Navier-Stokes equations have been widely used in the analysis of wall-bounded shear flows. In particular, the parabolized stability equations (PSE) and Floquet theory have been employed to capture the evolution of primary and secondary instabilities in spatially-evolving flows. We augment linear PSE with Floquet analysis to formally treat modal interactions and the evolution of secondary instabilities in the transitional boundary layer via a linear progression. To this end, we leverage Floquet theory by incorporating the primary instability into the base flow and accounting for different harmonics in the flow state. A stochastic forcing is introduced into the resulting linear dynamics to model the effect of nonlinear interactions on the evolution of modes. We examine the H-type transition scenario to demonstrate how our approach can be used to model nonlinear effects and capture the growth of the fundamental and subharmonic modes observed in direct numerical simulations and experiments.

Cosmological Ohm's law and dynamics of non-minimal electromagnetism

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

Hollenstein, Lukas; Jain, Rajeev Kumar; Urban, Federico R., E-mail: lukas.hollenstein@cea.fr, E-mail: jain@cp3.dias.sdu.dk, E-mail: furban@ulb.ac.be

2013-01-01

The origin of large-scale magnetic fields in cosmic structures and the intergalactic medium is still poorly understood. We explore the effects of non-minimal couplings of electromagnetism on the cosmological evolution of currents and magnetic fields. In this context, we revisit the mildly non-linear plasma dynamics around recombination that are known to generate weak magnetic fields. We use the covariant approach to obtain a fully general and non-linear evolution equation for the plasma currents and derive a generalised Ohm law valid on large scales as well as in the presence of non-minimal couplings to cosmological (pseudo-)scalar fields. Due to the sizeablemore » conductivity of the plasma and the stringent observational bounds on such couplings, we conclude that modifications of the standard (adiabatic) evolution of magnetic fields are severely limited in these scenarios. Even at scales well beyond a Mpc, any departure from flux freezing behaviour is inhibited.« less

New numerical solutions of three-dimensional compressible hydrodynamic convection. [in stars

NASA Technical Reports Server (NTRS)

Hossain, Murshed; Mullan, D. J.

1990-01-01

Numerical solutions of three-dimensional compressible hydrodynamics (including sound waves) in a stratified medium with open boundaries are presented. Convergent/divergent points play a controlling role in the flows, which are dominated by a single frequency related to the mean sound crossing time. Superposed on these rapid compressive flows, slower eddy-like flows eventually create convective transport. The solutions contain small structures stacked on top of larger ones, with vertical scales equal to the local pressure scale heights, H sub p. Although convective transport starts later in the evolution, vertical scales of H sub p are apparently selected at much earlier times by nonlinear compressive effects.

Auger heating of carriers in {GaAs}/{AlAs} heterostructures

NASA Astrophysics Data System (ADS)

Borri, P.; Ceccherini, S.; Gurioli, M.; Bogani, F.

1997-07-01

The photoluminescence of {GaAs}/{AlAs} multiple quantum wells structures under optical ps excitation is investigated for carrier densities in the range 10 18-4 × 10 19 cm -3 with frequency and time-resolved spectroscopic techniques. The measurements give a direct evidence of the occurrence in the sample of carrier heating. This energy up-conversion gives rise to photoluminescence from the states near the Fermi level whose intensity and time evolution depend on the carrier density in a strongly non-linear way. The observed behaviour can be explained introducing in the carrier dynamics an up-conversion mechanism due to Auger-like processes.

Crossflow-Vortex Breakdown on Swept Wings: Correlation of Nonlinear Physics

NASA Technical Reports Server (NTRS)

Joslin, R. D.; Streett, C. L.

1994-01-01

The spatial evolution of cross flow-vortex packets in a laminar boundary layer on a swept wing are computed by the direct numerical simulation of the incompressible Navier- Stokes equations. A wall-normal velocity distribution of steady suction and blowing at the wing surface is used to generate a strip of equally spaced and periodic disturbances along the span. Three simulations are conducted to study the effect of initial amplitude on the disturbance evolution, to determine the role of traveling cross ow modes in transition, and to devise a correlation function to guide theories of transition prediction. In each simulation, the vortex packets first enter a chordwise region of linear independent growth, then, the individual packets coalesce downstream and interact with adjacent packets, and, finally, the vortex packets nonlinearly interact to generate inflectional velocity profiles. As the initial amplitude of the disturbance is increased, the length of the evolution to breakdown decreases. For this pressure gradient, stationary modes dominate the disturbance evolution. A two-coeffcient function was devised to correlate the simulation results. The coefficients, combined with a single simulation result, provide sufficient information to generate the evolution pattern for disturbances of any initial amplitude.

Population ecology, nonlinear dynamics, and social evolution. I. Associations among nonrelatives.

PubMed

Avilés, Leticia; Abbot, Patrick; Cutter, Asher D

2002-02-01

Using an individual-based and genetically explicit simulation model, we explore the evolution of sociality within a population-ecology and nonlinear-dynamics framework. Assuming that individual fitness is a unimodal function of group size and that cooperation may carry a relative fitness cost, we consider the evolution of one-generation breeding associations among nonrelatives. We explore how parameters such as the intrinsic rate of growth and group and global carrying capacities may influence social evolution and how social evolution may, in turn, influence and be influenced by emerging group-level and population-wide dynamics. We find that group living and cooperation evolve under a wide range of parameter values, even when cooperation is costly and the interactions can be defined as altruistic. Greater levels of cooperation, however, did evolve when cooperation carried a low or no relative fitness cost. Larger group carrying capacities allowed the evolution of larger groups but also resulted in lower cooperative tendencies. When the intrinsic rate of growth was not too small and control of the global population size was density dependent, the evolution of large cooperative tendencies resulted in dynamically unstable groups and populations. These results are consistent with the existence and typical group sizes of organisms ranging from the pleometrotic ants to the colonial birds and the global population outbreaks and crashes characteristic of organisms such as the migratory locusts and the tree-killing bark beetles.

Flight control optimization from design to assessment application on the Cessna Citation X business aircraft =

NASA Astrophysics Data System (ADS)

Boughari, Yamina

New methodologies have been developed to optimize the integration, testing and certification of flight control systems, an expensive process in the aerospace industry. This thesis investigates the stability of the Cessna Citation X aircraft without control, and then optimizes two different flight controllers from design to validation. The aircraft's model was obtained from the data provided by the Research Aircraft Flight Simulator (RAFS) of the Cessna Citation business aircraft. To increase the stability and control of aircraft systems, optimizations of two different flight control designs were performed: 1) the Linear Quadratic Regulation and the Proportional Integral controllers were optimized using the Differential Evolution algorithm and the level 1 handling qualities as the objective function. The results were validated for the linear and nonlinear aircraft models, and some of the clearance criteria were investigated; and 2) the Hinfinity control method was applied on the stability and control augmentation systems. To minimize the time required for flight control design and its validation, an optimization of the controllers design was performed using the Differential Evolution (DE), and the Genetic algorithms (GA). The DE algorithm proved to be more efficient than the GA. New tools for visualization of the linear validation process were also developed to reduce the time required for the flight controller assessment. Matlab software was used to validate the different optimization algorithms' results. Research platforms of the aircraft's linear and nonlinear models were developed, and compared with the results of flight tests performed on the Research Aircraft Flight Simulator. Some of the clearance criteria of the optimized H-infinity flight controller were evaluated, including its linear stability, eigenvalues, and handling qualities criteria. Nonlinear simulations of the maneuvers criteria were also investigated during this research to assess the Cessna Citation X's flight controller clearance, and therefore, for its anticipated certification.

Experimental Investigation of the Acoustic Nonlinear Behavior in Granular Polymer Bonded Explosives with Progressive Fatigue Damage

PubMed Central

Yang, Zhanfeng; Tian, Yong; Li, Weibin; Zhou, Haiqiang; Zhang, Weibin; Li, Jingming

2017-01-01

The measurement of acoustic nonlinear response is known as a promising technique to characterize material micro-damages. In this paper, nonlinear ultrasonic approach is used to characterize the evolution of fatigue induced micro-cracks in polymer bonded explosives. The variations of acoustic nonlinearity with respect to fatigue cycles in the specimens are obtained in this investigation. The present results show a significant increase of acoustic nonlinearity with respect to fatigue cycles. The experimental observation of the correlation between the acoustic nonlinearity and fatigue cycles in carbon/epoxy laminates, verifies that an acoustic nonlinear response can be used to evaluate the progressive fatigue damage in the granular polymer bonded explosives. The sensitivity comparison of nonlinear and linear parameters of ultrasonic waves in the specimens shows that nonlinear acoustic parameters are more promising indicators to fatigue induced micro-damage than linear ones. The feasibility study of the micro-damage assessment of polymer bonded explosives by nonlinear ultrasonic technique in this work can be applied to damage identification, material degradation monitoring, and lifetime prediction of the explosive parts. PMID:28773017

Experimental Investigation of the Acoustic Nonlinear Behavior in Granular Polymer Bonded Explosives with Progressive Fatigue Damage.

PubMed

Yang, Zhanfeng; Tian, Yong; Li, Weibin; Zhou, Haiqiang; Zhang, Weibin; Li, Jingming

2017-06-16

The measurement of acoustic nonlinear response is known as a promising technique to characterize material micro-damages. In this paper, nonlinear ultrasonic approach is used to characterize the evolution of fatigue induced micro-cracks in polymer bonded explosives. The variations of acoustic nonlinearity with respect to fatigue cycles in the specimens are obtained in this investigation. The present results show a significant increase of acoustic nonlinearity with respect to fatigue cycles. The experimental observation of the correlation between the acoustic nonlinearity and fatigue cycles in carbon/epoxy laminates, verifies that an acoustic nonlinear response can be used to evaluate the progressive fatigue damage in the granular polymer bonded explosives. The sensitivity comparison of nonlinear and linear parameters of ultrasonic waves in the specimens shows that nonlinear acoustic parameters are more promising indicators to fatigue induced micro-damage than linear ones. The feasibility study of the micro-damage assessment of polymer bonded explosives by nonlinear ultrasonic technique in this work can be applied to damage identification, material degradation monitoring, and lifetime prediction of the explosive parts.

Analysis and gyrokinetic simulation of MHD Alfven wave interactions

NASA Astrophysics Data System (ADS)

Nielson, Kevin Derek

The study of low-frequency turbulence in magnetized plasmas is a difficult problem due to both the enormous range of scales involved and the variety of physics encompassed over this range. Much of the progress that has been made in turbulence theory is based upon a result from incompressible magnetohydrodynamics (MHD), in which energy is only transferred from large scales to small via the collision of Alfven waves propagating oppositely along the mean magnetic field. Improvements in laboratory devices and satellite measurements have demonstrated that, while theories based on this premise are useful over inertial ranges, describing turbulence at scales that approach particle gyroscales requires new theory. In this thesis, we examine the limits of incompressible MHD theory in describing collisions between pairs of Alfven waves. This interaction represents the fundamental unit of plasma turbulence. To study this interaction, we develop an analytic theory describing the nonlinear evolution of interacting Alfven waves and compare this theory to simulations performed using the gyrokinetic code AstroGK. Gyrokinetics captures a much richer set of physics than that described by incompressible MHD, and is well-suited to describing Alfvenic turbulence around the ion gyroscale. We demonstrate that AstroGK is well suited to the study of physical Alfven waves by reproducing laboratory Alfven dispersion data collected using the LAPD. Additionally, we have developed an initialization alogrithm for use with AstroGK that allows exact Alfven eigenmodes to be initialized with user specified amplitudes and phases. We demonstrate that our analytic theory based upon incompressible MHD gives excellent agreement with gyrokinetic simulations for weakly turbulent collisions in the limit that k⊥rho i << 1. In this limit, agreement is observed in the time evolution of nonlinear products, and in the strength of nonlinear interaction with respect to polarization and scale. We also examine the effect of wave amplitude upon the validity of our analytic solution, exploring the nature of strong turbulence. In the kinetic limit where k⊥ rhoi ≳ 1 where incompressible MHD is no longer a valid description, we illustrate how the nonlinear evolution departs from our analytic expression. The analytic theory we develop provides a framework from which more sophisticated of weak and strong inertial-range turbulence theories may be developed. Characterization of the limits of this theory may provide guidance in the development of kinetic Alfven wave turbulence.

Propagation of a finite-amplitude elastic pulse in a bar of Berea sandstone: A detailed look at the mechanisms of classical nonlinearity, hysteresis, and nonequilibrium dynamics: Nonlinear propagation of elastic pulse

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

Remillieux, Marcel C.; Ulrich, T. J.; Goodman, Harvey E.

