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

Lee, Wonjung; Kovacic, Gregor; Cai, David

Using the (1+1)D Majda-McLaughlin-Tabak model as an example, we present an extension of the wave turbulence (WT) theory to systems with strong nonlinearities. We demonstrate that nonlinear wave interactions renormalize the dynamics, leading to (i) a possible destruction of scaling structures in the bare wave systems and a drastic deformation of the resonant manifold even at weak nonlinearities, and (ii) creation of nonlinear resonance quartets in wave systems for which there would be no resonances as predicted by the linear dispersion relation. Finally, we derive an effective WT kinetic equation and show that our prediction of the renormalized Rayleigh-Jeans distributionmore » is in excellent agreement with the simulation of the full wave system in equilibrium.« less

Detection of weak signals through nonlinear relaxation times for a Brownian particle in an electromagnetic field.

PubMed

Jiménez-Aquino, J I; Romero-Bastida, M

2011-07-01

The detection of weak signals through nonlinear relaxation times for a Brownian particle in an electromagnetic field is studied in the dynamical relaxation of the unstable state, characterized by a two-dimensional bistable potential. The detection process depends on a dimensionless quantity referred to as the receiver output, calculated as a function of the nonlinear relaxation time and being a characteristic time scale of our system. The latter characterizes the complete dynamical relaxation of the Brownian particle as it relaxes from the initial unstable state of the bistable potential to its corresponding steady state. The one-dimensional problem is also studied to complement the description.

Nonlinear dynamics induced in a structure by seismic and environmental loading

DOE PAGES

Gueguen, Philippe; Johnson, Paul Allan; Roux, Philippe

2016-07-26

In this study,we show that under very weak dynamic and quasi-static deformation, that is orders of magnitude below the yield deformation of the equivalent stress strain curve (around 10 -3), the elastic parameters of a civil engineering structure (resonance frequency and damping) exhibit nonlinear softening and recovery. These observations bridge the gap between laboratory and seismic scales where elastic nonlinear behavior has been previously observed. Under weak seismic or atmospheric loading, modal frequencies are modified by around 1% and damping by more than 100% for strain levels between 10 -7 and 10 -4. These observations support the concept of universalmore » behavior of nonlinear elastic behavior in diverse systems, including granular materials and damaged solids that scale from millimeter dimensions to the scale of structures to fault dimensions in the Earth.« less

Nonlinear dynamics induced in a structure by seismic and environmental loading

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

Gueguen, Philippe; Johnson, Paul Allan; Roux, Philippe

In this study,we show that under very weak dynamic and quasi-static deformation, that is orders of magnitude below the yield deformation of the equivalent stress strain curve (around 10 -3), the elastic parameters of a civil engineering structure (resonance frequency and damping) exhibit nonlinear softening and recovery. These observations bridge the gap between laboratory and seismic scales where elastic nonlinear behavior has been previously observed. Under weak seismic or atmospheric loading, modal frequencies are modified by around 1% and damping by more than 100% for strain levels between 10 -7 and 10 -4. These observations support the concept of universalmore » behavior of nonlinear elastic behavior in diverse systems, including granular materials and damaged solids that scale from millimeter dimensions to the scale of structures to fault dimensions in the Earth.« less

Dynamics in terahertz semiconductor microcavity: quantum noise spectra

NASA Astrophysics Data System (ADS)

Jabri, H.; Eleuch, H.

2018-05-01

We investigate the physics of an optical semiconductor microcavity containing a coupled double quantum well interacting with cavity photons. The photon statistics of the transmitted light by the cavity is explored. We show that the nonlinear interactions in the direct and indirect excitonic modes generate an important squeezing despite the weak nonlinearities. When the strong coupling regime is achieved, the noise spectra of the system is dominated by the indirect exciton distribution. At the opposite, in the weak regime, direct excitons contribute much larger in the noise spectra.

Generating giant and tunable nonlinearity in a macroscopic mechanical resonator from a single chemical bond

NASA Astrophysics Data System (ADS)

Huang, Pu; Zhou, Jingwei; Zhang, Liang; Hou, Dong; Lin, Shaochun; Deng, Wen; Meng, Chao; Duan, Changkui; Ju, Chenyong; Zheng, Xiao; Xue, Fei; Du, Jiangfeng

2016-05-01

Nonlinearity in macroscopic mechanical systems may lead to abundant phenomena for fundamental studies and potential applications. However, it is difficult to generate nonlinearity due to the fact that macroscopic mechanical systems follow Hooke's law and respond linearly to external force, unless strong drive is used. Here we propose and experimentally realize high cubic nonlinear response in a macroscopic mechanical system by exploring the anharmonicity in chemical bonding interactions. We demonstrate the high tunability of nonlinear response by precisely controlling the chemical bonding interaction, and realize, at the single-bond limit, a cubic elastic constant of 1 × 1020 N m-3. This enables us to observe the resonator's vibrational bi-states transitions driven by the weak Brownian thermal noise at 6 K. This method can be flexibly applied to a variety of mechanical systems to improve nonlinear responses, and can be used, with further improvements, to explore macroscopic quantum mechanics.

Superdiffusive transport and energy localization in disordered granular crystals

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

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

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

Superdiffusive transport and energy localization in disordered granular crystals

DOE PAGES

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

2016-02-12

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

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 hybrid modal synthesis based on branch modes for dynamic analysis of assembled structure

NASA Astrophysics Data System (ADS)

Huang, Xing-Rong; Jézéquel, Louis; Besset, Sébastien; Li, Lin; Sauvage, Olivier

2018-01-01

This paper describes a simple and fast numerical procedure to study the steady state responses of assembled structures with nonlinearities along continuous interfaces. The proposed strategy is based on a generalized nonlinear modal superposition approach supplemented by a double modal synthesis strategy. The reduced nonlinear modes are derived by combining a single nonlinear mode method with reduction techniques relying on branch modes. The modal parameters containing essential nonlinear information are determined and then employed to calculate the stationary responses of the nonlinear system subjected to various types of excitation. The advantages of the proposed nonlinear modal synthesis are mainly derived in three ways: (1) computational costs are considerably reduced, when analyzing large assembled systems with weak nonlinearities, through the use of reduced nonlinear modes; (2) based on the interpolation models of nonlinear modal parameters, the nonlinear modes introduced during the first step can be employed to analyze the same system under various external loads without having to reanalyze the entire system; and (3) the nonlinear effects can be investigated from a modal point of view by analyzing these nonlinear modal parameters. The proposed strategy is applied to an assembled system composed of plates and nonlinear rubber interfaces. Simulation results have proven the efficiency of this hybrid nonlinear modal synthesis, and the computation time has also been significantly reduced.

Optical Wave Turbulence and Wave Condensation in a Nonlinear Optical Experiment

NASA Astrophysics Data System (ADS)

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

We present theory, numerical simulations and experimental observations of a 1D optical wave system. We show that this system is of a dual cascade type, namely, the energy cascading directly to small scales, and the photons or wave action cascading to large scales. In the optical context the inverse cascade is particularly interesting because it means the condensation of photons. We show that the cascades are induced by a six-wave resonant interaction process described by weak turbulence theory. We show that by starting with weakly nonlinear randomized waves as an initial condition, there exists an inverse cascade of photons towards the lowest wavenumbers. During the cascade nonlinearity becomes strong at low wavenumbers and, due to the focusing nature of the nonlinearity, it leads to modulational instability resulting in the formation of solitons. Further interaction of the solitons among themselves and with incoherent waves leads to the final condensate state dominated by a single strong soliton. In addition, we show the existence of the direct energy cascade numerically and that it agrees with the wave turbulence prediction.

Nonlinear Dynamics of a Magnetically Driven Duffing-Type Spring-Magnet Oscillator in the Static Magnetic Field of a Coil

ERIC Educational Resources Information Center

Donoso, Guillermo; Ladera, Celso L.

2012-01-01

We study the nonlinear oscillations of a forced and weakly dissipative spring-magnet system moving in the magnetic fields of two fixed coaxial, hollow induction coils. As the first coil is excited with a dc current, both a linear and a cubic magnet-position dependent force appear on the magnet-spring system. The second coil, located below the…

Phase slips in superconducting weak links

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

Kimmel, Gregory; Glatz, Andreas; Aranson, Igor S.

2017-01-01

Superconducting vortices and phase slips are primary mechanisms of dissipation in superconducting, superfluid, and cold-atom systems. While the dynamics of vortices is fairly well described, phase slips occurring in quasi-one- dimensional superconducting wires still elude understanding. The main reason is that phase slips are strongly nonlinear time-dependent phenomena that cannot be cast in terms of small perturbations of the superconducting state. Here we study phase slips occurring in superconducting weak links. Thanks to partial suppression of superconductivity in weak links, we employ a weakly nonlinear approximation for dynamic phase slips. This approximation is not valid for homogeneous superconducting wires andmore » slabs. Using the numerical solution of the time-dependent Ginzburg-Landau equation and bifurcation analysis of stationary solutions, we show that the onset of phase slips occurs via an infinite period bifurcation, which is manifested in a specific voltage-current dependence. Our analytical results are in good agreement with simulations.« less

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

NASA Astrophysics Data System (ADS)

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

2017-04-01

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

Stationary states of extended nonlinear Schrödinger equation with a source

NASA Astrophysics Data System (ADS)

Borich, M. A.; Smagin, V. V.; Tankeev, A. P.

2007-02-01

Structure of nonlinear stationary states of the extended nonlinear Schrödinger equation (ENSE) with a source has been analyzed with allowance for both third-order and nonlinearity dispersion. A new class of particular solutions (solitary waves) of the ENSe has been obtained. The scenario of the destruction of these states under the effect of an external perturbation has been investigated analytically and numerically. The results obtained can be used to interpret experimental data on the weakly nonlinear dynamics of the magnetostatic envelope in heterophase ferromagnet-insulator-metal, metal-insulator-ferromagnet-insulator-metal, and other similar structures and upon the simulation of nonlinear processes in optical systems.

Nonlinear interactions in mixing layers and compressible heated round jets. Ph.D. Thesis Final Report

NASA Technical Reports Server (NTRS)

Jarrah, Yousef Mohd

1989-01-01

The nonlinear interactions between a fundamental instability mode and both its harmonics and the changing mean flow are studied using the weakly nonlinear stability theory of Stuart and Watson, and numerical solutions of coupled nonlinear partial differential equations. The first part focuses on incompressible cold (or isothermal; constant temperature throughout) mixing layers, and for these, the first and second Landau constants are calculated as functions of wavenumber and Reynolds number. It is found that the dominant contribution to the Landau constants arises from the mean flow changes and not from the higher harmonics. In order to establish the range of validity of the weakly nonlinear theory, the weakly nonlinear and numerical solutions are compared and the limitation of each is discussed. At small amplitudes and at low-to-moderate Reynolds numbers, the two results compare well in describing the saturation of the fundamental, the distortion of the mean flow, and the initial stages of vorticity roll-up. At larger amplitudes, the interaction between the fundamental, second harmonic, and the mean flow is strongly nonlinear and the numerical solution predicts flow oscillations, whereas the weakly nonlinear theory yields saturation. In the second part, the weakly nonlinear theory is extended to heated (or nonisothermal; mean temperature distribution) subsonic round jets where quadratic and cubic nonlinear interactions are present, and the Landau constants also depend on jet temperature ratio, Mach number and azimuthal mode number. Under exponential growth and nonlinear saturation, it is found that heating and compressibility suppress the growth of instability waves, that the first azimuthal mode is the dominant instability mode, and that the weakly nonlinear solution describes the early stages of the roll-up of an axisymmetric shear layer. The receptivity of a typical jet flow to pulse type input disturbance is also studied by solving the initial value problem and then examining the behavior of the long-time solution.

Special discontinuities in nonlinearly elastic media

NASA Astrophysics Data System (ADS)

Chugainova, A. P.

2017-06-01

Solutions of a nonlinear hyperbolic system of equations describing weakly nonlinear quasitransverse waves in a weakly anisotropic elastic medium are studied. The influence of small-scale processes of dissipation and dispersion is investigated. The small-scale processes determine the structure of discontinuities (shocks) and a set of discontinuities with a stationary structure. Among the discontinuities with a stationary structure, there are special ones that, in addition to relations following from conservation laws, satisfy additional relations required for the existence of their structure. In the phase plane, the structure of such discontinuities is represented by an integral curve joining two saddles. Special discontinuities lead to nonunique self-similar solutions of the Riemann problem. Asymptotics of non-self-similar problems for equations with dissipation and dispersion are found numerically. These asymptotics correspond to self-similar solutions of the problems.

Generating giant and tunable nonlinearity in a macroscopic mechanical resonator from a single chemical bond.

PubMed

Huang, Pu; Zhou, Jingwei; Zhang, Liang; Hou, Dong; Lin, Shaochun; Deng, Wen; Meng, Chao; Duan, Changkui; Ju, Chenyong; Zheng, Xiao; Xue, Fei; Du, Jiangfeng

2016-05-26

Nonlinearity in macroscopic mechanical systems may lead to abundant phenomena for fundamental studies and potential applications. However, it is difficult to generate nonlinearity due to the fact that macroscopic mechanical systems follow Hooke's law and respond linearly to external force, unless strong drive is used. Here we propose and experimentally realize high cubic nonlinear response in a macroscopic mechanical system by exploring the anharmonicity in chemical bonding interactions. We demonstrate the high tunability of nonlinear response by precisely controlling the chemical bonding interaction, and realize, at the single-bond limit, a cubic elastic constant of 1 × 10(20) N m(-3). This enables us to observe the resonator's vibrational bi-states transitions driven by the weak Brownian thermal noise at 6 K. This method can be flexibly applied to a variety of mechanical systems to improve nonlinear responses, and can be used, with further improvements, to explore macroscopic quantum mechanics.

Generating giant and tunable nonlinearity in a macroscopic mechanical resonator from a single chemical bond

PubMed Central

Huang, Pu; Zhou, Jingwei; Zhang, Liang; Hou, Dong; Lin, Shaochun; Deng, Wen; Meng, Chao; Duan, Changkui; Ju, Chenyong; Zheng, Xiao; Xue, Fei; Du, Jiangfeng

2016-01-01

Nonlinearity in macroscopic mechanical systems may lead to abundant phenomena for fundamental studies and potential applications. However, it is difficult to generate nonlinearity due to the fact that macroscopic mechanical systems follow Hooke's law and respond linearly to external force, unless strong drive is used. Here we propose and experimentally realize high cubic nonlinear response in a macroscopic mechanical system by exploring the anharmonicity in chemical bonding interactions. We demonstrate the high tunability of nonlinear response by precisely controlling the chemical bonding interaction, and realize, at the single-bond limit, a cubic elastic constant of 1 × 1020 N m−3. This enables us to observe the resonator's vibrational bi-states transitions driven by the weak Brownian thermal noise at 6 K. This method can be flexibly applied to a variety of mechanical systems to improve nonlinear responses, and can be used, with further improvements, to explore macroscopic quantum mechanics. PMID:27225287

Cross-Diffusion Driven Instability for a Lotka-Volterra Competitive Reaction-Diffusion System

NASA Astrophysics Data System (ADS)

Gambino, G.; Lombardo, M. C.; Sammartino, M.

2008-04-01

In this work we investigate the possibility of the pattern formation for a reaction-diffusion system with nonlinear diffusion terms. Through a linear stability analysis we find the conditions which allow a homogeneous steady state (stable for the kinetics) to become unstable through a Turing mechanism. In particular, we show how cross-diffusion effects are responsible for the initiation of spatial patterns. Finally, we find a Fisher amplitude equation which describes the weakly nonlinear dynamics of the system near the marginal stability.

Single-photon blockade in a hybrid cavity-optomechanical system via third-order nonlinearity

NASA Astrophysics Data System (ADS)

Sarma, Bijita; Sarma, Amarendra K.

2018-04-01

Photon statistics in a weakly driven optomechanical cavity, with Kerr-type nonlinearity, are analyzed both analytically and numerically. The single-photon blockade effect is demonstrated via calculations of the zero-time-delay second-order correlation function g (2)(0). The analytical results obtained by solving the Schrödinger equation are in complete conformity with the results obtained through numerical solution of the quantum master equation. A systematic study on the parameter regime for observing photon blockade in the weak coupling regime is reported. The parameter regime where the photon blockade is not realizable due to the combined effect of nonlinearities owing to the optomechanical coupling and the Kerr-effect is demonstrated. The experimental feasibility with state-of-the-art device parameters is discussed and it is observed that photon blockade could be generated at the telecommunication wavelength. An elaborate analysis of the thermal effects on photon antibunching is presented. The system is found to be robust against pure dephasing-induced decoherences and thermal phonon number fluctuations.

Mach stem formation in reflection and focusing of weak shock acoustic pulses.

PubMed

Karzova, Maria M; Khokhlova, Vera A; Salze, Edouard; Ollivier, Sébastien; Blanc-Benon, Philippe

2015-06-01

The aim of this study is to show the evidence of Mach stem formation for very weak shock waves with acoustic Mach numbers on the order of 10(-3) to 10(-2). Two representative cases are considered: reflection of shock pulses from a rigid surface and focusing of nonlinear acoustic beams. Reflection experiments are performed in air using spark-generated shock pulses. Shock fronts are visualized using a schlieren system. Both regular and irregular types of reflection are observed. Numerical simulations are performed to demonstrate the Mach stem formation in the focal region of periodic and pulsed nonlinear beams in water.

O Wave Interactions: Explosive Resonant Triads and Critical Layers.

NASA Astrophysics Data System (ADS)

Mahoney, Daniel J.

This thesis considers the phenomenon of explosive resonant triads in weakly nonlinear, dispersive wave systems. These are nearly linear waves with slowly varying amplitudes which become unbounded in finite time. It is shown that such interactions are much stronger than previously thought. These waves can be thought of as a nonlinear instability, in the sense that a weakly nonlinear perturbation to some system grows to such magnitudes that the behavior of the system is governed by strongly nonlinear effects. This may occur for systems which are linearly or neutrally stable. This is contrasted with previous resolutions of this problem, which treated such perturbations as being large amplitude, nearly linear waves. Analytical and numerical evidence is presented to support these claims. These waves represent a potentially important effect in a variety of physical systems, most notably plasma physics. Attention here is turned to their occurrence in fluid mechanics. Here previous work is extended to include flow systems with continuously varying basic velocities and densities. Many of the problems encountered here will be found to be of a singular nature themselves, and the techniques for analyzing these difficulties will be developed. This will involve the concept of a critical layer in a fluid, a level at which a wave phase speed equals the unperturbed fluid velocity in the direction of propagation. Examples of such waves in this context will be presented. (Copies available exclusively from MIT Libraries, Rm. 14-0551, Cambridge, MA 02139-4307. Ph. 617-253-5668; Fax 617-253 -1690.).

Weak measurements and quantum weak values for NOON states

NASA Astrophysics Data System (ADS)

Rosales-Zárate, L.; Opanchuk, B.; Reid, M. D.

2018-03-01

Quantum weak values arise when the mean outcome of a weak measurement made on certain preselected and postselected quantum systems goes beyond the eigenvalue range for a quantum observable. Here, we propose how to determine quantum weak values for superpositions of states with a macroscopically or mesoscopically distinct mode number, that might be realized as two-mode Bose-Einstein condensate or photonic NOON states. Specifically, we give a model for a weak measurement of the Schwinger spin of a two-mode NOON state, for arbitrary N . The weak measurement arises from a nondestructive measurement of the two-mode occupation number difference, which for atomic NOON states might be realized via phase contrast imaging and the ac Stark effect using an optical meter prepared in a coherent state. The meter-system coupling results in an entangled cat-state. By subsequently evolving the system under the action of a nonlinear Josephson Hamiltonian, we show how postselection leads to quantum weak values, for arbitrary N . Since the weak measurement can be shown to be minimally invasive, the weak values provide a useful strategy for a Leggett-Garg test of N -scopic realism.

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

The Weakly Nonlinear Magnetorotational Instability in a Local Geometry

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

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

2017-05-20

The magnetorotational instability (MRI) is a fundamental process of accretion disk physics, but its saturation mechanism remains poorly understood despite considerable theoretical and computational effort. We present a multiple-scales analysis of the non-ideal MRI in the weakly nonlinear regime—that is, when the most unstable MRI mode has a growth rate asymptotically approaching zero from above. Here, we develop our theory in a local, Cartesian channel. Our results confirm the finding by Umurhan et al. that the perturbation amplitude follows a Ginzburg–Landau equation. We further find that the Ginzburg–Landau equation will arise for the local MRI system with shear-periodic boundary conditions,more » when the effects of ambipolar diffusion are considered. A detailed force balance for the saturated azimuthal velocity and vertical magnetic field demonstrates that, even when diffusive effects are important, the bulk flow saturates via the combined processes of reducing the background shear and rearranging and strengthening the background vertical magnetic field. We directly simulate the Ginzburg–Landau amplitude evolution for our system, and demonstrate the pattern formation our model predicts on long scales of length- and timescales. We compare the weakly nonlinear theory results to a direct numerical simulation of the MRI in a thin-gap Taylor Couette flow.« less

Nonlinear dynamics of a magnetically driven Duffing-type spring-magnet oscillator in the static magnetic field of a coil

NASA Astrophysics Data System (ADS)

Donoso, Guillermo; Ladera, Celso L.

2012-11-01

We study the nonlinear oscillations of a forced and weakly dissipative spring-magnet system moving in the magnetic fields of two fixed coaxial, hollow induction coils. As the first coil is excited with a dc current, both a linear and a cubic magnet-position dependent force appear on the magnet-spring system. The second coil, located below the first, excited with an ac current, provides the oscillating magnetic driving force on the system. From the magnet-coil interactions, we obtain, analytically, the nonlinear motion equation of the system, found to be a forced and damped cubic Duffing oscillator moving in a quartic potential. The relative strengths of the coefficients of the motion equation can be easily set by varying the coils’ dc and ac currents. We demonstrate, theoretically and experimentally, the nonlinear behaviour of this oscillator, including its oscillation modes and nonlinear resonances, the fold-over effect, the hysteresis and amplitude jumps, and its chaotic behaviour. It is an oscillating system suitable for teaching an advanced experiment in nonlinear dynamics both at senior undergraduate and graduate levels.

Regularity of Solutions of the Nonlinear Sigma Model with Gravitino

NASA Astrophysics Data System (ADS)

Jost, Jürgen; Keßler, Enno; Tolksdorf, Jürgen; Wu, Ruijun; Zhu, Miaomiao

2018-02-01

We propose a geometric setup to study analytic aspects of a variant of the super symmetric two-dimensional nonlinear sigma model. This functional extends the functional of Dirac-harmonic maps by gravitino fields. The system of Euler-Lagrange equations of the two-dimensional nonlinear sigma model with gravitino is calculated explicitly. The gravitino terms pose additional analytic difficulties to show smoothness of its weak solutions which are overcome using Rivière's regularity theory and Riesz potential theory.

Nonlinear vibrations and dynamic stability of viscoelastic orthotropic rectangular plates

NASA Astrophysics Data System (ADS)

Eshmatov, B. Kh.

2007-03-01

This paper describes the analyses of the nonlinear vibrations and dynamic stability of viscoelastic orthotropic plates. The models are based on the Kirchhoff-Love (K.L.) hypothesis and Reissner-Mindlin (R.M.) generalized theory (with the incorporation of shear deformation and rotatory inertia) in geometrically nonlinear statements. It provides justification for the choice of the weakly singular Koltunov-Rzhanitsyn type kernel, with three rheological parameters. In addition, the implication of each relaxation kernel parameter has been studied. To solve problems of viscoelastic systems with weakly singular kernels of relaxation, a numerical method has been used, based on quadrature formulae. With a combination of the Bubnov-Galerkin and the presented method, problems of nonlinear vibrations and dynamic stability in viscoelastic orthotropic rectangular plates have been solved, according to the K.L. and R.M. hypotheses. A comparison of the results obtained via these theories is also presented. In all problems, the convergence of the Bubnov-Galerkin method has been investigated. The implications of material viscoelasticity on vibration and dynamic stability are presented graphically.

The interaction between a propagating coastal vortex and topographic waves

NASA Astrophysics Data System (ADS)

Parry, Simon Wyn

This thesis investigates the motion of a point vortex near coastal topography in a rotating frame of reference at constant latitude (f-plane) in the linear and weakly nonlinear limits. Topography is considered in the form of an infinitely long escarpment running parallel to a wall. The vortex motion and topographic waves are governed by the conservation of quasi-geostrophic potential vorticity in shallow water, from which a nonlinear system of equations is derived. First the linear limit is studied for three cases; a weak vortex on- and off-shelf and a weak vortex close to the wall. For the first two cases it is shown that to leading order the vortex motion is stationary and a solution for the topographic waves at the escarpment can be found in terms of Fourier integrals. For a weak vortex close to a wall, the leading order solution is a steadily propagating vortex with a topographic wavetrain at the step. Numerical results for the higher order interactions are also presented and explained in terms of conservation of momentum in the along-shore direction. For the second case a resonant interaction between the vortex and the waves occurs when the vortex speed is equal to the maximum group velocity of the waves and the linear response becomes unbounded at large times. Thus it becomes necessary to examine the weakly nonlinear near-resonant case. Using a long wave approximation a nonlinear evolution equation for the interface separating the two regions of differing relative potential vorticity is derived and has similar form to the BDA (Benjamin, Davies, Acrivos 1967) equation. Results for the leading order steadily propagating vortex and for the vortex-wave feedback problem are calculated numerically using spectral multi-step Adams methods.

Turbulence of Weak Gravitational Waves in the Early Universe.

PubMed

Galtier, Sébastien; Nazarenko, Sergey V

2017-12-01

We study the statistical properties of an ensemble of weak gravitational waves interacting nonlinearly in a flat space-time. We show that the resonant three-wave interactions are absent and develop a theory for four-wave interactions in the reduced case of a 2.5+1 diagonal metric tensor. In this limit, where only plus-polarized gravitational waves are present, we derive the interaction Hamiltonian and consider the asymptotic regime of weak gravitational wave turbulence. Both direct and inverse cascades are found for the energy and the wave action, respectively, and the corresponding wave spectra are derived. The inverse cascade is characterized by a finite-time propagation of the metric excitations-a process similar to an explosive nonequilibrium Bose-Einstein condensation, which provides an efficient mechanism to ironing out small-scale inhomogeneities. The direct cascade leads to an accumulation of the radiation energy in the system. These processes might be important for understanding the early Universe where a background of weak nonlinear gravitational waves is expected.

Quantum computation based on photonic systems with two degrees of freedom assisted by the weak cross-Kerr nonlinearity

PubMed Central

Luo, Ming-Xing; Li, Hui-Ran; Lai, Hong

2016-01-01

Most of previous quantum computations only take use of one degree of freedom (DoF) of photons. An experimental system may possess various DoFs simultaneously. In this paper, with the weak cross-Kerr nonlinearity, we investigate the parallel quantum computation dependent on photonic systems with two DoFs. We construct nearly deterministic controlled-not (CNOT) gates operating on the polarization spatial DoFs of the two-photon or one-photon system. These CNOT gates show that two photonic DoFs can be encoded as independent qubits without auxiliary DoF in theory. Only the coherent states are required. Thus one half of quantum simulation resources may be saved in quantum applications if more complicated circuits are involved. Hence, one may trade off the implementation complexity and simulation resources by using different photonic systems. These CNOT gates are also used to complete various applications including the quantum teleportation and quantum superdense coding. PMID:27424767

Quantum computation based on photonic systems with two degrees of freedom assisted by the weak cross-Kerr nonlinearity.

PubMed

Luo, Ming-Xing; Li, Hui-Ran; Lai, Hong

2016-07-18

Most of previous quantum computations only take use of one degree of freedom (DoF) of photons. An experimental system may possess various DoFs simultaneously. In this paper, with the weak cross-Kerr nonlinearity, we investigate the parallel quantum computation dependent on photonic systems with two DoFs. We construct nearly deterministic controlled-not (CNOT) gates operating on the polarization spatial DoFs of the two-photon or one-photon system. These CNOT gates show that two photonic DoFs can be encoded as independent qubits without auxiliary DoF in theory. Only the coherent states are required. Thus one half of quantum simulation resources may be saved in quantum applications if more complicated circuits are involved. Hence, one may trade off the implementation complexity and simulation resources by using different photonic systems. These CNOT gates are also used to complete various applications including the quantum teleportation and quantum superdense coding.

A Huygens principle for diffusion and anomalous diffusion in spatially extended systems

PubMed Central

Gottwald, Georg A.; Melbourne, Ian

2013-01-01

We present a universal view on diffusive behavior in chaotic spatially extended systems for anisotropic and isotropic media. For anisotropic systems, strong chaos leads to diffusive behavior (Brownian motion with drift) and weak chaos leads to superdiffusive behavior (Lévy processes with drift). For isotropic systems, the drift term vanishes and strong chaos again leads to Brownian motion. We establish the existence of a nonlinear Huygens principle for weakly chaotic systems in isotropic media whereby the dynamics behaves diffusively in even space dimension and exhibits superdiffusive behavior in odd space dimensions. PMID:23653481

Parameter estimating state reconstruction

NASA Technical Reports Server (NTRS)

George, E. B.

1976-01-01

Parameter estimation is considered for systems whose entire state cannot be measured. Linear observers are designed to recover the unmeasured states to a sufficient accuracy to permit the estimation process. There are three distinct dynamics that must be accommodated in the system design: the dynamics of the plant, the dynamics of the observer, and the system updating of the parameter estimation. The latter two are designed to minimize interaction of the involved systems. These techniques are extended to weakly nonlinear systems. The application to a simulation of a space shuttle POGO system test is of particular interest. A nonlinear simulation of the system is developed, observers designed, and the parameters estimated.

Identifiability Of Systems With Modeling Errors

NASA Technical Reports Server (NTRS)

Hadaegh, Yadolah " fred" ; Bekey, George A.

1988-01-01

Advances in theory of modeling errors reported. Recent paper on errors in mathematical models of deterministic linear or weakly nonlinear systems. Extends theoretical work described in NPO-16661 and NPO-16785. Presents concrete way of accounting for difference in structure between mathematical model and physical process or system that it represents.

Theoretical Investigation of Light Transmission in a Slab Cavity via Kerr Nonlinearity of Carbon Nanotube Quantum Dot Nanostructure

NASA Astrophysics Data System (ADS)

Solookinejad, Gh.; Jabbari, M.; Sangachin, E. Ahmadi; Asadpour, S. H.

2018-01-01

In this paper, we discuss the transmission properties of weak probe laser field propagate through slab cavity with defect layer of carbon-nanotube quantum dot (CNT-QD) nanostructure. We show that due to spin-orbit coupling, the double electromagnetically induced transparency (EIT) windows appear and the giant Kerr nonlinearity of the intracavity medium can lead to manipulating of transmission coefficient of weak probe light. The thickness effect of defect layer medium has also been analyzed on transmission properties of probe laser field. Our proposed model may be useful for integrated photonics devices based on CNT-QD for applications in all-optical systems which require multiple EIT effect.

Small systems of Duffing oscillators and the Fermi-Pasta-Ulam-Tsingou system An examination of the possible reasons for the unusual stability of localized nonlinear excitations in these systems

NASA Astrophysics Data System (ADS)

Kashyap, Rahul; Westley, Alexandra; Sen, Surajit

The Duffing oscillator, a nonlinear oscillator with a potential energy with both quadratic and cubic terms, is known to show highly chaotic solutions in certain regions of its parameter space. Here, we examine the behaviors of small chains of harmonically and anharmonically coupled Duffing oscillators and show that these chains exhibit localized nonlinear excitations (LNEs) similar to the ones seen in the Fermi-Pasta-Ulam-Tsingou (FPUT) system. These LNEs demonstrate properties such as long-time energy localization, high periodicity, and slow energy leaking which rapidly accelerates upon frequency matching with the adjacent particles all of which have been observed in the FPUT system. Furthermore, by examining bifurcation diagrams, we will show that many qualitative properties of this system during the transition from weakly to strongly nonlinear behavior depend directly upon the frequencies associated with the individual Duffing oscillators.

Four-wave mixing in an asymmetric double quantum dot molecule

NASA Astrophysics Data System (ADS)

Kosionis, Spyridon G.

2018-06-01

The four-wave mixing (FWM) effect of a weak probe field, in an asymmetric semiconductor double quantum dot (QD) structure driven by a strong pump field is theoretically studied. Similarly to the case of examining several other nonlinear optical processes, the nonlinear differential equations of the density matrix elements are used, under the rotating wave approximation. By suitably tuning the intensity and the frequency of the pump field as well as by changing the value of the applied bias voltage, a procedure used to properly adjust the electron tunneling coupling, we control the FWM in the same way as several other nonlinear optical processes of the system. While in the weak electron tunneling regime, the impact of the pump field intensity on the FWM is proven to be of crucial importance, for even higher rates of the electron tunneling it is evident that the intensity of the pump field has only a slight impact on the form of the FWM spectrum. The number of the spectral peaks, depends on the relation between specific parameters of the system.

Energy transfer in mesoscopic vibrational systems enabled by eigenfrequency fluctuations

NASA Astrophysics Data System (ADS)

Atalaya, Juan

Energy transfer between low-frequency vibrational modes can be achieved by means of nonlinear coupling if their eigenfrequencies fulfill certain nonlinear resonance conditions. Because of the discreteness of the vibrational spectrum at low frequencies, such conditions may be difficult to satisfy for most low-frequency modes in typical mesoscopic vibrational systems. Fluctuations of the vibrational eigenfrequencies can also be relatively strong in such systems. We show that energy transfer between modes can occur in the absence of nonlinear resonance if frequency fluctuations are allowed. The case of three modes with cubic nonlinear coupling and no damping is particularly interesting. It is found that the system has a non-thermal equilibrium state which depends only on the initial conditions. The rate at which the system approaches to such state is determined by the parameters such as the noise strength and correlation time, the nonlinearity strength and the detuning from exact nonlinear resonance. We also discuss the case of many weakly coupled modes. Our results shed light on the problem of energy relaxation of low-frequency vibrational modes into the continuum of high-frequency vibrational modes. The results have been obtained with Mark Dykman. Alternative email: jatalaya2012@gmail.com.

Non-linear analysis of wave progagation using transform methods and plates and shells using integral equations

NASA Astrophysics Data System (ADS)

Pipkins, Daniel Scott

Two diverse topics of relevance in modern computational mechanics are treated. The first involves the modeling of linear and non-linear wave propagation in flexible, lattice structures. The technique used combines the Laplace Transform with the Finite Element Method (FEM). The procedure is to transform the governing differential equations and boundary conditions into the transform domain where the FEM formulation is carried out. For linear problems, the transformed differential equations can be solved exactly, hence the method is exact. As a result, each member of the lattice structure is modeled using only one element. In the non-linear problem, the method is no longer exact. The approximation introduced is a spatial discretization of the transformed non-linear terms. The non-linear terms are represented in the transform domain by making use of the complex convolution theorem. A weak formulation of the resulting transformed non-linear equations yields a set of element level matrix equations. The trial and test functions used in the weak formulation correspond to the exact solution of the linear part of the transformed governing differential equation. Numerical results are presented for both linear and non-linear systems. The linear systems modeled are longitudinal and torsional rods and Bernoulli-Euler and Timoshenko beams. For non-linear systems, a viscoelastic rod and Von Karman type beam are modeled. The second topic is the analysis of plates and shallow shells under-going finite deflections by the Field/Boundary Element Method. Numerical results are presented for two plate problems. The first is the bifurcation problem associated with a square plate having free boundaries which is loaded by four, self equilibrating corner forces. The results are compared to two existing numerical solutions of the problem which differ substantially.

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

Immiscible three-dimensional fingering in porous media: A weakly nonlinear analysis

NASA Astrophysics Data System (ADS)

Brandão, Rodolfo; Dias, Eduardo O.; Miranda, José A.

2018-03-01

We present a weakly nonlinear theory for the development of fingering instabilities that arise at the interface between two immiscible viscous fluids flowing radially outward in a uniform three-dimensional (3D) porous medium. By employing a perturbative second-order mode-coupling scheme, we investigate the linear stability of the system as well as the emergence of intrinsically nonlinear finger branching events in this 3D environment. At the linear stage, we find several differences between the 3D radial fingering and its 2D counterpart (usual Saffman-Taylor flow in radial Hele-Shaw cells). These include the algebraic growth of disturbances and the existence of regions of absolute stability for finite values of viscosity contrast and capillary number in the 3D system. On the nonlinear level, our main focus is to get analytical insight into the physical mechanism resulting in the occurrence of finger tip-splitting phenomena. In this context, we show that the underlying mechanism leading to 3D tip splitting relies on the coupling between the fundamental interface modes and their first harmonics. However, we find that in three dimensions, in contrast to the usual 2D fingering structures normally encountered in radial Hele-Shaw flows, tip splitting into three branches can also be observed.

Weakly nonlinear behavior of a plate thickness-mode piezoelectric transformer.

PubMed

Yang, Jiashi; Chen, Ziguang; Hu, Yuantai; Jiang, Shunong; Guo, Shaohua

2007-04-01

We analyzed the weakly nonlinear behavior of a plate thickness-shear mode piezoelectric transformer near resonance. An approximate analytical solution was obtained. Numerical results based on the analytical solution are presented. It is shown that on one side of the resonant frequency the input-output relation becomes nonlinear, and on the other side the output voltage experiences jumps.

Controlling nonlinear optical response in an open four-level molecular system using quantum control of spin-orbit interaction

NASA Astrophysics Data System (ADS)

Jamshidi-Ghaleh, Kazem; Ebrahimi-hamed, Zahra; Sahrai, Mostafa

2017-10-01

This paper investigates the behavior of linear and nonlinear optical susceptibility of an open four-level molecular system, under two-step excitation based on electromagnetically induced transparency (EIT). The system was irradiated with a weak probe field and strong coupling field. It is shown that the use of a strong coupling field in the triplet states of an alkali-metal dimer can change the spin-orbit interaction (SOI). The optical response of the system can then be modified in a controllable way. The electromagnetically induced transparency transforms into electromagnetically induced absorption (EIA) in the presence of a coupling field. Changing the sign of the dispersion, this region is associated with switching subluminal and superluminal propagation. Furthermore, for the proper value of the coupling field, the controllable parameters, enhanced Kerr nonlinearity with reduced linear absorption, can be obtained under a weak probe field. With this approach, SOI can be controlled by changing only one of the controllable parameters, using triplet-triplet strong coupling with different spin state. Therefore, the desired region of the spectra can be obtained, in contrast to the other four-level system, in which at least two strong fields are used to change optical properties. This mechanism can be suitable in molecular systems or semiconductors to be used in optical bistability and fast all-optical switching devices.

Fully- and weakly-nonlinear biperiodic traveling waves in shallow water

NASA Astrophysics Data System (ADS)

Hirakawa, Tomoaki; Okamura, Makoto

2018-04-01

We directly calculate fully nonlinear traveling waves that are periodic in two independent horizontal directions (biperiodic) in shallow water. Based on the Riemann theta function, we also calculate exact periodic solutions to the Kadomtsev-Petviashvili (KP) equation, which can be obtained by assuming weakly-nonlinear, weakly-dispersive, weakly-two-dimensional waves. To clarify how the accuracy of the biperiodic KP solution is affected when some of the KP approximations are not satisfied, we compare the fully- and weakly-nonlinear periodic traveling waves of various wave amplitudes, wave depths, and interaction angles. As the interaction angle θ decreases, the wave frequency and the maximum wave height of the biperiodic KP solution both increase, and the central peak sharpens and grows beyond the height of the corresponding direct numerical solutions, indicating that the biperiodic KP solution cannot qualitatively model direct numerical solutions for θ ≲ 45^\\circ . To remedy the weak two-dimensionality approximation, we apply the correction of Yeh et al (2010 Eur. Phys. J. Spec. Top. 185 97-111) to the biperiodic KP solution, which substantially improves the solution accuracy and results in wave profiles that are indistinguishable from most other cases.

Experimental quantification of nonlinear time scales in inertial wave rotating turbulence

NASA Astrophysics Data System (ADS)

Yarom, Ehud; Salhov, Alon; Sharon, Eran

2017-12-01

We study nonlinearities of inertial waves in rotating turbulence. At small Rossby numbers the kinetic energy in the system is contained in helical inertial waves with time dependence amplitudes. In this regime the amplitude variations time scales are slow compared to wave periods, and the spectrum is concentrated along the dispersion relation of the waves. A nonlinear time scale was extracted from the width of the spectrum, which reflects the intensity of nonlinear wave interactions. This nonlinear time scale is found to be proportional to (U.k ) -1, where k is the wave vector and U is the root-mean-square horizontal velocity, which is dominated by large scales. This correlation, which indicates the existence of turbulence in which inertial waves undergo weak nonlinear interactions, persists only for small Rossby numbers.

A preconditioner for the finite element computation of incompressible, nonlinear elastic deformations

NASA Astrophysics Data System (ADS)

Whiteley, J. P.

2017-10-01

Large, incompressible elastic deformations are governed by a system of nonlinear partial differential equations. The finite element discretisation of these partial differential equations yields a system of nonlinear algebraic equations that are usually solved using Newton's method. On each iteration of Newton's method, a linear system must be solved. We exploit the structure of the Jacobian matrix to propose a preconditioner, comprising two steps. The first step is the solution of a relatively small, symmetric, positive definite linear system using the preconditioned conjugate gradient method. This is followed by a small number of multigrid V-cycles for a larger linear system. Through the use of exemplar elastic deformations, the preconditioner is demonstrated to facilitate the iterative solution of the linear systems arising. The number of GMRES iterations required has only a very weak dependence on the number of degrees of freedom of the linear systems.

A discontinuous Galerkin approach for conservative modeling of fully nonlinear and weakly dispersive wave transformations

NASA Astrophysics Data System (ADS)

Sharifian, Mohammad Kazem; Kesserwani, Georges; Hassanzadeh, Yousef

2018-05-01

This work extends a robust second-order Runge-Kutta Discontinuous Galerkin (RKDG2) method to solve the fully nonlinear and weakly dispersive flows, within a scope to simultaneously address accuracy, conservativeness, cost-efficiency and practical needs. The mathematical model governing such flows is based on a variant form of the Green-Naghdi (GN) equations decomposed as a hyperbolic shallow water system with an elliptic source term. Practical features of relevance (i.e. conservative modeling over irregular terrain with wetting and drying and local slope limiting) have been restored from an RKDG2 solver to the Nonlinear Shallow Water (NSW) equations, alongside new considerations to integrate elliptic source terms (i.e. via a fourth-order local discretization of the topography) and to enable local capturing of breaking waves (i.e. via adding a detector for switching off the dispersive terms). Numerical results are presented, demonstrating the overall capability of the proposed approach in achieving realistic prediction of nearshore wave processes involving both nonlinearity and dispersion effects within a single model.

