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

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.

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.

Reorientational versus Kerr dark and gray solitary waves using modulation theory.

PubMed

Assanto, Gaetano; Marchant, T R; Minzoni, Antonmaria A; Smyth, Noel F

2011-12-01

We develop a modulation theory model based on a Lagrangian formulation to investigate the evolution of dark and gray optical spatial solitary waves for both the defocusing nonlinear Schrödinger (NLS) equation and the nematicon equations describing nonlinear beams, nematicons, in self-defocusing nematic liquid crystals. Since it has an exact soliton solution, the defocusing NLS equation is used as a test bed for the modulation theory applied to the nematicon equations, which have no exact solitary wave solution. We find that the evolution of dark and gray NLS solitons, as well as nematicons, is entirely driven by the emission of diffractive radiation, in contrast to the evolution of bright NLS solitons and bright nematicons. Moreover, the steady nematicon profile is nonmonotonic due to the long-range nonlocality associated with the perturbation of the optic axis. Excellent agreement is obtained with numerical solutions of both the defocusing NLS and nematicon equations. The comparisons for the nematicon solutions raise a number of subtle issues relating to the definition and measurement of the width of a dark or gray nematicon.

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

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

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.

Tuning the control system of a nonlinear inverted pendulum by means of the new method of Lyapunov exponents estimation

NASA Astrophysics Data System (ADS)

Balcerzak, Marek; Dąbrowski, Artur; Pikunov, Danylo

2018-01-01

This paper presents a practical application of a new, simplified method of Lyapunov exponents estimation. The method has been applied to optimization of a real, nonlinear inverted pendulum system. Authors presented how the algorithm of the Largest Lyapunov Exponent (LLE) estimation can be applied to evaluate control systems performance. The new LLE-based control performance index has been proposed. Equations of the inverted pendulum system of the fourth order have been found. The nonlinear friction of the regulation object has been identified by means of the nonlinear least squares method. Three different friction models have been tested: linear, cubic and Coulomb model. The Differential Evolution (DE) algorithm has been used to search for the best set of parameters of the general linear regulator. This work proves that proposed method is efficient and results in faster perturbation rejection, especially when disturbances are significant.

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.

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.

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.

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.

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.

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.

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.

Accurate detection of hierarchical communities in complex networks based on nonlinear dynamical evolution

NASA Astrophysics Data System (ADS)

Zhuo, Zhao; Cai, Shi-Min; Tang, Ming; Lai, Ying-Cheng

2018-04-01

One of the most challenging problems in network science is to accurately detect communities at distinct hierarchical scales. Most existing methods are based on structural analysis and manipulation, which are NP-hard. We articulate an alternative, dynamical evolution-based approach to the problem. The basic principle is to computationally implement a nonlinear dynamical process on all nodes in the network with a general coupling scheme, creating a networked dynamical system. Under a proper system setting and with an adjustable control parameter, the community structure of the network would "come out" or emerge naturally from the dynamical evolution of the system. As the control parameter is systematically varied, the community hierarchies at different scales can be revealed. As a concrete example of this general principle, we exploit clustered synchronization as a dynamical mechanism through which the hierarchical community structure can be uncovered. In particular, for quite arbitrary choices of the nonlinear nodal dynamics and coupling scheme, decreasing the coupling parameter from the global synchronization regime, in which the dynamical states of all nodes are perfectly synchronized, can lead to a weaker type of synchronization organized as clusters. We demonstrate the existence of optimal choices of the coupling parameter for which the synchronization clusters encode accurate information about the hierarchical community structure of the network. We test and validate our method using a standard class of benchmark modular networks with two distinct hierarchies of communities and a number of empirical networks arising from the real world. Our method is computationally extremely efficient, eliminating completely the NP-hard difficulty associated with previous methods. The basic principle of exploiting dynamical evolution to uncover hidden community organizations at different scales represents a "game-change" type of approach to addressing the problem of community detection in complex networks.

Influence of asymmetric magnetic perturbation on the nonlinear evolution of double tearing modes

NASA Astrophysics Data System (ADS)

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

2017-06-01

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

Beam width evolution of astigmatic hollow Gaussian beams in highly nonlocal nonlinear media

NASA Astrophysics Data System (ADS)

Yang, Zhen-Feng; Jiang, Xue-Song; Yang, Zhen-Jun; Li, Jian-Xing; Zhang, Shu-Min

We investigate the beam width evolution of astigmatic hollow Gaussian beams propagating in highly nonlocal nonlinear media. The input-power-induced different evolutions of the beam width are illustrated: (i) the beam widths in two transverse directions are compressed or broadened at the same time; (ii) the beam width in one transverse direction keeps invariant, and the other is compressed or broadened; (iii) furthermore, the beam width in one transverse direction is compressed, whereas it in the other transverse direction is broadened.

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.

A Differential Evolution Algorithm Based on Nikaido-Isoda Function for Solving Nash Equilibrium in Nonlinear Continuous Games

PubMed Central

He, Feng; Zhang, Wei; Zhang, Guoqiang

2016-01-01

A differential evolution algorithm for solving Nash equilibrium in nonlinear continuous games is presented in this paper, called NIDE (Nikaido-Isoda differential evolution). At each generation, parent and child strategy profiles are compared one by one pairwisely, adapting Nikaido-Isoda function as fitness function. In practice, the NE of nonlinear game model with cubic cost function and quadratic demand function is solved, and this method could also be applied to non-concave payoff functions. Moreover, the NIDE is compared with the existing Nash Domination Evolutionary Multiplayer Optimization (NDEMO), the result showed that NIDE was significantly better than NDEMO with less iterations and shorter running time. These numerical examples suggested that the NIDE method is potentially useful. PMID:27589229

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.

Peakompactons: Peaked compact nonlinear waves

DOE PAGES

Christov, Ivan C.; Kress, Tyler; Saxena, Avadh

2017-04-20

This paper is meant as an accessible introduction to/tutorial on the analytical construction and numerical simulation of a class of nonstandard solitary waves termed peakompactons. We present that these peaked compactly supported waves arise as solutions to nonlinear evolution equations from a hierarchy of nonlinearly dispersive Korteweg–de Vries-type models. Peakompactons, like the now-well-known compactons and unlike the soliton solutions of the Korteweg–de Vries equation, have finite support, i.e., they are of finite wavelength. However, unlike compactons, peakompactons are also peaked, i.e., a higher spatial derivative suffers a jump discontinuity at the wave’s crest. Here, we construct such solutions exactly bymore » reducing the governing partial differential equation to a nonlinear ordinary differential equation and employing a phase-plane analysis. Lastly, a simple, but reliable, finite-difference scheme is also designed and tested for the simulation of collisions of peakompactons. In addition to the peakompacton class of solutions, the general physical features of the so-called K #(n,m) hierarchy of nonlinearly dispersive Korteweg–de Vries-type models are discussed as well.« less

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.

Nonlinear QED effects in X-ray emission of pulsars

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

Shakeri, Soroush; Haghighat, Mansour; Xue, She-Sheng, E-mail: Soroush.Shakeri@ph.iut.ac.ir, E-mail: m.haghighat@shirazu.ac.ir, E-mail: xue@icra.it

2017-10-01

In the presence of strong magnetic fields near pulsars, the QED vacuum becomes a birefringent medium due to nonlinear QED interactions. Here, we explore the impact of the effective photon-photon interaction on the polarization evolution of photons propagating through the magnetized QED vacuum of a pulsar. We solve the quantum Boltzmann equation within the framework of the Euler-Heisenberg Lagrangian to find the evolution of the Stokes parameters. We find that linearly polarized X-ray photons propagating outward in the magnetosphere of a rotating neutron star can acquire high values for the circular polarization parameter. Meanwhile, it is shown that the polarizationmore » characteristics of photons besides photon energy depend strongly on parameters of the pulsars such as magnetic field strength, inclination angle and rotational period. Our results are clear predictions of QED vacuum polarization effects in the near vicinity of magnetic stars which can be tested with the upcoming X-ray polarimetric observations.« less

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.

Strain transfer through film-substrate interface and surface curvature evolution during a tensile test

NASA Astrophysics Data System (ADS)

He, Wei; Han, Meidong; Goudeau, Philippe; Bourhis, Eric Le; Renault, Pierre-Olivier; Wang, Shibin; Li, Lin-an

2018-03-01

Uniaxial tensile tests on polyimide-supported thin metal films are performed to respectively study the macroscopic strain transfer through an interface and the surface curvature evolution. With a dual digital image correlation (DIC) system, the strains of the film and the substrate can be simultaneously measured in situ during the tensile test. For the true strains below 2% (far beyond the films' elastic limit), a complete longitudinal strain transfer is present irrespective of the film thickness, residual stresses and microstructure. By means of an optical surface profiler, the three-dimensional (3D) topography of film surface can be obtained during straining. As expected, the profile of the specimen center remains almost flat in the tensile direction. Nevertheless, a relatively significant curvature evolution (of the same order with the initial curvature induced by residual stresses) is observed along the transverse direction as a result of a Poisson's ratio mismatch between the film and the substrate. Furthermore, finite element method (FEM) has been performed to simulate the curvature evolution considering the geometric nonlinearity and the perfect strain transfer at the interface, which agrees well with the experimental results.

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

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

Evolution of Gas Cell Targets for Magnetized Liner Inertial Fusion Experiments at the Sandia National Laboratories PECOS Test Facility

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

Paguio, R. R.; Smith, G. E.; Taylor, J. L.

Z-Beamlet (ZBL) experiments conducted at the PECOS test facility at Sandia National Laboratories (SNL) investigated the nonlinear processes in laser plasma interaction (or laserplasma instabilities LPI) that complicate the deposition of laser energy by enhanced absorption, backscatter, filamentation and beam-spray that can occur in large-scale laser-heated gas cell targets. These targets and experiments were designed to provide better insight into the physics of the laser preheat stage of the Magnetized Liner Inertial Fusion (MagLIF) scheme being tested on the SNL Z-machine. The experiments aim to understand the tradeoffs between laser spot size, laser pulse shape, laser entrance hole (LEH) windowmore » thickness, and fuel density for laser preheat. Gas cell target design evolution and fabrication adaptations to accommodate the evolving experiment and scientific requirements are also described in this paper.« less

Evolution of Gas Cell Targets for Magnetized Liner Inertial Fusion Experiments at the Sandia National Laboratories PECOS Test Facility

DOE PAGES

Paguio, R. R.; Smith, G. E.; Taylor, J. L.; ...

2017-12-04

Z-Beamlet (ZBL) experiments conducted at the PECOS test facility at Sandia National Laboratories (SNL) investigated the nonlinear processes in laser plasma interaction (or laserplasma instabilities LPI) that complicate the deposition of laser energy by enhanced absorption, backscatter, filamentation and beam-spray that can occur in large-scale laser-heated gas cell targets. These targets and experiments were designed to provide better insight into the physics of the laser preheat stage of the Magnetized Liner Inertial Fusion (MagLIF) scheme being tested on the SNL Z-machine. The experiments aim to understand the tradeoffs between laser spot size, laser pulse shape, laser entrance hole (LEH) windowmore » thickness, and fuel density for laser preheat. Gas cell target design evolution and fabrication adaptations to accommodate the evolving experiment and scientific requirements are also described in this paper.« less

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

NARMAX model identification of a palm oil biodiesel engine using multi-objective optimization differential evolution

NASA Astrophysics Data System (ADS)

Mansor, Zakwan; Zakaria, Mohd Zakimi; Nor, Azuwir Mohd; Saad, Mohd Sazli; Ahmad, Robiah; Jamaluddin, Hishamuddin

2017-09-01

This paper presents the black-box modelling of palm oil biodiesel engine (POB) using multi-objective optimization differential evolution (MOODE) algorithm. Two objective functions are considered in the algorithm for optimization; minimizing the number of term of a model structure and minimizing the mean square error between actual and predicted outputs. The mathematical model used in this study to represent the POB system is nonlinear auto-regressive moving average with exogenous input (NARMAX) model. Finally, model validity tests are applied in order to validate the possible models that was obtained from MOODE algorithm and lead to select an optimal model.

Strongly nonlinear theory of rapid solidification near absolute stability

NASA Astrophysics Data System (ADS)

Kowal, Katarzyna N.; Altieri, Anthony L.; Davis, Stephen H.

2017-10-01

We investigate the nonlinear evolution of the morphological deformation of a solid-liquid interface of a binary melt under rapid solidification conditions near two absolute stability limits. The first of these involves the complete stabilization of the system to cellular instabilities as a result of large enough surface energy. We derive nonlinear evolution equations in several limits in this scenario and investigate the effect of interfacial disequilibrium on the nonlinear deformations that arise. In contrast to the morphological stability problem in equilibrium, in which only cellular instabilities appear and only one absolute stability boundary exists, in disequilibrium the system is prone to oscillatory instabilities and a second absolute stability boundary involving attachment kinetics arises. Large enough attachment kinetics stabilize the oscillatory instabilities. We derive a nonlinear evolution equation to describe the nonlinear development of the solid-liquid interface near this oscillatory absolute stability limit. We find that strong asymmetries develop with time. For uniform oscillations, the evolution equation for the interface reduces to the simple form f''+(βf')2+f =0 , where β is the disequilibrium parameter. Lastly, we investigate a distinguished limit near both absolute stability limits in which the system is prone to both cellular and oscillatory instabilities and derive a nonlinear evolution equation that captures the nonlinear deformations in this limit. Common to all these scenarios is the emergence of larger asymmetries in the resulting shapes of the solid-liquid interface with greater departures from equilibrium and larger morphological numbers. The disturbances additionally sharpen near the oscillatory absolute stability boundary, where the interface becomes deep-rooted. The oscillations are time-periodic only for small-enough initial amplitudes and their frequency depends on a single combination of physical parameters, including the morphological number, as well as the amplitude. The critical amplitude, at which solutions loose periodicity, depends on a single combination of parameters independent of the morphological number that indicate that non-periodic growth is most commonly present for moderate disequilibrium parameters. The spatial distribution of the interface develops deepening roots at late times. Similar spatial distributions are also seen in the limit in which both the cellular and oscillatory modes are close to absolute stability, and the roots deepen with larger departures from the two absolute stability boundaries.

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.

Toward a better understanding of nearshore meteotsunami evolution, and effective meteotsunami early-warning systems

NASA Astrophysics Data System (ADS)

Sheremet, A.; Li, C.; Shrira, V. I.

2017-12-01

We present high-resolution observations collected in 2008 on the Atcahfalaya shelf that capture the shoaling evolution of a meteotsunami (MT), including the disintegration into the train of solitons (solibore). One of the intriguing elements of this process is a spectacular 1.5-m solitary-wave (soliton), that precedes the arrival of the MT solibore by approximately 5 min, reaching the observation site propagating through a background of nearly-calm waters (20-cm height wind waves). Solitons, products of the MT disintegration process, are observed at all experiment sites, covering approx. 200 km shoreline. We interpret observations employing numerical simulations of a simplified hydrodynamic model based on the variable coefficient KdV equation. The analysis shows that observed wide-spread soliton presence and the soliton/solibore formation are the result of a complicated evolution process involving refraction, collision, and nonlinear interaction of multiple meteotsunami waves.Our results highlight the substantial lack of detail of the current picture of the nonlinear transformation of a MT from generation to its shoreline manifestation. A realistic reconstruction of MT evolution is at present almost impossible based on the current poor spatial and temporal resolution MT observations, overwhelmingly confined to the shoreline. Since the MTs tend to disintegrate into very short (down to 10s) pulses, even modern tidal gauges (1 min resolution) fail to capture essential features of its evolution. We also briefly discuss an ongoing field experiment that carries further the effort to collect high-resolution MT measurements, and that will investigate and test methodologies for early warning systems.

Time-evolution of quantum systems via a complex nonlinear Riccati equation. I. Conservative systems with time-independent Hamiltonian

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

Cruz, Hans, E-mail: hans@ciencias.unam.mx; Schuch, Dieter; Castaños, Octavio, E-mail: ocasta@nucleares.unam.mx

2015-09-15

The sensitivity of the evolution of quantum uncertainties to the choice of the initial conditions is shown via a complex nonlinear Riccati equation leading to a reformulation of quantum dynamics. This sensitivity is demonstrated for systems with exact analytic solutions with the form of Gaussian wave packets. In particular, one-dimensional conservative systems with at most quadratic Hamiltonians are studied.

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.

In-process, non-destructive multimodal dynamic testing of high-speed composite rotors

NASA Astrophysics Data System (ADS)

Kuschmierz, Robert; Filippatos, Angelos; Langkamp, Albert; Hufenbach, Werner; Czarske, Jürgern W.; Fischer, Andreas

2014-03-01

Fibre reinforced plastic (FRP) rotors are lightweight and offer great perspectives in high-speed applications such as turbo machinery. Currently, novel rotor structures and materials are investigated for the purpose of increasing machine efficiency, lifetime and loading limits. Due to complex rotor structures, high anisotropy and non-linear behavior of FRP under dynamic loads, an in-process measurement system is necessary to monitor and to investigate the evolution of damages under real operation conditions. A non-invasive, optical laser Doppler distance sensor measurement system is applied to determine the biaxial deformation of a bladed FRP rotor with micron uncertainty as well as the tangential blade vibrations at surface speeds above 300 m/s. The laser Doppler distance sensor is applicable under vacuum conditions. Measurements at varying loading conditions are used to determine elastic and plastic deformations. Furthermore they allow to determine hysteresis, fatigue, Eigenfrequency shifts and loading limits. The deformation measurements show a highly anisotropic and nonlinear behavior and offer a deeper understanding of the damage evolution in FRP rotors. The experimental results are used to validate and to calibrate a simulation model of the deformation. The simulation combines finite element analysis and a damage mechanics model. The combination of simulation and measurement system enables the monitoring and prediction of damage evolutions of FRP rotors in process.

Hyperboloidal evolution of test fields in three spatial dimensions

NASA Astrophysics Data System (ADS)

Zenginoǧlu, Anıl; Kidder, Lawrence E.

2010-06-01

We present the numerical implementation of a clean solution to the outer boundary and radiation extraction problems within the 3+1 formalism for hyperbolic partial differential equations on a given background. Our approach is based on compactification at null infinity in hyperboloidal scri fixing coordinates. We report numerical tests for the particular example of a scalar wave equation on Minkowski and Schwarzschild backgrounds. We address issues related to the implementation of the hyperboloidal approach for the Einstein equations, such as nonlinear source functions, matching, and evaluation of formally singular terms at null infinity.

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.

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.

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.

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.

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.

Evaluation of nonlinear impact resonance spectroscopy method for detecting delayed ettringite formation

NASA Astrophysics Data System (ADS)

Rashidi, M. M. N.; Paul, A.; Kim, J.-Y.; Jacobs, L. J.; Kurtis, K. E.

2015-03-01

The use of the Nonlinear Impact Resonance Acoustic Spectroscopy (NIRAS) method to monitor the evolution of damage due to delayed ettringite formation (DEF) is examined. In practice, the temperature of concrete during casting of precast concrete members or massive concrete structures may reach higher than 70°C which can provide suitable conditions for damage to occur due to DEF, particularly in concrete which is subsequently exposed to wet environments. While expansion - often in excess of 1% - is characteristic of DEF, the evolution of damage begins with microcracking. Unfortunately, there is no standard to test the susceptibility of materials or material combinations to DEF. On the other hand, NIRAS shows great sensitivity to the detection of microcracks and has been successfully applied to concrete to detect thermal and alkali silica reaction in concrete. In this preliminary research, the NIRAS method is used to discriminate among mortar samples which are relatively undamaged and those in the early stages of DEF. The results show that NIRAS could be a reliable and robust method in the detection of microcracks due to DEF.

Performance Assessment of Model-Based Optimal Feedforward and Feedback Current Profile Control in NSTX-U using the TRANSP Code

NASA Astrophysics Data System (ADS)

Ilhan, Z.; Wehner, W. P.; Schuster, E.; Boyer, M. D.; Gates, D. A.; Gerhardt, S.; Menard, J.

2015-11-01

Active control of the toroidal current density profile is crucial to achieve and maintain high-performance, MHD-stable plasma operation in NSTX-U. A first-principles-driven, control-oriented model describing the temporal evolution of the current profile has been proposed earlier by combining the magnetic diffusion equation with empirical correlations obtained at NSTX-U for the electron density, electron temperature, and non-inductive current drives. A feedforward + feedback control scheme for the requlation of the current profile is constructed by embedding the proposed nonlinear, physics-based model into the control design process. Firstly, nonlinear optimization techniques are used to design feedforward actuator trajectories that steer the plasma to a desired operating state with the objective of supporting the traditional trial-and-error experimental process of advanced scenario planning. Secondly, a feedback control algorithm to track a desired current profile evolution is developed with the goal of adding robustness to the overall control scheme. The effectiveness of the combined feedforward + feedback control algorithm for current profile regulation is tested in predictive simulations carried out in TRANSP. Supported by PPPL.

The impact law of confining pressure and plastic parameter on Dilatancy of rock

NASA Astrophysics Data System (ADS)

Wang, Bin; Zhang, Zhenjie; Zhu, Jiebing

2017-08-01

Based on cyclic loading-unloading triaxle test of marble, the double parameter dilation angle model is established considering confining pressure effect and plastic parameter. Research shows that not only the strength but also the militancy behavior is highly depended on its confining pressure and plastic parameter during process of failure. Dilation angle evolution law shows obvious nonlinear characteristic almost with a rapid increase to the peak and then decrease gradually with plastic increasing, and the peak dilation angle value is inversely proportional with confining pressure. The proposed double parameter nonlinear dilation angle model can be used to well describe the Dilatancy of rock, which helps to understand the failure mechanism of surrounding rock mass and predict the range of plastic zone.

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 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

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.

Dietary specialization is linked to reduced species durations in North American fossil canids

NASA Astrophysics Data System (ADS)

Balisi, Mairin; Casey, Corinna; Van Valkenburgh, Blaire

2018-04-01

How traits influence species persistence is a fundamental question in ecology, evolution and palaeontology. We test the relationship between dietary traits and both species duration and locality coverage over 40 million years in North American canids, a clade with considerable ecomorphological disparity and a dense fossil record. Because ecomorphological generalization-broad resource use-may enable species to withstand disturbance, we predicted that canids of average size and mesocarnivory would exhibit longer durations and wider distributions than specialized larger or smaller species. Second, because locality coverage might reflect dispersal ability and/or survivability in a range of habitats, we predicted that high coverage would correspond with longer durations. We find a nonlinear relationship between species duration and degree of carnivory: species at either end of the carnivory spectrum tend to have shorter durations than mesocarnivores. Locality coverage shows no relationship with size, diet or duration. To test whether generalization (medium size, mesocarnivory) corresponds to an adaptive optimum, we fit trait evolution models to previously generated canid phylogenies. Our analyses identify no single optimum in size or diet. Instead, the primary model of size evolution is a classic Cope's Rule increase over time, while dietary evolution does not conform to a single model.

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.

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

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

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.

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).

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).

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.

A Fully Associative, Non-Linear Kinematic, Unified Viscoplastic Model for Titanium Based Matrices

NASA Technical Reports Server (NTRS)

Arnold, S. M.; Saleeb, A. F.; Castelli, M. G.

1994-01-01

Specific forms for both the Gibb's and complementary dissipation potentials are chosen such that a complete (i.e., fully associative) potential based multiaxial unified viscoplastic model is obtained. This model possesses one tensorial internal state variable that is associated with dislocation substructure, with an evolutionary law that has nonlinear kinematic hardening and both thermal and strain induced recovery mechanisms. A unique aspect of the present model is the inclusion of non-linear hardening through the use of a compliance operator, derived from the Gibb's potential, in the evolution law for the back stress. This non-linear tensorial operator is significant in that it allows both the flow and evolutionary laws to be fully associative (and therefore easily integrated) and greatly influences the multiaxial response under non-proportional loading paths. In addition to this nonlinear compliance operator, a new consistent, potential preserving, internal strain unloading criterion has been introduced to prevent abnormalities in the predicted stress-strain curves, which are present with nonlinear hardening formulations, during unloading and reversed loading of the external variables. Specification of an experimental program for the complete determination of the material functions and parameters for characterizing a metallic matrix, e.g., TIMETAL 21S, is given. The experiments utilized are tensile, creep, and step creep tests. Finally, a comparison of this model and a commonly used Bodner-Partom model is made on the basis of predictive accuracy and numerical efficiency.

The gravitational wave strain in the characteristic formalism of numerical relativity

NASA Astrophysics Data System (ADS)

Bishop, Nigel T.; Reisswig, Christian

2014-01-01

The extraction of the gravitational wave signal, within the context of a characteristic numerical evolution is revisited. A formula for the gravitational wave strain is developed and tested, and is made publicly available as part of the PITT code within the Einstein Toolkit. Using the new strain formula, we show that artificial non-linear drifts inherent in time integrated waveforms can be reduced for the case of a binary black hole merger configuration. For the test case of a rapidly spinning stellar core collapse model, however, we find that the drift must have different roots.

Shape optimization of shear fracture specimen considering plastic anisotropy

NASA Astrophysics Data System (ADS)

Zhang, S.; Yoon, J. W.; Lee, S.; Lou, Y.

2017-10-01

It is important to fabricate fracture specimens with minimum variation of triaxiality in order to characterize the failure behaviors experimentally. Fracture in ductile materials is usually calibrated by uniaxial tensile, shear and plane strain tests. However, it is often observed that triaxiality for shear specimen changes severely during shear fracture test. The nonlinearity of triaxiality is most critical for shear test. In this study, a simple in-plane shear specimen is optimized by minimizing the variation of stress triaxiality in the shear zone. In the optimization, the Hill48 and Yld2000-2d criteria are employed to model the anisotropic plastic deformation of an aluminum alloy of 6k21. The evolution of the stress triaxiality of the optimized shear specimen is compared with that of the initial design of the shear specimen. The comparison reveals that the stress triaxiality changes much less for the optimized shear specimen than the evolution of the stress triaxiality with the original design of the shear specimen.

Infectious diseases in space and time: noise and nonlinearity in epidemiological dynamics

NASA Astrophysics Data System (ADS)

Grenfell, Bryan

2005-03-01

I illustrate the impact of noise and nonlinearity on the spatio-temporal dynamics and evolution of epidemics using mathematical models and analyses of detailed epidemiological data from childhood infections, such as measles.

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.

Homogeneous quantum electrodynamic turbulence

NASA Technical Reports Server (NTRS)

Shebalin, John V.

1992-01-01

The electromagnetic field equations and Dirac equations for oppositely charged wave functions are numerically time-integrated using a spatial Fourier method. The numerical approach used, a spectral transform technique, is based on a continuum representation of physical space. The coupled classical field equations contain a dimensionless parameter which sets the strength of the nonlinear interaction (as the parameter increases, interaction volume decreases). For a parameter value of unity, highly nonlinear behavior in the time-evolution of an individual wave function, analogous to ideal fluid turbulence, is observed. In the truncated Fourier representation which is numerically implemented here, the quantum turbulence is homogeneous but anisotropic and manifests itself in the nonlinear evolution of equilibrium modal spatial spectra for the probability density of each particle and also for the electromagnetic energy density. The results show that nonlinearly interacting fermionic wave functions quickly approach a multi-mode, dynamic equilibrium state, and that this state can be determined by numerical means.

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.

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

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

Reduced nonlinear prognostic model construction from high-dimensional data

NASA Astrophysics Data System (ADS)

Gavrilov, Andrey; Mukhin, Dmitry; Loskutov, Evgeny; Feigin, Alexander

2017-04-01

Construction of a data-driven model of evolution operator using universal approximating functions can only be statistically justified when the dimension of its phase space is small enough, especially in the case of short time series. At the same time in many applications real-measured data is high-dimensional, e.g. it is space-distributed and multivariate in climate science. Therefore it is necessary to use efficient dimensionality reduction methods which are also able to capture key dynamical properties of the system from observed data. To address this problem we present a Bayesian approach to an evolution operator construction which incorporates two key reduction steps. First, the data is decomposed into a set of certain empirical modes, such as standard empirical orthogonal functions or recently suggested nonlinear dynamical modes (NDMs) [1], and the reduced space of corresponding principal components (PCs) is obtained. Then, the model of evolution operator for PCs is constructed which maps a number of states in the past to the current state. The second step is to reduce this time-extended space in the past using appropriate decomposition methods. Such a reduction allows us to capture only the most significant spatio-temporal couplings. The functional form of the evolution operator includes separately linear, nonlinear (based on artificial neural networks) and stochastic terms. Explicit separation of the linear term from the nonlinear one allows us to more easily interpret degree of nonlinearity as well as to deal better with smooth PCs which can naturally occur in the decompositions like NDM, as they provide a time scale separation. Results of application of the proposed method to climate data are demonstrated and discussed. 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/srep15510

A new general circulation model of Jupiter's atmosphere based on the UKMO Unified Model: Three-dimensional evolution of isolated vortices and zonal jets in mid-latitudes

NASA Astrophysics Data System (ADS)

Yamazaki, Y. H.; Skeet, D. R.; Read, P. L.

2004-04-01

We have been developing a new three-dimensional general circulation model for the stratosphere and troposphere of Jupiter based on the dynamical core of a portable version of the Unified Model of the UK Meteorological Office. Being one of the leading terrestrial GCMs, employed for operational weather forecasting and climate research, the Unified Model has been thoroughly tested and performance tuned for both vector and parallel computers. It is formulated as a generalized form of the standard primitive equations to handle a thick atmosphere, using a scaled pressure as the vertical coordinate. It is able to accurately simulate the dynamics of a three-dimensional fully compressible atmosphere on the whole or a part of a spherical shell at high spatial resolution in all three directions. Using the current version of the GCM, we examine the characteristics of the Jovian winds in idealized configurations based on the observed vertical structure of temperature. Our initial focus is on the evolution of isolated eddies in the mid-latitudes. Following a brief theoretical investigation of the vertical structure of the atmosphere, limited-area cyclic channel domains are used to numerically investigate the nonlinear evolution of the mid-latitude winds. First, the evolution of deep and shallow cyclones and anticyclones are tested in the atmosphere at rest to identify a preferred horizontal and vertical structure of the vortices. Then, the dependency of the migration characteristics of the vortices are investigated against modelling parameters to find that it is most sensitive to the horizontal diffusion. We also examine the hydrodynamical stability of observed subtropical jets in both northern and southern hemispheres in the three-dimensional nonlinear model as initial value problems. In both cases, it was found that the prominent jets are unstable at various scales and that vorteces of various sizes are generated including those comparable to the White Ovals and the Great Red Spot.

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.

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.

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

Lie symmetry analysis, explicit solutions and conservation laws for the space-time fractional nonlinear evolution equations

NASA Astrophysics Data System (ADS)

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

2018-04-01

This paper studies the symmetry analysis, explicit solutions, convergence analysis, and conservation laws (Cls) for two different space-time fractional nonlinear evolution equations with Riemann-Liouville (RL) derivative. The governing equations are reduced to nonlinear ordinary differential equation (ODE) of fractional order using their Lie point symmetries. In the reduced equations, the derivative is in Erdelyi-Kober (EK) sense, power series technique is applied to derive an explicit solutions for the reduced fractional ODEs. The convergence of the obtained power series solutions is also presented. Moreover, the new conservation theorem and the generalization of the Noether operators are developed to construct the nonlocal Cls for the equations . Some interesting figures for the obtained explicit solutions are presented.

Dynamic weight evolution network with preferential attachment

NASA Astrophysics Data System (ADS)

Dai, Meifeng; Xie, Qi; Li, Lei

2014-12-01

A dynamic weight evolution network with preferential attachment is introduced. The network includes two significant characteristics. (i) Topological growth: triggered by newly added node with M links at each time step, each new edge carries an initial weight growing nonlinearly with time. (ii) Weight dynamics: the weight between two existing nodes experiences increasing or decreasing in a nonlinear way. By using continuum theory and mean-field method, we study the strength, the degree, the weight and their distributions. We find that the distributions exhibit a power-law feature. In particular, the relationship between the degree and the strength is nonlinear, and the power-law exponents of the three are the same. All the theoretical predictions are successfully contrasted with numerical simulations.

Nonlinear stability of oscillatory core-annular flow: A generalized Kuramoto-Sivashinsky equation with time periodic coefficients

NASA Technical Reports Server (NTRS)

Coward, Adrian V.; Papageorgiou, Demetrios T.; Smyrlis, Yiorgos S.

1994-01-01

In this paper the nonlinear stability of two-phase core-annular flow in a pipe is examined when the acting pressure gradient is modulated by time harmonic oscillations and viscosity stratification and interfacial tension is present. An exact solution of the Navier-Stokes equations is used as the background state to develop an asymptotic theory valid for thin annular layers, which leads to a novel nonlinear evolution describing the spatio-temporal evolution of the interface. The evolution equation is an extension of the equation found for constant pressure gradients and generalizes the Kuramoto-Sivashinsky equation with dispersive effects found by Papageorgiou, Maldarelli & Rumschitzki, Phys. Fluids A 2(3), 1990, pp. 340-352, to a similar system with time periodic coefficients. The distinct regimes of slow and moderate flow are considered and the corresponding evolution is derived. Certain solutions are described analytically in the neighborhood of the first bifurcation point by use of multiple scales asymptotics. Extensive numerical experiments, using dynamical systems ideas, are carried out in order to evaluate the effect of the oscillatory pressure gradient on the solutions in the presence of a constant pressure gradient.

Time-dependent spectral renormalization method

NASA Astrophysics Data System (ADS)

Cole, Justin T.; Musslimani, Ziad H.

2017-11-01

The spectral renormalization method was introduced by Ablowitz and Musslimani (2005) as an effective way to numerically compute (time-independent) bound states for certain nonlinear boundary value problems. In this paper, we extend those ideas to the time domain and introduce a time-dependent spectral renormalization method as a numerical means to simulate linear and nonlinear evolution equations. The essence of the method is to convert the underlying evolution equation from its partial or ordinary differential form (using Duhamel's principle) into an integral equation. The solution sought is then viewed as a fixed point in both space and time. The resulting integral equation is then numerically solved using a simple renormalized fixed-point iteration method. Convergence is achieved by introducing a time-dependent renormalization factor which is numerically computed from the physical properties of the governing evolution equation. The proposed method has the ability to incorporate physics into the simulations in the form of conservation laws or dissipation rates. This novel scheme is implemented on benchmark evolution equations: the classical nonlinear Schrödinger (NLS), integrable PT symmetric nonlocal NLS and the viscous Burgers' equations, each of which being a prototypical example of a conservative and dissipative dynamical system. Numerical implementation and algorithm performance are also discussed.