Here, we study the propagation of a finite-amplitude elastic pulse in a long thin bar of Berea sandstone. In previous work, this type of experiment has been conducted to quantify classical nonlinearity, based on the amplitude growth of the second harmonic as a function of propagation distance. To greatly expand on that early work, a non-contact scanning 3D laser Doppler vibrometer was used to track the evolution of the axial component of the particle velocity over the entire surface of the bar as functions of the propagation distance and source amplitude. With these new measurements, the combined effects of classicalmore » nonlinearity, hysteresis, and nonequilibrium dynamics have all been measured simultaneously. We then show that the numerical resolution of the 1D wave equation with terms for classical nonlinearity and attenuation accurately captures the spectral features of the waves up to the second harmonic. But, for higher harmonics the spectral content is shown to be strongly influenced by hysteresis. This work also shows data which not only quantifies classical nonlinearity but also the nonequilibrium dynamics based on the relative change in the arrival time of the elastic pulse as a function of strain and distance from the source. Finally, a comparison is made to a resonant bar measurement, a reference experiment used to quantify nonequilibrium dynamics, based on the relative shift of the resonance frequencies as a function of the maximum dynamic strain in the sample.« less

Ultrasound wave propagation in tissue and scattering from microbubbles for echo particle image velocimetry technique.

PubMed

Mukdadi, Osama; Shandas, Robin

2004-01-01

Nonlinear wave propagation in tissue can be employed for tissue harmonic imaging, ultrasound surgery, and more effective tissue ablation for high intensity focused ultrasound (HIFU). Wave propagation in soft tissue and scattering from microbubbles (ultrasound contrast agents) are modeled to improve detectability, signal-to-noise ratio, and contrast harmonic imaging used for echo particle image velocimetry (Echo-PIV) technique. The wave motion in nonlinear material (tissue) is studied using KZK-type parabolic evolution equation. This model considers ultrasound beam diffraction, attenuation, and tissue nonlinearity. Time-domain numerical model is based on that originally developed by Lee and Hamilton [J. Acoust. Soc. Am 97:906-917 (1995)] for axi-symmetric acoustic field. The initial acoustic waveform emitted from the transducer is assumed to be a broadband wave modulated by Gaussian envelope. Scattering from microbubbles seeded in the blood stream is characterized. Hence, we compute the pressure field impinges the wall of a coated microbubble; the dynamics of oscillating microbubble can be modeled using Rayleigh-Plesset-type equation. Here, the continuity and the radial-momentum equation of encapsulated microbubbles are used to account for the lipid layer surrounding the microbubble. Numerical results show the effects of tissue and microbubble nonlinearities on the propagating pressure wave field. These nonlinearities have a strong influence on the waveform distortion and harmonic generation of the propagating and scattering waves. Results also show that microbubbles have stronger nonlinearity than tissue, and thus improves S/N ratio. These theoretical predictions of wave phenomena provide further understanding of biomedical imaging technique and provide better system design.

Propagation of a finite-amplitude elastic pulse in a bar of Berea sandstone: A detailed look at the mechanisms of classical nonlinearity, hysteresis, and nonequilibrium dynamics: Nonlinear propagation of elastic pulse

DOE PAGES

Remillieux, Marcel C.; Ulrich, T. J.; Goodman, Harvey E.; ...

2017-10-18

Here, we study the propagation of a finite-amplitude elastic pulse in a long thin bar of Berea sandstone. In previous work, this type of experiment has been conducted to quantify classical nonlinearity, based on the amplitude growth of the second harmonic as a function of propagation distance. To greatly expand on that early work, a non-contact scanning 3D laser Doppler vibrometer was used to track the evolution of the axial component of the particle velocity over the entire surface of the bar as functions of the propagation distance and source amplitude. With these new measurements, the combined effects of classicalmore » nonlinearity, hysteresis, and nonequilibrium dynamics have all been measured simultaneously. We then show that the numerical resolution of the 1D wave equation with terms for classical nonlinearity and attenuation accurately captures the spectral features of the waves up to the second harmonic. But, for higher harmonics the spectral content is shown to be strongly influenced by hysteresis. This work also shows data which not only quantifies classical nonlinearity but also the nonequilibrium dynamics based on the relative change in the arrival time of the elastic pulse as a function of strain and distance from the source. Finally, a comparison is made to a resonant bar measurement, a reference experiment used to quantify nonequilibrium dynamics, based on the relative shift of the resonance frequencies as a function of the maximum dynamic strain in the sample.« less

Particle number dependence in the non-linear evolution of N-body self-gravitating systems

NASA Astrophysics Data System (ADS)

Benhaiem, D.; Joyce, M.; Sylos Labini, F.; Worrakitpoonpon, T.

2018-01-01

Simulations of purely self-gravitating N-body systems are often used in astrophysics and cosmology to study the collisionless limit of such systems. Their results for macroscopic quantities should then converge well for sufficiently large N. Using a study of the evolution from a simple space of spherical initial conditions - including a region characterized by so-called 'radial orbit instability' - we illustrate that the values of N at which such convergence is obtained can vary enormously. In the family of initial conditions we study, good convergence can be obtained up to a few dynamical times with N ∼ 103 - just large enough to suppress two body relaxation - for certain initial conditions, while in other cases such convergence is not attained at this time even in our largest simulations with N ∼ 105. The qualitative difference is due to the stability properties of fluctuations introduced by the N-body discretisation, of which the initial amplitude depends on N. We discuss briefly why the crucial role which such fluctuations can potentially play in the evolution of the N body system could, in particular, constitute a serious problem in cosmological simulations of dark matter.

Fast neural solution of a nonlinear wave equation

NASA Technical Reports Server (NTRS)

Toomarian, Nikzad; Barhen, Jacob

1992-01-01

A neural algorithm for rapidly simulating a certain class of nonlinear wave phenomena using analog VLSI neural hardware is presented and applied to the Korteweg-de Vries partial differential equation. The corresponding neural architecture is obtained from a pseudospectral representation of the spatial dependence, along with a leap-frog scheme for the temporal evolution. Numerical simulations demonstrated the robustness of the proposed approach.

Eclipse-Free-Time Assessment Tool for IRIS

NASA Technical Reports Server (NTRS)

Eagle, David

2012-01-01

IRIS_EFT is a scientific simulation that can be used to perform an Eclipse-Free- Time (EFT) assessment of IRIS (Infrared Imaging Surveyor) mission orbits. EFT is defined to be those time intervals longer than one day during which the IRIS spacecraft is not in the Earth s shadow. Program IRIS_EFT implements a special perturbation of orbital motion to numerically integrate Cowell's form of the system of differential equations. Shadow conditions are predicted by embedding this integrator within Brent s method for finding the root of a nonlinear equation. The IRIS_EFT software models the effects of the following types of orbit perturbations on the long-term evolution and shadow characteristics of IRIS mission orbits. (1) Non-spherical Earth gravity, (2) Atmospheric drag, (3) Point-mass gravity of the Sun, and (4) Point-mass gravity of the Moon. The objective of this effort was to create an in-house computer program that would perform eclipse-free-time analysis. of candidate IRIS spacecraft mission orbits in an accurate and timely fashion. The software is a suite of Fortran subroutines and data files organized as a "computational" engine that is used to accurately predict the long-term orbit evolution of IRIS mission orbits while searching for Earth shadow conditions.

Nonlinear evolution of magnetic flux ropes. 2: Finite beta plasma

NASA Technical Reports Server (NTRS)

Osherovich, V. A.; Farrugia, C. J.; Burlaga, L. F.

1995-01-01

In this second paper on the evolution of magnetic flux ropes we study the effects of gas pressure. We assume that the energy transport is described by a polytropic relationship and reduce the set of ideal MHD equations to a single, second-order, nonlinear, ordinary differential equation for the evolution function. For this conservative system we obtain a first integral of motion. To analyze the possible motions, we use a mechanical analogue -- a one-dimensional, nonlinear oscillator. We find that the effective potential for such an oscillator depends on two parameters: the polytropic index gamma and a dimensionless quantity kappa the latter being a function of the plasma beta, the strength of the azimuthal magnetic field relative to the axial field of the flux rope, and gamma. Through a study of this effective potential we classify all possible modes of evolution of the system. In the main body of the paper, we focus on magnetic flux ropes whose field and gas pressure increase steadily towards the symmetry axis. In this case, for gamma greater than 1 and all values of kappa, only oscillations are possible. For gamma less than 1, however, both oscillations and expansion are allowed. For gamma less than 1 and kappa below a critical value, the energy of the nonlinear oscillator determines whether the flux rope will oscillate or expand to infinity. For gamma less than 1 and kappa above critical, however, only expansion occurs. Thus by increasing kappa while keeping gamma fixed (less than 1), a phase transition occurs at kappa = kappa(sub critical) and the oscillatory mode disappears. We illustrate the above theoretical considerations by the example of a flux rope of constant field line twist evolving self-similarly. For this example, we present the full numerical MHD solution. In an appendix to the paper we catalogue all possible evolutions when (1) either the magnetic field or (2) the gas pressure decreases monotonically toward the axis. We find that in these cases critical conditions can occur for gamma greater than 1. While in most cases the flux rope collapses, there are notable exceptions when, for certain ranges of kappa and gamma, collapse may be averted.

A computational and theoretical analysis of falling frequency VLF emissions

NASA Astrophysics Data System (ADS)

Nunn, David; Omura, Yoshiharu

2012-08-01

Recently much progress has been made in the simulation and theoretical understanding of rising frequency triggered emissions and rising chorus. Both PIC and Vlasov VHS codes produce risers in the region downstream from the equator toward which the VLF waves are traveling. The VHS code only produces fallers or downward hooks with difficulty due to the coherent nature of wave particle interaction across the equator. With the VHS code we now confine the interaction region to be the region upstream from the equator, where inhomogeneity factor S is positive. This suppresses correlated wave particle interaction effects across the equator and the tendency of the code to trigger risers, and permits the formation of a proper falling tone generation region. The VHS code now easily and reproducibly triggers falling tones. The evolution of resonant particle current JE in space and time shows a generation point at -5224 km and the wavefield undergoes amplification of some 25 dB in traversing the nonlinear generation region. The current component parallel to wave magnetic field (JB) is positive, whereas it is negative for risers. The resonant particle trap shows an enhanced distribution function or `hill', whereas risers have a `hole'. According to recent theory (Omura et al., 2008, 2009) sweeping frequency is due primarily to the advective term. The nonlinear frequency shift term is now negative (˜-12 Hz) and the sweep rate of -800 Hz/s is approximately nonlinear frequency shift divided by TN, the transition time, of the order of a trapping time.

Nonlinear Landau damping and formation of Bernstein-Greene-Kruskal structures for plasmas with q-nonextensive velocity distributions

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

Raghunathan, M.; Ganesh, R.

2013-03-15

In the past, long-time evolution of an initial perturbation in collisionless Maxwellian plasma (q = 1) has been simulated numerically. The controversy over the nonlinear fate of such electrostatic perturbations was resolved by Manfredi [Phys. Rev. Lett. 79, 2815-2818 (1997)] using long-time simulations up to t=1600{omega}{sub p}{sup -1}. The oscillations were found to continue indefinitely leading to Bernstein-Greene-Kruskal (BGK)-like phase-space vortices (from here on referred as 'BGK structures'). Using a newly developed, high resolution 1D Vlasov-Poisson solver based on piecewise-parabolic method (PPM) advection scheme, we investigate the nonlinear Landau damping in 1D plasma described by toy q-distributions for long times,more » up to t=3000{omega}{sub p}{sup -1}. We show that BGK structures are found only for a certain range of q-values around q = 1. Beyond this window, for the generic parameters, no BGK structures were observed. We observe that for values of q<1 where velocity distributions have long tails, strong Landau damping inhibits the formation of BGK structures. On the other hand, for q>1 where distribution has a sharp fall in velocity, the formation of BGK structures is rendered difficult due to high wave number damping imposed by the steep velocity profile, which had not been previously reported. Wherever relevant, we compare our results with past work.« less

Influence of a density increase on the evolution of the Kelvin-Helmholtz instability and vortices

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

Amerstorfer, U. V.; Erkaev, N. V.; Institute of Computational Modelling, 660036 Krasnoyarsk

2010-07-15

Results of two-dimensional nonlinear numerical simulations of the magnetohydrodynamic Kelvin-Helmholtz instability are presented. A boundary layer of a certain width is assumed, which separates the plasma in the upper layer from the plasma in the lower layer. A special focus is given on the influence of a density increase toward the lower layer. The evolution of the Kelvin-Helmholtz instability can be divided into three different phases, namely, a linear growth phase at the beginning, followed by a nonlinear phase with regular structures of the vortices, and finally, a turbulent phase with nonregular structures. The spatial scales of the vortices aremore » about five times the initial width of the boundary layer. The considered configuration is similar to the situation around unmagnetized planets, where the solar wind (upper plasma layer) streams past the ionosphere (lower plasma layer), and thus the plasma density increases toward the planet. The evolving vortices might detach around the terminator of the planet and eventually so-called plasma clouds might be formed, through which ionospheric material can be lost. For the special case of a Venus-like planet, loss rates are estimated, which are of the order of estimated loss rates from observations at Venus.« less

Topological characterization and early detection of bifurcations and chaos in complex systems using persistent homology.