Breathing pulses in singularly perturbed reaction-diffusion systems

NASA Astrophysics Data System (ADS)

Veerman, Frits

2015-07-01

The weakly nonlinear stability of pulses in general singularly perturbed reaction-diffusion systems near a Hopf bifurcation is determined using a centre manifold expansion. A general framework to obtain leading order expressions for the (Hopf) centre manifold expansion for scale separated, localised structures is presented. Using the scale separated structure of the underlying pulse, directly calculable expressions for the Hopf normal form coefficients are obtained in terms of solutions to classical Sturm-Liouville problems. The developed theory is used to establish the existence of breathing pulses in a slowly nonlinear Gierer-Meinhardt system, and is confirmed by direct numerical simulation.

Double-Diffusive Convection at Low Prandtl Number

NASA Astrophysics Data System (ADS)

Garaud, Pascale

2018-01-01

This work reviews present knowledge of double-diffusive convection at low Prandtl number obtained using direct numerical simulations, in both the fingering regime and the oscillatory regime. Particular emphasis is given to modeling the induced turbulent mixing and its impact in various astrophysical applications. The nonlinear saturation of fingering convection at low Prandtl number usually drives small-scale turbulent motions whose transport properties can be predicted reasonably accurately using a simple semi-analytical model. In some instances, large-scale internal gravity waves can be excited by a collective instability and eventually cause layering. The nonlinear saturation of oscillatory double-diffusive convection exhibits much more complex behavior. Weakly stratified systems always spontaneously transition into layered convection associated with very efficient mixing. More strongly stratified systems remain dominated by weak wave turbulence unless they are initialized into a layered state. The effects of rotation, shear, lateral gradients, and magnetic fields are briefly discussed.

WaveAR: A software tool for calculating parameters for water waves with incident and reflected components

NASA Astrophysics Data System (ADS)

Landry, Blake J.; Hancock, Matthew J.; Mei, Chiang C.; García, Marcelo H.

2012-09-01

The ability to determine wave heights and phases along a spatial domain is vital to understanding a wide range of littoral processes. The software tool presented here employs established Stokes wave theory and sampling methods to calculate parameters for the incident and reflected components of a field of weakly nonlinear waves, monochromatic at first order in wave slope and propagating in one horizontal dimension. The software calculates wave parameters over an entire wave tank and accounts for reflection, weak nonlinearity, and a free second harmonic. Currently, no publicly available program has such functionality. The included MATLAB®-based open source code has also been compiled for Windows®, Mac® and Linux® operating systems. An additional companion program, VirtualWave, is included to generate virtual wave fields for WaveAR. Together, the programs serve as ideal analysis and teaching tools for laboratory water wave systems.

Optimal control in adaptive optics modeling of nonlinear systems

NASA Astrophysics Data System (ADS)

Herrmann, J.

The problem of using an adaptive optics system to correct for nonlinear effects like thermal blooming is addressed using a model containing nonlinear lenses through which Gaussian beams are propagated. The best correction of this nonlinear system can be formulated as a deterministic open loop optimal control problem. This treatment gives a limit for the best possible correction. Aspects of adaptive control and servo systems are not included at this stage. An attempt is made to determine that control in the transmitter plane which minimizes the time averaged area or maximizes the fluence in the target plane. The standard minimization procedure leads to a two-point-boundary-value problem, which is ill-conditioned in the case. The optimal control problem was solved using an iterative gradient technique. An instantaneous correction is introduced and compared with the optimal correction. The results of the calculations show that for short times or weak nonlinearities the instantaneous correction is close to the optimal correction, but that for long times and strong nonlinearities a large difference develops between the two types of correction. For these cases the steady state correction becomes better than the instantaneous correction and approaches the optimum correction.

Limits on amplification by Aharonov-Albert-Vaidman weak measurement

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

Koike, Tatsuhiko; Tanaka, Saki

2011-12-15

We analyze the amplification by the Aharonov-Albert-Vaidman weak quantum measurement on a Sagnac interferometer [Dixon et al., Phys. Rev. Lett. 102, 173601 (2009)] up to all orders of the coupling strength between the measured system and the measuring device. The amplifier transforms a small tilt of a mirror into a large transverse displacement of the laser beam. The conventional analysis has shown that the measured value is proportional to the weak value, so that the amplification can be made arbitrarily large in the cost of decreasing output laser intensity. It is shown that the measured displacement and the amplification factormore » are in fact not proportional to the weak value and rather vanish in the limit of infinitesimal output intensity. We derive the optimal overlap of the pre- and postselected states with which the amplification become maximum. We also show that the nonlinear effects begin to arise in the performed experiments so that any improvements in the experiment, typically with an amplification greater than 100, should require the nonlinear theory in translating the observed value to the original displacement.« less

Kinetic theory of nonlinear diffusion in a weakly disordered nonlinear Schrödinger chain in the regime of homogeneous chaos.

PubMed

Basko, D M

2014-02-01

We study the discrete nonlinear Schröinger equation with weak disorder, focusing on the regime when the nonlinearity is, on the one hand, weak enough for the normal modes of the linear problem to remain well resolved but, on the other, strong enough for the dynamics of the normal mode amplitudes to be chaotic for almost all modes. We show that in this regime and in the limit of high temperature, the macroscopic density ρ satisfies the nonlinear diffusion equation with a density-dependent diffusion coefficient, D(ρ) = D(0)ρ(2). An explicit expression for D(0) is obtained in terms of the eigenfunctions and eigenvalues of the linear problem, which is then evaluated numerically. The role of the second conserved quantity (energy) in the transport is also quantitatively discussed.

Dispersive solitary wave solutions of Kadomtsev-Petviashvili and modified Kadomtsev-Petviashvili dynamical equations in unmagnetized dust plasma

NASA Astrophysics Data System (ADS)

Seadawy, A. R.; El-Rashidy, K.

2018-03-01

The Kadomtsev-Petviashvili (KP) and modified KP equations are two of the most universal models in nonlinear wave theory, which arises as a reduction of system with quadratic nonlinearity which admit weakly dispersive waves. The generalized extended tanh method and the F-expansion method are used to derive exact solitary waves solutions of KP and modified KP equations. The region of solutions are displayed graphically.

Volterra series truncation and kernel estimation of nonlinear systems in the frequency domain

NASA Astrophysics Data System (ADS)

Zhang, B.; Billings, S. A.

2017-02-01

The Volterra series model is a direct generalisation of the linear convolution integral and is capable of displaying the intrinsic features of a nonlinear system in a simple and easy to apply way. Nonlinear system analysis using Volterra series is normally based on the analysis of its frequency-domain kernels and a truncated description. But the estimation of Volterra kernels and the truncation of Volterra series are coupled with each other. In this paper, a novel complex-valued orthogonal least squares algorithm is developed. The new algorithm provides a powerful tool to determine which terms should be included in the Volterra series expansion and to estimate the kernels and thus solves the two problems all together. The estimated results are compared with those determined using the analytical expressions of the kernels to validate the method. To further evaluate the effectiveness of the method, the physical parameters of the system are also extracted from the measured kernels. Simulation studies demonstrates that the new approach not only can truncate the Volterra series expansion and estimate the kernels of a weakly nonlinear system, but also can indicate the applicability of the Volterra series analysis in a severely nonlinear system case.

Electronic heterodyne moire deflectometry: A method for transient and three dimensional density fields measurements

NASA Technical Reports Server (NTRS)

Stricker, Josef

1987-01-01

Effects of diffraction and nonlinear photographic emulsion characteristics on the performance of deferred electronic heterodyne moire deflectometry are investigated. The deferred deflectometry is used for measurements of nonsteady phase objects where it is difficult to complete the analysis of the field in real time. The sensitivity, accuracy and resolution of the system are calculated and it is shown that they are weakly affected by diffraction and by nonlinear recording. The feactures of the system are significantly improved compared with the conventional deferred intensity moire technique, and are comparable with the online heterodyne moire. The system was evaluated experimentally by deferred measurements of the refractive index gradients of a weak phase object consisting of a large KD*P crystal. This was done by photographing the phase object through a Ronchi grating and analyzing the tranparency with the electronic heterodyne readout system. The results are compared with the measurements performed on the same phase object with online heterodyne moire deflectometry and with heterodyne holographic interferometry methods. Some practical considerations for system improvement are discussed.

Corrigendum and addendum. Modeling weakly nonlinear acoustic wave propagation

DOE PAGES

Christov, Ivan; Christov, C. I.; Jordan, P. M.

2014-12-18

This article presents errors, corrections, and additions to the research outlined in the following citation: Christov, I., Christov, C. I., & Jordan, P. M. (2007). Modeling weakly nonlinear acoustic wave propagation. The Quarterly Journal of Mechanics and Applied Mathematics, 60(4), 473-495.

Non-reciprocity in nonlinear elastodynamics

NASA Astrophysics Data System (ADS)

Blanchard, Antoine; Sapsis, Themistoklis P.; Vakakis, Alexander F.

2018-01-01

Reciprocity is a fundamental property of linear time-invariant (LTI) acoustic waveguides governed by self-adjoint operators with symmetric Green's functions. The break of reciprocity in LTI elastodynamics is only possible through the break of time reversal symmetry on the micro-level, and this can be achieved by imposing external biases, adding nonlinearities or allowing for time-varying system properties. We present a Volterra-series based asymptotic analysis for studying spatial non-reciprocity in a class of one-dimensional (1D), time-invariant elastic systems with weak stiffness nonlinearities. We show that nonlinearity is neither necessary nor sufficient for breaking reciprocity in this class of systems; rather, it depends on the boundary conditions, the symmetries of the governing linear and nonlinear operators, and the choice of the spatial points where the non-reciprocity criterion is tested. Extension of the analysis to higher dimensions and time-varying systems is straightforward from a mathematical point of view (but not in terms of new non-reciprocal physical phenomena), whereas the connection of non-reciprocity and time irreversibility can be studied as well. Finally, we show that suitably defined non-reciprocity measures enable optimization, and can provide physical understanding of the nonlinear effects in the dynamics, enabling one to establish regimes of "maximum nonlinearity." We highlight the theoretical developments by means of a numerical example.

High-frequency vibration energy harvesting from impulsive excitation utilizing intentional dynamic instability caused by strong nonlinearity

NASA Astrophysics Data System (ADS)

Remick, Kevin; Dane Quinn, D.; Michael McFarland, D.; Bergman, Lawrence; Vakakis, Alexander

2016-05-01

The authors investigate a vibration-based energy harvesting system utilizing essential (nonlinearizable) nonlinearities and electromagnetic coupling elements. The system consists of a grounded, weakly damped linear oscillator (primary system) subjected to a single impulsive load. This primary system is coupled to a lightweight, damped oscillating attachment (denoted as nonlinear energy sink, NES) via a neodymium magnet and an inductance coil, and a piano wire, which generates an essential geometric cubic stiffness nonlinearity. Under impulsive input, the transient damped dynamics of this system exhibit transient resonance captures (TRCs) causing intentional large-amplitude and high-frequency instabilities in the response of the NES. These TRCs result in strong energy transfer from the directly excited primary system to the light-weight attachment. The energy is harvested by the electromagnetic elements in the coupling and, in the present case, dissipated in a resistive element in the electrical circuit. The primary goal of this work is to numerically, analytically, and experimentally demonstrate the efficacy of employing this type of intentional high-frequency dynamic instability to achieve enhanced vibration energy harvesting under impulsive excitation.

Effects of weak nonlinearity on the dispersion relation and frequency band-gaps of a periodic Bernoulli–Euler beam

PubMed Central

Thomsen, Jon Juel

2016-01-01

The paper deals with analytically predicting the effects of weak nonlinearity on the dispersion relation and frequency band-gaps of a periodic Bernoulli–Euler beam performing bending oscillations. Two cases are considered: (i) large transverse deflections, where nonlinear (true) curvature, nonlinear material and nonlinear inertia owing to longitudinal motions of the beam are taken into account, and (ii) mid-plane stretching nonlinearity. A novel approach is employed, the method of varying amplitudes. As a result, the isolated as well as combined effects of the considered sources of nonlinearities are revealed. It is shown that nonlinear inertia has the most substantial impact on the dispersion relation of a non-uniform beam by removing all frequency band-gaps. Explanations of the revealed effects are suggested, and validated by experiments and numerical simulation. PMID:27118899

Coupled Particle Transport and Pattern Formation in a Nonlinear Leaky-Box Model

NASA Technical Reports Server (NTRS)

Barghouty, A. F.; El-Nemr, K. W.; Baird, J. K.

2009-01-01

Effects of particle-particle coupling on particle characteristics in nonlinear leaky-box type descriptions of the acceleration and transport of energetic particles in space plasmas are examined in the framework of a simple two-particle model based on the Fokker-Planck equation in momentum space. In this model, the two particles are assumed coupled via a common nonlinear source term. In analogy with a prototypical mathematical system of diffusion-driven instability, this work demonstrates that steady-state patterns with strong dependence on the magnetic turbulence but a rather weak one on the coupled particles attributes can emerge in solutions of a nonlinearly coupled leaky-box model. The insight gained from this simple model may be of wider use and significance to nonlinearly coupled leaky-box type descriptions in general.

Quantitative and qualitative characterization of zigzag spatiotemporal chaos in a system of amplitude equations for nematic electroconvection.

PubMed

Oprea, Iuliana; Triandaf, Ioana; Dangelmayr, Gerhard; Schwartz, Ira B

2007-06-01

It has been suggested by experimentalists that a weakly nonlinear analysis of the recently introduced equations of motion for the nematic electroconvection by M. Treiber and L. Kramer [Phys. Rev. E 58, 1973 (1998)] has the potential to reproduce the dynamics of the zigzag-type extended spatiotemporal chaos and localized solutions observed near onset in experiments [M. Dennin, D. S. Cannell, and G. Ahlers, Phys. Rev. E 57, 638 (1998); J. T. Gleeson (private communication)]. In this paper, we study a complex spatiotemporal pattern, identified as spatiotemporal chaos, that bifurcates at the onset from a spatially uniform solution of a system of globally coupled complex Ginzburg-Landau equations governing the weakly nonlinear evolution of four traveling wave envelopes. The Ginzburg-Landau system can be derived directly from the weak electrolyte model for electroconvection in nematic liquid crystals when the primary instability is a Hopf bifurcation to oblique traveling rolls. The chaotic nature of the pattern and the resemblance to the observed experimental spatiotemporal chaos in the electroconvection of nematic liquid crystals are confirmed through a combination of techniques including the Karhunen-Loeve decomposition, time-series analysis of the amplitudes of the dominant modes, statistical descriptions, and normal form theory, showing good agreement between theory and experiments.

Alternation of regular and chaotic dynamics in a simple two-degree-of-freedom system with nonlinear inertial coupling.

PubMed

Sigalov, G; Gendelman, O V; AL-Shudeifat, M A; Manevitch, L I; Vakakis, A F; Bergman, L A

2012-03-01

We show that nonlinear inertial coupling between a linear oscillator and an eccentric rotator can lead to very interesting interchanges between regular and chaotic dynamical behavior. Indeed, we show that this model demonstrates rather unusual behavior from the viewpoint of nonlinear dynamics. Specifically, at a discrete set of values of the total energy, the Hamiltonian system exhibits non-conventional nonlinear normal modes, whose shape is determined by phase locking of rotatory and oscillatory motions of the rotator at integer ratios of characteristic frequencies. Considering the weakly damped system, resonance capture of the dynamics into the vicinity of these modes brings about regular motion of the system. For energy levels far from these discrete values, the motion of the system is chaotic. Thus, the succession of resonance captures and escapes by a discrete set of the normal modes causes a sequence of transitions between regular and chaotic behavior, provided that the damping is sufficiently small. We begin from the Hamiltonian system and present a series of Poincaré sections manifesting the complex structure of the phase space of the considered system with inertial nonlinear coupling. Then an approximate analytical description is presented for the non-conventional nonlinear normal modes. We confirm the analytical results by numerical simulation and demonstrate the alternate transitions between regular and chaotic dynamics mentioned above. The origin of the chaotic behavior is also discussed.

Nonlinear evolution of coarse-grained quantum systems with generalized purity constraints

NASA Astrophysics Data System (ADS)

Burić, Nikola

2010-12-01

Constrained quantum dynamics is used to propose a nonlinear dynamical equation for pure states of a generalized coarse-grained system. The relevant constraint is given either by the generalized purity or by the generalized invariant fluctuation, and the coarse-grained pure states correspond to the generalized coherent, i.e. generalized nonentangled states. Open system model of the coarse-graining is discussed. It is shown that in this model and in the weak coupling limit the constrained dynamical equations coincide with an equation for pointer states, based on Hilbert-Schmidt distance, that was previously suggested in the context of the decoherence theory.

Maximizing entanglement in bosonic Josephson junctions using shortcuts to adiabaticity and optimal control

NASA Astrophysics Data System (ADS)

Stefanatos, Dionisis; Paspalakis, Emmanuel

2018-05-01

In this article we consider a bosonic Josephson junction, a model system composed by two coupled nonlinear quantum oscillators which can be implemented in various physical contexts, initially prepared in a product of weakly populated coherent states. We quantify the maximum achievable entanglement between the modes of the junction and then use shortcuts to adiabaticity, a method developed to speed up adiabatic quantum dynamics, as well as numerical optimization, to find time-dependent controls (the nonlinearity and the coupling of the junction) which bring the system to a maximally entangled state.

Nonlinear theory for axisymmetric self-similar two-dimensional oscillations of electrons in cold plasma with constant proton background

NASA Astrophysics Data System (ADS)

Osherovich, V. A.; Fainberg, J.

2018-01-01

We consider simultaneous oscillations of electrons moving both along the axis of symmetry and also in the direction perpendicular to the axis. We derive a system of three nonlinear ordinary differential equations which describe self-similar oscillations of cold electrons in a constant proton density background (np = n0 = constant). These three equations represent an exact class of solutions. For weak nonlinear conditions, the frequency spectra of electric field oscillations exhibit split frequency behavior at the Langmuir frequency ωp0 and its harmonics, as well as presence of difference frequencies at low spectral values. For strong nonlinear conditions, the spectra contain peaks at frequencies with values ωp0(n +m √{2 }) , where n and m are integer numbers (positive and negative). We predict that both spectral types (weak and strong) should be observed in plasmas where axial symmetry may exist. To illustrate possible applications of our theory, we present a spectrum of electric field oscillations observed in situ in the solar wind by the WAVES experiment on the Wind spacecraft during the passage of a type III solar radio burst.

Femtosecond Z-scan measurements of the nonlinear refractive index of fused silica

NASA Astrophysics Data System (ADS)

Zhang, Lin; Shi, Zhendong; Ma, Hua; Ren, Huan; Yuan, Quan; Ma, Yurong; Feng, Xiaoxuan; Chen, Bo; Yang, Yi

2018-01-01

Z-scan technology is a popular experimental technique for determining the nonlinear refractive index of the material. However, it encounters a great difficulty in measuring the weak nonlinear material like fused silica which is about two orders of magnitude below the nonlinear refractive index of most of the materials studied with the nanosecond and picosecond Z-scan methods. In this case, the change of refractive index introduced by accumulation of thermal effects cannot be neglected. In order to have a reliable measurement of the nonlinear refractive index, a metrology bench based on the femtosecond Z-scan technology is developed. The intensity modulation component and the differential measurement system are applied to guarantee the accuracy of the measuring system. Based on the femtosecond Z-scan theory, the femtosecond laser Z-scan technique is performed on fused silica, and the nonlinear refractive index of Fused silica is determined to be 9.2039×10-14esu for 800nm, 37fs pulse duration at I0=50GW/cm2 with a good repeatability of 6.7%.

Problems in Nonlinear Acoustics: Parametric Receiving Arrays, Focused Finite Amplitude Sound, & Noncollinear Tone-Noise Interactions

DTIC Science & Technology

1987-07-01

fields (see also Chapter 4 of Ref. 22). Like our investigation, theirs is based on the Khokhlov-Zabolotskaya-Kuznetsov ( KZK ) equa- tion [23,24...25,26], also based on the KZK e(iualiou, is limited to weakly nonlinear systems. However, the practical case of a focused circular source with gain of...iment. The demonstrated abihty of the KZK equation to accurately model focused sound fields from reahstic sources [i.e., having abrupt edges and

Models for short-wave instability in inviscid shear flows

NASA Astrophysics Data System (ADS)

Grimshaw, Roger

1999-11-01

The generation of instability in an invsicid fluid occurs by a resonance between two wave modes, where here the resonance occurs by a coincidence of phase speeds for a finite, non-zero wavenumber. We show that in the weakly nonlinear limit, the appropriate model consists of two coupled equations for the envelopes of the wave modes, in which the nonlinear terms are balanced with low-order cross-coupling linear dispersive terms rather than the more familiar high-order terms which arise in the nonlinear Schrodinger equation, for instance. We will show that this system may either contain gap solitons as solutions in the linearly stable case, or wave breakdown in the linearly unstable case. In this latter circumstance, the system either exhibits wave collapse in finite time, or disintegration into fine-scale structures.

Enhanced photon-phonon cross-Kerr nonlinearity with two-photon driving.

PubMed

Yin, Tai-Shuang; Lü, Xin-You; Wan, Liang-Liang; Bin, Shang-Wu; Wu, Ying

2018-05-01

We propose a scheme to significantly enhance the cross-Kerr (CK) nonlinearity between photons and phonons in a quadratically coupled optomechanical system (OMS) with two-photon driving. This CK nonlinear enhancement originates from the parametric-driving-induced squeezing and the underlying nonlinear optomechanical interaction. Moreover, the noise of the squeezed mode can be suppressed completely by introducing a squeezed vacuum reservoir. As a result of this dramatic nonlinear enhancement and the suppressed noise, we demonstrate the feasibility of the quantum nondemolition measurement of the phonon number in an originally weak coupled OMS. In addition, the photon-phonon blockade phenomenon is also investigated in this regime, which allows for performing manipulations between photons and phonons. This Letter offers a promising route towards the potential application for the OMS in quantum information processing and quantum networks.

Linear and weakly nonlinear aspects of free shear layer instability, roll-up, subharmonic interaction and wall influence

NASA Technical Reports Server (NTRS)

Cain, A. B.; Thompson, M. W.

1986-01-01

The growth of the momentum thickness and the modal disturbance energies are examined to study the nature and onset of nonlinearity in a temporally growing free shear layer. A shooting technique is used to find solutions to the linearized eigenvalue problem, and pseudospectral weakly nonlinear simulations of this flow are obtained for comparison. The roll-up of a fundamental disturbance follows linear theory predictions even with a 20 percent disturbance amplitude. A weak nonlinear interaction of the disturbance creates a finite-amplitude mean shear stress which dominates the growth of the layer momentum thickness, and the disturbance growth rate changes until the fundamental disturbance dominates. The fundamental then becomes an energy source for the harmonic, resulting in an increase in the growth rate of the subharmonic over the linear prediction even when the fundamental has no energy to give. Also considered are phase relations and the wall influence.

Layer contributions to the nonlinear acoustic radiation from stratified media.

PubMed

Vander Meulen, François; Haumesser, Lionel

2016-12-01

This study presents the thorough investigation of the second harmonic generation scenario in a three fluid layer system. An emphasis is on the evaluation of the nonlinear parameter B/A in each layer from remote measurements. A theoretical approach of the propagation of a finite amplitude acoustic wave in a multilayered medium is developed. In the frame of the KZK equation, the weak nonlinearity of the media, attenuation and diffraction effects are computed for the fundamental and second harmonic waves propagating back and forth in each of the layers of the system. The model uses a gaussian expansion to describe the beam propagation in order to quantitatively evaluate the contribution of each part of the system (layers and interfaces) to its nonlinearity. The model is validated through measurements on a water/aluminum/water system. Transmission as well as reflection configurations are studied. Good agreement is found between the theoretical results and the experimental data. The analysis of the second harmonic field sources measured by the transducers from outside the stratified medium highlights the factors that favor the cumulative effects. Copyright © 2016 Elsevier B.V. All rights reserved.

Laser-pulse compression in a collisional plasma under weak-relativistic ponderomotive nonlinearity

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

Singh, Mamta; Gupta, D. N., E-mail: dngupta@physics.du.ac.in

We present theory and numerical analysis which demonstrate laser-pulse compression in a collisional plasma under the weak-relativistic ponderomotive nonlinearity. Plasma equilibrium density is modified due to the ohmic heating of electrons, the collisions, and the weak relativistic-ponderomotive force during the interaction of a laser pulse with plasmas. First, within one-dimensional analysis, the longitudinal self-compression mechanism is discussed. Three-dimensional analysis (spatiotemporal) of laser pulse propagation is also investigated by coupling the self-compression with the self-focusing. In the regime in which the laser becomes self-focused due to the weak relativistic-ponderomotive nonlinearity, we provide results for enhanced pulse compression. The results show thatmore » the matched interplay between self-focusing and self-compression can improve significantly the temporal profile of the compressed pulse. Enhanced pulse compression can be achieved by optimizing and selecting the parameters such as collision frequency, ion-temperature, and laser intensity.« less

Global Existence and Uniqueness of Weak and Regular Solutions of Shallow Shells with Thermal Effects

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

Menzala, G. Perla, E-mail: perla@lncc.br; Cezaro, F. Travessini De, E-mail: fabianacezaro@furg.br

2016-10-15

We study a dynamical thin shallow shell whose elastic deformations are described by a nonlinear system of Marguerre–Vlasov’s type under the presence of thermal effects. Our main result is the proof of a global existence and uniqueness of a weak solution in the case of clamped boundary conditions. Standard techniques for uniqueness do not work directly in this case. We overcame this difficulty using recent work due to Lasiecka (Appl Anal 4:1376–1422, 1998).

Waveguides with Absorbing Boundaries: Nonlinearity Controlled by an Exceptional Point and Solitons

NASA Astrophysics Data System (ADS)

Midya, Bikashkali; Konotop, Vladimir V.

2017-07-01

We reveal the existence of continuous families of guided single-mode solitons in planar waveguides with weakly nonlinear active core and absorbing boundaries. Stable propagation of TE and TM-polarized solitons is accompanied by attenuation of all other modes, i.e., the waveguide features properties of conservative and dissipative systems. If the linear spectrum of the waveguide possesses exceptional points, which occurs in the case of TM polarization, an originally focusing (defocusing) material nonlinearity may become effectively defocusing (focusing). This occurs due to the geometric phase of the carried eigenmode when the surface impedance encircles the exceptional point. In its turn, the change of the effective nonlinearity ensures the existence of dark (bright) solitons in spite of focusing (defocusing) Kerr nonlinearity of the core. The existence of an exceptional point can also result in anomalous enhancement of the effective nonlinearity. In terms of practical applications, the nonlinearity of the reported waveguide can be manipulated by controlling the properties of the absorbing cladding.

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.

Numerical study on inter-tidal transports in coastal seas

NASA Astrophysics Data System (ADS)

Mao, Xinyan; Jiang, Wensheng; Zhang, Ping; Feng, Shizuo

2016-06-01

Inter-tidal (subtidal) transport processes in coastal sea depend on the residual motion, turbulent dispersion and relevant sources/sinks. In Feng et al. (2008), an updated Lagrangian inter-tidal transport equation, as well as new concept of Lagrangian inter-tidal concentration (LIC), has been proposed for a general nonlinear shallow water system. In the present study, the LIC is numerically applied for the first time to passive tracers in idealized settings and salinity in the Bohai Sea, China. Circulation and tracer motion in the three idealized model seas with different topography or coastline, termed as `flat-bottom', `stairs' and `cape' case, respectively, are simulated. The dependence of the LIC on initial tidal phase suggests that the nonlinearities in the stairs and cape cases are stronger than that in the flat-bottom case. Therefore, the `flat-bottom' case still meets the convectively weakly nonlinear condition. For the Bohai Sea, the simulation results show that most parts of it still meet the weakly nonlinear condition. However, the dependence of the LIS (Lagrangian inter-tidal salinity) on initial tidal phase is significant around the southern headland of the Liaodong Peninsula and near the mouth of the Yellow River. The nonlinearity in the former region is mainly related to the complicated coastlines, and that in the latter region is due to the presence of the estuarine salinity front.

Wave turbulence in shallow water models.

PubMed

Clark di Leoni, P; Cobelli, P J; Mininni, P D

2014-06-01

We study wave turbulence in shallow water flows in numerical simulations using two different approximations: the shallow water model and the Boussinesq model with weak dispersion. The equations for both models were solved using periodic grids with up to 2048{2} points. In all simulations, the Froude number varies between 0.015 and 0.05, while the Reynolds number and level of dispersion are varied in a broader range to span different regimes. In all cases, most of the energy in the system remains in the waves, even after integrating the system for very long times. For shallow flows, nonlinear waves are nondispersive and the spectrum of potential energy is compatible with ∼k{-2} scaling. For deeper (Boussinesq) flows, the nonlinear dispersion relation as directly measured from the wave and frequency spectrum (calculated independently) shows signatures of dispersion, and the spectrum of potential energy is compatible with predictions of weak turbulence theory, ∼k{-4/3}. In this latter case, the nonlinear dispersion relation differs from the linear one and has two branches, which we explain with a simple qualitative argument. Finally, we study probability density functions of the surface height and find that in all cases the distributions are asymmetric. The probability density function can be approximated by a skewed normal distribution as well as by a Tayfun distribution.

Energy transport in weakly nonlinear wave systems with narrow frequency band excitation.

PubMed

Kartashova, Elena

2012-10-01

A novel discrete model (D model) is presented describing nonlinear wave interactions in systems with small and moderate nonlinearity under narrow frequency band excitation. It integrates in a single theoretical frame two mechanisms of energy transport between modes, namely, intermittency and energy cascade, and gives the conditions under which each regime will take place. Conditions for the formation of a cascade, cascade direction, conditions for cascade termination, etc., are given and depend strongly on the choice of excitation parameters. The energy spectra of a cascade may be computed, yielding discrete and continuous energy spectra. The model does not require statistical assumptions, as all effects are derived from the interaction of distinct modes. In the example given-surface water waves with dispersion function ω(2)=gk and small nonlinearity-the D model predicts asymmetrical growth of side-bands for Benjamin-Feir instability, while the transition from discrete to continuous energy spectrum, excitation parameters properly chosen, yields the saturated Phillips' power spectrum ~g(2)ω(-5). The D model can be applied to the experimental and theoretical study of numerous wave systems appearing in hydrodynamics, nonlinear optics, electrodynamics, plasma, convection theory, etc.

A fully non-linear multi-species Fokker–Planck–Landau collision operator for simulation of fusion plasma

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

Hager, Robert, E-mail: rhager@pppl.gov; Yoon, E.S., E-mail: yoone@rpi.edu; Ku, S., E-mail: sku@pppl.gov

2016-06-15

Fusion edge plasmas can be far from thermal equilibrium and require the use of a non-linear collision operator for accurate numerical simulations. In this article, the non-linear single-species Fokker–Planck–Landau collision operator developed by Yoon and Chang (2014) [9] is generalized to include multiple particle species. The finite volume discretization used in this work naturally yields exact conservation of mass, momentum, and energy. The implementation of this new non-linear Fokker–Planck–Landau operator in the gyrokinetic particle-in-cell codes XGC1 and XGCa is described and results of a verification study are discussed. Finally, the numerical techniques that make our non-linear collision operator viable onmore » high-performance computing systems are described, including specialized load balancing algorithms and nested OpenMP parallelization. The collision operator's good weak and strong scaling behavior are shown.« less

A fully non-linear multi-species Fokker–Planck–Landau collision operator for simulation of fusion plasma

DOE PAGES

Hager, Robert; Yoon, E. S.; Ku, S.; ...

2016-04-04

Fusion edge plasmas can be far from thermal equilibrium and require the use of a non-linear collision operator for accurate numerical simulations. The non-linear single-species Fokker–Planck–Landau collision operator developed by Yoon and Chang (2014) [9] is generalized to include multiple particle species. Moreover, the finite volume discretization used in this work naturally yields exact conservation of mass, momentum, and energy. The implementation of this new non-linear Fokker–Planck–Landau operator in the gyrokinetic particle-in-cell codes XGC1 and XGCa is described and results of a verification study are discussed. Finally, the numerical techniques that make our non-linear collision operator viable on high-performance computingmore » systems are described, including specialized load balancing algorithms and nested OpenMP parallelization. As a result, the collision operator's good weak and strong scaling behavior are shown.« less

Out-of-unison resonance in weakly nonlinear coupled oscillators

PubMed Central

Hill, T. L.; Cammarano, A.; Neild, S. A.; Wagg, D. J.

2015-01-01

Resonance is an important phenomenon in vibrating systems and, in systems of nonlinear coupled oscillators, resonant interactions can occur between constituent parts of the system. In this paper, out-of-unison resonance is defined as a solution in which components of the response are 90° out-of-phase, in contrast to the in-unison responses that are normally considered. A well-known physical example of this is whirling, which can occur in a taut cable. Here, we use a normal form technique to obtain time-independent functions known as backbone curves. Considering a model of a cable, this approach is used to identify out-of-unison resonance and it is demonstrated that this corresponds to whirling. We then show how out-of-unison resonance can occur in other two degree-of-freedom nonlinear oscillators. Specifically, an in-line oscillator consisting of two masses connected by nonlinear springs—a type of system where out-of-unison resonance has not previously been identified—is shown to have specific parameter regions where out-of-unison resonance can occur. Finally, we demonstrate how the backbone curve analysis can be used to predict the responses of forced systems. PMID:25568619

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

NASA Technical Reports Server (NTRS)

Shortis, Trudi A.; Hall, Philip

1995-01-01

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

Nearly deterministic quantum Fredkin gate based on weak cross-Kerr nonlinearity

NASA Astrophysics Data System (ADS)

Wu, Yun-xiang; Zhu, Chang-hua; Pei, Chang-xing

2016-09-01

A scheme of an optical quantum Fredkin gate is presented based on weak cross-Kerr nonlinearity. By an auxiliary coherent state with the cross-Kerr nonlinearity effect, photons can interact with each other indirectly, and a non-demolition measurement for photons can be implemented. Combined with the homodyne detection, classical feedforward, polarization beam splitters and Pauli-X operations, a controlled-path gate is constructed. Furthermore, a quantum Fredkin gate is built based on the controlled-path gate. The proposed Fredkin gate is simple in structure and feasible by current experimental technology.

Resonant tunneling via a Ru-dye complex using a nanoparticle bridge junction.

PubMed

Nishijima, Satoshi; Otsuka, Yoichi; Ohoyama, Hiroshi; Kajimoto, Kentaro; Araki, Kento; Matsumoto, Takuya

2018-06-15

Nonlinear current-voltage (I-V) characteristics is an important property for the realization of information processing in molecular electronics. We studied the electrical conduction through a Ru-dye complex (N-719) on a 2-aminoethanethiol (2-AET) monolayer in a nanoparticle bridge junction system. The nonlinear I-V characteristics exhibited a threshold voltage at around 1.2 V and little temperature dependence. From the calculation of the molecular states using density functional theory and the energy alignment between the electrodes and molecules, the conduction mechanism in this system was considered to be resonant tunneling via the HOMO level of N-719. Our results indicate that the weak electronic coupling of electrodes and molecules is essential for obtaining nonlinear I-V characteristics with a clear threshold voltage that reflect the intrinsic molecular state.

Resonant tunneling via a Ru–dye complex using a nanoparticle bridge junction

NASA Astrophysics Data System (ADS)

Nishijima, Satoshi; Otsuka, Yoichi; Ohoyama, Hiroshi; Kajimoto, Kentaro; Araki, Kento; Matsumoto, Takuya

2018-06-01

Nonlinear current–voltage (I–V) characteristics is an important property for the realization of information processing in molecular electronics. We studied the electrical conduction through a Ru–dye complex (N-719) on a 2-aminoethanethiol (2-AET) monolayer in a nanoparticle bridge junction system. The nonlinear I–V characteristics exhibited a threshold voltage at around 1.2 V and little temperature dependence. From the calculation of the molecular states using density functional theory and the energy alignment between the electrodes and molecules, the conduction mechanism in this system was considered to be resonant tunneling via the HOMO level of N-719. Our results indicate that the weak electronic coupling of electrodes and molecules is essential for obtaining nonlinear I–V characteristics with a clear threshold voltage that reflect the intrinsic molecular state.

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

Quon, Eliot; Platt, Andrew; Yu, Yi-Hsiang

Extreme loads are often a key cost driver for wave energy converters (WECs). As an alternative to exhaustive Monte Carlo or long-term simulations, the most likely extreme response (MLER) method allows mid- and high-fidelity simulations to be used more efficiently in evaluating WEC response to events at the edges of the design envelope, and is therefore applicable to system design analysis. The study discussed in this paper applies the MLER method to investigate the maximum heave, pitch, and surge force of a point absorber WEC. Most likely extreme waves were obtained from a set of wave statistics data based onmore » spectral analysis and the response amplitude operators (RAOs) of the floating body; the RAOs were computed from a simple radiation-and-diffraction-theory-based numerical model. A weakly nonlinear numerical method and a computational fluid dynamics (CFD) method were then applied to compute the short-term response to the MLER wave. Effects of nonlinear wave and floating body interaction on the WEC under the anticipated 100-year waves were examined by comparing the results from the linearly superimposed RAOs, the weakly nonlinear model, and CFD simulations. Overall, the MLER method was successfully applied. In particular, when coupled to a high-fidelity CFD analysis, the nonlinear fluid dynamics can be readily captured.« less

Multi-Periodic Waves in Shallow Water

DTIC Science & Technology

1992-09-01

models-the Kadomtsev - Petviashvili (KP) equation . The KP equation describes the evolu- tion of weakly nonlinear, weakly two-dimensional waves on water of...experimentally. The analytical model is a family of periodic solutions of the Kadomtsev -Petviashuili equation . The experiments demonstrate the accuracy... Petviashvili Equation (with Norman Schef- fner & Harvey Segur). Proceedings, Nonlinear Water Waves Workshop, University of Bristol. England, 1991. Resonant

Residual delay maps unveil global patterns of atmospheric nonlinearity and produce improved local forecasts

PubMed Central

Sugihara, George; Casdagli, Martin; Habjan, Edward; Hess, Dale; Dixon, Paul; Holland, Greg

1999-01-01

We use residual-delay maps of observational field data for barometric pressure to demonstrate the structure of latitudinal gradients in nonlinearity in the atmosphere. Nonlinearity is weak and largely lacking in tropical and subtropical sites and increases rapidly into the temperate regions where the time series also appear to be much noisier. The degree of nonlinearity closely follows the meridional variation of midlatitude storm track frequency. We extract the specific functional form of this nonlinearity, a V shape in the lagged residuals that appears to be a basic feature of midlatitude synoptic weather systems associated with frontal passages. We present evidence that this form arises from the relative time scales of high-pressure versus low-pressure events. Finally, we show that this nonlinear feature is weaker in a well regarded numerical forecast model (European Centre for Medium-Range Forecasts) because small-scale temporal and spatial variation is smoothed out in the grided inputs. This is significant, in that it allows us to demonstrate how application of statistical corrections based on the residual-delay map may provide marked increases in local forecast accuracy, especially for severe weather systems. PMID:10588685

Nonlinear Alfvén wave propagating in ideal MHD plasmas

NASA Astrophysics Data System (ADS)

Zheng, Jugao; Chen, Yinhua; Yu, Mingyang

2016-01-01

The behavior of nonlinear Alfvén waves propagating in ideal MHD plasmas is investigated numerically. It is found that in a one-dimensional weakly nonlinear system an Alfvén wave train can excite two longitudinal disturbances, namely an acoustic wave and a ponderomotively driven disturbance, which behave differently for β \\gt 1 and β \\lt 1, where β is the ratio of plasma-to-magnetic pressures. In a strongly nonlinear system, the Alfvén wave train is modulated and can steepen to form shocks, leading to significant dissipation due to appearance of current sheets at magnetic-pressure minima. For periodic boundary condition, we find that the Alfvén wave transfers its energy to the plasma and heats it during the shock formation. In two-dimensional systems, fast magneto-acoustic wave generation due to Alfvén wave phase mixing is considered. It is found that the process depends on the amplitude and frequency of the Alfvén waves, as well as their speed gradients and the pressure of the background plasma.

Nonlinear response and bistability of driven ion acoustic waves

NASA Astrophysics Data System (ADS)

Akbari-Moghanjoughi, M.

2017-08-01

The hydrodynamic model is used to obtain a generalized pseudoforce equation through which the nonlinear response of periodically driven ion acoustic waves is studied in an electron-ion plasma with isothermal and adiabatic ion fluids. The pseudotime series, corresponding to different driving frequencies, indicates that nonlinearity effects appear more strongly for smaller frequency values. The existence of extra harmonic resonances in the nonlinear amplitude spectrum is a clear indication of the interaction of an external force with harmonic components of the nonlinear ion acoustic waves. It is shown that many plasma parameters significantly and differently affect the nonlinear resonance spectrum of ion acoustic excitations. A heuristic but accurate model for the foldover effect is used which quite satisfactorily predicts the bistability of driven plasma oscillations. It is remarked that the characteristic resonance peak of isothermal ion plasma oscillations appears at lower frequencies but is stronger compared to that of adiabatic ions. Comparison of the exact numerical results for fully nonlinear and approximate (weakly nonlinear) models indicates that a weakly nonlinear model exaggerates the hysteresis and jump phenomenon for higher values of the external force amplitude.

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

PubMed

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

2013-07-01

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

Limitations on the upconversion of ion sound to Langmuir turbulence

NASA Technical Reports Server (NTRS)

Vlahos, L.; Papadopoulos, K.