Fatigue Life Prediction of Metallic Materials Based on the Combined Nonlinear Ultrasonic Parameter

NASA Astrophysics Data System (ADS)

Zhang, Yuhua; Li, Xinxin; Wu, Zhenyong; Huang, Zhenfeng; Mao, Hanling

2017-08-01

The fatigue life prediction of metallic materials is always a tough problem that needs to be solved in the mechanical engineering field because it is very important for the secure service of mechanical components. In this paper, a combined nonlinear ultrasonic parameter based on the collinear wave mixing technique is applied for fatigue life prediction of a metallic material. Sweep experiments are first conducted to explore the influence of driving frequency on the interaction of two driving signals and the fatigue damage of specimens, and the amplitudes of sidebands at the difference frequency and sum frequency are tracked when the driving frequency changes. Then, collinear wave mixing tests are carried out on a pair of cylindrically notched specimens with different fatigue damage to explore the relationship between the fatigue damage and the relative nonlinear parameters. The experimental results show when the fatigue degree is below 65% the relative nonlinear parameter increases quickly, and the growth rate is approximately 130%. If the fatigue degree is above 65%, the increase in the relative nonlinear parameter is slow, which has a close relationship with the microstructure evolution of specimens. A combined nonlinear ultrasonic parameter is proposed to highlight the relationship of the relative nonlinear parameter and fatigue degree of specimens; the fatigue life prediction model is built based on the relationship, and the prediction error is below 3%, which is below the prediction error based on the relative nonlinear parameters at the difference and sum frequencies. Therefore, the combined nonlinear ultrasonic parameter using the collinear wave mixing method can effectively estimate the fatigue degree of specimens, which provides a fast and convenient method for fatigue life prediction.

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.

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.

Proton structure functions at small x

DOE PAGES

Hentschinski, Martin

2015-11-03

Proton structure functions are measured in electron-proton collision through inelastic scattering of virtual photons with virtuality Q on protons; x denotes the momentum fraction carried by the struck parton. Proton structure functions are currently described with excellent accuracy in terms of scale dependent parton distribution functions, defined in terms of collinear factorization and DGLAP evolution in Q. With decreasing x however, parton densities increase and are ultimately expected to saturate. In this regime DGLAP evolution will finally break down and non-linear evolution equations w.r.t x are expected to take over. In the first part of the talk we present recentmore » result on an implementation of physical DGLAP evolution. Unlike the conventional description in terms of parton distribution functions, the former describes directly the Q dependence of the measured structure functions. It is therefore physical insensitive to factorization scheme and scale ambiguities. It therefore provides a more stringent test of DGLAP evolution and eases the manifestation of (non-linear) small x effects. It however requires a precise measurement of both structure functions F 2 and F L, which will be only possible at future facilities, such as an Electron Ion Collider. In the second part we present a recent analysis of the small x region of the combined HERA data on the structure function F 2. We demonstrate that (linear) next-to-leading order BFKL evolution describes the effective Pomeron intercept, determined from the combined HERA data, once a resummation of collinear enhanced terms is included and the renormalization scale is fixed using the BLM optimal scale setting procedure. We also provide a detailed description of the Q and x dependence of the full structure functions F 2 in the small x region, as measured at HERA. As a result, predictions for the structure function F L are found to be in agreement with the existing HERA data.« less

Exploring equivalence domain in nonlinear inverse problems using Covariance Matrix Adaption Evolution Strategy (CMAES) and random sampling

NASA Astrophysics Data System (ADS)

Grayver, Alexander V.; Kuvshinov, Alexey V.

2016-05-01

This paper presents a methodology to sample equivalence domain (ED) in nonlinear partial differential equation (PDE)-constrained inverse problems. For this purpose, we first applied state-of-the-art stochastic optimization algorithm called Covariance Matrix Adaptation Evolution Strategy (CMAES) to identify low-misfit regions of the model space. These regions were then randomly sampled to create an ensemble of equivalent models and quantify uncertainty. CMAES is aimed at exploring model space globally and is robust on very ill-conditioned problems. We show that the number of iterations required to converge grows at a moderate rate with respect to number of unknowns and the algorithm is embarrassingly parallel. We formulated the problem by using the generalized Gaussian distribution. This enabled us to seamlessly use arbitrary norms for residual and regularization terms. We show that various regularization norms facilitate studying different classes of equivalent solutions. We further show how performance of the standard Metropolis-Hastings Markov chain Monte Carlo algorithm can be substantially improved by using information CMAES provides. This methodology was tested by using individual and joint inversions of magneotelluric, controlled-source electromagnetic (EM) and global EM induction data.

Wear-caused deflection evolution of a slide rail, considering linear and non-linear wear models

NASA Astrophysics Data System (ADS)

Kim, Dongwook; Quagliato, Luca; Park, Donghwi; Murugesan, Mohanraj; Kim, Naksoo; Hong, Seokmoo

2017-05-01

The research presented in this paper details an experimental-numerical approach for the quantitative correlation between wear and end-point deflection in a slide rail. Focusing the attention on slide rail utilized in white-goods applications, the aim is to evaluate the number of cycles the slide rail can operate, under different load conditions, before it should be replaced due to unacceptable end-point deflection. In this paper, two formulations are utilized to describe the wear: Archard model for the linear wear and Lemaitre damage model for the nonlinear wear. The linear wear gradually reduces the surface of the slide rail whereas the nonlinear one accounts for the surface element deletion (i.e. due to pitting). To determine the constants to use in the wear models, simple tension test and sliding wear test, by utilizing a designed and developed experiment machine, have been carried out. A full slide rail model simulation has been implemented in ABAQUS including both linear and non-linear wear models and the results have been compared with those of the real rails under different load condition, provided by the rail manufacturer. The comparison between numerically estimated and real rail results proved the reliability of the developed numerical model, limiting the error in a ±10% range. The proposed approach allows predicting the displacement vs cycle curves, parametrized for different loads and, based on a chosen failure criterion, to predict the lifetime of the rail.

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.

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.

Nonlinear wave vacillation in the atmosphere

NASA Technical Reports Server (NTRS)

Antar, Basil N.

1987-01-01

The problem of vacillation in a baroclinically unstable flow field is studied through the time evolution of a single nonlinearly unstable wave. To this end a computer code is being developed to solve numerically for the time evolution of the amplitude of such a wave. The final working code will be the end product resulting from the development of a heirarchy of codes with increasing complexity. The first code in this series was completed and is undergoing several diagnostic analyses to verify its validity. The development of this code is detailed.

Dietary specialization is linked to reduced species durations in North American fossil canids

PubMed Central

Casey, Corinna; Van Valkenburgh, Blaire

2018-01-01

How traits influence species persistence is a fundamental question in ecology, evolution and palaeontology. We test the relationship between dietary traits and both species duration and locality coverage over 40 million years in North American canids, a clade with considerable ecomorphological disparity and a dense fossil record. Because ecomorphological generalization—broad resource use—may enable species to withstand disturbance, we predicted that canids of average size and mesocarnivory would exhibit longer durations and wider distributions than specialized larger or smaller species. Second, because locality coverage might reflect dispersal ability and/or survivability in a range of habitats, we predicted that high coverage would correspond with longer durations. We find a nonlinear relationship between species duration and degree of carnivory: species at either end of the carnivory spectrum tend to have shorter durations than mesocarnivores. Locality coverage shows no relationship with size, diet or duration. To test whether generalization (medium size, mesocarnivory) corresponds to an adaptive optimum, we fit trait evolution models to previously generated canid phylogenies. Our analyses identify no single optimum in size or diet. Instead, the primary model of size evolution is a classic Cope's Rule increase over time, while dietary evolution does not conform to a single model. PMID:29765649

A fully associative, nonisothermal, nonlinear kinematic, unified viscoplastic model for titanium alloys

NASA Astrophysics Data System (ADS)

Arnold, S. M.; Saleeb, A. F.; Castelli, M. G.

1995-05-01

Specific forms for both the Gibb's and complementary dissipation potentials are chosen such that a complete (i.e., fully associative) potential base multiaxial, nonisothermal unified viscoplastic model is obtained. This model possesses one tensorial internal state variable (that is, associated with dislocation substructure) and an evolutionary law that has nonlinear kinematic hardening and both thermal and strain induced recovery mechanisms. A unique aspect of the present model is the inclusion of nonlinear hardening through the use of a compliance operator, derived from the Gibb's potential, in the evolution law for the back stress. This nonlinear tensorial operator is significant in that it allows both the flow and evolutionary laws to be fully associative (and therefore easily integrated), greatly influences the multiaxial response under non-proportional loading paths, and in the case of nonisothermal histories, introduces an instantaneous thermal softening mechanism proportional to the rate of change in temperature. In addition to this nonlinear compliance operator, a new consistent, potential preserving, internal strain unloading criterion has been introduced to prevent abnormalities in the predicted stress-strain curves, which are present with nonlinear hardening formulations, during unloading and reversed loading of the external variables. The specific model proposed is characterized for a representative titanium alloy commonly used as the matrix material in SiC fiber reinforced composites, i.e., TIMETAL 21S. Verification of the proposed model is shown using 'specialized' non-standard isothermal and thermomechanical deformation tests.

A fully associative, nonisothermal, nonlinear kinematic, unified viscoplastic model for titanium alloys

NASA Technical Reports Server (NTRS)

Arnold, S. M.; Saleeb, A. F.; Castelli, M. G.

1995-01-01

Specific forms for both the Gibb's and complementary dissipation potentials are chosen such that a complete (i.e., fully associative) potential base multiaxial, nonisothermal unified viscoplastic model is obtained. This model possesses one tensorial internal state variable (that is, associated with dislocation substructure) and an evolutionary law that has nonlinear kinematic hardening and both thermal and strain induced recovery mechanisms. A unique aspect of the present model is the inclusion of nonlinear hardening through the use of a compliance operator, derived from the Gibb's potential, in the evolution law for the back stress. This nonlinear tensorial operator is significant in that it allows both the flow and evolutionary laws to be fully associative (and therefore easily integrated), greatly influences the multiaxial response under non-proportional loading paths, and in the case of nonisothermal histories, introduces an instantaneous thermal softening mechanism proportional to the rate of change in temperature. In addition to this nonlinear compliance operator, a new consistent, potential preserving, internal strain unloading criterion has been introduced to prevent abnormalities in the predicted stress-strain curves, which are present with nonlinear hardening formulations, during unloading and reversed loading of the external variables. The specific model proposed is characterized for a representative titanium alloy commonly used as the matrix material in SiC fiber reinforced composites, i.e., TIMETAL 21S. Verification of the proposed model is shown using 'specialized' non-standard isothermal and thermomechanical deformation tests.

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.

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.

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.

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.

Experimental tests of coherence and entanglement conservation under unitary evolutions

NASA Astrophysics Data System (ADS)

Černoch, Antonín; Bartkiewicz, Karol; Lemr, Karel; Soubusta, Jan

2018-04-01

We experimentally demonstrate the migration of coherence between composite quantum systems and their subsystems. The quantum systems are implemented using polarization states of photons in two experimental setups. The first setup is based on a linear optical controlled-phase quantum gate and the second scheme utilizes effects of nonlinear optics. Our experiment allows one to verify the relation between correlations of the subsystems and the coherence of the composite system, which was given in terms of a conservation law for maximal accessible coherence by Svozilík et al. [J. Svozilík et al., Phys. Rev. Lett. 115, 220501 (2015), 10.1103/PhysRevLett.115.220501]. We observe that the maximal accessible coherence is conserved for the implemented class of global evolutions of the composite system.

Time-dependent behavior of passive skeletal muscle

NASA Astrophysics Data System (ADS)

Ahamed, T.; Rubin, M. B.; Trimmer, B. A.; Dorfmann, L.

2016-03-01

An isotropic three-dimensional nonlinear viscoelastic model is developed to simulate the time-dependent behavior of passive skeletal muscle. The development of the model is stimulated by experimental data that characterize the response during simple uniaxial stress cyclic loading and unloading. Of particular interest is the rate-dependent response, the recovery of muscle properties from the preconditioned to the unconditioned state and stress relaxation at constant stretch during loading and unloading. The model considers the material to be a composite of a nonlinear hyperelastic component in parallel with a nonlinear dissipative component. The strain energy and the corresponding stress measures are separated additively into hyperelastic and dissipative parts. In contrast to standard nonlinear inelastic models, here the dissipative component is modeled using an evolution equation that combines rate-independent and rate-dependent responses smoothly with no finite elastic range. Large deformation evolution equations for the distortional deformations in the elastic and in the dissipative component are presented. A robust, strongly objective numerical integration algorithm is used to model rate-dependent and rate-independent inelastic responses. The constitutive formulation is specialized to simulate the experimental data. The nonlinear viscoelastic model accurately represents the time-dependent passive response of skeletal muscle.

Quantifying the evolution of flow boiling bubbles by statistical testing and image analysis: toward a general model.

PubMed

Xiao, Qingtai; Xu, Jianxin; Wang, Hua

2016-08-16

A new index, the estimate of the error variance, which can be used to quantify the evolution of the flow patterns when multiphase components or tracers are difficultly distinguishable, was proposed. The homogeneity degree of the luminance space distribution behind the viewing windows in the direct contact boiling heat transfer process was explored. With image analysis and a linear statistical model, the F-test of the statistical analysis was used to test whether the light was uniform, and a non-linear method was used to determine the direction and position of a fixed source light. The experimental results showed that the inflection point of the new index was approximately equal to the mixing time. The new index has been popularized and applied to a multiphase macro mixing process by top blowing in a stirred tank. Moreover, a general quantifying model was introduced for demonstrating the relationship between the flow patterns of the bubble swarms and heat transfer. The results can be applied to investigate other mixing processes that are very difficult to recognize the target.

Modeling of yield surface evolution in uniaxial and biaxial loading conditions using a prestrained large scale specimen

NASA Astrophysics Data System (ADS)

Zaman, Shakil Bin; Barlat, Frédéric; Kim, Jin Hwan

2018-05-01

Large-scale advanced high strength steel (AHSS) sheet specimens were deformed in uniaxial tension, using a novel grip system mounted on a MTS universal tension machine. After pre-strain, they were used as a pre-strained material to examine the anisotropic response in the biaxial tension tests with various load ratios, and orthogonal tension tests at 45° and 90° from the pre-strain axis. The flow curve and the instantaneous r-value of the pre-strained steel in each of the aforementioned uniaxial testing conditions were also measured and compared with those of the undeformed steel. Furthermore, an exhaustive analysis of the yield surface was also conducted and the results, prior and post-prestrain were represented and compared. The homogeneous anisotropic hardening (HAH) model [1] was employed to predict the behavior of the pre-strained material. It was found that the HAH-predicted flow curves after non-linear strain path change and the yield loci after uniaxial pre-strain were in good agreement with the experiments, while the r-value evolution after strain path change was qualitatively well predicted.

Quantifying the evolution of flow boiling bubbles by statistical testing and image analysis: toward a general model

PubMed Central

Xiao, Qingtai; Xu, Jianxin; Wang, Hua

2016-01-01

A new index, the estimate of the error variance, which can be used to quantify the evolution of the flow patterns when multiphase components or tracers are difficultly distinguishable, was proposed. The homogeneity degree of the luminance space distribution behind the viewing windows in the direct contact boiling heat transfer process was explored. With image analysis and a linear statistical model, the F-test of the statistical analysis was used to test whether the light was uniform, and a non-linear method was used to determine the direction and position of a fixed source light. The experimental results showed that the inflection point of the new index was approximately equal to the mixing time. The new index has been popularized and applied to a multiphase macro mixing process by top blowing in a stirred tank. Moreover, a general quantifying model was introduced for demonstrating the relationship between the flow patterns of the bubble swarms and heat transfer. The results can be applied to investigate other mixing processes that are very difficult to recognize the target. PMID:27527065

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

Sexual selection and the evolution of secondary sexual traits: sex comb evolution in Drosophila.

PubMed

Snook, Rhonda R; Gidaszewski, Nelly A; Chapman, Tracey; Simmons, Leigh W

2013-04-01

Sexual selection can drive rapid evolutionary change in reproductive behaviour, morphology and physiology. This often leads to the evolution of sexual dimorphism, and continued exaggerated expression of dimorphic sexual characteristics, although a variety of other alternative selection scenarios exist. Here, we examined the evolutionary significance of a rapidly evolving, sexually dimorphic trait, sex comb tooth number, in two Drosophila species. The presence of the sex comb in both D. melanogaster and D. pseudoobscura is known to be positively related to mating success, although little is yet known about the sexually selected benefits of sex comb structure. In this study, we used experimental evolution to test the idea that enhancing or eliminating sexual selection would lead to variation in sex comb tooth number. However, the results showed no effect of either enforced monogamy or elevated promiscuity on this trait. We discuss several hypotheses to explain the lack of divergence, focussing on sexually antagonistic coevolution, stabilizing selection via species recognition and nonlinear selection. We discuss how these are important, but relatively ignored, alternatives in understanding the evolution of rapidly evolving sexually dimorphic traits. © 2013 The Authors. Journal of Evolutionary Biology © 2013 European Society For Evolutionary Biology.

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.

New methods of testing nonlinear hypothesis using iterative NLLS estimator

NASA Astrophysics Data System (ADS)

Mahaboob, B.; Venkateswarlu, B.; Mokeshrayalu, G.; Balasiddamuni, P.

2017-11-01

This research paper discusses the method of testing nonlinear hypothesis using iterative Nonlinear Least Squares (NLLS) estimator. Takeshi Amemiya [1] explained this method. However in the present research paper, a modified Wald test statistic due to Engle, Robert [6] is proposed to test the nonlinear hypothesis using iterative NLLS estimator. An alternative method for testing nonlinear hypothesis using iterative NLLS estimator based on nonlinear hypothesis using iterative NLLS estimator based on nonlinear studentized residuals has been proposed. In this research article an innovative method of testing nonlinear hypothesis using iterative restricted NLLS estimator is derived. Pesaran and Deaton [10] explained the methods of testing nonlinear hypothesis. This paper uses asymptotic properties of nonlinear least squares estimator proposed by Jenrich [8]. The main purpose of this paper is to provide very innovative methods of testing nonlinear hypothesis using iterative NLLS estimator, iterative NLLS estimator based on nonlinear studentized residuals and iterative restricted NLLS estimator. Eakambaram et al. [12] discussed least absolute deviation estimations versus nonlinear regression model with heteroscedastic errors and also they studied the problem of heteroscedasticity with reference to nonlinear regression models with suitable illustration. William Grene [13] examined the interaction effect in nonlinear models disused by Ai and Norton [14] and suggested ways to examine the effects that do not involve statistical testing. Peter [15] provided guidelines for identifying composite hypothesis and addressing the probability of false rejection for multiple hypotheses.

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.

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.

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.

Micromechanical Fatigue Visco-Damage Model for Short Glass Fiber Reinforced Polyamide-66

NASA Astrophysics Data System (ADS)

Despringre, N.; Chemisky, Y.; Robert, G.; Meraghni, F.

This work presents a micromechanical fatigue damage model developed for short glass fiber reinforced PA66. It has been developed to predict the high cycle fatigue behavior of PA66/GF30. The model is based on an extended Mori-Tanaka method which includes coated inclusions, matrix viscoelasticity and the evolution of micro-scale damage. The developed model accounts for the nonlinear matrix viscoelasticity and the reinforcement orientation. The description of the damage processes is based on the experimental investigation of damage mechanisms previously performed through in-situ SEM tests and X-ray micro-computed tomography observations. Damage chronologies have been proposed involving three different processes: interface debonding/coating, matrix micro-cracking and fiber breakages. Their occurrence strongly depends on the microstructure and the relative humidity. Each damage mechanism is introduced through an evolution law coupled to local stress fields. The developed model is implemented using a UMAT subroutine. Its experimental validation is achieved under stress or strain controlled fatigue tests.

Quantifying variation in speciation and extinction rates with clade data.

PubMed

Paradis, Emmanuel; Tedesco, Pablo A; Hugueny, Bernard

2013-12-01

High-level phylogenies are very common in evolutionary analyses, although they are often treated as incomplete data. Here, we provide statistical tools to analyze what we name "clade data," which are the ages of clades together with their numbers of species. We develop a general approach for the statistical modeling of variation in speciation and extinction rates, including temporal variation, unknown variation, and linear and nonlinear modeling. We show how this approach can be generalized to a wide range of situations, including testing the effects of life-history traits and environmental variables on diversification rates. We report the results of an extensive simulation study to assess the performance of some statistical tests presented here as well as of the estimators of speciation and extinction rates. These latter results suggest the possibility to estimate correctly extinction rate in the absence of fossils. An example with data on fish is presented. © 2013 The Author(s). Evolution © 2013 The Society for the Study of Evolution.

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.

Ultrashort dark solitons interactions and nonlinear tunneling in the modified nonlinear Schrödinger equation with variable coefficient

NASA Astrophysics Data System (ADS)

Musammil, N. M.; Porsezian, K.; Nithyanandan, K.; Subha, P. A.; Tchofo Dinda, P.

2017-09-01

We present the study of the dark soliton dynamics in an inhomogeneous fiber by means of a variable coefficient modified nonlinear Schrödinger equation (Vc-MNLSE) with distributed dispersion, self-phase modulation, self-steepening and linear gain/loss. The ultrashort dark soliton pulse evolution and interaction is studied by using the Hirota bilinear (HB) method. In particular, we give much insight into the effect of self-steepening (SS) on the dark soliton dynamics. The study reveals a shock wave formation, as a major effect of SS. Numerically, we study the dark soliton propagation in the continuous wave background, and the stability of the soliton solution is tested in the presence of photon noise. The elastic collision behaviors of the dark solitons are discussed by the asymptotic analysis. On the other hand, considering the nonlinear tunneling of dark soliton through barrier/well, we find that the tunneling of the dark soliton depends on the height of the barrier and the amplitude of the soliton. The intensity of the tunneling soliton either forms a peak or valley and retains its shape after the tunneling. For the case of exponential background, the soliton tends to compress after tunneling through the barrier/well.

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.

Beam tests of proton-irradiated PbWO4 crystals and evaluation of double-ended read-out technique for mitigation of radiation damage effects

NASA Astrophysics Data System (ADS)

Lucchini, Marco; CMS Collaboration

2017-11-01

The harsh radiation environment in which detectors will have to operate during the High Luminosity phase of LHC (HL-LHC) represents a crucial challenge for many calorimeter technologies. In the CMS forward calorimeters, ionizing doses and hadron fluences will reach up to 300 kGy (at a dose rate of 30 Gy/h) and 2 × 1014 cm-2, respectively, at the pseudo-rapidity region of |η| = 2.6. To evaluate the evolution of the CMS ECAL performance in such conditions, a set of PbWO4 crystals, exposed to 24 GeV protons up to integrated fluences between 2.1 × 1013 cm-2 and 1:3 × 1014 cm2, has been studied in beam tests. A degradation of the energy resolution and a non-linear response to electron showers are observed in damaged crystals. Direct measurements of the light output from the crystals show the amplitude decreasing and pulse becoming faster as the fluence increases. The evolution of the PbWO4 crystals calorimetric performance has been well understood and parameterized in terms of increasing light absorption inside the crystal volume. A double-ended read-out configuration, in which two identical photodetectors are coupled to the opposite ends of each crystal, has also been tested. The separate and simultaneous read out of the light from the two ends of the crystal allows to correct for longitudinal shower fluctuations and to mitigate the degradation of energy resolution in highly damaged crystals. The non-linear response to electromagnetic showers, arising from high non-uniformity of light collection efficiency along the longitudinal axis of irradiated crystals, can also be corrected by means of the double-ended read-out technique.

Experimental Hydromechanical Characterization and Numerical Modelling of a Fractured and Porous Sandstone

NASA Astrophysics Data System (ADS)

Souley, Mountaka; Lopez, Philippe; Boulon, Marc; Thoraval, Alain

2015-05-01

The experimental device previously used to study the hydromechanical behaviour of individual fractures on a laboratory scale, was adapted to make it possible to measure flow through porous rock mass samples in addition to fracture flows. A first series of tests was performed to characterize the hydromechanical behaviour of the fracture individually as well as the porous matrix (sandstone) comprising the fracture walls. A third test in this series was used to validate the experimental approach. These tests showed non-linear evolution of the contact area on the fracture walls with respect to effective normal stress. Consequently, a non-linear relationship was noted between the hydraulic aperture on the one hand, and the effective normal stress and mechanical opening on the other hand. The results of the three tests were then analysed by numerical modelling. The VIPLEF/HYDREF numerical codes used take into account the dual-porosity of the sample (fracture + rock matrix) and can be used to reproduce hydromechanical loading accurately. The analyses show that the relationship between the hydraulic aperture of the fracture and the mechanical closure has a significant effect on fracture flow rate predictions. By taking simultaneous measurements of flow in both fracture and rock matrix, we were able to carry out a global evaluation of the conceptual approach used.

Spinor Field Nonlinearity and Space-Time Geometry

NASA Astrophysics Data System (ADS)

Saha, Bijan

2018-03-01

Within the scope of Bianchi type VI,VI0,V, III, I, LRSBI and FRW cosmological models we have studied the role of nonlinear spinor field on the evolution of the Universe and the spinor field itself. It was found that due to the presence of non-trivial non-diagonal components of the energy-momentum tensor of the spinor field in the anisotropic space-time, there occur some severe restrictions both on the metric functions and on the components of the spinor field. In this report we have considered a polynomial nonlinearity which is a function of invariants constructed from the bilinear spinor forms. It is found that in case of a Bianchi type-VI space-time, depending of the sign of self-coupling constants, the model allows either late time acceleration or oscillatory mode of evolution. In case of a Bianchi VI 0 type space-time due to the specific behavior of the spinor field we have two different scenarios. In one case the invariants constructed from bilinear spinor forms become trivial, thus giving rise to a massless and linear spinor field Lagrangian. This case is equivalent to the vacuum solution of the Bianchi VI 0 type space-time. The second case allows non-vanishing massive and nonlinear terms and depending on the sign of coupling constants gives rise to accelerating mode of expansion or the one that after obtaining some maximum value contracts and ends in big crunch, consequently generating space-time singularity. In case of a Bianchi type-V model there occur two possibilities. In one case we found that the metric functions are similar to each other. In this case the Universe expands with acceleration if the self-coupling constant is taken to be a positive one, whereas a negative coupling constant gives rise to a cyclic or periodic solution. In the second case the spinor mass and the spinor field nonlinearity vanish and the Universe expands linearly in time. In case of a Bianchi type-III model the space-time remains locally rotationally symmetric all the time, though the isotropy of space-time can be attained for a large proportionality constant. As far as evolution is concerned, depending on the sign of coupling constant the model allows both accelerated and oscillatory mode of expansion. A negative coupling constant leads to an oscillatory mode of expansion, whereas a positive coupling constant generates expanding Universe with late time acceleration. Both deceleration parameter and EoS parameter in this case vary with time and are in agreement with modern concept of space-time evolution. In case of a Bianchi type-I space-time the non-diagonal components lead to three different possibilities. In case of a full BI space-time we find that the spinor field nonlinearity and the massive term vanish, hence the spinor field Lagrangian becomes massless and linear. In two other cases the space-time evolves into either LRSBI or FRW Universe. If we consider a locally rotationally symmetric BI( LRSBI) model, neither the mass term nor the spinor field nonlinearity vanishes. In this case depending on the sign of coupling constant we have either late time accelerated mode of expansion or oscillatory mode of evolution. In this case for an expanding Universe we have asymptotical isotropization. Finally, in case of a FRW model neither the mass term nor the spinor field nonlinearity vanishes. Like in LRSBI case we have either late time acceleration or cyclic mode of evolution. These findings allow us to conclude that the spinor field is very sensitive to the gravitational one.

3D Progressive Damage Modeling for Laminated Composite Based on Crack Band Theory and Continuum Damage Mechanics

NASA Technical Reports Server (NTRS)

Wang, John T.; Pineda, Evan J.; Ranatunga, Vipul; Smeltzer, Stanley S.

2015-01-01

A simple continuum damage mechanics (CDM) based 3D progressive damage analysis (PDA) tool for laminated composites was developed and implemented as a user defined material subroutine to link with a commercially available explicit finite element code. This PDA tool uses linear lamina properties from standard tests, predicts damage initiation with an easy-to-implement Hashin-Rotem failure criteria, and in the damage evolution phase, evaluates the degradation of material properties based on the crack band theory and traction-separation cohesive laws. It follows Matzenmiller et al.'s formulation to incorporate the degrading material properties into the damaged stiffness matrix. Since nonlinear shear and matrix stress-strain relations are not implemented, correction factors are used for slowing the reduction of the damaged shear stiffness terms to reflect the effect of these nonlinearities on the laminate strength predictions. This CDM based PDA tool is implemented as a user defined material (VUMAT) to link with the Abaqus/Explicit code. Strength predictions obtained, using this VUMAT, are correlated with test data for a set of notched specimens under tension and compression loads.

An evolutionary firefly algorithm for the estimation of nonlinear biological model parameters.

PubMed

Abdullah, Afnizanfaizal; Deris, Safaai; Anwar, Sohail; Arjunan, Satya N V

2013-01-01

The development of accurate computational models of biological processes is fundamental to computational systems biology. These models are usually represented by mathematical expressions that rely heavily on the system parameters. The measurement of these parameters is often difficult. Therefore, they are commonly estimated by fitting the predicted model to the experimental data using optimization methods. The complexity and nonlinearity of the biological processes pose a significant challenge, however, to the development of accurate and fast optimization methods. We introduce a new hybrid optimization method incorporating the Firefly Algorithm and the evolutionary operation of the Differential Evolution method. The proposed method improves solutions by neighbourhood search using evolutionary procedures. Testing our method on models for the arginine catabolism and the negative feedback loop of the p53 signalling pathway, we found that it estimated the parameters with high accuracy and within a reasonable computation time compared to well-known approaches, including Particle Swarm Optimization, Nelder-Mead, and Firefly Algorithm. We have also verified the reliability of the parameters estimated by the method using an a posteriori practical identifiability test.

An Evolutionary Firefly Algorithm for the Estimation of Nonlinear Biological Model Parameters

PubMed Central

Abdullah, Afnizanfaizal; Deris, Safaai; Anwar, Sohail; Arjunan, Satya N. V.

2013-01-01

The development of accurate computational models of biological processes is fundamental to computational systems biology. These models are usually represented by mathematical expressions that rely heavily on the system parameters. The measurement of these parameters is often difficult. Therefore, they are commonly estimated by fitting the predicted model to the experimental data using optimization methods. The complexity and nonlinearity of the biological processes pose a significant challenge, however, to the development of accurate and fast optimization methods. We introduce a new hybrid optimization method incorporating the Firefly Algorithm and the evolutionary operation of the Differential Evolution method. The proposed method improves solutions by neighbourhood search using evolutionary procedures. Testing our method on models for the arginine catabolism and the negative feedback loop of the p53 signalling pathway, we found that it estimated the parameters with high accuracy and within a reasonable computation time compared to well-known approaches, including Particle Swarm Optimization, Nelder-Mead, and Firefly Algorithm. We have also verified the reliability of the parameters estimated by the method using an a posteriori practical identifiability test. PMID:23469172

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.

Characterization and modeling of tensile behavior of ceramic woven fabric composites

NASA Technical Reports Server (NTRS)

Kuo, Wen-Shyong; Chen, Wennei Y.; Parvizi-Majidi, Azar; Chou, Tsu-Wei

1991-01-01

This paper examines the tensile behavior of SiC/SiC fabric composites. In the characterization effort, the stress-strain relation and damage evolution are studied with a series of loading and unloading tensile test experiments. The stress-strain relation is linear in response to the initial loading and becomes nonlinear when loading exceeds the proportional limit. Transverse cracking has been observed to be a dominant damage mode governing the nonlinear deformation. The damage is initiated at the inter-tow pores where fiber yarns cross over each other. In the modeling work, the analysis is based upon a fiber bundle model, in which fiber undulation in the warp and fill directions and gaps among fiber yarns have been taken into account. Two limiting cases of fabric stacking arrangements are studied. Closed form solutions are obtained for the composite stiffness and Poisson's ratio. Transverse cracking in the composite is discussed by applying a constant failure strain criterion.

A simple, stable, and accurate linear tetrahedral finite element for transient, nearly, and fully incompressible solid dynamics: A dynamic variational multiscale approach [A simple, stable, and accurate tetrahedral finite element for transient, nearly incompressible, linear and nonlinear elasticity: A dynamic variational multiscale approach

DOE PAGES

Scovazzi, Guglielmo; Carnes, Brian; Zeng, Xianyi; ...

2015-11-12

Here, we propose a new approach for the stabilization of linear tetrahedral finite elements in the case of nearly incompressible transient solid dynamics computations. Our method is based on a mixed formulation, in which the momentum equation is complemented by a rate equation for the evolution of the pressure field, approximated with piece-wise linear, continuous finite element functions. The pressure equation is stabilized to prevent spurious pressure oscillations in computations. Incidentally, it is also shown that many stabilized methods previously developed for the static case do not generalize easily to transient dynamics. Extensive tests in the context of linear andmore » nonlinear elasticity are used to corroborate the claim that the proposed method is robust, stable, and accurate.« less

A simple, stable, and accurate linear tetrahedral finite element for transient, nearly, and fully incompressible solid dynamics: A dynamic variational multiscale approach [A simple, stable, and accurate tetrahedral finite element for transient, nearly incompressible, linear and nonlinear elasticity: A dynamic variational multiscale approach

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

Scovazzi, Guglielmo; Carnes, Brian; Zeng, Xianyi

Here, we propose a new approach for the stabilization of linear tetrahedral finite elements in the case of nearly incompressible transient solid dynamics computations. Our method is based on a mixed formulation, in which the momentum equation is complemented by a rate equation for the evolution of the pressure field, approximated with piece-wise linear, continuous finite element functions. The pressure equation is stabilized to prevent spurious pressure oscillations in computations. Incidentally, it is also shown that many stabilized methods previously developed for the static case do not generalize easily to transient dynamics. Extensive tests in the context of linear andmore » nonlinear elasticity are used to corroborate the claim that the proposed method is robust, stable, and accurate.« less

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

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.

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).

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.

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.

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.

Nonlinearization and waves in bounded media: old wine in a new bottle

NASA Astrophysics Data System (ADS)

Mortell, Michael P.; Seymour, Brian R.

2017-02-01

We consider problems such as a standing wave in a closed straight tube, a self-sustained oscillation, damped resonance, evolution of resonance and resonance between concentric spheres. These nonlinear problems, and other similar ones, have been solved by a variety of techniques when it is seen that linear theory fails. The unifying approach given here is to initially set up the appropriate linear difference equation, where the difference is the linear travel time. When the linear travel time is replaced by a corrected nonlinear travel time, the nonlinear difference equation yields the required solution.

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.

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.

Electronic transport in disordered chains with saturable nonlinearity

NASA Astrophysics Data System (ADS)

dos Santos, J. L. L.; Nguyen, Ba Phi; de Moura, F. A. B. F.

2015-10-01

In this work we study numerically the dynamics of an initially localized wave packet in one-dimensional disordered chains with saturable nonlinearity. By using the generalized discrete nonlinear Schrödinger equation, we calculate two different physical quantities as a function of time, which are the participation number and the mean square displacement from the excitation site. From detailed numerical analysis, we find that the saturable nonlinearity can promote a sub-diffusive spreading of the wave packet even in the presence of diagonal disorder for a long time. In addition, we also investigate the effect of the saturated nonlinearity for initial times of the electronic evolution thus showing the possibility of mobile breather-like modes.

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

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.

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.

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.

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.

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.

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.

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.

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.

Two dimensional kinetic analysis of electrostatic harmonic plasma waves

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

Fonseca-Pongutá, E. C.; Ziebell, L. F.; Gaelzer, R.