PubMed

Mittal, Khushboo; Gupta, Shalabh

2017-05-01

Early detection of bifurcations and chaos and understanding their topological characteristics are essential for safe and reliable operation of various electrical, chemical, physical, and industrial processes. However, the presence of non-linearity and high-dimensionality in system behavior makes this analysis a challenging task. The existing methods for dynamical system analysis provide useful tools for anomaly detection (e.g., Bendixson-Dulac and Poincare-Bendixson criteria can detect the presence of limit cycles); however, they do not provide a detailed topological understanding about system evolution during bifurcations and chaos, such as the changes in the number of subcycles and their positions, lifetimes, and sizes. This paper addresses this research gap by using topological data analysis as a tool to study system evolution and develop a mathematical framework for detecting the topological changes in the underlying system using persistent homology. Using the proposed technique, topological features (e.g., number of relevant k-dimensional holes, etc.) are extracted from nonlinear time series data which are useful for deeper analysis of the system behavior and early detection of bifurcations and chaos. When applied to a Logistic map, a Duffing oscillator, and a real life Op-amp based Jerk circuit, these features are shown to accurately characterize the system dynamics and detect the onset of chaos.

Breaking Computational Barriers: Real-time Analysis and Optimization with Large-scale Nonlinear Models via Model Reduction

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

Carlberg, Kevin Thomas; Drohmann, Martin; Tuminaro, Raymond S.

2014-10-01

Model reduction for dynamical systems is a promising approach for reducing the computational cost of large-scale physics-based simulations to enable high-fidelity models to be used in many- query (e.g., Bayesian inference) and near-real-time (e.g., fast-turnaround simulation) contexts. While model reduction works well for specialized problems such as linear time-invariant systems, it is much more difficult to obtain accurate, stable, and efficient reduced-order models (ROMs) for systems with general nonlinearities. This report describes several advances that enable nonlinear reduced-order models (ROMs) to be deployed in a variety of time-critical settings. First, we present an error bound for the Gauss-Newton with Approximatedmore » Tensors (GNAT) nonlinear model reduction technique. This bound allows the state-space error for the GNAT method to be quantified when applied with the backward Euler time-integration scheme. Second, we present a methodology for preserving classical Lagrangian structure in nonlinear model reduction. This technique guarantees that important properties--such as energy conservation and symplectic time-evolution maps--are preserved when performing model reduction for models described by a Lagrangian formalism (e.g., molecular dynamics, structural dynamics). Third, we present a novel technique for decreasing the temporal complexity --defined as the number of Newton-like iterations performed over the course of the simulation--by exploiting time-domain data. Fourth, we describe a novel method for refining projection-based reduced-order models a posteriori using a goal-oriented framework similar to mesh-adaptive h -refinement in finite elements. The technique allows the ROM to generate arbitrarily accurate solutions, thereby providing the ROM with a 'failsafe' mechanism in the event of insufficient training data. Finally, we present the reduced-order model error surrogate (ROMES) method for statistically quantifying reduced- order-model errors. This enables ROMs to be rigorously incorporated in uncertainty-quantification settings, as the error model can be treated as a source of epistemic uncertainty. This work was completed as part of a Truman Fellowship appointment. We note that much additional work was performed as part of the Fellowship. One salient project is the development of the Trilinos-based model-reduction software module Razor , which is currently bundled with the Albany PDE code and currently allows nonlinear reduced-order models to be constructed for any application supported in Albany. Other important projects include the following: 1. ROMES-equipped ROMs for Bayesian inference: K. Carlberg, M. Drohmann, F. Lu (Lawrence Berkeley National Laboratory), M. Morzfeld (Lawrence Berkeley National Laboratory). 2. ROM-enabled Krylov-subspace recycling: K. Carlberg, V. Forstall (University of Maryland), P. Tsuji, R. Tuminaro. 3. A pseudo balanced POD method using only dual snapshots: K. Carlberg, M. Sarovar. 4. An analysis of discrete v. continuous optimality in nonlinear model reduction: K. Carlberg, M. Barone, H. Antil (George Mason University). Journal articles for these projects are in progress at the time of this writing.« less

Detecting nonlinear dynamics of functional connectivity

NASA Astrophysics Data System (ADS)

LaConte, Stephen M.; Peltier, Scott J.; Kadah, Yasser; Ngan, Shing-Chung; Deshpande, Gopikrishna; Hu, Xiaoping

2004-04-01

Functional magnetic resonance imaging (fMRI) is a technique that is sensitive to correlates of neuronal activity. The application of fMRI to measure functional connectivity of related brain regions across hemispheres (e.g. left and right motor cortices) has great potential for revealing fundamental physiological brain processes. Primarily, functional connectivity has been characterized by linear correlations in resting-state data, which may not provide a complete description of its temporal properties. In this work, we broaden the measure of functional connectivity to study not only linear correlations, but also those arising from deterministic, non-linear dynamics. Here the delta-epsilon approach is extended and applied to fMRI time series. The method of delays is used to reconstruct the joint system defined by a reference pixel and a candidate pixel. The crux of this technique relies on determining whether the candidate pixel provides additional information concerning the time evolution of the reference. As in many correlation-based connectivity studies, we fix the reference pixel. Every brain location is then used as a candidate pixel to estimate the spatial pattern of deterministic coupling with the reference. Our results indicate that measured connectivity is often emphasized in the motor cortex contra-lateral to the reference pixel, demonstrating the suitability of this approach for functional connectivity studies. In addition, discrepancies with traditional correlation analysis provide initial evidence for non-linear dynamical properties of resting-state fMRI data. Consequently, the non-linear characterization provided from our approach may provide a more complete description of the underlying physiology and brain function measured by this type of data.

Damping of Bernstein-Greene-Kruskal modes in collisional plasmas

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

Valentini, Francesco

2008-02-15

In this paper, the effect of Coulomb collisions on the stability of Bernstein-Greene-Kruskal (BGK) modes [I. B. Bernstein, J. M. Greene, and M. D. Krukal, Phys. Rev. 108, 546 (1957)] is analyzed by comparing the numerical results of collisional particle-in-cell (PIC) simulations with the theoretical predictions by Zakharov and Karpman [V. E. Zakharov and V. I. Karpman, Sov. Phys. JETP 16, 351 (1963)], for the collisional damping of nonlinear plasma waves. In the absence of collisions, BGK modes are undamped nonlinear electrostatic oscillations, solutions of the Vlasov-Poisson equations; in these structures nonlinearity manifests as the formation of a plateau inmore » the resonant region of the particle distribution function, due to trapping of resonant particles, thus preventing linear Landau damping. When particle-particle Coulomb collisions are effective, this plateau is smoothed out since collisions drive the velocity distribution towards the Maxwellian shape, thus destroying the BGK structure. As shown by Zakharov and Karpman in 1963, under certain assumptions, an exponential time decay with constant damping rate is predicted for the electric field amplitude and a linear dependence of the damping rate on the collision frequency is found. In this paper, the theory by Zakharov and Karpman is revisited and the effects of collisions on the stability of BGK modes and on the long time evolution of nonlinear Landau damping are numerically investigated. The numerical results are obtained through a collisional PIC code that reproduces a physical phenomenology also observed in recent experiments with trapped pure electron plasmas.« less

Two-dimensional evolution equation of finite-amplitude internal gravity waves in a uniformly stratified fluid

PubMed

Kataoka; Tsutahara; Akuzawa

2000-02-14

We derive a fully nonlinear evolution equation that can describe the two-dimensional motion of finite-amplitude long internal waves in a uniformly stratified three-dimensional fluid of finite depth. The derived equation is the two-dimensional counterpart of the evolution equation obtained by Grimshaw and Yi [J. Fluid Mech. 229, 603 (1991)]. In the small-amplitude limit, our equation is reduced to the celebrated Kadomtsev-Petviashvili equation.

Helical vortices: linear stability analysis and nonlinear dynamics

NASA Astrophysics Data System (ADS)

Selçuk, C.; Delbende, I.; Rossi, M.

2018-02-01

We numerically investigate, within the context of helical symmetry, the dynamics of a regular array of two or three helical vortices with or without a straight central hub vortex. The Navier-Stokes equations are linearised to study the instabilities of such basic states. For vortices with low pitches, an unstable mode is extracted which corresponds to a displacement mode and growth rates are found to compare well with results valid for an infinite row of point vortices or an infinite alley of vortex rings. For larger pitches, the system is stable with respect to helically symmetric perturbations. In the nonlinear regime, we follow the time-evolution of the above basic states when initially perturbed by the dominant instability mode. For two vortices, sequences of overtaking events, leapfrogging and eventually merging are observed. The transition between such behaviours occurs at a critical ratio involving the core size and the vortex-separation distance. Cases with three helical vortices are also presented.

Dark energy in the dark ages

NASA Astrophysics Data System (ADS)

Linder, Eric V.

2006-08-01

Non-negligible dark energy density at high redshifts would indicate dark energy physics distinct from a cosmological constant or "reasonable" canonical scalar fields. Such dark energy can be constrained tightly through investigation of the growth of structure, with limits of ≲2% of total energy density at z ≫ 1 for many models. Intermediate dark energy can have effects distinct from its energy density; the dark ages acceleration can be constrained to last less than 5% of a Hubble e-fold time, exacerbating the coincidence problem. Both the total linear growth, or equivalently σ8, and the shape and evolution of the nonlinear mass power spectrum for z < 2 (using the Linder-White nonlinear mapping prescription) provide important windows. Probes of growth, such as weak gravitational lensing, can interact with supernovae and CMB distance measurements to scan dark energy behavior over the entire range z = 0-1100.

Nonlinear Evolution and Final Fate of Charged Anti-de Sitter Black Hole Superradiant Instability

NASA Astrophysics Data System (ADS)

Bosch, Pablo; Green, Stephen R.; Lehner, Luis

2016-04-01

We describe the full nonlinear development of the superradiant instability for a charged massless scalar field coupled to general relativity and electromagnetism, in the vicinity of a Reissner-Nordström-anti-de Sitter black hole. The presence of the negative cosmological constant provides a natural context for considering perfectly reflecting boundary conditions and studying the dynamics as the scalar field interacts repeatedly with the black hole. At early times, small superradiant perturbations grow as expected from linearized studies. Backreaction then causes the black hole to lose charge and mass until the perturbation becomes nonsuperradiant, with the final state described by a stable hairy black hole. For large gauge coupling, the instability extracts a large amount of charge per unit mass, resulting in greater entropy increase. We discuss the implications of the observed behavior for the general problem of superradiance in black hole spacetimes.

Phases of New Physics in the BAO Spectrum

NASA Astrophysics Data System (ADS)

Baumann, Daniel; Green, Daniel; Zaldarriaga, Matias

2017-11-01

We show that the phase of the spectrum of baryon acoustic oscillations (BAO) is immune to the effects of nonlinear evolution. This suggests that any new physics that contributes to the initial phase of the BAO spectrum, such as extra light species in the early universe, can be extracted reliably at late times. We provide three arguments in support of our claim: first, we point out that a phase shift of the BAO spectrum maps to a characteristic sign change in the real space correlation function and that this feature cannot be generated or modified by nonlinear dynamics. Second, we confirm this intuition through an explicit computation, valid to all orders in cosmological perturbation theory. Finally, we provide a nonperturbative argument using general analytic properties of the linear response to the initial oscillations. Our result motivates measuring the phase of the BAO spectrum as a robust probe of new physics.

Quantum statistics and squeezing for a microwave-driven interacting magnon system.

PubMed

Haghshenasfard, Zahra; Cottam, Michael G

2017-02-01

Theoretical studies are reported for the statistical properties of a microwave-driven interacting magnon system. Both the magnetic dipole-dipole and the exchange interactions are included and the theory is developed for the case of parallel pumping allowing for the inclusion of the nonlinear processes due to the four-magnon interactions. The method of second quantization is used to transform the total Hamiltonian from spin operators to boson creation and annihilation operators. By using the coherent magnon state representation we have studied the magnon occupation number and the statistical behavior of the system. In particular, it is shown that the nonlinearities introduced by the parallel pumping field and the four-magnon interactions lead to non-classical quantum statistical properties of the system, such as magnon squeezing. Also control of the collapse-and-revival phenomena for the time evolution of the average magnon number is demonstrated by varying the parallel pumping amplitude and the four-magnon coupling.