1982-01-01

The weak turbulence theory of Tsytovich, Stenflo and Wilhelmsson (1981) for evaluation of the nonlinear transfer of ion acoustic waves to Langmuir waves is shown to be limited in its region of validity to the level of ion acoustic waves. It is also demonstrated that, in applying the upconversion of ion sound to Langmuir waves for electron acceleration, nonlinear scattering should be self-consistently included, with a suppression of the upconversion process resulting. The impossibility of accelerating electrons by such a process for any reasonable physical system is thereby reaffirmed.

Nonlinear dynamics; Proceedings of the International Conference, New York, NY, December 17-21, 1979

NASA Technical Reports Server (NTRS)

Helleman, R. H. G.

1980-01-01

Papers were presented on turbulence, ergodic and integrable behavior, chaotic maps and flows, chemical and fully developed turbulence, and strange attractors. Specific attention was given to measures describing a turbulent flow, stochastization and collapse of vortex systems, a subharmonic route to turbulent convection, and weakly nonlinear turbulence in a rotating convection layer. The Korteweg-de Vries and Hill equations, plasma transport in three dimensions, a horseshoe in the dynamics of a forced beam, and the explosion of strange attractors exhibited by Duffing's equation were also considered.

Existence regimes for the formation of nonlinear dissipative structures in inhomogeneous magnetoplasmas with non-Maxwellian electrons

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

Masood, W.; National Centre for Physics, Shahdara Valley Road, Islamabad; Zahoor, Sara

2016-09-15

Nonlinear dissipative structures are studied in one and two dimensions in nonuniform magnetized plasmas with non-Maxwellian electrons. The dissipation is incorporated in the system through ion-neutral collisions. Employing the drift approximation, nonlinear drift waves are derived in 1D, whereas coupled drift-ion acoustic waves are derived in 2D in the weak nonlinearity limit. It is found that the ratio of the diamagnetic drift velocity to the velocity of nonlinear structure determines the nature (compressive or rarefactive) of the shock structure. The upper and lower bounds for velocity of the nonlinear shock structures are also found. It is noticed that the existencemore » regimes for the drift shock waves in one and two dimensions for Cairns distributed electrons are very distinct from those with kappa distributed electrons. Interestingly, it is found that both compressive and rarefactive shock structures could be obtained for the one dimensional drift waves with kappa distributed electrons.« less

Existence regimes for the formation of nonlinear dissipative structures in inhomogeneous magnetoplasmas with non-Maxwellian electrons

NASA Astrophysics Data System (ADS)

Masood, W.; Zahoor, Sara; Gul-e-Ali, Ahmad, Ali

2016-09-01

Nonlinear dissipative structures are studied in one and two dimensions in nonuniform magnetized plasmas with non-Maxwellian electrons. The dissipation is incorporated in the system through ion-neutral collisions. Employing the drift approximation, nonlinear drift waves are derived in 1D, whereas coupled drift-ion acoustic waves are derived in 2D in the weak nonlinearity limit. It is found that the ratio of the diamagnetic drift velocity to the velocity of nonlinear structure determines the nature (compressive or rarefactive) of the shock structure. The upper and lower bounds for velocity of the nonlinear shock structures are also found. It is noticed that the existence regimes for the drift shock waves in one and two dimensions for Cairns distributed electrons are very distinct from those with kappa distributed electrons. Interestingly, it is found that both compressive and rarefactive shock structures could be obtained for the one dimensional drift waves with kappa distributed electrons.

Nonperturbative model for optical response under intense periodic fields with application to graphene in a strong perpendicular magnetic field

NASA Astrophysics Data System (ADS)

Cheng, J. L.; Guo, C.

2018-05-01

Graphene exhibits extremely strong optical nonlinearity in a perpendicular magnetic field, the optical conductivities show complicated field dependence at a moderate light intensity, and the perturbation theory fails. The full optical currents induced by a periodic field are nonperturbatively investigated in an equation-of-motion framework based on the Floquet theorem, with the scattering described phenomenologically. The nonlinear responses are understood in terms of the dressed electronic states, or Floquet states, which could be characterized by a weak probe light field. The method is illustrated for a magnetic field at 5 T and a driving field with photon energy 0.05 eV. Our results show that the perturbation theory works for weak fields <3 kV/cm, confirming the unusual strong light-matter interaction for Landau levels of graphene. Our approach can be easily extended to other systems.

The Alfvénic nature of energy transfer mediation in localized, strongly nonlinear Alfvén wavepacket collisions

NASA Astrophysics Data System (ADS)

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

2018-02-01

In space and astrophysical plasmas, violent events or instabilities inject energy into turbulent motions at large scales. Nonlinear interactions among the turbulent fluctuations drive a cascade of energy to small perpendicular scales at which the energy is ultimately converted into plasma heat. Previous work with the incompressible magnetohydrodynamic (MHD) equations has shown that this turbulent energy cascade is driven by the nonlinear interaction between counterpropagating Alfvén waves - also known as Alfvén wave collisions. Direct numerical simulations of weakly collisional plasma turbulence enables deeper insight into the nature of the nonlinear interactions underlying the turbulent cascade of energy. In this paper, we directly compare four cases: both periodic and localized Alfvén wave collisions in the weakly and strongly nonlinear limits. Our results reveal that in the more realistic case of localized Alfvén wave collisions (rather than the periodic case), all nonlinearly generated fluctuations are Alfvén waves, which mediates nonlinear energy transfer to smaller perpendicular scales.

Energetics of slope flows: linear and weakly nonlinear solutions of the extended Prandtl model

NASA Astrophysics Data System (ADS)

Güttler, Ivan; Marinović, Ivana; Večenaj, Željko; Grisogono, Branko

2016-07-01

The Prandtl model succinctly combines the 1D stationary boundary-layer dynamics and thermodynamics of simple anabatic and katabatic flows over uniformly inclined surfaces. It assumes a balance between the along-the-slope buoyancy component and adiabatic warming/cooling, and the turbulent mixing of momentum and heat. In this study, energetics of the Prandtl model is addressed in terms of the total energy (TE) concept. Furthermore, since the authors recently developed a weakly nonlinear version of the Prandtl model, the TE approach is also exercised on this extended model version, which includes an additional nonlinear term in the thermodynamic equation. Hence, interplay among diffusion, dissipation and temperature-wind interaction of the mean slope flow is further explored. The TE of the nonlinear Prandtl model is assessed in an ensemble of solutions where the Prandtl number, the slope angle and the nonlinearity parameter are perturbed. It is shown that nonlinear effects have the lowest impact on variability in the ensemble of solutions of the weakly nonlinear Prandtl model when compared to the other two governing parameters. The general behavior of the nonlinear solution is similar to the linear solution, except that the maximum of the along-the-slope wind speed in the nonlinear solution reduces for larger slopes. Also, the dominance of PE near the sloped surface, and the elevated maximum of KE in the linear and nonlinear energetics of the extended Prandtl model are found in the PASTEX-94 measurements. The corresponding level where KE>PE most likely marks the bottom of the sublayer subject to shear-driven instabilities. Finally, possible limitations of the weakly nonlinear solutions of the extended Prandtl model are raised. In linear solutions, the local storage of TE term is zero, reflecting the stationarity of solutions by definition. However, in nonlinear solutions, the diffusion, dissipation and interaction terms (where the height of the maximum interaction is proportional to the height of the low-level jet by the factor ≈4/9) do not balance and the local storage of TE attains non-zero values. In order to examine the issue of non-stationarity, the inclusion of velocity-pressure covariance in the momentum equation is suggested for future development of the extended Prandtl model.

A weakly nonlinear theory for wave-vortex interactions in curved channel flow

NASA Technical Reports Server (NTRS)

Singer, Bart A.; Erlebacher, Gordon; Zang, Thomas A.

1992-01-01

A weakly nonlinear theory is developed to study the interaction of Tollmien-Schlichting (TS) waves and Dean vortices in curved channel flow. The predictions obtained from the theory agree well with results obtained from direct numerical simulations of curved channel flow, especially for low amplitude disturbances. Some discrepancies in the results of a previous theory with direct numerical simulations are resolved.

Hong-Ou-Mandel Interference with a Single Atom.

PubMed

Ralley, K A; Lerner, I V; Yurkevich, I V

2015-09-14

The Hong-Ou-Mandel (HOM) effect is widely regarded as the quintessential quantum interference phenomenon in optics. In this work we examine how nonlinearity can smear statistical photon bunching in the HOM interferometer. We model both the nonlinearity and a balanced beam splitter with a single two-level system and calculate a finite probability of anti-bunching arising in this geometry. We thus argue that the presence of such nonlinearity would reduce the visibility in the standard HOM setup, offering some explanation for the diminution of the HOM visibility observed in many experiments. We use the same model to show that the nonlinearity affects a resonant two-photon propagation through a two-level impurity in a waveguide due to a "weak photon blockade" caused by the impossibility of double-occupancy and argue that this effect might be stronger for multi-photon propagation.

L(2) stability for weak solutions of the Navier-Stokes equations in R(3)

NASA Astrophysics Data System (ADS)

Secchi, P.

1985-11-01

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

On a nonlinear model for tumour growth with drug application

NASA Astrophysics Data System (ADS)

Donatelli, Donatella; Trivisa, Konstantina

2015-05-01

We investigate the dynamics of a nonlinear system modelling tumour growth with drug application. The tumour is viewed as a mixture consisting of proliferating, quiescent and dead cells as well as a nutrient in the presence of a drug. The system is given by a multi-phase flow model: the densities of the different cells are governed by a set of transport equations, the density of the nutrient and the density of the drug are governed by rather general diffusion equations, while the velocity of the tumour is given by Brinkman's equation. The domain occupied by the tumour in this setting is a growing continuum Ω with boundary ∂Ω both of which evolve in time. Global-in-time weak solutions are obtained using an approach based on penalization of the boundary behaviour, diffusion and viscosity in the weak formulation. Both the solutions and the domain are rather general, no symmetry assumption is required and the result holds for large initial data. This article is part of a research programme whose aim is the investigation of the effect of drug application in tumour growth.

q Breathers in Finite Lattices: Nonlinearity and Weak Disorder

NASA Astrophysics Data System (ADS)

Ivanchenko, M. V.

2009-05-01

Nonlinearity and disorder are the recognized ingredients of the lattice vibrational dynamics, the factors that could be diminished, but never excluded. We generalize the concept of q breathers—periodic orbits in nonlinear lattices, exponentially localized in the linear mode space—to the case of weak disorder, taking the Fermi-Pasta-Ulan chain as an example. We show that these nonlinear vibrational modes remain exponentially localized near the central mode and stable, provided the disorder is sufficiently small. The instability threshold depends sensitively on a particular realization of disorder and can be modified by specifically designed impurities. Based on this sensitivity, an approach to controlling the energy flow between the modes is proposed. The relevance to other model lattices and experimental miniature arrays is discussed.

Corrections to the Eckhaus' stability criterion for one-dimensional stationary structures

NASA Astrophysics Data System (ADS)

Malomed, B. A.; Staroselsky, I. E.; Konstantinov, A. B.

1989-01-01

Two amendments to the well-known Eckhaus' stability criterion for small-amplitude non-linear structures generated by weak instability of a spatially uniform state of a non-equilibrium one-dimensional system against small perturbations with finite wavelengths are obtained. Firstly, we evaluate small corrections to the main Eckhaus' term which, on the contrary so that term, do not have a universal form. Comparison of those non-universal corrections with experimental or numerical results gives a possibility to select a more relevant form of an effective nonlinear evolution equation. In particular, the comparison with such results for convective rolls and Taylor vortices gives arguments in favor of the Swift-Hohenberg equation. Secondly, we derive an analog of the Eckhaus criterion for systems degenerate in the sense that in an expansion of their non-linear parts in powers of dynamical variables, the second and third degree terms are absent.

Stepwise photochromism of bisnaphthopyrans exhibiting an excitation intensity-dependent color change.

PubMed

Inagaki, Yuki; Mutoh, Katsuya; Abe, Jiro

2018-06-07

Non-linear photoresponses against excitation light intensity are important for the development of attractive photofunctional materials exhibiting high spatial selective photoswitching that is not affected by weak background light. Biphotochromic systems composed of two fast photochromic units have the potential to show a stepwise two-photon absorption process in which the optical properties can be non-linearly controlled by changing the excitation light conditions. Herein, we designed and synthesized novel bisnaphthopyran derivatives containing fast photoswitchable naphthopyran units. The bisnaphthopyran derivatives show a stepwise two-photon-induced photochromic reaction upon UV light irradiation accompanied by a drastic color change due to a large change in the molecular structure between the one-photon product and the two-photon product. Consequently, the color of the bisnaphthopyran derivatives can be non-linearly controlled by changing the excitation intensity. This characteristic photochromic property of the biphotochromic system provides important insight into advanced photoresponsive materials.

Time and space analysis of turbulence of gravity surface waves

NASA Astrophysics Data System (ADS)

Mordant, Nicolas; Aubourg, Quentin; Viboud, Samuel; Sommeria, Joel

2016-11-01

Wave turbulence is a statistical state made of a very large number of nonlinearly interacting waves. The Weak Turbulence Theory was developed to describe such a situation in the weakly nonlinear regime. Although, oceanic data tend to be compatible with the theory, laboratory data fail to fulfill the theoretical predictions. A space-time resolved measurement of the waves have proven to be especially fruitful to identify the mechanism at play in turbulence of gravity-capillary waves. We developed an image processing algorithm to measure the motion of the surface of water with both space and time resolution. We first seed the surface with slightly buoyant polystyrene particles and use 3 cameras to reconstruct the surface. Our stereoscopic algorithm is coupled to PIV so that to obtain both the surface deformation and the velocity of the water surface. Such a coupling is shown to improve the sensitivity of the measurement by one order of magnitude. We use this technique to probe the existence of weakly nonlinear turbulence excited by two small wedge wavemakers in a 13-m diameter wave flume. We observe a truly weakly nonlinear regime of isotropic wave turbulence. This project has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (Grant Agreement No 647018-WATU).

Modification of optical properties by adiabatic shifting of resonances in a four-level atom

NASA Astrophysics Data System (ADS)

Dutta, Bibhas Kumar; Panchadhyayee, Pradipta

2018-04-01

We describe the linear and nonlinear optical properties of a four-level atomic system, after reducing it to an effective two-level atomic model under the condition of adiabatic shifting of resonances driven by two coherent off-resonant fields. The reduced form of the Hamiltonian corresponding to the two-level system is obtained by employing an adiabatic elimination procedure in the rate equations of the probability amplitudes for the proposed four-level model. For a weak probe field operating in the system, the nonlinear dependence of complex susceptibility on the Rabi frequencies and the detuning parameters of the off-resonant driving fields makes it possible to exhibit coherent control of single-photon and two-photon absorption and transparency, the evolution of enhanced Self-Kerr nonlinearity and noticeable dispersive switching. We have shown how the quantum interference results in the generic four-level model at the adiabatic limit. The present scheme describes the appearance of single-photon transparency without invoking any exact two-photon resonance.

Chaos and Order in Weakly Coupled Systems of Nonlinear Oscillators

NASA Astrophysics Data System (ADS)

Bruhn, B.

1987-01-01

We consider in this paper perturbations of two degree of freedom Hamiltonian systems which contain periodic and heteroclinic orbits. The Melnikov-Keener condition is used to proof the existence of horseshoes in the dynamics. The same condition is applied to prove a high degree of order in the motion of the swinging Atwood's machine. For some selected parameter values the theoretical predictions are checked by numerical calculations.

FOCUSING OF HIGH POWER ULTRASOUND BEAMS AND LIMITING VALUES OF SHOCK WAVE PARAMETERS

PubMed Central

Bessonova, O.V.; Khokhlova, V.A.; Bailey, M.R.; Canney, M.S.; Crum, L.A.

2009-01-01

In this work, the influence of nonlinear and diffraction effects on amplification factors of focused ultrasound systems is investigated. The limiting values of acoustic field parameters obtained by focusing of high power ultrasound are studied. The Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation was used for the numerical modeling. Solutions for the nonlinear acoustic field were obtained at output levels corresponding to both pre- and post- shock formation conditions in the focal area of the beam in a weakly dissipative medium. Numerical solutions were compared with experimental data as well as with known analytic predictions. PMID:20161349

FOCUSING OF HIGH POWER ULTRASOUND BEAMS AND LIMITING VALUES OF SHOCK WAVE PARAMETERS.

PubMed

Bessonova, O V; Khokhlova, V A; Bailey, M R; Canney, M S; Crum, L A

2009-07-21

In this work, the influence of nonlinear and diffraction effects on amplification factors of focused ultrasound systems is investigated. The limiting values of acoustic field parameters obtained by focusing of high power ultrasound are studied. The Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation was used for the numerical modeling. Solutions for the nonlinear acoustic field were obtained at output levels corresponding to both pre- and post- shock formation conditions in the focal area of the beam in a weakly dissipative medium. Numerical solutions were compared with experimental data as well as with known analytic predictions.

Focusing of high power ultrasound beams and limiting values of shock wave parameters

NASA Astrophysics Data System (ADS)

Bessonova, O. V.; Khokhlova, V. A.; Bailey, M. R.; Canney, M. S.; Crum, L. A.

2009-10-01

In this work, the influence of nonlinear and diffraction effects on amplification factors of focused ultrasound systems is investigated. The limiting values of acoustic field parameters obtained by focusing of high power ultrasound are studied. The Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation was used for the numerical modeling. Solutions for the nonlinear acoustic field were obtained at output levels corresponding to both pre- and post-shock formation conditions in the focal area of the beam in a weakly dissipative medium. Numerical solutions were compared with experimental data as well as with known analytic predictions.

SPECIAL ISSUE ON OPTICAL PROCESSING OF INFORMATION: Information transmission systems based on two-mode lasers with controlled emission frequencies

NASA Astrophysics Data System (ADS)

Naumov, N. V.; Petrovskii, V. N.; Protsenko, E. D.; Shananin, R. A.

1995-10-01

Various information transmission systems, based on two-mode lasers with controlled emission frequencies, are proposed. It is suggested that these systems can be implemented by modulation of the intermode spacing of a two-mode laser. An experimental investigation is reported of frequency control methods. It is shown that these methods should make it possible to construct information transmission systems with high transmission rates subject to weak nonlinear distortions of the information-carrying signal.

Ion acoustic shock wave in collisional equal mass plasma

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

Adak, Ashish, E-mail: ashish-adak@yahoo.com; Ghosh, Samiran, E-mail: sran-g@yahoo.com; Chakrabarti, Nikhil, E-mail: nikhil.chakrabarti@saha.ac.in

The effect of ion-ion collision on the dynamics of nonlinear ion acoustic wave in an unmagnetized pair-ion plasma has been investigated. The two-fluid model has been used to describe the dynamics of both positive and negative ions with equal masses. It is well known that in the dynamics of the weakly nonlinear wave, the viscosity mediates wave dissipation in presence of weak nonlinearity and dispersion. This dissipation is responsible for the shock structures in pair-ion plasma. Here, it has been shown that the ion-ion collision in presence of collective phenomena mediated by the plasma current is the source of dissipationmore » that causes the Burgers' term which is responsible for the shock structures in equal mass pair-ion plasma. The dynamics of the weakly nonlinear wave is governed by the Korteweg-de Vries Burgers equation. The analytical and numerical investigations revealed that the ion acoustic wave exhibits both oscillatory and monotonic shock structures depending on the frequency of ion-ion collision parameter. The results have been discussed in the context of the fullerene pair-ion plasma experiments.« less

Linear and nonlinear stability of the Blasius boundary layer

NASA Technical Reports Server (NTRS)

Bertolotti, F. P.; Herbert, TH.; Spalart, P. R.

1992-01-01

Two new techniques for the study of the linear and nonlinear instability in growing boundary layers are presented. The first technique employs partial differential equations of parabolic type exploiting the slow change of the mean flow, disturbance velocity profiles, wavelengths, and growth rates in the streamwise direction. The second technique solves the Navier-Stokes equation for spatially evolving disturbances using buffer zones adjacent to the inflow and outflow boundaries. Results of both techniques are in excellent agreement. The linear and nonlinear development of Tollmien-Schlichting (TS) waves in the Blasius boundary layer is investigated with both techniques and with a local procedure based on a system of ordinary differential equations. The results are compared with previous work and the effects of non-parallelism and nonlinearity are clarified. The effect of nonparallelism is confirmed to be weak and, consequently, not responsible for the discrepancies between measurements and theoretical results for parallel flow.

Information flow to assess cardiorespiratory interactions in patients on weaning trials.

PubMed

Vallverdú, M; Tibaduisa, O; Clariá, F; Hoyer, D; Giraldo, B; Benito, S; Caminal, P

2006-01-01

Nonlinear processes of the autonomic nervous system (ANS) can produce breath-to-breath variability in the pattern of breathing. In order to provide assess to these nonlinear processes, nonlinear statistical dependencies between heart rate variability and respiratory pattern variability are analyzed. In this way, auto-mutual information and cross-mutual information concepts are applied. This information flow analysis is presented as a short-term non linear analysis method to investigate the information flow interactions in patients on weaning trials. 78 patients from mechanical ventilation were studied: Group A of 28 patients that failed to maintain spontaneous breathing and were reconnected; Group B of 50 patients with successful trials. The results show lower complexity with an increase of information flow in group A than in group B. Furthermore, a more (weakly) coupled nonlinear oscillator behavior is observed in the series of group A than in B.

Spectro-spatial analysis of wave packet propagation in nonlinear acoustic metamaterials

NASA Astrophysics Data System (ADS)

Zhou, W. J.; Li, X. P.; Wang, Y. S.; Chen, W. Q.; Huang, G. L.

2018-01-01

The objective of this work is to analyze wave packet propagation in weakly nonlinear acoustic metamaterials and reveal the interior nonlinear wave mechanism through spectro-spatial analysis. The spectro-spatial analysis is based on full-scale transient analysis of the finite system, by which dispersion curves are generated from the transmitted waves and also verified by the perturbation method (the L-P method). We found that the spectro-spatial analysis can provide detailed information about the solitary wave in short-wavelength region which cannot be captured by the L-P method. It is also found that the optical wave modes in the nonlinear metamaterial are sensitive to the parameters of the nonlinear constitutive relation. Specifically, a significant frequency shift phenomenon is found in the middle-wavelength region of the optical wave branch, which makes this frequency region behave like a band gap for transient waves. This special frequency shift is then used to design a direction-biased waveguide device, and its efficiency is shown by numerical simulations.

The modulational instability for the TDNLS equations for weakly nonlinear dispersive MHD waves

NASA Technical Reports Server (NTRS)

Webb, G. M.; Brio, M.; Zank, G. P.

1995-01-01

In this paper we study the modulational instability for the TDNLS equations derived by Hada (1993) and Brio, Hunter, and Johnson to describe the propagation of weakly nonlinear dispersive MHD waves in beta approximately 1 plasmas. We employ Whitham's averaged Lagrangian method to study the modulational instability. This complements studies of the modulational instability by Hada (1993) and Hollweg (1994), who did not use the averaged Lagrangian approach.

Non-Destructive Evaluation of Material System Using Highly Nonlinear Acoustic Waves

NASA Astrophysics Data System (ADS)

Khatri, Devvrath

A chain of granular particles is one of the most studied examples of highly nonlinear systems deriving its response from the nonlinear Hertzian contact interaction between particles. Interest in these systems derives from their tunable dynamic response, encompassing linear, weakly nonlinear, and strongly nonlinear regimes, controlled by varying the static and dynamic load applied. In chains with a very weak (or zero) static precompression, the system supports the formation and propagation of highly nonlinear solitary waves (HNSWs). The dual-nonlinear interaction between particles (i.e., a power-law type contact potential in compression, and zero strength in tension) combined with discreteness of the system, makes the granular system highly tunable. The propagation properties of these waves, such as traveling pulse width, wave speed, number of separated pulses (single or train of pulses), etc., can be controlled by modifying one or many of the parameters, like the particle's dimension, material properties, static and dynamic force amplitude, the type and duration of the initial excitation applied to the system, and/or the periodicity of the chain. The ability to control the wave properties in such chains has been proposed for several different practical engineering applications. The dynamic properties of these granular chains have been conventionally studied using discrete particle models (DPMs) which consider the particles in the chains as point masses connected by nonlinear Hertzian springs with the neighboring particles. Although, this is a good approximation under proper circumstances, it does not capture many features of the three dimensional elastic particles such as the elastic wave propagation within the particles, the local deformation of the particles in the vicinity of the contact point, the corresponding changes in the contact area, and the collective vibrations of the particles among others. This thesis focuses on the development of a finite element model (FEM) using the commercially available software Abaqus, which takes into account many of these characteristic features. The finite element model discretizes particles by considering them as three-dimensional deformable bodies of revolution and describes the nonlinear dynamic response of one-dimensional granular chains composed of particles with various geometries and orientations. We showed that particles' geometries and orientations provide additional design parameters for controlling the dynamic response of the system, compared to chains composed of spherical particles. We also showed that the tunable and compact nature of these waves can be used to tailor the properties of HNSWs for specific application, such as information carriers for actuation and sensing of mechanical properties and boundary effects of adjoining media in Non-Destructive Evaluation (NDE) and Structural Health Monitoring (SHM). Using experiments and numerics, we characterized interface dynamics between granular media and adjoining linear elastic media, and found that the coupling produced temporary localization of the incident waves at the boundaries between the two media and their decomposition into reflected waves. We monitored the formation of reflected solitary waves propagating back from the interface and found that their properties are sensitive to the geometric and material properties of the adjoining media. The work done in this research enhances our understanding of the basic physics and tunability of nonlinear granular media, and further establishes a theoretical and numerical foundation in the applications of HNSWs as information carriers.

A Taylor weak-statement algorithm for hyperbolic conservation laws

NASA Technical Reports Server (NTRS)

Baker, A. J.; Kim, J. W.

1987-01-01

Finite element analysis, applied to computational fluid dynamics (CFD) problem classes, presents a formal procedure for establishing the ingredients of a discrete approximation numerical solution algorithm. A classical Galerkin weak-statement formulation, formed on a Taylor series extension of the conservation law system, is developed herein that embeds a set of parameters eligible for constraint according to specification of suitable norms. The derived family of Taylor weak statements is shown to contain, as special cases, over one dozen independently derived CFD algorithms published over the past several decades for the high speed flow problem class. A theoretical analysis is completed that facilitates direct qualitative comparisons. Numerical results for definitive linear and nonlinear test problems permit direct quantitative performance comparisons.

On a Nonlinear Model for Tumor Growth: Global in Time Weak Solutions

NASA Astrophysics Data System (ADS)

Donatelli, Donatella; Trivisa, Konstantina

2014-07-01

We investigate the dynamics of a class of tumor growth models known as mixed models. The key characteristic of these type of tumor growth models is that the different populations of cells are continuously present everywhere in the tumor at all times. In this work we focus on the evolution of tumor growth in the presence of proliferating, quiescent and dead cells as well as a nutrient. The system is given by a multi-phase flow model and the tumor is described as a growing continuum Ω with boundary ∂Ω both of which evolve in time. Global-in-time weak solutions are obtained using an approach based on penalization of the boundary behavior, diffusion and viscosity in the weak formulation.

Route to thermalization in the α-Fermi–Pasta–Ulam system

PubMed Central

Onorato, Miguel; Vozella, Lara; Lvov, Yuri V.

2015-01-01

We study the original α-Fermi–Pasta–Ulam (FPU) system with N = 16, 32, and 64 masses connected by a nonlinear quadratic spring. Our approach is based on resonant wave–wave interaction theory; i.e., we assume that, in the weakly nonlinear regime (the one in which Fermi was originally interested), the large time dynamics is ruled by exact resonances. After a detailed analysis of the α-FPU equation of motion, we find that the first nontrivial resonances correspond to six-wave interactions. Those are precisely the interactions responsible for the thermalization of the energy in the spectrum. We predict that, for small-amplitude random waves, the timescale of such interactions is extremely large and it is of the order of 1/ϵ8, where ϵ is the small parameter in the system. The wave–wave interaction theory is not based on any threshold: Equipartition is predicted for arbitrary small nonlinearity. Our results are supported by extensive numerical simulations. A key role in our finding is played by the Umklapp (flip-over) resonant interactions, typical of discrete systems. The thermodynamic limit is also briefly discussed. PMID:25805822

Nonlinear Blind Compensation for Array Signal Processing Application

PubMed Central

Ma, Hong; Jin, Jiang; Zhang, Hua

2018-01-01

Recently, nonlinear blind compensation technique has attracted growing attention in array signal processing application. However, due to the nonlinear distortion stemming from array receiver which consists of multi-channel radio frequency (RF) front-ends, it is too difficult to estimate the parameters of array signal accurately. A novel nonlinear blind compensation algorithm aims at the nonlinearity mitigation of array receiver and its spurious-free dynamic range (SFDR) improvement, which will be more precise to estimate the parameters of target signals such as their two-dimensional directions of arrival (2-D DOAs). Herein, the suggested method is designed as follows: the nonlinear model parameters of any channel of RF front-end are extracted to synchronously compensate the nonlinear distortion of the entire receiver. Furthermore, a verification experiment on the array signal from a uniform circular array (UCA) is adopted to testify the validity of our approach. The real-world experimental results show that the SFDR of the receiver is enhanced, leading to a significant improvement of the 2-D DOAs estimation performance for weak target signals. And these results demonstrate that our nonlinear blind compensation algorithm is effective to estimate the parameters of weak array signal in concomitance with strong jammers. PMID:29690571

Bivariate spline solution of time dependent nonlinear PDE for a population density over irregular domains.

PubMed

Gutierrez, Juan B; Lai, Ming-Jun; Slavov, George

2015-12-01

We study a time dependent partial differential equation (PDE) which arises from classic models in ecology involving logistic growth with Allee effect by introducing a discrete weak solution. Existence, uniqueness and stability of the discrete weak solutions are discussed. We use bivariate splines to approximate the discrete weak solution of the nonlinear PDE. A computational algorithm is designed to solve this PDE. A convergence analysis of the algorithm is presented. We present some simulations of population development over some irregular domains. Finally, we discuss applications in epidemiology and other ecological problems. Copyright © 2015 Elsevier Inc. All rights reserved.

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.

Effect of nonlinearity saturation on hot-image formation in cascaded saturable nonlinear medium slabs

NASA Astrophysics Data System (ADS)

Wang, Youwen; Dai, Zhiping; Ling, Xiaohui; Chen, Liezun; Lu, Shizhuan; You, Kaiming

2016-11-01

In high-power laser system such as Petawatt lasers, the laser beam can be intense enough to result in saturation of nonlinear refraction index of medium. Based on the standard linearization method of small-scale self-focusing and the split-step Fourier numerical calculation method, we present analytical and simulative investigations on the hot-image formation in cascaded saturable nonlinear medium slabs, to disclose the effect of nonlinearity saturation on the distribution and intensity of hot images. The analytical and simulative results are found in good agreement. It is shown that, saturable nonlinearity does not change the distribution of hot images, while may greatly affect the intensity of hot images, i.e., for a given saturation light intensity, with the intensity of the incident laser beam, the intensity of hot images firstly increases monotonously and eventually reaches a saturation; for the incident laser beam of a given intensity, with the saturation light intensity lowering, the intensity of hot images decreases rapidly, even resulting in a few hot images too weak to be visible.

Noise-induced shifts in the population model with a weak Allee effect

NASA Astrophysics Data System (ADS)

Bashkirtseva, Irina; Ryashko, Lev

2018-02-01

We consider the Truscott-Brindley system of interacting phyto- and zooplankton populations with a weak Allee effect. We add a random noise to the parameter of the prey carrying capacity, and study how the noise affects the dynamic behavior of this nonlinear prey-predator model. Phenomena of the stochastic excitement and noise-induced shifts in zones of the Andronov-Hopf bifurcation and Canard explosion are analyzed on the base of the direct numerical simulation and stochastic sensitivity functions technique. A relationship of these phenomena with transitions between order and chaos is discussed.

Guided solitary waves.

PubMed

Miles, J

1980-04-01

Transversely periodic solitary-wave solutions of the Boussinesq equations (which govern wave propagation in a weakly dispersive, weakly nonlinear physical system) are determined. The solutions for negative dispersion (e.g., gravity waves) are singular and therefore physically unacceptable. The solutions for positive dispersion (e.g., capillary waves or magnetosonic waves in a plasma) are physically acceptable except in a limited parametric interval, in which they are complex. The two end points of this interval are associated with (two different) resonant interactions among three basic solitary waves, two of which are two-dimensional complex conjugates and the third of which is one-dimensional and real.

Image compression-encryption scheme based on hyper-chaotic system and 2D compressive sensing

NASA Astrophysics Data System (ADS)

Zhou, Nanrun; Pan, Shumin; Cheng, Shan; Zhou, Zhihong

2016-08-01

Most image encryption algorithms based on low-dimensional chaos systems bear security risks and suffer encryption data expansion when adopting nonlinear transformation directly. To overcome these weaknesses and reduce the possible transmission burden, an efficient image compression-encryption scheme based on hyper-chaotic system and 2D compressive sensing is proposed. The original image is measured by the measurement matrices in two directions to achieve compression and encryption simultaneously, and then the resulting image is re-encrypted by the cycle shift operation controlled by a hyper-chaotic system. Cycle shift operation can change the values of the pixels efficiently. The proposed cryptosystem decreases the volume of data to be transmitted and simplifies the keys distribution simultaneously as a nonlinear encryption system. Simulation results verify the validity and the reliability of the proposed algorithm with acceptable compression and security performance.

Nonlinear and Dissipation Characteristics of Ocean Surface Waves in Estuarine Environments

DTIC Science & Technology

2013-09-30

developed models while using the general framework of operational wave models. We will conduct robustness tests of the system to determine the...and Guza (1984) model is weakly dispersive, in line with the assumptions behind the Boussinesq equations from which it was derived. The Kaihatu and...interactions across both frequency and directions. This system of equations is solved over a 2D frequency (f) and shore parallel wave number (κ) space. The

Recurrence in truncated Boussinesq models for nonlinear waves in shallow water

NASA Technical Reports Server (NTRS)

Elgar, Steve; Freilich, M. H.; Guza, R. T.

1990-01-01

The rapid spatial recurrence of weakly nonlinear and weakly dispersive progressive shallow-water waves is examined using a numerical integration technique on the discretized and truncated form of the Boussinesq equations. This study primarily examines recurrence in wave fields with Ursell number O(1) and characterizes the sensitivity of recurrence to initial spectral shape and number of allowed frequency modes. It is shown that the rapid spatial recurrence is not an inherent property of the considered Boussinesq systems for evolution distances of 10-50 wavelengths. The main result of the study is that highly truncated Boussinesq models of resonant shallow-water ocean surface gravity waves predict rapid multiple recurrence cycles, but that this is an artifact dependent on the number of allowed modes. For initial conditions consisting of essentially all energy concentrated in a single mode, damping of the recurrence cycles increases as the number of low-power background modes increases. When more than 32 modes are allowed, the recurrence behavior is relatively insensitive to the number of allowed modes.

The nonlinear Schrödinger equation and the propagation of weakly nonlinear waves in optical fibers and on the water surface

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

Chabchoub, A., E-mail: achabchoub@swin.edu.au; Kibler, B.; Finot, C.

2015-10-15

The dynamics of waves in weakly nonlinear dispersive media can be described by the nonlinear Schrödinger equation (NLSE). An important feature of the equation is that it can be derived in a number of different physical contexts; therefore, analogies between different fields, such as for example fiber optics, water waves, plasma waves and Bose–Einstein condensates, can be established. Here, we investigate the similarities between wave propagation in optical Kerr media and water waves. In particular, we discuss the modulation instability (MI) in both media. In analogy to the water wave problem, we derive for Kerr-media the Benjamin–Feir index, i.e. amore » nondimensional parameter related to the probability of formation of rogue waves in incoherent wave trains.« less

Exploration of multiphoton entangled states by using weak nonlinearities

PubMed Central

He, Ying-Qiu; Ding, Dong; Yan, Feng-Li; Gao, Ting

2016-01-01

We propose a fruitful scheme for exploring multiphoton entangled states based on linear optics and weak nonlinearities. Compared with the previous schemes the present method is more feasible because there are only small phase shifts instead of a series of related functions of photon numbers in the process of interaction with Kerr nonlinearities. In the absence of decoherence we analyze the error probabilities induced by homodyne measurement and show that the maximal error probability can be made small enough even when the number of photons is large. This implies that the present scheme is quite tractable and it is possible to produce entangled states involving a large number of photons. PMID:26751044

Intermittency and emergence of coherent structures in wave turbulence of a vibrating plate.

PubMed

Mordant, Nicolas; Miquel, Benjamin

2017-10-01

We report numerical investigations of wave turbulence in a vibrating plate. The possibility to implement advanced measurement techniques and long-time numerical simulations makes this system extremely valuable for wave turbulence studies. The purely 2D character of dynamics of the elastic plate makes it much simpler to handle compared to much more complex 3D physical systems that are typical of geo- and astrophysical issues (ocean surface or internal waves, magnetized plasmas or strongly rotating and/or stratified flows). When the forcing is small the observed wave turbulence is consistent with the predictions of the weak turbulent theory. Here we focus on the case of stronger forcing for which coherent structures can be observed. These structures look similar to the folds and D-cones that are commonly observed for strongly deformed static thin elastic sheets (crumpled paper) except that they evolve dynamically in our forced system. We describe their evolution and show that their emergence is associated with statistical intermittency (lack of self similarity) of strongly nonlinear wave turbulence. This behavior is reminiscent of intermittency in Navier-Stokes turbulence. Experimental data show hints of the weak to strong turbulence transition. However, due to technical limitations and dissipation, the strong nonlinear regime remains out of reach of experiments and therefore has been explored numerically.

Intermittency and emergence of coherent structures in wave turbulence of a vibrating plate

NASA Astrophysics Data System (ADS)

Mordant, Nicolas; Miquel, Benjamin

2017-10-01

We report numerical investigations of wave turbulence in a vibrating plate. The possibility to implement advanced measurement techniques and long-time numerical simulations makes this system extremely valuable for wave turbulence studies. The purely 2D character of dynamics of the elastic plate makes it much simpler to handle compared to much more complex 3D physical systems that are typical of geo- and astrophysical issues (ocean surface or internal waves, magnetized plasmas or strongly rotating and/or stratified flows). When the forcing is small the observed wave turbulence is consistent with the predictions of the weak turbulent theory. Here we focus on the case of stronger forcing for which coherent structures can be observed. These structures look similar to the folds and D-cones that are commonly observed for strongly deformed static thin elastic sheets (crumpled paper) except that they evolve dynamically in our forced system. We describe their evolution and show that their emergence is associated with statistical intermittency (lack of self similarity) of strongly nonlinear wave turbulence. This behavior is reminiscent of intermittency in Navier-Stokes turbulence. Experimental data show hints of the weak to strong turbulence transition. However, due to technical limitations and dissipation, the strong nonlinear regime remains out of reach of experiments and therefore has been explored numerically.

Closed-loop suppression of chaos in nonlinear driven oscillators

NASA Astrophysics Data System (ADS)

Aguirre, L. A.; Billings, S. A.

1995-05-01

This paper discusses the suppression of chaos in nonlinear driven oscillators via the addition of a periodic perturbation. Given a system originally undergoing chaotic motions, it is desired that such a system be driven to some periodic orbit. This can be achieved by the addition of a weak periodic signal to the oscillator input. This is usually accomplished in open loop, but this procedure presents some difficulties which are discussed in the paper. To ensure that this is attained despite uncertainties and possible disturbances on the system, a procedure is suggested to perform control in closed loop. In addition, it is illustrated how a model, estimated from input/output data, can be used in the design. Numerical examples which use the Duffing-Ueda and modified van der Pol oscillators are included to illustrate some of the properties of the new approach.

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.

Perturbed invariant subspaces and approximate generalized functional variable separation solution for nonlinear diffusion-convection equations with weak source

NASA Astrophysics Data System (ADS)

Xia, Ya-Rong; Zhang, Shun-Li; Xin, Xiang-Peng

2018-03-01

In this paper, we propose the concept of the perturbed invariant subspaces (PISs), and study the approximate generalized functional variable separation solution for the nonlinear diffusion-convection equation with weak source by the approximate generalized conditional symmetries (AGCSs) related to the PISs. Complete classification of the perturbed equations which admit the approximate generalized functional separable solutions (AGFSSs) is obtained. As a consequence, some AGFSSs to the resulting equations are explicitly constructed by way of examples.

Stability of discrete time recurrent neural networks and nonlinear optimization problems.

PubMed

Singh, Jayant; Barabanov, Nikita

2016-02-01

We consider the method of Reduction of Dissipativity Domain to prove global Lyapunov stability of Discrete Time Recurrent Neural Networks. The standard and advanced criteria for Absolute Stability of these essentially nonlinear systems produce rather weak results. The method mentioned above is proved to be more powerful. It involves a multi-step procedure with maximization of special nonconvex functions over polytopes on every step. We derive conditions which guarantee an existence of at most one point of local maximum for such functions over every hyperplane. This nontrivial result is valid for wide range of neuron transfer functions. Copyright © 2015 Elsevier Ltd. All rights reserved.

Remarks on the derivation of the governing equations for the dynamics of a nonlinear beam to a non ideal shaft coupling

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

Fenili, André; Lopes Rebello da Fonseca Brasil, Reyolando Manoel; Balthazar, José M., E-mail: jmbaltha@gmail.com

We derive nonlinear governing equations without assuming that the beam is inextensible. The derivation couples the equations that govern a weak electric motor, which is used to rotate the base of the beam, to those that govern the motion of the beam. The system is considered non-ideal in the sense that the response of the motor to an applied voltage and the motion of the beam must be obtained interactively. The moment that the motor exerts on the base of the beam cannot be determined without solving for the motion of the beam.

Numerical Calculation and Measurement of Nonlinear Acoustic Fields in Ultrasound Diagnosis

NASA Astrophysics Data System (ADS)

Kawagishi, Tetsuya; Saito, Shigemi; Mine, Yoshitaka

2002-05-01

In order to develop a tool for designing on the ultrasonic probe and its peripheral devices for tissue-harmonic-imaging systems, a study is carried out to compare the calculation and observation results of nonlinear acoustic fields for a diagnostic ultrasound system. The pulsed ultrasound with a center frequency of 2.5 MHz is emanated from a weakly focusing sector probe with a 6.5 mm aperture radius and a 50 mm focal length into an agar phantom with an attenuation coefficient of about 0.6 dB/cm/MHz or 1.2 dB/cm/MHz. The nonlinear acoustic field is measured using a needle-type hydrophone. The calculation is based on the Khokhlov-Zabolotskaya-Kuznetsov(KZK) equation which is modified so that the frequency dependence of the attenuation coefficient is the same as that in biological tissue. This equation is numerically solved with the implicit backward method employing the iterative method. The measured and calculated amplitude spectra show good agreement with each other.