2016-06-15

Electrostatic harmonic Langmuir waves are virtual modes excited in weakly turbulent plasmas, first observed in early laboratory beam-plasma experiments as well as in rocket-borne active experiments in space. However, their unequivocal presence was confirmed through computer simulated experiments and subsequently theoretically explained. The peculiarity of harmonic Langmuir waves is that while their existence requires nonlinear response, their excitation mechanism and subsequent early time evolution are governed by essentially linear process. One of the unresolved theoretical issues regards the role of nonlinear wave-particle interaction process over longer evolution time period. Another outstanding issue is that existing theories for these modes aremore » limited to one-dimensional space. The present paper carries out two dimensional theoretical analysis of fundamental and (first) harmonic Langmuir waves for the first time. The result shows that harmonic Langmuir wave is essentially governed by (quasi)linear process and that nonlinear wave-particle interaction plays no significant role in the time evolution of the wave spectrum. The numerical solutions of the two-dimensional wave spectra for fundamental and harmonic Langmuir waves are also found to be consistent with those obtained by direct particle-in-cell simulation method reported in the literature.« less

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

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.

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.

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

Secular resonances with Ceres and Vesta

NASA Astrophysics Data System (ADS)

Tsirvoulis, Georgios; Novaković, Bojan

2016-12-01

In this work we explore dynamical perturbations induced by the massive asteroids Ceres and Vesta on main-belt asteroids through secular resonances. First we determine the location of the linear secular resonances with Ceres and Vesta in the main belt, using a purely numerical technique. Then we use a set of numerical simulations of fictitious asteroids to investigate the importance of these secular resonances in the orbital evolution of main-belt asteroids. We found, evaluating the magnitude of the perturbations in the proper elements of the test particles, that in some cases the strength of these secular resonances is comparable to that of known non-linear secular resonances with the giant planets. Finally we explore the asteroid families that are crossed by the secular resonances we studied, and identified several cases where the latter seem to play an important role in their post-impact evolution.

Kalman filter with a linear state model for PDR+WLAN positioning and its application to assisting a particle filter

NASA Astrophysics Data System (ADS)

Raitoharju, Matti; Nurminen, Henri; Piché, Robert

2015-12-01

Indoor positioning based on wireless local area network (WLAN) signals is often enhanced using pedestrian dead reckoning (PDR) based on an inertial measurement unit. The state evolution model in PDR is usually nonlinear. We present a new linear state evolution model for PDR. In simulated-data and real-data tests of tightly coupled WLAN-PDR positioning, the positioning accuracy with this linear model is better than with the traditional models when the initial heading is not known, which is a common situation. The proposed method is computationally light and is also suitable for smoothing. Furthermore, we present modifications to WLAN positioning based on Gaussian coverage areas and show how a Kalman filter using the proposed model can be used for integrity monitoring and (re)initialization of a particle filter.

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.

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.

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.

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

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.

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

A coupled "AB" system: Rogue waves and modulation instabilities.

PubMed

Wu, C F; Grimshaw, R H J; Chow, K W; Chan, H N

2015-10-01

Rogue waves are unexpectedly large and localized displacements from an equilibrium position or an otherwise calm background. For the nonlinear Schrödinger (NLS) model widely used in fluid mechanics and optics, these waves can occur only when dispersion and nonlinearity are of the same sign, a regime of modulation instability. For coupled NLS equations, rogue waves will arise even if dispersion and nonlinearity are of opposite signs in each component as new regimes of modulation instability will appear in the coupled system. The same phenomenon will be demonstrated here for a coupled "AB" system, a wave-current interaction model describing baroclinic instability processes in geophysical flows. Indeed, the onset of modulation instability correlates precisely with the existence criterion for rogue waves for this system. Transitions from "elevation" rogue waves to "depression" rogue waves are elucidated analytically. The dispersion relation as a polynomial of the fourth order may possess double pairs of complex roots, leading to multiple configurations of rogue waves for a given set of input parameters. For special parameter regimes, the dispersion relation reduces to a cubic polynomial, allowing the existence criterion for rogue waves to be computed explicitly. Numerical tests correlating modulation instability and evolution of rogue waves were conducted.

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.

State Space Formulation of Nonlinear Vibration Responses Collected from a Dynamic Rotor-Bearing System: An Extension of Bearing Diagnostics to Bearing Prognostics

PubMed Central

Tse, Peter W.; Wang, Dong

2017-01-01

Bearings are widely used in various industries to support rotating shafts. Their failures accelerate failures of other adjacent components and may cause unexpected machine breakdowns. In recent years, nonlinear vibration responses collected from a dynamic rotor-bearing system have been widely analyzed for bearing diagnostics. Numerous methods have been proposed to identify different bearing faults. However, these methods are unable to predict the future health conditions of bearings. To extend bearing diagnostics to bearing prognostics, this paper reports the design of a state space formulation of nonlinear vibration responses collected from a dynamic rotor-bearing system in order to intelligently predict bearing remaining useful life (RUL). Firstly, analyses of nonlinear vibration responses were conducted to construct a bearing health indicator (BHI) so as to assess the current bearing health condition. Secondly, a state space model of the BHI was developed to mathematically track the health evolution of the BHI. Thirdly, unscented particle filtering was used to predict bearing RUL. Lastly, a new bearing acceleration life testing setup was designed to collect natural bearing degradation data, which were used to validate the effectiveness of the proposed bearing prognostic method. Results show that the prediction accuracy of the proposed bearing prognostic method is promising and the proposed bearing prognostic method is able to reflect future bearing health conditions. PMID:28216586

State Space Formulation of Nonlinear Vibration Responses Collected from a Dynamic Rotor-Bearing System: An Extension of Bearing Diagnostics to Bearing Prognostics.

PubMed

Tse, Peter W; Wang, Dong

2017-02-14

Bearings are widely used in various industries to support rotating shafts. Their failures accelerate failures of other adjacent components and may cause unexpected machine breakdowns. In recent years, nonlinear vibration responses collected from a dynamic rotor-bearing system have been widely analyzed for bearing diagnostics. Numerous methods have been proposed to identify different bearing faults. However, these methods are unable to predict the future health conditions of bearings. To extend bearing diagnostics to bearing prognostics, this paper reports the design of a state space formulation of nonlinear vibration responses collected from a dynamic rotor-bearing system in order to intelligently predict bearing remaining useful life (RUL). Firstly, analyses of nonlinear vibration responses were conducted to construct a bearing health indicator (BHI) so as to assess the current bearing health condition. Secondly, a state space model of the BHI was developed to mathematically track the health evolution of the BHI. Thirdly, unscented particle filtering was used to predict bearing RUL. Lastly, a new bearing acceleration life testing setup was designed to collect natural bearing degradation data, which were used to validate the effectiveness of the proposed bearing prognostic method. Results show that the prediction accuracy of the proposed bearing prognostic method is promising and the proposed bearing prognostic method is able to reflect future bearing health conditions.

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.

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.

Development of a pneumatic high-angle-of-attack Flush Airdata Sensing (HI-FADS) system

NASA Technical Reports Server (NTRS)

Whitmore, Stephen A.; Moes, Timothy R.; Leondes, Cornelius T.

1992-01-01

The HI-FADS system design is an evolution of the FADS systems (e.g., Larson et al., 1980, 1987), which emphasizes the entire airdata system development. This paper describes the HI-FADS measurement system, with particular consideration given to the basic measurement hardware and the development of the HI-FADS aerodynamic model and the basic nonlinear regression algorithm. Algorithm initialization techniques are developed, and potential algorithm divergence problems are discussed. Data derived from HI-FADS flight tests are used to demonstrate the system accuracies and to illustrate the developed concepts and methods.

Assessment of the Damage Tolerance of Postbuckled Hat-Stiffened Panels Using Single-Stringer Specimens

NASA Technical Reports Server (NTRS)

Bisagni, Chiara; Vescovini, Riccardo; Davila, Carlos G.

2010-01-01

A procedure is proposed for the assessment of the damage tolerance and collapse of stiffened composite panels using a single-stringer compression specimen. The dimensions of the specimen are determined such that the specimen s nonlinear response and collapse are representative of an equivalent multi-stringer panel in compression. Experimental tests are conducted on specimens with and without an embedded delamination. A shell-based finite element model with intralaminar and interlaminar damage capabilities is developed to predict the postbuckling response as well as the damage evolution from initiation to collapse.

Twirling and Whirling: Viscous Dynamics of Rotating Elastica

NASA Astrophysics Data System (ADS)

Powers, Thomas R.; Wolgemuth, Charles W.; Goldstein, Raymond E.

1999-11-01

Motivated by diverse phenomena in cellular biophysics, including bacterial flagellar motion and DNA transcription and replication, we study the overdamped nonlinear dynamics of a rotationally forced filament with twist and bend elasticity. The competition between twist diffusion and writhing instabilities is described by a novel pair of coupled PDEs for twist and bend evolution. Analytical and numerical methods elucidate the twist-bend coupling and reveal two dynamical regimes separated by a Hopf bifurcation: (i) diffusion-dominated axial rotation, or twirling, and (ii) steady-state crankshafting motion, or whirling. The consequences of these phenomena for self-propulsion are investigated, and experimental tests proposed.

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.

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.

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.

Energy, time, and channel evolution in catastrophically disturbed fluvial systems

USGS Publications Warehouse

Simon, A.

1992-01-01

Specific energy is shown to decrease nonlinearly with time during channel evolution and provides a measure of reductions in available energy at the channel bed. Data from two sites show convergence towards a minimum specific energy with time. Time-dependent reductions in specific energy at a point act in concert with minimization of the rate of energy dissipation over a reach during channel evolution as the fluvial systems adjust to a new equilibrium.

Single-point nonlinearity indicators for the propagation of high-amplitude acoustic signals

NASA Astrophysics Data System (ADS)

Falco, Lauren E.

In the study of jet noise, prediction schemes and impact assessment models based on linear acoustic theory are not always sufficient to describe the character of the radiated noise. Typically, a spectral comparison method is employed to determine whether nonlinear effects are important. A power spectral density recorded at one propagation distance is extrapolated to a different distance using linear theory and compared with a measurement at the second distance. Discrepancies between the measured and extrapolated spectra are often attributed to nonlinearity. There are many other factors that can influence the outcome of this operation, though, including meteorological factors such as wind and temperature gradients, ground reflections, and uncertainty in the source location. Therefore, an improved method for assessing the importance of nonlinearity that requires only a single measurement is desirable. This work examines four candidate single-point nonlinearity indicators derived from the quantity Qp2 p found in the work of Morfey and Howell. These include: Qneg/Qpos, a ratio designed to test for conservation of energy; Qpos/p3rms , a bandlimited quantity that describes energy lost from a certain part of the spectrum due to nonlinearity; the spectral Gol'dberg number Gamma s, a dimensionless quantity whose sign indicates the direction of nonlinear energy transfer and whose magnitude can be used to compare the relative importance of linear and nonlinear effects; and the coherence indicator gamma Q, which also denotes the direction of nonlinear energy transfer and which is bounded between -1 and 1. Two sets of experimental data are presented. The first was recorded in a plane wave tube built of 2" inner-diameter PVC pipe with four evenly-spaced microphones flush-mounted with the inside wall of the tube. One or two compression drivers were used as the sound source, and an anechoic termination made of fiberglass served to minimize reflections from the far end of the tube. Both single-frequency signals and band-limited noise were used as sources, and waveforms were recorded at all four propagation distances. The second set of data was obtained at the model-scale jet facility at the University of Mississippi's National Center for Physical Acoustics. A computer controlled microphone boom was constructed to hold an array of six microphones. The array was rotated about the presumed location of the acoustic source center (4 jet diameters downstream of the nozzle exit), and two stationary microphones were mounted on the walls. Measurements were made for several jet conditions; data presented here represent Mach 0.85 and Mach 2 conditions. Application of the four candidate nonlinearity indicators to the experimental data reveals that each indicator has advantages and disadvantages. Qneg/Qpos does not detect the presence of shocks as postulated, but it does conform to expectations in the shock-free region and support the use of Qpos as an indicator. The main advantage of Qpos/p3rms is that it can be used for band-limited measurements. Increased indicator values are seen for signals with higher source frequencies and amplitudes that are expected to undergo stronger nonlinear evolution. However, no physical meaning can yet be derived from the numerical value of the indicator. The spectral Gol'dberg number Gammas is the most promising of the candidate quantities. It has the ability to indicate the direction of nonlinear energy transfer as well as provide a comparison between the strengths of linear and nonlinear effects. These attributes allow it to be used to qualitatively predict the evolution of a spectrum. The coherence indicator gammaQ also specifies the direction of nonlinear energy transfer, but its numerical value holds less meaning. However, it is bounded between -1 and 1, so values near zero denote very weak or no nonlinearity, and values near -1 or 1 denote strong nonlinearity. Further, because it is bounded, it does not become unstable for spectral components beneath the system noise floor.

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.

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.

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

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.

Test-electron analysis of the magnetic reconnection topology

NASA Astrophysics Data System (ADS)

Borgogno, D.; Perona, A.; Grasso, D.

2017-12-01

Three-dimensional (3D) investigations of the magnetic reconnection field topology in space and laboratory plasmas have identified the abidance of magnetic coherent structures in the stochastic region, which develop during the nonlinear stage of the reconnection process. Further analytical and numerical analyses highlighted the efficacy of some of these structures in limiting the magnetic transport. The question then arises as to what is the possible role played by these patterns in the dynamics of the plasma particles populating the chaotic region. In order to explore this aspect, we provide a detailed description of the nonlinear 3D magnetic field topology in a collisionless magnetic reconnection event with a strong guide field. In parallel, we study the evolution of a population of test electrons in the guiding-center approximation all along the reconnection process. In particular, we focus on the nonlinear spatial redistribution of the initially thermal electrons and show how the electron dynamics in the stochastic region depends on the sign and on the value of their velocities. While the particles with the highest positive speed populate the coherent current structures that survive in the chaotic sea, the presence of the manifolds calculated in the stochastic region defines the confinement area for the electrons with the largest negative velocity. These results stress the link between the magnetic topology and the electron motion and contribute to the overall picture of a non-stationary fluid magnetic reconnection description in a geometry proper to physical systems where the effects of the curvature can be neglected.

Nonlinear Dynamics of Non-uniform Current-Vortex Sheets in Magnetohydrodynamic Flows

NASA Astrophysics Data System (ADS)

Matsuoka, C.; Nishihara, K.; Sano, T.

2017-04-01

A theoretical model is proposed to describe fully nonlinear dynamics of interfaces in two-dimensional MHD flows based on an idea of non-uniform current-vortex sheet. Application of vortex sheet model to MHD flows has a crucial difficulty because of non-conservative nature of magnetic tension. However, it is shown that when a magnetic field is initially parallel to an interface, the concept of vortex sheet can be extended to MHD flows (current-vortex sheet). Two-dimensional MHD flows are then described only by a one-dimensional Lagrange parameter on the sheet. It is also shown that bulk magnetic field and velocity can be calculated from their values on the sheet. The model is tested by MHD Richtmyer-Meshkov instability with sinusoidal vortex sheet strength. Two-dimensional ideal MHD simulations show that the nonlinear dynamics of a shocked interface with density stratification agrees fairly well with that for its corresponding potential flow. Numerical solutions of the model reproduce properly the results of the ideal MHD simulations, such as the roll-up of spike, exponential growth of magnetic field, and its saturation and oscillation. Nonlinear evolution of the interface is found to be determined by the Alfvén and Atwood numbers. Some of their dependence on the sheet dynamics and magnetic field amplification are discussed. It is shown by the model that the magnetic field amplification occurs locally associated with the nonlinear dynamics of the current-vortex sheet. We expect that our model can be applicable to a wide variety of MHD shear flows.

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.

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.

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.

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.

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.

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.

Spherical collapse and virialization in f ( T ) gravities

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

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

2017-03-01

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

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.

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.

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

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.

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.

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

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.

High Order Semi-Lagrangian Advection Scheme

NASA Astrophysics Data System (ADS)

Malaga, Carlos; Mandujano, Francisco; Becerra, Julian

2014-11-01

In most fluid phenomena, advection plays an important roll. A numerical scheme capable of making quantitative predictions and simulations must compute correctly the advection terms appearing in the equations governing fluid flow. Here we present a high order forward semi-Lagrangian numerical scheme specifically tailored to compute material derivatives. The scheme relies on the geometrical interpretation of material derivatives to compute the time evolution of fields on grids that deform with the material fluid domain, an interpolating procedure of arbitrary order that preserves the moments of the interpolated distributions, and a nonlinear mapping strategy to perform interpolations between undeformed and deformed grids. Additionally, a discontinuity criterion was implemented to deal with discontinuous fields and shocks. Tests of pure advection, shock formation and nonlinear phenomena are presented to show performance and convergence of the scheme. The high computational cost is considerably reduced when implemented on massively parallel architectures found in graphic cards. The authors acknowledge funding from Fondo Sectorial CONACYT-SENER Grant Number 42536 (DGAJ-SPI-34-170412-217).

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.

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.

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.

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.

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).

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.

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.

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.

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.

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.

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.

Boundary-Layer Receptivity and Integrated Transition Prediction

NASA Technical Reports Server (NTRS)

Chang, Chau-Lyan; Choudhari, Meelan

2005-01-01

The adjoint parabold stability equations (PSE) formulation is used to calculate the boundary layer receptivity to localized surface roughness and suction for compressible boundary layers. Receptivity efficiency functions predicted by the adjoint PSE approach agree well with results based on other nonparallel methods including linearized Navier-Stokes equations for both Tollmien-Schlichting waves and crossflow instability in swept wing boundary layers. The receptivity efficiency function can be regarded as the Green's function to the disturbance amplitude evolution in a nonparallel (growing) boundary layer. Given the Fourier transformed geometry factor distribution along the chordwise direction, the linear disturbance amplitude evolution for a finite size, distributed nonuniformity can be computed by evaluating the integral effects of both disturbance generation and linear amplification. The synergistic approach via the linear adjoint PSE for receptivity and nonlinear PSE for disturbance evolution downstream of the leading edge forms the basis for an integrated transition prediction tool. Eventually, such physics-based, high fidelity prediction methods could simulate the transition process from the disturbance generation through the nonlinear breakdown in a holistic manner.

Evolution of inviscid Kelvin-Helmholtz instability from a piecewise linear shear layer

NASA Astrophysics Data System (ADS)

Guha, Anirban; Rahmani, Mona; Lawrence, Gregory

2012-11-01

Here we study the evolution of 2D, inviscid Kelvin-Helmholtz instability (KH) ensuing from a piecewise linear shear layer. Although KH pertaining to smooth shear layers (eg. Hyperbolic tangent profile) has been thorough investigated in the past, very little is known about KH resulting from sharp shear layers. Pozrikidis and Higdon (1985) have shown that piecewise shear layer evolves into elliptical vortex patches. This non-linear state is dramatically different from the well known spiral-billow structure of KH. In fact, there is a little acknowledgement that elliptical vortex patches can represent non-linear KH. In this work, we show how such patches evolve through the interaction of vorticity waves. Our work is based on two types of computational methods (i) Contour Dynamics: a boundary-element method which tracks the evolution of the contour of a vortex patch using Lagrangian marker points, and (ii) Direct Numerical Simulation (DNS): an Eulerian pseudo-spectral method heavily used in studying hydrodynamic instability and turbulence.

Calibration of a stochastic health evolution model using NHIS data

NASA Astrophysics Data System (ADS)

Gupta, Aparna; Li, Zhisheng

2011-10-01

This paper presents and calibrates an individual's stochastic health evolution model. In this health evolution model, the uncertainty of health incidents is described by a stochastic process with a finite number of possible outcomes. We construct a comprehensive health status index (HSI) to describe an individual's health status, as well as a health risk factor system (RFS) to classify individuals into different risk groups. Based on the maximum likelihood estimation (MLE) method and the method of nonlinear least squares fitting, model calibration is formulated in terms of two mixed-integer nonlinear optimization problems. Using the National Health Interview Survey (NHIS) data, the model is calibrated for specific risk groups. Longitudinal data from the Health and Retirement Study (HRS) is used to validate the calibrated model, which displays good validation properties. The end goal of this paper is to provide a model and methodology, whose output can serve as a crucial component of decision support for strategic planning of health related financing and risk management.

Similarity solutions of some two-space-dimensional nonlinear wave evolution equations

NASA Technical Reports Server (NTRS)

Redekopp, L. G.

1980-01-01

Similarity reductions of the two-space-dimensional versions of the Korteweg-de Vries, modified Korteweg-de Vries, Benjamin-Davis-Ono, and nonlinear Schroedinger equations are presented, and some solutions of the reduced equations are discussed. Exact dispersive solutions of the two-dimensional Korteweg-de Vries equation are obtained, and the similarity solution of this equation is shown to be reducible to the second Painleve transcendent.

Pair correlation function and nonlinear kinetic equation for a spatially uniform polarizable nonideal plasma

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

Belyi, V.V.; Kukharenko, Y.A.; Wallenborn, J.

Taking into account the first non-Markovian correction to the Balescu-Lenard equation, we have derived an expression for the pair correlation function and a nonlinear kinetic equation valid for a nonideal polarized classical plasma. This last equation allows for the description of the correlational energy evolution and shows the global conservation of energy with dynamical polarization. {copyright} {ital 1996 The American Physical Society.}

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.

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.

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)

Nonlinear derating of high-intensity focused ultrasound beams using Gaussian modal sums.

PubMed

Dibaji, Seyed Ahmad Reza; Banerjee, Rupak K; Soneson, Joshua E; Myers, Matthew R

2013-11-01

A method is introduced for using measurements made in water of the nonlinear acoustic pressure field produced by a high-intensity focused ultrasound transducer to compute the acoustic pressure and temperature rise in a tissue medium. The acoustic pressure harmonics generated by nonlinear propagation are represented as a sum of modes having a Gaussian functional dependence in the radial direction. While the method is derived in the context of Gaussian beams, final results are applicable to general transducer profiles. The focal acoustic pressure is obtained by solving an evolution equation in the axial variable. The nonlinear term in the evolution equation for tissue is modeled using modal amplitudes measured in water and suitably reduced using a combination of "source derating" (experiments in water performed at a lower source acoustic pressure than in tissue) and "endpoint derating" (amplitudes reduced at the target location). Numerical experiments showed that, with proper combinations of source derating and endpoint derating, direct simulations of acoustic pressure and temperature in tissue could be reproduced by derating within 5% error. Advantages of the derating approach presented include applicability over a wide range of gains, ease of computation (a single numerical quadrature is required), and readily obtained temperature estimates from the water measurements.

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.

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.

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.

An ansatz for solving nonlinear partial differential equations in mathematical physics.

PubMed

Akbar, M Ali; Ali, Norhashidah Hj Mohd

2016-01-01

In this article, we introduce an ansatz involving exact traveling wave solutions to nonlinear partial differential equations. To obtain wave solutions using direct method, the choice of an appropriate ansatz is of great importance. We apply this ansatz to examine new and further general traveling wave solutions to the (1+1)-dimensional modified Benjamin-Bona-Mahony equation. Abundant traveling wave solutions are derived including solitons, singular solitons, periodic solutions and general solitary wave solutions. The solutions emphasize the nobility of this ansatz in providing distinct solutions to various tangible phenomena in nonlinear science and engineering. The ansatz could be more efficient tool to deal with higher dimensional nonlinear evolution equations which frequently arise in many real world physical problems.

The evolution of hyperboloidal data with the dual foliation formalism: mathematical analysis and wave equation tests

NASA Astrophysics Data System (ADS)

Hilditch, David; Harms, Enno; Bugner, Marcus; Rüter, Hannes; Brügmann, Bernd

2018-03-01

A long-standing problem in numerical relativity is the satisfactory treatment of future null-infinity. We propose an approach for the evolution of hyperboloidal initial data in which the outer boundary of the computational domain is placed at infinity. The main idea is to apply the ‘dual foliation’ formalism in combination with hyperboloidal coordinates and the generalized harmonic gauge formulation. The strength of the present approach is that, following the ideas of Zenginoğlu, a hyperboloidal layer can be naturally attached to a central region using standard coordinates of numerical relativity applications. Employing a generalization of the standard hyperboloidal slices, developed by Calabrese et al, we find that all formally singular terms take a trivial limit as we head to null-infinity. A byproduct is a numerical approach for hyperboloidal evolution of nonlinear wave equations violating the null-condition. The height-function method, used often for fixed background spacetimes, is generalized in such a way that the slices can be dynamically ‘waggled’ to maintain the desired outgoing coordinate lightspeed precisely. This is achieved by dynamically solving the eikonal equation. As a first numerical test of the new approach we solve the 3D flat space scalar wave equation. The simulations, performed with the pseudospectral bamps code, show that outgoing waves are cleanly absorbed at null-infinity and that errors converge away rapidly as resolution is increased.

Non-gaussianity versus nonlinearity of cosmological perturbations.

PubMed

Verde, L

2001-06-01

Following the discovery of the cosmic microwave background, the hot big-bang model has become the standard cosmological model. In this theory, small primordial fluctuations are subsequently amplified by gravity to form the large-scale structure seen today. Different theories for unified models of particle physics, lead to different predictions for the statistical properties of the primordial fluctuations, that can be divided in two classes: gaussian and non-gaussian. Convincing evidence against or for gaussian initial conditions would rule out many scenarios and point us toward a physical theory for the origin of structures. The statistical distribution of cosmological perturbations, as we observe them, can deviate from the gaussian distribution in several different ways. Even if perturbations start off gaussian, nonlinear gravitational evolution can introduce non-gaussian features. Additionally, our knowledge of the Universe comes principally from the study of luminous material such as galaxies, but galaxies might not be faithful tracers of the underlying mass distribution. The relationship between fluctuations in the mass and in the galaxies distribution (bias), is often assumed to be local, but could well be nonlinear. Moreover, galaxy catalogues use the redshift as third spatial coordinate: the resulting redshift-space map of the galaxy distribution is nonlinearly distorted by peculiar velocities. Nonlinear gravitational evolution, biasing, and redshift-space distortion introduce non-gaussianity, even in an initially gaussian fluctuation field. I investigate the statistical tools that allow us, in principle, to disentangle the above different effects, and the observational datasets we require to do so in practice.

Testing for nonlinear dependence in financial markets.

PubMed

Dore, Mohammed; Matilla-Garcia, Mariano; Marin, Manuel Ruiz

2011-07-01

This article addresses the question of improving the detection of nonlinear dependence by means of recently developed nonparametric tests. To this end a generalized version of BDS test and a new test based on symbolic dynamics are used on realizations from a well-known artificial market for which the dynamic equation governing the market is known. Comparisons with other tests for detecting nonlinearity are also provided. We show that the test based on symbolic dynamics outperforms other tests with the advantage that it depends only on one free parameter, namely the embedding dimension. This does not hold for other tests for nonlinearity.

Methods of geometrical integration in accelerator physics

NASA Astrophysics Data System (ADS)

Andrianov, S. N.

2016-12-01

In the paper we consider a method of geometric integration for a long evolution of the particle beam in cyclic accelerators, based on the matrix representation of the operator of particles evolution. This method allows us to calculate the corresponding beam evolution in terms of two-dimensional matrices including for nonlinear effects. The ideology of the geometric integration introduces in appropriate computational algorithms amendments which are necessary for preserving the qualitative properties of maps presented in the form of the truncated series generated by the operator of evolution. This formalism extends both on polarized and intense beams. Examples of practical applications are described.

Evidence of directional and stabilizing selection in contemporary humans.

PubMed

Sanjak, Jaleal S; Sidorenko, Julia; Robinson, Matthew R; Thornton, Kevin R; Visscher, Peter M

2018-01-02

Modern molecular genetic datasets, primarily collected to study the biology of human health and disease, can be used to directly measure the action of natural selection and reveal important features of contemporary human evolution. Here we leverage the UK Biobank data to test for the presence of linear and nonlinear natural selection in a contemporary population of the United Kingdom. We obtain phenotypic and genetic evidence consistent with the action of linear/directional selection. Phenotypic evidence suggests that stabilizing selection, which acts to reduce variance in the population without necessarily modifying the population mean, is widespread and relatively weak in comparison with estimates from other species.

Implicit solvers for unstructured meshes

NASA Technical Reports Server (NTRS)

Venkatakrishnan, V.; Mavriplis, Dimitri J.

1991-01-01

Implicit methods for unstructured mesh computations are developed and tested. The approximate system which arises from the Newton-linearization of the nonlinear evolution operator is solved by using the preconditioned generalized minimum residual technique. These different preconditioners are investigated: the incomplete LU factorization (ILU), block diagonal factorization, and the symmetric successive over-relaxation (SSOR). The preconditioners have been optimized to have good vectorization properties. The various methods are compared over a wide range of problems. Ordering of the unknowns, which affects the convergence of these sparse matrix iterative methods, is also investigated. Results are presented for inviscid and turbulent viscous calculations on single and multielement airfoil configurations using globally and adaptively generated meshes.

Temporal and Spatial Evolution Characteristics of Disturbance Wave in a Hypersonic Boundary Layer due to Single-Frequency Entropy Disturbance

PubMed Central

Lv, Hongqing; Shi, Jianqiang

2014-01-01

By using a high-order accurate finite difference scheme, direct numerical simulation of hypersonic flow over an 8° half-wedge-angle blunt wedge under freestream single-frequency entropy disturbance is conducted; the generation and the temporal and spatial nonlinear evolution of boundary layer disturbance waves are investigated. Results show that, under the freestream single-frequency entropy disturbance, the entropy state of boundary layer is changed sharply and the disturbance waves within a certain frequency range are induced in the boundary layer. Furthermore, the amplitudes of disturbance waves in the period phase are larger than that in the response phase and ablation phase and the frequency range in the boundary layer in the period phase is narrower than that in these two phases. In addition, the mode competition, dominant mode transformation, and disturbance energy transfer exist among different modes both in temporal and in spatial evolution. The mode competition changes the characteristics of nonlinear evolution of the unstable waves in the boundary layer. The development of the most unstable mode along streamwise relies more on the motivation of disturbance waves in the upstream than that of other modes on this motivation. PMID:25143983

Temporal and spatial evolution characteristics of disturbance wave in a hypersonic boundary layer due to single-frequency entropy disturbance.

PubMed

Wang, Zhenqing; Tang, Xiaojun; Lv, Hongqing; Shi, Jianqiang

2014-01-01

By using a high-order accurate finite difference scheme, direct numerical simulation of hypersonic flow over an 8° half-wedge-angle blunt wedge under freestream single-frequency entropy disturbance is conducted; the generation and the temporal and spatial nonlinear evolution of boundary layer disturbance waves are investigated. Results show that, under the freestream single-frequency entropy disturbance, the entropy state of boundary layer is changed sharply and the disturbance waves within a certain frequency range are induced in the boundary layer. Furthermore, the amplitudes of disturbance waves in the period phase are larger than that in the response phase and ablation phase and the frequency range in the boundary layer in the period phase is narrower than that in these two phases. In addition, the mode competition, dominant mode transformation, and disturbance energy transfer exist among different modes both in temporal and in spatial evolution. The mode competition changes the characteristics of nonlinear evolution of the unstable waves in the boundary layer. The development of the most unstable mode along streamwise relies more on the motivation of disturbance waves in the upstream than that of other modes on this motivation.

Direct Numerical Simulation of Fingering Instabilities in Coating Flows

NASA Astrophysics Data System (ADS)

Eres, Murat H.; Schwartz, Leonard W.

1998-11-01

We consider stability and finger formation in free surface flows. Gravity driven downhill drainage and temperature gradient driven climbing flows are two examples of such problems. The former situation occurs when a mound of viscous liquid on a vertical wall is allowed to flow. Constant surface shear stress due to temperature gradients (Marangoni stress) can initiate the latter problem. The evolution equations are derived using the lubrication approximation. We also include the effects of finite-contact angles in the evolution equations using a disjoining pressure model. Evolution equations for both problems are solved using an efficient alternating-direction-implicit method. For both problems a one-dimensional base state is established, that is steady in a moving reference frame. This base state is unstable to transverse perturbations. The transverse wavenumbers for the most rapidly growing modes are found through direct numerical solution of the nonlinear evolution equations, and are compared with published experimental results. For a range of finite equilibrium contact angles, the fingers can grow without limit leading to semi-finite steady fingers in a moving coordinate system. A computer generated movie of the nonlinear simulation results, for several sets of input parameters, will be shown.

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.

Self-consistent theory for the linear and nonlinear propagation of a sinusoidal electron plasma wave. Application to stimulated Raman scattering in a non-uniform and non-stationary plasma

NASA Astrophysics Data System (ADS)

Bénisti, Didier

2018-01-01

In this paper, we address the theoretical resolution of the Vlasov-Gauss system from the linear regime to the strongly nonlinear one, when significant trapping has occurred. The electric field is that of a sinusoidal electron plasma wave (EPW) which is assumed to grow from the noise level, and to keep growing at least up to the amplitude when linear theory in no longer valid (while the wave evolution in the nonlinear regime may be arbitrary). The ions are considered as a neutralizing fluid, while the electron response to the wave is derived by matching two different techniques. We make use of a perturbation analysis similar to that introduced to prove the Kolmogorov-Arnold-Moser theorem, up to amplitudes large enough for neo-adiabatic results to be valid. Our theory is applied to the growth and saturation of the beam-plasma instability, and to the three-dimensional propagation of a driven EPW in a non-uniform and non-stationary plasma. For the latter example, we lay a special emphasis on nonlinear collisionless dissipation. We provide an explicit theoretical expression for the nonlinear Landau-like damping rate which, in some instances, is amenable to a simple analytic formula. We also insist on the irreversible evolution of the electron distribution function, which is nonlocal in the wave amplitude and phase velocity. This makes trapping an effective means of dissipation for the electrostatic energy, and also makes the wave dispersion relation nonlocal. Our theory is generalized to allow for stimulated Raman scattering, which we address up to saturation by accounting for plasma inhomogeneity and non-stationarity, nonlinear kinetic effects, and interspeckle coupling.

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.

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.

Stochastic functional evolution equations with monotone nonlinearity: Existence and stability of the mild solutions

NASA Astrophysics Data System (ADS)

Jahanipur, Ruhollah

In this paper, we study a class of semilinear functional evolution equations in which the nonlinearity is demicontinuous and satisfies a semimonotone condition. We prove the existence, uniqueness and exponentially asymptotic stability of the mild solutions. Our approach is to apply a convenient version of Burkholder inequality for convolution integrals and an iteration method based on the existence and measurability results for the functional integral equations in Hilbert spaces. An Itô-type inequality is the main tool to study the uniqueness, p-th moment and almost sure sample path asymptotic stability of the mild solutions. We also give some examples to illustrate the applications of the theorems and meanwhile we compare the results obtained in this paper with some others appeared in the literature.

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.

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

Brain-Inspired Constructive Learning Algorithms with Evolutionally Additive Nonlinear Neurons

NASA Astrophysics Data System (ADS)

Fang, Le-Heng; Lin, Wei; Luo, Qiang

In this article, inspired partially by the physiological evidence of brain’s growth and development, we developed a new type of constructive learning algorithm with evolutionally additive nonlinear neurons. The new algorithms have remarkable ability in effective regression and accurate classification. In particular, the algorithms are able to sustain a certain reduction of the loss function when the dynamics of the trained network are bogged down in the vicinity of the local minima. The algorithm augments the neural network by adding only a few connections as well as neurons whose activation functions are nonlinear, nonmonotonic, and self-adapted to the dynamics of the loss functions. Indeed, we analytically demonstrate the reduction dynamics of the algorithm for different problems, and further modify the algorithms so as to obtain an improved generalization capability for the augmented neural networks. Finally, through comparing with the classical algorithm and architecture for neural network construction, we show that our constructive learning algorithms as well as their modified versions have better performances, such as faster training speed and smaller network size, on several representative benchmark datasets including the MNIST dataset for handwriting digits.