Monolithic multigrid methods for two-dimensional resistive magnetohydrodynamics

DOE PAGES

Adler, James H.; Benson, Thomas R.; Cyr, Eric C.; ...

2016-01-06

Magnetohydrodynamic (MHD) representations are used to model a wide range of plasma physics applications and are characterized by a nonlinear system of partial differential equations that strongly couples a charged fluid with the evolution of electromagnetic fields. The resulting linear systems that arise from discretization and linearization of the nonlinear problem are generally difficult to solve. In this paper, we investigate multigrid preconditioners for this system. We consider two well-known multigrid relaxation methods for incompressible fluid dynamics: Braess--Sarazin relaxation and Vanka relaxation. We first extend these to the context of steady-state one-fluid viscoresistive MHD. Then we compare the two relaxationmore » procedures within a multigrid-preconditioned GMRES method employed within Newton's method. To isolate the effects of the different relaxation methods, we use structured grids, inf-sup stable finite elements, and geometric interpolation. Furthermore, we present convergence and timing results for a two-dimensional, steady-state test problem.« less

Stochastic response and bifurcation of periodically driven nonlinear oscillators by the generalized cell mapping method

NASA Astrophysics Data System (ADS)

Han, Qun; Xu, Wei; Sun, Jian-Qiao

2016-09-01

The stochastic response of nonlinear oscillators under periodic and Gaussian white noise excitations is studied with the generalized cell mapping based on short-time Gaussian approximation (GCM/STGA) method. The solutions of the transition probability density functions over a small fraction of the period are constructed by the STGA scheme in order to construct the GCM over one complete period. Both the transient and steady-state probability density functions (PDFs) of a smooth and discontinuous (SD) oscillator are computed to illustrate the application of the method. The accuracy of the results is verified by direct Monte Carlo simulations. The transient responses show the evolution of the PDFs from being Gaussian to non-Gaussian. The effect of a chaotic saddle on the stochastic response is also studied. The stochastic P-bifurcation in terms of the steady-state PDFs occurs with the decrease of the smoothness parameter, which corresponds to the deterministic pitchfork bifurcation.

Simple estimation of linear 1+1 D tsunami run-up

NASA Astrophysics Data System (ADS)

Fuentes, M.; Campos, J. A.; Riquelme, S.

2016-12-01

An analytical expression is derived concerning the linear run-up for any given initial wave generated over a sloping bathymetry. Due to the simplicity of the linear formulation, complex transformations are unnecessay, because the shoreline motion is directly obtained in terms of the initial wave. This analytical result not only supports maximum run-up invariance between linear and non-linear theories, but also the time evolution of shoreline motion and velocity. The results exhibit good agreement with the non-linear theory. The present formulation also allows computing the shoreline motion numerically from a customised initial waveform, including non-smooth functions. This is useful for numerical tests, laboratory experiments or realistic cases in which the initial disturbance might be retrieved from seismic data rather than using a theoretical model. It is also shown that the real case studied is consistent with the field observations.

Gain-phase modulation in chirped-pulse amplification

NASA Astrophysics Data System (ADS)

Shen, Yijie; Gao, Gan; Meng, Yuan; Fu, Xing; Gong, Mali

2017-10-01

The cross-modulation between the gain and chirped phase in chirped-pulse amplification (CPA) is theoretically and experimentally demonstrated. We propose a gain-phase coupled nonlinear Schrödinger equation (GPC-NLSE) for solving chirped-pulse propagation in a nonlinear gain medium involved in the gain-phase modulation (GPM) process. With the GPC-NLSE, the space-time-frequency-dependent gain, chirped phase, pulse, and spectrum evolutions can be precisely calculated. Moreover, a short-length high-gain Yb-doped fiber CPA experiment is presented in which a self-steepening distortion of the seed pulse is automatically compensated after amplification. This phenomenon can be explained by the GPM theory whereas conventional models cannot. The experimental results for the temporal and spectral intensities show excellent agreement with our theory. Our GPM theory paves the way for further investigations of the finer structures of the pulse and spectrum in CPA systems.

Nonlinear Simulation of DIII-D Plasma and Poloidal Systems Using DINA and Simulink

NASA Astrophysics Data System (ADS)

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

2002-11-01

Hardware-in-the-loop simulation capability was developed previously for poloidal shape control testing using Matlab Simulink [1]. This has been upgraded by replacing a linearized plasma model with the DINA nonlinear plasma evolution code [2]. In addition to its use for shape control studies, this new capability will allow study of current profile control using the DINA model of electron cyclotron current drive (ECCD) and current profile information soon to be available from the Plasma Control System (PCS) real time EFIT [3] calculation. We describe the incorporation of DINA into the Simulink DIII-D tokamak systems model and results of validating this combined model against DIII-D data. \\vspace0.1em [1] J.A. Leuer, et al., 18th IEEE/NPSS SOFE (1999), p. 531. [2] R.R. Khayrutdinov, V.E. Lukash, J. Comput. Phys. 109, 193 (1993). [3] J.R. Ferron, et al., Nucl. Fusion 38, 1055 (1988).

Nonlinear Evolution and Final Fate of Charged Anti-de Sitter Black Hole Superradiant Instability.

PubMed

Bosch, Pablo; Green, Stephen R; Lehner, Luis

2016-04-08

We describe the full nonlinear development of the superradiant instability for a charged massless scalar field coupled to general relativity and electromagnetism, in the vicinity of a Reissner-Nordström-anti-de Sitter black hole. The presence of the negative cosmological constant provides a natural context for considering perfectly reflecting boundary conditions and studying the dynamics as the scalar field interacts repeatedly with the black hole. At early times, small superradiant perturbations grow as expected from linearized studies. Backreaction then causes the black hole to lose charge and mass until the perturbation becomes nonsuperradiant, with the final state described by a stable hairy black hole. For large gauge coupling, the instability extracts a large amount of charge per unit mass, resulting in greater entropy increase. We discuss the implications of the observed behavior for the general problem of superradiance in black hole spacetimes.

Probabilistic density function method for nonlinear dynamical systems driven by colored noise

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

Barajas-Solano, David A.; Tartakovsky, Alexandre M.

2016-05-01

We present a probability density function (PDF) method for a system of nonlinear stochastic ordinary differential equations driven by colored noise. The method provides an integro-differential equation for the temporal evolution of the joint PDF of the system's state, which we close by means of a modified Large-Eddy-Diffusivity-type closure. Additionally, we introduce the generalized local linearization (LL) approximation for deriving a computable PDF equation in the form of the second-order partial differential equation (PDE). We demonstrate the proposed closure and localization accurately describe the dynamics of the PDF in phase space for systems driven by noise with arbitrary auto-correlation time.more » We apply the proposed PDF method to the analysis of a set of Kramers equations driven by exponentially auto-correlated Gaussian colored noise to study the dynamics and stability of a power grid.« less

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

NASA Astrophysics Data System (ADS)

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

2018-06-01

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

Hybrid simulation of fishbone instabilities in the EAST tokamak

NASA Astrophysics Data System (ADS)

Shen, Wei; Fu, Guoyong; Wang, Feng; Xu, Liqing; Li, Guoqiang; Liu, Chengyue; EAST Team

2017-10-01

Hybrid simulations with the global kinetic- MHD code M3D-K have been carried out to investigate the linear stability and nonlinear dynamics of beam-driven fishbone in EAST experiment. Linear simulations show that a low frequency fishbone instability is excited at experimental value of beam ion pressure. The mode is mainly driven by low energy beam ions via precessional resonance. The results are consistent with the experimental measurement with respect to mode frequency and mode structure. When the beam ion pressure is increased to exceed a critical value, the low frequency mode transits to a BAE with much higher frequency. Nonlinear simulations show that the frequency of the low frequency fishbone chirps up and down with corresponding hole-clump structures in phase space, consistent with the Berk-Breizman theory. In addition to the low frequency mode, the high frequency BAE is excited during the nonlinear evolution. For the transient case of beam pressure fraction where the low and high frequency modes are simultaneously excited in the linear phase, only one dominant mode appears in the nonlinear phase with frequency jumps up and down during nonlinear evolution. This work is supported by the National Natural Science Foundation of China under Grant Nos. 11605245 and 11505022, and the CASHIPS Director's Fund under Grant No. YZJJ201510, and the Department of Energy Scientific Discovery through Advanced Computing (SciDAC) under Grant No. DE-AC02-09CH11466.

Theory of multiple quantum dot formation in strained-layer heteroepitaxy

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

Du, Lin; Maroudas, Dimitrios, E-mail: maroudas@ecs.umass.edu

2016-07-11

We develop a theory for the experimentally observed formation of multiple quantum dots (QDs) in strained-layer heteroepitaxy based on surface morphological stability analysis of a coherently strained epitaxial thin film on a crystalline substrate. Using a fully nonlinear model of surface morphological evolution that accounts for a wetting potential contribution to the epitaxial film's free energy as well as surface diffusional anisotropy, we demonstrate the formation of multiple QD patterns in self-consistent dynamical simulations of the evolution of the epitaxial film surface perturbed from its planar state. The simulation predictions are supported by weakly nonlinear analysis of the epitaxial filmmore » surface morphological stability. We find that, in addition to the Stranski-Krastanow instability, long-wavelength perturbations from the planar film surface morphology can trigger a nonlinear instability, resulting in the splitting of a single QD into multiple QDs of smaller sizes, and predict the critical wavelength of the film surface perturbation for the onset of the nonlinear tip-splitting instability. The theory provides a fundamental interpretation for the observations of “QD pairs” or “double QDs” and other multiple QDs reported in experimental studies of epitaxial growth of semiconductor strained layers and sets the stage for precise engineering of tunable-size nanoscale surface features in strained-layer heteroepitaxy by exploiting film surface nonlinear, pattern forming phenomena.« less

The non-linear power spectrum of the Lyman alpha forest

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

Arinyo-i-Prats, Andreu; Miralda-Escudé, Jordi; Viel, Matteo

2015-12-01

The Lyman alpha forest power spectrum has been measured on large scales by the BOSS survey in SDSS-III at z∼ 2.3, has been shown to agree well with linear theory predictions, and has provided the first measurement of Baryon Acoustic Oscillations at this redshift. However, the power at small scales, affected by non-linearities, has not been well examined so far. We present results from a variety of hydrodynamic simulations to predict the redshift space non-linear power spectrum of the Lyα transmission for several models, testing the dependence on resolution and box size. A new fitting formula is introduced to facilitate themore » comparison of our simulation results with observations and other simulations. The non-linear power spectrum has a generic shape determined by a transition scale from linear to non-linear anisotropy, and a Jeans scale below which the power drops rapidly. In addition, we predict the two linear bias factors of the Lyα forest and provide a better physical interpretation of their values and redshift evolution. The dependence of these bias factors and the non-linear power on the amplitude and slope of the primordial fluctuations power spectrum, the temperature-density relation of the intergalactic medium, and the mean Lyα transmission, as well as the redshift evolution, is investigated and discussed in detail. A preliminary comparison to the observations shows that the predicted redshift distortion parameter is in good agreement with the recent determination of Blomqvist et al., but the density bias factor is lower than observed. We make all our results publicly available in the form of tables of the non-linear power spectrum that is directly obtained from all our simulations, and parameters of our fitting formula.« less

Monitoring localized cracks on under pressure concrete nuclear containment wall using linear and nonlinear ultrasonic coda wave interferometry

NASA Astrophysics Data System (ADS)

Legland, J.-B.; Abraham, O.; Durand, O.; Henault, J.-M.

2018-04-01

Civil engineering is constantly demanding new methods for evaluation and non-destructive testing (NDT), particularly to prevent and monitor serious damage to concrete structures. Tn this work, experimental results are presented on the detection and characterization of cracks using nonlinear modulation of coda waves interferometry (NCWT) [1]. This method consists in mixing high-amplitude low-frequency acoustic waves with multi-scattered probe waves (coda) and analyzing their effects by interferometry. Unlike the classic method of coda analysis (CWT), the NCWT does not require the recording of a coda as a reference before damage to the structure. Tn the framework of the PTA-ENDE project, a 1/3 model of a preconstrained concrete containment (EDF VeRCoRs mock-up) is placed under pressure to study the leakage of the structure. During this evaluation protocol, specific areas are monitored by the NCWT (during 5 days, which correspond to the protocol of nuclear power plant pressurization under maintenance test). The acoustic nonlinear response due to the high amplitude of the acoustic modulation gives pertinent information about the elastic and dissipative nonlinearities of the concrete. Tts effective level is evaluated by two nonlinear observables extracted from the interferometry. The increase of nonlinearities is in agreement with the creation of a crack with a network of microcracks located at its base; however, a change in the dynamics of the evolution of the nonlinearities may indicate the opening of a through crack. Tn addition, as during the experimental campaign, reference codas have been recorded. We used CWT to follow the stress evolution and the gas leaks ratio of the structure. Both CWT and NCWT results are presented in this paper.