All-Phononic Digital Transistor on the Basis of Gap-Soliton Dynamics in an Anharmonic Oscillator Ladder.

PubMed

Malishava, Merab; Khomeriki, Ramaz

2015-09-04

A conceptual mechanism of amplification of phonons by phonons on the basis of a nonlinear band-gap transmission (supratransmission) phenomenon is presented. As an example, a system of weakly coupled chains of anharmonic oscillators is considered. One (source) chain is driven harmonically by a boundary with a frequency located in the upper band close to the band edge of the ladder system. Amplification happens when a second (gate) chain is driven by a small signal in the counterphase and with the same frequency as the first chain. If the total driving of both chains overcomes the band-gap transmission threshold, the large amplitude band-gap soliton emerges and the amplification scenario is realized. The mechanism is interpreted as the nonlinear superposition of evanescent and propagating nonlinear modes manifesting in a single or double soliton generation working in band-gap or bandpass regimes, respectively. The results could be straightforwardly generalized for all-optical or all-magnonic contexts and have all the promise of logic gate operations.

All-Phononic Digital Transistor on the Basis of Gap-Soliton Dynamics in an Anharmonic Oscillator Ladder

NASA Astrophysics Data System (ADS)

Malishava, Merab; Khomeriki, Ramaz

2015-09-01

A conceptual mechanism of amplification of phonons by phonons on the basis of a nonlinear band-gap transmission (supratransmission) phenomenon is presented. As an example, a system of weakly coupled chains of anharmonic oscillators is considered. One (source) chain is driven harmonically by a boundary with a frequency located in the upper band close to the band edge of the ladder system. Amplification happens when a second (gate) chain is driven by a small signal in the counterphase and with the same frequency as the first chain. If the total driving of both chains overcomes the band-gap transmission threshold, the large amplitude band-gap soliton emerges and the amplification scenario is realized. The mechanism is interpreted as the nonlinear superposition of evanescent and propagating nonlinear modes manifesting in a single or double soliton generation working in band-gap or bandpass regimes, respectively. The results could be straightforwardly generalized for all-optical or all-magnonic contexts and have all the promise of logic gate operations.

Weak Value Amplification of a Post-Selected Single Photon

NASA Astrophysics Data System (ADS)

Hallaji, Matin

Weak value amplification (WVA) is a measurement technique in which the effect of a pre- and post-selected system on a weakly interacting probe is magnified. In this thesis, I present the first experimental observation of WVA of a single photon. We observed that a signal photon --- sent through a polarization interferometer and post-selected by photodetection in the almost-dark port --- can act like eight photons. The effect of this single photon is measured as a nonlinear phase shift on a separate laser beam. The interaction between the two is mediated by a sample of laser- cooled 85Rb atoms. Electromagnetically induced transparency (EIT) is used to enhance the nonlinearity and overcome resonant absorption. I believe this work to be the first demonstration of WVA where a deterministic interaction is used to entangle two distinct optical systems. In WVA, the amplification is contingent on discarding a large portion of the original data set. While amplification increases measurement sensitivity, discarding data worsens it. Questioning whether these competing effects conspire to improve or diminish measurement accuracy has resulted recently in controversy. I address this question by calculating the maximum amount of information achievable with the WVA technique. By comparing this information to that achievable by the standard technique, where no post-selection is employed, I show that the WVA technique can be advantageous under a certain class of noise models. Finally, I propose a way to optimally apply the WVA technique.

A coupled electro-thermal Discontinuous Galerkin method

NASA Astrophysics Data System (ADS)

Homsi, L.; Geuzaine, C.; Noels, L.

2017-11-01

This paper presents a Discontinuous Galerkin scheme in order to solve the nonlinear elliptic partial differential equations of coupled electro-thermal problems. In this paper we discuss the fundamental equations for the transport of electricity and heat, in terms of macroscopic variables such as temperature and electric potential. A fully coupled nonlinear weak formulation for electro-thermal problems is developed based on continuum mechanics equations expressed in terms of energetically conjugated pair of fluxes and fields gradients. The weak form can thus be formulated as a Discontinuous Galerkin method. The existence and uniqueness of the weak form solution are proved. The numerical properties of the nonlinear elliptic problems i.e., consistency and stability, are demonstrated under specific conditions, i.e. use of high enough stabilization parameter and at least quadratic polynomial approximations. Moreover the prior error estimates in the H1-norm and in the L2-norm are shown to be optimal in the mesh size with the polynomial approximation degree.

Weighted interior penalty discretization of fully nonlinear and weakly dispersive free surface shallow water flows

NASA Astrophysics Data System (ADS)

Di Pietro, Daniele A.; Marche, Fabien

2018-02-01

In this paper, we further investigate the use of a fully discontinuous Finite Element discrete formulation for the study of shallow water free surface flows in the fully nonlinear and weakly dispersive flow regime. We consider a decoupling strategy in which we approximate the solutions of the classical shallow water equations supplemented with a source term globally accounting for the non-hydrostatic effects. This source term can be computed through the resolution of elliptic second-order linear sub-problems, which only involve second order partial derivatives in space. We then introduce an associated Symmetric Weighted Internal Penalty discrete bilinear form, allowing to deal with the discontinuous nature of the elliptic problem's coefficients in a stable and consistent way. Similar discrete formulations are also introduced for several recent optimized fully nonlinear and weakly dispersive models. These formulations are validated again several benchmarks involving h-convergence, p-convergence and comparisons with experimental data, showing optimal convergence properties.

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.

Bidirectional negative differential thermal resistance in three-segment Frenkel-Kontorova lattices.

PubMed

Ou, Ya-Li; Lu, Shi-Cai; Hu, Cai-Tian; Ai, Bao-Quan

2016-12-14

By coupling three nonlinear 1D lattice segments, we demonstrate a thermal insulator model, where the system acts like an insulator for large temperature bias and a conductor for very small temperature bias. We numerically investigate the parameter range of the thermal insulator and find that the nonlinear response (the role of on-site potential), the weakly coupling interaction between each segment, and the small system size collectively contribute to the appearance of bidirectional negative differential thermal resistance (BNDTR). The corresponding exhibition of BNDTR can be explained in terms of effective phonon-band shifts. Our results can provide a new perspective for understanding the microscopic mechanism of negative differential thermal resistance and also would be conducive to further developments in designing and fabricating thermal devices and functional materials.

On the instability of a three-dimensional attachment-line boundary layer - Weakly nonlinear theory and a numerical approach

NASA Technical Reports Server (NTRS)

Hall, P.; Malik, M. R.

1986-01-01

The instability of a three-dimensional attachment-line boundary layer is considered in the nonlinear regime. Using weakly nonlinear theory, it is found that, apart from a small interval near the (linear) critical Reynolds number, finite-amplitude solutions bifurcate subcritically from the upper branch of the neutral curve. The time-dependent Navier-Stokes equations for the attachment-line flow have been solved using a Fourier-Chebyshev spectral method and the subcritical instability is found at wavenumbers that correspond to the upper branch. Both the theory and the numerical calculations show the existence of supercritical finite-amplitude (equilibrium) states near the lower branch which explains why the observed flow exhibits a preference for the lower branch modes. The effect of blowing and suction on nonlinear stability of the attachment-line boundary layer is also investigated.

On the instability of a 3-dimensional attachment line boundary layer: Weakly nonlinear theory and a numerical approach

NASA Technical Reports Server (NTRS)

Hall, P.; Malik, M. R.

1984-01-01

The instability of a three dimensional attachment line boundary layer is considered in the nonlinear regime. Using weakly nonlinear theory, it is found that, apart from a small interval near the (linear) critical Reynolds number, finite amplitude solutions bifurcate subcritically from the upper branch of the neutral curve. The time dependent Navier-Stokes equations for the attachment line flow have been solved using a Fourier-Chebyshev spectral method and the subcritical instability is found at wavenumbers that correspond to the upper branch. Both the theory and the numerical calculations show the existence of supercritical finite amplitude (equilibrium) states near the lower branch which explains why the observed flow exhibits a preference for the lower branch modes. The effect of blowing and suction on nonlinear stability of the attachment line boundary layer is also investigated.

The estimation of nonlinearity in problems of the building of initial confidence regions for small bodies motion. (Russian Title: Оценивание нелинейности в задачах построения начальных доверительных областей движения малых тел)

NASA Astrophysics Data System (ADS)

Syusina, O. M.; Chernitsov, A. M.; Tamarov, V. A.

2011-07-01

Simple and mathematically rigorous methods for calculating of nonlinearity coefficients are proposed. These coefficients allow us to make classification for the least squares problem as strongly or weakly nonlinear one. The advices are given on how to reduce a concrete estimation problem to weakly nonlinear one where a more efficient linear approach can be used.

Propagation of electromagnetic soliton in a spin polarized current driven weak ferromagnetic nanowire

NASA Astrophysics Data System (ADS)

Senthil Kumar, V.; Kavitha, L.; Gopi, D.

2017-11-01

We investigate the nonlinear spin dynamics of a spin polarized current driven anisotropic ferromagnetic nanowire with Dzyaloshinskii-Moriya interaction (DMI) under the influence of electromagnetic wave (EMW) propagating along the axis of the nanowire. The magnetization dynamics and electromagnetic wave propagation in the ferromagnetic nanowire with weak anti-symmetric interaction is governed by a coupled vector Landau-Lifshitz-Gilbert and Maxwell's equations. These coupled nonlinear vector equations are recasted into the extended derivative nonlinear Schrödinger (EDNLS) equation in the framework of reductive perturbation method. As it is well known, the modulational instability is a precursor for the emergence of localized envelope structures of various kinds, we compute the instability criteria for the weak ferromagnetic nanowire through linear stability analysis. Further, we invoke the homogeneous balance method to construct kink and anti-solitonic like electromagnetic (EM) soliton profiles for the EDNLS equation. We also explore the appreciable effect of the anti-symmetric weak interaction on the magnetization components of the propagating EM soliton. We find that the combination of spin-polarized current and the anti-symmetric DMI have a profound effect on the propagating EMW in a weak ferromagnetic nanowire. Thus, the anti-symmetric DMI in a spin polarized current driven ferromagnetic nanowire supports the lossless propagation of EM solitons, which may have potential applications in magnetic data storage devices.

Marginal Matter

NASA Astrophysics Data System (ADS)

van Hecke, Martin

2013-03-01

All around us, things are falling apart. The foam on our cappuccinos appears solid, but gentle stirring irreversibly changes its shape. Skin, a biological fiber network, is firm when you pinch it, but soft under light touch. Sand mimics a solid when we walk on the beach but a liquid when we pour it out of our shoes. Crucially, a marginal point separates the rigid or jammed state from the mechanical vacuum (freely flowing) state - at their marginal points, soft materials are neither solid nor liquid. Here I will show how the marginal point gives birth to a third sector of soft matter physics: intrinsically nonlinear mechanics. I will illustrate this with shock waves in weakly compressed granular media, the nonlinear rheology of foams, and the nonlinear mechanics of weakly connected elastic networks.

Nonlinear dynamics of mini-satellite respinup by weak internal controllable torques

NASA Astrophysics Data System (ADS)

Somov, Yevgeny

2014-12-01

Contemporary space engineering advanced new problem before theoretical mechanics and motion control theory: a spacecraft directed respinup by the weak restricted control internal forces. The paper presents some results on this problem, which is very actual for energy supply of information mini-satellites (for communication, geodesy, radio- and opto-electronic observation of the Earth et al.) with electro-reaction plasma thrusters and gyro moment cluster based on the reaction wheels or the control moment gyros. The solution achieved is based on the methods for synthesis of nonlinear robust control and on rigorous analytical proof for the required spacecraft rotation stability by Lyapunov function method. These results were verified by a computer simulation of strongly nonlinear oscillatory processes at respinuping of a flexible spacecraft.

Interactions of large amplitude solitary waves in viscous fluid conduits

NASA Astrophysics Data System (ADS)

Lowman, Nicholas K.; Hoefer, M. A.; El, G. A.

2014-07-01

The free interface separating an exterior, viscous fluid from an intrusive conduit of buoyant, less viscous fluid is known to support strongly nonlinear solitary waves due to a balance between viscosity-induced dispersion and buoyancy-induced nonlinearity. The overtaking, pairwise interaction of weakly nonlinear solitary waves has been classified theoretically for the Korteweg-de Vries equation and experimentally in the context of shallow water waves, but a theoretical and experimental classification of strongly nonlinear solitary wave interactions is lacking. The interactions of large amplitude solitary waves in viscous fluid conduits, a model physical system for the study of one-dimensional, truly dissipationless, dispersive nonlinear waves, are classified. Using a combined numerical and experimental approach, three classes of nonlinear interaction behavior are identified: purely bimodal, purely unimodal, and a mixed type. The magnitude of the dispersive radiation due to solitary wave interactions is quantified numerically and observed to be beyond the sensitivity of our experiments, suggesting that conduit solitary waves behave as "physical solitons." Experimental data are shown to be in excellent agreement with numerical simulations of the reduced model. Experimental movies are available with the online version of the paper.

Optimal antibunching in passive photonic devices based on coupled nonlinear resonators

NASA Astrophysics Data System (ADS)

Ferretti, S.; Savona, V.; Gerace, D.

2013-02-01

We propose the use of weakly nonlinear passive materials for prospective applications in integrated quantum photonics. It is shown that strong enhancement of native optical nonlinearities by electromagnetic field confinement in photonic crystal resonators can lead to single-photon generation only exploiting the quantum interference of two coupled modes and the effect of photon blockade under resonant coherent driving. For realistic system parameters in state of the art microcavities, the efficiency of such a single-photon source is theoretically characterized by means of the second-order correlation function at zero-time delay as the main figure of merit, where major sources of loss and decoherence are taken into account within a standard master equation treatment. These results could stimulate the realization of integrated quantum photonic devices based on non-resonant material media, fully integrable with current semiconductor technology and matching the relevant telecom band operational wavelengths, as an alternative to single-photon nonlinear devices based on cavity quantum electrodynamics with artificial atoms or single atomic-like emitters.

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.

Modulational instability in a PT-symmetric vector nonlinear Schrödinger system

NASA Astrophysics Data System (ADS)

Cole, J. T.; Makris, K. G.; Musslimani, Z. H.; Christodoulides, D. N.; Rotter, S.

2016-12-01

A class of exact multi-component constant intensity solutions to a vector nonlinear Schrödinger (NLS) system in the presence of an external PT-symmetric complex potential is constructed. This type of uniform wave pattern displays a non-trivial phase whose spatial dependence is induced by the lattice structure. In this regard, light can propagate without scattering while retaining its original form despite the presence of inhomogeneous gain and loss. These constant-intensity continuous waves are then used to perform a modulational instability analysis in the presence of both non-hermitian media and cubic nonlinearity. A linear stability eigenvalue problem is formulated that governs the dynamical evolution of the periodic perturbation and its spectrum is numerically determined using Fourier-Floquet-Bloch theory. In the self-focusing case, we identify an intensity threshold above which the constant-intensity modes are modulationally unstable for any Floquet-Bloch momentum belonging to the first Brillouin zone. The picture in the self-defocusing case is different. Contrary to the bulk vector case, where instability develops only when the waves are strongly coupled, here an instability occurs in the strong and weak coupling regimes. The linear stability results are supplemented with direct (nonlinear) numerical simulations.

Galilean-invariant scalar fields can strengthen gravitational lensing.

PubMed

Wyman, Mark

2011-05-20

The mystery of dark energy suggests that there is new gravitational physics on long length scales. Yet light degrees of freedom in gravity are strictly limited by Solar System observations. We can resolve this apparent contradiction by adding a Galilean-invariant scalar field to gravity. Called Galileons, these scalars have strong self-interactions near overdensities, like the Solar System, that suppress their dynamical effect. These nonlinearities are weak on cosmological scales, permitting new physics to operate. In this Letter, we point out that a massive-gravity-inspired coupling of Galileons to stress energy can enhance gravitational lensing. Because the enhancement appears at a fixed scaled location for dark matter halos of a wide range of masses, stacked cluster analysis of weak lensing data should be able to detect or constrain this effect.

Open-Shell-Character-Based Molecular Design Principles: Applications to Nonlinear Optics and Singlet Fission.

PubMed

Nakano, Masayoshi

2017-01-01

Open-shell character, e. g., diradical character, is a quantum chemically well-defined quantity in ground-state molecular systems, which is not an observable but can quantify the degree of effective bond weakness in the chemical sense or electron correlation strength in the physical sense. Because this quantity also correlates to specific excited states, physicochemical properties concerned with those states are expected to strongly correlate to the open-shell character. This feature enables us to open a new path to revealing the mechanism of these properties as well as to realizing new design principles for efficient functional molecular systems. This account explains the open-shell-character-based molecular design principles and introduces their applications to the rational design of highly efficient nonlinear optical and singlet fission molecular systems. © 2017 The Chemical Society of Japan & Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim.

A Lagrangian meshfree method applied to linear and nonlinear elasticity.

PubMed

Walker, Wade A

2017-01-01

The repeated replacement method (RRM) is a Lagrangian meshfree method which we have previously applied to the Euler equations for compressible fluid flow. In this paper we present new enhancements to RRM, and we apply the enhanced method to both linear and nonlinear elasticity. We compare the results of ten test problems to those of analytic solvers, to demonstrate that RRM can successfully simulate these elastic systems without many of the requirements of traditional numerical methods such as numerical derivatives, equation system solvers, or Riemann solvers. We also show the relationship between error and computational effort for RRM on these systems, and compare RRM to other methods to highlight its strengths and weaknesses. And to further explain the two elastic equations used in the paper, we demonstrate the mathematical procedure used to create Riemann and Sedov-Taylor solvers for them, and detail the numerical techniques needed to embody those solvers in code.

A Lagrangian meshfree method applied to linear and nonlinear elasticity

PubMed Central

2017-01-01

The repeated replacement method (RRM) is a Lagrangian meshfree method which we have previously applied to the Euler equations for compressible fluid flow. In this paper we present new enhancements to RRM, and we apply the enhanced method to both linear and nonlinear elasticity. We compare the results of ten test problems to those of analytic solvers, to demonstrate that RRM can successfully simulate these elastic systems without many of the requirements of traditional numerical methods such as numerical derivatives, equation system solvers, or Riemann solvers. We also show the relationship between error and computational effort for RRM on these systems, and compare RRM to other methods to highlight its strengths and weaknesses. And to further explain the two elastic equations used in the paper, we demonstrate the mathematical procedure used to create Riemann and Sedov-Taylor solvers for them, and detail the numerical techniques needed to embody those solvers in code. PMID:29045443

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.

Synthetic magnetism for photon fluids

NASA Astrophysics Data System (ADS)

Westerberg, N.; Maitland, C.; Faccio, D.; Wilson, K.; Öhberg, P.; Wright, E. M.

2016-08-01

We develop a theory of artificial gauge fields in photon fluids for the cases of both second-order and third-order optical nonlinearities. This applies to weak excitations in the presence of pump fields carrying orbital angular momentum and is thus a type of Bogoliubov theory. The resulting artificial gauge fields experienced by the weak excitations are an interesting generalization of previous cases and reflect the PT-symmetry properties of the underlying non-Hermitian Hamiltonian. We illustrate the observable consequences of the resulting synthetic magnetic fields for examples involving both second-order and third-order nonlinearities.

Thermodynamics of random reaction networks.

PubMed

Fischer, Jakob; Kleidon, Axel; Dittrich, Peter

2015-01-01

Reaction networks are useful for analyzing reaction systems occurring in chemistry, systems biology, or Earth system science. Despite the importance of thermodynamic disequilibrium for many of those systems, the general thermodynamic properties of reaction networks are poorly understood. To circumvent the problem of sparse thermodynamic data, we generate artificial reaction networks and investigate their non-equilibrium steady state for various boundary fluxes. We generate linear and nonlinear networks using four different complex network models (Erdős-Rényi, Barabási-Albert, Watts-Strogatz, Pan-Sinha) and compare their topological properties with real reaction networks. For similar boundary conditions the steady state flow through the linear networks is about one order of magnitude higher than the flow through comparable nonlinear networks. In all networks, the flow decreases with the distance between the inflow and outflow boundary species, with Watts-Strogatz networks showing a significantly smaller slope compared to the three other network types. The distribution of entropy production of the individual reactions inside the network follows a power law in the intermediate region with an exponent of circa -1.5 for linear and -1.66 for nonlinear networks. An elevated entropy production rate is found in reactions associated with weakly connected species. This effect is stronger in nonlinear networks than in the linear ones. Increasing the flow through the nonlinear networks also increases the number of cycles and leads to a narrower distribution of chemical potentials. We conclude that the relation between distribution of dissipation, network topology and strength of disequilibrium is nontrivial and can be studied systematically by artificial reaction networks.

Thermodynamics of Random Reaction Networks

PubMed Central

Fischer, Jakob; Kleidon, Axel; Dittrich, Peter

2015-01-01

Reaction networks are useful for analyzing reaction systems occurring in chemistry, systems biology, or Earth system science. Despite the importance of thermodynamic disequilibrium for many of those systems, the general thermodynamic properties of reaction networks are poorly understood. To circumvent the problem of sparse thermodynamic data, we generate artificial reaction networks and investigate their non-equilibrium steady state for various boundary fluxes. We generate linear and nonlinear networks using four different complex network models (Erdős-Rényi, Barabási-Albert, Watts-Strogatz, Pan-Sinha) and compare their topological properties with real reaction networks. For similar boundary conditions the steady state flow through the linear networks is about one order of magnitude higher than the flow through comparable nonlinear networks. In all networks, the flow decreases with the distance between the inflow and outflow boundary species, with Watts-Strogatz networks showing a significantly smaller slope compared to the three other network types. The distribution of entropy production of the individual reactions inside the network follows a power law in the intermediate region with an exponent of circa −1.5 for linear and −1.66 for nonlinear networks. An elevated entropy production rate is found in reactions associated with weakly connected species. This effect is stronger in nonlinear networks than in the linear ones. Increasing the flow through the nonlinear networks also increases the number of cycles and leads to a narrower distribution of chemical potentials. We conclude that the relation between distribution of dissipation, network topology and strength of disequilibrium is nontrivial and can be studied systematically by artificial reaction networks. PMID:25723751

Semiconductor quantum well irradiated by a two-mode electromagnetic field as a terahertz emitter

NASA Astrophysics Data System (ADS)

Mandal, S.; Liew, T. C. H.; Kibis, O. V.

2018-04-01

We study theoretically the nonlinear optical properties of a semiconductor quantum well (QW) irradiated by a two-mode electromagnetic wave consisting of a strong resonant dressing field and a weak off-resonant driving field. In the considered strongly coupled electron-field system, the dressing field opens dynamic Stark gaps in the electron energy spectrum of the QW, whereas the driving field induces electron oscillations in the QW plane. Since the gapped electron spectrum restricts the amplitude of the oscillations, the emission of a frequency comb from the QW appears. Therefore, the doubly driven QW operates as a nonlinear optical element which can be used, particularly, for optically controlled generation of terahertz radiation.

Nonlinear mode interaction in equal-leg angle struts susceptible to cellular buckling.

PubMed

Bai, L; Wang, F; Wadee, M A; Yang, J

2017-11-01

A variational model that describes the interactive buckling of a thin-walled equal-leg angle strut under pure axial compression is presented. A formulation combining the Rayleigh-Ritz method and continuous displacement functions is used to derive a system of differential and integral equilibrium equations for the structural component. Solving the equations using numerical continuation reveals progressive cellular buckling (or snaking) arising from the nonlinear interaction between the weak-axis flexural buckling mode and the strong-axis flexural-torsional buckling mode for the first time-the resulting behaviour being highly unstable. Physical experiments conducted on 10 cold-formed steel specimens are presented and the results show good agreement with the variational model.

Nonlinear dynamics of mini-satellite respinup by weak internal controllable torques

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

Somov, Yevgeny, E-mail: e-somov@mail.ru

Contemporary space engineering advanced new problem before theoretical mechanics and motion control theory: a spacecraft directed respinup by the weak restricted control internal forces. The paper presents some results on this problem, which is very actual for energy supply of information mini-satellites (for communication, geodesy, radio- and opto-electronic observation of the Earth et al.) with electro-reaction plasma thrusters and gyro moment cluster based on the reaction wheels or the control moment gyros. The solution achieved is based on the methods for synthesis of nonlinear robust control and on rigorous analytical proof for the required spacecraft rotation stability by Lyapunov functionmore » method. These results were verified by a computer simulation of strongly nonlinear oscillatory processes at respinuping of a flexible spacecraft.« less

Magnetically charged regular black hole in a model of nonlinear electrodynamics

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

Ma, Meng-Sen, E-mail: mengsenma@gmail.com

2015-11-15

We obtain a magnetically charged regular black hole in general relativity. The source to the Einstein field equations is nonlinear electrodynamic field in a physically reasonable model of nonlinear electrodynamics (NED). “Physically” here means the NED model is constructed on the basis of three conditions: the Maxwell asymptotic in the weak electromagnetic field limit; the presence of vacuum birefringence phenomenon; and satisfying the weak energy condition (WEC). In addition, we analyze the thermodynamic properties of the regular black hole in two ways. According to the usual black hole thermodynamics, we calculate the heat capacity at constant charge, from which wemore » know the smaller black hole is more stable. We also employ the horizon thermodynamics to discuss the thermodynamic quantities, especially the heat capacity at constant pressure.« less

Switchable thulium-doped fiber laser from polarization rotation vector to scalar soliton

NASA Astrophysics Data System (ADS)

Wu, Zhichao; Fu, Songnian; Jiang, Kai; Song, Jue; Li, Huizi; Tang, Ming; Shum, Ping; Liu, Deming

2016-10-01

We experimentally demonstrate switchable temporal soliton generation from a thulium-doped fiber laser (TDFL), using carbon nanotubes as the mode-locker. With the help of residual polarization dependent loss of a wavelength division multiplexer, a weak nonlinear polarization rotation (NPR) effect can be achieved within the laser cavity, which may provide joint contribution for passive mode-locking operation. By finely adjusting the polarization to alter the strength of NPR-based saturable absorption, the TDFL either approaches the operation regime of scalar soliton with strong NPR effect, or generates polarization rotation locked vector soliton (PRLVS) with weak NPR effect. The scalar solitons and PRLVSs possess 3-dB optical spectrum bandwidth of 2.2 nm and 2 nm, pulse-width of 1.8 ps and 2 ps, respectively. Moreover, the PRLVSs demonstrate a typical energy exchange between two polarized components on optical spectra and a period-doubling feature in time domain. Such operation principle can also be used in 1550 nm band fiber lasers and other nonlinear systems.

Switchable thulium-doped fiber laser from polarization rotation vector to scalar soliton

PubMed Central

Wu, Zhichao; Fu, Songnian; Jiang, Kai; Song, Jue; Li, Huizi; Tang, Ming; Shum, Ping; Liu, Deming

2016-01-01

We experimentally demonstrate switchable temporal soliton generation from a thulium-doped fiber laser (TDFL), using carbon nanotubes as the mode-locker. With the help of residual polarization dependent loss of a wavelength division multiplexer, a weak nonlinear polarization rotation (NPR) effect can be achieved within the laser cavity, which may provide joint contribution for passive mode-locking operation. By finely adjusting the polarization to alter the strength of NPR-based saturable absorption, the TDFL either approaches the operation regime of scalar soliton with strong NPR effect, or generates polarization rotation locked vector soliton (PRLVS) with weak NPR effect. The scalar solitons and PRLVSs possess 3-dB optical spectrum bandwidth of 2.2 nm and 2 nm, pulse-width of 1.8 ps and 2 ps, respectively. Moreover, the PRLVSs demonstrate a typical energy exchange between two polarized components on optical spectra and a period-doubling feature in time domain. Such operation principle can also be used in 1550 nm band fiber lasers and other nonlinear systems. PMID:27708427

Switchable thulium-doped fiber laser from polarization rotation vector to scalar soliton.

PubMed

Wu, Zhichao; Fu, Songnian; Jiang, Kai; Song, Jue; Li, Huizi; Tang, Ming; Shum, Ping; Liu, Deming

2016-10-06

We experimentally demonstrate switchable temporal soliton generation from a thulium-doped fiber laser (TDFL), using carbon nanotubes as the mode-locker. With the help of residual polarization dependent loss of a wavelength division multiplexer, a weak nonlinear polarization rotation (NPR) effect can be achieved within the laser cavity, which may provide joint contribution for passive mode-locking operation. By finely adjusting the polarization to alter the strength of NPR-based saturable absorption, the TDFL either approaches the operation regime of scalar soliton with strong NPR effect, or generates polarization rotation locked vector soliton (PRLVS) with weak NPR effect. The scalar solitons and PRLVSs possess 3-dB optical spectrum bandwidth of 2.2 nm and 2 nm, pulse-width of 1.8 ps and 2 ps, respectively. Moreover, the PRLVSs demonstrate a typical energy exchange between two polarized components on optical spectra and a period-doubling feature in time domain. Such operation principle can also be used in 1550 nm band fiber lasers and other nonlinear systems.

Self-similar regimes of turbulence in weakly coupled plasmas under compression

NASA Astrophysics Data System (ADS)

Viciconte, Giovanni; Gréa, Benoît-Joseph; Godeferd, Fabien S.

2018-02-01

Turbulence in weakly coupled plasmas under compression can experience a sudden dissipation of kinetic energy due to the abrupt growth of the viscosity coefficient governed by the temperature increase. We investigate in detail this phenomenon by considering a turbulent velocity field obeying the incompressible Navier-Stokes equations with a source term resulting from the mean velocity. The system can be simplified by a nonlinear change of variable, and then solved using both highly resolved direct numerical simulations and a spectral model based on the eddy-damped quasinormal Markovian closure. The model allows us to explore a wide range of initial Reynolds and compression numbers, beyond the reach of simulations, and thus permits us to evidence the presence of a nonlinear cascade phase. We find self-similarity of intermediate regimes as well as of the final decay of turbulence, and we demonstrate the importance of initial distribution of energy at large scales. This effect can explain the global sensitivity of the flow dynamics to initial conditions, which we also illustrate with simulations of compressed homogeneous isotropic turbulence and of imploding spherical turbulent layers relevant to inertial confinement fusion.

Quantum control and measurement of atomic spins in polarization spectroscopy

NASA Astrophysics Data System (ADS)

Deutsch, Ivan H.; Jessen, Poul S.

2010-03-01

Quantum control and measurement are two sides of the same coin. To affect a dynamical map, well-designed time-dependent control fields must be applied to the system of interest. To read out the quantum state, information about the system must be transferred to a probe field. We study a particular example of this dual action in the context of quantum control and measurement of atomic spins through the light-shift interaction with an off-resonant optical probe. By introducing an irreducible tensor decomposition, we identify the coupling of the Stokes vector of the light field with moments of the atomic spin state. This shows how polarization spectroscopy can be used for continuous weak measurement of atomic observables that evolve as a function of time. Simultaneously, the state-dependent light shift induced by the probe field can drive nonlinear dynamics of the spin, and can be used to generate arbitrary unitary transformations on the atoms. We revisit the derivation of the master equation in order to give a unified description of spin dynamics in the presence of both nonlinear dynamics and photon scattering. Based on this formalism, we review applications to quantum control, including the design of state-to-state mappings, and quantum-state reconstruction via continuous weak measurement on a dynamically controlled ensemble.

Natural approach to quantum dissipation

NASA Astrophysics Data System (ADS)

Taj, David; Öttinger, Hans Christian

2015-12-01

The dissipative dynamics of a quantum system weakly coupled to one or several reservoirs is usually described in terms of a Lindblad generator. The popularity of this approach is certainly due to the linear character of the latter. However, while such linearity finds justification from an underlying Hamiltonian evolution in some scaling limit, it does not rely on solid physical motivations at small but finite values of the coupling constants, where the generator is typically used for applications. The Markovian quantum master equations we propose are instead supported by very natural thermodynamic arguments. They themselves arise from Markovian master equations for the system and the environment which preserve factorized states and mean energy and generate entropy at a non-negative rate. The dissipative structure is driven by an entropic map, called modular, which introduces nonlinearity. The generated modular dynamical semigroup (MDS) guarantees for the positivity of the time evolved state the correct steady state properties, the positivity of the entropy production, and a positive Onsager matrix with symmetry relations arising from Green-Kubo formulas. We show that the celebrated Davies Lindblad generator, obtained through the Born and the secular approximations, generates a MDS. In doing so we also provide a nonlinear MDS which is supported by a weak coupling argument and is free from the limitations of the Davies generator.

Recovery of Spectrally Overlapping QPSK Signals Using a Nonlinear Optoelectronic Filter

DTIC Science & Technology

2017-03-19

Spectrally Overlapping QPSK Signals Using a Nonlinear Optoelectronic Filter William Loh, Siva Yegnanarayanan, Kenneth E. Kolodziej, and Paul...recovery of a weak QPSK signal buried 35-dB beneath an interfering QPSK signal having an overlapping spectrum. This nonlinear optoelectronic filter ...from increased detection sensitivity. Here, we demonstrate an optoelectronic filter that enables the detection of a desired signal hidden beneath a

Nonlocal interferometry with macroscopic coherent states and its application to quantum communications

NASA Astrophysics Data System (ADS)

Kirby, Brian

Macroscopic quantum effects are of fundamental interest because they help us to understand the quantum-classical boundary, and may also have important practical applications in long-range quantum communications. Specifically we analyze a macroscopic generalization of the Franson interferometer, where violations of Bell's inequality can be observed using phase entangled coherent states created using weak nonlinearities. Furthermore we want to understand how these states, and other macroscopic quantum states, can be applied to secure quantum communications. We find that Bell's inequality can be violated at ranges of roughly 400 km in optical fiber when various unambiguous state discrimination techniques are applied. In addition Monte Carlo simulations suggest that quantum communications schemes based on macroscopic quantum states and random unitary transformations can be potentially secure at long distances. Lastly, we calculate the feasibility of creating the weak nonlinearity needed for the experimental realization of these proposals using metastable xenon in a high finesse cavity. This research suggests that quantum states created using macroscopic coherent states and weak nonlinearities may be a realistic path towards the realization of secure long-range quantum communications.

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

On degenerate coupled transport processes in porous media with memory phenomena

NASA Astrophysics Data System (ADS)

Beneš, Michal; Pažanin, Igor

2018-06-01

In this paper we prove the existence of weak solutions to degenerate parabolic systems arising from the fully coupled moisture movement, solute transport of dissolved species and heat transfer through porous materials. Physically relevant mixed Dirichlet-Neumann boundary conditions and initial conditions are considered. Existence of a global weak solution of the problem is proved by means of semidiscretization in time, proving necessary uniform estimates and by passing to the limit from discrete approximations. Degeneration occurs in the nonlinear transport coefficients which are not assumed to be bounded below and above by positive constants. Degeneracies in transport coefficients are overcome by proving suitable a-priori $L^{\\infty}$-estimates based on De Giorgi and Moser iteration technique.

Simulation of Nonlinear Instabilities in an Attachment-Line Boundary Layer

NASA Technical Reports Server (NTRS)

Joslin, Ronald D.

1996-01-01

The linear and the nonlinear stability of disturbances that propagate along the attachment line of a three-dimensional boundary layer is considered. The spatially evolving disturbances in the boundary layer are computed by direct numerical simulation (DNS) of the unsteady, incompressible Navier-Stokes equations. Disturbances are introduced either by forcing at the in ow or by applying suction and blowing at the wall. Quasi-parallel linear stability theory and a nonparallel theory yield notably different stability characteristics for disturbances near the critical Reynolds number; the DNS results con rm the latter theory. Previously, a weakly nonlinear theory and computations revealed a high wave-number region of subcritical disturbance growth. More recent computations have failed to achieve this subcritical growth. The present computational results indicate the presence of subcritically growing disturbances; the results support the weakly nonlinear theory. Furthermore, an explanation is provided for the previous theoretical and computational discrepancy. In addition, the present results demonstrate that steady suction can be used to stabilize disturbances that otherwise grow subcritically along the attachment line.

Shock wave structure in a strongly nonlinear lattice with viscous dissipation.

PubMed

Herbold, E B; Nesterenko, V F

2007-02-01

The shock wave structure in a one-dimensional lattice (e.g., granular chain of elastic particles) with a power law dependence of force on displacement between particles (F proportional to delta(n)) with viscous dissipation is considered and compared to the corresponding long wave approximation. A dissipative term depending on the relative velocity between neighboring particles is included to investigate its influence on the shape of a steady shock. The critical viscosity coefficient p(c), defining the transition from an oscillatory to a monotonic shock profile in strongly nonlinear systems, is obtained from the long-wave approximation for arbitrary values of the exponent n. The expression for the critical viscosity is comparable to the value obtained in the numerical analysis of a discrete system with a Hertzian contact interaction (n=3/2) . The expression for p(c) in the weakly nonlinear case converges to the known equation for the critical viscosity. An initial disturbance in a discrete system approaches a stationary shock profile after traveling a short distance that is comparable to the width of the leading pulse of a stationary shock front. The shock front width is minimized when the viscosity is equal to its critical value.

Driven superconducting quantum circuits

NASA Astrophysics Data System (ADS)

Nakamura, Yasunobu

2014-03-01

Driven nonlinear quantum systems show rich phenomena in various fields of physics. Among them, superconducting quantum circuits have very attractive features such as well-controlled quantum states with design flexibility, strong nonlinearity of Josephson junctions, strong coupling to electromagnetic driving fields, little internal dissipation, and tailored coupling to the electromagnetic environment. We have investigated properties and functionalities of driven superconducting quantum circuits. A transmon qubit coupled to a transmission line shows nearly perfect spatial mode matching between the incident and scattered microwave field in the 1D mode. Dressed states under a driving field are studied there and also in a semi-infinite 1D mode terminated by a resonator containing a flux qubit. An effective Λ-type three-level system is realized under an appropriate driving condition. It allows ``impedance-matched'' perfect absorption of incident probe photons and down conversion into another frequency mode. Finally, the weak signal from the qubit is read out using a Josephson parametric amplifier/oscillator which is another nonlinear circuit driven by a strong pump field. This work was partly supported by the Funding Program for World-Leading Innovative R&D on Science and Technology (FIRST), Project for Developing Innovation Systems of MEXT, MEXT KAKENHI ``Quantum Cybernetics,'' and the NICT Commissioned Research.

Wave propagation in a strongly nonlinear locally resonant granular crystal

NASA Astrophysics Data System (ADS)

Vorotnikov, K.; Starosvetsky, Y.; Theocharis, G.; Kevrekidis, P. G.

2018-02-01

In this work, we study the wave propagation in a recently proposed acoustic structure, the locally resonant granular crystal. This structure is composed of a one-dimensional granular crystal of hollow spherical particles in contact, containing linear resonators. The relevant model is presented and examined through a combination of analytical approximations (based on ODE and nonlinear map analysis) and of numerical results. The generic dynamics of the system involves a degradation of the well-known traveling pulse of the standard Hertzian chain of elastic beads. Nevertheless, the present system is richer, in that as the primary pulse decays, secondary ones emerge and eventually interfere with it creating modulated wavetrains. Remarkably, upon suitable choices of parameters, this interference "distills" a weakly nonlocal solitary wave (a "nanopteron"). This motivates the consideration of such nonlinear structures through a separate Fourier space technique, whose results suggest the existence of such entities not only with a single-side tail, but also with periodic tails on both ends. These tails are found to oscillate with the intrinsic oscillation frequency of the out-of-phase motion between the outer hollow bead and its internal linear attachment.

Multifractality Signatures in Quasars Time Series. I. 3C 273

NASA Astrophysics Data System (ADS)

Belete, A. Bewketu; Bravo, J. P.; Canto Martins, B. L.; Leão, I. C.; De Araujo, J. M.; De Medeiros, J. R.

2018-05-01

The presence of multifractality in a time series shows different correlations for different time scales as well as intermittent behaviour that cannot be captured by a single scaling exponent. The identification of a multifractal nature allows for a characterization of the dynamics and of the intermittency of the fluctuations in non-linear and complex systems. In this study, we search for a possible multifractal structure (multifractality signature) of the flux variability in the quasar 3C 273 time series for all electromagnetic wavebands at different observation points, and the origins for the observed multifractality. This study is intended to highlight how the scaling behaves across the different bands of the selected candidate which can be used as an additional new technique to group quasars based on the fractal signature observed in their time series and determine whether quasars are non-linear physical systems or not. The Multifractal Detrended Moving Average algorithm (MFDMA) has been used to study the scaling in non-linear, complex and dynamic systems. To achieve this goal, we applied the backward (θ = 0) MFDMA method for one-dimensional signals. We observe weak multifractal (close to monofractal) behaviour in some of the time series of our candidate except in the mm, UV and X-ray bands. The non-linear temporal correlation is the main source of the observed multifractality in the time series whereas the heaviness of the distribution contributes less.

Symmetries of the TDNLS equations for weakly nonlinear dispersive MHD waves

NASA Technical Reports Server (NTRS)

Webb, G. M.; Brio, M.; Zank, G. P.

1995-01-01

In this paper we consider the symmetries and conservation laws for the TDNLS equations derived by Hada (1993) and Brio, Hunter and Johnson, to describe the propagation of weakly nonlinear dispersive MHD waves in beta approximately 1 plasmas. The equations describe the interaction of the Alfven and magnetoacoustic modes near the triple umbilic, where the fast magnetosonic, slow magnetosonic and Alfven speeds coincide and a(g)(exp 2) = V(A)(exp 2) where a(g) is the gas sound speed and V(A) is the Alfven speed. We discuss Lagrangian and Hamiltonian formulations, and similarity solutions for the equations.