Growth and Interaction of Colloid Nuclei

NASA Astrophysics Data System (ADS)

Lam, Michael-Angelo; Khusid, Boris; Meyer, William; Kondic, Lou

2017-11-01

We study evolution of colloid systems under zero-gravity conditions. In particular, we focus on the regime where there is a coexistence between a liquid and a solid state. Under zero gravity, the dominating process in the bulk of the fluid phase and the solid phase is diffusion. At the moving solid/liquid interface, osmotic pressure is balanced by surface tension, as well as balancing fluxes (conservation of mass) with the kinematics of nuclei growth (Wilson-Frenkel law). Due to the highly nonlinear boundary condition at the moving boundary, care has to be taken when performing numerical simulations. In this work, we present a nonlinear model for colloid nuclei growth. Numerical simulations using a finite volume method are compared with asymptotic analysis of the governing equation and experimental results for nuclei growth. Novel component in our numerical simulations is the inclusion of nonlinear (collective) diffusion terms that depend on the chemical potentials of the colloid in the solid and fluid phase. The results include growth and dissolution of a single colloidal nucleus, as well as evolution of multiple interacting nuclei. Supported by NASA Grant No. NNX16AQ79G.

On nonlinear evolution of low-frequency Alfvén waves in weakly-expanding solar wind plasmas

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

Nariyuki, Y.

A multi-dimensional nonlinear evolution equation for Alfvén waves in weakly-expanding solar wind plasmas is derived by using the reductive perturbation method. The expansion of solar wind plasma parcels is modeled by an expanding box model, which includes the accelerating expansion. It is shown that the resultant equation agrees with the Wentzel-Kramers-Brillouin prediction of the low-frequency Alfvén waves in the linear limit. In the cold and one-dimensional limit, a modified derivative nonlinear Schrodinger equation is obtained. Direct numerical simulations are carried out to discuss the effect of the expansion on the modulational instability of monochromatic Alfvén waves and the propagation ofmore » Alfvén solitons. By using the instantaneous frequency, it is quantitatively shown that as far as the expansion rate is much smaller than wave frequencies, effects of the expansion are almost adiabatic. It is also confirmed that while shapes of Alfvén solitons temporally change due to the expansion, some of them can stably propagate after their collision in weakly-expanding plasmas.« 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.

Experimentally observed evolution between dynamic patterns and intrinsic localized modes in a driven nonlinear electrical cyclic lattice

NASA Astrophysics Data System (ADS)

Shige, S.; Miyasaka, K.; Shi, W.; Soga, Y.; Sato, M.; Sievers, A. J.

2018-02-01

Locked intrinsic localized modes (ILMs) and large amplitude lattice spatial modes (LSMs) have been experimentally measured for a driven 1-D nonlinear cyclic electric transmission line, where the nonlinear element is a saturable capacitor. Depending on the number of cells and electrical lattice damping an LSM of fixed shape can be tuned across the modal spectrum. Interestingly, by tuning the driver frequency away from this spectrum the LSM can be continuously converted into ILMs and vice versa. The differences in pattern formation between simulations and experimental findings are due to a low concentration of impurities. Through this novel nonlinear excitation and switching channel in cyclic lattices either energy balanced or unbalanced LSMs and ILMs may occur. Because of the general nature of these dynamical results for nonintegrable lattices applications are to be expected. The ultimate stability of driven aero machinery containing nonlinear periodic structures may be one example.

Nonlinear self-sustained structures and fronts in spatially developing wake flows

NASA Astrophysics Data System (ADS)

Pier, Benoît; Huerre, Patrick

2001-05-01

A family of slowly spatially developing wakes with variable pressure gradient is numerically demonstrated to sustain a synchronized finite-amplitude vortex street tuned at a well-defined frequency. This oscillating state is shown to be described by a steep global mode exhibiting a sharp Dee Langer-type front at the streamwise station of marginal absolute instability. The front acts as a wavemaker which sends out nonlinear travelling waves in the downstream direction, the global frequency being imposed by the real absolute frequency prevailing at the front station. The nonlinear travelling waves are determined to be governed by the local nonlinear dispersion relation resulting from a temporal evolution problem on a local wake profile considered as parallel. Although the vortex street is fully nonlinear, its frequency is dictated by a purely linear marginal absolute instability criterion applied to the local linear dispersion relation.

Dispersive optical soliton solutions for higher order nonlinear Sasa-Satsuma equation in mono mode fibers via new auxiliary equation method

NASA Astrophysics Data System (ADS)

Khater, Mostafa M. A.; Seadawy, Aly R.; Lu, Dianchen

2018-01-01

In this research, we apply new technique for higher order nonlinear Schrödinger equation which is representing the propagation of short light pulses in the monomode optical fibers and the evolution of slowly varying packets of quasi-monochromatic waves in weakly nonlinear media that have dispersion. Nonlinear Schrödinger equation is one of the basic model in fiber optics. We apply new auxiliary equation method for nonlinear Sasa-Satsuma equation to obtain a new optical forms of solitary traveling wave solutions. Exact and solitary traveling wave solutions are obtained in different kinds like trigonometric, hyperbolic, exponential, rational functions, …, etc. These forms of solutions that we represent in this research prove the superiority of our new technique on almost thirteen powerful methods. The main merits of this method over the other methods are that it gives more general solutions with some free parameters.

Physics of Alfvén waves and energetic particles in burning plasmas

NASA Astrophysics Data System (ADS)

Chen, Liu; Zonca, Fulvio

2016-01-01

Dynamics of shear Alfvén waves and energetic particles are crucial to the performance of burning fusion plasmas. This article reviews linear as well as nonlinear physics of shear Alfvén waves and their self-consistent interaction with energetic particles in tokamak fusion devices. More specifically, the review on the linear physics deals with wave spectral properties and collective excitations by energetic particles via wave-particle resonances. The nonlinear physics deals with nonlinear wave-wave interactions as well as nonlinear wave-energetic particle interactions. Both linear as well as nonlinear physics demonstrate the qualitatively important roles played by realistic equilibrium nonuniformities, magnetic field geometries, and the specific radial mode structures in determining the instability evolution, saturation, and, ultimately, energetic-particle transport. These topics are presented within a single unified theoretical framework, where experimental observations and numerical simulation results are referred to elucidate concepts and physics processes.

Effect of emplaced nZVI mass and groundwater velocity on PCE dechlorination and hydrogen evolution in water-saturated sand.

PubMed

Kim, Hye-Jin; Leitch, Megan; Naknakorn, Bhanuphong; Tilton, Robert D; Lowry, Gregory V

2017-01-15

The effect of nZVI mass loading and groundwater velocity on the tetrachloroethylene (PCE) dechlorination rate and the hydrogen evolution rate for poly(maleic acid-co-olefin) (MW=12K) coated nZVI was examined. In batch reactors, the PCE reaction rate constant (3.7×10 -4 Lhr -1 m -2 ) and hydrogen evolution rate constant (1.4 nanomolLhr -1 m -2 ) were independent of nZVI concentration above 10g/L, but the PCE dechlorination rate decreased and the hydrogen evolution rate increased for nZVI concentration below 10g/L. The nonlinearity between nZVI mass loading and PCE dechlorination and H 2 evolution was explained by differences in pH and E h at each nZVI mass loading; PCE reactivity increased when solution E h decreased, and the H 2 evolution rate increased with decreasing pH. Thus, nZVI mass loading of <5g/L yields lower reactivity with PCE and lower efficiency of Fe° utilization than for higher nZVI mass loading. The PCE dechlorination rate increased with increasing pore-water velocity, suggesting that mass transfer limits the reaction at low porewater velocity. Overall, this work suggests that design of nZVI-based reactive barriers for groundwater treatment should consider the non-linear effects of both mass loading and flow velocity on performance and expected reactive lifetime. Copyright © 2016 Elsevier B.V. All rights reserved.

Femtosecond Optics: Advanced Devices and Ultrafast Phenomena

DTIC Science & Technology

2007-05-31

repetition rate from a soliton fiber laser [6]. Because the mode- locking mechanism is passive, no external oscillator is required, leading to a more...nonlinearity, 1.8 m of LNL-SMF is included in the laser. Mode- locked operation of the laser was obtained through nonlinear polarization evolution [6]. For pump...Generation in Photonic Crystal Fibers for Optical Coherence Tomography H. Frequency Swept Lasers and Fourier Domain Mode Locking (FDML) I. Physics of

Non-linear thermal evolution of the crystal structure and phase transitions of LaFeO{sub 3} investigated by high temperature X-ray diffraction

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

Selbach, Sverre M.; Tolchard, Julian R.; Fossdal, Anita

2012-12-15

The crystal structure, anisotropic thermal expansion and structural phase transition of the perovskite LaFeO{sub 3} has been studied by high-temperature X-ray diffraction from room temperature to 1533 K. The structural evolution of the orthorhombic phase with space group Pbnm and the rhombohedral phase with R3{sup Macron }c structure of LaFeO{sub 3} is reported in terms of lattice parameters, thermal expansion coefficients, atomic positions, octahedral rotations and polyhedral volumes. Non-linear lattice expansion across the antiferromagnetic to paramagnetic transition of LaFeO{sub 3} at T{sub N}=735 K was compared to the corresponding behavior of the ferroelectric antiferromagnet BiFeO{sub 3} to gain insight tomore » the magnetoelectric coupling in BiFeO{sub 3}, which is also multiferroic. The first order phase transition of LaFeO{sub 3} from Pbnm to R3{sup Macron }c was observed at 1228{+-}9 K, and a subsequent transition to Pm3{sup Macron }m was extrapolated to occur at 2140{+-}30 K. The stability of the Pbnm and R3{sup Macron }c polymorphs of LaFeO{sub 3} is discussed in terms of the competing enthalpy and entropy of the two crystal polymorphs and the thermal evolution of the polyhedral volume ratio V{sub A}/V{sub B}. - Graphical abstract: Aniostropic thermal evolution of the lattice parameters and phase transition of LaFeO{sub 3}. Highlights: Black-Right-Pointing-Pointer The crystal structure of LaFeO{sub 3} is studied by HTXRD from RT to 1533 K. Black-Right-Pointing-Pointer A non-linear expansion across the Neel temperature is observed for LaFeO{sub 3}. Black-Right-Pointing-Pointer The ratio V{sub A}/V{sub B} is used to rationalize the thermal evolution of the structure.« less

On the coupled evolution of oceanic internal waves and quasi-geostrophic flow

NASA Astrophysics Data System (ADS)

Wagner, Gregory LeClaire

Oceanic motion outside thin boundary layers is primarily a mixture of quasi-geostrophic flow and internal waves with either near-inertial frequencies or the frequency of the semidiurnal lunar tide. This dissertation seeks a deeper understanding of waves and flow through reduced models that isolate their nonlinear and coupled evolution from the Boussinesq equations. Three physical-space models are developed: an equation that describes quasi-geostrophic evolution in an arbitrary and prescribed field of hydrostatic internal waves; a three-component model that couples quasi-geostrophic flow to both near-inertial waves and the near-inertial second harmonic; and a model for the slow evolution of hydrostatic internal tides in quasi-geostrophic flow of near-arbitrary scale. This slow internal tide equation opens the path to a coupled model for the energetic interaction of quasi-geostrophic flow and oceanic internal tides. Four results emerge. First, the wave-averaged quasi-geostrophic equation reveals that finite-amplitude waves give rise to a mean flow that advects quasi-geostrophic potential vorticity. Second is the definition of a new material invariant: Available Potential Vorticity, or APV. APV isolates the part of Ertel potential vorticity available for balanced-flow evolution in Eulerian frames and proves necessary in the separating waves and quasi-geostrophic flow. The third result, hashed out for near-inertial waves and quasi-geostrophic flow, is that wave-flow interaction leads to energy exchange even under conditions of weak nonlinearity. For storm-forced oceanic near-inertial waves the interaction often energizes waves at the expense of flow. We call this extraction of balanced quasi-geostrophic energy 'stimulated generation' since it requires externally-forced rather than spontaneously-generated waves. The fourth result is that quasi-geostrophic flow can encourage or 'catalyze' a nonlinear interaction between a near-inertial wave field and its second harmonic that transfers energy to the small near-inertial vertical scales of wave breaking and mixing.

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.

Effect of P T symmetry on nonlinear waves for three-wave interaction models in the quadratic nonlinear media

NASA Astrophysics Data System (ADS)

Shen, Yujia; Wen, Zichao; Yan, Zhenya; Hang, Chao

2018-04-01

We study the three-wave interaction that couples an electromagnetic pump wave to two frequency down-converted daughter waves in a quadratic optical crystal and P T -symmetric potentials. P T symmetric potentials are shown to modulate stably nonlinear modes in two kinds of three-wave interaction models. The first one is a spatially extended three-wave interaction system with odd gain-and-loss distribution in the channel. Modulated by the P T -symmetric single-well or multi-well Scarf-II potentials, the system is numerically shown to possess stable soliton solutions. Via adiabatical change of system parameters, numerical simulations for the excitation and evolution of nonlinear modes are also performed. The second one is a combination of P T -symmetric models which are coupled via three-wave interactions. Families of nonlinear modes are found with some particular choices of parameters. Stable and unstable nonlinear modes are shown in distinct families by means of numerical simulations. These results will be useful to further investigate nonlinear modes in three-wave interaction models.

Nonlinear effects in evolution - an ab initio study: A model in which the classical theory of evolution occurs as a special case.

PubMed

Clerc, Daryl G

2016-07-21

An ab initio approach was used to study the molecular-level interactions that connect gene-mutation to changes in an organism׳s phenotype. The study provides new insights into the evolutionary process and presents a simplification whereby changes in phenotypic properties may be studied in terms of the binding affinities of the chemical interactions affected by mutation, rather than by correlation to the genes. The study also reports the role that nonlinear effects play in the progression of organs, and how those effects relate to the classical theory of evolution. Results indicate that the classical theory of evolution occurs as a special case within the ab initio model - a case having two attributes. The first attribute: proteins and promoter regions are not shared among organs. The second attribute: continuous limiting behavior exists in the physical properties of organs as well as in the binding affinity of the associated chemical interactions, with respect to displacements in the chemical properties of proteins and promoter regions induced by mutation. Outside of the special case, second-order coupling contributions are significant and nonlinear effects play an important role, a result corroborated by analyses of published activity levels in binding and transactivation assays. Further, gradations in the state of perfection of an organ may be small or large depending on the type of mutation, and not necessarily closely-separated as maintained by the classical theory. Results also indicate that organs progress with varying degrees of interdependence, the likelihood of successful mutation decreases with increasing complexity of the affected chemical system, and differences between the ab initio model and the classical theory increase with increasing complexity of the organism. Copyright © 2016 The Author. Published by Elsevier Ltd.. All rights reserved.

3D non-linear inversion of magnetic anomalies caused by prismatic bodies using differential evolution algorithm

NASA Astrophysics Data System (ADS)

Balkaya, Çağlayan; Ekinci, Yunus Levent; Göktürkler, Gökhan; Turan, Seçil

2017-01-01

3D non-linear inversion of total field magnetic anomalies caused by vertical-sided prismatic bodies has been achieved by differential evolution (DE), which is one of the population-based evolutionary algorithms. We have demonstrated the efficiency of the algorithm on both synthetic and field magnetic anomalies by estimating horizontal distances from the origin in both north and east directions, depths to the top and bottom of the bodies, inclination and declination angles of the magnetization, and intensity of magnetization of the causative bodies. In the synthetic anomaly case, we have considered both noise-free and noisy data sets due to two vertical-sided prismatic bodies in a non-magnetic medium. For the field case, airborne magnetic anomalies originated from intrusive granitoids at the eastern part of the Biga Peninsula (NW Turkey) which is composed of various kinds of sedimentary, metamorphic and igneous rocks, have been inverted and interpreted. Since the granitoids are the outcropped rocks in the field, the estimations for the top depths of two prisms representing the magnetic bodies were excluded during inversion studies. Estimated bottom depths are in good agreement with the ones obtained by a different approach based on 3D modelling of pseudogravity anomalies. Accuracy of the estimated parameters from both cases has been also investigated via probability density functions. Based on the tests in the present study, it can be concluded that DE is a useful tool for the parameter estimation of source bodies using magnetic anomalies.

Nonlinear Dynamics of a Diffusing Interface

NASA Technical Reports Server (NTRS)

Duval, Walter M. B.

2001-01-01

Excitation of two miscible-viscous liquids inside a bounded enclosure in a microgravity environment has shown the evolution of quasi-stationary waves of various modes for a range of parameters. We examine computationally the nonlinear dynamics of the system as the interface breakup and bifurcates to resonance structures typified by the Rayleigh-Taylor instability mechanism. Results show that when the mean steady field is much smaller than the amplitude of the sinusoidal excitation, the system behaves linearly, and growth of quasi-stationary waves occurs through the Kelvin-Helmholtz instability mechanism. However, as the amplitude of excitation increases, nonlinearity occurs through subharmonic bifurcation prior to broadband chaos.

Exact solutions for (1 + 1)-dimensional nonlinear dispersive modified Benjamin-Bona-Mahony equation and coupled Klein-Gordon equations.

PubMed

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

2014-01-01

In this work, recently developed modified simple equation (MSE) method is applied to find exact traveling wave solutions of nonlinear evolution equations (NLEEs). To do so, we consider the (1 + 1)-dimensional nonlinear dispersive modified Benjamin-Bona-Mahony (DMBBM) equation and coupled Klein-Gordon (cKG) equations. Two classes of explicit exact solutions-hyperbolic and trigonometric solutions of the associated equations are characterized with some free parameters. Then these exact solutions correspond to solitary waves for particular values of the parameters. 02.30.Jr; 02.70.Wz; 05.45.Yv; 94.05.Fg.

Femtosecond Fiber Lasers Based on Dissipative Processes for Nonlinear Microscopy

PubMed Central

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. PMID:23869163

Nonlinear Wave Propagation

DTIC Science & Technology

2009-02-12

describes the mode- locking and dynamics of solitons . A characteristic of short pulse lasers is the carrier-envelope phase (CEP) slip which is the change in...and evolution of pulses in mode- locked lasers that are operating in the soliton regime. To describe our research in more detail, we fix typical...solutions with mode- locking evolution. Otherwise the solitons are found to be unstable; either dispersing to radiation or evolving into nonlocalized

Generation and Evolution of Internal Waves in Luzon Strait

DTIC Science & Technology

2015-09-30

1 DISTRIBUTION STATEMENT A. Approved for public release; distribution is unlimited. Generation and Evolution of Internal Waves in Luzon...inertial waves , nonlinear internal waves (NLIWs), and turbulence mixing––in the ocean and thereby help develop improved parameterizations of mixing for...ocean models. Mixing within the stratified ocean is a particular focus as the complex interplay of internal waves from a variety of sources and

Generation and Evolution of Internal Waves in Luzon Strait

DTIC Science & Technology

2016-03-01

1 DISTRIBUTION STATEMENT A: Distribution approved for public release; distribution is unlimited. Generation and Evolution of Internal Waves in...internal tides, inertial waves , nonlinear internal waves (NLIWs), and turbulence mixing––in the ocean and thereby help develop improved parameterizations of...mixing for ocean models. Mixing within the stratified ocean is a particular focus as the complex interplay of internal waves from a variety of

Generation mechanisms of fundamental rogue wave spatial-temporal structure.

PubMed

Ling, Liming; Zhao, Li-Chen; Yang, Zhan-Ying; Guo, Boling

2017-08-01

We discuss the generation mechanism of fundamental rogue wave structures in N-component coupled systems, based on analytical solutions of the nonlinear Schrödinger equation and modulational instability analysis. Our analysis discloses that the pattern of a fundamental rogue wave is determined by the evolution energy and growth rate of the resonant perturbation that is responsible for forming the rogue wave. This finding allows one to predict the rogue wave pattern without the need to solve the N-component coupled nonlinear Schrödinger equation. Furthermore, our results show that N-component coupled nonlinear Schrödinger systems may possess N different fundamental rogue wave patterns at most. These results can be extended to evaluate the type and number of fundamental rogue wave structure in other coupled nonlinear systems.

Numerical studies of identification in nonlinear distributed parameter systems

NASA Technical Reports Server (NTRS)

Banks, H. T.; Lo, C. K.; Reich, Simeon; Rosen, I. G.

1989-01-01

An abstract approximation framework and convergence theory for the identification of first and second order nonlinear distributed parameter systems developed previously by the authors and reported on in detail elsewhere are summarized and discussed. The theory is based upon results for systems whose dynamics can be described by monotone operators in Hilbert space and an abstract approximation theorem for the resulting nonlinear evolution system. The application of the theory together with numerical evidence demonstrating the feasibility of the general approach are discussed in the context of the identification of a first order quasi-linear parabolic model for one dimensional heat conduction/mass transport and the identification of a nonlinear dissipation mechanism (i.e., damping) in a second order one dimensional wave equation. Computational and implementational considerations, in particular, with regard to supercomputing, are addressed.

A Practice-Oriented Bifurcation Analysis for Pulse Energy Converters. Part 2: An Operating Regime

NASA Astrophysics Data System (ADS)

Kolokolov, Yury; Monovskaya, Anna

The paper continues the discussion on bifurcation analysis for applications in practice-oriented solutions for pulse energy conversion systems (PEC-systems). Since a PEC-system represents a nonlinear object with a variable structure, then the description of its dynamics evolution involves bifurcation analysis conceptions. This means the necessity to resolve the conflict-of-units between the notions used to describe natural evolution (i.e. evolution of the operating process towards nonoperating processes and vice versa) and the notions used to describe a desirable artificial regime (i.e. an operating regime). We consider cause-effect relations in the following sequence: nonlinear dynamics-output signal-operating characteristics, where these characteristics include stability and performance. Then regularities of nonlinear dynamics should be translated into regularities of the output signal dynamics, and, after, into an evolutional picture of each operating characteristic. In order to make the translation without losses, we first take into account heterogeneous properties within the structures of the operating process in the parametrical (P-) and phase (X-) spaces, and analyze regularities of the operating stability and performance on the common basis by use of the modified bifurcation diagrams built in joint PX-space. Then, the correspondence between causes (degradation of the operating process stability) and effects (changes of the operating characteristics) is decomposed into three groups of abnormalities: conditionally unavoidable abnormalities (CU-abnormalities); conditionally probable abnormalities (CP-abnormalities); conditionally regular abnormalities (CR-abnormalities). Within each of these groups the evolutional homogeneity is retained. After, the resultant evolution of each operating characteristic is naturally aggregated through the superposition of cause-effect relations in accordance with each of the abnormalities. We demonstrate that the practice-oriented bifurcation analysis has fundamentally specific purposes and tools, like for the computer-based bifurcation analysis and the experimental bifurcation analysis. That is why, from our viewpoint, it seems to be a rather novel direction in the general context of bifurcation analysis conceptions. We believe that the discussion could be interesting to pioneer research intended for the design of promising systems of pulse energy conversion.

Simulation of Vortex Structure in Supersonic Free Shear Layer Using Pse Method

NASA Astrophysics Data System (ADS)

Guo, Xin; Wang, Qiang

The method of parabolized stability equations (PSE) are applied in the analysis of nonlinear stability and the simulation of flow structure in supersonic free shear layer. High accuracy numerical techniques including self-similar basic flow, high order differential method, appropriate transformation and decomposition of nonlinear terms are adopted and developed to solve the PSE effectively for free shear layer. The spatial evolving unstable waves which dominate the flow structure are investigated through nonlinear coupling spatial marching methods. The nonlinear interactions between harmonic waves are further analyzed and instantaneous flow field are obtained by adding the harmonic waves into basic flow. Relevant data agree well with that of DNS. The results demonstrate that T-S wave does not keeping growing exponential as the linear evolution, the energy transfer to high order harmonic modes and finally all harmonic modes get saturation due to the nonlinear interaction; Mean flow distortion is produced by the nonlinear interaction between the harmonic and its conjugate harmonic, makes great change to the average flow and increases the thickness of shear layer; PSE methods can well capture the large scale nonlinear flow structure in the supersonic free shear layer such as vortex roll-up, vortex pairing and nonlinear saturation.

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.

Constitutive modelling of creep in a long fiber random glass mat thermoplastic composite

NASA Astrophysics Data System (ADS)

Dasappa, Prasad

The primary objective of this proposed research is to characterize and model the creep behaviour of Glass Mat Thermoplastic (GMT) composites under thermo-mechanical loads. In addition, tensile testing has been performed to study the variability in mechanical properties. The thermo-physical properties of the polypropylene matrix including crystallinity level, transitions and the variation of the stiffness with temperature have also been determined. In this work, the creep of a long fibre GMT composite has been investigated for a relatively wide range of stresses from 5 to 80 MPa and temperatures from 25 to 90°C. The higher limit for stress is approximately 90% of the nominal tensile strength of the material. A Design of Experiments (ANOVA) statistical method was applied to determine the effects of stress and temperature in the random mat material which is known for wild experimental scatter. Two sets of creep tests were conducted. First, preliminary short-term creep tests consisting of 30 minutes creep followed by recovery were carried out over a wide range of stresses and temperatures. These tests were carried out to determine the linear viscoelastic region of the material. From these tests, the material was found to be linear viscoelastic up-to 20 MPa at room temperature and considerable non-linearities were observed with both stress and temperature. Using Time-Temperature superposition (TTS) a long term master curve for creep compliance for up-to 185 years at room temperature has been obtained. Further, viscoplastic strains were developed in these tests indicating the need for a non-linear viscoelastic viscoplastic constitutive model. The second set of creep tests was performed to develop a general non-linear viscoelastic viscoplastic constitutive model. Long term creep-recovery tests consisting of 1 day creep followed by recovery has been conducted over the stress range between 20 and 70 MPa at four temperatures: 25°C, 40°C, 60°C and 80°C. Findley's model, which is the reduced form of the Schapery non-linear viscoelastic model, was found to be sufficient to model the viscoelastic behaviour. The viscoplastic strains were modeled using the Zapas and Crissman viscoplastic model. A parameter estimation method which isolates the viscoelastic component from the viscoplastic part of the non-linear model has been developed. The non-linear parameters in the Findley's non-linear viscoelastic model have been found to be dependent on both stress and temperature and have been modeled as a product of functions of stress and temperature. The viscoplastic behaviour for temperatures up to 40°C was similar indicating similar damage mechanisms. Moreover, the development of viscoplastic strains at 20 and 30 MPa were similar over all the entire temperature range considered implying similar damage mechanisms. It is further recommended that the material should not be used at temperature greater than 60°C at stresses over 50 MPa. To further study the viscoplastic behaviour of continuous fibre glass mat thermoplastic composite at room temperature, multiple creep-recovery experiments of increasing durations between 1 and 24 hours have been conducted on a single specimen. The purpose of these tests was to experimentally and numerically decouple the viscoplastic strains from total creep response. This enabled the characterization of the evolution of viscoplastic strains as a function of time, stress and loading cycles and also to co-relate the development of viscoplastic strains with progression of failure mechanisms such as interfacial debonding and matrix cracking which were captured in-situ. A viscoplastic model developed from partial data analysis, as proposed by Nordin, had excellent agreement with experimental results for all stresses and times considered. Furthermore, the viscoplastic strain development is accelerated with increasing number of cycles at higher stress levels. These tests further validate the technique proposed for numerical separation of viscoplastic strains employed in obtaining the non-linear viscoelastic viscoplastic model parameters. These tests also indicate that the viscoelastic strains during creep are affected by the previous viscoplastic strain history. (Abstract shortened by UMI.)

Chaos, patterns, coherent structures, and turbulence: Reflections on nonlinear science.

PubMed

Ecke, Robert E

2015-09-01

The paradigms of nonlinear science were succinctly articulated over 25 years ago as deterministic chaos, pattern formation, coherent structures, and adaptation/evolution/learning. For chaos, the main unifying concept was universal routes to chaos in general nonlinear dynamical systems, built upon a framework of bifurcation theory. Pattern formation focused on spatially extended nonlinear systems, taking advantage of symmetry properties to develop highly quantitative amplitude equations of the Ginzburg-Landau type to describe early nonlinear phenomena in the vicinity of critical points. Solitons, mathematically precise localized nonlinear wave states, were generalized to a larger and less precise class of coherent structures such as, for example, concentrated regions of vorticity from laboratory wake flows to the Jovian Great Red Spot. The combination of these three ideas was hoped to provide the tools and concepts for the understanding and characterization of the strongly nonlinear problem of fluid turbulence. Although this early promise has been largely unfulfilled, steady progress has been made using the approaches of nonlinear science. I provide a series of examples of bifurcations and chaos, of one-dimensional and two-dimensional pattern formation, and of turbulence to illustrate both the progress and limitations of the nonlinear science approach. As experimental and computational methods continue to improve, the promise of nonlinear science to elucidate fluid turbulence continues to advance in a steady manner, indicative of the grand challenge nature of strongly nonlinear multi-scale dynamical systems.

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.

Hillslope, river, and Mountain: some surprises in Landscape evolution (Ralph Alger Bagnold Medal Lecture)

NASA Astrophysics Data System (ADS)

Tucker, G. E.

2012-04-01

Geomorphology, like the rest of geoscience, has always had two major themes: a quest to understand the earth's history and 'products' - its landscapes and seascapes - and, in parallel, a quest to understand its formative processes. This dualism is manifest in the remarkable career of R. A. Bagnold, who was inspired by landforms such as dunes, and dedicated to understanding the physical processes that shaped them. His legacy inspires us to emulate two principles at the heart of his contributions: the benefits of rooting geomorphic theory in basic physics, and the importance of understanding geomorphic systems in terms of simple equations framed around energy or force. Today, following Bagnold's footsteps, the earth-surface process community is engaged in a quest to build, test, and refine an ever-improving body of theory to describe our planet's surface and its evolution. In this lecture, I review a small sample of some of the fruits of that quest, emphasizing the value of surprises encountered along the way. The first example involves models of long-term river incision into bedrock. When the community began to grapple with how to represent this process mathematically, several different ideas emerged. Some were based on the assumption that sediment transport is the limiting factor; others assumed that hydraulic stress on rock is the key, while still others treated rivers as first-order 'reactors.' Thanks in part to advances in digital topography and numerical computing, the predictions of these models can be tested using natural-experiment case studies. Examples from the King Range, USA, the Central Apennines, Italy, and the fold-thrust belt of Taiwan, illustrate that independent knowledge of history and/or tectonics makes it possible to quantify how the rivers have responded to external forcing. Some interesting surprises emerge, such as: that the relief-uplift relationship can be highly nonlinear in a steady-state landscape because of grain-entrainment thresholds; that transient landscapes are better than steady state cases for discriminating between models; and that an important part of the job for some rivers is unearthing their valleys after a major event such as an earthquake fills them up. These examples suggest that the 'the simplest possible model' isn't always the one that our intuition expects. A second example concerns hillslope evolution. Laboratory experiments, field measurements, and the- ory make it clear that, as with rivers, the evolution of hillslopes can involve a strongly nonlinear relationship between relief and erosion rate. Models of particle transport suggest that this nonlinearity can arise from increasingly long-distance particle motions as the gradient increases. One current challenge, therefore, is understanding the dynamics of steep, rocky hillslopes. Among the best natural laboratories for studying such hillslopes are normal-fault facets. These features are a bit like time machines: the higher you go, the longer the surface has been exposed to erosion. A simple mathematical model of facet evolution predicts that the slope of the facet is set by the ratio of erosion rate to fault slip rate. Applying this concept to a case study in Italy where the slip rate is known leads to the startling conclusion that the average hillslope erosion rates over the past ~100 ky is about 20 times faster than the Holocene rate. Thus, facet analysis seems to provide a method for documenting hillslope erosion rates and their variation with climate. As the quest continues, there are surely more fascinating surprises in store.

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.

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

Research on the time-temperature-damage superposition principle of NEPE propellant

NASA Astrophysics Data System (ADS)

Han, Long; Chen, Xiong; Xu, Jin-sheng; Zhou, Chang-sheng; Yu, Jia-quan

2015-11-01

To describe the relaxation behavior of NEPE (Nitrate Ester Plasticized Polyether) propellant, we analyzed the equivalent relationships between time, temperature, and damage. We conducted a series of uniaxial tensile tests and employed a cumulative damage model to calculate the damage values for relaxation tests at different strain levels. The damage evolution curve of the tensile test at 100 mm/min was obtained through numerical analysis. Relaxation tests were conducted over a range of temperature and strain levels, and the equivalent relationship between time, temperature, and damage was deduced based on free volume theory. The equivalent relationship was then used to generate predictions of the long-term relaxation behavior of the NEPE propellant. Subsequently, the equivalent relationship between time and damage was introduced into the linear viscoelastic model to establish a nonlinear model which is capable of describing the mechanical behavior of composite propellants under a uniaxial tensile load. The comparison between model prediction and experimental data shows that the presented model provides a reliable forecast of the mechanical behavior of propellants.

Intermittency Statistics in the Expanding Solar Wind

NASA Astrophysics Data System (ADS)

Cuesta, M. E.; Parashar, T. N.; Matthaeus, W. H.

2017-12-01

The solar wind is observed to be turbulent. One of the open questions in solar wind research is how the turbulence evolves as the solar wind expands to great distances. Some studies have focused on evolution of the outer scale but not much has been done to understand how intermittency evolves in the expanding wind beyond 1 AU (see [1,2]). We use magnetic field data from Voyager I spacecraft from 1 to 10AU to study the evolution of statistics of magnetic discontinuities. We perform various statistical tests on these discontinuities and make connections to the physical processes occurring in the expanding wind.[1] Tsurutani, Bruce T., and Edward J. Smith. "Interplanetary discontinuities: Temporal variations and the radial gradient from 1 to 8.5 AU." Journal of Geophysical Research: Space Physics 84.A6 (1979): 2773-2787.[2] Greco, A., et al. "Evidence for nonlinear development of magnetohydrodynamic scale intermittency in the inner heliosphere." The Astrophysical Journal 749.2 (2012): 105.

4-wave dynamics in kinetic wave turbulence

NASA Astrophysics Data System (ADS)

Chibbaro, Sergio; Dematteis, Giovanni; Rondoni, Lamberto

2018-01-01

A general Hamiltonian wave system with quartic resonances is considered, in the standard kinetic limit of a continuum of weakly interacting dispersive waves with random phases. The evolution equation for the multimode characteristic function Z is obtained within an ;interaction representation; and a perturbation expansion in the small nonlinearity parameter. A frequency renormalization is performed to remove linear terms that do not appear in the 3-wave case. Feynman-Wyld diagrams are used to average over phases, leading to a first order differential evolution equation for Z. A hierarchy of equations, analogous to the Boltzmann hierarchy for low density gases is derived, which preserves in time the property of random phases and amplitudes. This amounts to a general formalism for both the N-mode and the 1-mode PDF equations for 4-wave turbulent systems, suitable for numerical simulations and for investigating intermittency. Some of the main results which are developed here in detail have been tested numerically in a recent work.