Internal transport barrier triggered by non-linear lower hybrid wave deposition under condition of beam-driven toroidal rotation

NASA Astrophysics Data System (ADS)

Gao, Q. D.; Budny, R. V.

2015-03-01

By using gyro-Landau fluid transport model (GLF23), time-dependent integrated modeling is carried out using TRANSP to explore the dynamic process of internal transport barrier (ITB) formation in the neutral beam heating discharges. When the current profile is controlled by LHCD (lower hybrid current drive), with appropriate neutral beam injection, the nonlinear interplay between the transport determined gradients in the plasma temperature (Ti,e) and toroidal velocity (Vϕ) and the E×B flow shear (including q-profile) produces transport bifurcations, generating spontaneously a stepwise growing ITB. In the discharge, the constraints imposed by the wave propagation condition causes interplay of the LH driven current distribution with the plasma configuration modification, which constitutes non-linearity in the LH wave deposition. The non-linear effects cause bifurcation in LHCD, generating two distinct quasi-stationary reversed magnetic shear configurations. The change of current profile during the transition period between the two quasi-stationary states results in increase of the E×B shearing flow arising from toroidal rotation. The turbulence transport suppression by sheared E×B flow during the ITB development is analysed, and the temporal evolution of some parameters characterized the plasma confinement is examined. Ample evidence shows that onset of the ITB development is correlated with the enhancement of E×B shearing rate caused by the bifurcation in LHCD. It is suggested that the ITB triggering is associated with the non-linear effects of the LH power deposition.

Ultrashort pulse chirp measurement via transverse second-harmonic generation in strontium barium niobate crystal

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

Trull, J.; Wang, B.; Parra, A.

2015-06-01

Pulse compression in dispersive strontium barium niobate crystal with a random size and distribution of the anti-parallel orientated nonlinear domains is observed via transverse second harmonic generation. The dependence of the transverse width of the second harmonic trace along the propagation direction allows for the determination of the initial chirp and duration of pulses in the femtosecond regime. This technique permits a real-time analysis of the pulse evolution and facilitates fast in-situ correction of pulse chirp acquired in the propagation through an optical system.

Optical Phase Conjugation via Stimulated Brillouin Scattering in Multimode Optical Fiber

DTIC Science & Technology

1990-09-01

3.78 x 10- 5 cm - 1 (16.4 dB/km). . . 27 9. The evolution of the transmitted and backscattered powers as the pump power is scaled in a 200 m fiber...km and a gain coef- * ficient of 10.2 x 10- 9 cm/W ............................ 33 v 0 Figure Page 12. Laser power stability. The zero level is at...gain was 10.2 x 10- 9 cm/W with an error of 10%. Most importantly, nonlinear optical phase conjugation was demonstrated for the first time

New Type of the Interface Evolution in the Richtmyer-Meshkov Instability

NASA Technical Reports Server (NTRS)

Abarzhi, S. I.; Herrmann, M.

2003-01-01

We performed systematic theoretical and numerical studies of the nonlinear large-scale coherent dynamics in the Richtmyer-Meshkov instability for fluids with contrast densities. Our simulations modeled the interface dynamics for compressible and viscous uids. For a two-fluid system we observed that in the nonlinear regime of the instability the bubble velocity decays and its surface attens, and the attening is accompanied by slight oscillations. We found the theoretical solution for the system of conservation laws, describing the principal influence of the density ratio on the motion of the nonlinear bubble. The solution has no adjustable parameters, and shows that the attening of the bubble front is a distinct property universal for all values of the density ratio. This property follows from the fact that the RM bubbles decelerate. The theoretical and numerical results validate each other, describe the new type of the bubble front evolution in RMI, and identify the bubble curvature as important and sensitive diagnostic parameter.

Controlling the motion of solitons in 1-D magnonic crystal

NASA Astrophysics Data System (ADS)

Giridharan, D.; Sabareesan, P.; Daniel, M.

2018-04-01

We investigate nonlinear localized magnetic excitations in a simple form of one dimensional magnonic crystal by considering a ferromagnetic medium under periodic applied magnetic field of spatially varying strength. The governing Landau-Lifshitz equation is transformed into nonlinear evolution equation of a complex function through stereographic projection technique. The associated evolution equation numerically solved by using split-step Fourier method (SSFM). From the obtained results it is observed that the excitations appear in the form of solitons and the periodic magnetic field of spatially varying strength perturbs the soliton propagation. Bright and dark soliton solutions are constructed and studied the effect of tuning the strength of spatially periodic applied magnetic field on the nonlinear excitation of magnetization. The results show that the amplitude and velocity of the soliton can be effectively managed by varying the strength of spatially periodic applied magnetic field and it act as periodic potential which provides an additional degree of freedom to control the nature of soliton propagation in a ferromagnetic medium.

Instantaneous Frequency Analysis on Nonlinear EMIC Emissions: Arase Observation

NASA Astrophysics Data System (ADS)

Shoji, M.; Yoshizumi, M.; Omura, Y.; Kasaba, Y.; Ishisaka, K.; Matsuda, S.; Kasahara, Y.; Yagitani, S.; Matsuoka, A.; Teramoto, M.; Takashima, T.; Shinohara, I.

2017-12-01

In the inner magnetosphere, electromagnetic ion cyclotron (EMIC) waves cause nonlinear interactions with energetic protons. The waves drastically modify the proton distribution function, resulting in the particle loss in the radiation belt. Arase spacecraft, launched in late 2016, observed a nonlinear EMIC falling tone emission in the high magnetic latitude (MLAT) region of the inner magnetosphere. The wave growth with sub-packet structures of the falling tone emission is found by waveform data from PWE/EFD instrument. The evolution of the instantaneous frequency of the electric field of the EMIC falling tone emission is analyzed by Hilbert-Huang transform (HHT). We find several sub-packets with rising frequency in the falling tone wave. A self-consistent hybrid simulation suggested the complicate frequency evolution of the EMIC sub-packet emissions in the generation region. The intrinsic mode functions of Arase data derived from HHT are compared with the simulation data. The origin of the falling tone emission in the high MLAT region is also discussed.

Nonlinear tumor evolution from dysplastic nodules to hepatocellular carcinoma.

PubMed

Joung, Je-Gun; Ha, Sang Yun; Bae, Joon Seol; Nam, Jae-Yong; Gwak, Geum-Youn; Lee, Hae-Ock; Son, Dae-Soon; Park, Cheol-Keun; Park, Woong-Yang

2017-01-10

Dysplastic nodules are premalignant neoplastic nodules found in explanted livers with cirrhosis. Genetic signatures of premalignant dysplastic nodules (DNs) with concurrent hepatocellular carcinoma (HCC) may provide an insight in the molecular evolution of hepatocellular carcinogenesis. We analyzed four patients with multifocal nodular lesions and cirrhotic background by whole-exome sequencing (WES). The genomic profiles of somatic single nucleotide variations (SNV) and copy number variations (CNV) in DNs were compared to those of HCCs. The number and variant allele frequency of somatic SNVs of DNs and HCCs in each patient was identical along the progression of pathological grade. The somatic SNVs in DNs showed little conservation in HCC. Additionally, CNVs showed no conservation. Phylogenetic analysis based on SNVs and copy number profiles indicated a nonlinear segregation pattern, implying independent development of DNs and HCC in each patient. Thus, somatic mutations in DNs may be developed separately from other malignant nodules in the same liver, suggesting a nonlinear model for hepatocarcinogenesis from DNs to HCC.

Multiple secondary islands formation in nonlinear evolution of double tearing mode simulations

NASA Astrophysics Data System (ADS)

Guo, W.; Ma, J.; Yu, Z.

2017-03-01

A new numerical code solving the conservative perturbed resistive magnetohydrodynamic (MHD) model is developed. Numerical tests of the ideal Kelvin-Helmholtz instability and the resistive double tearing mode (DTM) show its capability in solving linear and nonlinear MHD instabilities. The nonlinear DTM evolution in 2D geometry is numerically investigated with low guiding field B z 0 , short half-distance y 0 between the equilibrium current sheets, and small resistivity η. The interaction of islands on the two initial current sheets may generate an unstable flow driven current sheet with a high length-to-thickness aspect ratio (α), and multiple secondary islands can form. In general, the length-to-thickness aspect ratio α and the number of secondary islands increase with decreasing guide field B z 0 , decreasing half-distance y 0 , and increasing Lundquist number of the flow driven current sheet S L although the dependence may be non-monotonic. The reconnection rate dependence on S L , B z 0 , and y 0 is also investigated.

Exact traveling wave solutions of modified KdV-Zakharov-Kuznetsov equation and viscous Burgers equation.

PubMed

Islam, Md Hamidul; Khan, Kamruzzaman; Akbar, M Ali; Salam, Md Abdus

2014-01-01

Mathematical modeling of many physical systems leads to nonlinear evolution equations because most physical systems are inherently nonlinear in nature. The investigation of traveling wave solutions of nonlinear partial differential equations (NPDEs) plays a significant role in the study of nonlinear physical phenomena. In this article, we construct the traveling wave solutions of modified KDV-ZK equation and viscous Burgers equation by using an enhanced (G '/G) -expansion method. A number of traveling wave solutions in terms of unknown parameters are obtained. Derived traveling wave solutions exhibit solitary waves when special values are given to its unknown parameters. 35C07; 35C08; 35P99.

Self-Supervised Dynamical Systems

NASA Technical Reports Server (NTRS)

Zak, Michail

2003-01-01

Some progress has been made in a continuing effort to develop mathematical models of the behaviors of multi-agent systems known in biology, economics, and sociology (e.g., systems ranging from single or a few biomolecules to many interacting higher organisms). Living systems can be characterized by nonlinear evolution of probability distributions over different possible choices of the next steps in their motions. One of the main challenges in mathematical modeling of living systems is to distinguish between random walks of purely physical origin (for instance, Brownian motions) and those of biological origin. Following a line of reasoning from prior research, it has been assumed, in the present development, that a biological random walk can be represented by a nonlinear mathematical model that represents coupled mental and motor dynamics incorporating the psychological concept of reflection or self-image. The nonlinear dynamics impart the lifelike ability to behave in ways and to exhibit patterns that depart from thermodynamic equilibrium. Reflection or self-image has traditionally been recognized as a basic element of intelligence. The nonlinear mathematical models of the present development are denoted self-supervised dynamical systems. They include (1) equations of classical dynamics, including random components caused by uncertainties in initial conditions and by Langevin forces, coupled with (2) the corresponding Liouville or Fokker-Planck equations that describe the evolutions of probability densities that represent the uncertainties. The coupling is effected by fictitious information-based forces, denoted supervising forces, composed of probability densities and functionals thereof. The equations of classical mechanics represent motor dynamics that is, dynamics in the traditional sense, signifying Newton s equations of motion. The evolution of the probability densities represents mental dynamics or self-image. Then the interaction between the physical and metal aspects of a monad is implemented by feedback from mental to motor dynamics, as represented by the aforementioned fictitious forces. This feedback is what makes the evolution of probability densities nonlinear. The deviation from linear evolution can be characterized, in a sense, as an expression of free will. It has been demonstrated that probability densities can approach prescribed attractors while exhibiting such patterns as shock waves, solitons, and chaos in probability space. The concept of self-supervised dynamical systems has been considered for application to diverse phenomena, including information-based neural networks, cooperation, competition, deception, games, and control of chaos. In addition, a formal similarity between the mathematical structures of self-supervised dynamical systems and of quantum-mechanical systems has been investigated.

State and parameter estimation of spatiotemporally chaotic systems illustrated by an application to Rayleigh-Bénard convection.

PubMed

Cornick, Matthew; Hunt, Brian; Ott, Edward; Kurtuldu, Huseyin; Schatz, Michael F

2009-03-01

Data assimilation refers to the process of estimating a system's state from a time series of measurements (which may be noisy or incomplete) in conjunction with a model for the system's time evolution. Here we demonstrate the applicability of a recently developed data assimilation method, the local ensemble transform Kalman filter, to nonlinear, high-dimensional, spatiotemporally chaotic flows in Rayleigh-Bénard convection experiments. Using this technique we are able to extract the full temperature and velocity fields from a time series of shadowgraph measurements. In addition, we describe extensions of the algorithm for estimating model parameters. Our results suggest the potential usefulness of our data assimilation technique to a broad class of experimental situations exhibiting spatiotemporal chaos.