Photoelectron transport tuning of self-assembled subbands

NASA Astrophysics Data System (ADS)

Xiong, Zhengwei; Wang, Xinmin; Wu, Weidong; Wang, Xuemin; Peng, Liping; Zhao, Yan; Yan, Dawei; Jiang, Tao; Shen, Changle; Zhan, Zhiqiang; Cao, Linhong; Li, Weihua

2016-02-01

Conventionally, electrical transport of quantum subbands occurs at very high electric fields, indicating that the medium is easy to break down. In the experiments and practical applications, the extreme condition is difficult to satisfy. For quantum information transmission, low power consumption and convenient implementation are what we expect. In this paper, we engineered a special quantum dot array (QDA) embedded in a single crystal matrix. By external optical field excitation, we found a series of subbands made of the self-assembled QDA discretely located in the matrix. Changing the spacing between the quantum dots leads to the variation of subband spacing. Artificially manipulating the microcosmic QDA system can bring interesting macroscopic effects, such as an enhanced absorption intensity in the ultraviolet range, a blue-shift of the surface plasmon resonance peak and nonlinear absorption changed from two-photon absorption to saturated absorption. The intrinsic mechanism of the subband optical response was revealed due to the strong quantum confinement effect and dominant intraband transitions. The weak surface plasmon resonance absorption of Ni QDA gave an excellent figure of merit of the order of 10-10. The composite films are expectation enough to become a prime candidate for nonlinear applications near 532 nm. Therefore with interplay of the weak optical field and subbands, we achieved a tunable photoelectron transport process.Conventionally, electrical transport of quantum subbands occurs at very high electric fields, indicating that the medium is easy to break down. In the experiments and practical applications, the extreme condition is difficult to satisfy. For quantum information transmission, low power consumption and convenient implementation are what we expect. In this paper, we engineered a special quantum dot array (QDA) embedded in a single crystal matrix. By external optical field excitation, we found a series of subbands made of the self-assembled QDA discretely located in the matrix. Changing the spacing between the quantum dots leads to the variation of subband spacing. Artificially manipulating the microcosmic QDA system can bring interesting macroscopic effects, such as an enhanced absorption intensity in the ultraviolet range, a blue-shift of the surface plasmon resonance peak and nonlinear absorption changed from two-photon absorption to saturated absorption. The intrinsic mechanism of the subband optical response was revealed due to the strong quantum confinement effect and dominant intraband transitions. The weak surface plasmon resonance absorption of Ni QDA gave an excellent figure of merit of the order of 10-10. The composite films are expectation enough to become a prime candidate for nonlinear applications near 532 nm. Therefore with interplay of the weak optical field and subbands, we achieved a tunable photoelectron transport process. Electronic supplementary information (ESI) available: Tables 1 and 2. See DOI: 10.1039/c5nr07861j

Finite element method for optimal guidance of an advanced launch vehicle

NASA Technical Reports Server (NTRS)

Hodges, Dewey H.; Bless, Robert R.; Calise, Anthony J.; Leung, Martin

1992-01-01

A temporal finite element based on a mixed form of Hamilton's weak principle is summarized for optimal control problems. The resulting weak Hamiltonian finite element method is extended to allow for discontinuities in the states and/or discontinuities in the system equations. An extension of the formulation to allow for control inequality constraints is also presented. The formulation does not require element quadrature, and it produces a sparse system of nonlinear algebraic equations. To evaluate its feasibility for real-time guidance applications, this approach is applied to the trajectory optimization of a four-state, two-stage model with inequality constraints for an advanced launch vehicle. Numerical results for this model are presented and compared to results from a multiple-shooting code. The results show the accuracy and computational efficiency of the finite element method.

Weak gravitational lensing effects on the determination of Omega_mega_m and Omega_mega Lambda from SNeIa

NASA Astrophysics Data System (ADS)

Valageas, P.

2000-02-01

In this article we present an analytical calculation of the probability distribution of the magnification of distant sources due to weak gravitational lensing from non-linear scales. We use a realistic description of the non-linear density field, which has already been compared with numerical simulations of structure formation within hierarchical scenarios. Then, we can directly express the probability distribution P(mu ) of the magnification in terms of the probability distribution of the density contrast realized on non-linear scales (typical of galaxies) where the local slope of the initial linear power-spectrum is n=-2. We recover the behaviour seen by numerical simulations: P(mu ) peaks at a value slightly smaller than the mean < mu >=1 and it shows an extended large mu tail (as described in another article our predictions also show a good quantitative agreement with results from N-body simulations for a finite smoothing angle). Then, we study the effects of weak lensing on the derivation of the cosmological parameters from SNeIa. We show that the inaccuracy introduced by weak lensing is not negligible: {cal D}lta Omega_mega_m >~ 0.3 for two observations at z_s=0.5 and z_s=1. However, observations can unambiguously discriminate between Omega_mega_m =0.3 and Omega_mega_m =1. Moreover, in the case of a low-density universe one can clearly distinguish an open model from a flat cosmology (besides, the error decreases as the number of observ ed SNeIa increases). Since distant sources are more likely to be ``demagnified'' the most probable value of the observed density parameter Omega_mega_m is slightly smaller than its actual value. On the other hand, one may obtain some valuable information on the properties of the underlying non-linear density field from the measure of weak lensing distortions.

Harmonic Phase Response of Nonlinear Radar Targets

DTIC Science & Technology

2015-10-01

while allowing its harmonics to pass through. The weak harmonic responses are then amplified to allow for easier detection and measurement . 4...where the phase of the 2nd and 3rd harmonic of the received electromagnetic wave from nonlinear targets was measured and plotted against the frequency

The Kadomtsev-Petviashvili equation under rapid forcing

NASA Astrophysics Data System (ADS)

Moroz, Irene M.

1997-06-01

We consider the initial value problem for the forced Kadomtsev-Petviashvili equation (KP) when the forcing is assumed to be fast compared to the evolution of the unforced equation. This suggests the introduction of two time scales. Solutions to the forced KP are sought by expanding the dependent variable in powers of a small parameter, which is inversely related to the forcing time scale. The unforced system describes weakly nonlinear, weakly dispersive, weakly two-dimensional wave propagation and is studied in two forms, depending upon whether gravity dominates surface tension or vice versa. We focus on the effect that the forcing has on the one-lump solution to the KPI equation (where surface tension dominates) and on the one- and two-line soliton solutions to the KPII equation (when gravity dominates). Solutions to second order in the expansion are computed analytically for some specific choices of the forcing function, which are related to the choice of initial data.

Integrated analysis of energy transfers in elastic-wave turbulence.

PubMed

Yokoyama, Naoto; Takaoka, Masanori

2017-08-01

In elastic-wave turbulence, strong turbulence appears in small wave numbers while weak turbulence does in large wave numbers. Energy transfers in the coexistence of these turbulent states are numerically investigated in both the Fourier space and the real space. An analytical expression of a detailed energy balance reveals from which mode to which mode energy is transferred in the triad interaction. Stretching energy excited by external force is transferred nonlocally and intermittently to large wave numbers as the kinetic energy in the strong turbulence. In the weak turbulence, the resonant interactions according to the weak turbulence theory produce cascading net energy transfer to large wave numbers. Because the system's nonlinearity shows strong temporal intermittency, the energy transfers are investigated at active and moderate phases separately. The nonlocal interactions in the Fourier space are characterized by the intermittent bundles of fibrous structures in the real space.

Weakly Nonlinear Description of Parametric Instabilities in Vibrating Flows

NASA Technical Reports Server (NTRS)

Knobloch, E.; Vega, J. M.

1999-01-01

This project focuses on the effects of weak dissipation on vibrational flows in microgravity and in particular on (a) the generation of mean flows through viscous effects and their reaction on the flows themselves, and (b) the effects of finite group velocity and dispersion on the resulting dynamics in large domains. The basic mechanism responsible for the generation of such flows is nonlinear and was identified by Schlichting [21] and Longuet-Higgins. However, only recently has it become possible to describe such flows self-consistently in terms of amplitude equations for the parametrically excited waves coupled to a mean flow equation. The derivation of these equations is nontrivial because the limit of zero viscosity is singular. This project focuses on various aspects of this singular problem (i.e., the limit C equivalent to (nu)((g)(h(exp 3)))exp -1/2 << 1,where nu is the kinematic viscosity and h is the liquid depth) in the weakly nonlinear regime. A number of distinct cases is identified depending on the values of the Bond number, the size of the nonlinear terms, distance above threshold and the length scales of interest. The theory provides a quantitative explanation of a number of experiments on the vibration modes of liquid bridges and related experiments on parametric excitation of capillary waves in containers of both small and large aspect ratio. The following is a summary of results obtained thus far.

Investigation of focused and unfocused transducer beam patterns in moderately nonlinear absorbing media

NASA Astrophysics Data System (ADS)

Kharin, Nikolay A.

2001-05-01

The novel solution of the KZK equation for acoustic pressure of the second harmonic in slightly focused beam of a circular transducer was obtained in a closed form for moderately nonlinear absorbing media (Gol'dberg numbers ~ 1). The solution is based on the method of slowly changing wave profile in combination with the method of successive approximations. Two pairs of transducers (Valpey-Fisher Corp.) Were compared to investigate the influence of focusing on the applicability of the moderate nonlinearity approach. The first pair was of 0.25' diameter and the second was of 0.5' diameter. Both pairs has one transducer with flat surface and the other geometrically focused at 4'. The central frequency for all transducers was 5 MHz. Measurements were undertaken in the blood-mimicking solution of water and glycerine. The results demonstrated that for slightly focused transducers with circular apertures, the moderate nonlinearity approach is still valid, as it was proved for flat sources with the same source level, despite the higher pressures in the focal region. The peak pressure for the weakly focused system occurs at a shorter range than focal length.

Nonlinear cross-field coupling on the route to broadband turbulence

NASA Astrophysics Data System (ADS)

Brandt, Christian; Thakur, Saikat C.; Cui, Lang; Gosselin, Jordan J.; Negrete, Jose, Jr.; Holland, Chris; Tynan, George R.

2013-10-01

In the linear magnetized plasma device CSDX (Controlled Shear De-correlation eXperiment) drift interchange modes are studied coexisting on top of a weak turbulence driven azimuthally symmetric, radially sheared plasma flow. In helicon discharges (helicon antenna diameter 15 cm) with increasing magnetic field (B <= 0 . 24 T) the system can be driven to fully developed broadband turbulence. Fast imaging using a refractive telescope setup is applied to study the dynamics in the azimuthal-radial cross-section. The image data is supported by Langmuir probe measurements. In the present study we examine the development of nonlinear transfer as the fully developed turbulence emerges. Nonlinear cross-field coupling between eigenmodes at different radial positions is investigated using Fourier decomposition of azimuthal eigenmodes. The coupling strength between waves at different radial positions is inferred to radial profiles and cross-field transport between adjacent magnetic flux surfaces. Nonlinear effects like synchronization, phase slippages, phase pulling and periodic pulling are observed. The effects of mode coupling and the stability of modes is compared to the dynamics of a coupled chain of Kuramoto oscillators.

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

Budker, D.; Nuclear Science Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720; Rochester, S.M.

Recent work on {lambda} resonances in alkali-metal vapors (E. Mikhailov, I. Novikova, Yu. V. Rostovtsev, and G. R. Welch, e-print quant-ph/0309171, and references therein) investigated a type of electromagnetically induced absorption resonance that occurs in three-level systems under specific conditions normally associated with electromagnetically induced transparency. In this note, we show that these resonances have a direct analog in nonlinear magneto-optics, and support this conclusion with a calculation for a J=1{yields}J{sup '}=0 system interacting with a single, nearly circularly polarized light field in the presence of a weak longitudinal magnetic field.

Gravitational Waves from Isolated Systems: Surprising Consequences of a Positive Cosmological Constant.

PubMed

Ashtekar, Abhay; Bonga, Béatrice; Kesavan, Aruna

2016-02-05

There is a deep tension between the well-developed theory of gravitational waves from isolated systems and the presence of a positive cosmological constant Λ, however tiny. In particular a generalization of Einstein's 1918 quadrupole formula that would allow a positive Λ is not yet available. We first explain the principal difficulties and then show that it is possible to overcome them in the weak field limit. These results also provide concrete hints for constructing the Λ>0 generalization of the Bondi-Sachs framework for full, nonlinear general relativity.

Gravitational Waves from Isolated Systems: Surprising Consequences of a Positive Cosmological Constant

NASA Astrophysics Data System (ADS)

Ashtekar, Abhay; Bonga, Béatrice; Kesavan, Aruna

2016-02-01

There is a deep tension between the well-developed theory of gravitational waves from isolated systems and the presence of a positive cosmological constant Λ , however tiny. In particular a generalization of Einstein's 1918 quadrupole formula that would allow a positive Λ is not yet available. We first explain the principal difficulties and then show that it is possible to overcome them in the weak field limit. These results also provide concrete hints for constructing the Λ >0 generalization of the Bondi-Sachs framework for full, nonlinear general relativity.

Power generation in random diode arrays

NASA Astrophysics Data System (ADS)

Shvydka, Diana; Karpov, V. G.

2005-03-01

We discuss nonlinear disordered systems, random diode arrays (RDAs), which can represent such objects as large-area photovoltaics and ion channels of biological membranes. Our numerical modeling has revealed several interesting properties of RDAs. In particular, the geometrical distribution of nonuniformities across a RDA has only a minor effect on its integral characteristics determined by RDA parameter statistics. In the meantime, the dispersion of integral characteristics vs system size exhibits a nontrivial scaling dependence. Our theoretical interpretation here remains limited and is based on the picture of eddy currents flowing through weak diodes in the RDA.

Theoretical and experimental evidence of non-symmetric doubly localized rogue waves.

PubMed

He, Jingsong; Guo, Lijuan; Zhang, Yongshuai; Chabchoub, Amin

2014-11-08

We present determinant expressions for vector rogue wave (RW) solutions of the Manakov system, a two-component coupled nonlinear Schrödinger (NLS) equation. As a special case, we generate a family of exact and non-symmetric RW solutions of the NLS equation up to third order, localized in both space and time. The derived non-symmetric doubly localized second-order solution is generated experimentally in a water wave flume for deep-water conditions. Experimental results, confirming the characteristic non-symmetric pattern of the solution, are in very good agreement with theory as well as with numerical simulations, based on the modified NLS equation, known to model accurately the dynamics of weakly nonlinear wave packets in deep water.

Theoretical and experimental evidence of non-symmetric doubly localized rogue waves

PubMed Central

He, Jingsong; Guo, Lijuan; Zhang, Yongshuai; Chabchoub, Amin

2014-01-01

We present determinant expressions for vector rogue wave (RW) solutions of the Manakov system, a two-component coupled nonlinear Schrödinger (NLS) equation. As a special case, we generate a family of exact and non-symmetric RW solutions of the NLS equation up to third order, localized in both space and time. The derived non-symmetric doubly localized second-order solution is generated experimentally in a water wave flume for deep-water conditions. Experimental results, confirming the characteristic non-symmetric pattern of the solution, are in very good agreement with theory as well as with numerical simulations, based on the modified NLS equation, known to model accurately the dynamics of weakly nonlinear wave packets in deep water. PMID:25383023

A silicon Brillouin laser

NASA Astrophysics Data System (ADS)

Otterstrom, Nils T.; Behunin, Ryan O.; Kittlaus, Eric A.; Wang, Zheng; Rakich, Peter T.

2018-06-01

Brillouin laser oscillators offer powerful and flexible dynamics as the basis for mode-locked lasers, microwave oscillators, and optical gyroscopes in a variety of optical systems. However, Brillouin interactions are markedly weak in conventional silicon photonic waveguides, stifling progress toward silicon-based Brillouin lasers. The recent advent of hybrid photonic-phononic waveguides has revealed Brillouin interactions to be one of the strongest and most tailorable nonlinearities in silicon. In this study, we have harnessed these engineered nonlinearities to demonstrate Brillouin lasing in silicon. Moreover, we show that this silicon-based Brillouin laser enters a regime of dynamics in which optical self-oscillation produces phonon linewidth narrowing. Our results provide a platform to develop a range of applications for monolithic integration within silicon photonic circuits.

Falling films on flexible inclines

NASA Astrophysics Data System (ADS)

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

2007-11-01

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

Enhancing a slow and weak optomechanical nonlinearity with delayed quantum feedback

PubMed Central

Wang, Zhaoyou; Safavi-Naeini, Amir H.

2017-01-01

A central goal of quantum optics is to generate large interactions between single photons so that one photon can strongly modify the state of another one. In cavity optomechanics, photons interact with the motional degrees of freedom of an optical resonator, for example, by imparting radiation pressure forces on a movable mirror or sensing minute fluctuations in the position of the mirror. Here, we show that the optical nonlinearity arising from these effects, typically too small to operate on single photons, can be sufficiently enhanced with feedback to generate large interactions between single photons. We propose a protocol that allows photons propagating in a waveguide to interact with each other through multiple bounces off an optomechanical system. The protocol is analysed by evolving the full many-body quantum state of the waveguide-coupled system, illustrating that large photon–photon interactions mediated by mechanical motion may be within experimental reach. PMID:28677674

Faraday effect in a short pulse propagating in a resonant medium under an ultra-strong magnetic field

NASA Astrophysics Data System (ADS)

Huang, J. G.; Slavcheva, G.; Hess, O.

2008-04-01

We propose a dynamical model for description of the nonlinear Faraday rotation experienced by a short pulse propagating in a resonant medium subject to an ultra-strong static magnetic field. Under the assumptions of a sufficiently strong external magnetic field, such that the Zeeman splitting of the quantum system energy levels is large compared to the linewidth of the optical transitions involved and the bandwidth of the incident light, the light effectively interacts with a two-level system. Our numerical simulations show that the Faraday effect under these conditions is significantly distinctive from the one caused by weak to moderately strong magnetic field. Nonlinear coherent effects such as inhomogeneous polarization rotation along the pulse duration and an onset of a circularly polarized stimulated emission and coherent ringing have been demonstrated. Some views on the experimental observation of the predicted phenomena are given.

Enhancing a slow and weak optomechanical nonlinearity with delayed quantum feedback

NASA Astrophysics Data System (ADS)

Wang, Zhaoyou; Safavi-Naeini, Amir H.

2017-07-01

A central goal of quantum optics is to generate large interactions between single photons so that one photon can strongly modify the state of another one. In cavity optomechanics, photons interact with the motional degrees of freedom of an optical resonator, for example, by imparting radiation pressure forces on a movable mirror or sensing minute fluctuations in the position of the mirror. Here, we show that the optical nonlinearity arising from these effects, typically too small to operate on single photons, can be sufficiently enhanced with feedback to generate large interactions between single photons. We propose a protocol that allows photons propagating in a waveguide to interact with each other through multiple bounces off an optomechanical system. The protocol is analysed by evolving the full many-body quantum state of the waveguide-coupled system, illustrating that large photon-photon interactions mediated by mechanical motion may be within experimental reach.

Hyperextended Cosmological Perturbation Theory: Predicting Nonlinear Clustering Amplitudes

NASA Astrophysics Data System (ADS)

Scoccimarro, Román; Frieman, Joshua A.

1999-07-01

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

Cylindrical effects on Richtmyer-Meshkov instability for arbitrary Atwood numbers in weakly nonlinear regime

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

Liu, W. H.; He, X. T.; LCP, Institute of Applied Physics and Computational Mathematics, Beijing 100088

2012-07-15

When an incident shock collides with a corrugated interface separating two fluids of different densities, the interface is prone to Richtmyer-Meshkov instability (RMI). Based on the formal perturbation expansion method as well as the potential flow theory, we present a simple method to investigate the cylindrical effects in weakly nonlinear RMI with the transmitted and reflected cylindrical shocks by considering the nonlinear corrections up to fourth order. The cylindrical results associated with the material interface show that the interface expression consists of two parts: the result in the planar system and that from the cylindrical effects. In the limit ofmore » the cylindrical radius tending to infinity, the cylindrical results can be reduced to those in the planar system. Our explicit results show that the cylindrical effects exert an inward velocity on the whole perturbed interface, regardless of bubbles or spikes of the interface. On the one hand, outgoing bubbles are constrained and ingoing spikes are accelerated for different Atwood numbers (A) and mode numbers k'. On the other hand, for ingoing bubbles, when |A|k'{sup 3/2} Less-Than-Or-Equivalent-To 1, bubbles are considerably accelerated especially at the small |A| and k'; otherwise, bubbles are decelerated. For outgoing spikes, when |A|k' Greater-Than-Or-Equivalent-To 1, spikes are dramatically accelerated especially at large |A| and k'; otherwise, spikes are decelerated. Furthermore, the cylindrical effects have a significant influence on the amplitudes of the ingoing spike and bubble for large k'. Thus, it should be included in applications where the cylindrical effects play a role, such as inertial confinement fusion ignition target design.« less

Enhancement of temporal contrast of high-power laser pulses in an anisotropic medium with cubic nonlinearity

NASA Astrophysics Data System (ADS)

Kuz'mina, M. S.; Khazanov, E. A.

2015-05-01

We consider the methods for enhancing the temporal contrast of super-high-power laser pulses, based on the conversion of radiation polarisation in a medium with cubic nonlinearity. For a medium with weak birefringence and isotropic nonlinearity, we propose a new scheme to enhance the temporal contrast. For a medium with anisotropic nonlinearity, the efficiency of the temporal contrast optimisation is shown to depend not only on the spatial orientation of the crystal and B-integral, but also on the type of the crystal lattice symmetry.

Optical wave turbulence and the condensation of light

NASA Astrophysics Data System (ADS)

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

2009-11-01

In an optical experiment, we report a wave turbulence regime that, starting with weakly nonlinear waves with randomized phases, shows an inverse cascade of photons towards the lowest wavenumbers. We show that the cascade is induced by a six-wave resonant interaction process and is characterized by increasing nonlinearity. At low wavenumbers the nonlinearity becomes strong and leads to modulational instability developing into solitons, whose number is decreasing further along the beam.

On Critical Behaviour in Systems of Hamiltonian Partial Differential Equations.

PubMed

Dubrovin, Boris; Grava, Tamara; Klein, Christian; Moro, Antonio

2015-01-01

We study the critical behaviour of solutions to weakly dispersive Hamiltonian systems considered as perturbations of elliptic and hyperbolic systems of hydrodynamic type with two components. We argue that near the critical point of gradient catastrophe of the dispersionless system, the solutions to a suitable initial value problem for the perturbed equations are approximately described by particular solutions to the Painlevé-I (P[Formula: see text]) equation or its fourth-order analogue P[Formula: see text]. As concrete examples, we discuss nonlinear Schrödinger equations in the semiclassical limit. A numerical study of these cases provides strong evidence in support of the conjecture.

New type of synchronization of oscillators with hard excitation

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

Kovaleva, M. A., E-mail: margo.kovaleva@gmail.com; Manevich, L. I., E-mail: manevichleonid3@gmail.com; Pilipchuk, V. N.

2013-08-15

It is shown that stable limiting cycles corresponding to nonlinear beats with complete energy exchange between oscillators can exist in a system of two weakly coupled active oscillators (generators). The oscillatory regime of this type, which implements a new type of synchronization in an active system, is an alternative to the well-studied synchronization in a regime close to a nonlinear normal mode. In this case, the ranges of dissipative parameters corresponding to different types of synchronization do not intersect. The analytic description of attractors revealed in analysis is based on the concept of limiting phase trajectories, which was developed earliermore » by one of the authors for conservative systems. A transition (in the parametric space) from the complete energy exchange between oscillators to predominant localization of energy in one of the oscillators can be naturally described using this concept. The localized normal mode is an attractor in the range of parameters in which neither the limiting phase trajectory nor any of the collective normal modes is an attractor.« less

Intrasystem Analysis Program (IAP) code summaries

NASA Astrophysics Data System (ADS)

Dobmeier, J. J.; Drozd, A. L. S.; Surace, J. A.

1983-05-01

This report contains detailed descriptions and capabilities of the codes that comprise the Intrasystem Analysis Program. The four codes are: Intrasystem Electromagnetic Compatibility Analysis Program (IEMCAP), General Electromagnetic Model for the Analysis of Complex Systems (GEMACS), Nonlinear Circuit Analysis Program (NCAP), and Wire Coupling Prediction Models (WIRE). IEMCAP is used for computer-aided evaluation of electromagnetic compatibility (ECM) at all stages of an Air Force system's life cycle, applicable to aircraft, space/missile, and ground-based systems. GEMACS utilizes a Method of Moments (MOM) formalism with the Electric Field Integral Equation (EFIE) for the solution of electromagnetic radiation and scattering problems. The code employs both full matrix decomposition and Banded Matrix Iteration solution techniques and is expressly designed for large problems. NCAP is a circuit analysis code which uses the Volterra approach to solve for the transfer functions and node voltage of weakly nonlinear circuits. The Wire Programs deal with the Application of Multiconductor Transmission Line Theory to the Prediction of Cable Coupling for specific classes of problems.

Kelvin-wave cascade in the vortex filament model

NASA Astrophysics Data System (ADS)

Baggaley, Andrew W.; Laurie, Jason

2014-01-01

The small-scale energy-transfer mechanism in zero-temperature superfluid turbulence of helium-4 is still a widely debated topic. Currently, the main hypothesis is that weakly nonlinear interacting Kelvin waves (KWs) transfer energy to sufficiently small scales such that energy is dissipated as heat via phonon excitations. Theoretically, there are at least two proposed theories for Kelvin-wave interactions. We perform the most comprehensive numerical simulation of weakly nonlinear interacting KWs to date and show, using a specially designed numerical algorithm incorporating the full Biot-Savart equation, that our results are consistent with the nonlocal six-wave KW interactions as proposed by L'vov and Nazarenko.

Detection of weak signals in memory thermal baths.

PubMed

Jiménez-Aquino, J I; Velasco, R M; Romero-Bastida, M

2014-11-01

The nonlinear relaxation time and the statistics of the first passage time distribution in connection with the quasideterministic approach are used to detect weak signals in the decay process of the unstable state of a Brownian particle embedded in memory thermal baths. The study is performed in the overdamped approximation of a generalized Langevin equation characterized by an exponential decay in the friction memory kernel. A detection criterion for each time scale is studied: The first one is referred to as the receiver output, which is given as a function of the nonlinear relaxation time, and the second one is related to the statistics of the first passage time distribution.

Changes in cytoskeletal dynamics and nonlinear rheology with metastatic ability in cancer cell lines

NASA Astrophysics Data System (ADS)

Coughlin, Mark F.; Fredberg, Jeffrey J.

2013-12-01

Metastatic outcome is impacted by the biophysical state of the primary tumor cell. To determine if changes in cancer cell biophysical properties facilitate metastasis, we quantified cytoskeletal biophysics in well-characterized human skin, bladder, prostate and kidney cell line pairs that differ in metastatic ability. Using magnetic twisting cytometry with optical detection, cytoskeletal dynamics was observed through spontaneous motion of surface bound marker beads and nonlinear rheology was characterized through large amplitude forced oscillations of probe beads. Measurements of cytoskeletal dynamics and nonlinear rheology differed between strongly and weakly metastatic cells. However, no set of biophysical parameters changed systematically with metastatic ability across all cell lines. Compared to their weakly metastatic counterparts, the strongly metastatic kidney cancer cells exhibited both increased cytoskeletal dynamics and stiffness at large deformation which are thought to facilitate the process of vascular invasion.

Soliton interactions, Bäcklund transformations, Lax pair for a variable-coefficient generalized dispersive water-wave system

NASA Astrophysics Data System (ADS)

Liu, Lei; Tian, Bo; Zhen, Hui-Ling; Liu, De-Yin; Xie, Xi-Yang

2018-04-01

Under investigation in this paper is a variable-coefficient generalized dispersive water-wave system, which can simulate the propagation of the long weakly non-linear and weakly dispersive surface waves of variable depth in the shallow water. Under certain variable-coefficient constraints, by virtue of the Bell polynomials, Hirota method and symbolic computation, the bilinear forms, one- and two-soliton solutions are obtained. Bäcklund transformations and new Lax pair are also obtained. Our Lax pair is different from that previously reported. Based on the asymptotic and graphic analysis, with different forms of the variable coefficients, we find that there exist the elastic interactions for u, while either the elastic or inelastic interactions for v, with u and v as the horizontal velocity field and deviation height from the equilibrium position of the water, respectively. When the interactions are inelastic, we see the fission and fusion phenomena.

Solitons of the coupled Schrödinger-Korteweg-de Vries system with arbitrary strengths of the nonlinearity and dispersion

NASA Astrophysics Data System (ADS)

Gromov, Evgeny; Malomed, Boris

2017-11-01

New two-component soliton solutions of the coupled high-frequency (HF)—low-frequency (LF) system, based on Schrödinger-Korteweg-de Vries (KdV) system with the Zakharov's coupling, are obtained for arbitrary relative strengths of the nonlinearity and dispersion in the LF component. The complex HF field is governed by the linear Schrödinger equation with a potential generated by the real LF component, which, in turn, is governed by the KdV equation including the ponderomotive coupling term, representing the feedback of the HF field onto the LF component. First, we study the evolution of pulse-shaped pulses by means of direct simulations. In the case when the dispersion of the LF component is weak in comparison to its nonlinearity, the input gives rise to several solitons in which the HF component is much broader than its LF counterpart. In the opposite case, the system creates a single soliton with approximately equal widths of both components. Collisions between stable solitons are studied too, with a conclusion that the collisions are inelastic, with a greater soliton getting still stronger, and the smaller one suffering further attenuation. Robust intrinsic modes are excited in the colliding solitons. A new family of approximate analytical two-component soliton solutions with two free parameters is found for an arbitrary relative strength of the nonlinearity and dispersion of the LF component, assuming weak feedback of the HF field onto the LF component. Further, a one-parameter (non-generic) family of exact bright-soliton solutions, with mutually proportional HF and LF components, is produced too. Intrinsic dynamics of the two-component solitons, induced by a shift of their HF component against the LF one, is also studied, by means of numerical simulations, demonstrating excitation of a robust intrinsic mode. In addition to the above-mentioned results for LF-dominated two-component solitons, which always run in one (positive) velocities, we produce HF-dominated soliton complexes, which travel in the opposite (negative) direction. They are obtained in a numerical form and by means of a quasi-adiabatic analytical approximation. The solutions with positive and negative velocities correspond, respectively, to super- and subsonic Davydov-Scott solitons.

Unidimensional and Multidimensional Models for Item Response Theory.

ERIC Educational Resources Information Center

McDonald, Roderick P.

This paper provides an up-to-date review of the relationship between item response theory (IRT) and (nonlinear) common factor theory and draws out of this relationship some implications for current and future research in IRT. Nonlinear common factor analysis yields a natural embodiment of the weak principle of local independence in appropriate…

A displacement-based finite element formulation for incompressible and nearly-incompressible cardiac mechanics

PubMed Central

Hadjicharalambous, Myrianthi; Lee, Jack; Smith, Nicolas P.; Nordsletten, David A.

2014-01-01

The Lagrange Multiplier (LM) and penalty methods are commonly used to enforce incompressibility and compressibility in models of cardiac mechanics. In this paper we show how both formulations may be equivalently thought of as a weakly penalized system derived from the statically condensed Perturbed Lagrangian formulation, which may be directly discretized maintaining the simplicity of penalty formulations with the convergence characteristics of LM techniques. A modified Shamanskii–Newton–Raphson scheme is introduced to enhance the nonlinear convergence of the weakly penalized system and, exploiting its equivalence, modifications are developed for the penalty form. Focusing on accuracy, we proceed to study the convergence behavior of these approaches using different interpolation schemes for both a simple test problem and more complex models of cardiac mechanics. Our results illustrate the well-known influence of locking phenomena on the penalty approach (particularly for lower order schemes) and its effect on accuracy for whole-cycle mechanics. Additionally, we verify that direct discretization of the weakly penalized form produces similar convergence behavior to mixed formulations while avoiding the use of an additional variable. Combining a simple structure which allows the solution of computationally challenging problems with good convergence characteristics, the weakly penalized form provides an accurate and efficient alternative to incompressibility and compressibility in cardiac mechanics. PMID:25187672

A displacement-based finite element formulation for incompressible and nearly-incompressible cardiac mechanics.

PubMed

Hadjicharalambous, Myrianthi; Lee, Jack; Smith, Nicolas P; Nordsletten, David A

2014-06-01

The Lagrange Multiplier (LM) and penalty methods are commonly used to enforce incompressibility and compressibility in models of cardiac mechanics. In this paper we show how both formulations may be equivalently thought of as a weakly penalized system derived from the statically condensed Perturbed Lagrangian formulation, which may be directly discretized maintaining the simplicity of penalty formulations with the convergence characteristics of LM techniques. A modified Shamanskii-Newton-Raphson scheme is introduced to enhance the nonlinear convergence of the weakly penalized system and, exploiting its equivalence, modifications are developed for the penalty form. Focusing on accuracy, we proceed to study the convergence behavior of these approaches using different interpolation schemes for both a simple test problem and more complex models of cardiac mechanics. Our results illustrate the well-known influence of locking phenomena on the penalty approach (particularly for lower order schemes) and its effect on accuracy for whole-cycle mechanics. Additionally, we verify that direct discretization of the weakly penalized form produces similar convergence behavior to mixed formulations while avoiding the use of an additional variable. Combining a simple structure which allows the solution of computationally challenging problems with good convergence characteristics, the weakly penalized form provides an accurate and efficient alternative to incompressibility and compressibility in cardiac mechanics.

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).

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.

Modelling nonlinearity in piezoceramic transducers: From equations to nonlinear equivalent circuits.

PubMed

Parenthoine, D; Tran-Huu-Hue, L-P; Haumesser, L; Vander Meulen, F; Lematre, M; Lethiecq, M

2011-02-01

Quadratic nonlinear equations of a piezoelectric element under the assumptions of 1D vibration and weak nonlinearity are derived by the perturbation theory. It is shown that the nonlinear response can be represented by controlled sources that are added to the classical hexapole used to model piezoelectric ultrasonic transducers. As a consequence, equivalent electrical circuits can be used to predict the nonlinear response of a transducer taking into account the acoustic loads on the rear and front faces. A generalisation of nonlinear equivalent electrical circuits to cases including passive layers and propagation media is then proposed. Experimental results, in terms of second harmonic generation, on a coupled resonator are compared to theoretical calculations from the proposed model. Copyright © 2010 Elsevier B.V. All rights reserved.

Experimental study of a hybrid electro-acoustic nonlinear membrane absorber

NASA Astrophysics Data System (ADS)

Bryk, P. Y.; Bellizzi, S.; Côte, R.

2018-06-01

A hybrid electro-acoustic nonlinear membrane absorber working as a nonlinear energy sink (here after named EA-NES) is described. The device is composed of a thin circular visco-elastic membrane working as an essentially cubic oscillator. One face of the membrane is coupled to the acoustic field to be reduced and the other face is enclosed. The enclosure includes a loudspeaker for the control of the acoustic pressure felt by the rear face of the membrane through proportional feedback control. An experimental set-up has been developed where the EA-NES is weakly coupled to a linear acoustic system. The linear acoustic system is an open-ended tube, coupled on one side to the EA-NES by a box, and on the other side to a source loudspeaker by another box. Only sinusoidal forcing is considered. It is shown that the EA-NES is able to perform resonance capture with the acoustic field, resulting in noise reduction by targeted energy transfer, and to operate in a large frequency band, tuning itself passively to any linear system. We demonstrate the ability of the feedback gain defining the active loop to modify the resonance frequency of the EA-NES, which is a key factor to tune the triggering threshold of energy pumping. The novelty of this work is to use active control combined to passive nonlinear transfer energy to improve it. In this paper, only experimental results are analyzed.

Kinetic Analysis of Weakly ionized Plasmas in presence of collecting walls

NASA Astrophysics Data System (ADS)

Gonzalez, J.; Donoso, J. M.

2018-02-01

Description of plasmas in contact with a wall able to collecting or emitting charged particles is a research topic of great importance. This situation arises in a great variety of phenomena such as the characterization of plasmas by means of electric probes, in the surface treatment of materials and in the service-life of coatings in electric thrusters. In particular, in this work we devote attention to the dynamics of an argon weakly ionized plasma in the presence of a collecting wall. It is proposed a kinetic model in a 1D1V planar phase-space geometry. The model accounts for the electric field coupled to the system by solving the associated Poisson’s equation. To solve numerically the resulting non-linear system of equations, the Propagator Integral Method is used in conjunction with a slabbing method. On each interrelating plasma slab the integral advancing scheme operates in velocity space, in such a way that the all the species dynamics dominating the system evolution are kinetically described.

Relativistic weak lensing from a fully non-linear cosmological density field

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

Thomas, D.B.; Bruni, M.; Wands, D., E-mail: thomas.daniel@ucy.ac.cy, E-mail: marco.bruni@port.ac.uk, E-mail: david.wands@port.ac.uk

2015-09-01

In this paper we examine cosmological weak lensing on non-linear scales and show that there are Newtonian and relativistic contributions and that the latter can also be extracted from standard Newtonian simulations. We use the post-Friedmann formalism, a post-Newtonian type framework for cosmology, to derive the full weak-lensing deflection angle valid on non-linear scales for any metric theory of gravity. We show that the only contributing term that is quadratic in the first order deflection is the expected Born correction and lens-lens coupling term. We use this deflection angle to analyse the vector and tensor contributions to the E- andmore » B- mode cosmic shear power spectra. In our approach, once the gravitational theory has been specified, the metric components are related to the matter content in a well-defined manner. Specifying General Relativity, we write down a complete set of equations for a GR+ΛCDM universe for computing all of the possible lensing terms from Newtonian N-body simulations. We illustrate this with the vector potential and show that, in a GR+ΛCDM universe, its contribution to the E-mode is negligible with respect to that of the conventional Newtonian scalar potential, even on non-linear scales. Thus, under the standard assumption that Newtonian N-body simulations give a good approximation of the matter dynamics, we show that the standard ray tracing approach gives a good description for a ΛCDM cosmology.« less

Interesting features of nonlinear shock equations in dissipative pair-ion-electron plasmas

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

Masood, W.; National Centre for Physics; Rizvi, H.

2011-09-15

Two dimensional nonlinear electrostatic waves are studied in unmagnetized, dissipative pair-ion-electron plasmas in the presence of weak transverse perturbation. The dissipation in the system is taken into account by incorporating the kinematic viscosity of both positive and negative ions. In the linear case, a biquadratic dispersion relation is obtained, which yields the fast and slow modes in a pair-ion-electron plasma. It is shown that the limiting cases of electron-ion and pair-ion can be retrieved from the general biquadratic dispersion relation, and the differences in the characters of the waves propagating in both the cases are also highlighted. Using the smallmore » amplitude approximation method, the nonlinear Kadomtsev Petviashvili Burgers as well as Burgers-Kadomtsev Petviashvili equations are derived and their applicability for pair-ion-electron plasma is explained in detail. The present study may have relevance to understand the formation of two dimensional electrostatic shocks in laboratory produced pair-ion-electron plasmas.« less

On nonlinear Tollmien-Schlichting/vortex interaction in three-dimensional boundary layers

NASA Technical Reports Server (NTRS)

Davis, Dominic A. R.; Smith, Frank T.

1993-01-01

The instability of an incompressible three-dimensional boundary layer (that is, one with cross-flow) is considered theoretically and computationally in the context of vortex/wave interactions. Specifically the work centers on two low amplitude, lower-branch Tollmien-Schlichting waves which mutually interact to induce a weak longitudinal vortex flow; the vortex motion, in turn, gives rise to significant wave-modulation via wall-shear forcing. The characteristic Reynolds number is taken as a large parameter and, as a consequence, the waves' and the vortex motion are governed primarily by triple-deck theory. The nonlinear interaction is captured by a viscous partial-differential system for the vortex coupled with a pair of amplitude equations for each wave pressure. Three distinct possibilities were found to emerge for the nonlinear behavior of the flow solution downstream - an algebraic finite-distance singularity, far downstream saturation or far-downstream wave-decay (leaving pure vortex flow) - depending on the input conditions, the wave angles, and the size of the cross-flow.

Dynamic analysis of geometrically non-linear three-dimensional beams under moving mass

NASA Astrophysics Data System (ADS)

Zupan, E.; Zupan, D.

2018-01-01

In this paper, we present a coupled dynamic analysis of a moving particle on a deformable three-dimensional frame. The presented numerical model is capable of considering arbitrary curved and twisted initial geometry of the beam and takes into account geometric non-linearity of the structure. Coupled with dynamic equations of the structure, the equations of moving particle are solved. The moving particle represents the dynamic load and varies the mass distribution of the structure and at the same time its path is adapting due to deformability of the structure. A coupled geometrically non-linear behaviour of beam and particle is studied. The equation of motion of the particle is added to the system of the beam dynamic equations and an additional unknown representing the coordinate of the curvilinear path of the particle is introduced. The specially designed finite-element formulation of the three-dimensional beam based on the weak form of consistency conditions is employed where only the boundary conditions are affected by the contact forces.

Acoustic signatures of sound source-tract coupling.

PubMed

Arneodo, Ezequiel M; Perl, Yonatan Sanz; Mindlin, Gabriel B

2011-04-01

Birdsong is a complex behavior, which results from the interaction between a nervous system and a biomechanical peripheral device. While much has been learned about how complex sounds are generated in the vocal organ, little has been learned about the signature on the vocalizations of the nonlinear effects introduced by the acoustic interactions between a sound source and the vocal tract. The variety of morphologies among bird species makes birdsong a most suitable model to study phenomena associated to the production of complex vocalizations. Inspired by the sound production mechanisms of songbirds, in this work we study a mathematical model of a vocal organ, in which a simple sound source interacts with a tract, leading to a delay differential equation. We explore the system numerically, and by taking it to the weakly nonlinear limit, we are able to examine its periodic solutions analytically. By these means we are able to explore the dynamics of oscillatory solutions of a sound source-tract coupled system, which are qualitatively different from those of a sound source-filter model of a vocal organ. Nonlinear features of the solutions are proposed as the underlying mechanisms of observed phenomena in birdsong, such as unilaterally produced "frequency jumps," enhancement of resonances, and the shift of the fundamental frequency observed in heliox experiments. ©2011 American Physical Society

Acoustic signatures of sound source-tract coupling

PubMed Central

Arneodo, Ezequiel M.; Perl, Yonatan Sanz; Mindlin, Gabriel B.