Thin layer model for nonlinear evolution of the Rayleigh-Taylor instability

NASA Astrophysics Data System (ADS)

Zhao, K. G.; Wang, L. F.; Xue, C.; Ye, W. H.; Wu, J. F.; Ding, Y. K.; Zhang, W. Y.

2018-03-01

On the basis of the thin layer approximation [Ott, Phys. Rev. Lett. 29, 1429 (1972)], a revised thin layer model for incompressible Rayleigh-Taylor instability has been developed to describe the deformation and nonlinear evolution of the perturbed interface. The differential equations for motion are obtained by analyzing the forces (the gravity and pressure difference) of fluid elements (i.e., Newton's second law). The positions of the perturbed interface are obtained from the numerical solution of the motion equations. For the case of vacuum on both sides of the layer, the positions of the upper and lower interfaces obtained from the revised thin layer approximation agree with that from the weakly nonlinear (WN) model of a finite-thickness fluid layer [Wang et al., Phys. Plasmas 21, 122710 (2014)]. For the case considering the fluids on both sides of the layer, the bubble-spike amplitude from the revised thin layer model agrees with that from the WN model [Wang et al., Phys. Plasmas 17, 052305 (2010)] and the expanded Layzer's theory [Goncharov, Phys. Rev. Lett. 88, 134502 (2002)] in the early nonlinear growth regime. Note that the revised thin layer model can be applied to investigate the perturbation growth at arbitrary Atwood numbers. In addition, the large deformation (the large perturbed amplitude and the arbitrary perturbed distributions) in the initial stage can also be described by the present model.

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.

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.

Orbit-based analysis of nonlinear energetic ion dynamics in tokamaks. II. Mechanisms for rapid chirping and convective amplification

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

Bierwage, Andreas; Shinohara, Kouji

2016-04-15

The nonlinear interactions between shear Alfvén modes and tangentially injected beam ions in the 150–400 keV range are studied numerically in realistic geometry for a JT-60U tokamak scenario. In Paper I, which was reported in the companion paper, the recently developed orbit-based resonance analysis method was used to track the resonant frequency of fast ions during their nonlinear evolution subject to large magnetic and electric drifts. Here, that method is applied to map the wave-particle power transfer from the canonical guiding center phase space into the frequency-radius plane, where it can be directly compared with the evolution of the fluctuation spectramore » of fast-ion-driven modes. Using this technique, we study the nonlinear dynamics of strongly driven shear Alfvén modes with low toroidal mode numbers n = 1 and n = 3. In the n = 3 case, both chirping and convective amplification can be attributed to the mode following the resonant frequency of the radially displaced particles, i.e., the usual one-dimensional phase locking process. In the n = 1 case, a new chirping mechanism is found, which involves multiple dimensions, namely, wave-particle trapping in the radial direction and phase mixing across velocity coordinates.« less

Nonlinearities of heart rate variability in animal models of impaired cardiac control: contribution of different time scales.

PubMed

Silva, Luiz Eduardo Virgilio; Lataro, Renata Maria; Castania, Jaci Airton; Silva, Carlos Alberto Aguiar; Salgado, Helio Cesar; Fazan, Rubens; Porta, Alberto

2017-08-01

Heart rate variability (HRV) has been extensively explored by traditional linear approaches (e.g., spectral analysis); however, several studies have pointed to the presence of nonlinear features in HRV, suggesting that linear tools might fail to account for the complexity of the HRV dynamics. Even though the prevalent notion is that HRV is nonlinear, the actual presence of nonlinear features is rarely verified. In this study, the presence of nonlinear dynamics was checked as a function of time scales in three experimental models of rats with different impairment of the cardiac control: namely, rats with heart failure (HF), spontaneously hypertensive rats (SHRs), and sinoaortic denervated (SAD) rats. Multiscale entropy (MSE) and refined MSE (RMSE) were chosen as the discriminating statistic for the surrogate test utilized to detect nonlinearity. Nonlinear dynamics is less present in HF animals at both short and long time scales compared with controls. A similar finding was found in SHR only at short time scales. SAD increased the presence of nonlinear dynamics exclusively at short time scales. Those findings suggest that a working baroreflex contributes to linearize HRV and to reduce the likelihood to observe nonlinear components of the cardiac control at short time scales. In addition, an increased sympathetic modulation seems to be a source of nonlinear dynamics at long time scales. Testing nonlinear dynamics as a function of the time scales can provide a characterization of the cardiac control complementary to more traditional markers in time, frequency, and information domains. NEW & NOTEWORTHY Although heart rate variability (HRV) dynamics is widely assumed to be nonlinear, nonlinearity tests are rarely used to check this hypothesis. By adopting multiscale entropy (MSE) and refined MSE (RMSE) as the discriminating statistic for the nonlinearity test, we show that nonlinear dynamics varies with time scale and the type of cardiac dysfunction. Moreover, as complexity metrics and nonlinearities provide complementary information, we strongly recommend using the test for nonlinearity as an additional index to characterize HRV. Copyright © 2017 the American Physiological Society.

Experimental investigation of acoustic streaming in a cylindrical wave guide up to high streaming Reynolds numbers.

PubMed

Reyt, Ida; Bailliet, Hélène; Valière, Jean-Christophe

2014-01-01

Measurements of streaming velocity are performed by means of Laser Doppler Velocimetry and Particle Image Velociimetry in an experimental apparatus consisting of a cylindrical waveguide having one loudspeaker at each end for high intensity sound levels. The case of high nonlinear Reynolds number ReNL is particularly investigated. The variation of axial streaming velocity with respect to the axial and to the transverse coordinates are compared to available Rayleigh streaming theory. As expected, the measured streaming velocity agrees well with the Rayleigh streaming theory for small ReNL but deviates significantly from such predictions for high ReNL. When the nonlinear Reynolds number is increased, the outer centerline axial streaming velocity gets distorted towards the acoustic velocity nodes until counter-rotating additional vortices are generated near the acoustic velocity antinodes. This kind of behavior is followed by outer streaming cells only and measurements in the near wall region show that inner streaming vortices are less affected by this substantial evolution of fast streaming pattern. Measurements of the transient evolution of streaming velocity provide an additional insight into the evolution of fast streaming.

Supercomputations and big-data analysis in strong-field ultrafast optical physics: filamentation of high-peak-power ultrashort laser pulses

NASA Astrophysics Data System (ADS)

Voronin, A. A.; Panchenko, V. Ya; Zheltikov, A. M.

2016-06-01

High-intensity ultrashort laser pulses propagating in gas media or in condensed matter undergo complex nonlinear spatiotemporal evolution where temporal transformations of optical field waveforms are strongly coupled to an intricate beam dynamics and ultrafast field-induced ionization processes. At the level of laser peak powers orders of magnitude above the critical power of self-focusing, the beam exhibits modulation instabilities, producing random field hot spots and breaking up into multiple noise-seeded filaments. This problem is described by a (3  +  1)-dimensional nonlinear field evolution equation, which needs to be solved jointly with the equation for ultrafast ionization of a medium. Analysis of this problem, which is equivalent to solving a billion-dimensional evolution problem, is only possible by means of supercomputer simulations augmented with coordinated big-data processing of large volumes of information acquired through theory-guiding experiments and supercomputations. Here, we review the main challenges of supercomputations and big-data processing encountered in strong-field ultrafast optical physics and discuss strategies to confront these challenges.

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.

Weakly Nonlinear Model with Exact Coefficients for the Fluttering and Spiraling Motion of Buoyancy-Driven Bodies

NASA Astrophysics Data System (ADS)

Tchoufag, Joël; Fabre, David; Magnaudet, Jacques

2015-09-01

Gravity- or buoyancy-driven bodies moving in a slightly viscous fluid frequently follow fluttering or helical paths. Current models of such systems are largely empirical and fail to predict several of the key features of their evolution, especially close to the onset of path instability. Here, using a weakly nonlinear expansion of the full set of governing equations, we present a new generic reduced-order model based on a pair of amplitude equations with exact coefficients that drive the evolution of the first pair of unstable modes. We show that the predictions of this model for the style (e.g., fluttering or spiraling) and characteristics (e.g., frequency and maximum inclination angle) of path oscillations compare well with various recent data for both solid disks and air bubbles.

A weakly nonlinear model with exact coefficients for the fluttering and spiraling motions of buoyancy-driven bodies

NASA Astrophysics Data System (ADS)

Magnaudet, Jacques; Tchoufag, Joel; Fabre, David

2015-11-01

Gravity/buoyancy-driven bodies moving in a slightly viscous fluid frequently follow fluttering or helical paths. Current models of such systems are largely empirical and fail to predict several of the key features of their evolution, especially close to the onset of path instability. Using a weakly nonlinear expansion of the full set of governing equations, we derive a new generic reduced-order model of this class of phenomena based on a pair of amplitude equations with exact coefficients that drive the evolution of the first pair of unstable modes. We show that the predictions of this model for the style (eg. fluttering or spiraling) and characteristics (eg. frequency and maximum inclination angle) of path oscillations compare well with various recent data for both solid disks and air bubbles.

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.

Optimal Control of Evolution Mixed Variational Inclusions

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

Alduncin, Gonzalo, E-mail: alduncin@geofisica.unam.mx

2013-12-15

Optimal control problems of primal and dual evolution mixed variational inclusions, in reflexive Banach spaces, are studied. The solvability analysis of the mixed state systems is established via duality principles. The optimality analysis is performed in terms of perturbation conjugate duality methods, and proximation penalty-duality algorithms to mixed optimality conditions are further presented. Applications to nonlinear diffusion constrained problems as well as quasistatic elastoviscoplastic bilateral contact problems exemplify the theory.

A Two Species Bump-On-Tail Model With Relaxation for Energetic Particle Driven Modes

NASA Astrophysics Data System (ADS)

Aslanyan, V.; Porkolab, M.; Sharapov, S. E.; Spong, D. A.

2017-10-01

Energetic particle driven Alfvén Eigenmodes (AEs) observed in present day experiments exhibit various nonlinear behaviours varying from steady state amplitude at a fixed frequency to bursting amplitudes and sweeping frequency. Using the appropriate action-angle variables, the problem of resonant wave-particle interaction becomes effectively one-dimensional. Previously, a simple one-dimensional Bump-On-Tail (BOT) model has proven to be one of the most effective in describing characteristic nonlinear near-threshold wave evolution scenarios. In particular, dynamical friction causes bursting mode evolution, while diffusive relaxation may give steady-state, periodic or chaotic mode evolution. BOT has now been extended to include two populations of fast particles, with one dominated by dynamical friction at the resonance and the other by diffusion; the relative size of the populations determines the temporal evolution of the resulting wave. This suggests an explanation for recent observations on the TJ-II stellarator, where a transition between steady state and bursting occured as the magnetic configuration varied. The two species model is then applied to burning plasma with drag-dominated alpha particles and diffusion-dominated ICRH accelerated minority ions. This work was supported by the US DoE and the RCUK Energy Programme [Grant Number EP/P012450/1].

Optimization of Straight Cylindrical Turning Using Artificial Bee Colony (ABC) Algorithm

NASA Astrophysics Data System (ADS)

Prasanth, Rajanampalli Seshasai Srinivasa; Hans Raj, Kandikonda

2017-04-01

Artificial bee colony (ABC) algorithm, that mimics the intelligent foraging behavior of honey bees, is increasingly gaining acceptance in the field of process optimization, as it is capable of handling nonlinearity, complexity and uncertainty. Straight cylindrical turning is a complex and nonlinear machining process which involves the selection of appropriate cutting parameters that affect the quality of the workpiece. This paper presents the estimation of optimal cutting parameters of the straight cylindrical turning process using the ABC algorithm. The ABC algorithm is first tested on four benchmark problems of numerical optimization and its performance is compared with genetic algorithm (GA) and ant colony optimization (ACO) algorithm. Results indicate that, the rate of convergence of ABC algorithm is better than GA and ACO. Then, the ABC algorithm is used to predict optimal cutting parameters such as cutting speed, feed rate, depth of cut and tool nose radius to achieve good surface finish. Results indicate that, the ABC algorithm estimated a comparable surface finish when compared with real coded genetic algorithm and differential evolution algorithm.

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.

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

Propagation of hypergeometric Gaussian beams in strongly nonlocal nonlinear media

NASA Astrophysics Data System (ADS)

Tang, Bin; Bian, Lirong; Zhou, Xin; Chen, Kai

2018-01-01

Optical vortex beams have attracted lots of interest due to its potential application in image processing, optical trapping and optical communications, etc. In this work, we theoretically and numerically investigated the propagation properties of hypergeometric Gaussian (HyGG) beams in strongly nonlocal nonlinear media. Based on the Snyder-Mitchell model, analytical expressions for propagation of the HyGG beams in strongly nonlocal nonlinear media were obtained. The influence of input power and optical parameters on the evolutions of the beam width and radius of curvature is illustrated, respectively. The results show that the beam width and radius of curvature of the HyGG beams remain invariant, like a soliton when the input power is equal to the critical power. Otherwise, it varies periodically like a breather, which is the result of competition between the beam diffraction and nonlinearity of the medium.

Measurement Model Nonlinearity in Estimation of Dynamical Systems

NASA Astrophysics Data System (ADS)

Majji, Manoranjan; Junkins, J. L.; Turner, J. D.

2012-06-01

The role of nonlinearity of the measurement model and its interactions with the uncertainty of measurements and geometry of the problem is studied in this paper. An examination of the transformations of the probability density function in various coordinate systems is presented for several astrodynamics applications. Smooth and analytic nonlinear functions are considered for the studies on the exact transformation of uncertainty. Special emphasis is given to understanding the role of change of variables in the calculus of random variables. The transformation of probability density functions through mappings is shown to provide insight in to understanding the evolution of uncertainty in nonlinear systems. Examples are presented to highlight salient aspects of the discussion. A sequential orbit determination problem is analyzed, where the transformation formula provides useful insights for making the choice of coordinates for estimation of dynamic systems.

Evolution Nonlinear Diffusion-Convection PDE Models for Spectrogram Enhancement

NASA Astrophysics Data System (ADS)

Dugnol, B.; Fernández, C.; Galiano, G.; Velasco, J.

2008-09-01

In previous works we studied the application of PDE-based image processing techniques applied to the spectrogram of audio signals in order to improve the readability of the signal. In particular we considered the implementation of the nonlinear diffusive model proposed by Álvarez, Lions and Morel [1](ALM) combined with a convective term inspired by the differential reassignment proposed by Chassandre-Mottin, Daubechies, Auger and Flandrin [2]-[3]. In this work we consider the possibility of replacing the diffusive model of ALM by diffusive terms in divergence form. In particular we implement finite element approximations of nonlinear diffusive terms studied by Chen, Levine, Rao [4] and Antontsev, Shmarev [5]-[8] with a convective term.

A conformal approach for the analysis of the non-linear stability of radiation cosmologies

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

Luebbe, Christian, E-mail: c.luebbe@ucl.ac.uk; Department of Mathematics, University of Leicester, University Road, LE1 8RH; Valiente Kroon, Juan Antonio, E-mail: j.a.valiente-kroon@qmul.ac.uk

2013-01-15

The conformal Einstein equations for a trace-free (radiation) perfect fluid are derived in terms of the Levi-Civita connection of a conformally rescaled metric. These equations are used to provide a non-linear stability result for de Sitter-like trace-free (radiation) perfect fluid Friedman-Lemaitre-Robertson-Walker cosmological models. The solutions thus obtained exist globally towards the future and are future geodesically complete. - Highlights: Black-Right-Pointing-Pointer We study the Einstein-Euler system in General Relativity using conformal methods. Black-Right-Pointing-Pointer We analyze the structural properties of the associated evolution equations. Black-Right-Pointing-Pointer We establish the non-linear stability of pure radiation cosmological models.

3D simulation for solitons used in optical fibers

NASA Astrophysics Data System (ADS)

Vasile, F.; Tebeica, C. M.; Schiopu, P.; Vladescu, M.

2016-12-01

In this paper is described 3D simulation for solitions used in optical fibers. In the scientific works is started from nonlinear propagation equation and the solitons represents its solutions. This paper presents the simulation of the fundamental soliton in 3D together with simulation of the second order soliton in 3D. These simulations help in the study of the optical fibers for long distances and in the interactions between the solitons. This study helps the understanding of the nonlinear propagation equation and for nonlinear waves. These 3D simulations are obtained using MATLAB programming language, and we can observe fundamental difference between the soliton and the second order/higher order soliton and in their evolution.

Reconstructing the primordial spectrum of fluctuations of the universe from the observed nonlinear clustering of galaxies

NASA Technical Reports Server (NTRS)

Hamilton, A. J. S.; Matthews, Alex; Kumar, P.; Lu, Edward

1991-01-01

It was discovered that the nonlinear evolution of the two point correlation function in N-body experiments of galaxy clustering with Omega = 1 appears to be described to good approximation by a simple general formula. The underlying form of the formula is physically motivated, but its detailed representation is obtained empirically by fitting to N-body experiments. In this paper, the formula is presented along with an inverse formula which converts a final, nonlinear correlation function into the initial linear correlation function. The inverse formula is applied to observational data from the CfA, IRAs, and APM galaxy surveys, and the initial spectrum of fluctuations of the universe, if Omega = 1.

Nonequilibrium Precondensation of Classical Waves in Two Dimensions Propagating through Atomic Vapors

NASA Astrophysics Data System (ADS)

Šantić, Neven; Fusaro, Adrien; Salem, Sabeur; Garnier, Josselin; Picozzi, Antonio; Kaiser, Robin

2018-02-01

The nonlinear Schrödinger equation, used to describe the dynamics of quantum fluids, is known to be valid not only for massive particles but also for the propagation of light in a nonlinear medium, predicting condensation of classical waves. Here we report on the initial evolution of random waves with Gaussian statistics using atomic vapors as an efficient two dimensional nonlinear medium. Experimental and theoretical analysis of near field images reveal a phenomenon of nonequilibrium precondensation, characterized by a fast relaxation towards a precondensate fraction of up to 75%. Such precondensation is in contrast to complete thermalization to the Rayleigh-Jeans equilibrium distribution, requiring prohibitive long interaction lengths.

Vortex-soliton complexes in coupled nonlinear Schrödinger equations with unequal dispersion coefficients.

PubMed

Charalampidis, E G; Kevrekidis, P G; Frantzeskakis, D J; Malomed, B A

2016-08-01

We consider a two-component, two-dimensional nonlinear Schrödinger system with unequal dispersion coefficients and self-defocusing nonlinearities, chiefly with equal strengths of the self- and cross-interactions. In this setting, a natural waveform with a nonvanishing background in one component is a vortex, which induces an effective potential well in the second component, via the nonlinear coupling of the two components. We show that the potential well may support not only the fundamental bound state, but also multiring excited radial state complexes for suitable ranges of values of the dispersion coefficient of the second component. We systematically explore the existence, stability, and nonlinear dynamics of these states. The complexes involving the excited radial states are weakly unstable, with a growth rate depending on the dispersion of the second component. Their evolution leads to transformation of the multiring complexes into stable vortex-bright solitons ones with the fundamental state in the second component. The excited states may be stabilized by a harmonic-oscillator trapping potential, as well as by unequal strengths of the self- and cross-repulsive nonlinearities.

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.

Finite-amplitude strain waves in laser-excited plates.

PubMed

Mirzade, F Kh

2008-07-09

The governing equations for two-dimensional finite-amplitude longitudinal strain waves in isotropic laser-excited solid plates are derived. Geometric and weak material nonlinearities are included, and the interaction of longitudinal displacements with the field of concentration of non-equilibrium laser-generated atomic defects is taken into account. An asymptotic approach is used to show that the equations are reducible to the Kadomtsev-Petviashvili-Burgers nonlinear evolution equation for a longitudinal self-consistent strain field. It is shown that two-dimensional shock waves can propagate in plates.

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

Quantum morphogenesis: A variation on Thom's catastrophe theory

NASA Astrophysics Data System (ADS)

Aerts, Dirk; Czachor, Marek; Gabora, Liane; Kuna, Maciej; Posiewnik, Andrzej; Pykacz, Jarosław; Syty, Monika

2003-05-01

Noncommutative propositions are characteristic of both quantum and nonquantum (sociological, biological, and psychological) situations. In a Hilbert space model, states, understood as correlations between all the possible propositions, are represented by density matrices. If systems in question interact via feedback with environment, their dynamics is nonlinear. Nonlinear evolutions of density matrices lead to the phenomenon of morphogenesis that may occur in noncommutative systems. Several explicit exactly solvable models are presented, including “birth and death of an organism” and “development of complementary properties.”

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.

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.

Real-Time Onboard Global Nonlinear Aerodynamic Modeling from Flight Data

NASA Technical Reports Server (NTRS)

Brandon, Jay M.; Morelli, Eugene A.

2014-01-01

Flight test and modeling techniques were developed to accurately identify global nonlinear aerodynamic models onboard an aircraft. The techniques were developed and demonstrated during piloted flight testing of an Aermacchi MB-326M Impala jet aircraft. Advanced piloting techniques and nonlinear modeling techniques based on fuzzy logic and multivariate orthogonal function methods were implemented with efficient onboard calculations and flight operations to achieve real-time maneuver monitoring and analysis, and near-real-time global nonlinear aerodynamic modeling and prediction validation testing in flight. Results demonstrated that global nonlinear aerodynamic models for a large portion of the flight envelope were identified rapidly and accurately using piloted flight test maneuvers during a single flight, with the final identified and validated models available before the aircraft landed.

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

Appraisal of jump distributions in ensemble-based sampling algorithms

NASA Astrophysics Data System (ADS)

Dejanic, Sanda; Scheidegger, Andreas; Rieckermann, Jörg; Albert, Carlo

2017-04-01

Sampling Bayesian posteriors of model parameters is often required for making model-based probabilistic predictions. For complex environmental models, standard Monte Carlo Markov Chain (MCMC) methods are often infeasible because they require too many sequential model runs. Therefore, we focused on ensemble methods that use many Markov chains in parallel, since they can be run on modern cluster architectures. Little is known about how to choose the best performing sampler, for a given application. A poor choice can lead to an inappropriate representation of posterior knowledge. We assessed two different jump moves, the stretch and the differential evolution move, underlying, respectively, the software packages EMCEE and DREAM, which are popular in different scientific communities. For the assessment, we used analytical posteriors with features as they often occur in real posteriors, namely high dimensionality, strong non-linear correlations or multimodality. For posteriors with non-linear features, standard convergence diagnostics based on sample means can be insufficient. Therefore, we resorted to an entropy-based convergence measure. We assessed the samplers by means of their convergence speed, robustness and effective sample sizes. For posteriors with strongly non-linear features, we found that the stretch move outperforms the differential evolution move, w.r.t. all three aspects.

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

Emergence, evolution, and control of multistability in a hybrid topological quantum/classical system.

PubMed

Wang, Guanglei; Xu, Hongya; Lai, Ying-Cheng

2018-03-01

We present a novel class of nonlinear dynamical systems-a hybrid of relativistic quantum and classical systems and demonstrate that multistability is ubiquitous. A representative setting is coupled systems of a topological insulator and an insulating ferromagnet, where the former possesses an insulating bulk with topologically protected, dissipationless, and conducting surface electronic states governed by the relativistic quantum Dirac Hamiltonian and the latter is described by the nonlinear classical evolution of its magnetization vector. The interactions between the two are essentially the spin transfer torque from the topological insulator to the ferromagnet and the local proximity induced exchange coupling in the opposite direction. The hybrid system exhibits a rich variety of nonlinear dynamical phenomena besides multistability such as bifurcations, chaos, and phase synchronization. The degree of multistability can be controlled by an external voltage. In the case of two coexisting states, the system is effectively binary, opening a door to exploitation for developing spintronic memory devices. Because of the dissipationless and spin-momentum locking nature of the surface currents of the topological insulator, little power is needed for generating a significant current, making the system appealing for potential applications in next generation of low power memory devices.

Emergence, evolution, and control of multistability in a hybrid topological quantum/classical system

NASA Astrophysics Data System (ADS)

Wang, Guanglei; Xu, Hongya; Lai, Ying-Cheng

2018-03-01

We present a novel class of nonlinear dynamical systems—a hybrid of relativistic quantum and classical systems and demonstrate that multistability is ubiquitous. A representative setting is coupled systems of a topological insulator and an insulating ferromagnet, where the former possesses an insulating bulk with topologically protected, dissipationless, and conducting surface electronic states governed by the relativistic quantum Dirac Hamiltonian and the latter is described by the nonlinear classical evolution of its magnetization vector. The interactions between the two are essentially the spin transfer torque from the topological insulator to the ferromagnet and the local proximity induced exchange coupling in the opposite direction. The hybrid system exhibits a rich variety of nonlinear dynamical phenomena besides multistability such as bifurcations, chaos, and phase synchronization. The degree of multistability can be controlled by an external voltage. In the case of two coexisting states, the system is effectively binary, opening a door to exploitation for developing spintronic memory devices. Because of the dissipationless and spin-momentum locking nature of the surface currents of the topological insulator, little power is needed for generating a significant current, making the system appealing for potential applications in next generation of low power memory devices.

Steady induction effects in geomagnetism. Part 1B: Geomagnetic estimation of steady surficial core motions: A non-linear inverse problem

NASA Technical Reports Server (NTRS)

Voorhies, Coerte V.

1993-01-01

The problem of estimating a steady fluid velocity field near the top of Earth's core which induces the secular variation (SV) indicated by models of the observed geomagnetic field is examined in the source-free mantle/frozen-flux core (SFI/VFFC) approximation. This inverse problem is non-linear because solutions of the forward problem are deterministically chaotic. The SFM/FFC approximation is inexact, and neither the models nor the observations they represent are either complete or perfect. A method is developed for solving the non-linear inverse motional induction problem posed by the hypothesis of (piecewise, statistically) steady core surface flow and the supposition of a complete initial geomagnetic condition. The method features iterative solution of the weighted, linearized least-squares problem and admits optional biases favoring surficially geostrophic flow and/or spatially simple flow. Two types of weights are advanced radial field weights for fitting the evolution of the broad-scale portion of the radial field component near Earth's surface implied by the models, and generalized weights for fitting the evolution of the broad-scale portion of the scalar potential specified by the models.

Using genetic algorithms to determine near-optimal pricing, investment and operating strategies in the electric power industry

NASA Astrophysics Data System (ADS)

Wu, Dongjun

Network industries have technologies characterized by a spatial hierarchy, the "network," with capital-intensive interconnections and time-dependent, capacity-limited flows of products and services through the network to customers. This dissertation studies service pricing, investment and business operating strategies for the electric power network. First-best solutions for a variety of pricing and investment problems have been studied. The evaluation of genetic algorithms (GA, which are methods based on the idea of natural evolution) as a primary means of solving complicated network problems, both w.r.t. pricing: as well as w.r.t. investment and other operating decisions, has been conducted. New constraint-handling techniques in GAs have been studied and tested. The actual application of such constraint-handling techniques in solving practical non-linear optimization problems has been tested on several complex network design problems with encouraging initial results. Genetic algorithms provide solutions that are feasible and close to optimal when the optimal solution is know; in some instances, the near-optimal solutions for small problems by the proposed GA approach can only be tested by pushing the limits of currently available non-linear optimization software. The performance is far better than several commercially available GA programs, which are generally inadequate in solving any of the problems studied in this dissertation, primarily because of their poor handling of constraints. Genetic algorithms, if carefully designed, seem very promising in solving difficult problems which are intractable by traditional analytic methods.

Nonlinear oscillations and waves in multi-species cold plasmas

NASA Astrophysics Data System (ADS)

Verma, Prabal Singh

2016-12-01

The spatio-temporal evolution of nonlinear oscillations in multi-species plasma is revisited to provide more insight into the physics of phase mixing by constructing two sets of nonlinear solutions up to the second order. The first solution exhibits perfect oscillations in the linear regime and phase mixing appears only nonlinearly in the second order as a response to the ponderomotive forces. This response can be both direct and indirect. The indirect contribution of the ponderomotive forces appears through self-consistently generated low frequency fields. Furthermore, the direct and indirect contributions of the ponderomotive forces on the phase mixing process is explored and it is found that the indirect contribution is negligible in an electron-ion plasma and it disappears in the case of electron-positron plasma, yet represents an equal contribution in the electron-positron-ion plasma. However, the second solution does not exhibit any phase mixing due to the absence of ponderomotive forces but results in an undistorted nonlinear traveling wave. These investigations have relevance for laboratory/astrophysical multi-species plasma.

Linear and Nonlinear Coupling of Electrostatic Drift and Acoustic Perturbations in a Nonuniform Bi-Ion Plasma with Non-Maxwellian Electrons

NASA Astrophysics Data System (ADS)

Ali, Gul-e.; Ahmad, Ali; Masood, W.; Mirza, Arshad M.

2017-12-01

Linear and nonlinear coupling of drift and ion acoustic waves are studied in a nonuniform magnetized plasma comprising of Oxygen and Hydrogen ions with nonthermal distribution of electrons. It has been observed that different ratios of ion number densities and kappa and Cairns distributed electrons significantly modify the linear dispersion characteristics of coupled drift-ion acoustic waves. In the nonlinear regime, KdV (for pure drift waves) and KP (for coupled drift-ion acoustic waves) like equations have been derived to study the nonlinear evolution of drift solitary waves in one and two dimensions. The dependence of drift solitary structures on different ratios of ion number densities and nonthermal distribution of electrons has also been explored in detail. It has been found that the ratio of the diamagnetic drift velocity to the velocity of the nonlinear structure determines the existence regimes for the drift solitary waves. The present investigation may be beneficial to understand the formation of solitons in the ionospheric F-region.

An Efficient Numerical Approach for Nonlinear Fokker-Planck equations

NASA Astrophysics Data System (ADS)

Otten, Dustin; Vedula, Prakash

2009-03-01

Fokker-Planck equations which are nonlinear with respect to their probability densities that occur in many nonequilibrium systems relevant to mean field interaction models, plasmas, classical fermions and bosons can be challenging to solve numerically. To address some underlying challenges in obtaining numerical solutions, we propose a quadrature based moment method for efficient and accurate determination of transient (and stationary) solutions of nonlinear Fokker-Planck equations. In this approach the distribution function is represented as a collection of Dirac delta functions with corresponding quadrature weights and locations, that are in turn determined from constraints based on evolution of generalized moments. Properties of the distribution function can be obtained by solution of transport equations for quadrature weights and locations. We will apply this computational approach to study a wide range of problems, including the Desai-Zwanzig Model (for nonlinear muscular contraction) and multivariate nonlinear Fokker-Planck equations describing classical fermions and bosons, and will also demonstrate good agreement with results obtained from Monte Carlo and other standard numerical methods.

Gaussian variational ansatz in the problem of anomalous sea waves: Comparison with direct numerical simulation

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

Ruban, V. P., E-mail: ruban@itp.ac.ru

2015-05-15

The nonlinear dynamics of an obliquely oriented wave packet on a sea surface is analyzed analytically and numerically for various initial parameters of the packet in relation to the problem of the so-called rogue waves. Within the Gaussian variational ansatz applied to the corresponding (1+2)-dimensional hyperbolic nonlinear Schrödinger equation (NLSE), a simplified Lagrangian system of differential equations is derived that describes the evolution of the coefficients of the real and imaginary quadratic forms appearing in the Gaussian. This model provides a semi-quantitative description of the process of nonlinear spatiotemporal focusing, which is one of the most probable mechanisms of roguemore » wave formation in random wave fields. The system of equations is integrated in quadratures, which allows one to better understand the qualitative differences between linear and nonlinear focusing regimes of a wave packet. Predictions of the Gaussian model are compared with the results of direct numerical simulation of fully nonlinear long-crested waves.« less

Multi-fluid Approach to High-frequency Waves in Plasmas. III. Nonlinear Regime and Plasma Heating

NASA Astrophysics Data System (ADS)

Martínez-Gómez, David; Soler, Roberto; Terradas, Jaume

2018-03-01

The multi-fluid modeling of high-frequency waves in partially ionized plasmas has shown that the behavior of magnetohydrodynamic waves in the linear regime is heavily influenced by the collisional interaction between the different species that form the plasma. Here, we go beyond linear theory and study large-amplitude waves in partially ionized plasmas using a nonlinear multi-fluid code. It is known that in fully ionized plasmas, nonlinear Alfvén waves generate density and pressure perturbations. Those nonlinear effects are more pronounced for standing oscillations than for propagating waves. By means of numerical simulations and analytical approximations, we examine how the collisional interaction between ions and neutrals affects the nonlinear evolution. The friction due to collisions dissipates a fraction of the wave energy, which is transformed into heat and consequently raises the temperature of the plasma. As an application, we investigate frictional heating in a plasma with physical conditions akin to those in a quiescent solar prominence.

Towards homoscedastic nonlinear cointegration for structural health monitoring

NASA Astrophysics Data System (ADS)

Zolna, Konrad; Dao, Phong B.; Staszewski, Wieslaw J.; Barszcz, Tomasz

2016-06-01

The paper presents the homoscedastic nonlinear cointegration. The method leads to stable variances in nonlinear cointegration residuals. The adapted Breusch-Pagan test procedure is developed to test for the presence of heteroscedasticity (or homoscedasticity) in the cointegration residuals obtained from the nonlinear cointegration analysis. Three different time series - i.e. one with a nonlinear quadratic deterministic trend, simulated vibration data and experimental wind turbine data - are used to illustrate the application of the proposed method. The proposed approach can be used for effective removal of nonlinear trends from various types of data and for reliable structural damage detection based on data that are corrupted by environmental and/or operational nonlinear trends.