Ultrafast Single-Shot Optical Oscilloscope based on Time-to-Space Conversion due to Temporal and Spatial Walk-Off Effects in Nonlinear Mixing Crystal

NASA Astrophysics Data System (ADS)

Takagi, Yoshihiro; Yamada, Yoshifumi; Ishikawa, Kiyoshi; Shimizu, Seiji; Sakabe, Shuji

2005-09-01

A simple method for single-shot sub-picosecond optical pulse diagnostics has been demonstrated by imaging the time evolution of the optical mixing onto the beam cross section of the sum-frequency wave when the interrogating pulse passes over the tested pulse in the mixing crystal as a result of the combined effect of group-velocity difference and walk-off beam propagation. A high linearity of the time-to-space projection is deduced from the process solely dependent upon the spatial uniformity of the refractive indices. A snap profile of the accidental coincidence between asynchronous pulses from separate mode-locked lasers has been detected, which demonstrates the single-shot ability.

SMALL-SCALE SOLAR WIND TURBULENCE DUE TO NONLINEAR ALFVÉN WAVES

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

Kumar, Sanjay; Moon, Y.-J.; Sharma, R. P., E-mail: sanjaykumar@khu.ac.kr

We present an evolution of wave localization and magnetic power spectra in solar wind plasma using kinetic Alfvén waves (AWs) and fast AWs. We use a two-fluid model to derive the dynamical equations of these wave modes and then numerically solve these nonlinear dynamical equations to analyze the power spectra and wave localization at different times. The ponderomotive force associated with the kinetic AW (or pump) is responsible for the wave localization, and these thin slabs (or sheets) become more chaotic as the system evolves with time until the modulational instability (or oscillating two-stream instability) saturates. From our numerical results,more » we notice a steepening of the spectra from the inertial range (k{sup −1.67}) to the dispersion range (k{sup −3.0}). The steepening of the spectra could be described as the energy transference from longer to smaller scales. The formation of complex magnetic thin slabs and the change of the spectral index may be considered to be the main reason for the charged particles acceleration in solar wind plasma.« less

An application of the Maslov complex germ method to the one-dimensional nonlocal Fisher-KPP equation

NASA Astrophysics Data System (ADS)

Shapovalov, A. V.; Trifonov, A. Yu.

A semiclassical approximation approach based on the Maslov complex germ method is considered in detail for the one-dimensional nonlocal Fisher-Kolmogorov-Petrovskii-Piskunov (Fisher-KPP) equation under the supposition of weak diffusion. In terms of the semiclassical formalism developed, the original nonlinear equation is reduced to an associated linear partial differential equation and some algebraic equations for the coefficients of the linear equation with a given accuracy of the asymptotic parameter. The solutions of the nonlinear equation are constructed from the solutions of both the linear equation and the algebraic equations. The solutions of the linear problem are found with the use of symmetry operators. A countable family of the leading terms of the semiclassical asymptotics is constructed in explicit form. The semiclassical asymptotics are valid by construction in a finite time interval. We construct asymptotics which are different from the semiclassical ones and can describe evolution of the solutions of the Fisher-KPP equation at large times. In the example considered, an initial unimodal distribution becomes multimodal, which can be treated as an example of a space structure.

Plasma diffusion at the magnetopause? The case of lower hybrid drift waves

NASA Technical Reports Server (NTRS)

Treumann, R. A.; Labelle, J.; Pottelette, R.; Gary, S. P.

1990-01-01

The diffusion expected from the quasilinear theory of the lower hybrid drift instability at the Earth's magnetopause is recalculated. The resulting diffusion coefficient is in principle just marginally large enough to explain the thickness of the boundary layer under quiet conditions, based on observational upper limits for the wave intensities. Thus, one possible model for the boundary layer could involve equilibrium between the diffusion arising from lower hybrid waves and various low processes. However, some recent data and simulations seems to indicate that the magnetopause is not consistent with such a soft diffusive equilibrium model. Furthermore, investigation of the nonlinear equations for the lower hybrid waves for magnetopause parameters indicates that the quasilinear state may never arise because coalescence to large wavelengths, followed by collapse once a critical wavelengths is reached, occur on a time scale faster than the quasilinear diffusion. In this case, an inhomogeneous boundary layer is to be expected. More simulations are required over longer time periods to explore whether this nonlinear evolution really takes place at the magnetopause.

Acceleration of incremental-pressure-correction incompressible flow computations using a coarse-grid projection method

NASA Astrophysics Data System (ADS)

Kashefi, Ali; Staples, Anne

2016-11-01

Coarse grid projection (CGP) methodology is a novel multigrid method for systems involving decoupled nonlinear evolution equations and linear elliptic equations. The nonlinear equations are solved on a fine grid and the linear equations are solved on a corresponding coarsened grid. Mapping functions transfer data between the two grids. Here we propose a version of CGP for incompressible flow computations using incremental pressure correction methods, called IFEi-CGP (implicit-time-integration, finite-element, incremental coarse grid projection). Incremental pressure correction schemes solve Poisson's equation for an intermediate variable and not the pressure itself. This fact contributes to IFEi-CGP's efficiency in two ways. First, IFEi-CGP preserves the velocity field accuracy even for a high level of pressure field grid coarsening and thus significant speedup is achieved. Second, because incremental schemes reduce the errors that arise from boundaries with artificial homogenous Neumann conditions, CGP generates undamped flows for simulations with velocity Dirichlet boundary conditions. Comparisons of the data accuracy and CPU times for the incremental-CGP versus non-incremental-CGP computations are presented.

Quantitative Simulation of QARBM Challenge Events During Radiation Belt Enhancements

NASA Astrophysics Data System (ADS)

Li, W.; Ma, Q.; Thorne, R. M.; Bortnik, J.; Chu, X.

2017-12-01

Various physical processes are known to affect energetic electron dynamics in the Earth's radiation belts, but their quantitative effects at different times and locations in space need further investigation. This presentation focuses on discussing the quantitative roles of various physical processes that affect Earth's radiation belt electron dynamics during radiation belt enhancement challenge events (storm-time vs. non-storm-time) selected by the GEM Quantitative Assessment of Radiation Belt Modeling (QARBM) focus group. We construct realistic global distributions of whistler-mode chorus waves, adopt various versions of radial diffusion models (statistical and event-specific), and use the global evolution of other potentially important plasma waves including plasmaspheric hiss, magnetosonic waves, and electromagnetic ion cyclotron waves from all available multi-satellite measurements. These state-of-the-art wave properties and distributions on a global scale are used to calculate diffusion coefficients, that are then adopted as inputs to simulate the dynamical electron evolution using a 3D diffusion simulation during the storm-time and the non-storm-time acceleration events respectively. We explore the similarities and differences in the dominant physical processes that cause radiation belt electron dynamics during the storm-time and non-storm-time acceleration events. The quantitative role of each physical process is determined by comparing against the Van Allen Probes electron observations at different energies, pitch angles, and L-MLT regions. This quantitative comparison further indicates instances when quasilinear theory is sufficient to explain the observed electron dynamics or when nonlinear interaction is required to reproduce the energetic electron evolution observed by the Van Allen Probes.

Simulation of Corrosion Process for Structure with the Cellular Automata Method

NASA Astrophysics Data System (ADS)

Chen, M. C.; Wen, Q. Q.

2017-06-01

In this paper, from the mesoscopic point of view, under the assumption of metal corrosion damage evolution being a diffusive process, the cellular automata (CA) method was proposed to simulate numerically the uniform corrosion damage evolution of outer steel tube of concrete filled steel tubular columns subjected to corrosive environment, and the effects of corrosive agent concentration, dissolution probability and elapsed etching time on the corrosion damage evolution were also investigated. It was shown that corrosion damage increases nonlinearly with increasing elapsed etching time, and the longer the etching time, the more serious the corrosion damage; different concentration of corrosive agents had different impacts on the corrosion damage degree of the outer steel tube, but the difference between the impacts was very small; the heavier the concentration, the more serious the influence. The greater the dissolution probability, the more serious the corrosion damage of the outer steel tube, but with the increase of dissolution probability, the difference between its impacts on the corrosion damage became smaller and smaller. To validate present method, corrosion damage measurements for concrete filled square steel tubular columns (CFSSTCs) sealed at both their ends and immersed fully in a simulating acid rain solution were conducted, and Faraday’s law was used to predict their theoretical values. Meanwhile, the proposed CA mode was applied for the simulation of corrosion damage evolution of the CFSSTCs. It was shown by the comparisons of results from the three methods aforementioned that they were in good agreement, implying that the proposed method used for the simulation of corrosion damage evolution of concrete filled steel tubular columns is feasible and effective. It will open a new approach to study and evaluate further the corrosion damage, loading capacity and lifetime prediction of concrete filled steel tubular structures.

Adiabatic decay of internal solitons due to Earth's rotation within the framework of the Gardner-Ostrovsky equation

NASA Astrophysics Data System (ADS)

Obregon, Maria; Raj, Nawin; Stepanyants, Yury

2018-03-01

The adiabatic decay of different types of internal wave solitons caused by the Earth's rotation is studied within the framework of the Gardner-Ostrovsky equation. The governing equation describing such processes includes quadratic and cubic nonlinear terms, as well as the Boussinesq and Coriolis dispersions: (ut + c ux + α u ux + α1 u2 ux + β uxxx)x = γ u. It is shown that at the early stage of evolution solitons gradually decay under the influence of weak Earth's rotation described by the parameter γ. The characteristic decay time is derived for different types of solitons for positive and negative coefficients of cubic nonlinearity α1 (both signs of that parameter may occur in the oceans). The coefficient of quadratic nonlinearity α determines only a polarity of solitary wave when α1 < 0 or the asymmetry of solitary waves of opposite polarity when α1 > 0. It is found that the adiabatic theory describes well the decay of solitons having bell-shaped profiles. In contrast to that, large amplitude table-top solitons, which can exist when α1 is negative, are structurally unstable. Under the influence of Earth's rotation, they transfer first to the bell-shaped solitons, which decay then adiabatically. Estimates of the characteristic decay time of internal solitons are presented for the real oceanographic conditions.

A stochastic differential equation analysis of cerebrospinal fluid dynamics.

PubMed

Raman, Kalyan

2011-01-18

Clinical measurements of intracranial pressure (ICP) over time show fluctuations around the deterministic time path predicted by a classic mathematical model in hydrocephalus research. Thus an important issue in mathematical research on hydrocephalus remains unaddressed--modeling the effect of noise on CSF dynamics. Our objective is to mathematically model the noise in the data. The classic model relating the temporal evolution of ICP in pressure-volume studies to infusions is a nonlinear differential equation based on natural physical analogies between CSF dynamics and an electrical circuit. Brownian motion was incorporated into the differential equation describing CSF dynamics to obtain a nonlinear stochastic differential equation (SDE) that accommodates the fluctuations in ICP. The SDE is explicitly solved and the dynamic probabilities of exceeding critical levels of ICP under different clinical conditions are computed. A key finding is that the probabilities display strong threshold effects with respect to noise. Above the noise threshold, the probabilities are significantly influenced by the resistance to CSF outflow and the intensity of the noise. Fluctuations in the CSF formation rate increase fluctuations in the ICP and they should be minimized to lower the patient's risk. The nonlinear SDE provides a scientific methodology for dynamic risk management of patients. The dynamic output of the SDE matches the noisy ICP data generated by the actual intracranial dynamics of patients better than the classic model used in prior research.

Nonlinear Waves

DTIC Science & Technology

1989-06-15

Hamiltonian Formulation of the Kadomtsev - Petviashvili and Benjamin-Ono Equations , A.S. Fokas and P.M. Santini, J. Math. Phys. 29 (3) 604-617 (1988...Prototypes are the so-called Kadomtsev -Petviashvilli and Davey-Stewartson equations . These equations arise in a variety of physical instances such as water...plasma physics. Moreover the study of solutions to some of the underlying nonlinear evolution equations has led naturally to the investigation and new

Time-dependent local-to-normal mode transition in triatomic molecules

NASA Astrophysics Data System (ADS)

Cruz, Hans; Bermúdez-Montaña, Marisol; Lemus, Renato

2018-01-01

Time-evolution of the vibrational states of two interacting harmonic oscillators in the local mode scheme is presented. A local-to-normal mode transition (LNT) is identified and studied from temporal perspective through time-dependent frequencies of the oscillators. The LNT is established as a polyad-breaking phenomenon from the local standpoint for the stretching degrees of freedom in a triatomic molecule. This study is carried out in the algebraic representation of bosonic operators. The dynamics of the states are determined via the solutions of the corresponding nonlinear Ermakov equation and a local time-dependent polyad is obtained as a tool to identify the LNT. Applications of this formalism to H2O, CO2, O3 and NO2 molecules in the adiabatic, sudden and linear regime are considered.