2014-01-01

Birdsong is a complex behavior, which results from the interaction between a nervous system and a biomechanical peripheral device. While much has been learned about how complex sounds are generated in the vocal organ, little has been learned about the signature on the vocalizations of the nonlinear effects introduced by the acoustic interactions between a sound source and the vocal tract. The variety of morphologies among bird species makes birdsong a most suitable model to study phenomena associated to the production of complex vocalizations. Inspired by the sound production mechanisms of songbirds, in this work we study a mathematical model of a vocal organ, in which a simple sound source interacts with a tract, leading to a delay differential equation. We explore the system numerically, and by taking it to the weakly nonlinear limit, we are able to examine its periodic solutions analytically. By these means we are able to explore the dynamics of oscillatory solutions of a sound source-tract coupled system, which are qualitatively different from those of a sound source-filter model of a vocal organ. Nonlinear features of the solutions are proposed as the underlying mechanisms of observed phenomena in birdsong, such as unilaterally produced “frequency jumps,” enhancement of resonances, and the shift of the fundamental frequency observed in heliox experiments. PMID:21599213

Locally optimum nonlinearities for DCT watermark detection.

PubMed

Briassouli, Alexia; Strintzis, Michael G

2004-12-01

The issue of copyright protection of digital multimedia data has attracted a lot of attention during the last decade. An efficient copyright protection method that has been gaining popularity is watermarking, i.e., the embedding of a signature in a digital document that can be detected only by its rightful owner. Watermarks are usually blindly detected using correlating structures, which would be optimal in the case of Gaussian data. However, in the case of DCT-domain image watermarking, the data is more heavy-tailed and the correlator is clearly suboptimal. Nonlinear receivers have been shown to be particularly well suited for the detection of weak signals in heavy-tailed noise, as they are locally optimal. This motivates the use of the Gaussian-tailed zero-memory nonlinearity, as well as the locally optimal Cauchy nonlinearity for the detection of watermarks in DCT transformed images. We analyze the performance of these schemes theoretically and compare it to that of the traditionally used Gaussian correlator, but also to the recently proposed generalized Gaussian detector, which outperforms the correlator. The theoretical analysis and the actual performance of these systems is assessed through experiments, which verify the theoretical analysis and also justify the use of nonlinear structures for watermark detection. The performance of the correlator and the nonlinear detectors in the presence of quantization is also analyzed, using results from dither theory, and also verified experimentally.

Full analogue electronic realisation of the Hodgkin-Huxley neuronal dynamics in weak-inversion CMOS.

PubMed

Lazaridis, E; Drakakis, E M; Barahona, M

2007-01-01

This paper presents a non-linear analog synthesis path towards the modeling and full implementation of the Hodgkin-Huxley neuronal dynamics in silicon. The proposed circuits have been realized in weak-inversion CMOS technology and take advantage of both log-domain and translinear transistor-level techniques.

Experimental observations of nonlinearly enhanced 2omega-UH electromagnetic radiation excited by steady-state colliding electron beams

NASA Technical Reports Server (NTRS)

Intrator, T.; Hershkowitz, N.; Chan, C.

1984-01-01

Counterstreaming large-diameter electron beams in a steady-state laboratory experiment are observed to generate transverse radiation at twice the upper-hybrid frequency (2omega-UH) with a quadrupole radiation pattern. The electromagnetic wave power density is nonlinearly enhanced over the power density obtained from a single beam-plasma system. Electromagnetic power density scales exponentially with beam energy and increases with ion mass. Weak turbulence theory can predict similar (but weaker) beam energy scaling but not the high power density, or the predominance of the 2omega-UH radiation peak over the omega-UH peak. Significant noise near the upper-hybrid and ion plasma frequencies is also measured, with normalized electrostatic wave energy density W(ES)/n(e)T(e) approximately 0.01.

Signal detection via residence-time asymmetry in noisy bistable devices.

PubMed

Bulsara, A R; Seberino, C; Gammaitoni, L; Karlsson, M F; Lundqvist, B; Robinson, J W C

2003-01-01

We introduce a dynamical readout description for a wide class of nonlinear dynamic sensors operating in a noisy environment. The presence of weak unknown signals is assessed via the monitoring of the residence time in the metastable attractors of the system, in the presence of a known, usually time-periodic, bias signal. This operational scenario can mitigate the effects of sensor noise, providing a greatly simplified readout scheme, as well as significantly reduced processing procedures. Such devices can also show a wide variety of interesting dynamical features. This scheme for quantifying the response of a nonlinear dynamic device has been implemented in experiments involving a simple laboratory version of a fluxgate magnetometer. We present the results of the experiments and demonstrate that they match the theoretical predictions reasonably well.

Advanced data assimilation in strongly nonlinear dynamical systems

NASA Technical Reports Server (NTRS)

Miller, Robert N.; Ghil, Michael; Gauthiez, Francois

1994-01-01

Advanced data assimilation methods are applied to simple but highly nonlinear problems. The dynamical systems studied here are the stochastically forced double well and the Lorenz model. In both systems, linear approximation of the dynamics about the critical points near which regime transitions occur is not always sufficient to track their occurrence or nonoccurrence. Straightforward application of the extended Kalman filter yields mixed results. The ability of the extended Kalman filter to track transitions of the double-well system from one stable critical point to the other depends on the frequency and accuracy of the observations relative to the mean-square amplitude of the stochastic forcing. The ability of the filter to track the chaotic trajectories of the Lorenz model is limited to short times, as is the ability of strong-constraint variational methods. Examples are given to illustrate the difficulties involved, and qualitative explanations for these difficulties are provided. Three generalizations of the extended Kalman filter are described. The first is based on inspection of the innovation sequence, that is, the successive differences between observations and forecasts; it works very well for the double-well problem. The second, an extension to fourth-order moments, yields excellent results for the Lorenz model but will be unwieldy when applied to models with high-dimensional state spaces. A third, more practical method--based on an empirical statistical model derived from a Monte Carlo simulation--is formulated, and shown to work very well. Weak-constraint methods can be made to perform satisfactorily in the context of these simple models, but such methods do not seem to generalize easily to practical models of the atmosphere and ocean. In particular, it is shown that the equations derived in the weak variational formulation are difficult to solve conveniently for large systems.

Diffuse-charge dynamics of ionic liquids in electrochemical systems.

PubMed

Zhao, Hui

2011-11-01

We employ a continuum theory of solvent-free ionic liquids accounting for both short-range electrostatic correlations and steric effects (finite ion size) [Bazant et al., Phys. Rev. Lett. 106, 046102 (2011)] to study the response of a model microelectrochemical cell to a step voltage. The model problem consists of a 1-1 symmetric ionic liquid between two parallel blocking electrodes, neglecting any transverse transport phenomena. Matched asymptotic expansions in the limit of thin double layers are applied to analyze the resulting one-dimensional equations and study the overall charge-time relation in the weakly nonlinear regime. One important conclusion is that our simple scaling analysis suggests that the length scale √(λ*(D)l*(c)) accurately characterizes the double-layer structure of ionic liquids with strong electrostatic correlations where l*(c) is the electrostatic correlation length (in contrast, the Debye screening length λ*(D) is the primary double-layer length for electrolytes) and the response time of λ(D)(*3/2)L*/(D*l(c)(1/2)) (not λ*(D)L*/D* that is the primary charging time of electrolytes) is the correct charging time scale of ionic liquids with strong electrostatic correlations where D* is the diffusivity and L* is the separation length of the cell. With these two new scales, data of both electric potential versus distance from the electrode and the total diffuse charge versus time collapse onto each individual master curve in the presence of strong electrostatic correlations. In addition, the dependance of the total diffuse charge on steric effects, short-range correlations, and driving voltages is thoroughly examined. The results from the asymptotic analysis are compared favorably with those from full numerical simulations. Finally, the absorption of excess salt by the double layer creates a depletion region outside the double layer. Such salt depletion may bring a correction to the leading order terms and break down the weakly nonlinear analysis. A criterion which justifies the weakly nonlinear analysis is verified with numerical simulations.

Nonlinear optical waves with the second Painleve transcendent shape of envelope in Kerr media

NASA Astrophysics Data System (ADS)

Shcherbakov, Alexandre S.; Tepichin Rodriguez, Eduardo; Sanchez Sanchez, Mauro

2004-05-01

Nonlinear optical wave packets with the second Painleve transcendent shape of envelope are revealed in Kerr media, manifesting weakly focusing cubic nonlinearity, square-law dispersion, and linear losses. When the state of nonlinear optical transmission is realized, two possible types of boundary conditions turn out to be satisfied for these wave packets. The propagation of initially unchirped optical wave packets under consideration could be supported by lossless medium in both normal and anomalous dispersion regimes. At the same time initially chirped optical waves with the second Painleve transcendent shape in low-loss medium and need matching the magnitude of optical losses by the dispersion and nonlinear properties of that medium.

Influence of nonlinear detuning at plasma wavebreaking threshold on backward Raman compression of non-relativistic laser pulses

NASA Astrophysics Data System (ADS)

Balakin, A. A.; Fraiman, G. M.; Jia, Q.; Fisch, N. J.

2018-06-01

Taking into account the nonlinear dispersion of the plasma wave, the fluid equations for the three-wave (Raman) interaction in plasmas are derived. It is found that, in some parameter regimes, the nonlinear detuning resulting from the plasma wave dispersion during Raman compression limits the plasma wave amplitude to noticeably below the generally recognized wavebreaking threshold. Particle-in-cell simulations confirm the theoretical estimates. For weakly nonlinear dispersion, the detuning effect can be counteracted by pump chirping or, equivalently, by upshifting slightly the pump frequency, so that the frequency-upshifted pump interacts with the seed at the point where the plasma wave enters the nonlinear stage.

Nonlinear Wave Process Hierarchies and the Cyclic Development of Quasi-Ordered Structures in Turbulent Shear Flows.

DTIC Science & Technology

1979-11-01

can be evaluated semi- analitically in both the strongly nonlinear inner (critical layer) region and the weakly nonlinear outer region, reproduce the...experimental evidence of Ref. 8 (Figure 3, stage 3). Whereas the exact s~lutions of the Schridinger equation (Ref. 13) predict that an arbitrary smooth...peaks and valleys, different from the comon rate predicted by linear theory) arise suddenly and at surpris- ingly low disturbance levels [(u’/U 10-2] as

Study of HV Dielectrics for High Frequency Operation in Linear & Nonlinear Transmission Lines & Simulation & Development of Hybrid Nonlinear Lines for RF Generation

DTIC Science & Technology

2015-08-27

applied reverse voltage [8], [9]. In this report, the experimental results of a varactor diode NLTL built with 30 sections are presented. Besides, Spice ...capacitive line (NLCL) using commercial BT and PZT ceramic capacitors. Corresponding NLCL Spice simulation is provided for comparison with experimental...the output pulse. In special for PZT, Spice simulation of a line with respective linear capacitors illustrates its weak nonlinearity as the

Study of HV Dielectrics for High Frequency Operation in Linear and Nonlinear Transmission Lines (NLTLs) and Simulation and Development of Hybrid Nonlinear Lines for RF Generation

DTIC Science & Technology

2016-01-27

presented. Besides, Spice simulation provides an excellent way of studying the NLTL principle operation by comparing them with the experimental...high voltage nonlinear capacitive line (NLCL) using commercial BT and PZT ceramic capacitors. Corresponding NLCL Spice simulation is provided for...which causes a long tail on the output pulse. In special for PZT, Spice simulation of a line with respective linear capacitors illustrates its weak

On a modified form of navier-stokes equations for three-dimensional flows.

PubMed

Venetis, J

2015-01-01

A rephrased form of Navier-Stokes equations is performed for incompressible, three-dimensional, unsteady flows according to Eulerian formalism for the fluid motion. In particular, we propose a geometrical method for the elimination of the nonlinear terms of these fundamental equations, which are expressed in true vector form, and finally arrive at an equivalent system of three semilinear first order PDEs, which hold for a three-dimensional rectangular Cartesian coordinate system. Next, we present the related variational formulation of these modified equations as well as a general type of weak solutions which mainly concern Sobolev spaces.

On a Modified Form of Navier-Stokes Equations for Three-Dimensional Flows

PubMed Central

Venetis, J.

2015-01-01

A rephrased form of Navier-Stokes equations is performed for incompressible, three-dimensional, unsteady flows according to Eulerian formalism for the fluid motion. In particular, we propose a geometrical method for the elimination of the nonlinear terms of these fundamental equations, which are expressed in true vector form, and finally arrive at an equivalent system of three semilinear first order PDEs, which hold for a three-dimensional rectangular Cartesian coordinate system. Next, we present the related variational formulation of these modified equations as well as a general type of weak solutions which mainly concern Sobolev spaces. PMID:25918743

Stationary Shock Waves with Oscillating Front in Dislocation Systems of Semiconductors

NASA Astrophysics Data System (ADS)

Gestrin, S. G.; Shchukina, E. V.

2018-05-01

The paper presents a study of weakly nonlinear wave processes in the cylindrical region of a hole gas surrounding a negatively charged dislocation in an n-type semiconductor crystal. It is shown that shock waves propagating along the dislocation are the solutions of the Korteweg-de Vries-Burgers equation when the dispersion and dissipation of medium are taken into account. Estimates are obtained for the basic physical parameters characterizing the shock wave and the region inside the Reed cylinder.

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

Azimuthal Seismic Amplitude Variation with Offset and Azimuth Inversion in Weakly Anisotropic Media with Orthorhombic Symmetry

NASA Astrophysics Data System (ADS)

Pan, Xinpeng; Zhang, Guangzhi; Yin, Xingyao

2018-01-01

Seismic amplitude variation with offset and azimuth (AVOaz) inversion is well known as a popular and pragmatic tool utilized to estimate fracture parameters. A single set of vertical fractures aligned along a preferred horizontal direction embedded in a horizontally layered medium can be considered as an effective long-wavelength orthorhombic medium. Estimation of Thomsen's weak-anisotropy (WA) parameters and fracture weaknesses plays an important role in characterizing the orthorhombic anisotropy in a weakly anisotropic medium. Our goal is to demonstrate an orthorhombic anisotropic AVOaz inversion approach to describe the orthorhombic anisotropy utilizing the observable wide-azimuth seismic reflection data in a fractured reservoir with the assumption of orthorhombic symmetry. Combining Thomsen's WA theory and linear-slip model, we first derive a perturbation in stiffness matrix of a weakly anisotropic medium with orthorhombic symmetry under the assumption of small WA parameters and fracture weaknesses. Using the perturbation matrix and scattering function, we then derive an expression for linearized PP-wave reflection coefficient in terms of P- and S-wave moduli, density, Thomsen's WA parameters, and fracture weaknesses in such an orthorhombic medium, which avoids the complicated nonlinear relationship between the orthorhombic anisotropy and azimuthal seismic reflection data. Incorporating azimuthal seismic data and Bayesian inversion theory, the maximum a posteriori solutions of Thomsen's WA parameters and fracture weaknesses in a weakly anisotropic medium with orthorhombic symmetry are reasonably estimated with the constraints of Cauchy a priori probability distribution and smooth initial models of model parameters to enhance the inversion resolution and the nonlinear iteratively reweighted least squares strategy. The synthetic examples containing a moderate noise demonstrate the feasibility of the derived orthorhombic anisotropic AVOaz inversion method, and the real data illustrate the inversion stabilities of orthorhombic anisotropy in a fractured reservoir.

A powerful local shear instability in weakly magnetized disks. I - Linear analysis. II - Nonlinear evolution

NASA Technical Reports Server (NTRS)

Balbus, Steven A.; Hawley, John F.

1991-01-01

A broad class of astronomical accretion disks is presently shown to be dynamically unstable to axisymmetric disturbances in the presence of a weak magnetic field, an insight with consequently broad applicability to gaseous, differentially-rotating systems. In the first part of this work, a linear analysis is presented of the instability, which is local and extremely powerful; the maximum growth rate, which is of the order of the angular rotation velocity, is independent of the strength of the magnetic field. Fluid motions associated with the instability directly generate both poloidal and toroidal field components. In the second part of this investigation, the scaling relation between the instability's wavenumber and the Alfven velocity is demonstrated, and the independence of the maximum growth rate from magnetic field strength is confirmed.

Seismic waves in a self-gravitating planet

NASA Astrophysics Data System (ADS)

Brazda, Katharina; de Hoop, Maarten V.; Hörmann, Günther

2013-04-01

The elastic-gravitational equations describe the propagation of seismic waves including the effect of self-gravitation. We rigorously derive and analyze this system of partial differential equations and boundary conditions for a general, uniformly rotating, elastic, but aspherical, inhomogeneous, and anisotropic, fluid-solid earth model, under minimal assumptions concerning the smoothness of material parameters and geometry. For this purpose we first establish a consistent mathematical formulation of the low regularity planetary model within the framework of nonlinear continuum mechanics. Using calculus of variations in a Sobolev space setting, we then show how the weak form of the linearized elastic-gravitational equations directly arises from Hamilton's principle of stationary action. Finally we prove existence and uniqueness of weak solutions by the method of energy estimates and discuss additional regularity properties.

The third-order optical nonlinearities of Ge-Ga-Sb(In)-S chalcogenide glasses

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

Guo, Haitao, E-mail: guoht_001@opt.ac.cn; Chen, Hongyan; Hou, Chaoqi

2011-05-15

Research highlights: {yields} It is firstly demonstrated that the nonlinear refractive index n{sub 2} is dependent on the covalency of bonds in chalcogenide glass. {yields} Homopolar metallic bonds in chalcogenide glass have positive contribution to large nonlinear refractive index n{sub 2} also. {yields} The 80GeS{sub 2}.20Sb{sub 2}S{sub 3} glass would be expected to be used in the all-optical switches working at 1330 nm and 1550 nm telecommunication wavelengths. -- Abstract: The third-order optical nonlinearities of 80GeS{sub 2}.(20 - x)Ga{sub 2}S{sub 3}.xY{sub 2}S{sub 3} (x = 0, 5, 10, 15, 20 and Y = Sb or In) chalcogenide glasses were investigatedmore » utilizing the Z-scan method at the wavelength of 800 nm and their linear optical properties and structure were also studied. By analyzing the compositional dependences and possible influencing factors including the linear refractive index, the concentration of lone electron pairs, the optical bandgap and the amount of weak covalent/homopolar bonds, it indicates that the electronic contribution in weak heteropolar covalent and homopolar metallic bonds is responsible for large nonlinear refractive index n{sub 2} in the chalcogenide glasses. These chalcogenide glasses have characteristics of environmentally friendship, wide transparency in the visible region, high nonlinear refractive index n{sub 2} and low nonlinear absorption coefficient {beta}, and would be expected to be used in the all-optical switches working at 1330 nm and 1550 nm telecommunication wavelengths.« less

Synchronization crossover of polariton condensates in weakly disordered lattices

NASA Astrophysics Data System (ADS)

Ohadi, H.; del Valle-Inclan Redondo, Y.; Ramsay, A. J.; Hatzopoulos, Z.; Liew, T. C. H.; Eastham, P. R.; Savvidis, P. G.; Baumberg, J. J.

2018-05-01

We demonstrate that the synchronization of a lattice of solid-state condensates when intersite tunneling is switched on depends strongly on the weak local disorder. This finding is vital for implementation of condensate arrays as computation devices. The condensates here are nonlinear bosonic fluids of exciton-polaritons trapped in a weakly disordered Bose-Hubbard potential, where the nearest-neighboring tunneling rate (Josephson coupling) can be dynamically tuned. The system can thus be tuned from a localized to a delocalized fluid as the number density or the Josephson coupling between nearest neighbors increases. The localized fluid is observed as a lattice of unsynchronized condensates emitting at different energies set by the disorder potential. In the delocalized phase, the condensates synchronize and long-range order appears, evidenced by narrowing of momentum and energy distributions, new diffraction peaks in momentum space, and spatial coherence between condensates. Our paper identifies similarities and differences of this nonequilibrium crossover to the traditional Bose-glass to superfluid transition in atomic condensates.

The kink-soliton and antikink-soliton in quasi-one-dimensional nonlinear monoatomic lattice

NASA Astrophysics Data System (ADS)

Xu, Quan; Tian, Qiang

2005-04-01

The quasi-one-dimensional nonlinear monoatomic lattice is analyzed. The kink-soliton and antikink-soliton are presented. When the interaction of the lattice is strong in the x-direction and weak in the y-direction, the two-dimensional (2D) lattice changes to a quasi-one-dimensional lattice. Taking nearest-neighbor interaction into account, the vibration equation can be transformed into the KPI, KPII and MKP equation. Considering the cubic nonlinear potential of the vibration in the lattice, the kink-soliton solution is presented. Considering the quartic nonlinear potential and the cubic interaction potential, the kink-soliton and antikink-soliton solutions are presented.

Magnetosonic shock wave in collisional pair-ion plasma

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

Adak, Ashish, E-mail: ashish-adak@yahoo.com; Khan, Manoranjan, E-mail: mkhan.ju@gmail.com; Sikdar, Arnab, E-mail: arnabs.ju@gmail.com

2016-06-15

Nonlinear propagation of magnetosonic shock wave has been studied in collisional magnetized pair-ion plasma. The masses of both ions are same but the temperatures are slightly different. Two fluid model has been taken to describe the model. Two different modes of the magnetosonic wave have been obtained. The dynamics of the nonlinear magnetosonic wave is governed by the Korteweg-de Vries Burgers' equation. It has been shown that the ion-ion collision is the source of dissipation that causes the Burgers' term which is responsible for the shock structures in equal mass pair-ion plasma. The numerical investigations reveal that the magnetosonic wavemore » exhibits both oscillatory and monotonic shock structures depending on the strength of the dissipation. The nonlinear wave exhibited the oscillatory shock wave for strong magnetic field (weak dissipation) and monotonic shock wave for weak magnetic field (strong dissipation). The results have been discussed in the context of the fullerene pair-ion plasma experiments.« less

An iterated cubature unscented Kalman filter for large-DoF systems identification with noisy data

NASA Astrophysics Data System (ADS)

Ghorbani, Esmaeil; Cha, Young-Jin

2018-04-01

Structural and mechanical system identification under dynamic loading has been an important research topic over the last three or four decades. Many Kalman-filtering-based approaches have been developed for linear and nonlinear systems. For example, to predict nonlinear systems, an unscented Kalman filter was applied. However, from extensive literature reviews, the unscented Kalman filter still showed weak performance on systems with large degrees of freedom. In this research, a modified unscented Kalman filter is proposed by integration of a cubature Kalman filter to improve the system identification performance of systems with large degrees of freedom. The novelty of this work lies on conjugating the unscented transform with the cubature integration concept to find a more accurate output from the transformation of the state vector and its related covariance matrix. To evaluate the proposed method, three different numerical models (i.e., the single degree-of-freedom Bouc-Wen model, the linear 3-degrees-of-freedom system, and the 10-degrees-of-freedom system) are investigated. To evaluate the robustness of the proposed method, high levels of noise in the measured response data are considered. The results show that the proposed method is significantly superior to the traditional UKF for noisy measured data in systems with large degrees of freedom.

Josephson parametric phase-locked oscillator and its application to dispersive readout of superconducting qubits

NASA Astrophysics Data System (ADS)

Lin, Z. R.; Inomata, K.; Koshino, K.; Oliver, W. D.; Nakamura, Y.; Tsai, J. S.; Yamamoto, T.

2014-07-01

The parametric phase-locked oscillator (PPLO) is a class of frequency-conversion device, originally based on a nonlinear element such as a ferrite ring, that served as a fundamental logic element for digital computers more than 50 years ago. Although it has long since been overtaken by the transistor, there have been numerous efforts more recently to realize PPLOs in different physical systems such as optical photons, trapped atoms, and electromechanical resonators. This renewed interest is based not only on the fundamental physics of nonlinear systems, but also on the realization of new, high-performance computing devices with unprecedented capabilities. Here we realize a PPLO with Josephson-junction circuitry and operate it as a sensitive phase detector. Using a PPLO, we demonstrate the demodulation of a weak binary phase-shift keying microwave signal of the order of a femtowatt. We apply PPLO to dispersive readout of a superconducting qubit, and achieved high-fidelity, single-shot and non-destructive readout with Rabi-oscillation contrast exceeding 90%.

Dispersive shock waves in systems with nonlocal dispersion of Benjamin-Ono type

NASA Astrophysics Data System (ADS)

El, G. A.; Nguyen, L. T. K.; Smyth, N. F.

2018-04-01

We develop a general approach to the description of dispersive shock waves (DSWs) for a class of nonlinear wave equations with a nonlocal Benjamin-Ono type dispersion term involving the Hilbert transform. Integrability of the governing equation is not a pre-requisite for the application of this method which represents a modification of the DSW fitting method previously developed for dispersive-hydrodynamic systems of Korteweg-de Vries (KdV) type (i.e. reducible to the KdV equation in the weakly nonlinear, long wave, unidirectional approximation). The developed method is applied to the Calogero-Sutherland dispersive hydrodynamics for which the classification of all solution types arising from the Riemann step problem is constructed and the key physical parameters (DSW edge speeds, lead soliton amplitude, intermediate shelf level) of all but one solution type are obtained in terms of the initial step data. The analytical results are shown to be in excellent agreement with results of direct numerical simulations.

Mapping superintegrable quantum mechanics to resonant spacetimes

NASA Astrophysics Data System (ADS)

Evnin, Oleg; Demirchian, Hovhannes; Nersessian, Armen

2018-01-01

We describe a procedure naturally associating relativistic Klein-Gordon equations in static curved spacetimes to nonrelativistic quantum motion on curved spaces in the presence of a potential. Our procedure is particularly attractive in application to (typically, superintegrable) problems whose energy spectrum is given by a quadratic function of the energy level number, since for such systems the spacetimes one obtains possess evenly spaced, resonant spectra of frequencies for scalar fields of a certain mass. This construction emerges as a generalization of the previously studied correspondence between the Higgs oscillator and anti-de Sitter spacetime, which has been useful for both understanding weakly nonlinear dynamics in anti-de Sitter spacetime and algebras of conserved quantities of the Higgs oscillator. Our conversion procedure ("Klein-Gordonization") reduces to a nonlinear elliptic equation closely reminiscent of the one emerging in relation to the celebrated Yamabe problem of differential geometry. As an illustration, we explicitly demonstrate how to apply this procedure to superintegrable Rosochatius systems, resulting in a large family of spacetimes with resonant spectra for massless wave equations.

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.

Stochastic P-bifurcation and stochastic resonance in a noisy bistable fractional-order system

NASA Astrophysics Data System (ADS)

Yang, J. H.; Sanjuán, Miguel A. F.; Liu, H. G.; Litak, G.; Li, X.

2016-12-01

We investigate the stochastic response of a noisy bistable fractional-order system when the fractional-order lies in the interval (0, 2]. We focus mainly on the stochastic P-bifurcation and the phenomenon of the stochastic resonance. We compare the generalized Euler algorithm and the predictor-corrector approach which are commonly used for numerical calculations of fractional-order nonlinear equations. Based on the predictor-corrector approach, the stochastic P-bifurcation and the stochastic resonance are investigated. Both the fractional-order value and the noise intensity can induce an stochastic P-bifurcation. The fractional-order may lead the stationary probability density function to turn from a single-peak mode to a double-peak mode. However, the noise intensity may transform the stationary probability density function from a double-peak mode to a single-peak mode. The stochastic resonance is investigated thoroughly, according to the linear and the nonlinear response theory. In the linear response theory, the optimal stochastic resonance may occur when the value of the fractional-order is larger than one. In previous works, the fractional-order is usually limited to the interval (0, 1]. Moreover, the stochastic resonance at the subharmonic frequency and the superharmonic frequency are investigated respectively, by using the nonlinear response theory. When it occurs at the subharmonic frequency, the resonance may be strong and cannot be ignored. When it occurs at the superharmonic frequency, the resonance is weak. We believe that the results in this paper might be useful for the signal processing of nonlinear systems.

Mitigation of nonlinear fiber distortion using optical phase conjugation for mode-division multiplexed transmission

NASA Astrophysics Data System (ADS)

Zhang, Kai; Gao, Guanjun; Zhang, Jie; Fei, Aimei; Cvijetic, Milorad

2018-07-01

We have investigated and proposed the use of optical phase conjugation (OPC) technique to mitigate the impact of fiber nonlinearities in mode-division multiplexed transmission systems. Numerical simulations are performed for three wavelengths, each loaded with 200 Gb/s dual-polarization 16-level quadrature amplitude modulation (DP-16QAM) format, in weakly guided two-mode fiber. It is known that differential mode group delay (DMGD) in mode-division multiplexed (MDM) transmission systems could be beneficial for system performance of MDM system with MIMO compensation in place. On the other side, for MDM system with OPC in place, the presence of DMGD may limit the overall benefits since signal power evolution per spatial modes should be symmetrical at the system midpoint in order to realize an effective compensation of the nonlinear effects. Our simulation results show that in the reference case (in the absence of DMGD), the employment of OPC module would lead to an average Q-factor improvement of approximately 10 dB. At the same time, in the presence of DMGD, an average Q-factor improvement would be ∼2.8 dB for WDM case. In addition, due to asymmetrical signal power map, the penalties induced by a periodic amplification process cannot be ideally compensated by the midpoint insertion of OPC. However, by accounting the impacts of both DMGD and asymmetrical signal power map, the insertion of the OPC system will still lead to an average Q-factor improvement of ∼1 dB for WDM channel arrangement.

Ion acoustic solitary wave with weakly transverse perturbations in quantum electron-positron-ion plasma

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

Mushtaq, A.; Khan, S. A.; Department of Physics, COMSATS Institute of Information Technology, Islamabad

2007-05-15

The characteristics and stability of ion acoustic solitary wave with transverse perturbations are examined in ultracold quantum magnetospheric plasma consisting of electrons, positrons, and ions. Using the quantum hydrodynamic model, a dispersion relation in the linear regime, and the Kadomtsev-Petviashvili equation in the nonlinear regime are derived. The quantum corrections are studied through quantum statistics and diffraction effects. It is found that compressive solitary wave can propagate in this system. The quantum effects are also studied graphically for both linear and nonlinear profiles of ion acoustic wave. Using energy consideration method, conditions for existence of stable solitary waves are obtained.more » It is found that stable solitary waves depend on quantum corrections, positron concentration, and direction cosine of the wave vector k along the x axis.« less

Computation of Large-Scale Structure Jet Noise Sources With Weak Nonlinear Effects Using Linear Euler

NASA Technical Reports Server (NTRS)

Dahl, Milo D.; Hixon, Ray; Mankbadi, Reda R.

2003-01-01

An approximate technique is presented for the prediction of the large-scale turbulent structure sound source in a supersonic jet. A linearized Euler equations code is used to solve for the flow disturbances within and near a jet with a given mean flow. Assuming a normal mode composition for the wave-like disturbances, the linear radial profiles are used in an integration of the Navier-Stokes equations. This results in a set of ordinary differential equations representing the weakly nonlinear self-interactions of the modes along with their interaction with the mean flow. Solutions are then used to correct the amplitude of the disturbances that represent the source of large-scale turbulent structure sound in the jet.

On Interactions of Oscillation Modes for a Weakly Non-Linear Undamped Elastic Beam with AN External Force

NASA Astrophysics Data System (ADS)

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

2000-08-01

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

Laser-absorption effect on pulse-compression under Ohmic and weak-relativistic ponderomotive nonlinearity in plasmas

NASA Astrophysics Data System (ADS)

Singh, Mamta; Gupta, D. N.

2018-01-01

The inclusion of laser absorption in plasmas plays an important role in laser-plasma interactions. In this work, the laser pulse compression in weakly relativistic plasmas has been revisited by incorporating the collision-based laser absorption effects. By considering the role of laser absorption in plasmas, a set of coupled nonlinear equations is derived to describe the evolution of pulse compression. The laser pulse compression is reduced due to the collisional absorption in the plasmas. Fast dispersion is also observed with increasing the absorption coefficient, which is obviously due to the strong energy attenuation in plasmas. Using our theoretical model, the involvement and importance of a particular absorption mechanism for pulse compression in plasmas is analyzed.

Non-conventional synchronization of weakly coupled active oscillators

NASA Astrophysics Data System (ADS)

Manevitch, L. I.; Kovaleva, M. A.; Pilipchuk, V. N.

2013-03-01

We present a new type of self-sustained vibrations in the fundamental physical model covering a broad area of applications from wave generation in radiophysics and nonlinear optics to the heart muscle contraction and eyesight disorder in biophysics. Such a diversity of applications is due to the universal physical phenomenon of synchronization. Previous studies of this phenomenon, originating from Huygens famous observation, are based mainly on the model of two weakly coupled Van der Pol oscillators and usually deal with their synchronization in the regimes close to nonlinear normal modes (NNMs). In this work, we show for the first time that, in the important case of threshold excitation, an alternative synchronization mechanism can develop when the conventional synchronization becomes impossible. We identify this mechanism as an appearance of dynamic attractor with the complete periodic energy exchange between the oscillators, which is the dissipative analogue of highly intensive beats in a conservative system. This type of motion is therefore opposite to the NNM-type synchronization with no energy exchange by definition. The analytical description of these vibrations employs the concept of Limiting Phase Trajectories (LPTs) introduced by one of the authors earlier for conservative systems. Finally, within the LPT approach, we describe the transition from the complete energy exchange between the oscillators to the energy localization mostly on one of the two oscillators. The localized mode is an attractor in the range of model parameters wherein the LPT as well as the in-phase and out-of-phase NNMs become unstable.

Multiplicative stochastic processes in nonlinear systems: Noise-induced transition from the overdamped to the inertial regime

NASA Astrophysics Data System (ADS)

Faetti, Sandro; Festa, Crescenzo; Fronzoni, Leone; Grigolini, Paolo; Martano, Paolo

1984-12-01

An experimental apparatus is set up to check, via analog circuits, the recent theoretical predictions of Graham and Schenzle

Characteristics of nonlinear imaging of broadband laser stacked by chirped pulses

NASA Astrophysics Data System (ADS)

Wang, Youwen; You, Kaiming; Chen, Liezun; Lu, Shizhuan; Dai, Zhiping; Ling, Xiaohui

2014-11-01

Nanosecond-level pulses of specific shape is usually generated by stacking chirped pulses for high-power inertial confinement fusion driver, in which nonlinear imaging of scatterers may damage precious optical elements. We present a numerical study of the characteristics of nonlinear imaging of scatterers in broadband laser stacked by chirped pulses to disclose the dependence of location and intensity of images on the parameters of the stacked pulse. It is shown that, for sub-nanosecond long sub-pulses with chirp or transform-limited sub-pulses, the time-mean intensity and location of images through normally dispersive and anomalously dispersive self-focusing medium slab are almost identical; While for picosecond-level short sub-pulses with chirp, the time-mean intensity of images for weak normal dispersion is slightly higher than that for weak anomalous dispersion through a thin nonlinear slab; the result is opposite to that for strong dispersion in a thick nonlinear slab; Furthermore, for given time delay between neighboring sub-pulses, the time-mean intensity of images varies periodically with chirp of the sub-pulse increasing; for a given pulse width of sub-pulse, the time-mean intensity of images decreases with the time delay between neighboring sub-pulses increasing; additionally, there is a little difference in the time-mean intensity of images of the laser stacked by different numbers of sub-pulses. Finally, the obtained results are also given physical explanations.

A Weakly Nonlinear Model for the Damping of Resonantly Forced Density Waves in Dense Planetary Rings

NASA Astrophysics Data System (ADS)

Lehmann, Marius; Schmidt, Jürgen; Salo, Heikki

2016-10-01

In this paper, we address the stability of resonantly forced density waves in dense planetary rings. Goldreich & Tremaine have already argued that density waves might be unstable, depending on the relationship between the ring’s viscosity and the surface mass density. In the recent paper Schmidt et al., we have pointed out that when—within a fluid description of the ring dynamics—the criterion for viscous overstability is satisfied, forced spiral density waves become unstable as well. In this case, linear theory fails to describe the damping, but nonlinearity of the underlying equations guarantees a finite amplitude and eventually a damping of the wave. We apply the multiple scale formalism to derive a weakly nonlinear damping relation from a hydrodynamical model. This relation describes the resonant excitation and nonlinear viscous damping of spiral density waves in a vertically integrated fluid disk with density dependent transport coefficients. The model consistently predicts density waves to be (linearly) unstable in a ring region where the conditions for viscous overstability are met. Sufficiently far away from the Lindblad resonance, the surface mass density perturbation is predicted to saturate to a constant value due to nonlinear viscous damping. The wave’s damping lengths of the model depend on certain input parameters, such as the distance to the threshold for viscous overstability in parameter space and the ground state surface mass density.

Solitonic characteristics of Airy beam nonlinear propagation

NASA Astrophysics Data System (ADS)

Bouchet, Thomas; Marsal, Nicolas; Sciamanna, Marc; Wolfersberger, Delphine

2018-05-01

We analyze the nonlinear propagation of a one-dimensional Airy beam. Under nonlinear focusing conditions, the Airy beam splits into a weak accelerating structure and a beam that has been named an "off-shooting soliton." Experimental measurements and numerical results related to the off-shooting Airy beam are compared to soliton theoretical profiles and a good agreement is found in terms of transverse shape, width, and amplitude. We identify the different parameters to generate an Airy beam off-shooting soliton and demonstrate that its profile is also preserved through propagation over long distances.

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

Tessore, Nicolas; Metcalf, R. Benton; Winther, Hans A.

A number of alternatives to general relativity exhibit gravitational screening in the non-linear regime of structure formation. We describe a set of algorithms that can produce weak lensing maps of large scale structure in such theories and can be used to generate mock surveys for cosmological analysis. By analysing a few basic statistics we indicate how these alternatives can be distinguished from general relativity with future weak lensing surveys.

Rotation-induced nonlinear wavepackets in internal waves

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

Whitfield, A. J., E-mail: ashley.whitfield.12@ucl.ac.uk; Johnson, E. R., E-mail: e.johnson@ucl.ac.uk

2014-05-15

The long time effect of weak rotation on an internal solitary wave is the decay into inertia-gravity waves and the eventual formation of a localised wavepacket. Here this initial value problem is considered within the context of the Ostrovsky, or the rotation-modified Korteweg-de Vries (KdV), equation and a numerical method for obtaining accurate wavepacket solutions is presented. The flow evolutions are described in the regimes of relatively-strong and relatively-weak rotational effects. When rotational effects are relatively strong a second-order soliton solution of the nonlinear Schrödinger equation accurately predicts the shape, and phase and group velocities of the numerically determined wavepackets.more » It is suggested that these solitons may form from a local Benjamin-Feir instability in the inertia-gravity wave-train radiated when a KdV solitary wave rapidly adjusts to the presence of strong rotation. When rotational effects are relatively weak the initial KdV solitary wave remains coherent longer, decaying only slowly due to weak radiation and modulational instability is no longer relevant. Wavepacket solutions in this regime appear to consist of a modulated KdV soliton wavetrain propagating on a slowly varying background of finite extent.« less

Nonlinearity and Scaling Behavior in Lead Zirconate Titanate Piezoceramic

NASA Astrophysics Data System (ADS)

Mueller, V.

1998-03-01

The results of a comprehensive study of the nonlinear dielectric and electromechanical response of lead zirconate titanate (PZT) piezoceramics are presented. The piezoelectric strain of a series of donor doped (soft PZT) and acceptor doped (hard PZT) polycrystalline systems was measured under quasistatic (nonresonant) conditions. The measuring field was applied both parallel and perpendicular to the poling direction of the ceramic in order to investigate the influence of different symmetry conditions. Dielectric properties were studied in addition to the electromechanical measurements which enables us to compare piezoelectric and dielectric nonlinearities. Due to the different level and type of dopants, the piezoceramics examined differ significantly with regard to its Curie temperature (190^o CE_c2 the nonlinearity can be described in the same way as in soft PZT. The results indicate that irreversible motion of (ferroelastic) non-180^o walls causes the nonlinearity of PZT and that the contribution of (non-ferroelastic) 180^o walls to the linear and nonlinear coefficients is negligibly small. The experimentally observed non-analytic scaling behavior is qualitatively inconsistent with the assumption that the nonlinearity is related to the anharmonicity of the domain wall potential. We suggest that the dynamics of the domain wall in a randomly pinned medium dominates the piezoelectric and dielectric nonlinearity at field strengths well below the limiting field necessary to depole the piezoceramic. The analysis of results obtained at different ceramic systems indicates that linear and nonlinear coefficients are not independent from each other. The observed relationship between linear and nonlinear properties leads us to the suggestion that another extrinsic contribution to the permittivity exists in PZT which may not be attributed to domain wall motion but related to the dielectric dispersion at microwave frequencies.

Large data well-posedness in the energy space of the Chern-Simons-Schrödinger system

NASA Astrophysics Data System (ADS)

Lim, Zhuo Min

2018-02-01

We consider the initial-value problem for the Chern-Simons-Schrödinger system, which is a gauge-covariant Schrödinger system in Rt × Rx2 with a long-range electromagnetic field. We show that, in the Coulomb gauge, it is locally well-posed in Hs for s ⩾ 1, and the solution map satisfies a local-in-time weak Lipschitz bound. By energy conservation, we also obtain a global regularity result. The key is to retain the non-perturbative part of the derivative nonlinearity in the principal operator, and exploit the dispersive properties of the resulting paradifferential-type principal operator using adapted Up and Vp spaces.

Robust scalable stabilisability conditions for large-scale heterogeneous multi-agent systems with uncertain nonlinear interactions: towards a distributed computing architecture

NASA Astrophysics Data System (ADS)

Manfredi, Sabato

2016-06-01

Large-scale dynamic systems are becoming highly pervasive in their occurrence with applications ranging from system biology, environment monitoring, sensor networks, and power systems. They are characterised by high dimensionality, complexity, and uncertainty in the node dynamic/interactions that require more and more computational demanding methods for their analysis and control design, as well as the network size and node system/interaction complexity increase. Therefore, it is a challenging problem to find scalable computational method for distributed control design of large-scale networks. In this paper, we investigate the robust distributed stabilisation problem of large-scale nonlinear multi-agent systems (briefly MASs) composed of non-identical (heterogeneous) linear dynamical systems coupled by uncertain nonlinear time-varying interconnections. By employing Lyapunov stability theory and linear matrix inequality (LMI) technique, new conditions are given for the distributed control design of large-scale MASs that can be easily solved by the toolbox of MATLAB. The stabilisability of each node dynamic is a sufficient assumption to design a global stabilising distributed control. The proposed approach improves some of the existing LMI-based results on MAS by both overcoming their computational limits and extending the applicative scenario to large-scale nonlinear heterogeneous MASs. Additionally, the proposed LMI conditions are further reduced in terms of computational requirement in the case of weakly heterogeneous MASs, which is a common scenario in real application where the network nodes and links are affected by parameter uncertainties. One of the main advantages of the proposed approach is to allow to move from a centralised towards a distributed computing architecture so that the expensive computation workload spent to solve LMIs may be shared among processors located at the networked nodes, thus increasing the scalability of the approach than the network size. Finally, a numerical example shows the applicability of the proposed method and its advantage in terms of computational complexity when compared with the existing approaches.