Structure of multiphoton quantum optics. II. Bipartite systems, physical processes, and heterodyne squeezed states

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

Dell'Anno, Fabio; De Siena, Silvio; Illuminati, Fabrizio

2004-03-01

Extending the scheme developed for a single mode of the electromagnetic field in the preceding paper [F. Dell'Anno, S. De Siena, and F. Illuminati, Phys. Rev. A 69, 033812 (2004)], we introduce two-mode nonlinear canonical transformations depending on two heterodyne mixing angles. They are defined in terms of Hermitian nonlinear functions that realize heterodyne superpositions of conjugate quadratures of bipartite systems. The canonical transformations diagonalize a class of Hamiltonians describing nondegenerate and degenerate multiphoton processes. We determine the coherent states associated with the canonical transformations, which generalize the nondegenerate two-photon squeezed states. Such heterodyne multiphoton squeezed states are defined asmore » the simultaneous eigenstates of the transformed, coupled annihilation operators. They are generated by nonlinear unitary evolutions acting on two-mode squeezed states. They are non-Gaussian, highly nonclassical, entangled states. For a quadratic nonlinearity the heterodyne multiphoton squeezed states define two-mode cubic phase states. The statistical properties of these states can be widely adjusted by tuning the heterodyne mixing angles, the phases of the nonlinear couplings, as well as the strength of the nonlinearity. For quadratic nonlinearity, we study the higher-order contributions to the susceptibility in nonlinear media and we suggest possible experimental realizations of multiphoton conversion processes generating the cubic-phase heterodyne squeezed states.« less

Structure of multiphoton quantum optics. II. Bipartite systems, physical processes, and heterodyne squeezed states

NASA Astrophysics Data System (ADS)

dell'Anno, Fabio; de Siena, Silvio; Illuminati, Fabrizio

2004-03-01

Extending the scheme developed for a single mode of the electromagnetic field in the preceding paper [

Energy evolution mechanism in process of Sandstone failure and energy strength criterion

NASA Astrophysics Data System (ADS)

Wang, Yunfei; Cui, Fang

2018-07-01

To reveal the inherent relation between energy change and confining pressure during the process of sandstone damage, and its characteristics of energy storage and energy dissipation in different deformation stage. Obtaining the mechanical parameters by testing the Sandstone of two1 coal seam roof under uniaxial compression in Zhaogu coalmine, using Particle Flow Code (PFC) and fish program to get the meso-mechanical parameters, studying Sandstone energy evolution mechanism under different confining pressures, and deducing energy strength criterion based on energy principle of rock failure, some main researching results are reached as follows: with the increasing of confining pressure, the Sandstone yield stage and ductility increases, but brittleness decreases; Under higher confining pressure, the elastic strain energy of Sandstone before peak approximately keeps constant in a certain strain range, and rock absorbs all the energy which converts into surface energy required for internal damage development; Under lower confining pressure, Sandstone no longer absorbs energy with increasing strain after peak under lower confining pressure, while it sequentially absorbs energy under higher confining pressure; Under lower confining pressure, the energy Sandstone before peak absorbed mainly converts into elastic strain energy, while under higher confining pressure, dissipation energy significantly increases before peak, which indicates that the degree rock strength loss is higher under higher confining pressure; with the increasing of confining pressure, the limit of elastic strain energy increases and there exists a favourable linear variation relationship; At the peak point, the ratio of elastic strain energy to total energy of Sandstone nonlinearly decreases, while the ratio of dissipation energy to total energy nonlinearly increases with the increasing of confining pressure; According to energy evolution mechanism of rock failure, an energy strength criterion is derived. The criterion equation includes lithology constants and three principal stresses, and its physical meaning is clear. This criterion has an evident advantage than Hoek-Brown and Drucker-Prager criterion in calculation accuracy and can commendably describe rock failure characteristics.

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.

Application of Deep Learning and Supervised Learning Methods to Recognize Nonlinear Hidden Pattern in Water Stress Levels from Spatiotemporal Datasets across Rural and Urban US Counties

NASA Astrophysics Data System (ADS)

Eisenhart, T.; Josset, L.; Rising, J. A.; Devineni, N.; Lall, U.

2017-12-01

In the wake of recent water crises, the need to understand and predict the risk of water stress in urban and rural areas has grown. This understanding has the potential to improve decision making in public resource management, policy making, risk management and investment decisions. Assuming an underlying relationship between urban and rural water stress and observable features, we apply Deep Learning and Supervised Learning models to uncover hidden nonlinear patterns from spatiotemporal datasets. Results of interest includes prediction accuracy on extreme categories (i.e. urban areas highly prone to water stress) and not solely the average risk for urban or rural area, which adds complexity to the tuning of model parameters. We first label urban water stressed counties using annual water quality violations and compile a comprehensive spatiotemporal dataset that captures the yearly evolution of climatic, demographic and economic factors of more than 3,000 US counties over the 1980-2010 period. As county-level data reporting is not done on a yearly basis, we test multiple imputation methods to get around the issue of missing data. Using Python libraries, TensorFlow and scikit-learn, we apply and compare the ability of, amongst other methods, Recurrent Neural Networks (testing both LSTM and GRU cells), Convolutional Neural Networks and Support Vector Machines to predict urban water stress. We evaluate the performance of those models over multiple time spans and combine methods to diminish the risk of overfitting and increase prediction power on test sets. This methodology seeks to identify hidden nonlinear patterns to assess the predominant data features that influence urban and rural water stress. Results from this application at the national scale will assess the performance of deep learning models to predict water stress risk areas across all US counties and will highlight a predominant Machine Learning method for modeling water stress risk using spatiotemporal data.

Empirical tests of harvest-induced body-size evolution along a geographic gradient in Australian macropods.

PubMed

Prowse, Thomas A A; Correll, Rachel A; Johnson, Christopher N; Prideaux, Gavin J; Brook, Barry W

2015-01-01

Life-history theory predicts the progressive dwarfing of animal populations that are subjected to chronic mortality stress, but the evolutionary impact of harvesting terrestrial herbivores has seldom been tested. In Australia, marsupials of the genus Macropus (kangaroos and wallabies) are subjected to size-selective commercial harvesting. Mathematical modelling suggests that harvest quotas (c. 10-20% of population estimates annually) could be driving body-size evolution in these species. We tested this hypothesis for three harvested macropod species with continental-scale distributions. To do so, we measured more than 2000 macropod skulls sourced from wildlife collections spanning the last 130 years. We analysed these data using spatial Bayesian models that controlled for the age and sex of specimens as well as environmental drivers and island effects. We found no evidence for the hypothesized decline in body size for any species; rather, models that fit trend terms supported minor body size increases over time. This apparently counterintuitive result is consistent with reduced mortality due to a depauperate predator guild and increased primary productivity of grassland vegetation following European settlement in Australia. Spatial patterns in macropod body size supported the heat dissipation limit and productivity hypotheses proposed to explain geographic body-size variation (i.e. skull size increased with decreasing summer maximum temperature and increasing rainfall, respectively). There is no empirical evidence that size-selective harvesting has driven the evolution of smaller body size in Australian macropods. Bayesian models are appropriate for investigating the long-term impact of human harvesting because they can impute missing data, fit nonlinear growth models and account for non-random spatial sampling inherent in wildlife collections. © 2014 The Authors. Journal of Animal Ecology © 2014 British Ecological Society.

Simulations of coupled, Antarctic ice-ocean evolution using POP2x and BISICLES (Invited)

NASA Astrophysics Data System (ADS)

Price, S. F.; Asay-Davis, X.; Martin, D. F.; Maltrud, M. E.; Hoffman, M. J.

2013-12-01

We present initial results from Antarctic, ice-ocean coupled simulations using large-scale ocean circulation and land ice evolution models. The ocean model, POP2x is a modified version of POP, a fully eddying, global-scale ocean model (Smith and Gent, 2002). POP2x allows for circulation beneath ice shelf cavities using the method of partial top cells (Losch, 2008). Boundary layer physics, which control fresh water and salt exchange at the ice-ocean interface, are implemented following Holland and Jenkins (1999), Jenkins (1999), and Jenkins et al. (2010). Standalone POP2x output compares well with standard ice-ocean test cases (e.g., ISOMIP; Losch, 2008; Kimura et al., 2013) and with results from other idealized ice-ocean coupling test cases (e.g., Goldberg et al., 2012). The land ice model, BISICLES (Cornford et al., 2012), includes a 1st-order accurate momentum balance (L1L2) and uses block structured, adaptive-mesh refinement to more accurately model regions of dynamic complexity, such as ice streams, outlet glaciers, and grounding lines. For idealized test cases focused on marine-ice sheet dynamics, BISICLES output compares very favorably relative to simulations based on the full, nonlinear Stokes momentum balance (MISMIP-3d; Pattyn et al., 2013). Here, we present large-scale (southern ocean) simulations using POP2x with fixed ice shelf geometries, which are used to obtain and validate modeled submarine melt rates against observations. These melt rates are, in turn, used to force evolution of the BISICLES model. An offline-coupling scheme, which we compare with the ice-ocean coupling work of Goldberg et al. (2012), is then used to sequentially update the sub-shelf cavity geometry seen by POP2x.

Nonlinear evolution of the Kelvin-Helmholtz instability in the double current sheet configuration

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

Mao, Aohua; Li, Jiquan, E-mail: lijq@energy.kyoto-u.ac.jp; Kishimoto, Yasuaki

2016-03-15

The nonlinear evolution of the Kelvin-Helmholtz (KH) instability driven by a radially antisymmetric shear flow in the double current sheet configuration is numerically investigated based on a reduced magnetohydrodynamic model. Simulations reveal different nonlinear fate of the KH instability depending on the amplitude of the shear flow, which restricts the strength of the KH instability. For strong shear flows far above the KH instability threshold, the linear electrostatic-type KH instability saturates and achieves a vortex flow dominated quasi-steady state of the electromagnetic (EM) KH turbulence with large-amplitude zonal flows as well as zonal fields. The magnetic surfaces are twisted significantlymore » due to strong vortices but without the formation of magnetic islands. However, for the shear flow just over the KH instability threshold, a weak EM-type KH instability is saturated and remarkably damped by zonal flows through modifying the equilibrium shear flow. Interestingly, a secondary double tearing mode (DTM) is excited subsequently in highly damped KH turbulence, behaving as a pure DTM in a flowing plasma as described in Mao et al. [Phys. Plasmas 21, 052304 (2014)]. However, the explosive growth phenomenon is replaced by a gradually growing oscillation due to the extremely twisted islands. As a result, the release of the magnetic energy becomes slow and the global magnetic reconnection tends to be gentle. A complex nonlinear interaction between the EM KH turbulence and the DTMs occurs for the medium shear flows above the KH instability threshold, turbulent EM fluctuations experience oscillatory nonlinear growth of the DTMs, finally achieves a quasi-steady state with the interplay of the fluctuations between the DTMs and the EM KH instability.« less

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.

Predicting knee replacement damage in a simulator machine using a computational model with a consistent wear factor.

PubMed

Zhao, Dong; Sakoda, Hideyuki; Sawyer, W Gregory; Banks, Scott A; Fregly, Benjamin J

2008-02-01

Wear of ultrahigh molecular weight polyethylene remains a primary factor limiting the longevity of total knee replacements (TKRs). However, wear testing on a simulator machine is time consuming and expensive, making it impractical for iterative design purposes. The objectives of this paper were first, to evaluate whether a computational model using a wear factor consistent with the TKR material pair can predict accurate TKR damage measured in a simulator machine, and second, to investigate how choice of surface evolution method (fixed or variable step) and material model (linear or nonlinear) affect the prediction. An iterative computational damage model was constructed for a commercial knee implant in an AMTI simulator machine. The damage model combined a dynamic contact model with a surface evolution model to predict how wear plus creep progressively alter tibial insert geometry over multiple simulations. The computational framework was validated by predicting wear in a cylinder-on-plate system for which an analytical solution was derived. The implant damage model was evaluated for 5 million cycles of simulated gait using damage measurements made on the same implant in an AMTI machine. Using a pin-on-plate wear factor for the same material pair as the implant, the model predicted tibial insert wear volume to within 2% error and damage depths and areas to within 18% and 10% error, respectively. Choice of material model had little influence, while inclusion of surface evolution affected damage depth and area but not wear volume predictions. Surface evolution method was important only during the initial cycles, where variable step was needed to capture rapid geometry changes due to the creep. Overall, our results indicate that accurate TKR damage predictions can be made with a computational model using a constant wear factor obtained from pin-on-plate tests for the same material pair, and furthermore, that surface evolution method matters only during the initial "break in" period of the simulation.

Atmospheric planetary-wave response to external forcing

NASA Technical Reports Server (NTRS)

Stevens, D. E.; Reiter, E. R.

1983-01-01

A summary of the progress report is given, covering the following areas: atmospheric circulation, planetary waves, adaption of the model to the Cyber 205, continental heat flux anomalies, and nonlinear evolution of inertial instabilities in the tropics.

Evolution of the axial electron cyclotron maser instability, with applications to solar microwave spikes

NASA Technical Reports Server (NTRS)

Vlahos, Loukas; Sprangle, Phillip

1987-01-01

The nonlinear evolution of cyclotron radiation from streaming and gyrating electrons in an external magnetic field is analyzed. The nonlinear dynamics of both the fields and the particles are treated fully relativistically and self-consistently. The model includes a background plasma and electrostatic effects. The analytical and numerical results show that a substantial portion of the beam particle energy can be converted to electromagnetic wave energy at frequencies far above the electron cyclotron frequency. In general, the excited radiation can propagate parallel to the magnetic field and, hence, escape gyrothermal absorption at higher cyclotron harmonics. The high-frequency Doppler-shifted cyclotron instability can have saturation efficiencies far higher than those associated with well-known instabilities of the electron cyclotron maser type. Although the analysis is general, the possibility of using this model to explain the intense radio emission observed from the sun is explored in detail.

Dynamical systems theory for nonlinear evolution equations.

PubMed

Choudhuri, Amitava; Talukdar, B; Das, Umapada

2010-09-01

We observe that the fully nonlinear evolution equations of Rosenau and Hymann, often abbreviated as K(n,m) equations, can be reduced to Hamiltonian form only on a zero-energy hypersurface belonging to some potential function associated with the equations. We treat the resulting Hamiltonian equations by the dynamical systems theory and present a phase-space analysis of their stable points. The results of our study demonstrate that the equations can, in general, support both compacton and soliton solutions. For the K(2,2) and K(3,3) cases one type of solutions can be obtained from the other by continuously varying a parameter of the equations. This is not true for the K(3,2) equation for which the parameter can take only negative values. The K(2,3) equation does not have any stable point and, in the language of mechanics, represents a particle moving with constant acceleration.

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 new (2+1) dimensional integrable evolution equation for an ion acoustic wave in a magnetized plasma

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

Mukherjee, Abhik, E-mail: abhik.mukherjee@saha.ac.in; Janaki, M. S., E-mail: ms.janaki@saha.ac.in; Kundu, Anjan, E-mail: anjan.kundu@saha.ac.in

2015-07-15

A new, completely integrable, two dimensional evolution equation is derived for an ion acoustic wave propagating in a magnetized, collisionless plasma. The equation is a multidimensional generalization of a modulated wavepacket with weak transverse propagation, which has resemblance to nonlinear Schrödinger (NLS) equation and has a connection to Kadomtsev-Petviashvili equation through a constraint relation. Higher soliton solutions of the equation are derived through Hirota bilinearization procedure, and an exact lump solution is calculated exhibiting 2D structure. Some mathematical properties demonstrating the completely integrable nature of this equation are described. Modulational instability using nonlinear frequency correction is derived, and the correspondingmore » growth rate is calculated, which shows the directional asymmetry of the system. The discovery of this novel (2+1) dimensional integrable NLS type equation for a magnetized plasma should pave a new direction of research in the field.« less

Role of electric fields in the MHD evolution of the kink instability

DOE PAGES

Lapenta, Giovanni; Skender, Marina

2017-02-17

Here, the discovery of electrostatic fields playing a crucial role in establishing plasma motion in the flux conversion and dynamo processes in reversed field pinches is revisited. In order to further elucidate the role of the electrostatic fields, a flux rope configuration susceptible to the kink instability is numerically studied with anMHDcode. Simulated nonlinear evolution of the kink instability is found to confirm the crucial role of the electrostatic fields. Anew insight is gained on the special function of the electrostatic fields: they lead the plasma towards the reconnection site at the mode resonant surface. Without this step the plasmamore » column could not relax to its nonlinear state, since no other agent is present to perform this role. While the inductive field generated directly by the kink instability is the dominant flow driver, the electrostatic field is found to allow the motion in the vicinity of the reconnection region.« less

Nonlinear evolution of the Rayleigh-Taylor and Richtmyer-Meshkov instabilities

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

Dimonte, G

Scaled experiments on the nonlinear evolution of the Rayleigh- Taylor (RT) and Richtmyer-Meshkov (RM) instabilities are described under a variety, of conditions that occur in nature. At high Reynolds number, the mixing layer grows self-similarly - {alpha}{sub i}Agt{sup 2} for a constant acceleration (g), and as a power law t{sup {theta}{sub i}} for impulsive accelerations U{delta}(t) at low and high Mach numbers. The growth coefficients {alpha}{sub i} and {theta}{sub i} exponents are measured over a comprehensive range of Atwood numbers A. The RT instability is also investigated with Non- Newtonian materials which are independently characterized. A critical wavelength and amplitudemore » for instability is observed associated with the shear modulus and tensile yield of the material. The results are applicable from supernova explosions to geophysical flows subject to these hydrodynamic instabilities.« less

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.

Simulation of magnetic holes formation in the magnetosheath

NASA Astrophysics Data System (ADS)

Ahmadi, Narges; Germaschewski, Kai; Raeder, Joachim

2017-12-01

Magnetic holes have been frequently observed in the Earth's magnetosheath and are believed to be the consequence of the nonlinear evolution of the mirror instability. Mirror mode perturbations mainly form as magnetic holes in regions where the plasma is marginally mirror stable with respect to the linear instability criterion. We present an expanding box particle-in-cell simulation to mimic the changing conditions in the magnetosheath as the plasma is convected through it that produces mirror mode magnetic holes. We show that in the initial nonlinear evolution, where the plasma conditions are mirror unstable, the magnetic peaks are dominant, while later, as the plasma relaxes toward marginal stability, the fluctuations evolve into deep magnetic holes. While the averaged plasma parameters in the simulation remain close to the mirror instability threshold, the local plasma in the magnetic holes is highly unstable to mirror instability and locally mirror stable in the magnetic peaks.

Role of electric fields in the MHD evolution of the kink instability

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

Lapenta, Giovanni; Skender, Marina

Here, the discovery of electrostatic fields playing a crucial role in establishing plasma motion in the flux conversion and dynamo processes in reversed field pinches is revisited. In order to further elucidate the role of the electrostatic fields, a flux rope configuration susceptible to the kink instability is numerically studied with anMHDcode. Simulated nonlinear evolution of the kink instability is found to confirm the crucial role of the electrostatic fields. Anew insight is gained on the special function of the electrostatic fields: they lead the plasma towards the reconnection site at the mode resonant surface. Without this step the plasmamore » column could not relax to its nonlinear state, since no other agent is present to perform this role. While the inductive field generated directly by the kink instability is the dominant flow driver, the electrostatic field is found to allow the motion in the vicinity of the reconnection region.« less

Adiabatic Berry phase in an atom-molecule conversion system

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

Fu Libin; Center for Applied Physics and Technology, Peking University, Beijing 100084; Liu Jie, E-mail: liu_jie@iapcm.ac.c

2010-11-15

We investigate the Berry phase of adiabatic quantum evolution in the atom-molecule conversion system that is governed by a nonlinear Schroedinger equation. We find that the Berry phase consists of two parts: the usual Berry connection term and a novel term from the nonlinearity brought forth by the atom-molecule coupling. The total geometric phase can be still viewed as the flux of the magnetic field of a monopole through the surface enclosed by a closed path in parameter space. The charge of the monopole, however, is found to be one third of the elementary charge of the usual quantized monopole.more » We also derive the classical Hannay angle of a geometric nature associated with the adiabatic evolution. It exactly equals minus Berry phase, indicating a novel connection between Berry phase and Hannay angle in contrast to the usual derivative form.« less

Instability, finite amplitude pulsation and mass-loss in models of massive OB-type stars

NASA Astrophysics Data System (ADS)

Yadav, Abhay Pratap; Glatzel, Wolfgang

2017-11-01

Variability and mass-loss are common phenomena in massive OB-type stars. It is argued that they are caused by violent strange mode instabilities identified in corresponding stellar models. We present a systematic linear stability analysis with respect to radial perturbations of massive OB-type stars with solar chemical composition and masses between 23 and 100 M⊙. For selected unstable stellar models, we perform non-linear simulations of the evolution of the instabilities into the non-linear regime. Finite amplitude pulsations with periods in the range between hours and 100 d are found to be the final result of the instabilities. The pulsations are associated with a mean acoustic luminosity which can be the origin of a pulsationally driven wind. Corresponding mass-loss rates lie in the range between 10-9 and 10-4 M⊙ yr-1 and may thus affect the evolution of massive stars.

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.

Number-phase minimum-uncertainty state with reduced number uncertainty in a Kerr nonlinear interferometer

NASA Astrophysics Data System (ADS)

Kitagawa, M.; Yamamoto, Y.

1987-11-01

An alternative scheme for generating amplitude-squeezed states of photons based on unitary evolution which can properly be described by quantum mechanics is presented. This scheme is a nonlinear Mach-Zehnder interferometer containing an optical Kerr medium. The quasi-probability density (QPD) and photon-number distribution of the output field are calculated, and it is demonstrated that the reduced photon-number uncertainty and enhanced phase uncertainty maintain the minimum-uncertainty product. A self-phase-modulation of the single-mode quantized field in the Kerr medium is described based on localized operators. The spatial evolution of the state is demonstrated by QPD in the Schroedinger picture. It is shown that photon-number variance can be reduced to a level far below the limit for an ordinary squeezed state, and that the state prepared using this scheme remains a number-phase minimum-uncertainty state until the maximum reduction of number fluctuations is surpassed.

Nonlinear Ultrasonic Measurements in Nuclear Reactor Environments

NASA Astrophysics Data System (ADS)

Reinhardt, Brian T.

Several Department of Energy Office of Nuclear Energy (DOE-NE) programs, such as the Fuel Cycle Research and Development (FCRD), Advanced Reactor Concepts (ARC), Light Water Reactor Sustainability, and Next Generation Nuclear Power Plants (NGNP), are investigating new fuels, materials, and inspection paradigms for advanced and existing reactors. A key objective of such programs is to understand the performance of these fuels and materials during irradiation. In DOE-NE's FCRD program, ultrasonic based technology was identified as a key approach that should be pursued to obtain the high-fidelity, high-accuracy data required to characterize the behavior and performance of new candidate fuels and structural materials during irradiation testing. The radiation, high temperatures, and pressure can limit the available tools and characterization methods. In this thesis, two ultrasonic characterization techniques will be explored. The first, finite amplitude wave propagation has been demonstrated to be sensitive to microstructural material property changes. It is a strong candidate to determine fuel evolution; however, it has not been demonstrated for in-situ reactor applications. In this thesis, finite amplitude wave propagation will be used to measure the microstructural evolution in Al-6061. This is the first demonstration of finite amplitude wave propagation at temperatures in excess of 200 °C and during an irradiation test. Second, a method based on contact nonlinear acoustic theory will be developed to identify compressed cracks. Compressed cracks are typically transparent to ultrasonic wave propagation; however, by measuring harmonic content developed during finite amplitude wave propagation, it is shown that even compressed cracks can be characterized. Lastly, piezoelectric transducers capable of making these measurements are developed. Specifically, three piezoelectric sensors (Bismuth Titanate, Aluminum Nitride, and Zinc Oxide) are tested in the Massachusetts Institute of Technology Research reactor to a fast neutron fluence of 8.65x10 20 n/cm2. It is demonstrated that Bismuth Titanate is capable of transduction up to 5 x1020 n/cm2, Zinc Oxide is capable of transduction up to 6.27 x1020 n/cm 2, and Aluminum Nitride is capable of transduction up to 8.65x x10 20 n/cm2.

Contribution a la caracterisation des betons endommages par des methodes de l'acoustique non lineaire. Application a la reaction alcalis-silice

NASA Astrophysics Data System (ADS)

Kodjo, Apedovi

The aim of this thesis is to contribute to the non-destructive characterization of concrete materials damaged by alkali-silica reaction (ASR). For this purpose, some nonlinear characterization techniques have been developed, as well as a nonlinear resonance test device. In order to optimize the sensitivity of the test device, the excitation module and signal processing have been improved. The nonlinear tests were conducted on seven samples of concrete damaged by ASR, three samples of concrete damaged by heat, three concrete samples damaged mechanically and three sound concrete samples. Since, nonlinear behaviour of the material is often attribute to its micro-defects hysteretic behaviour, it was shown at first that concrete damaged by ASR exhibits an hysteresis behaviour. To conduct this study, an acoustoelastic test was set, and then nonlinear resonance test device was used for characterizing sound concrete and concrete damaged by ASR. It was shown that the nonlinear technique can be used for characterizing the material without knowing its initial state, and also for detecting early damage in the reactive material. Studies were also carried out on the effect of moisture regarding the nonlinear parameters; they allowed understanding the low values of nonlinear parameters measured on concrete samples that were kept in high moisture conditions. In order to find a specific characteristic of damage caused by ASR, the viscosity of ASR gel was used. An approach, based on static creep analysis, performed on the material, while applying the nonlinear resonance technique. The spring-damping model of Maxwell was used for the interpretation of the results. Then, the creep time was analysed on samples damaged by ASR. It appears that the ASR gel increases the creep time. Finally, the limitations of the nonlinear resonance technique for in situ application have been explained and a new applicable nonlinear technique was initiated. This technique use an external source such as a mass for making non-linearity behaviour in the material, while an ultrasound wave is investigating the medium. Keywords. Concrete, Alkali-silica reaction, Nonlinear acoustics, Nonlinearity, Hysteresis, Damage diagnostics.

New solitary wave solutions of (3 + 1)-dimensional nonlinear extended Zakharov-Kuznetsov and modified KdV-Zakharov-Kuznetsov equations and their applications

NASA Astrophysics Data System (ADS)

Lu, Dianchen; Seadawy, A. R.; Arshad, M.; Wang, Jun

In this paper, new exact solitary wave, soliton and elliptic function solutions are constructed in various forms of three dimensional nonlinear partial differential equations (PDEs) in mathematical physics by utilizing modified extended direct algebraic method. Soliton solutions in different forms such as bell and anti-bell periodic, dark soliton, bright soliton, bright and dark solitary wave in periodic form etc are obtained, which have large applications in different branches of physics and other areas of applied sciences. The obtained solutions are also presented graphically. Furthermore, many other nonlinear evolution equations arising in mathematical physics and engineering can also be solved by this powerful, reliable and capable method. The nonlinear three dimensional extended Zakharov-Kuznetsov dynamica equation and (3 + 1)-dimensional modified KdV-Zakharov-Kuznetsov equation are selected to show the reliability and effectiveness of the current method.

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.

Engineering the quantum states of light in a Kerr-nonlinear resonator by two-photon driving

NASA Astrophysics Data System (ADS)

Puri, Shruti; Boutin, Samuel; Blais, Alexandre

2017-04-01

Photonic cat states stored in high-Q resonators show great promise for hardware efficient universal quantum computing. We propose an approach to efficiently prepare such cat states in a Kerr-nonlinear resonator by the use of a two-photon drive. Significantly, we show that this preparation is robust against single-photon loss. An outcome of this observation is that a two-photon drive can eliminate undesirable phase evolution induced by a Kerr nonlinearity. By exploiting the concept of transitionless quantum driving, we moreover demonstrate how non-adiabatic initialization of cat states is possible. Finally, we present a universal set of quantum logical gates that can be performed on the engineered eigenspace of such a two-photon driven resonator and discuss a possible realization using superconducting circuits. The robustness of the engineered subspace to higher-order circuit nonlinearities makes this implementation favorable for scalable quantum computation.

Temporal and Spatio-Temporal Dynamic Instabilities: Novel Computational and Experimental approaches

NASA Astrophysics Data System (ADS)

Doedel, Eusebius J.; Panayotaros, Panayotis; Lambruschini, Carlos L. Pando

2016-11-01

This special issue contains a concise account of significant research results presented at the international workshop on Advanced Computational and Experimental Techniques in Nonlinear Dynamics, which was held in Cusco, Peru in August 2015. The meeting gathered leading experts, as well as new researchers, who have contributed to different aspects of Nonlinear Dynamics. Particularly significant was the presence of many active scientists from Latin America. The topics covered in this special issue range from advanced numerical techniques to novel physical experiments, and reflect the present state of the art in several areas of Nonlinear Dynamics. It contains seven review articles, followed by twenty-one regular papers that are organized in five categories, namely (1) Nonlinear Evolution Equations and Applications, (2) Numerical Continuation in Self-sustained Oscillators, (3) Synchronization, Control and Data Analysis, (4) Hamiltonian Systems, and (5) Scaling Properties in Maps.

Investigation of Solitary wave solutions for Vakhnenko-Parkes equation via exp-function and Exp(-ϕ(ξ))-expansion method.

PubMed

Roshid, Harun-Or; Kabir, Md Rashed; Bhowmik, Rajandra Chadra; Datta, Bimal Kumar

2014-01-01

In this paper, we have described two dreadfully important methods to solve nonlinear partial differential equations which are known as exp-function and the exp(-ϕ(ξ)) -expansion method. Recently, there are several methods to use for finding analytical solutions of the nonlinear partial differential equations. The methods are diverse and useful for solving the nonlinear evolution equations. With the help of these methods, we are investigated the exact travelling wave solutions of the Vakhnenko- Parkes equation. The obtaining soliton solutions of this equation are described many physical phenomena for weakly nonlinear surface and internal waves in a rotating ocean. Further, three-dimensional plots of the solutions such as solitons, singular solitons, bell type solitary wave i.e. non-topological solitons solutions and periodic solutions are also given to visualize the dynamics of the equation.

The Weakly Nonlinear Magnetorotational Instability in a Global, Cylindrical Taylor–Couette Flow

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

Clark, S. E.; Oishi, Jeffrey S., E-mail: seclark@astro.columbia.edu

We conduct a global, weakly nonlinear analysis of the magnetorotational instability (MRI) in a Taylor–Couette flow. This is a multiscale, perturbative treatment of the nonideal, axisymmetric MRI near threshold, subject to realistic radial boundary conditions and cylindrical geometry. We analyze both the standard MRI, initialized by a constant vertical background magnetic field, and the helical MRI, with an azimuthal background field component. This is the first weakly nonlinear analysis of the MRI in a global Taylor–Couette geometry, as well as the first weakly nonlinear analysis of the helical MRI. We find that the evolution of the amplitude of the standardmore » MRI is described by a real Ginzburg–Landau equation (GLE), whereas the amplitude of the helical MRI takes the form of a complex GLE. This suggests that the saturated state of the helical MRI may itself be unstable on long spatial and temporal scales.« less

Subdiffraction focusing of scanning beams by a negative-refraction layer combined with a nonlinear layer.

PubMed

Husakou, A; Herrmann, J

2006-11-13

We evaluate the possibility to focus scanning light beams below the diffraction limit by using the combination of a nonlinear material with a Kerr-type nonlinearity or two-photon absorption to create seed evanescent components of the beam and a negative-refraction material to enhance them. Superfocusing to spots with a FWHM in the range of 0.2 lambda is theoretically predicted both in the context of the effective-medium theory and by the direct numerical solution of Maxwell equations for an inhomogeneous pho-tonic crystal. The evolution of the transverse spectrum and the dependence of superfocusing on the parameters of the negative-refraction material are also studied. We show that the use of a Kerr-type nonlinear layer for the creation of seed evanescent components yields focused spots with a higher intensity compared with those obtained by the application of a saturable absorber.

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.

Nonlinear evolution of energetic-particles-driven waves in collisionless plasmas

NASA Astrophysics Data System (ADS)

Li, Shuhan; Liu, Jinyuan; Wang, Feng; Shen, Wei; Li, Dong

2018-06-01

A one-dimensional electrostatic collisionless particle-in-cell code has been developed to study the nonlinear interaction between electrostatic waves and energetic particles (EPs). For a single wave, the results are clear and agree well with the existing theories. For coexisting two waves, although the mode nonlinear coupling between two wave fields is ignored, the second-order phase space islands can still exist between first-order islands generated by the two waves. However, the second-order phase islands are not formed by the superposed wave fields and the perturbed motions of EPs induced by the combined effect of two main resonances make these structures in phase space. Owing to these second-order islands, energy can be transferred between waves, even if the overlap of two main resonances never occurs. Depending on the distance between the main resonance islands in velocity space, the second-order island can affect the nonlinear dynamics and saturations of waves.

New method for rekindling the nonlinear solitary waves in Maxwellian complex space plasma

NASA Astrophysics Data System (ADS)

Das, G. C.; Sarma, Ridip

2018-04-01

Our interest is to study the nonlinear wave phenomena in complex plasma constituents with Maxwellian electrons and ions. The main reason for this consideration is to exhibit the effects of dust charge fluctuations on acoustic modes evaluated by the use of a new method. A special method (G'/G) has been developed to yield the coherent features of nonlinear waves augmented through the derivation of a Korteweg-de Vries equation and found successfully the different nature of solitons recognized in space plasmas. Evolutions have shown with the input of appropriate typical plasma parameters to support our theoretical observations in space plasmas. All conclusions are in good accordance with the actual occurrences and could be of interest to further the investigations in experiments and satellite observations in space. In this paper, we present not only the model that exhibited nonlinear solitary wave propagation but also a new mathematical method to the execution.

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

Parametric and nonparametric Granger causality testing: Linkages between international stock markets

NASA Astrophysics Data System (ADS)

De Gooijer, Jan G.; Sivarajasingham, Selliah

2008-04-01

This study investigates long-term linear and nonlinear causal linkages among eleven stock markets, six industrialized markets and five emerging markets of South-East Asia. We cover the period 1987-2006, taking into account the on-set of the Asian financial crisis of 1997. We first apply a test for the presence of general nonlinearity in vector time series. Substantial differences exist between the pre- and post-crisis period in terms of the total number of significant nonlinear relationships. We then examine both periods, using a new nonparametric test for Granger noncausality and the conventional parametric Granger noncausality test. One major finding is that the Asian stock markets have become more internationally integrated after the Asian financial crisis. An exception is the Sri Lankan market with almost no significant long-term linear and nonlinear causal linkages with other markets. To ensure that any causality is strictly nonlinear in nature, we also examine the nonlinear causal relationships of VAR filtered residuals and VAR filtered squared residuals for the post-crisis sample. We find quite a few remaining significant bi- and uni-directional causal nonlinear relationships in these series. Finally, after filtering the VAR-residuals with GARCH-BEKK models, we show that the nonparametric test statistics are substantially smaller in both magnitude and statistical significance than those before filtering. This indicates that nonlinear causality can, to a large extent, be explained by simple volatility effects.

Nonlinear interaction of near-planar TS waves and longitudinal vortices in boundary-layer transition

NASA Technical Reports Server (NTRS)

Smith, F. T.

1988-01-01

The nonlinear interactions that evolve between a planar or nearly planar Tollmien-Schlichting (TS) wave and the associated longitudinal vortices are considered theoretically for a boundary layer at high Reynolds number. The vortex flow is either induced by the TS nonlinear forcing or is input upstream, and similarly for the nonlinear wave development. Three major kinds of nonlinear spatial evolution, Types 1-3, are found. Each can start from secondary instability and then become nonlinear, Type 1 proving to be relatively benign but able to act as a pre-cursor to the Types 2, 3 which turn out to be very powerful nonlinear interactions. Type 2 involves faster stream-wise dependence and leads to a finite-distance blow-up in the amplitudes, which then triggers the full nonlinear 3-D triple-deck response, thus entirely altering the mean-flow profile locally. In contrast, Type 3 involves slower streamwise dependence but a faster spanwise response, with a small TS amplitude thereby causing an enhanced vortex effect which, again, is substantial enough to entirely alter the meanflow profile, on a more global scale. Streak-like formations in which there is localized concentration of streamwise vorticity and/or wave amplitude can appear, and certain of the nonlinear features also suggest by-pass processes for transition and significant changes in the flow structure downstream. The powerful nonlinear 3-D interactions 2, 3 are potentially very relevant to experimental findings in transition.

Efficient analytical implementation of the DOT Riemann solver for the de Saint Venant-Exner morphodynamic model

NASA Astrophysics Data System (ADS)

Carraro, F.; Valiani, A.; Caleffi, V.