Dark solitons, modulation instability and breathers in a chain of weakly nonlinear oscillators with cyclic symmetry

NASA Astrophysics Data System (ADS)

Fontanela, F.; Grolet, A.; Salles, L.; Chabchoub, A.; Hoffmann, N.

2018-01-01

In the aerospace industry the trend for light-weight structures and the resulting complex dynamic behaviours currently challenge vibration engineers. In many cases, these light-weight structures deviate from linear behaviour, and complex nonlinear phenomena can be expected. We consider a cyclically symmetric system of coupled weakly nonlinear undamped oscillators that could be considered a minimal model for different cyclic and symmetric aerospace structures experiencing large deformations. The focus is on localised vibrations that arise from wave envelope modulation of travelling waves. For the defocussing parameter range of the approximative nonlinear evolution equation, we show the possible existence of dark solitons and discuss their characteristics. For the focussing parameter range, we characterise modulation instability and illustrate corresponding nonlinear breather dynamics. Furthermore, we show that for stronger nonlinearity or randomness in initial conditions, transient breather-type dynamics and decay into bright solitons appear. The findings suggest that significant vibration localisation may arise due to mechanisms of nonlinear modulation dynamics.

The femur-tibia control system in a proscopiid (Caelifera, Orthoptera): a test for assumptions on the functional basis and evolution of twig mimesis in stick insects.

PubMed

Wolf, H; Bässler, U; Spiess, R; Kittmann, R

2001-11-01

The extremely slow return movements observed in stick insects (phasmids) after imposed changes in posture are termed catalepsy. In the literature, catalepsy is treated as a behavioural component of the twig mimesis observed in walking stick insects. It is produced by the high gain of the velocity-sensitive component of the relevant joint control systems and by the non-linear dependency of its time constant on movement velocity. The high gain, in turn, causes the system to work close to instability, and this may have driven the evolution of gain control mechanisms. Although these statements represent plausible assumptions, based on correlated occurrence, they remain largely hypothetical like many ideas concerning evolutionary tendencies. To test these hypotheses, we studied catalepsy and the relevant properties of the femur-tibia control system in the middle and hind legs of Prosarthria teretrirostris.cf. Prosarthria teretrirostris is a proscopiid closely related to grasshoppers and locusts. With its slender, green-to-brown body and legs, it shows clear morphological twig mimesis, which has evolved independently of the well-known twig mimesis in stick insects. The animals show clear catalepsy. The main properties of femur-tibia joint control are remarkably similar between proscopiids and stick insects (e.g. the marked sensitivity to movement velocity rather than to joint position and the non-linear dependency of the time constants of response decay on movement velocity), but there are also important differences (habituation and activity-related mechanisms of gain control are absent). Together, these results validate the main concepts that have been developed concerning the neural basis and evolution of catalepsy in stick insects and its relationship to twig mimesis, while demonstrating that ideas on the role of habituation and gain control should be refined.

Dynamical AdS strings across horizons

DOE PAGES

Ishii, Takaaki; Murata, Keiju

2016-03-01

We examine the nonlinear classical dynamics of a fundamental string in anti-deSitter spacetime. The string is dual to the flux tube between an external quark-antiquark pair in $N = 4$ super Yang-Mills theory. We perturb the string by shaking the endpoints and compute its time evolution numerically. We find that with sufficiently strong perturbations the string continues extending and plunges into the Poincare´ horizon. In the evolution, effective horizons are also dynamically created on the string worldsheet. The quark and antiquark are thus causally disconnected, and the string transitions to two straight strings. The forces acting on the endpoints vanishmore » with a power law whose slope depends on the perturbations. Lastly, the condition for this transition to occur is that energy injection exceeds the static energy between the quark-antiquark pair.« less

Frequency-Domain Streak Camera and Tomography for Ultrafast Imaging of Evolving and Channeled Plasma Accelerator Structures

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

Li Zhengyan; Zgadzaj, Rafal; Wang Xiaoming

2010-11-04

We demonstrate a prototype Frequency Domain Streak Camera (FDSC) that can capture the picosecond time evolution of the plasma accelerator structure in a single shot. In our prototype Frequency-Domain Streak Camera, a probe pulse propagates obliquely to a sub-picosecond pump pulse that creates an evolving nonlinear index 'bubble' in fused silica glass, supplementing a conventional Frequency Domain Holographic (FDH) probe-reference pair that co-propagates with the 'bubble'. Frequency Domain Tomography (FDT) generalizes Frequency-Domain Streak Camera by probing the 'bubble' from multiple angles and reconstructing its morphology and evolution using algorithms similar to those used in medical CAT scans. Multiplexing methods (Temporalmore » Multiplexing and Angular Multiplexing) improve data storage and processing capability, demonstrating a compact Frequency Domain Tomography system with a single spectrometer.« less

Proceedings of the MECA Workshop on The Evoluation of the Martian Atmosphere

NASA Technical Reports Server (NTRS)

Carr, M. (Editor); James, P. (Editor); Conway, L. (Editor); Pepin, R. (Editor); Pollack, J. (Editor)

1985-01-01

Topics addressed include: Mars' volatile budget; climatic implications of martian channels; bulk composition of Mars; accreted water inventory; evolution of CO2; dust storms; nonlinear frost albedo feedback on Mars; martian atmospheric evolution; effects of asteroidal and cometary impacts; and water exchange between the regolith and the atmosphere/cap system over obliquity timescales.

Numerical modeling of the atmosphere with an isentropic vertical coordinate

NASA Technical Reports Server (NTRS)

Hsu, Yueh-Jiuan G.; Arakawa, Akio

1990-01-01

A theta-coordinate model simulating the nonlinear evolution of a baroclinic wave is presented. In the model, vertical discretization maintains important integral constraints such as conservation of the angular momentum and total energy. A massless-layer approach is used in the treatment of the intersections of coordinate surfaces with the lower boundary. This formally eliminates the intersection problem, but raises other computational problems. Horizontal discretization of the continuity and momentum equations in the model are designed to overcome these problems. Selected results from a 10-day integration with the 25-layer, beta-plane version of the model are presented. It is concluded that the model can simulate the nonlinear evolution of a baroclinic wave and associated dynamical processes without major computational difficulties.

Recursion equations in predicting band width under gradient elution.

PubMed

Liang, Heng; Liu, Ying

2004-06-18

The evolution of solute zone under gradient elution is a typical problem of non-linear continuity equation since the local diffusion coefficient and local migration velocity of the mass cells of solute zones are the functions of position and time due to space- and time-variable mobile phase composition. In this paper, based on the mesoscopic approaches (Lagrangian description, the continuity theory and the local equilibrium assumption), the evolution of solute zones in space- and time-dependent fields is described by the iterative addition of local probability density of the mass cells of solute zones. Furthermore, on macroscopic levels, the recursion equations have been proposed to simulate zone migration and spreading in reversed-phase high-performance liquid chromatography (RP-HPLC) through directly relating local retention factor and local diffusion coefficient to local mobile phase concentration. This new approach differs entirely from the traditional theories on plate concept with Eulerian description, since band width recursion equation is actually the accumulation of local diffusion coefficients of solute zones to discrete-time slices. Recursion equations and literature equations were used in dealing with same experimental data in RP-HPLC, and the comparison results show that the recursion equations can accurately predict band width under gradient elution.

Stabilization of burn conditions in a thermonuclear reactor using artificial neural networks

NASA Astrophysics Data System (ADS)

Vitela, Javier E.; Martinell, Julio J.

1998-02-01

In this work we develop an artificial neural network (ANN) for the feedback stabilization of a thermonuclear reactor at nearly ignited burn conditions. A volume-averaged zero-dimensional nonlinear model is used to represent the time evolution of the electron density, the relative density of alpha particles and the temperature of the plasma, where a particular scaling law for the energy confinement time previously used by other authors, was adopted. The control actions include the concurrent modulation of the D-T refuelling rate, the injection of a neutral He-4 beam and an auxiliary heating power modulation, which are constrained to take values within a maximum and minimum levels. For this purpose a feedforward multilayer artificial neural network with sigmoidal activation function is trained using a back-propagation through-time technique. Numerical examples are used to illustrate the behaviour of the resulting ANN-dynamical system configuration. It is concluded that the resulting ANN can successfully stabilize the nonlinear model of the thermonuclear reactor at nearly ignited conditions for temperature and density departures significantly far from their nominal operating values. The NN-dynamical system configuration is shown to be robust with respect to the thermalization time of the alpha particles for perturbations within the region used to train the NN.

Studying Climate Response to Forcing by the Nonlinear Dynamical Mode Decomposition

NASA Astrophysics Data System (ADS)

Mukhin, Dmitry; Gavrilov, Andrey; Loskutov, Evgeny; Feigin, Alexander

2017-04-01

An analysis of global climate response to external forcing, both anthropogenic (mainly, CO2 and aerosol) and natural (solar and volcanic), is needed for adequate predictions of global climate change. Being complex dynamical system, the climate reacts to external perturbations exciting feedbacks (both positive and negative) making the response non-trivial and poorly predictable. Thus an extraction of internal modes of climate system, investigation of their interaction with external forcings and further modeling and forecast of their dynamics, are all the problems providing the success of climate modeling. In the report the new method for principal mode extraction from climate data is presented. The method is based on the Nonlinear Dynamical Mode (NDM) expansion [1,2], but takes into account a number of external forcings applied to the system. Each NDM is represented by hidden time series governing the observed variability, which, together with external forcing time series, are mapped onto data space. While forcing time series are considered to be known, the hidden unknown signals underlying the internal climate dynamics are extracted from observed data by the suggested method. In particular, it gives us an opportunity to study the evolution of principal system's mode structure in changing external conditions and separate the internal climate variability from trends forced by external perturbations. Furthermore, the modes so obtained can be extrapolated beyond the observational time series, and long-term prognosis of modes' structure including characteristics of interconnections and responses to external perturbations, can be carried out. In this work the method is used for reconstructing and studying the principal modes of climate variability on inter-annual and decadal time scales accounting the external forcings such as anthropogenic emissions, variations of the solar activity and volcanic activity. The structure of the obtained modes as well as their response to external factors, e.g. forecast their change in 21 century under different CO2 emission scenarios, are discussed. [1] Mukhin, D., Gavrilov, A., Feigin, A., Loskutov, E., & Kurths, J. (2015). Principal nonlinear dynamical modes of climate variability. Scientific Reports, 5, 15510. http://doi.org/10.1038/srep15510 [2] Gavrilov, A., Mukhin, D., Loskutov, E., Volodin, E., Feigin, A., & Kurths, J. (2016). Method for reconstructing nonlinear modes with adaptive structure from multidimensional data. Chaos: An Interdisciplinary Journal of Nonlinear Science, 26(12), 123101. http://doi.org/10.1063/1.4968852

Dynamic evolution characteristics of a fractional order hydropower station system

NASA Astrophysics Data System (ADS)

Gao, Xiang; Chen, Diyi; Yan, Donglin; Xu, Beibei; Wang, Xiangyu

2018-01-01

This paper investigates the dynamic evolution characteristics of the hydropower station by introducing the fractional order damping forces. A careful analysis of the dynamic characteristics of the generator shaft system is carried out under different values of fractional order. It turns out the vibration state of the axis coordinates has a certain evolution law with the increase of the fractional order. Significantly, the obtained law exists in the horizontal evolution and vertical evolution of the dynamical behaviors. Meanwhile, some interesting dynamical phenomena were found in this process. The outcomes of this study enrich the nonlinear dynamic theory from the engineering practice of hydropower stations.