Thrust generation by a heaving flexible foil: Resonance, nonlinearities, and optimality

NASA Astrophysics Data System (ADS)

Paraz, Florine; Schouveiler, Lionel; Eloy, Christophe

2016-01-01

Flexibility of marine animal fins has been thought to enhance swimming performance. However, despite numerous experimental and numerical studies on flapping flexible foils, there is still no clear understanding of the effect of flexibility and flapping amplitude on thrust generation and swimming efficiency. Here, to address this question, we combine experiments on a model system and a weakly nonlinear analysis. Experiments consist in immersing a flexible rectangular plate in a uniform flow and forcing this plate into a heaving motion at its leading edge. A complementary theoretical model is developed assuming a two-dimensional inviscid problem. In this model, nonlinear effects are taken into account by considering a transverse resistive drag. Under these hypotheses, a modal decomposition of the system motion allows us to predict the plate response amplitude and the generated thrust, as a function of the forcing amplitude and frequency. We show that this model can correctly predict the experimental data on plate kinematic response and thrust generation, as well as other data found in the literature. We also discuss the question of efficiency in the context of bio-inspired propulsion. Using the proposed model, we show that the optimal propeller for a given thrust and a given swimming speed is achieved when the actuating frequency is tuned to a resonance of the system, and when the optimal forcing amplitude scales as the square root of the required thrust.

Combined genetic algorithm and multiple linear regression (GA-MLR) optimizer: Application to multi-exponential fluorescence decay surface.

PubMed

Fisz, Jacek J

2006-12-07

The optimization approach based on the genetic algorithm (GA) combined with multiple linear regression (MLR) method, is discussed. The GA-MLR optimizer is designed for the nonlinear least-squares problems in which the model functions are linear combinations of nonlinear functions. GA optimizes the nonlinear parameters, and the linear parameters are calculated from MLR. GA-MLR is an intuitive optimization approach and it exploits all advantages of the genetic algorithm technique. This optimization method results from an appropriate combination of two well-known optimization methods. The MLR method is embedded in the GA optimizer and linear and nonlinear model parameters are optimized in parallel. The MLR method is the only one strictly mathematical "tool" involved in GA-MLR. The GA-MLR approach simplifies and accelerates considerably the optimization process because the linear parameters are not the fitted ones. Its properties are exemplified by the analysis of the kinetic biexponential fluorescence decay surface corresponding to a two-excited-state interconversion process. A short discussion of the variable projection (VP) algorithm, designed for the same class of the optimization problems, is presented. VP is a very advanced mathematical formalism that involves the methods of nonlinear functionals, algebra of linear projectors, and the formalism of Fréchet derivatives and pseudo-inverses. Additional explanatory comments are added on the application of recently introduced the GA-NR optimizer to simultaneous recovery of linear and weakly nonlinear parameters occurring in the same optimization problem together with nonlinear parameters. The GA-NR optimizer combines the GA method with the NR method, in which the minimum-value condition for the quadratic approximation to chi(2), obtained from the Taylor series expansion of chi(2), is recovered by means of the Newton-Raphson algorithm. The application of the GA-NR optimizer to model functions which are multi-linear combinations of nonlinear functions, is indicated. The VP algorithm does not distinguish the weakly nonlinear parameters from the nonlinear ones and it does not apply to the model functions which are multi-linear combinations of nonlinear functions.

Multiscale Metabolic Modeling of C4 Plants: Connecting Nonlinear Genome-Scale Models to Leaf-Scale Metabolism in Developing Maize Leaves

PubMed Central

Bogart, Eli; Myers, Christopher R.

2016-01-01

C4 plants, such as maize, concentrate carbon dioxide in a specialized compartment surrounding the veins of their leaves to improve the efficiency of carbon dioxide assimilation. Nonlinear relationships between carbon dioxide and oxygen levels and reaction rates are key to their physiology but cannot be handled with standard techniques of constraint-based metabolic modeling. We demonstrate that incorporating these relationships as constraints on reaction rates and solving the resulting nonlinear optimization problem yields realistic predictions of the response of C4 systems to environmental and biochemical perturbations. Using a new genome-scale reconstruction of maize metabolism, we build an 18000-reaction, nonlinearly constrained model describing mesophyll and bundle sheath cells in 15 segments of the developing maize leaf, interacting via metabolite exchange, and use RNA-seq and enzyme activity measurements to predict spatial variation in metabolic state by a novel method that optimizes correlation between fluxes and expression data. Though such correlations are known to be weak in general, we suggest that developmental gradients may be particularly suited to the inference of metabolic fluxes from expression data, and we demonstrate that our method predicts fluxes that achieve high correlation with the data, successfully capture the experimentally observed base-to-tip transition between carbon-importing tissue and carbon-exporting tissue, and include a nonzero growth rate, in contrast to prior results from similar methods in other systems. PMID:26990967

Modulational instability and higher-order rogue waves with parameters modulation in a coupled integrable AB system via the generalized Darboux transformation.

PubMed

Wen, Xiao-Yong; Yan, Zhenya

2015-12-01

We study higher-order rogue wave (RW) solutions of the coupled integrable dispersive AB system (also called Pedlosky system), which describes the evolution of wave-packets in a marginally stable or unstable baroclinic shear flow in geophysical fluids. We propose its continuous-wave (CW) solutions and existent conditions for their modulation instability to form the rogue waves. A new generalized N-fold Darboux transformation (DT) is proposed in terms of the Taylor series expansion for the spectral parameter in the Darboux matrix and its limit procedure and applied to the CW solutions to generate multi-rogue wave solutions of the coupled AB system, which satisfy the general compatibility condition. The dynamical behaviors of these higher-order rogue wave solutions demonstrate both strong and weak interactions by modulating parameters, in which some weak interactions can generate the abundant triangle, pentagon structures, etc. Particularly, the trajectories of motion of peaks and depressions of profiles of the first-order RWs are explicitly analyzed. The generalized DT method used in this paper can be extended to other nonlinear integrable systems. These results may be useful for understanding the corresponding rogue-wave phenomena in fluid mechanics and related fields.

Marginal states in a cubic autocatalytic reaction

NASA Astrophysics Data System (ADS)

Das, Debojyoti; Ghosh, Pushpita; Ray, Deb Shankar

2011-09-01

Marginal steady state belongs to a special class of states in nonlinear dynamics. To realize this state we consider a cubic autocatalytic reaction A + 2B → 3B in a continuous-stirred-tank-reactor, where the flow rate of the reactant A can be controlled to manipulate the dynamical behavior of the open system. We demonstrate that when the flow rate is weakly noisy the autocatalytic reaction admits of a steady state which is marginal in nature and is surrounded by infinite number of periodic trajectories. When the uncatalyzed reaction A → B is included in the reaction scheme, there exists a marginal steady state which is a critical state corresponding to the point of transition between the flow branch and the equilibrium branch, similar to gas-liquid critical point of transition. This state loses its stability in the weak noise limit.

Linear and nonlinear ion-acoustic waves in nonrelativistic quantum plasmas with arbitrary degeneracy.

PubMed

Haas, Fernando; Mahmood, Shahzad

2015-11-01

Linear and nonlinear ion-acoustic waves are studied in a fluid model for nonrelativistic, unmagnetized quantum plasma with electrons with an arbitrary degeneracy degree. The equation of state for electrons follows from a local Fermi-Dirac distribution function and applies equally well both to fully degenerate and classical, nondegenerate limits. Ions are assumed to be cold. Quantum diffraction effects through the Bohm potential are also taken into account. A general coupling parameter valid for dilute and dense plasmas is proposed. The linear dispersion relation of the ion-acoustic waves is obtained and the ion-acoustic speed is discussed for the limiting cases of extremely dense or dilute systems. In the long-wavelength limit, the results agree with quantum kinetic theory. Using the reductive perturbation method, the appropriate Korteweg-de Vries equation for weakly nonlinear solutions is obtained and the corresponding soliton propagation is analyzed. It is found that soliton hump and dip structures are formed depending on the value of the quantum parameter for the degenerate electrons, which affect the phase velocities in the dispersive medium.

Linear and nonlinear ion-acoustic waves in nonrelativistic quantum plasmas with arbitrary degeneracy

NASA Astrophysics Data System (ADS)

Haas, Fernando; Mahmood, Shahzad

2015-11-01

Linear and nonlinear ion-acoustic waves are studied in a fluid model for nonrelativistic, unmagnetized quantum plasma with electrons with an arbitrary degeneracy degree. The equation of state for electrons follows from a local Fermi-Dirac distribution function and applies equally well both to fully degenerate and classical, nondegenerate limits. Ions are assumed to be cold. Quantum diffraction effects through the Bohm potential are also taken into account. A general coupling parameter valid for dilute and dense plasmas is proposed. The linear dispersion relation of the ion-acoustic waves is obtained and the ion-acoustic speed is discussed for the limiting cases of extremely dense or dilute systems. In the long-wavelength limit, the results agree with quantum kinetic theory. Using the reductive perturbation method, the appropriate Korteweg-de Vries equation for weakly nonlinear solutions is obtained and the corresponding soliton propagation is analyzed. It is found that soliton hump and dip structures are formed depending on the value of the quantum parameter for the degenerate electrons, which affect the phase velocities in the dispersive medium.

Transport processes in magnetically confined plasmas in the nonlinear regime.

PubMed

Sonnino, Giorgio

2006-06-01

A field theory approach to transport phenomena in magnetically confined plasmas is presented. The thermodynamic field theory (TFT), previously developed for treating the generic thermodynamic system out of equilibrium, is applied to plasmas physics. Transport phenomena are treated here as the effect of the field linking the thermodynamic forces with their conjugate flows combined with statistical mechanics. In particular, the Classical and the Pfirsch-Schluter regimes are analyzed by solving the thermodynamic field equations of the TFT in the weak-field approximation. We found that, the TFT does not correct the expressions of the ionic heat fluxes evaluated by the neoclassical theory in these two regimes. On the other hand, the fluxes of matter and electronic energy (heat flow) is further enhanced in the nonlinear Classical and Pfirsch-Schluter regimes. These results seem to be in line with the experimental observations. The complete set of the electronic and ionic transport equations in the nonlinear Banana regime, is also reported. A paper showing the comparison between our theoretic results and the experimental observations in the JET machine is currently in preparation.

Nonlinear conductance in weakly disordered mesoscopic wires: Interaction and magnetic field asymmetry

NASA Astrophysics Data System (ADS)

Texier, Christophe; Mitscherling, Johannes

2018-02-01

We study the nonlinear conductance G ˜∂2I /∂ V2|V =0 in coherent quasi-one-dimensional weakly disordered metallic wires. Our analysis is based on the scattering approach and includes the effect of Coulomb interaction. The nonlinear conductance correlations can be related to integrals of two fundamental correlation functions: the correlator of functional derivatives of the conductance and the correlator of injectivities (the injectivity is the contribution to the local density of states of eigenstates incoming from one contact). These correlators are obtained explicitly by using diagrammatic techniques for weakly disordered metals. In a coherent wire of length L , we obtain rms (G )≃0.006 ETh-1 (and =0 ), where ETh=ℏ D /L2 is the Thouless energy of the wire and D the diffusion constant; the small dimensionless factor results from screening, i.e., cannot be obtained within a simple theory for noninteracting electrons. Electronic interactions are also responsible for an asymmetry under magnetic field reversal; the antisymmetric part of the nonlinear conductance (at high magnetic field) being much smaller than the symmetric one, rms (Ga)≃0.001 (gETh) -1 , where g ≫1 is the dimensionless (linear) conductance of the wire. In a weakly coherent wire (i.e., Lφ≪L , where Lφ is the phase coherence length), the nonlinear conductance is of the same order as the result G0 of a free electron calculation (although screening again strongly reduces the dimensionless prefactor); we get G ˜G0˜(Lφ/L ) 7 /2ETh-1 , while the antisymmetric part (at high magnetic field) now behaves as Ga˜(Lφ/L ) 11 /2(gETh) -1≪G . The effect of thermal fluctuations is studied: when the thermal length LT=√{ℏ D /kBT } is the smallest length scale, LT≪Lφ≪L , the free electron result G0˜(LT/L ) 3(Lφ/L ) 1 /2ETh-1 is negligible and the dominant contribution is provided by screening, G ˜(LT/L ) (Lφ/L ) 7 /2ETh-1 ; in this regime, the antisymmetric part is Ga˜(LT/L ) 2(Lφ/L ) 7 /2(gETh) -1 . All the precise dimensionless prefactors are obtained. Crossovers from zero to strong magnetic field regimes are also analyzed.

Travelling-wave solutions of a weakly nonlinear two-dimensional higher-order Kadomtsev-Petviashvili dynamical equation for dispersive shallow-water waves

NASA Astrophysics Data System (ADS)

Seadawy, Aly R.

2017-01-01

The propagation of three-dimensional nonlinear irrotational flow of an inviscid and incompressible fluid of the long waves in dispersive shallow-water approximation is analyzed. The problem formulation of the long waves in dispersive shallow-water approximation lead to fifth-order Kadomtsev-Petviashvili (KP) dynamical equation by applying the reductive perturbation theory. By using an extended auxiliary equation method, the solitary travelling-wave solutions of the two-dimensional nonlinear fifth-order KP dynamical equation are derived. An analytical as well as a numerical solution of the two-dimensional nonlinear KP equation are obtained and analyzed with the effects of external pressure flow.

Variations of cosmic large-scale structure covariance matrices across parameter space

NASA Astrophysics Data System (ADS)

Reischke, Robert; Kiessling, Alina; Schäfer, Björn Malte

2017-03-01

The likelihood function for cosmological parameters, given by e.g. weak lensing shear measurements, depends on contributions to the covariance induced by the non-linear evolution of the cosmic web. As highly non-linear clustering to date has only been described by numerical N-body simulations in a reliable and sufficiently precise way, the necessary computational costs for estimating those covariances at different points in parameter space are tremendous. In this work, we describe the change of the matter covariance and the weak lensing covariance matrix as a function of cosmological parameters by constructing a suitable basis, where we model the contribution to the covariance from non-linear structure formation using Eulerian perturbation theory at third order. We show that our formalism is capable of dealing with large matrices and reproduces expected degeneracies and scaling with cosmological parameters in a reliable way. Comparing our analytical results to numerical simulations, we find that the method describes the variation of the covariance matrix found in the SUNGLASS weak lensing simulation pipeline within the errors at one-loop and tree-level for the spectrum and the trispectrum, respectively, for multipoles up to ℓ ≤ 1300. We show that it is possible to optimize the sampling of parameter space where numerical simulations should be carried out by minimizing interpolation errors and propose a corresponding method to distribute points in parameter space in an economical way.

Evidence for self-refraction in a convergence zone: NPE (Nonlinear progressive wave equation) model results

NASA Technical Reports Server (NTRS)

Mcdonald, B. Edward; Plante, Daniel R.

1989-01-01

The nonlinear progressive wave equation (NPE) model was developed by the Naval Ocean Research and Development Activity during 1982 to 1987 to study nonlinear effects in long range oceanic propagation of finite amplitude acoustic waves, including weak shocks. The NPE model was applied to propagation of a generic shock wave (initial condition provided by Sandia Division 1533) in a few illustrative environments. The following consequences of nonlinearity are seen by comparing linear and nonlinear NPE results: (1) a decrease in shock strength versus range (a well-known result of entropy increases at the shock front); (2) an increase in the convergence zone range; and (3) a vertical meandering of the energy path about the corresponding linear ray path. Items (2) and (3) are manifestations of self-refraction.

Giant nonlinear response at a plasmonic nanofocus drives efficient four-wave mixing

NASA Astrophysics Data System (ADS)

Nielsen, Michael P.; Shi, Xingyuan; Dichtl, Paul; Maier, Stefan A.; Oulton, Rupert F.

2017-12-01

Efficient optical frequency mixing typically must accumulate over large interaction lengths because nonlinear responses in natural materials are inherently weak. This limits the efficiency of mixing processes owing to the requirement of phase matching. Here, we report efficient four-wave mixing (FWM) over micrometer-scale interaction lengths at telecommunications wavelengths on silicon. We used an integrated plasmonic gap waveguide that strongly confines light within a nonlinear organic polymer. The gap waveguide intensifies light by nanofocusing it to a mode cross-section of a few tens of nanometers, thus generating a nonlinear response so strong that efficient FWM accumulates over wavelength-scale distances. This technique opens up nonlinear optics to a regime of relaxed phase matching, with the possibility of compact, broadband, and efficient frequency mixing integrated with silicon photonics.

Tu(r)ning weakness to strength: Mechanomutable bioinspired materials

DTIC Science & Technology

2017-04-03

into Strength,” Bio-inspired Materials, Potsdam, Germany March 2012 - “Nonlinear behaviour of silk minimizes damage and begets spider web robustness...atoms to structures – how spiders turn weakness into strength,” Society of Engineering Science Meeting, Atlanta, GA Keynote Lecture October 2012...Georgia Tech, October 19, 2015, Atlanta, GA October 2015 DISTRIBUTION A: Distribution approved for public release. 8 - "Multiscale materials by

Weakly nonlinear dynamics of near-CJ detonation waves

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

Bdzil, J.B.; Klein, R.

1993-01-01

The renewed interest in safety issues for large scale industrial devices and in high speed combustion has driven recent intense efforts to gain a deeper theoretical understanding of detonation wave dynamics. Linear stability analyses, weakly nonlinear bifurcation calculations as well as full scale multi-dimensional direct numerical simulations have been pursued for a standard model problem based on the reactive Euler equations for an ideal gas with constant specific heat capacities and simplified chemical reaction models. Most of these studies are concerned with overdriven detonations. This is true despite the fact that the majority of all detonations observed in nature aremore » running at speeds close to the Chapman-Jouguet (CJ) limit value. By focusing on overdriven waves one removes an array of difficulties from the analysis that is associated with the sonic flow conditions in the wake of a CJ-detonation. In particular, the proper formulation of downstream boundary conditions in the CJ-case is a yet unsolved analytical problem. A proper treatment of perturbations in the back of a Chapman-Jouguet detonation has to account for two distinct weakly nonlinear effects in the forward acoustic wave component. The first is a nonlinear interactionof highly temperature sensitive chemistry with the forward acoustic wave component in a transonic boundary layer near the end of the reaction zone. The second is a cumulative three-wave-resonance in the sense of Majda et al. which is active in the near-sonic burnt gas flow and which is essentially independent of the details of the chemical model. In this work, we consider detonations in mixtures with moderate state sensitivity of the chemical reactions. Then, the acoustic perturbations do not influence the chemistry at the order considered and we may concentrate on the second effect; the three-wave resonance.« less

Weakly nonlinear dynamics of near-CJ detonation waves

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

Bdzil, J.B.; Klein, R.

1993-02-01

The renewed interest in safety issues for large scale industrial devices and in high speed combustion has driven recent intense efforts to gain a deeper theoretical understanding of detonation wave dynamics. Linear stability analyses, weakly nonlinear bifurcation calculations as well as full scale multi-dimensional direct numerical simulations have been pursued for a standard model problem based on the reactive Euler equations for an ideal gas with constant specific heat capacities and simplified chemical reaction models. Most of these studies are concerned with overdriven detonations. This is true despite the fact that the majority of all detonations observed in nature aremore » running at speeds close to the Chapman-Jouguet (CJ) limit value. By focusing on overdriven waves one removes an array of difficulties from the analysis that is associated with the sonic flow conditions in the wake of a CJ-detonation. In particular, the proper formulation of downstream boundary conditions in the CJ-case is a yet unsolved analytical problem. A proper treatment of perturbations in the back of a Chapman-Jouguet detonation has to account for two distinct weakly nonlinear effects in the forward acoustic wave component. The first is a nonlinear interactionof highly temperature sensitive chemistry with the forward acoustic wave component in a transonic boundary layer near the end of the reaction zone. The second is a cumulative three-wave-resonance in the sense of Majda et al. which is active in the near-sonic burnt gas flow and which is essentially independent of the details of the chemical model. In this work, we consider detonations in mixtures with moderate state sensitivity of the chemical reactions. Then, the acoustic perturbations do not influence the chemistry at the order considered and we may concentrate on the second effect; the three-wave resonance.« less

Assessing the performance of formulations for nonlinear feedback of surface gravity waves on ocean currents over coastal waters

NASA Astrophysics Data System (ADS)

Wang, Pengcheng; Sheng, Jinyu; Hannah, Charles

2017-08-01

This study presents applications of a two-way coupled wave-circulation modelling system over coastal waters, with a special emphasis of performance assessments of two different methods for nonlinear feedback of ocean surface gravity waves on three-dimensional (3D) ocean currents. These two methods are the vortex force (VF) formulation suggested by Bennis et al. (2011) and the latest version of radiation stress (RS) formulation suggested by Mellor (2015). The coupled modelling system is first applied to two idealized test cases of surf-zone scales to validate implementations of these two methods in the coupled wave-circulation system. Model results show that the latest version of RS has difficulties in producing the undertow over the surf zone. The coupled system is then applied to Lunenburg Bay (LB) of Nova Scotia during Hurricane Juan in 2003. The coupled system using both the VF and RS formulations generates much stronger and more realistic 3D circulation in the Bay during Hurricane Juan than the circulation-only model, demonstrating the importance of surface wave forces to the 3D ocean circulation over coastal waters. However, the RS formulation generates some weak unphysical currents outside the wave breaking zone due to a less reasonable representation for the vertical distribution of the RS gradients over a slopping bottom. These weak unphysical currents are significantly magnified in a two-way coupled system when interacting with large surface waves, degrading the model performance in simulating currents at one observation site. Our results demonstrate that the VF formulation with an appropriate parameterization of wave breaking effects is able to produce reasonable results for applications over coastal waters during extreme weather events. The RS formulation requires a complex wave theory rather than the linear wave theory for the approximation of a vertical RS term to improve its performance under both breaking and non-breaking wave conditions.

Thermostatistically approaching living systems: Boltzmann Gibbs or nonextensive statistical mechanics?

NASA Astrophysics Data System (ADS)

Tsallis, Constantino

2006-03-01

Boltzmann-Gibbs ( BG) statistical mechanics is, since well over one century, successfully used for many nonlinear dynamical systems which, in one way or another, exhibit strong chaos. A typical case is a classical many-body short-range-interacting Hamiltonian system (e.g., the Lennard-Jones model for a real gas at moderately high temperature). Its Lyapunov spectrum (which characterizes the sensitivity to initial conditions) includes positive values. This leads to ergodicity, the stationary state being thermal equilibrium, hence standard applicability of the BG theory is verified. The situation appears to be of a different nature for various phenomena occurring in living organisms. Indeed, such systems exhibit a complexity which does not really accommodate with this standard dynamical behavior. Life appears to emerge and evolve in a kind of delicate situation, at the frontier between large order (low adaptability and long memory; typically characterized by regular dynamics, hence only nonpositive Lyapunov exponents) and large disorder (high adaptability and short memory; typically characterized by strong chaos, hence at least one positive Lyapunov exponent). Along this frontier, the maximal relevant Lyapunov exponents are either zero or close to that, characterizing what is currently referred to as weak chaos. This type of situation is shared by a great variety of similar complex phenomena in economics, linguistics, to cite but a few. BG statistical mechanics is built upon the entropy S=-k∑plnp. A generalization of this form, S=k(1-∑piq)/(q-1) (with S=S), has been proposed in 1988 as a basis for formulating what is nowadays currently called nonextensive statistical mechanics. This theory appears to be particularly adapted for nonlinear dynamical systems exhibiting, precisely, weak chaos. Here, we briefly review the theory, its dynamical foundation, its applications in a variety of disciplines (with special emphasis to living systems), and its connections with the ubiquitous scale-free networks.

Modeling the propagation of nonlinear three-dimensional acoustic beams in inhomogeneous media.

PubMed

Jing, Yuan; Cleveland, Robin O

2007-09-01

A three-dimensional model of the forward propagation of nonlinear sound beams in inhomogeneous media, a generalized Khokhlov-Zabolotskaya-Kuznetsov equation, is described. The Texas time-domain code (which accounts for paraxial diffraction, nonlinearity, thermoviscous absorption, and absorption and dispersion associated with multiple relaxation processes) was extended to solve for the propagation of nonlinear beams for the case where all medium properties vary in space. The code was validated with measurements of the nonlinear acoustic field generated by a phased array transducer operating at 2.5 MHz in water. A nonuniform layer of gel was employed to create an inhomogeneous medium. There was good agreement between the code and measurements in capturing the shift in the pressure distribution of both the fundamental and second harmonic due to the gel layer. The results indicate that the numerical tool described here is appropriate for propagation of nonlinear sound beams through weakly inhomogeneous media.

Self-induced parametric amplification arising from nonlinear elastic coupling in a micromechanical resonating disk gyroscope

PubMed Central

Nitzan, Sarah H.; Zega, Valentina; Li, Mo; Ahn, Chae H.; Corigliano, Alberto; Kenny, Thomas W.; Horsley, David A.

2015-01-01

Parametric amplification, resulting from intentionally varying a parameter in a resonator at twice its resonant frequency, has been successfully employed to increase the sensitivity of many micro- and nano-scale sensors. Here, we introduce the concept of self-induced parametric amplification, which arises naturally from nonlinear elastic coupling between the degenerate vibration modes in a micromechanical disk-resonator, and is not externally applied. The device functions as a gyroscope wherein angular rotation is detected from Coriolis coupling of elastic vibration energy from a driven vibration mode into a second degenerate sensing mode. While nonlinear elasticity in silicon resonators is extremely weak, in this high quality-factor device, ppm-level nonlinear elastic effects result in an order-of-magnitude increase in the observed sensitivity to Coriolis force relative to linear theory. Perfect degeneracy of the primary and secondary vibration modes is achieved through electrostatic frequency tuning, which also enables the phase and frequency of the parametric coupling to be varied, and we show that the resulting phase and frequency dependence of the amplification follow the theory of parametric resonance. We expect that this phenomenon will be useful for both fundamental studies of dynamic systems with low dissipation and for increasing signal-to-noise ratio in practical applications such as gyroscopes. PMID:25762243

Self-induced parametric amplification arising from nonlinear elastic coupling in a micromechanical resonating disk gyroscope.

PubMed

Nitzan, Sarah H; Zega, Valentina; Li, Mo; Ahn, Chae H; Corigliano, Alberto; Kenny, Thomas W; Horsley, David A

2015-03-12

Parametric amplification, resulting from intentionally varying a parameter in a resonator at twice its resonant frequency, has been successfully employed to increase the sensitivity of many micro- and nano-scale sensors. Here, we introduce the concept of self-induced parametric amplification, which arises naturally from nonlinear elastic coupling between the degenerate vibration modes in a micromechanical disk-resonator, and is not externally applied. The device functions as a gyroscope wherein angular rotation is detected from Coriolis coupling of elastic vibration energy from a driven vibration mode into a second degenerate sensing mode. While nonlinear elasticity in silicon resonators is extremely weak, in this high quality-factor device, ppm-level nonlinear elastic effects result in an order-of-magnitude increase in the observed sensitivity to Coriolis force relative to linear theory. Perfect degeneracy of the primary and secondary vibration modes is achieved through electrostatic frequency tuning, which also enables the phase and frequency of the parametric coupling to be varied, and we show that the resulting phase and frequency dependence of the amplification follow the theory of parametric resonance. We expect that this phenomenon will be useful for both fundamental studies of dynamic systems with low dissipation and for increasing signal-to-noise ratio in practical applications such as gyroscopes.

A Boussinesq-scaled, pressure-Poisson water wave model

NASA Astrophysics Data System (ADS)

Donahue, Aaron S.; Zhang, Yao; Kennedy, Andrew B.; Westerink, Joannes J.; Panda, Nishant; Dawson, Clint

2015-02-01

Through the use of Boussinesq scaling we develop and test a model for resolving non-hydrostatic pressure profiles in nonlinear wave systems over varying bathymetry. A Green-Nagdhi type polynomial expansion is used to resolve the pressure profile along the vertical axis, this is then inserted into the pressure-Poisson equation, retaining terms up to a prescribed order and solved using a weighted residual approach. The model shows rapid convergence properties with increasing order of polynomial expansion which can be greatly improved through the application of asymptotic rearrangement. Models of Boussinesq scaling of the fully nonlinear O (μ2) and weakly nonlinear O (μN) are presented, the analytical and numerical properties of O (μ2) and O (μ4) models are discussed. Optimal basis functions in the Green-Nagdhi expansion are determined through manipulation of the free-parameters which arise due to the Boussinesq scaling. The optimal O (μ2) model has dispersion accuracy equivalent to a Padé [2,2] approximation with one extra free-parameter. The optimal O (μ4) model obtains dispersion accuracy equivalent to a Padé [4,4] approximation with two free-parameters which can be used to optimize shoaling or nonlinear properties. In comparison to experimental results the O (μ4) model shows excellent agreement to experimental data.

The development of a mixing layer under the action of weak streamwise vortices

NASA Technical Reports Server (NTRS)

Goldstein, Marvin E.; Mathew, Joseph

1993-01-01

The action of weak, streamwise vortices on a plane, incompressible, steady mixing layer is examined in the large Reynolds-number limit. The outer, inviscid region is bounded by a vortex sheet to which the viscous region is confined. It is shown that the local linear analysis becomes invalid at streamwise distances O(epsilon(sup -1)), where epsilon is much less than 1 is the cross flow amplitude, and a new nonlinear analysis is constructed for this region. Numerical solutions of the nonlinear problem show that the vortex sheet undergoes an O(1) change in position and that the solution is ultimately terminated by the appearance of a singularity. The corresponding viscous layer shows downstream thickening, but appears to remain well behaved up to the singular location.

The development of a mixing layer under the action of weak streamwise vortices

NASA Technical Reports Server (NTRS)

Goldstein, M. E.; Mathew, Joseph

1993-01-01

The action of weak, streamwise vortices on a plane, incompressible, steady mixing layer is examined in the large Reynolds number limit. The outer, inviscid region is bounded by a vortex sheet to which the viscous region is confined. It is shown that the local linear analysis becomes invalid at streamwise distances O(epsilon sup -1), where (epsilon much less than 1) is the crossflow amplitude, and a new nonlinear analysis is constructed for this region. Numerical solutions of the nonlinear problem show that the vortex sheet undergoes an O(1) change in position and that the solution is ultimately terminated by a breakdown in the numerical procedure. The corresponding viscous layer shows downstream thickening, but appears to remain well behaved up to the terminal location.

Two-dimensional nonlinear finite element analysis of well damage due to reservoir compaction, well-to-well interactions, and localization on weak layers

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

Hilbert, L.B. Jr.; Fredrich, J.T.; Bruno, M.S.

1996-05-01

In this paper the authors present the results of a coupled nonlinear finite element geomechanics model for reservoir compaction and well-to-well interactions for the high-porosity, low strength diatomite reservoirs of the Belridge field near Bakersfield, California. They show that well damage and failures can occur under the action of two distinct mechanisms: shear deformations induced by pore compaction, and subsidence, and shear deformations due to well-to-well interactions during production or water injection. They show such casting damage or failure can be localized to weak layers that slide or slip under shear due to subsidence. The magnitude of shear displacements andmore » surface subsidence agree with field observations.« less

Nonlinear Schrödinger equation and classical-field description of thermal radiation

NASA Astrophysics Data System (ADS)

Rashkovskiy, Sergey A.

2018-03-01

It is shown that the thermal radiation can be described without quantization of energy in the framework of classical field theory using the nonlinear Schrödinger equation which is considered as a classical field equation. Planck's law for the spectral energy density of thermal radiation and the Einstein A-coefficient for spontaneous emission are derived without using the concept of the energy quanta. It is shown that the spectral energy density of thermal radiation is apparently not a universal function of frequency, as follows from the Planck's law, but depends weakly on the nature of atoms, while Planck's law is valid only as an approximation in the limit of weak excitation of atoms. Spin and relativistic effects are not considered in this paper.

SKA weak lensing - III. Added value of multiwavelength synergies for the mitigation of systematics

NASA Astrophysics Data System (ADS)

Camera, Stefano; Harrison, Ian; Bonaldi, Anna; Brown, Michael L.

2017-02-01

In this third paper of a series on radio weak lensing for cosmology with the Square Kilometre Array, we scrutinize synergies between cosmic shear measurements in the radio and optical/near-infrared (IR) bands for mitigating systematic effects. We focus on three main classes of systematics: (I) experimental systematic errors in the observed shear; (II) signal contamination by intrinsic alignments and (III) systematic effects due to an incorrect modelling of non-linear scales. First, we show that a comprehensive, multiwavelength analysis provides a self-calibration method for experimental systematic effects, only implying <50 per cent increment on the errors on cosmological parameters. We also illustrate how the cross-correlation between radio and optical/near-IR surveys alone is able to remove residual systematics with variance as large as 10-5, I.e. the same order of magnitude of the cosmological signal. This also opens the possibility of using such a cross-correlation as a means to detect unknown experimental systematics. Secondly, we demonstrate that, thanks to polarization information, radio weak lensing surveys will be able to mitigate contamination by intrinsic alignments, in a way similar but fully complementary to available self-calibration methods based on position-shear correlations. Lastly, we illustrate how radio weak lensing experiments, reaching higher redshifts than those accessible to optical surveys, will probe dark energy and the growth of cosmic structures in regimes less contaminated by non-linearities in the matter perturbations. For instance, the higher redshift bins of radio catalogues peak at z ≃ 0.8-1, whereas their optical/near-IR counterparts are limited to z ≲ 0.5-0.7. This translates into having a cosmological signal 2-5 times less contaminated by non-linear perturbations.

Global gradient estimates for divergence-type elliptic problems involving general nonlinear operators

NASA Astrophysics Data System (ADS)

Cho, Yumi

2018-05-01

We study nonlinear elliptic problems with nonstandard growth and ellipticity related to an N-function. We establish global Calderón-Zygmund estimates of the weak solutions in the framework of Orlicz spaces over bounded non-smooth domains. Moreover, we prove a global regularity result for asymptotically regular problems which are getting close to the regular problems considered, when the gradient variable goes to infinity.

Two types of nonlinear wave equations for diffractive beams in bubbly liquids with nonuniform bubble number density.

PubMed

Kanagawa, Tetsuya

2015-05-01

This paper theoretically treats the weakly nonlinear propagation of diffracted sound beams in nonuniform bubbly liquids. The spatial distribution of the number density of the bubbles, initially in a quiescent state, is assumed to be a slowly varying function of the spatial coordinates; the amplitude of variation is assumed to be small compared to the mean number density. A previous derivation method of nonlinear wave equations for plane progressive waves in uniform bubbly liquids [Kanagawa, Yano, Watanabe, and Fujikawa (2010). J. Fluid Sci. Technol. 5(3), 351-369] is extended to handle quasi-plane beams in weakly nonuniform bubbly liquids. The diffraction effect is incorporated by adding a relation that scales the circular sound source diameter to the wavelength into the original set of scaling relations composed of nondimensional physical parameters. A set of basic equations for bubbly flows is composed of the averaged equations of mass and momentum, the Keller equation for bubble wall, and supplementary equations. As a result, two types of evolution equations, a nonlinear Schrödinger equation including dissipation, diffraction, and nonuniform effects for high-frequency short-wavelength case, and a Khokhlov-Zabolotskaya-Kuznetsov equation including dispersion and nonuniform effects for low-frequency long-wavelength case, are derived from the basic set.

Stability of matter-wave solitons in optical lattices

NASA Astrophysics Data System (ADS)

Ali, Sk. Golam; Roy, S. K.; Talukdar, B.

2010-08-01

We consider localized states of both single- and two-component Bose-Einstein condensates (BECs) confined in a potential resulting from the superposition of linear and nonlinear optical lattices and make use of Vakhitov-Kolokolov criterion to investigate the effect of nonlinear lattice on the stability of the soliton solutions in the linear optical lattice (LOL). For the single-component case we show that a weak nonlinear lattice has very little effect on the stability of such solitons while sufficiently strong nonlinear optical lattice (NOL) squeezes them to produce narrow bound states. For two-component condensates we find that when the strength of the NOL (γ1) is less than that of the LOL (V0) a relatively weak intra-atomic interaction (IAI) has little effect on the stability of the component solitons. This is true for both attractive and repulsive IAI. A strong attractive IAI, however, squeezes the BEC solitons while a similar repulsive IAI makes the component solitons wider. For γ1 > V0, only a strong attractive IAI squeezes the BEC solitons but the squeezing effect is less prominent than that found for γ1 < V0. We make useful checks on the results of our semianalytical stability analysis by solving the appropriate Gross-Pitaevskii equations numerically.

Conical wave propagation and diffraction in two-dimensional hexagonally packed granular lattices

DOE PAGES

Chong, C.; Kevrekidis, P. G.; Ablowitz, M. J.; ...

2016-01-25

We explore linear and nonlinear mechanisms for conical wave propagation in two-dimensional lattices in the realm of phononic crystals. As a prototypical example, a statically compressed granular lattice of spherical particles arranged in a hexagonal packing configuration is analyzed. Upon identifying the dispersion relation of the underlying linear problem, the resulting diffraction properties are considered. Analysis both via a heuristic argument for the linear propagation of a wave packet and via asymptotic analysis leading to the derivation of a Dirac system suggests the occurrence of conical diffraction. This analysis is valid for strong precompression, i.e., near the linear regime. Formore » weak precompression, conical wave propagation is still possible, but the resulting expanding circular wave front is of a nonoscillatory nature, resulting from the complex interplay among the discreteness, nonlinearity, and geometry of the packing. Lastly, the transition between these two types of propagation is explored.« less

Nonlinear optics of fibre event horizons.

PubMed

Webb, Karen E; Erkintalo, Miro; Xu, Yiqing; Broderick, Neil G R; Dudley, John M; Genty, Goëry; Murdoch, Stuart G

2014-09-17

The nonlinear interaction of light in an optical fibre can mimic the physics at an event horizon. This analogue arises when a weak probe wave is unable to pass through an intense soliton, despite propagating at a different velocity. To date, these dynamics have been described in the time domain in terms of a soliton-induced refractive index barrier that modifies the velocity of the probe. Here we complete the physical description of fibre-optic event horizons by presenting a full frequency-domain description in terms of cascaded four-wave mixing between discrete single-frequency fields, and experimentally demonstrate signature frequency shifts using continuous wave lasers. Our description is confirmed by the remarkable agreement with experiments performed in the continuum limit, reached using ultrafast lasers. We anticipate that clarifying the description of fibre event horizons will significantly impact on the description of horizon dynamics and soliton interactions in photonics and other systems.

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

Energy and maximum norm estimates for nonlinear conservation laws

NASA Technical Reports Server (NTRS)

Olsson, Pelle; Oliger, Joseph

1994-01-01

We have devised a technique that makes it possible to obtain energy estimates for initial-boundary value problems for nonlinear conservation laws. The two major tools to achieve the energy estimates are a certain splitting of the flux vector derivative f(u)(sub x), and a structural hypothesis, referred to as a cone condition, on the flux vector f(u). These hypotheses are fulfilled for many equations that occur in practice, such as the Euler equations of gas dynamics. It should be noted that the energy estimates are obtained without any assumptions on the gradient of the solution u. The results extend to weak solutions that are obtained as point wise limits of vanishing viscosity solutions. As a byproduct we obtain explicit expressions for the entropy function and the entropy flux of symmetrizable systems of conservation laws. Under certain circumstances the proposed technique can be applied repeatedly so as to yield estimates in the maximum norm.

Antibunching and unconventional photon blockade with Gaussian squeezed states

NASA Astrophysics Data System (ADS)

Lemonde, Marc-Antoine; Didier, Nicolas; Clerk, Aashish A.

2014-12-01

Photon antibunching is a quantum phenomenon typically observed in strongly nonlinear systems where photon blockade suppresses the probability of detecting two photons at the same time. Antibunching has also been reported with Gaussian states, where optimized amplitude squeezing yields classically forbidden values of the intensity correlation, g(2 )(0 ) <1 . As a consequence, observation of antibunching is not necessarily a signature of photon-photon interactions. To clarify the significance of the intensity correlations, we derive a sufficient condition for deducing whether a field is non-Gaussian based on a g(2 )(0 ) measurement. We then show that the Gaussian antibunching obtained with a degenerate parametric amplifier is close to the ideal case reached using dissipative squeezing protocols. We finally shed light on the so-called unconventional photon blockade effect predicted in a driven two-cavity setup with surprisingly weak Kerr nonlinearities, stressing that it is a particular realization of optimized Gaussian amplitude squeezing.

Non-linear Heart Rate Variability as a Discriminator of Internalizing Psychopathology and Negative Affect in Children With Internalizing Problems and Healthy Controls

PubMed Central

Fiskum, Charlotte; Andersen, Tonje G.; Bornas, Xavier; Aslaksen, Per M.; Flaten, Magne A.; Jacobsen, Karl

2018-01-01

Background: Internalizing psychopathology and dysregulated negative affect are characterized by dysregulation in the autonomic nervous system and reduced heart rate variability (HRV) due to increases in sympathetic activity alongside reduced vagal tone. The neurovisceral system is however, a complex nonlinear system, and nonlinear indices related to psychopathology are so far less studied in children. Essential nonlinear properties of a system can be found in two main domains: the informational domain and the invariant domain. sample entropy (SampEn) is a much-used method from the informational domain, while detrended fluctuation analysis (DFA) represents a widely-used method from the invariant domain. To see if nonlinear HRV can provide information beyond linear indices of autonomic activation, this study investigated SampEn and DFA as discriminators of internalizing psychopathology and negative affect alongside measures of vagally-mediated HRV and sympathetic activation. Material and Methods: Thirty-Two children with internalizing difficulties and 25 healthy controls (aged 9–13) were assessed with the Child Behavior Checklist and the Early Adolescent Temperament Questionnaire, Revised, giving an estimate of internalizing psychopathology, negative affect and effortful control, a protective factor against psychopathology. Five minute electrocardiogram and impedance cardiography recordings were collected during a resting baseline, giving estimates of SampEn, DFA short-term scaling exponent α1, root mean square of successive differences (RMSSD), and pre-ejection period (PEP). Between-group differences and correlations were assessed with parametric and non-parametric tests, and the relationships between cardiac variables, psychopathology and negative affect were assessed using generalized linear modeling. Results: SampEn and DFA were not significantly different between the groups. SampEn was weakly negatively related to heart rate (HR) in the controls, while DFA was moderately negatively related to RMSSD in both groups, and moderately positively related to HR in the clinical sample. SampEn was significantly associated with internalizing psychopathology and negative affect. DFA was significantly related to internalizing psychopathology. Conclusions: Higher invariant self-similarity was linked to less psychopathology. Higher informational entropy was related to less psychopathology and less negative affect, and may provide an index of the organizational flexibility of the neurovisceral system. PMID:29875679

Non-linear Heart Rate Variability as a Discriminator of Internalizing Psychopathology and Negative Affect in Children With Internalizing Problems and Healthy Controls.