2018-03-01

Within the framework of the de Saint Venant equations coupled with the Exner equation for morphodynamic evolution, this work presents a new efficient implementation of the Dumbser-Osher-Toro (DOT) scheme for non-conservative problems. The DOT path-conservative scheme is a robust upwind method based on a complete Riemann solver, but it has the drawback of requiring expensive numerical computations. Indeed, to compute the non-linear time evolution in each time step, the DOT scheme requires numerical computation of the flux matrix eigenstructure (the totality of eigenvalues and eigenvectors) several times at each cell edge. In this work, an analytical and compact formulation of the eigenstructure for the de Saint Venant-Exner (dSVE) model is introduced and tested in terms of numerical efficiency and stability. Using the original DOT and PRICE-C (a very efficient FORCE-type method) as reference methods, we present a convergence analysis (error against CPU time) to study the performance of the DOT method with our new analytical implementation of eigenstructure calculations (A-DOT). In particular, the numerical performance of the three methods is tested in three test cases: a movable bed Riemann problem with analytical solution; a problem with smooth analytical solution; a test in which the water flow is characterised by subcritical and supercritical regions. For a given target error, the A-DOT method is always the most efficient choice. Finally, two experimental data sets and different transport formulae are considered to test the A-DOT model in more practical case studies.

Groundwater flow and heat transport for systems undergoing freeze-thaw: Intercomparison of numerical simulators for 2D test cases

NASA Astrophysics Data System (ADS)

Grenier, Christophe; Anbergen, Hauke; Bense, Victor; Chanzy, Quentin; Coon, Ethan; Collier, Nathaniel; Costard, François; Ferry, Michel; Frampton, Andrew; Frederick, Jennifer; Gonçalvès, Julio; Holmén, Johann; Jost, Anne; Kokh, Samuel; Kurylyk, Barret; McKenzie, Jeffrey; Molson, John; Mouche, Emmanuel; Orgogozo, Laurent; Pannetier, Romain; Rivière, Agnès; Roux, Nicolas; Rühaak, Wolfram; Scheidegger, Johanna; Selroos, Jan-Olof; Therrien, René; Vidstrand, Patrik; Voss, Clifford

2018-04-01

In high-elevation, boreal and arctic regions, hydrological processes and associated water bodies can be strongly influenced by the distribution of permafrost. Recent field and modeling studies indicate that a fully-coupled multidimensional thermo-hydraulic approach is required to accurately model the evolution of these permafrost-impacted landscapes and groundwater systems. However, the relatively new and complex numerical codes being developed for coupled non-linear freeze-thaw systems require verification. This issue is addressed by means of an intercomparison of thirteen numerical codes for two-dimensional test cases with several performance metrics (PMs). These codes comprise a wide range of numerical approaches, spatial and temporal discretization strategies, and computational efficiencies. Results suggest that the codes provide robust results for the test cases considered and that minor discrepancies are explained by computational precision. However, larger discrepancies are observed for some PMs resulting from differences in the governing equations, discretization issues, or in the freezing curve used by some codes.

Nonlinear viscoelastic characterization of polymer materials using a dynamic-mechanical methodology

NASA Technical Reports Server (NTRS)

Strganac, Thomas W.; Payne, Debbie Flowers; Biskup, Bruce A.; Letton, Alan

1995-01-01

Polymer materials retrieved from LDEF exhibit nonlinear constitutive behavior; thus the authors present a method to characterize nonlinear viscoelastic behavior using measurements from dynamic (oscillatory) mechanical tests. Frequency-derived measurements are transformed into time-domain properties providing the capability to predict long term material performance without a lengthy experimentation program. Results are presented for thin-film high-performance polymer materials used in the fabrication of high-altitude scientific balloons. Predictions based upon a linear test and analysis approach are shown to deteriorate for moderate to high stress levels expected for extended applications. Tests verify that nonlinear viscoelastic response is induced by large stresses. Hence, an approach is developed in which the stress-dependent behavior is examined in a manner analogous to modeling temperature-dependent behavior with time-temperature correspondence and superposition principles. The development leads to time-stress correspondence and superposition of measurements obtained through dynamic mechanical tests. Predictions of material behavior using measurements based upon linear and nonlinear approaches are compared with experimental results obtained from traditional creep tests. Excellent agreement is shown for the nonlinear model.

Nonlinear Modeling of Joint Dominated Structures

NASA Technical Reports Server (NTRS)

Chapman, J. M.

1990-01-01

The development and verification of an accurate structural model of the nonlinear joint-dominated NASA Langley Mini-Mast truss are described. The approach is to characterize the structural behavior of the Mini-Mast joints and struts using a test configuration that can directly measure the struts' overall stiffness and damping properties, incorporate this data into the structural model using the residual force technique, and then compare the predicted response with empirical data taken by NASA/LaRC during the modal survey tests of the Mini-Mast. A new testing technique, referred to as 'link' testing, was developed and used to test prototype struts of the Mini-Masts. Appreciable nonlinearities including the free-play and hysteresis were demonstrated. Since static and dynamic tests performed on the Mini-Mast also exhibited behavior consistent with joints having free-play and hysteresis, nonlinear models of the Mini-Mast were constructed and analyzed. The Residual Force Technique was used to analyze the nonlinear model of the Mini-Mast having joint free-play and hysteresis.

Dynamics of double-polarity subduction: application to the Western Mediterranean

NASA Astrophysics Data System (ADS)

Peral, M.; Zlotnik, S.; Fernandez, M.; Verges, J.; Jiménez-Munt, I.; Torne, M.

2015-12-01

The evolution of the Western Mediterranean is a highly debated question by geologists and geophysicists. Even though most scientists agree in considering slab roll-back to be the driving mechanism of the tectonic evolution of this area, there is still no consensus about the initial setup and its time evolution. A recent model proposed by Vergés and Fernàndez (2012) suggests a lateral change in subduction polarity of the Ligurian-Thetys oceanic domain to explain the formation and evolution of the Betic-Rif orogenic system and the associated Alboran back-arc basin. Such geodynamic scenario is also proposed for different converging regions. The aim of this study is to analyze the dynamic evolution of a double-polarity subduction process and its consequences in order to test the physical feasibility of this interaction and provide geometries and evolutions comparable to those proposed for the Western Mediterranean. The 3D numerical model of double-polarity subduction is carried out via the Underworld framework. Tectonic plate behavior is described by equations of fluid dynamics in the presence of several different phases. Underworld solves a non-linear Stokes flow problem using Finite Elements combined with particle-in-cell approach, thus the discretization combines a standard Eulerian Finite Element mesh with Lagrangian particles to track the location of the phases. The final model consists of two oceanic plates with viscoplastic rheology subducting into the upper mantle and the problem is driven by Rayleigh-Taylor instability. The main factors to be studied are the interaction between the two plates, the poloidal and toroidal mantle fluxes, the velocity variations of slabs, the stress distribution and the variations in the trench morphology.

Finding all solutions of nonlinear equations using the dual simplex method

NASA Astrophysics Data System (ADS)

Yamamura, Kiyotaka; Fujioka, Tsuyoshi

2003-03-01

Recently, an efficient algorithm has been proposed for finding all solutions of systems of nonlinear equations using linear programming. This algorithm is based on a simple test (termed the LP test) for nonexistence of a solution to a system of nonlinear equations using the dual simplex method. In this letter, an improved version of the LP test algorithm is proposed. By numerical examples, it is shown that the proposed algorithm could find all solutions of a system of 300 nonlinear equations in practical computation time.

The evolution of cooperative turn-taking in animal conflict

PubMed Central

2011-01-01

Background A fundamental assumption in animal socio-ecology is that animals compete over limited resources. This view has been challenged by the finding that individuals might cooperatively partition resources by "taking turns". Turn-taking occurs when two individuals coordinate their agonistic behaviour in a way that leads to an alternating pattern in who obtains a resource without engaging in costly fights. Cooperative turn-taking has been largely ignored in models of animal conflict and socio-ecological models that explain the evolution of social behaviours based only on contest and scramble competition. Currently it is unclear whether turn-taking should be included in socio-ecological models because the evolution of turn-taking is not well understood. In particular, it is unknown whether turn-taking can evolve when fighting costs and assessment of fighting abilities are not fixed but emerge from evolved within-fight behaviour. We address this problem with an evolutionary agent-based model. Results We found that turn-taking evolves for small resource values, alongside a contest strategy that leads to stable dominance relationships. Turn-taking leads to egalitarian societies with unclear dominance relationships and non-linear dominance hierarchies. Evolutionary stability of turn-taking emerged despite strength differences among individuals and the possibility to evolve within-fight behaviour that allows good assessment of fighting abilities. Evolutionary stability emerged from frequency-dependent effects on fitness, which are modulated by feedbacks between the evolution of within-fight behaviour and the evolution of higher-level conflict strategies. Conclusions Our results reveal the impact of feedbacks between the evolution of within-fight behaviour and the evolution of higher-level conflict strategies, such as turn-taking. Similar feedbacks might be important for the evolution of other conflict strategies such as winner-loser effects or coalitions. However, we are not aware of any study that investigated such feedbacks. Furthermore, our model suggests that turn-taking could be used by animals to partition low value resources, but to our knowledge this has never been tested. The existence of turn-taking might have been overlooked because it leads to societies with similar characteristics that have been expected to emerge from scramble competition. Analyses of temporal interaction patterns could be used to test whether turn-taking occurs in animals. PMID:22054254

The evolution of cooperative turn-taking in animal conflict.

PubMed

Franz, Mathias; van der Post, Daniel; Schülke, Oliver; Ostner, Julia

2011-11-03

A fundamental assumption in animal socio-ecology is that animals compete over limited resources. This view has been challenged by the finding that individuals might cooperatively partition resources by "taking turns". Turn-taking occurs when two individuals coordinate their agonistic behaviour in a way that leads to an alternating pattern in who obtains a resource without engaging in costly fights. Cooperative turn-taking has been largely ignored in models of animal conflict and socio-ecological models that explain the evolution of social behaviours based only on contest and scramble competition. Currently it is unclear whether turn-taking should be included in socio-ecological models because the evolution of turn-taking is not well understood. In particular, it is unknown whether turn-taking can evolve when fighting costs and assessment of fighting abilities are not fixed but emerge from evolved within-fight behaviour. We address this problem with an evolutionary agent-based model. We found that turn-taking evolves for small resource values, alongside a contest strategy that leads to stable dominance relationships. Turn-taking leads to egalitarian societies with unclear dominance relationships and non-linear dominance hierarchies. Evolutionary stability of turn-taking emerged despite strength differences among individuals and the possibility to evolve within-fight behaviour that allows good assessment of fighting abilities. Evolutionary stability emerged from frequency-dependent effects on fitness, which are modulated by feedbacks between the evolution of within-fight behaviour and the evolution of higher-level conflict strategies. Our results reveal the impact of feedbacks between the evolution of within-fight behaviour and the evolution of higher-level conflict strategies, such as turn-taking. Similar feedbacks might be important for the evolution of other conflict strategies such as winner-loser effects or coalitions. However, we are not aware of any study that investigated such feedbacks. Furthermore, our model suggests that turn-taking could be used by animals to partition low value resources, but to our knowledge this has never been tested. The existence of turn-taking might have been overlooked because it leads to societies with similar characteristics that have been expected to emerge from scramble competition. Analyses of temporal interaction patterns could be used to test whether turn-taking occurs in animals.

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.

The Hamiltonian structure of the (2+1)-dimensional Ablowitz--Kaup--Newell--Segur hierarchy

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

Athorne, C.; Dorfman, I.Y.

1993-08-01

By considering Hamiltonian theory over a suitable (noncommutative) ring the nonlinear evolution equations of the Ablowitz--Kaup--Newell--Segur (2+1) hierarchy are incorporated into a Hamiltonian framework and a modified Lenard scheme.

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

Krasnobaeva, L. A., E-mail: kla1983@mail.ru; Siberian State Medical University Moscowski Trakt 2, Tomsk, 634050; Shapovalov, A. V.

Within the formalism of the Fokker–Planck equation, the influence of nonstationary external force, random force, and dissipation effects on dynamics local conformational perturbations (kink) propagating along the DNA molecule is investigated. Such waves have an important role in the regulation of important biological processes in living systems at the molecular level. As a dynamic model of DNA was used a modified sine-Gordon equation, simulating the rotational oscillations of bases in one of the chains DNA. The equation of evolution of the kink momentum is obtained in the form of the stochastic differential equation in the Stratonovich sense within the frameworkmore » of the well-known McLaughlin and Scott energy approach. The corresponding Fokker–Planck equation for the momentum distribution function coincides with the equation describing the Ornstein–Uhlenbek process with a regular nonstationary external force. The influence of the nonlinear stochastic effects on the kink dynamics is considered with the help of the Fokker– Planck nonlinear equation with the shift coefficient dependent on the first moment of the kink momentum distribution function. Expressions are derived for average value and variance of the momentum. Examples are considered which demonstrate the influence of the external regular and random forces on the evolution of the average value and variance of the kink momentum. Within the formalism of the Fokker–Planck equation, the influence of nonstationary external force, random force, and dissipation effects on the kink dynamics is investigated in the sine–Gordon model. The equation of evolution of the kink momentum is obtained in the form of the stochastic differential equation in the Stratonovich sense within the framework of the well-known McLaughlin and Scott energy approach. The corresponding Fokker–Planck equation for the momentum distribution function coincides with the equation describing the Ornstein–Uhlenbek process with a regular nonstationary external force. The influence of the nonlinear stochastic effects on the kink dynamics is considered with the help of the Fokker–Planck nonlinear equation with the shift coefficient dependent on the first moment of the kink momentum distribution function. Expressions are derived for average value and variance of the momentum. Examples are considered which demonstrate the influence of the external regular and random forces on the evolution of the average value and variance of the kink momentum.« less

Nonlinear structures and anomalous transport in partially magnetized E×B plasmas

DOE PAGES

Janhunen, Salomon; Smolyakov, Andrei; Chapurin, Oleksandr; ...

2017-12-29

Nonlinear dynamics of the electron-cyclotron instability driven by the electron E x B current in a crossed electric and magnetic field is studied. In the nonlinear regime, the instability proceeds by developing a large amplitude coherent wave driven by the energy input from the fundamental cyclotron resonance. Further evolution shows the formation of the long wavelength envelope akin to the modulational instability. Simultaneously, the ion density shows the development of a high-k content responsible for wave focusing and sharp peaks on the periodic cnoidal wave structure. Here, it is shown that the anomalous electron transport (along the direction of themore » applied electric field) is dominated by the long wavelength part of the turbulent spectrum.« less

Galerkin approximation for inverse problems for nonautonomous nonlinear distributed systems

NASA Technical Reports Server (NTRS)

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

1988-01-01

An abstract framework and convergence theory is developed for Galerkin approximation for inverse problems involving the identification of nonautonomous nonlinear distributed parameter systems. A set of relatively easily verified conditions is provided which are sufficient to guarantee the existence of optimal solutions and their approximation by a sequence of solutions to a sequence of approximating finite dimensional identification problems. The approach is based on the theory of monotone operators in Banach spaces and is applicable to a reasonably broad class of nonlinear distributed systems. Operator theoretic and variational techniques are used to establish a fundamental convergence result. An example involving evolution systems with dynamics described by nonstationary quasilinear elliptic operators along with some applications are presented and discussed.

Adiabatic Soliton Laser

NASA Astrophysics Data System (ADS)

Bednyakova, Anastasia; Turitsyn, Sergei K.

2015-03-01

The key to generating stable optical pulses is mastery of nonlinear light dynamics in laser resonators. Modern techniques to control the buildup of laser pulses are based on nonlinear science and include classical solitons, dissipative solitons, parabolic pulses (similaritons) and various modifications and blending of these methods. Fiber lasers offer remarkable opportunities to apply one-dimensional nonlinear science models for the design and optimization of very practical laser systems. Here, we propose a new concept of a laser based on the adiabatic amplification of a soliton pulse in the cavity—the adiabatic soliton laser. The adiabatic change of the soliton parameters during evolution in the resonator relaxes the restriction on the pulse energy inherent in traditional soliton lasers. Theoretical analysis is confirmed by extensive numerical modeling.

On new classes of solutions of nonlinear partial differential equations in the form of convergent special series

NASA Astrophysics Data System (ADS)

Filimonov, M. Yu.

2017-12-01

The method of special series with recursively calculated coefficients is used to solve nonlinear partial differential equations. The recurrence of finding the coefficients of the series is achieved due to a special choice of functions, in powers of which the solution is expanded in a series. We obtain a sequence of linear partial differential equations to find the coefficients of the series constructed. In many cases, one can deal with a sequence of linear ordinary differential equations. We construct classes of solutions in the form of convergent series for a certain class of nonlinear evolution equations. A new class of solutions of generalized Boussinesque equation with an arbitrary function in the form of a convergent series is constructed.

Demonstrating the improvement of predictive maturity of a computational model

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

Hemez, Francois M; Unal, Cetin; Atamturktur, Huriye S

2010-01-01

We demonstrate an improvement of predictive capability brought to a non-linear material model using a combination of test data, sensitivity analysis, uncertainty quantification, and calibration. A model that captures increasingly complicated phenomena, such as plasticity, temperature and strain rate effects, is analyzed. Predictive maturity is defined, here, as the accuracy of the model to predict multiple Hopkinson bar experiments. A statistical discrepancy quantifies the systematic disagreement (bias) between measurements and predictions. Our hypothesis is that improving the predictive capability of a model should translate into better agreement between measurements and predictions. This agreement, in turn, should lead to a smallermore » discrepancy. We have recently proposed to use discrepancy and coverage, that is, the extent to which the physical experiments used for calibration populate the regime of applicability of the model, as basis to define a Predictive Maturity Index (PMI). It was shown that predictive maturity could be improved when additional physical tests are made available to increase coverage of the regime of applicability. This contribution illustrates how the PMI changes as 'better' physics are implemented in the model. The application is the non-linear Preston-Tonks-Wallace (PTW) strength model applied to Beryllium metal. We demonstrate that our framework tracks the evolution of maturity of the PTW model. Robustness of the PMI with respect to the selection of coefficients needed in its definition is also studied.« less

Spin-electron acoustic soliton and exchange interaction in separate spin evolution quantum plasmas

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

Andreev, Pavel A., E-mail: andreevpa@physics.msu.ru

Separate spin evolution quantum hydrodynamics is generalized to include the Coulomb exchange interaction, which is considered as interaction between the spin-down electrons being in quantum states occupied by one electron. The generalized model is applied to study the non-linear spin-electron acoustic waves. Existence of the spin-electron acoustic soliton is demonstrated. Contributions of concentration, spin polarization, and exchange interaction to the properties of the spin electron acoustic soliton are studied.

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.

Helicity evolution at small-x

DOE PAGES

Kovchegov, Yuri V.; Pitonyak, Daniel; Sievert, Matthew D.

2016-01-13

We construct small-x evolution equations which can be used to calculate quark and anti-quark helicity TMDs and PDFs, along with the g1 structure function. These evolution equations resum powers of α s ln 2(1/x) in the polarization-dependent evolution along with the powers of α s ln(1/x) in the unpolarized evolution which includes saturation efects. The equations are written in an operator form in terms of polarization-dependent Wilson line-like operators. While the equations do not close in general, they become closed and self-contained systems of non-linear equations in the large-N c and large-N c & N f limits. As a cross-check,more » in the ladder approximation, our equations map onto the same ladder limit of the infrared evolution equations for g 1 structure function derived previously by Bartels, Ermolaev and Ryskin.« less

Conceptual problems in detecting the evolution of dark energy when using distance measurements

NASA Astrophysics Data System (ADS)

Bolejko, K.

2011-01-01

Context. Dark energy is now one of the most important and topical problems in cosmology. The first step to reveal its nature is to detect the evolution of dark energy or to prove beyond doubt that the cosmological constant is indeed constant. However, in the standard approach to cosmology, the Universe is described by the homogeneous and isotropic Friedmann models. Aims: We aim to show that in the perturbed universe (even if perturbations vanish if averaged over sufficiently large scales) the distance-redshift relation is not the same as in the unperturbed universe. This has a serious consequence when studying the nature of dark energy and, as shown here, can impair the analysis and studies of dark energy. Methods: The analysis is based on two methods: the linear lensing approximation and the non-linear Szekeres Swiss-Cheese model. The inhomogeneity scale is ~50 Mpc, and both models have the same density fluctuations along the line of sight. Results: The comparison between linear and non-linear methods shows that non-linear corrections are not negligible. When inhomogeneities are present the distance changes by several percent. To show how this change influences the measurements of dark energy, ten future observations with 2% uncertainties are generated. It is shown the using the standard methods (i.e. under the assumption of homogeneity) the systematics due to inhomogeneities can distort our analysis, and may lead to a conclusion that dark energy evolves when in fact it is constant (or vice versa). Conclusions: Therefore, if future observations are analysed only within the homogeneous framework then the impact of inhomogeneities (such as voids and superclusters) can be mistaken for evolving dark energy. Since the robust distinction between the evolution and non-evolution of dark energy is the first step to understanding the nature of dark energy a proper handling of inhomogeneities is essential.

Evolution of Hyperbolic-Secant Pulses Towards Cross-Phase Modulation Induced Optical Wave Breaking and Soliton or Soliton Trains Generation in Quintic Nonlinear Fibers

NASA Astrophysics Data System (ADS)

Zhong, Xian-Qiong; Zhang, Xiao-Xia; Du, Xian-Tong; Liu, Yong; Cheng, Ke

2015-10-01

The approximate analytical frequency chirps and the critical distances for cross-phase modulation induced optical wave breaking (OWB) of the initial hyperbolic-secant optical pulses propagating in optical fibers with quintic nonlinearity (QN) are presented. The pulse evolutions in terms of the frequency chirps, shapes and spectra are numerically calculated in the normal dispersion regime. The results reveal that, depending on different QN parameters, the traditional OWB or soliton or soliton pulse trains may occur. The approximate analytical critical distances are found to be in good agreement with the numerical ones only for the traditional OWB whereas the approximate analytical frequency chirps accords well with the numerical ones at the initial evolution stages of the pulses. Supported by the Postdoctoral Fund of China under Grant No. 2011M501402, the Key Project of Chinese Ministry of Education under Grant No. 210186, the Major Project of Natural Science Supported by the Educational Department of Sichuan Province under Grant No. 13ZA0081, the Key Project of National Natural Science Foundation of China under Grant No 61435010, and the National Natural Science Foundation of China under Grant No. 61275039

One-dimensional optical wave turbulence: Experiment and theory

NASA Astrophysics Data System (ADS)

Laurie, Jason; Bortolozzo, Umberto; Nazarenko, Sergey; Residori, Stefania

2012-05-01

We present a review of the latest developments in one-dimensional (1D) optical wave turbulence (OWT). Based on an original experimental setup that allows for the implementation of 1D OWT, we are able to show that an inverse cascade occurs through the spontaneous evolution of the nonlinear field up to the point when modulational instability leads to soliton formation. After solitons are formed, further interaction of the solitons among themselves and with incoherent waves leads to a final condensate state dominated by a single strong soliton. Motivated by the observations, we develop a theoretical description, showing that the inverse cascade develops through six-wave interaction, and that this is the basic mechanism of nonlinear wave coupling for 1D OWT. We describe theory, numerics and experimental observations while trying to incorporate all the different aspects into a consistent context. The experimental system is described by two coupled nonlinear equations, which we explore within two wave limits allowing for the expression of the evolution of the complex amplitude in a single dynamical equation. The long-wave limit corresponds to waves with wave numbers smaller than the electrical coherence length of the liquid crystal, and the opposite limit, when wave numbers are larger. We show that both of these systems are of a dual cascade type, analogous to two-dimensional (2D) turbulence, which can be described by wave turbulence (WT) theory, and conclude that the cascades are induced by a six-wave resonant interaction process. WT theory predicts several stationary solutions (non-equilibrium and thermodynamic) to both the long- and short-wave systems, and we investigate the necessary conditions required for their realization. Interestingly, the long-wave system is close to the integrable 1D nonlinear Schrödinger equation (NLSE) (which contains exact nonlinear soliton solutions), and as a result during the inverse cascade, nonlinearity of the system at low wave numbers becomes strong. Subsequently, due to the focusing nature of the nonlinearity, this leads to modulational instability (MI) of the condensate and the formation of solitons. Finally, with the aid of the probability density function (PDF) description of WT theory, we explain the coexistence and mutual interactions between solitons and the weakly nonlinear random wave background in the form of a wave turbulence life cycle (WTLC).

A Criterion to Control Nonlinear Error in the Mixed-Mode Bending Test

NASA Technical Reports Server (NTRS)

Reeder, James R.

2002-01-01

The mixed-mode bending test ha: been widely used to measure delamination toughness and was recently standardized by ASTM as Standard Test Method D6671-01. This simple test is a combination of the standard Mode I (opening) test and a Mode II (sliding) test. This test uses a unidirectional composite test specimen with an artificial delamination subjected to bending loads to characterize when a delamination will extend. When the displacements become large, the linear theory used to analyze the results of the test yields errors in the calcu1ated toughness values. The current standard places no limit on the specimen loading and therefore test data can be created using the standard that are significantly in error. A method of limiting the error that can be incurred in the calculated toughness values is needed. In this paper, nonlinear models of the MMB test are refined. One of the nonlinear models is then used to develop a simple criterion for prescribing conditions where thc nonlinear error will remain below 5%.

From solitons to rogue waves in nonlinear left-handed metamaterials.

PubMed

Shen, Yannan; Kevrekidis, P G; Veldes, G P; Frantzeskakis, D J; DiMarzio, D; Lan, X; Radisic, V

2017-03-01

In the present work, we explore soliton and roguelike wave solutions in the transmission line analog of a nonlinear left-handed metamaterial. The nonlinearity is expressed through a voltage-dependent, symmetric capacitance motivated by recently developed ferroelectric barium strontium titanate thin-film capacitor designs. We develop both the corresponding nonlinear dynamical lattice and its reduction via a multiple scales expansion to a nonlinear Schrödinger (NLS) model for the envelope of a given carrier wave. The reduced model can feature either a focusing or a defocusing nonlinearity depending on the frequency (wave number) of the carrier. We then consider the robustness of different types of solitary waves of the reduced model within the original nonlinear left-handed medium. We find that both bright and dark solitons persist in a suitable parametric regime, where the reduction to the NLS model is valid. Additionally, for suitable initial conditions, we observe a rogue wave type of behavior that differs significantly from the classic Peregrine rogue wave evolution, including most notably the breakup of a single Peregrine-like pattern into solutions with multiple wave peaks. Finally, we touch upon the behavior of generalized members of the family of the Peregrine solitons, namely, Akhmediev breathers and Kuznetsov-Ma solitons, and explore how these evolve in the left-handed transmission line.

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.

Implicit solvers for unstructured meshes

NASA Technical Reports Server (NTRS)

Venkatakrishnan, V.; Mavriplis, Dimitri J.

1991-01-01

Implicit methods were developed and tested for unstructured mesh computations. The approximate system which arises from the Newton linearization of the nonlinear evolution operator is solved by using the preconditioned GMRES (Generalized Minimum Residual) technique. Three different preconditioners were studied, namely, the incomplete LU factorization (ILU), block diagonal factorization, and the symmetric successive over relaxation (SSOR). The preconditioners were optimized to have good vectorization properties. SSOR and ILU were also studied as iterative schemes. The various methods are compared over a wide range of problems. Ordering of the unknowns, which affects the convergence of these sparse matrix iterative methods, is also studied. Results are presented for inviscid and turbulent viscous calculations on single and multielement airfoil configurations using globally and adaptively generated meshes.

Solving nonlinear evolution equation system using two different methods

NASA Astrophysics Data System (ADS)

Kaplan, Melike; Bekir, Ahmet; Ozer, Mehmet N.

2015-12-01

This paper deals with constructing more general exact solutions of the coupled Higgs equation by using the (G0/G, 1/G)-expansion and (1/G0)-expansion methods. The obtained solutions are expressed by three types of functions: hyperbolic, trigonometric and rational functions with free parameters. It has been shown that the suggested methods are productive and will be used to solve nonlinear partial differential equations in applied mathematics and engineering. Throughout the paper, all the calculations are made with the aid of the Maple software.

Prolongation structures of nonlinear evolution equations

NASA Technical Reports Server (NTRS)

Wahlquist, H. D.; Estabrook, F. B.

1975-01-01

A technique is developed for systematically deriving a 'prolongation structure' - a set of interrelated potentials and pseudopotentials - for nonlinear partial differential equations in two independent variables. When this is applied to the Korteweg-de Vries equation, a new infinite set of conserved quantities is obtained. Known solution techniques are shown to result from the discovery of such a structure: related partial differential equations for the potential functions, linear 'inverse scattering' equations for auxiliary functions, Backlund transformations. Generalizations of these techniques will result from the use of irreducible matrix representations of the prolongation structure.

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.

Three key regimes of single pulse generation per round trip of all-normal-dispersion fiber lasers mode-locked with nonlinear polarization rotation.

PubMed

Smirnov, Sergey; Kobtsev, Sergey; Kukarin, Sergey; Ivanenko, Aleksey

2012-11-19

We show experimentally and numerically new transient lasing regime between stable single-pulse generation and noise-like generation. We characterize qualitatively all three regimes of single pulse generation per round-trip of all-normal-dispersion fiber lasers mode-locked due to effect of nonlinear polarization evolution. We study spectral and temporal features of pulses produced in all three regimes as well as compressibility of such pulses. Simple criteria are proposed to identify lasing regime in experiment.

Note on Solutions to a Class of Nonlinear Singular Integro-Differential Equations,

DTIC Science & Technology

1986-08-01

KdV) ut + 2uu x +Uxx x a 0, (1) the sine-Gordon equation Uxt a sin u, (2) and the Kadomtsev - Petviashvili (KP) equation (Ut + 2uu x + UXXx)x -3a 2u yy...SOUIN OA LSFNN ! /" / M.. \\boiz A.S ::-:- and ,M.O.. .- :1/1 / NOTE ON SOLUTIONS TO A CLASS OF NON \\ / LINEAR SINGULAR INTEGRO-DIFFERENTIA[ EQUATIONS by...important nonlinear evolution equations which can be linearized. Many of these equations fall into the category of linearization via soliton theory and

Soliton's eigenvalue based analysis on the generation mechanism of rogue wave phenomenon in optical fibers exhibiting weak third order dispersion.

PubMed

Weerasekara, Gihan; Tokunaga, Akihiro; Terauchi, Hiroki; Eberhard, Marc; Maruta, Akihiro

2015-01-12

One of the extraordinary aspects of nonlinear wave evolution which has been observed as the spontaneous occurrence of astonishing and statistically extraordinary amplitude wave is called rogue wave. We show that the eigenvalues of the associated equation of nonlinear Schrödinger equation are almost constant in the vicinity of rogue wave and we validate that optical rogue waves are formed by the collision between quasi-solitons in anomalous dispersion fiber exhibiting weak third order dispersion.

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.

A family of nonlinear Schrödinger equations admitting q-plane wave solutions

NASA Astrophysics Data System (ADS)

Nobre, F. D.; Plastino, A. R.

2017-08-01

Nonlinear Schrödinger equations with power-law nonlinearities have attracted considerable attention recently. Two previous proposals for these types of equations, corresponding respectively to the Gross-Pitaievsky equation and to the one associated with nonextensive statistical mechanics, are here unified into a single, parameterized family of nonlinear Schrödinger equations. Power-law nonlinear terms characterized by exponents depending on a real index q, typical of nonextensive statistical mechanics, are considered in such a way that the Gross-Pitaievsky equation is recovered in the limit q → 1. A classical field theory shows that, due to these nonlinearities, an extra field Φ (x → , t) (besides the usual one Ψ (x → , t)) must be introduced for consistency. The new field can be identified with Ψ* (x → , t) only when q → 1. For q ≠ 1 one has a pair of coupled nonlinear wave equations governing the joint evolution of the complex valued fields Ψ (x → , t) and Φ (x → , t). These equations reduce to the usual pair of complex-conjugate ones only in the q → 1 limit. Interestingly, the nonlinear equations obeyed by Ψ (x → , t) and Φ (x → , t) exhibit a common, soliton-like, traveling solution, which is expressible in terms of the q-exponential function that naturally emerges within nonextensive statistical mechanics.

Nonlinear Field Equations and Solitons as Particles

NASA Astrophysics Data System (ADS)

Maccari, Attilio

2006-05-01

Profound advances have recently interested nonlinear field theories and their exact or approximate solutions. We review the last results and point out some important unresolved questions. It is well known that quantum field theories are based upon Fourier series and the identification of plane waves with free particles. On the contrary, nonlinear field theories admit the existence of coherent solutions (dromions, solitons and so on). Moreover, one can construct lower dimensional chaotic patterns, periodic-chaotic patterns, chaotic soliton and dromion patterns. In a similar way, fractal dromion and lump patterns as well as stochastic fractal excitations can appear in the solution. We discuss in some detail a nonlinear Dirac field and a spontaneous symmetry breaking model that are reduced by means of the asymptotic perturbation method to a system of nonlinear evolution equations integrable via an appropriate change of variables. Their coherent, chaotic and fractal solutions are examined in some detail. Finally, we consider the possible identification of some types of coherent solutions with extended particles along the de Broglie-Bohm theory. However, the last findings suggest an inadequacy of the particle concept that appears only as a particular case of nonlinear field theories excitations.

Nonlinear Interaction of Detuned Instability Waves in Boundary-Layer Transition: Resonant-Triad Interaction

NASA Technical Reports Server (NTRS)

Lee, Sang Soo

1998-01-01

The non-equilibrium critical-layer analysis of a system of frequency-detuned resonant-triads is presented using the generalized scaling of Lee. It is shown that resonant-triads can interact nonlinearly within the common critical layer when their (fundamental) Strouhal numbers are different by a factor whose magnitude is of the order of the growth rate multiplied by the wavenumber of the instability wave. Since the growth rates of the instability modes become larger and the critical layers become thicker as the instability waves propagate downstream, the frequency-detuned resonant-triads that grow independently of each other in the upstream region can interact nonlinearly in the later downstream stage. In the final stage of the non-equilibrium critical-layer evolution, a wide range of instability waves with the scaled frequencies differing by almost an Order of (l) can nonlinearly interact. Low-frequency modes are also generated by the nonlinear interaction between oblique waves in the critical layer. The system of partial differential critical-layer equations along with the jump equations are presented here. The amplitude equations with their numerical solutions are given in Part 2. The nonlinearly generated low-frequency components are also investigated in Part 2.

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.

Recent Applications of Higher-Order Spectral Analysis to Nonlinear Aeroelastic Phenomena

NASA Technical Reports Server (NTRS)

Silva, Walter A.; Hajj, Muhammad R.; Dunn, Shane; Strganac, Thomas W.; Powers, Edward J.; Stearman, Ronald

2005-01-01

Recent applications of higher-order spectral (HOS) methods to nonlinear aeroelastic phenomena are presented. Applications include the analysis of data from a simulated nonlinear pitch and plunge apparatus and from F-18 flight flutter tests. A MATLAB model of the Texas A&MUniversity s Nonlinear Aeroelastic Testbed Apparatus (NATA) is used to generate aeroelastic transients at various conditions including limit cycle oscillations (LCO). The Gaussian or non-Gaussian nature of the transients is investigated, related to HOS methods, and used to identify levels of increasing nonlinear aeroelastic response. Royal Australian Air Force (RAAF) F/A-18 flight flutter test data is presented and analyzed. The data includes high-quality measurements of forced responses and LCO phenomena. Standard power spectral density (PSD) techniques and HOS methods are applied to the data and presented. The goal of this research is to develop methods that can identify the onset of nonlinear aeroelastic phenomena, such as LCO, during flutter testing.