The Effects of Thermal Energetics on Three-dimensional Hydrodynamic Instabilities in Massive Protostellar Disks. II. High-Resolution and Adiabatic Evolutions

NASA Astrophysics Data System (ADS)

Pickett, Brian K.; Cassen, Patrick; Durisen, Richard H.; Link, Robert

2000-02-01

In this paper, the effects of thermal energetics on the evolution of gravitationally unstable protostellar disks are investigated by means of three-dimensional hydrodynamic calculations. The initial states for the simulations correspond to stars with equilibrium, self-gravitating disks that are formed early in the collapse of a uniformly rotating, singular isothermal sphere. In a previous paper (Pickett et al.), it was shown that the nonlinear development of locally isentropic disturbances can be radically different than that of locally isothermal disturbances, even though growth in the linear regime may be similar. When multiple low-order modes grew rapidly in the star and inner disk region and saturated at moderate nonlinear levels in the isentropic evolution, the same modes in the isothermal evolution led to shredding of the disk into dense arclets and ejection of material. In this paper, we (1) examine the fate of the shredded disk with calculations at higher spatial resolution than the previous simulations had and (2) follow the evolution of the same initial state using an internal energy equation rather than the assumption of locally isentropic or locally isothermal conditions. Despite the complex structure of the nonlinear features that developed in the violently unstable isothermal disk referred to above, our previous calculation produced no gravitationally independent, long-lived stellar or planetary companions. The higher resolution calculations presented here confirm this result. When the disk of this model is cooled further, prompting even more violent instabilities, the end result is qualitatively the same--a shredded disk. At least for the disks studied here, it is difficult to produce condensations of material that do not shear away into fragmented spirals. It is argued that the ultimate fate of such fragments depends on how readily local internal energy is lost. On the other hand, if a dynamically unstable disk is to survive for very long times without shredding, then some mechanism must mitigate and control any violent phenomena that do occur. The prior simulations demonstrated a marked difference in final outcome, depending upon the efficiency of disk cooling under two different, idealized thermal conditions. We have here incorporated an internal energy equation that allows for arbitrary heating and cooling. Simulations are presented for adiabatic models with and without artificial viscosity. The artificial viscosity accounts for dissipation and heating due to shocks in the code physics. The expected nonaxisymmetric instabilities occur and grow as before in these energy equation evolutions. When artificial viscosity is not present, the model protostar displays behavior between the locally isentropic and locally isothermal cases of the last paper; a strong two-armed spiral grows to nonlinear amplitudes and saturates at a level higher than in the locally isentropic case. Since the amplitude of the spiral disturbance is large, it is expected that continued transport of material and angular momentum will occur well after the end of the calculation at nearly four outer rotation periods. The spiral is not strong enough, however, to disrupt the disk as in the locally isothermal case. When artificial viscosity is present, the same disturbances reach moderate nonlinear amplitude, then heat the gas, which in turn greatly reduces their strength and effects on the disk. Additional heating in the low-density regions of the disk also leads to a gentle flow of material vertically off the computational grid. The energy equation and high-resolution isothermal calculations are used to discuss the importance and relevance of the different thermal regimes so far examined, with particular attention to applications to star and planet formation.

Meandering rivers: Interpreting dynamics from planform geometry and the secret lives of migrating meanders

NASA Astrophysics Data System (ADS)

Schwenk, Jonathan

Meandering rivers are dynamic agents of geomorphic change that rework landscapes through migration while maintaining beautiful looping planforms. This work investigates the relationships between the alluring planform geometries of meandering rivers, the dynamics of individual meander bend migration, and the dynamic processes driving meander evolution. A simple yet physically-based model of long-time meander migration is employed to understand the dynamic trajectories of individual meander bends and establish relationships between historic dynamics and cutoff bend geometry. At the reach scale, concepts from nonlinear dynamic theory are applied to river centerlines to determine if the dynamic nonlinearities driving meander evolution are preserved in the reachwide planform structure. Understanding how rivers move across their floodplains requires snapshots of planforms over long time periods from aerial photography or historic maps and surveys which are often taken at irregular and long intervals. Migration occurring between snapshots has thus largely remained a mystery. More recently, worldwide satellite imagery collected at least every 18 days by the NASA Landsat family of satellites offers the potential to reveal the secret lives of migrating, meandering rivers. This research mines the vault of Landsat imagery to resolve over 30 years of planform migration along more than 1,300 km of one of the Earth's most active meandering rivers: the Ucayali River in Peru. Analysis of the resulting annual binary channel masks suggests that migration rates are controlled by processes acting across bend-to-reach scales. An exciting new geomorphic discovery emerges from the analysis revealing the role of cutoffs as drivers of nonlocal morphodynamic change.

Evaluation of nonlinearity and validity of nonlinear modeling for complex time series.

PubMed

Suzuki, Tomoya; Ikeguchi, Tohru; Suzuki, Masuo

2007-10-01

Even if an original time series exhibits nonlinearity, it is not always effective to approximate the time series by a nonlinear model because such nonlinear models have high complexity from the viewpoint of information criteria. Therefore, we propose two measures to evaluate both the nonlinearity of a time series and validity of nonlinear modeling applied to it by nonlinear predictability and information criteria. Through numerical simulations, we confirm that the proposed measures effectively detect the nonlinearity of an observed time series and evaluate the validity of the nonlinear model. The measures are also robust against observational noises. We also analyze some real time series: the difference of the number of chickenpox and measles patients, the number of sunspots, five Japanese vowels, and the chaotic laser. We can confirm that the nonlinear model is effective for the Japanese vowel /a/, the difference of the number of measles patients, and the chaotic laser.

Evaluation of nonlinearity and validity of nonlinear modeling for complex time series

NASA Astrophysics Data System (ADS)

Suzuki, Tomoya; Ikeguchi, Tohru; Suzuki, Masuo

2007-10-01

Even if an original time series exhibits nonlinearity, it is not always effective to approximate the time series by a nonlinear model because such nonlinear models have high complexity from the viewpoint of information criteria. Therefore, we propose two measures to evaluate both the nonlinearity of a time series and validity of nonlinear modeling applied to it by nonlinear predictability and information criteria. Through numerical simulations, we confirm that the proposed measures effectively detect the nonlinearity of an observed time series and evaluate the validity of the nonlinear model. The measures are also robust against observational noises. We also analyze some real time series: the difference of the number of chickenpox and measles patients, the number of sunspots, five Japanese vowels, and the chaotic laser. We can confirm that the nonlinear model is effective for the Japanese vowel /a/, the difference of the number of measles patients, and the chaotic laser.

Boltzmann sampling from the Ising model using quantum heating of coupled nonlinear oscillators.

PubMed

Goto, Hayato; Lin, Zhirong; Nakamura, Yasunobu

2018-05-08

A network of Kerr-nonlinear parametric oscillators without dissipation has recently been proposed for solving combinatorial optimization problems via quantum adiabatic evolution through its bifurcation point. Here we investigate the behavior of the quantum bifurcation machine (QbM) in the presence of dissipation. Our numerical study suggests that the output probability distribution of the dissipative QbM is Boltzmann-like, where the energy in the Boltzmann distribution corresponds to the cost function of the optimization problem. We explain the Boltzmann distribution by generalizing the concept of quantum heating in a single nonlinear oscillator to the case of multiple coupled nonlinear oscillators. The present result also suggests that such driven dissipative nonlinear oscillator networks can be applied to Boltzmann sampling, which is used, e.g., for Boltzmann machine learning in the field of artificial intelligence.

Dispersive optical soliton solutions for the hyperbolic and cubic-quintic nonlinear Schrödinger equations via the extended sinh-Gordon equation expansion method

NASA Astrophysics Data System (ADS)

Seadawy, Aly R.; Kumar, Dipankar; Chakrabarty, Anuz Kumar

2018-05-01

The (2+1)-dimensional hyperbolic and cubic-quintic nonlinear Schrödinger equations describe the propagation of ultra-short pulses in optical fibers of nonlinear media. By using an extended sinh-Gordon equation expansion method, some new complex hyperbolic and trigonometric functions prototype solutions for two nonlinear Schrödinger equations were derived. The acquired new complex hyperbolic and trigonometric solutions are expressed by dark, bright, combined dark-bright, singular and combined singular solitons. The obtained results are more compatible than those of other applied methods. The extended sinh-Gordon equation expansion method is a more powerful and robust mathematical tool for generating new optical solitary wave solutions for many other nonlinear evolution equations arising in the propagation of optical pulses.

Magnetic field evolution in white dwarfs: The hall effect and complexity of the field

NASA Technical Reports Server (NTRS)

Muslimov, A. G.; Van Horn, H. M.; Wood, M. A.

1995-01-01

We calculate the evolution of the magnetic fields in white dwarfs, taking into account the Hall effect. Because this effect depends nonlinearly upon the magnetic field strength B, the time dependences of the various multipole field components are coupled. The evolution of the field is thus significantly more complicated than has been indicated by previous investigations. Our calculations employ recent white dwarf evolutionary sequences computed for stars with masses 0.4, 0.6, 0.8, and 1.0 solar mass. We show that in the presence of a strong (up to approximately 10(exp 9) G) internal toroidal magnetic field; the evolution of even the lowest order poloidal modes can be substantially changed by the Hall effect. As an example, we compute the evolution of an initially weak quadrupole component, which we take arbitrarily to be approximately 0.1%-1% of the strength of a dominant dipole field. We find that coupling provided by the Hall effect can produce growth of the ratio of the quadrupole to the dipole component of the surface value of the magnetic field strength by more than a factor of 10 over the 10(exp 9) to 10(exp 10) year cooling lifetime of the white dwarf. Some consequences of these results for the process of magnetic-field evolution in white dwarfs are briefly discussed.

Semiclassical limit of the focusing NLS: Whitham equations and the Riemann-Hilbert Problem approach

NASA Astrophysics Data System (ADS)

Tovbis, Alexander; El, Gennady A.

2016-10-01

The main goal of this paper is to put together: a) the Whitham theory applicable to slowly modulated N-phase nonlinear wave solutions to the focusing nonlinear Schrödinger (fNLS) equation, and b) the Riemann-Hilbert Problem approach to particular solutions of the fNLS in the semiclassical (small dispersion) limit that develop slowly modulated N-phase nonlinear wave in the process of evolution. Both approaches have their own merits and limitations. Understanding of the interrelations between them could prove beneficial for a broad range of problems involving the semiclassical fNLS.

Universality of the Peregrine Soliton in the Focusing Dynamics of the Cubic Nonlinear Schrödinger Equation

NASA Astrophysics Data System (ADS)

Tikan, Alexey; Billet, Cyril; El, Gennady; Tovbis, Alexander; Bertola, Marco; Sylvestre, Thibaut; Gustave, Francois; Randoux, Stephane; Genty, Goëry; Suret, Pierre; Dudley, John M.

2017-07-01

We report experimental confirmation of the universal emergence of the Peregrine soliton predicted to occur during pulse propagation in the semiclassical limit of the focusing nonlinear Schrödinger equation. Using an optical fiber based system, measurements of temporal focusing of high power pulses reveal both intensity and phase signatures of the Peregrine soliton during the initial nonlinear evolution stage. Experimental and numerical results are in very good agreement, and show that the universal mechanism that yields the Peregrine soliton structure is highly robust and can be observed over a broad range of parameters.

Mammalian cochlea as a physics guided evolution-optimized hearing sensor.

PubMed

Lorimer, Tom; Gomez, Florian; Stoop, Ruedi

2015-07-28

Nonlinear physics plays an essential role in hearing. We demonstrate on a mesoscopic description level that during the evolutionary perfection of the hearing sensor, nonlinear physics led to the unique design of the cochlea observed in mammals, and that this design requests as a consequence the perception of pitch. Our insight challenges the view that mostly genetics is responsible for the uniformity of the construction of the mammalian hearing sensor. Our analysis also suggests that scaleable and non-scaleable arrangements of nonlinear sound detectors may be at the origin of the differences between hearing sensors in amniotic lineages.

Femtosecond Fiber Lasers Based on Dissipative Processes for Nonlinear Microscopy.

PubMed

Wise, Frank W

2012-01-01

Recent progress in the development of femtosecond-pulse fiber lasers with parameters appropriate for nonlinear microscopy is reviewed. Pulse-shaping in lasers with only normal-dispersion components is briefly described, and the performance of the resulting lasers is summarized. Fiber lasers based on the formation of dissipative solitons now offer performance competitive with that of solid-state lasers, but with the benefits of the fiber medium. Lasers based on self-similar pulse evolution in the gain section of a laser also offer a combination of short pulse duration and high pulse energy that will be attractive for applications in nonlinear bioimaging.

Cavity equations for a positive- or negative-refraction-index material with electric and magnetic nonlinearities.

PubMed

Mártin, Daniel A; Hoyuelos, Miguel

2009-11-01

We study evolution equations for electric and magnetic field amplitudes in a ring cavity with plane mirrors. The cavity is filled with a positive or negative-refraction-index material with third-order effective electric and magnetic nonlinearities. Two coupled nonlinear equations for the electric and magnetic amplitudes are obtained. We prove that the description can be reduced to one Lugiato-Lefever equation with generalized coefficients. A stability analysis of the homogeneous solution, complemented with numerical integration, shows that any combination of the parameters should correspond to one of three characteristic behaviors.