Nonlinear dynamics and anisotropic structure of rotating sheared turbulence.

PubMed

Salhi, A; Jacobitz, F G; Schneider, K; Cambon, C

2014-01-01

Homogeneous turbulence in rotating shear flows is studied by means of pseudospectral direct numerical simulation and analytical spectral linear theory (SLT). The ratio of the Coriolis parameter to shear rate is varied over a wide range by changing the rotation strength, while a constant moderate shear rate is used to enable significant contributions to the nonlinear interscale energy transfer and to the nonlinear intercomponental redistribution terms. In the destabilized and neutral cases, in the sense of kinetic energy evolution, nonlinearity cannot saturate the growth of the largest scales. It permits the smallest scale to stabilize by a scale-by-scale quasibalance between the nonlinear energy transfer and the dissipation spectrum. In the stabilized cases, the role of rotation is mainly nonlinear, and interacting inertial waves can affect almost all scales as in purely rotating flows. In order to isolate the nonlinear effect of rotation, the two-dimensional manifold with vanishing spanwise wave number is revisited and both two-component spectra and single-point two-dimensional energy components exhibit an important effect of rotation, whereas the SLT as well as the purely two-dimensional nonlinear analysis are unaffected by rotation as stated by the Proudman theorem. The other two-dimensional manifold with vanishing streamwise wave number is analyzed with similar tools because it is essential for any shear flow. Finally, the spectral approach is used to disentangle, in an analytical way, the linear and nonlinear terms in the dynamical equations.

Use of the dynamic stiffness method to interpret experimental data from a nonlinear system

NASA Astrophysics Data System (ADS)

Tang, Bin; Brennan, M. J.; Gatti, G.

2018-05-01

The interpretation of experimental data from nonlinear structures is challenging, primarily because of dependency on types and levels of excitation, and coupling issues with test equipment. In this paper, the use of the dynamic stiffness method, which is commonly used in the analysis of linear systems, is used to interpret the data from a vibration test of a controllable compressed beam structure coupled to a test shaker. For a single mode of the system, this method facilitates the separation of mass, stiffness and damping effects, including nonlinear stiffness effects. It also allows the separation of the dynamics of the shaker from the structure under test. The approach needs to be used with care, and is only suitable if the nonlinear system has a response that is predominantly at the excitation frequency. For the structure under test, the raw experimental data revealed little about the underlying causes of the dynamic behaviour. However, the dynamic stiffness approach allowed the effects due to the nonlinear stiffness to be easily determined.

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

The initial instability and finite-amplitude stability of alternate bars in straight channels

USGS Publications Warehouse

Nelson, J.M.

1990-01-01

The initial instability and fully developed stability of alternate bars in straight channels are investigated using linearized and nonlinear analyses. The fundamental instability leading to these features is identified through a linear stability analysis of the equations governing the flow and sediment transport fields. This instability is explained in terms of topographically induced steering of the flow and the associated pattern of erosion and deposition on the bed. While the linear theory is useful for examining the instability mechanism, this approach is shown to yield relatively little information about well-developed alternate bars and, specifically, the linear analysis is shown to yield poor predictions of the fully developed bar wavelength. A fully nonlinear approach is presented that permits computation of the evolution of these bed features from an initial perturbation to their fully developed morphology. This analysis indicates that there is typically substantial elongation of the bar wavelength during the evolution process, a result that is consistent with observations of bar development in flumes and natural channels. The nonlinear approach demonstrates that the eventual stability of these features is a result of the interplay between topographic steering effects, secondary flow production as a result of streamline curvature, and gravitationally induced modifications of sediment fluxes over a sloping bed. ?? 1990.

Parabolized Stability Equations analysis of nonlinear interactions with forced eigenmodes to control subsonic jet instabilities

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

Itasse, Maxime, E-mail: Maxime.Itasse@onera.fr; Brazier, Jean-Philippe, E-mail: Jean-Philippe.Brazier@onera.fr; Léon, Olivier, E-mail: Olivier.Leon@onera.fr

2015-08-15

Nonlinear evolution of disturbances in an axisymmetric, high subsonic, high Reynolds number hot jet with forced eigenmodes is studied using the Parabolized Stability Equations (PSE) approach to understand how modes interact with one another. Both frequency and azimuthal harmonic interactions are analyzed by setting up one or two modes at higher initial amplitudes and various phases. While single mode excitation leads to harmonic growth and jet noise amplification, controlling the evolution of a specific mode has been made possible by forcing two modes (m{sub 1}, n{sub 1}), (m{sub 2}, n{sub 2}), such that the difference in azimuth and in frequencymore » matches the desired “target” mode (m{sub 1} − m{sub 2}, n{sub 1} − n{sub 2}). A careful setup of the initial amplitudes and phases of the forced modes, defined as the “killer” modes, has allowed the minimizing of the initially dominant instability in the near pressure field, as well as its estimated radiated noise with a 15 dB loss. Although an increase of the overall sound pressure has been found in the range of azimuth and frequency analyzed, the present paper reveals the possibility to make the initially dominant instability ineffective acoustically using nonlinear interactions with forced eigenmodes.« less

Nonlinear development and secondary instability of Gortler vortices in hypersonic flows

NASA Technical Reports Server (NTRS)

Fu, Yibin B.; Hall, Philip

1991-01-01

In a hypersonic boundary layer over a wall of variable curvature, the region most susceptible to Goertler vortices is the temperature adjustment layer over which the basic state temperature decreases monotonically to its free stream value. Except for a special wall curvature distribution, the evolution of Goertler vortices trapped in the temperature adjustment layer will in general be strongly affected by the boundary layer growth through the O(M sup 3/2) curvature of the basic state, where M is the free stream Mach number. Only when the local wavenumber becomes as large as of order M sup 3/8, do nonparallel effects become negligible in the determination of stability properties. In the latter case, Goertler vortices will be trapped in a thin layer of O(epsilon sup 1/2) thickness which is embedded in the temperature adjustment layer; here epsilon is the inverse of the local wavenumber. A weakly nonlinear theory is presented in which the initial nonlinear development of Goertler vortices in the neighborhood of the neutral position is studied and two coupled evolution equations are derived. From these, it can be determined whether the vortices are decaying or growing depending on the sign of a constant which is related to wall curvature and the basic state temperature.

Evolutionary Developmental Robotics: Improving Morphology and Control of Physical Robots.

PubMed

Vujovic, Vuk; Rosendo, Andre; Brodbeck, Luzius; Iida, Fumiya

2017-01-01

Evolutionary algorithms have previously been applied to the design of morphology and control of robots. The design space for such tasks can be very complex, which can prevent evolution from efficiently discovering fit solutions. In this article we introduce an evolutionary-developmental (evo-devo) experiment with real-world robots. It allows robots to grow their leg size to simulate ontogenetic morphological changes, and this is the first time that such an experiment has been performed in the physical world. To test diverse robot morphologies, robot legs of variable shapes were generated during the evolutionary process and autonomously built using additive fabrication. We present two cases with evo-devo experiments and one with evolution, and we hypothesize that the addition of a developmental stage can be used within robotics to improve performance. Moreover, our results show that a nonlinear system-environment interaction exists, which explains the nontrivial locomotion patterns observed. In the future, robots will be present in our daily lives, and this work introduces for the first time physical robots that evolve and grow while interacting with the environment.

Automated palpation for breast tissue discrimination based on viscoelastic biomechanical properties.

PubMed

Tsukune, Mariko; Kobayashi, Yo; Miyashita, Tomoyuki; Fujie, G Masakatsu

2015-05-01

Accurate, noninvasive methods are sought for breast tumor detection and diagnosis. In particular, a need for noninvasive techniques that measure both the nonlinear elastic and viscoelastic properties of breast tissue has been identified. For diagnostic purposes, it is important to select a nonlinear viscoelastic model with a small number of parameters that highly correlate with histological structure. However, the combination of conventional viscoelastic models with nonlinear elastic models requires a large number of parameters. A nonlinear viscoelastic model of breast tissue based on a simple equation with few parameters was developed and tested. The nonlinear viscoelastic properties of soft tissues in porcine breast were measured experimentally using fresh ex vivo samples. Robotic palpation was used for measurements employed in a finite element model. These measurements were used to calculate nonlinear viscoelastic parameters for fat, fibroglandular breast parenchyma and muscle. The ability of these parameters to distinguish the tissue types was evaluated in a two-step statistical analysis that included Holm's pairwise [Formula: see text] test. The discrimination error rate of a set of parameters was evaluated by the Mahalanobis distance. Ex vivo testing in porcine breast revealed significant differences in the nonlinear viscoelastic parameters among combinations of three tissue types. The discrimination error rate was low among all tested combinations of three tissue types. Although tissue discrimination was not achieved using only a single nonlinear viscoelastic parameter, a set of four nonlinear viscoelastic parameters were able to reliably and accurately discriminate fat, breast fibroglandular tissue and muscle.

The effects of five-order nonlinear on the dynamics of dark solitons in optical fiber.

PubMed

He, Feng-Tao; Wang, Xiao-Lin; Duan, Zuo-Liang

2013-01-01

We study the influence of five-order nonlinear on the dynamic of dark soliton. Starting from the cubic-quintic nonlinear Schrodinger equation with the quadratic phase chirp term, by using a similarity transformation technique, we give the exact solution of dark soliton and calculate the precise expressions of dark soliton's width, amplitude, wave central position, and wave velocity which can describe the dynamic behavior of soliton's evolution. From two different kinds of quadratic phase chirps, we mainly analyze the effect on dark soliton's dynamics which different fiver-order nonlinear term generates. The results show the following two points with quintic nonlinearities coefficient increasing: (1) if the coefficients of the quadratic phase chirp term relate to the propagation distance, the solitary wave displays a periodic change and the soliton's width increases, while its amplitude and wave velocity reduce. (2) If the coefficients of the quadratic phase chirp term do not depend on propagation distance, the wave function only emerges in a fixed area. The soliton's width increases, while its amplitude and the wave velocity reduce.

The Effects of Five-Order Nonlinear on the Dynamics of Dark Solitons in Optical Fiber

PubMed Central

Wang, Xiao-Lin; Duan, Zuo-Liang

2013-01-01

We study the influence of five-order nonlinear on the dynamic of dark soliton. Starting from the cubic-quintic nonlinear Schrodinger equation with the quadratic phase chirp term, by using a similarity transformation technique, we give the exact solution of dark soliton and calculate the precise expressions of dark soliton's width, amplitude, wave central position, and wave velocity which can describe the dynamic behavior of soliton's evolution. From two different kinds of quadratic phase chirps, we mainly analyze the effect on dark soliton's dynamics which different fiver-order nonlinear term generates. The results show the following two points with quintic nonlinearities coefficient increasing: (1) if the coefficients of the quadratic phase chirp term relate to the propagation distance, the solitary wave displays a periodic change and the soliton's width increases, while its amplitude and wave velocity reduce. (2) If the coefficients of the quadratic phase chirp term do not depend on propagation distance, the wave function only emerges in a fixed area. The soliton's width increases, while its amplitude and the wave velocity reduce. PMID:23818814

Nonlinear evolution equations for surface plasmons for nano-focusing at a Kerr/metallic interface and tapered waveguide

NASA Astrophysics Data System (ADS)

Crutcher, Sihon H.; Osei, Albert; Biswas, Anjan

2012-06-01

Maxwell's equations for a metallic and nonlinear Kerr interface waveguide at the nanoscale can be approximated to a (1+1) D Nonlinear Schrodinger type model equation (NLSE) with appropriate assumptions and approximations. Theoretically, without losses or perturbations spatial plasmon solitons profiles are easily produced. However, with losses, the amplitude or beam profile is no longer stationary and adiabatic parameters have to be considered to understand propagation. For this model, adiabatic parameters are calculated considering losses resulting in linear differential coupled integral equations with constant definite integral coefficients not dependent on the transverse and longitudinal coordinates. Furthermore, by considering another configuration, a waveguide that is an M-NL-M (metal-nonlinear Kerr-metal) that tapers, the tapering can balance the loss experienced at a non-tapered metal/nonlinear Kerr interface causing attenuation of the beam profile, so these spatial plasmon solitons can be produced. In this paper taking into consideration the (1+1)D NLSE model for a tapered waveguide, we derive a one soliton solution based on He's Semi-Inverse Variational Principle (HPV).

GEOPHYSICS, ASTRONOMY AND ASTROPHYSICS: Numerical method of studying nonlinear interactions between long waves and multiple short waves

NASA Astrophysics Data System (ADS)

Xie, Tao; Kuang, Hai-Lan; William, Perrie; Zou, Guang-Hui; Nan, Cheng-Feng; He, Chao; Shen, Tao; Chen, Wei

2009-07-01

Although the nonlinear interactions between a single short gravity wave and a long wave can be solved analytically, the solution is less tractable in more general cases involving multiple short waves. In this work we present a numerical method of studying nonlinear interactions between a long wave and multiple short harmonic waves in infinitely deep water. Specifically, this method is applied to the calculation of the temporal and spatial evolutions of the surface elevations in which a given long wave interacts with several short harmonic waves. Another important application of our method is to quantitatively analyse the nonlinear interactions between an arbitrary short wave train and another short wave train. From simulation results, we obtain that the mechanism for the nonlinear interactions between one short wave train and another short wave train (expressed as wave train 2) leads to the energy focusing of the other short wave train (expressed as wave train 3). This mechanism occurs on wave components with a narrow frequency bandwidth, whose frequencies are near that of wave train 3.

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.

A Review of Alfvénic Turbulence in High-Speed Solar Wind Streams: Hints From Cometary Plasma Turbulence

NASA Astrophysics Data System (ADS)

Tsurutani, Bruce T.; Lakhina, Gurbax S.; Sen, Abhijit; Hellinger, Petr; Glassmeier, Karl-Heinz; Mannucci, Anthony J.

2018-04-01

Solar wind turbulence within high-speed streams is reviewed from the point of view of embedded single nonlinear Alfvén wave cycles, discontinuities, magnetic decreases (MDs), and shocks. For comparison and guidance, cometary plasma turbulence is also briefly reviewed. It is demonstrated that cometary nonlinear magnetosonic waves phase-steepen, with a right-hand circular polarized foreshortened front and an elongated, compressive trailing edge. The former part is a form of "wave breaking" and the latter that of "period doubling." Interplanetary nonlinear Alfvén waves, which are arc polarized, have a 180° foreshortened front and with an elongated trailing edge. Alfvén waves have polarizations different from those of cometary magnetosonic waves, indicating that helicity is a durable feature of plasma turbulence. Interplanetary Alfvén waves are noted to be spherical waves, suggesting the possibility of additional local generation. They kinetically dissipate, forming MDs, indicating that the solar wind is partially "compressive" and static. The 2 MeV protons can nonresonantly interact with MDs leading to rapid cross-field ( 5.5% Bohm) diffusion. The possibility of local ( 1 AU) generation of Alfvén waves may make it difficult to forecast High-Intensity, Long-Duration AE Activity and relativistic magnetospheric electrons with great accuracy. The future Solar Orbiter and Solar Probe Plus missions should be able to not only test these ideas but to also extend our knowledge of plasma turbulence evolution.

Nonlinear structure formation in flat cosmological models

NASA Technical Reports Server (NTRS)

Martel, Hugo

1995-01-01

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

Resonant Column Tests and Nonlinear Elasticity in Simulated Rocks

NASA Astrophysics Data System (ADS)

Sebastian, Resmi; Sitharam, T. G.

2018-01-01

Rocks are generally regarded as linearly elastic even though the manifestations of nonlinearity are prominent. The variations of elastic constants with varying strain levels and stress conditions, disagreement between static and dynamic moduli, etc., are some of the examples of nonlinear elasticity in rocks. The grain-to-grain contact, presence of pores and joints along with other compliant features induce the nonlinear behavior in rocks. The nonlinear elastic behavior of rocks is demonstrated through resonant column tests and numerical simulations in this paper. Resonant column tests on intact and jointed gypsum samples across varying strain levels have been performed in laboratory and using numerical simulations. The paper shows the application of resonant column apparatus to obtain the wave velocities of stiff samples at various strain levels under long wavelength condition, after performing checks and incorporating corrections to the obtained resonant frequencies. The numerical simulation and validation of the resonant column tests using distinct element method are presented. The stiffness reductions of testing samples under torsional and flexural vibrations with increasing strain levels have been analyzed. The nonlinear elastic behavior of rocks is reflected in the results, which is enhanced by the presence of joints. The significance of joint orientation and influence of joint spacing during wave propagation have also been assessed and presented using the numerical simulations. It has been found that rock joints also exhibit nonlinear behavior within the elastic limit.

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

Popovich, P.; Carter, T. A.; Friedman, B.

Numerical simulation of plasma turbulence in the Large Plasma Device (LAPD) [W. Gekelman, H. Pfister, Z. Lucky et al., Rev. Sci. Instrum. 62, 2875 (1991)] is presented. The model, implemented in the BOUndary Turbulence code [M. Umansky, X. Xu, B. Dudson et al., Contrib. Plasma Phys. 180, 887 (2009)], includes three-dimensional (3D) collisional fluid equations for plasma density, electron parallel momentum, and current continuity, and also includes the effects of ion-neutral collisions. In nonlinear simulations using measured LAPD density profiles but assuming constant temperature profile for simplicity, self-consistent evolution of instabilities and nonlinearly generated zonal flows results in a saturatedmore » turbulent state. Comparisons of these simulations with measurements in LAPD plasmas reveal good qualitative and reasonable quantitative agreement, in particular in frequency spectrum, spatial correlation, and amplitude probability distribution function of density fluctuations. For comparison with LAPD measurements, the plasma density profile in simulations is maintained either by direct azimuthal averaging on each time step, or by adding particle source/sink function. The inferred source/sink values are consistent with the estimated ionization source and parallel losses in LAPD. These simulations lay the groundwork for more a comprehensive effort to test fluid turbulence simulation against LAPD data.« less

Secondary Instability of Second Modes in Hypersonic Boundary Layers

NASA Technical Reports Server (NTRS)

Li, Fei; Choudhari, Meelan M.; Chang, Chau-Lyan; White, Jeffery A.

2012-01-01

Second mode disturbances dominate the primary instability stage of transition in a number of hypersonic flow configurations. The highest amplification rates of second mode disturbances are usually associated with 2D (or axisymmetric) perturbations and, therefore, a likely scenario for the onset of the three-dimensionality required for laminar-turbulent transition corresponds to the parametric amplification of 3D secondary instabilities in the presence of 2D, finite amplitude second mode disturbances. The secondary instability of second mode disturbances is studied for selected canonical flow configurations. The basic state for the secondary instability analysis is obtained by tracking the linear and nonlinear evolution of 2D, second mode disturbances using nonlinear parabolized stability equations. Unlike in previous studies, the selection of primary disturbances used for the secondary instability analysis was based on their potential relevance to transition in a low disturbance environment and the effects of nonlinearity on the evolution of primary disturbances was accounted for. Strongly nonlinear effects related to the self-interaction of second mode disturbances lead to an upstream shift in the upper branch neutral location. Secondary instability computations confirm the previously known dominance of subharmonic modes at relatively small primary amplitudes. However, for the Purdue Mach 6 compression cone configuration, it was shown that a strong fundamental secondary instability can exist for a range of initial amplitudes of the most amplified second mode disturbance, indicating that the exclusive focus on subharmonic modes in the previous applications of secondary instability theory to second mode primary instability may not have been fully justified.

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.

Linear and nonlinear propagation of water wave groups

NASA Technical Reports Server (NTRS)

Pierson, W. J., Jr.; Donelan, M. A.; Hui, W. H.

1992-01-01

Results are presented from a study of the evolution of waveforms with known analytical group shapes, in the form of both transient wave groups and the cloidal (cn) and dnoidal (dn) wave trains as derived from the nonlinear Schroedinger equation. The waveforms were generated in a long wind-wave tank of the Canada Centre for Inland Waters. It was found that the low-amplitude transients behaved as predicted by the linear theory and that the cn and dn wave trains of moderate steepness behaved almost as predicted by the nonlinear Schroedinger equation. Some of the results did not fit into any of the available theories for waves on water, but they provide important insight on how actual groups of waves propagate and on higher-order effects for a transient waveform.

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

Real-Time Global Nonlinear Aerodynamic Modeling for Learn-To-Fly

NASA Technical Reports Server (NTRS)

Morelli, Eugene A.

2016-01-01

Flight testing and modeling techniques were developed to accurately identify global nonlinear aerodynamic models for aircraft in real time. The techniques were developed and demonstrated during flight testing of a remotely-piloted subscale propeller-driven fixed-wing aircraft using flight test maneuvers designed to simulate a Learn-To-Fly scenario. Prediction testing was used to evaluate the quality of the global models identified in real time. The real-time global nonlinear aerodynamic modeling algorithm will be integrated and further tested with learning adaptive control and guidance for NASA Learn-To-Fly concept flight demonstrations.

Dynamics of double-polarity subduction: application to the Western Mediterranean

NASA Astrophysics Data System (ADS)

Peral, Mireia; Zlotnik, Sergio; Fernandez, Manel; Vergés, Jaume; Jiménez-Munt, Ivone; Torne, Montserrat

2016-04-01

The evolution of the Western Mediterranean is a highly debated question by geologists and geophysicists. Even though most scientists agree in considering slab roll-back to be the driving mechanism of the tectonic evolution of this area, there is still no consensus about the initial setup and its time evolution. A recent model suggests a lateral change in subduction polarity of the Ligurian-Thetys oceanic domain to explain the formation and evolution of the Betic-Rif orogenic system and the associated Alboran back-arc basin. Such geodynamic scenario is also proposed for different converging regions. The aim of this study is to analyze the dynamic evolution of a double-polarity subduction process and its consequences in order to test the physical feasibility of this interaction and provide geometries and evolutions comparable to those proposed for the Western Mediterranean. The 3D numerical model is carried out via the Underworld framework. Tectonic plate behavior is described by equations of fluid dynamics in the presence of several different phases. Underworld solves a non-linear Stokes flow problem using Finite Elements combined with particle-in-cell approach, thus the discretization combines a standard Eulerian Finite Element mesh with Lagrangian particles to track the location of the phases. The final model consists of two oceanic plates with viscoplastic rheology subducting into the upper mantle in opposite direction and the problem is driven by Rayleigh-Taylor instability. We study the influence of the boundary conditions in the model evolution, and the slab deformation produced by the proximity between both plates. Moreover the case of asymmetric friction on the lateral sides of slabs is also considered. Simulations of single subduction models are used as a reference, to compare results and understand the influence of the second plate. We observe slight differences in the trench retreat velocity and the slab morphology near the contact area when plates are spaced less than 100 km.

A simple predistortion technique for suppression of nonlinear effects in periodic signals generated by nonlinear transducers

NASA Astrophysics Data System (ADS)

Novak, A.; Simon, L.; Lotton, P.

2018-04-01

Mechanical transducers, such as shakers, loudspeakers and compression drivers that are used as excitation devices to excite acoustical or mechanical nonlinear systems under test are imperfect. Due to their nonlinear behaviour, unwanted contributions appear at their output besides the wanted part of the signal. Since these devices are used to study nonlinear systems, it should be required to measure properly the systems under test by overcoming the influence of the nonlinear excitation device. In this paper, a simple method that corrects distorted output signal of the excitation device by means of predistortion of its input signal is presented. A periodic signal is applied to the input of the excitation device and, from analysing the output signal of the device, the input signal is modified in such a way that the undesirable spectral components in the output of the excitation device are cancelled out after few iterations of real-time processing. The experimental results provided on an electrodynamic shaker show that the spectral purity of the generated acceleration output approaches 100 dB after few iterations (1 s). This output signal, applied to the system under test, is thus cleaned from the undesirable components produced by the excitation device; this is an important condition to ensure a correct measurement of the nonlinear system under test.

Symmetry breaking in the opinion dynamics of a multi-group project organization

NASA Astrophysics Data System (ADS)

Zhu, Zhen-Tao; Zhou, Jing; Li, Ping; Chen, Xing-Guang

2012-10-01

A bounded confidence model of opinion dynamics in multi-group projects is presented in which each group's opinion evolution is driven by two types of forces: (i) the group's cohesive force which tends to restore the opinion back towards the initial status because of its company culture; and (ii) nonlinear coupling forces with other groups which attempt to bring opinions closer due to collaboration willingness. Bifurcation analysis for the case of a two-group project shows a cusp catastrophe phenomenon and three distinctive evolutionary regimes, i.e., a deadlock regime, a convergence regime, and a bifurcation regime in opinion dynamics. The critical value of initial discord between the two groups is derived to discriminate which regime the opinion evolution belongs to. In the case of a three-group project with a symmetric social network, both bifurcation analysis and simulation results demonstrate that if each pair has a high initial discord, instead of symmetrically converging to consensus with the increase of coupling scale as expected by Gabbay's result (Physica A 378 (2007) p. 125 Fig. 5), project organization (PO) may be split into two distinct clusters because of the symmetry breaking phenomenon caused by pitchfork bifurcations, which urges that apart from divergence in participants' interests, nonlinear interaction can also make conflict inevitable in the PO. The effects of two asymmetric level parameters are tested in order to explore the ways of inducing dominant opinion in the whole PO. It is found that the strong influence imposed by a leader group with firm faith on the flexible and open minded follower groups can promote the formation of a positive dominant opinion in the PO.

Parametric instability, inverse cascade and the range of solar-wind turbulence

NASA Astrophysics Data System (ADS)

Chandran, Benjamin D. G.

2018-02-01

In this paper, weak-turbulence theory is used to investigate the nonlinear evolution of the parametric instability in three-dimensional low- plasmas at wavelengths much greater than the ion inertial length under the assumption that slow magnetosonic waves are strongly damped. It is shown analytically that the parametric instability leads to an inverse cascade of Alfvén wave quanta, and several exact solutions to the wave kinetic equations are presented. The main results of the paper concern the parametric decay of Alfvén waves that initially satisfy +\\gg e-$ , where +$ and -$ are the frequency ( ) spectra of Alfvén waves propagating in opposite directions along the magnetic field lines. If +$ initially has a peak frequency 0$ (at which +$ is maximized) and an `infrared' scaling p$ at smaller with , then +$ acquires an -1$ scaling throughout a range of frequencies that spreads out in both directions from 0$ . At the same time, -$ acquires an -2$ scaling within this same frequency range. If the plasma parameters and infrared +$ spectrum are chosen to match conditions in the fast solar wind at a heliocentric distance of 0.3 astronomical units (AU), then the nonlinear evolution of the parametric instability leads to an +$ spectrum that matches fast-wind measurements from the Helios spacecraft at 0.3 AU, including the observed -1$ scaling at -4~\\text{Hz}$ . The results of this paper suggest that the -1$ spectrum seen by Helios in the fast solar wind at -4~\\text{Hz}$ is produced in situ by parametric decay and that the -1$ range of +$ extends over an increasingly narrow range of frequencies as decreases below 0.3 AU. This prediction will be tested by measurements from the Parker Solar Probe.

Nonlinear Evolution of Azimuthally Compact Crossflow-Vortex Packet over a Yawed Cone

NASA Astrophysics Data System (ADS)

Choudhari, Meelan; Li, Fei; Paredes, Pedro; Duan, Lian; NASA Langley Research Center Team; Missouri Univ of Sci; Tech Team

2017-11-01

Hypersonic boundary-layer flows over a circular cone at moderate incidence angle can support strong crossflow instability and, therefore, a likely scenario for laminar-turbulent transition in such flows corresponds to rapid amplification of high-frequency secondary instabilities sustained by finite amplitude stationary crossflow vortices. Direct numerical simulations (DNS) are used to investigate the nonlinear evolution of azimuthally compact crossflow vortex packets over a 7-degree half-angle, yawed circular cone in a Mach 6 free stream. Simulation results indicate that the azimuthal distribution of forcing has a strong influence on the stationary crossflow amplitudes; however, the vortex trajectories are nearly the same for both periodic and localized roughness height distributions. The frequency range, mode shapes, and amplification characteristics of strongly amplified secondary instabilities in the DNS are found to overlap with the predictions of secondary instability theory. The DNS computations also provide valuable insights toward the application of planar, partial-differential-equation based eigenvalue analysis to spanwise inhomogeneous, fully three-dimensional, crossflow-dominated flow configurations.

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.

Bell-polynomial approach and Wronskian determinant solutions for three sets of differential-difference nonlinear evolution equations with symbolic computation

NASA Astrophysics Data System (ADS)

Qin, Bo; Tian, Bo; Wang, Yu-Feng; Shen, Yu-Jia; Wang, Ming

2017-10-01

Under investigation in this paper are the Belov-Chaltikian (BC), Leznov and Blaszak-Marciniak (BM) lattice equations, which are associated with the conformal field theory, UToda(m_1,m_2) system and r-matrix, respectively. With symbolic computation, the Bell-polynomial approach is developed to directly bilinearize those three sets of differential-difference nonlinear evolution equations (NLEEs). This Bell-polynomial approach does not rely on any dependent variable transformation, which constitutes the key step and main difficulty of the Hirota bilinear method, and thus has the advantage in the bilinearization of the differential-difference NLEEs. Based on the bilinear forms obtained, the N-soliton solutions are constructed in terms of the N × N Wronskian determinant. Graphic illustrations demonstrate that those solutions, more general than the existing results, permit some new properties, such as the solitonic propagation and interactions for the BC lattice equations, and the nonnegative dark solitons for the BM lattice equations.

Evolution of finite-amplitude localized vortices in planar homogeneous shear flows

NASA Astrophysics Data System (ADS)

Karp, Michael; Shukhman, Ilia G.; Cohen, Jacob

2017-02-01

An analytical-based method is utilized to follow the evolution of localized initially Gaussian disturbances in flows with homogeneous shear, in which the base velocity components are at most linear functions of the coordinates, including hyperbolic, elliptic, and simple shear. Coherent structures, including counterrotating vortex pairs (CVPs) and hairpin vortices, are formed for the cases where the streamlines of the base flow are open (hyperbolic and simple shear). For hyperbolic base flows, the dominance of shear over rotation leads to elongation of the localized disturbance along the outlet asymptote and formation of CVPs. For simple shear CVPs are formed from linear and nonlinear disturbances, whereas hairpins are observed only for highly nonlinear disturbances. For elliptic base flows CVPs, hairpins and vortex loops form initially, however they do not last and break into various vortical structures that spread in the spanwise direction. The effect of the disturbance's initial amplitude and orientation is examined and the optimal orientation achieving maximal growth is identified.

Stability of hypersonic compression cones

NASA Astrophysics Data System (ADS)

Reed, Helen; Kuehl, Joseph; Perez, Eduardo; Kocian, Travis; Oliviero, Nicholas

2012-11-01

Our activities focus on the identification and understanding of the second-mode instability for representative configurations in hypersonic flight. These include the Langley 93-10 flared cone and the Purdue compression cone, both at 0 degrees angle of attack at Mach 6. Through application of nonlinear parabolized stability equations (NPSE) and linear parabolized stability equations (PSE) to both geometries, it is concluded that mean-flow distortion tends to amplify frequencies less than the peak frequency and stabilize those greater by modifying the boundary-layer thickness. As initial disturbance amplitude is increased and/or a broad spectrum disturbance is introduced, direct numerical simulations (DNS) or NPSE appear to be the proper choices to model the evolution, and relative evolution, because these computational tools include these nonlinear effects (mean-flow distortion). Support from AFOSR/NASA National Center for Hypersonic Research in Laminar-Turbulent Transition through Grant FA9550-09-1-0341 is gratefully acknowledged. The authors also thank Pointwise, AeroSoft, and Texas Advanced Computing Center (TACC).

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

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.

Evolution of helical perturbations in a thin-shell model of an imploding liner

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

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

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

Nonlinear stochastic interacting dynamics and complexity of financial gasket fractal-like lattice percolation

NASA Astrophysics Data System (ADS)

Zhang, Wei; Wang, Jun

2018-05-01

A novel nonlinear stochastic interacting price dynamics is proposed and investigated by the bond percolation on Sierpinski gasket fractal-like lattice, aim to make a new approach to reproduce and study the complexity dynamics of real security markets. Fractal-like lattices correspond to finite graphs with vertices and edges, which are similar to fractals, and Sierpinski gasket is a well-known example of fractals. Fractional ordinal array entropy and fractional ordinal array complexity are introduced to analyze the complexity behaviors of financial signals. To deeper comprehend the fluctuation characteristics of the stochastic price evolution, the complexity analysis of random logarithmic returns and volatility are preformed, including power-law distribution, fractional sample entropy and fractional ordinal array complexity. For further verifying the rationality and validity of the developed stochastic price evolution, the actual security market dataset are also studied with the same statistical methods for comparison. The empirical results show that this stochastic price dynamics can reconstruct complexity behaviors of the actual security markets to some extent.

Physics-based Control-oriented Modeling of the Current Profile Evolution in NSTX-Upgrade

NASA Astrophysics Data System (ADS)

Ilhan, Zeki; Barton, Justin; Shi, Wenyu; Schuster, Eugenio; Gates, David; Gerhardt, Stefan; Kolemen, Egemen; Menard, Jonathan

2013-10-01

The operational goals for the NSTX-Upgrade device include non-inductive sustainment of high- β plasmas, realization of the high performance equilibrium scenarios with neutral beam heating, and achievement of longer pulse durations. Active feedback control of the current profile is proposed to enable these goals. Motivated by the coupled, nonlinear, multivariable, distributed-parameter plasma dynamics, the first step towards feedback control design is the development of a physics-based, control-oriented model for the current profile evolution in response to non-inductive current drives and heating systems. For this purpose, the nonlinear magnetic-diffusion equation is coupled with empirical models for the electron density, electron temperature, and non-inductive current drives (neutral beams). The resulting first-principles-driven, control-oriented model is tailored for NSTX-U based on the PTRANSP predictions. Main objectives and possible challenges associated with the use of the developed model for control design are discussed. This work was supported by PPPL.

Salient features of solitary waves in dusty plasma under the influence of Coriolis force

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

Das, G. C.; Nag, Apratim; Department of Physics, G. C. College, Silchar-788004

The main interest is to study the nonlinear acoustic wave in rotating dusty plasma augmented through the derivation of a modified Sagdeev potential equation. Small rotation causes the interaction of Coriolis force in the dynamical system, and leads to the complexity in the derivation of the nonlinear wave equation. As a result, the finding of solitary wave propagation in dusty plasma ought to be of merit. However, the nonlinear wave equation has been successfully solved by the use of the hyperbolic method. Main emphasis has been given to the changes on the evolution and propagation of soliton, and the variationmore » caused by the dusty plasma constituents as well as by the Coriolis force have been highlighted. Some interesting nonlinear wave behavior has been found which can be elaborately studied for the interest of laboratory and space plasmas. Further, to support the theoretical investigations, numeric plasma parameters have been taken for finding the inherent features of solitons.« less

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.