PubMed

Fiskum, Charlotte; Andersen, Tonje G; Bornas, Xavier; Aslaksen, Per M; Flaten, Magne A; Jacobsen, Karl

2018-01-01

Background: Internalizing psychopathology and dysregulated negative affect are characterized by dysregulation in the autonomic nervous system and reduced heart rate variability (HRV) due to increases in sympathetic activity alongside reduced vagal tone. The neurovisceral system is however, a complex nonlinear system, and nonlinear indices related to psychopathology are so far less studied in children. Essential nonlinear properties of a system can be found in two main domains: the informational domain and the invariant domain. sample entropy (SampEn) is a much-used method from the informational domain, while detrended fluctuation analysis (DFA) represents a widely-used method from the invariant domain. To see if nonlinear HRV can provide information beyond linear indices of autonomic activation, this study investigated SampEn and DFA as discriminators of internalizing psychopathology and negative affect alongside measures of vagally-mediated HRV and sympathetic activation. Material and Methods: Thirty-Two children with internalizing difficulties and 25 healthy controls (aged 9-13) were assessed with the Child Behavior Checklist and the Early Adolescent Temperament Questionnaire, Revised, giving an estimate of internalizing psychopathology, negative affect and effortful control, a protective factor against psychopathology. Five minute electrocardiogram and impedance cardiography recordings were collected during a resting baseline, giving estimates of SampEn, DFA short-term scaling exponent α 1 , root mean square of successive differences (RMSSD), and pre-ejection period (PEP). Between-group differences and correlations were assessed with parametric and non-parametric tests, and the relationships between cardiac variables, psychopathology and negative affect were assessed using generalized linear modeling. Results: SampEn and DFA were not significantly different between the groups. SampEn was weakly negatively related to heart rate (HR) in the controls, while DFA was moderately negatively related to RMSSD in both groups, and moderately positively related to HR in the clinical sample. SampEn was significantly associated with internalizing psychopathology and negative affect. DFA was significantly related to internalizing psychopathology. Conclusions: Higher invariant self-similarity was linked to less psychopathology. Higher informational entropy was related to less psychopathology and less negative affect, and may provide an index of the organizational flexibility of the neurovisceral system.

Optical measurement of the weak non-linearity in the eardrum vibration response to auditory stimuli

NASA Astrophysics Data System (ADS)

Aerts, Johan

The mammalian hearing organ consists of the external ear (auricle and ear canal) followed by the middle ear (eardrum and ossicles) and the inner ear (cochlea). Its function is to convert the incoming sound waves and convert them into nerve pulses which are processed in the final stage by the brain. The main task of the external and middle ear is to concentrate the incoming sound waves on a smaller surface to reduce the loss that would normally occur in transmission from air to inner ear fluid. In the past it has been shown that this is a linear process, thus without serious distortions, for sound waves going up to pressures of 130 dB SPL (˜90 Pa). However, at large pressure changes up to several kPa, the middle ear movement clearly shows non-linear behaviour. Thus, it is possible that some small non-linear distortions are also present in the middle ear vibration at lower sound pressures. In this thesis a sensitive measurement set-up is presented to detect this weak non-linear behaviour. Essentially, this set-up consists of a loud-speaker which excites the middle ear, and the resulting vibration is measured with an heterodyne vibrometer. The use of specially designed acoustic excitation signals (odd random phase multisines) enables the separation of the linear and non-linear response. The application of this technique on the middle ear demonstrates that there are already non-linear distortions present in the vibration of the middle ear at a sound pressure of 93 dB SPL. This non-linear component also grows strongly with increasing sound pressure. Knowledge of this non-linear component can contribute to the improvement of modern hearing aids, which operate at higher sound pressures where the non-linearities could distort the signal considerably. It is also important to know the contribution of middle ear non-linearity to otoacoustic emissions. This are non-linearities caused by the active feedback amplifier in the inner ear, and can be detected in the external and middle ear. These signals are used for diagnostic purposes, and therefore it is important to have an estimate the non-linear middle ear contribution to these emissions.

Dispersion in tidally averaged transport equation

USGS Publications Warehouse

Cheng, R.T.; Casulli, V.

1992-01-01

A general governing inter-tidal transport equation for conservative solutes has been derived without invoking the weakly nonlinear approximation. The governing inter-tidal transport equation is a convection-dispersion equation in which the convective velocity is a mean Lagrangian residual current, and the inter-tidal dispersion coefficient is defined by a dispersion patch. When the weakly nonlinear condition is violated, the physical significance of the Stokes' drift, as used in tidal dynamics, becomes questionable. For nonlinear problems, analytical solutions for the mean Lagrangian residual current and for the inter-tidal dispersion coefficient do not exist, they must be determined numerically. A rectangular tidal inlet with a constriction is used in the first example. The solutions of the residual currents and the computed properties of the inter-tidal dispersion coefficient are used to illuminate the mechanisms of the inter-tidal transport processes. Then, the present formulation is tested in a geometrically complex tidal estuary – San Francisco Bay, California. The computed inter-tidal dispersion coefficients are in the range between 5×104 and 5×106 cm2/sec., which are consistent with the values reported in the literature

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.

A Modal Model to Simulate Typical Structural Dynamic Nonlinearity [PowerPoint

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

Mayes, Randall L.; Pacini, Benjamin Robert; Roettgen, Dan

2016-01-01

Some initial investigations have been published which simulate nonlinear response with almost traditional modal models: instead of connecting the modal mass to ground through the traditional spring and damper, a nonlinear Iwan element was added. This assumes that the mode shapes do not change with amplitude and there are no interactions between modal degrees of freedom. This work expands on these previous studies. An impact experiment is performed on a structure which exhibits typical structural dynamic nonlinear response, i.e. weak frequency dependence and strong damping dependence on the amplitude of vibration. Use of low level modal test results in combinationmore » with high level impacts are processed using various combinations of modal filtering, the Hilbert Transform and band-pass filtering to develop response data that are then fit with various nonlinear elements to create a nonlinear pseudo-modal model. Simulations of forced response are compared with high level experimental data for various nonlinear element assumptions.« less

A Modal Model to Simulate Typical Structural Dynamic Nonlinearity

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

Pacini, Benjamin Robert; Mayes, Randall L.; Roettgen, Daniel R

2015-10-01

Some initial investigations have been published which simulate nonlinear response with almost traditional modal models: instead of connecting the modal mass to ground through the traditional spring and damper, a nonlinear Iwan element was added. This assumes that the mode shapes do not change with amplitude and there are no interactions between modal degrees of freedom. This work expands on these previous studies. An impact experiment is performed on a structure which exhibits typical structural dynamic nonlinear response, i.e. weak frequency dependence and strong damping dependence on the amplitude of vibration. Use of low level modal test results in combinationmore » with high level impacts are processed using various combinations of modal filtering, the Hilbert Transform and band-pass filtering to develop response data that are then fit with various nonlinear elements to create a nonlinear pseudo-modal model. Simulations of forced response are compared with high level experimental data for various nonlinear element assumptions.« less

Traveling wave solution of driven nonlinear Schrödinger equation

NASA Astrophysics Data System (ADS)

Akbari-Moghanjoughi, M.

2017-09-01

The traveling solitary and cnoidal wave solutions of the one dimensional driven nonlinear Schrödinger equation with a generalized form of nonlinearity are presented in this paper. We examine the modulation of nonlinear solitary excitations in two known weakly nonlinear models of classic oscillators, namely, the Helmholtz and Duffing oscillators and envelope structure formations for different oscillator and driver parameters. It is shown that two distinct regimes of subcritical and supercritical modulations may occur for nonlinear excitations with propagation speeds v <√{4 F0 } and v >√{4 F0 } , respectively, in which F0 is the driver force strength. The envelope soliton and cnoidal waves in these regimes are observed to be fundamentally different. The effect of pseudoenergy on the structure of the modulated envelope excitations is studied in detail for both sub- and supercritical modulation types. The current model for traveling envelope excitations may be easily extended to pseudopotentials with full nonlinearity relevant to more realistic gases, fluids, and plasmas.

Schlieren imaging of loud sounds and weak shock waves in air near the limit of visibility

NASA Astrophysics Data System (ADS)

Hargather, Michael John; Settles, Gary S.; Madalis, Matthew J.

2010-02-01

A large schlieren system with exceptional sensitivity and a high-speed digital camera are used to visualize loud sounds and a variety of common phenomena that produce weak shock waves in the atmosphere. Frame rates varied from 10,000 to 30,000 frames/s with microsecond frame exposures. Sound waves become visible to this instrumentation at frequencies above 10 kHz and sound pressure levels in the 110 dB (6.3 Pa) range and above. The density gradient produced by a weak shock wave is examined and found to depend upon the profile and thickness of the shock as well as the density difference across it. Schlieren visualizations of weak shock waves from common phenomena include loud trumpet notes, various impact phenomena that compress a bubble of air, bursting a toy balloon, popping a champagne cork, snapping a wooden stick, and snapping a wet towel. The balloon burst, snapping a ruler on a table, and snapping the towel and a leather belt all produced readily visible shock-wave phenomena. In contrast, clapping the hands, snapping the stick, and the champagne cork all produced wave trains that were near the weak limit of visibility. Overall, with sensitive optics and a modern high-speed camera, many nonlinear acoustic phenomena in the air can be observed and studied.

Early Warning Signals for Regime Transition in the Stable Boundary Layer: A Model Study

NASA Astrophysics Data System (ADS)

van Hooijdonk, I. G. S.; Moene, A. F.; Scheffer, M.; Clercx, H. J. H.; van de Wiel, B. J. H.

2017-02-01

The evening transition is investigated in an idealized model for the nocturnal boundary layer. From earlier studies it is known that the nocturnal boundary layer may manifest itself in two distinct regimes, depending on the ambient synoptic conditions: strong-wind or overcast conditions typically lead to weakly stable, turbulent nights; clear-sky and weak-wind conditions, on the other hand, lead to very stable, weakly turbulent conditions. Previously, the dynamical behaviour near the transition between these regimes was investigated in an idealized setting, relying on Monin-Obukhov (MO) similarity to describe turbulent transport. Here, we investigate a similar set-up, using direct numerical simulation; in contrast to MO-based models, this type of simulation does not need to rely on turbulence closure assumptions. We show that previous predictions are verified, but now independent of turbulence parametrizations. Also, it appears that a regime shift to the very stable state is signaled in advance by specific changes in the dynamics of the turbulent boundary layer. Here, we show how these changes may be used to infer a quantitative estimate of the transition point from the weakly stable boundary layer to the very stable boundary layer. In addition, it is shown that the idealized, nocturnal boundary-layer system shares important similarities with generic non-linear dynamical systems that exhibit critical transitions. Therefore, the presence of other, generic early warning signals is tested as well. Indeed, indications are found that such signals are present in stably stratified turbulent flows.

Global Well-posedness of the Spatially Homogeneous Kolmogorov-Vicsek Model as a Gradient Flow

NASA Astrophysics Data System (ADS)

Figalli, Alessio; Kang, Moon-Jin; Morales, Javier

2018-03-01

We consider the so-called spatially homogenous Kolmogorov-Vicsek model, a non-linear Fokker-Planck equation of self-driven stochastic particles with orientation interaction under the space-homogeneity. We prove the global existence and uniqueness of weak solutions to the equation. We also show that weak solutions exponentially converge to a steady state, which has the form of the Fisher-von Mises distribution.

Nonlinear saturation of the slab ITG instability and zonal flow generation with fully kinetic ions

NASA Astrophysics Data System (ADS)

Miecnikowski, Matthew T.; Sturdevant, Benjamin J.; Chen, Yang; Parker, Scott E.

2018-05-01

Fully kinetic turbulence models are of interest for their potential to validate or replace gyrokinetic models in plasma regimes where the gyrokinetic expansion parameters are marginal. Here, we demonstrate fully kinetic ion capability by simulating the growth and nonlinear saturation of the ion-temperature-gradient instability in shearless slab geometry assuming adiabatic electrons and including zonal flow dynamics. The ion trajectories are integrated using the Lorentz force, and the cyclotron motion is fully resolved. Linear growth and nonlinear saturation characteristics show excellent agreement with analogous gyrokinetic simulations across a wide range of parameters. The fully kinetic simulation accurately reproduces the nonlinearly generated zonal flow. This work demonstrates nonlinear capability, resolution of weak gradient drive, and zonal flow physics, which are critical aspects of modeling plasma turbulence with full ion dynamics.

Directed electromagnetic wave propagation in 1D metamaterial: Projecting operators method

NASA Astrophysics Data System (ADS)

Ampilogov, Dmitrii; Leble, Sergey

2016-07-01

We consider a boundary problem for 1D electrodynamics modeling of a pulse propagation in a metamaterial medium. We build and apply projecting operators to a Maxwell system in time domain that allows to split the linear propagation problem to directed waves for a material relations with general dispersion. Matrix elements of the projectors act as convolution integral operators. For a weak nonlinearity we generalize the linear results still for arbitrary dispersion and derive the system of interacting right/left waves with combined (hybrid) amplitudes. The result is specified for the popular metamaterial model with Drude formula for both permittivity and permeability coefficients. We also discuss and investigate stationary solutions of the system related to some boundary regimes.

Asynchronous error-correcting secure communication scheme based on fractional-order shifting chaotic system

NASA Astrophysics Data System (ADS)

Chao, Luo

2015-11-01

In this paper, a novel digital secure communication scheme is firstly proposed. Different from the usual secure communication schemes based on chaotic synchronization, the proposed scheme employs asynchronous communication which avoids the weakness of synchronous systems and is susceptible to environmental interference. Moreover, as to the transmission errors and data loss in the process of communication, the proposed scheme has the ability to be error-checking and error-correcting in real time. In order to guarantee security, the fractional-order complex chaotic system with the shifting of order is utilized to modulate the transmitted signal, which has high nonlinearity and complexity in both frequency and time domains. The corresponding numerical simulations demonstrate the effectiveness and feasibility of the scheme.

Theory of wing rock

NASA Technical Reports Server (NTRS)

Hsu, C.-H.; Lan, C. E.

1985-01-01

Wing rock is one type of lateral-directional instabilities at high angles of attack. To predict wing rock characteristics and to design airplanes to avoid wing rock, parameters affecting wing rock characteristics must be known. A new nonlinear aerodynamic model is developed to investigate the main aerodynamic nonlinearities causing wing rock. In the present theory, the Beecham-Titchener asymptotic method is used to derive expressions for the limit-cycle amplitude and frequency of wing rock from nonlinear flight dynamics equations. The resulting expressions are capable of explaining the existence of wing rock for all types of aircraft. Wing rock is developed by negative or weakly positive roll damping, and sustained by nonlinear aerodynamic roll damping. Good agreement between theoretical and experimental results is obtained.

Lax Integrability and the Peakon Problem for the Modified Camassa-Holm Equation

NASA Astrophysics Data System (ADS)

Chang, Xiangke; Szmigielski, Jacek

2018-02-01

Peakons are special weak solutions of a class of nonlinear partial differential equations modelling non-linear phenomena such as the breakdown of regularity and the onset of shocks. We show that the natural concept of weak solutions in the case of the modified Camassa-Holm equation studied in this paper is dictated by the distributional compatibility of its Lax pair and, as a result, it differs from the one proposed and used in the literature based on the concept of weak solutions used for equations of the Burgers type. Subsequently, we give a complete construction of peakon solutions satisfying the modified Camassa-Holm equation in the sense of distributions; our approach is based on solving certain inverse boundary value problem, the solution of which hinges on a combination of classical techniques of analysis involving Stieltjes' continued fractions and multi-point Padé approximations. We propose sufficient conditions needed to ensure the global existence of peakon solutions and analyze the large time asymptotic behaviour whose special features include a formation of pairs of peakons that share asymptotic speeds, as well as Toda-like sorting property.

The role of trauma scoring in developing trauma clinical governance in the Defence Medical Services

PubMed Central

Russell, R. J.; Hodgetts, T. J.; McLeod, J.; Starkey, K.; Mahoney, P.; Harrison, K.; Bell, E.

2011-01-01

This paper discusses mathematical models of expressing severity of injury and probability of survival following trauma and their use in establishing clinical governance of a trauma system. There are five sections: (i) Historical overview of scoring systems—anatomical, physiological and combined systems and the advantages and disadvantages of each. (ii) Definitions used in official statistics—definitions of ‘killed in action’ and other categories and the importance of casualty reporting rates and comparison across conflicts and nationalities. (iii) Current scoring systems and clinical governance—clinical governance of the trauma system in the Defence Medical Services (DMS) by using trauma scoring models to analyse injury and clinical patterns. (iv) Unexpected outcomes—unexpected outcomes focus clinical governance tools. Unexpected survivors signify good practice to be promulgated. Unexpected deaths pick up areas of weakness to be addressed. Seventy-five clinically validated unexpected survivors were identified over 2 years during contemporary combat operations. (v) Future developments—can the trauma scoring methods be improved? Trauma scoring systems use linear approaches and have significant weaknesses. Trauma and its treatment is a complex system. Nonlinear methods need to be investigated to determine whether these will produce a better approach to the analysis of the survival from major trauma. PMID:21149354

Tunable, high-sensitive measurement of inter-dot transition via tunneling induced absorption

NASA Astrophysics Data System (ADS)

Peng, Yandong; Yang, Aihong; Chen, Bing; Li, Lei; Liu, Shande; Guo, Hongju

2016-10-01

A tunable, narrow absorption spectrum induced by resonant tunneling is demonstrated and proposed for measuring interdot tunneling. Tunneling-induced absorption (TIA) arises from constructive interference between different transition paths, and the large nonlinear TIA significantly enhances the total absorption. The narrow nonlinear TIA spectrum is sensitive to inter-dot tunneling, and its sensor characteristics, including sensitivity and bandwidth, are investigated in weak-coupling and strong-coupling regimes, respectively.

Design of cladding rods-assisted depressed-core few-mode fibers with improved modal spacing

NASA Astrophysics Data System (ADS)

Han, Jiawei; Zhang, Jie

2018-03-01

This paper investigates the design details of cladding rods-assisted (CRA) depressed-core (DC) few-mode fibers (FMFs) that feature more equally spaced linearly polarized (LP) modal effective indices, suitable for high-spatial-density weakly-coupled mode-division multiplexing systems. The influences of the index profile of cladding rods on LP mode-resolved effective index, bending sensitivity, and effective area Aeff, are numerically described. Based on the design considerations of LP modal Aeff-dependent spatial efficiency and LP modal bending loss-dependent robustness, the small LP21-LP02 and LP22-LP03 modal spacing limitations, encountered in state-of-the-art weakly-coupled step-index FMFs, have been substantially improved by at least 25%. In addition, the proposed CRA DC FMFs also show sufficiently large effective areas (in excess of 110 μm2) for all guided LP modes, which are expected to exhibit good nonlinear performance.

Two-photon excited fluorescence from a pseudoisocyanine-attached gold-coated tip via a thin tapered fiber under a weak continuous wave excitation.

PubMed

Ren, Fang; Takashima, Hideaki; Tanaka, Yoshito; Fujiwara, Hideki; Sasaki, Keiji

2013-11-18

A simple tapered fiber based photonic-plasmonic hybrid nanostructure composed of a thin tapered fiber and a pseudoisocyanine (PIC)-attached Au-coated tip was demonstrated. Using this simple hybrid nanostructure, we succeeded in observing two-photon excited fluorescence from the PIC dye molecules under a weak continuous wave excitation condition. From the results of the tip-fiber distance dependence and excitation polarization dependence, we found that using a thin tapered fiber and an Au-coated tip realized efficient coupling of the incident light (~95%) and LSP excitation at the Au-coated tip, suggesting the possibility of efficiently inducing two-photon excited fluorescence from the PIC dye molecules attached on the Au-coated tip. This simple photonic-plasmonic hybrid system is one of the promising tools for single photon sources, highly efficient plasmonic sensors, and integrated nonlinear plasmonic devices.

Pressure-anisotropy-induced nonlinearities in the kinetic magnetorotational instability

NASA Astrophysics Data System (ADS)

Squire, J.; Quataert, E.; Kunz, M. W.

2017-12-01

In collisionless and weakly collisional plasmas, such as hot accretion flows onto compact objects, the magnetorotational instability (MRI) can differ significantly from the standard (collisional) MRI. In particular, pressure anisotropy with respect to the local magnetic-field direction can both change the linear MRI dispersion relation and cause nonlinear modifications to the mode structure and growth rate, even when the field and flow perturbations are very small. This work studies these pressure-anisotropy-induced nonlinearities in the weakly nonlinear, high-ion-beta regime, before the MRI saturates into strong turbulence. Our goal is to better understand how the saturation of the MRI in a low-collisionality plasma might differ from that in the collisional regime. We focus on two key effects: (i) the direct impact of self-induced pressure-anisotropy nonlinearities on the evolution of an MRI mode, and (ii) the influence of pressure anisotropy on the `parasitic instabilities' that are suspected to cause the mode to break up into turbulence. Our main conclusions are: (i) The mirror instability regulates the pressure anisotropy in such a way that the linear MRI in a collisionless plasma is an approximate nonlinear solution once the mode amplitude becomes larger than the background field (just as in magnetohyrodynamics). This implies that differences between the collisionless and collisional MRI become unimportant at large amplitudes. (ii) The break up of large-amplitude MRI modes into turbulence via parasitic instabilities is similar in collisionless and collisional plasmas. Together, these conclusions suggest that the route to magnetorotational turbulence in a collisionless plasma may well be similar to that in a collisional plasma, as suggested by recent kinetic simulations. As a supplement to these findings, we offer guidance for the design of future kinetic simulations of magnetorotational turbulence.

Detection the nonlinear ultrasonic signals based on modified Duffing equations

NASA Astrophysics Data System (ADS)

Zhang, Yuhua; Mao, Hanling; Mao, Hanying; Huang, Zhenfeng

The nonlinear ultrasonic signals, like second harmonic generation (SHG) signals, could reflect the nonlinearity of material induced by fatigue damage in nonlinear ultrasonic technique which are weak nonlinear signals and usually submerged by strong background noise. In this paper the modified Duffing equations are applied to detect the SHG signals relating to the fatigue damage of material. Due to the Duffing equation could only detect the signal with specific frequency and initial phase, firstly the frequency transformation is carried on the Duffing equation which could detect the signal with any frequency. Then the influence of initial phases of to-be-detected signal and reference signal on the detection result is studied in detail, four modified Duffing equations are proposed to detect actual engineering signals with any initial phase. The relationship between the response amplitude and the total driving force is applied to estimate the amplitude of weak periodic signal. The detection results show the modified Duffing equations could effectively detect the second harmonic in SHG signals. When the SHG signals include strong background noise, the noise doesn't change the motion state of Duffing equation and the second harmonic signal could be detected until the SNR of noisy SHG signals are -26.3, yet the frequency spectrum method could only identify when the SNR is greater than 0.5. When estimation the amplitude of second harmonic signal, the estimation error of Duffing equation is obviously less than the frequency spectrum analysis method under the same noise level, which illustrates the Duffing equation has the noise immune capacity. The presence of the second harmonic signal in nonlinear ultrasonic experiments could provide an insight about the early fatigue damage of engineering components.

Traveling wave solutions of the nonlinear Schrödinger equation

NASA Astrophysics Data System (ADS)

Akbari-Moghanjoughi, M.

2017-10-01

In this paper, we investigate the traveling soliton and the periodic wave solutions of the nonlinear Schrödinger equation (NLSE) with generalized nonlinear functionality. We also explore the underlying close connection between the well-known KdV equation and the NLSE. It is remarked that both one-dimensional KdV and NLSE models share the same pseudoenergy spectrum. We also derive the traveling wave solutions for two cases of weakly nonlinear mathematical models, namely, the Helmholtz and the Duffing oscillators' potentials. It is found that these models only allow gray-type NLSE solitary propagations. It is also found that the pseudofrequency ratio for the Helmholtz potential between the nonlinear periodic carrier and the modulated sinusoidal waves is always in the range 0.5 ≤ Ω/ω ≤ 0.537285 regardless of the potential parameter values. The values of Ω/ω = {0.5, 0.537285} correspond to the cnoidal waves modulus of m = {0, 1} for soliton and sinusoidal limits and m = 0.5, respectively. Moreover, the current NLSE model is extended to fully NLSE (FNLSE) situation for Sagdeev oscillator pseudopotential which can be derived using a closed set of hydrodynamic fluid equations with a fully integrable Hamiltonian system. The generalized quasi-three-dimensional traveling wave solution is also derived. The current simple hydrodynamic plasma model may also be generalized to two dimensions and other complex situations including different charged species and cases with magnetic or gravitational field effects.

Moderately nonlinear ultrasound propagation in blood-mimicking fluid.

PubMed

Kharin, Nikolay A; Vince, D Geoffrey

2004-04-01

In medical diagnostic ultrasound (US), higher than-in-water nonlinearity of body fluids and tissue usually does not produce strong nonlinearly distorted waves because of the high absorption. The relative influence of absorption and nonlinearity can be characterized by the Gol'dberg number Gamma. There are two limiting cases in nonlinear acoustics: weak waves (Gamma < 1) or strong waves (Gamma > 1). However, at diagnostic frequencies in tissue and body fluids, the nonlinear effects and effects of absorption more likely are comparable (Gol'dberg number Gamma approximately 1). The aim of this work was to study the nonlinear propagation of a moderately nonlinear US second harmonic signal in a blood-mimicking fluid. Quasilinear solutions to the KZK equation are presented, assuming radiation from a flat and geometrically focused circular Gaussian source. The solutions are expressed in a new simplified closed form and are in very good agreement with those of previous studies measuring and modeling Gaussian beams. The solutions also show good agreement with the measurements of the beams produced by commercially available transducers, even without special Gaussian shading.

Shock waves in weakly compressed granular media.

PubMed

van den Wildenberg, Siet; van Loo, Rogier; van Hecke, Martin

2013-11-22

We experimentally probe nonlinear wave propagation in weakly compressed granular media and observe a crossover from quasilinear sound waves at low impact to shock waves at high impact. We show that this crossover impact grows with the confining pressure P0, whereas the shock wave speed is independent of P0-two hallmarks of granular shocks predicted recently. The shocks exhibit surprising power law attenuation, which we model with a logarithmic law implying that shock dissipation is weak and qualitatively different from other granular dissipation mechanisms. We show that elastic and potential energy balance in the leading part of the shocks.

Vector solitons in coupled nonlinear Schrödinger equations with spatial stimulated scattering and inhomogeneous dispersion

NASA Astrophysics Data System (ADS)

Gromov, E. M.; Malomed, B. A.; Tyutin, V. V.

2018-01-01

The dynamics of two-component solitons is studied, analytically and numerically, in the framework of a system of coupled extended nonlinear Schrödinger equations, which incorporate the cross-phase modulation, pseudo-stimulated-Raman-scattering (pseudo-SRS), cross-pseudo-SRS, and spatially inhomogeneous second-order dispersion (SOD). The system models co-propagation of electromagnetic waves with orthogonal polarizations in plasmas. It is shown that the soliton's wavenumber downshift, caused by pseudo-SRS, may be compensated by an upshift, induced by the inhomogeneous SOD, to produce stable stationary two-component solitons. The corresponding approximate analytical solutions for stable solitons are found. Analytical results are well confirmed by their numerical counterparts. Further, the evolution of inputs composed of spatially even and odd components is investigated by means of systematic simulations, which reveal three different outcomes: formation of a breather which keeps opposite parities of the components; splitting into a pair of separating vector solitons; and spreading of the weak odd component into a small-amplitude pedestal with an embedded dark soliton.

Optical proposals for controlled delayed-choice experiment based on weak cross-Kerr nonlinearities

NASA Astrophysics Data System (ADS)

Dong, Li; Lin, Yan-Fang; Li, Qing-Yang; Xiu, Xiao-Ming; Dong, Hai-Kuan; Gao, Ya-Jun

2017-05-01

Employing polarization modes of a photon, we propose two theoretical proposals to exhibit the wave-particle duality of the photon with the assistance of weak cross-Kerr nonlinearities. The first proposal is a classical controlled delayed-choice experiment (that is, Wheeler's delayed-choice experiment), where we can observe selectively wave property or particle property of the photon relying on the experimenter's selection, whereas the second proposal is a quantum controlled delayed-choice experiment, by which the mixture phenomenon of a wave and a particle will be exhibited. Both of them can be realized with near-unity probability and embody the charming characteristics of quantum mechanics. The employment of the mature techniques and simple operations (e.g., Homodyne measurement, classical feed forward, and single-photon transformations) provides the feasibility of the delayed-choice experiment proposals presented here.

DEMNUni: ISW, Rees-Sciama, and weak-lensing in the presence of massive neutrinos

NASA Astrophysics Data System (ADS)

Carbone, Carmelita; Petkova, Margarita; Dolag, Klaus

2016-07-01

We present, for the first time in the literature, a full reconstruction of the total (linear and non-linear) ISW/Rees-Sciama effect in the presence of massive neutrinos, together with its cross-correlations with CMB-lensing and weak-lensing signals. The present analyses make use of all-sky maps extracted via ray-tracing across the gravitational potential distribution provided by the ``Dark Energy and Massive Neutrino Universe'' (DEMNUni) project, a set of large-volume, high-resolution cosmological N-body simulations, where neutrinos are treated as separate collisionless particles. We correctly recover, at 1-2% accuracy, the linear predictions from CAMB. Concerning the CMB-lensing and weak-lensing signals, we also recover, with similar accuracy, the signal predicted by Boltzmann codes, once non-linear neutrino corrections to HALOFIT are accounted for. Interestingly, in the ISW/Rees-Sciama signal, and its cross correlation with lensing, we find an excess of power with respect to the massless case, due to free streaming neutrinos, roughly at the transition scale between the linear and non-linear regimes. The excess is ~ 5 - 10% at l ~ 100 for the ISW/Rees-Sciama auto power spectrum, depending on the total neutrino mass Mν, and becomes a factor of ~ 4 for Mν = 0.3 eV, at l ~ 600, for the ISW/Rees-Sciama cross power with CMB-lensing. This effect should be taken into account for the correct estimation of the CMB temperature bispectrum in the presence of massive neutrinos.

Characteristics of solitary waves in a relativistic degenerate ion beam driven magneto plasma

NASA Astrophysics Data System (ADS)

Deka, Manoj Kr.; Dev, Apul N.; Misra, Amar P.; Adhikary, Nirab C.

2018-01-01

The nonlinear propagation of a small amplitude ion acoustic solitary wave in a relativistic degenerate magneto plasma in the presence of an ion beam is investigated in detail. The nonlinear equations describing the evolution of a solitary wave in the presence of relativistic non-degenerate magnetized positive ions and ion beams including magnetized degenerate relativistic electrons are derived in terms of Zakharov-Kuznetsov (Z-K) equation for such plasma systems. The ion beams which are a ubiquitous ingredient in such plasma systems are found to have a decisive role in the propagation of a solitary wave in such a highly dense plasma system. The conditions of a wave, propagating with typical solitonic characteristics, are examined and discussed in detail under suitable conditions of different physical parameters. Both a subsonic and supersonic wave can propagate in such plasmas bearing different characteristics under different physical situations. A detailed analysis of waves propagating in subsonic and/or supersonic regime is carried out. The ion beam concentrations, magnetic field, as well as ion beam streaming velocity are found to play a momentous role on the control of the amplitude and width of small amplitude perturbation in both weakly (or non-relativistic) and relativistic plasmas.

Soret and Dufour effects on thermohaline convection in rotating fluids

NASA Astrophysics Data System (ADS)

Duba, C. T.; Shekar, M.; Narayana, M.; Sibanda, P.

2016-07-01

Using linear and weakly nonlinear stability theory, the effects of Soret and Dufour parameters are investigated on thermohaline convection in a horizontal layer of rotating fluid, specifically the ocean. Thermohaline circulation is important in mixing processes and contributes to heat and mass transports and hence the earth's climate. A general conception is that due to the smallness of the Soret and Dufour parameters their effect is negligible. However, it is shown here that the Soret parameter, salinity and rotation stabilise the system, whereas temperature destabilises it and the Dufour parameter has minimal effect on stationary convection. For oscillatory convection, the analysis is difficult as it shows that the Rayleigh number depends on six parameters, the Soret and Dufour parameters, the salinity Rayleigh number, the Lewis number, the Prandtl number, and the Taylor number. We demonstrate the interplay between these parameters and their effects on oscillatory convection in a graphical manner. Furthermore, we find that the Soret parameter enhances oscillatory convection whereas the Dufour parameter, salinity Rayleigh number, the Lewis number, and rotation delay instability. We believe that these results have not been elucidated in this way before for large-scale fluids. Furthermore, we investigate weakly nonlinear stability and the effect of cross diffusive terms on heat and mass transports. We show the existence of new solution bifurcations not previously identified in literature.

Workshop on Coherent Structure of Turbulent Boundary Layers.

DTIC Science & Technology

1978-11-01

indicate the occurrence of "internal fronts" of ejected parcels of slightly heated fluid from the region near the wall out to the intermit - tent region...doesn’t lift very fast . Which indicates that the vorticity lifting it up is rather weak after that. Blackwelder: What would you call weak, in terms of...developed to handle nonlinear wall boundary conditions using techniques for fast conformal transformation recently developed by the author.] It follows

Excitation and propagation of nonlinear waves in a rotating fluid

NASA Astrophysics Data System (ADS)

Hanazaki, Hideshi

1993-09-01

A numerical study of the nonlinear waves excited in an axisymmetric rotating flow through a circular tube is described. The waves are excited by either an undulation of the tube wall or an obstacle on the axis of the tube. The results are compared with the weakly nonlinear theory (forced KdV equation). The computations are done when the upstream swirling velocity is that of Burgers' vortex type. The flow behaves like the solution of the forced KdV equation, and the upstream advancing of the waves appear even when the flow is critical or slightly supercritical to the fastest inertial wave mode.

Theory of wing rock

NASA Technical Reports Server (NTRS)

Hsu, C. H.; Lan, C. E.

1984-01-01

A theory is developed for predicting wing rock characteristics. From available data, it can be concluded that wing rock is triggered by flow asymmetries, developed by negative or weakly positive roll damping, and sustained by nonlinear aerodynamic roll damping. A new nonlinear aerodynamic model that includes all essential aerodynamic nonlinearities is developed. The Beecham-Titchener method is applied to obtain approximate analytic solutions for the amplitude and frequency of the limit cycle based on the three degree-of-freedom equations of motion. An iterative scheme is developed to calculate the average aerodynamic derivatives and dynamic characteristics at limit cycle conditions. Good agreement between theoretical and experimental results is obtained.

Finite-amplitude, pulsed, ultrasonic beams

NASA Astrophysics Data System (ADS)

Coulouvrat, François; Frøysa, Kjell-Eivind

An analytical, approximate solution of the inviscid KZK equation for a nonlinear pulsed sound beam radiated by an acoustic source with a Gaussian velocity distribution, is obtained by means of the renormalization method. This method involves two steps. First, the transient, weakly nonlinear field is computed. However, because of cumulative nonlinear effects, that expansion is non-uniform and breaks down at some distance away from the source. So, in order to extend its validity, it is re-written in a new frame of co-ordinates, better suited to following the nonlinear distorsion of the wave profile. Basically, the nonlinear coordinate transform introduces additional terms in the expansion, which are chosen so as to counterbalance the non-uniform ones. Special care is devoted to the treatment of shock waves. Finally, comparisons with the results of a finite-difference scheme turn out favorable, and show the efficiency of the method for a rather large range of parameters.

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.

Nonlinear and Dissipation Characteristics of Ocean Surface Waves in Estuarine Environments

DTIC Science & Technology

2010-01-01

determines the time scale over which the interactions occur, in the manner of Hill and Foda (1998) and Jamali et al. (2003). RESULTS Contrary to...the intermediate-depth work of Hill and Foda (1998) and Jamali et al. (2003), the interactions in this wealky-dispersive, weakly-nonlinear model...occur very quickly. Figure 1 shows the amplitude of one surface wave mode and two interface mode as a function of time resulting from the analysis . We

Simulating the effect of non-linear mode coupling in cosmological parameter estimation

NASA Astrophysics Data System (ADS)

Kiessling, A.; Taylor, A. N.; Heavens, A. F.

2011-09-01

Fisher Information Matrix methods are commonly used in cosmology to estimate the accuracy that cosmological parameters can be measured with a given experiment and to optimize the design of experiments. However, the standard approach usually assumes both data and parameter estimates are Gaussian-distributed. Further, for survey forecasts and optimization it is usually assumed that the power-spectrum covariance matrix is diagonal in Fourier space. However, in the low-redshift Universe, non-linear mode coupling will tend to correlate small-scale power, moving information from lower to higher order moments of the field. This movement of information will change the predictions of cosmological parameter accuracy. In this paper we quantify this loss of information by comparing naïve Gaussian Fisher matrix forecasts with a maximum likelihood parameter estimation analysis of a suite of mock weak lensing catalogues derived from N-body simulations, based on the SUNGLASS pipeline, for a 2D and tomographic shear analysis of a Euclid-like survey. In both cases, we find that the 68 per cent confidence area of the Ωm-σ8 plane increases by a factor of 5. However, the marginal errors increase by just 20-40 per cent. We propose a new method to model the effects of non-linear shear-power mode coupling in the Fisher matrix by approximating the shear-power distribution as a multivariate Gaussian with a covariance matrix derived from the mock weak lensing survey. We find that this approximation can reproduce the 68 per cent confidence regions of the full maximum likelihood analysis in the Ωm-σ8 plane to high accuracy for both 2D and tomographic weak lensing surveys. Finally, we perform a multiparameter analysis of Ωm, σ8, h, ns, w0 and wa to compare the Gaussian and non-linear mode-coupled Fisher matrix contours. The 6D volume of the 1σ error contours for the non-linear Fisher analysis is a factor of 3 larger than for the Gaussian case, and the shape of the 68 per cent confidence volume is modified. We propose that future Fisher matrix estimates of cosmological parameter accuracies should include mode-coupling effects.

Detuned resonances of Tollmien-Schlichting waves in an airfoil boundary layer: Experiment, theory, and direct numerical simulation

NASA Astrophysics Data System (ADS)

Würz, W.; Sartorius, D.; Kloker, M.; Borodulin, V. I.; Kachanov, Y. S.; Smorodsky, B. V.

2012-09-01

Transition prediction in two-dimensional laminar boundary layers developing on airfoil sections at subsonic speeds and very low turbulence levels is still a challenge. The commonly used semi-empirical prediction tools are mainly based on linear stability theory and do not account for nonlinear effects present unavoidably starting with certain stages of transition. One reason is the lack of systematic investigations of the weakly nonlinear stages of transition, especially of the strongest interactions of the instability modes predominant in non-self-similar boundary layers. The present paper is devoted to the detailed experimental, numerical, and theoretical study of weakly nonlinear subharmonic resonances of Tollmien-Schlichting waves in an airfoil boundary layer, representing main candidates for the strongest mechanism of these initial nonlinear stages. The experimental approach is based on phase-locked hot-wire measurements under controlled disturbance conditions using a new disturbance source being capable to produce well-defined, complex wave compositions in a wide range of streamwise and spanwise wave numbers. The tests were performed in a low-turbulence wind tunnel at a chord Reynolds number of Re = 0.7 × 106. Direct numerical simulations (DNS) were utilized to provide a detailed comparison for the test cases. The results of weakly nonlinear theory (WNT) enabled a profound understanding of the underlying physical mechanisms observed in the experiments and DNS. The data obtained in experiment, DNS and WNT agree basically and provide a high degree of reliability of the results. Interactions occurring between components of various initial frequency-wavenumber spectra of instability waves are investigated by systematic variation of parameters. It is shown that frequency-detuned and spanwise-wavenumber-detuned subharmonic-type resonant interactions have an extremely large spectral width. Similar to results obtained for self-similar base flows it is found that the amplification factors in the frequency-detuned resonances can be even higher than in tuned cases, in spite of the strong base-flow non-self-similarity. An explanation of this unusual phenomenon is found based on the theoretical analysis and comparison of experimental, theoretical, and DNS data.

Nonlinear dynamics analysis of the human balance control subjected to physical and sensory perturbations.

PubMed

Ashtiani, Mohammed N; Mahmood-Reza, Azghani

2017-01-01

Postural control after applying perturbation involves neural and muscular efforts to limit the center of mass (CoM) motion. Linear dynamical approaches may not unveil all complexities of body efforts. This study was aimed at determining two nonlinear dynamics parameters (fractal dimension (FD) and largest Lyapunov exponent (LLE)) in addition to the linear standing metrics of balance in perturbed stance. Sixteen healthy young males were subjected to sudden rotations of the standing platform. The vision and cognition during the standing were also interfered. Motion capturing was used to measure the lower limb joints and the CoM displacements. The CoM path length as a linear parameter was increased by elimination of vision (p<0.01) and adding a cognitive load (p<0.01). The CoM nonlinear metric FD was decreased due to the cognitive loads (p<0.001). The visual interference increased the FD of all joints when the task included the cognitive loads (p<0.01). The slightly positive LLE values showed weakly-chaotic behavior of the whole body. The local joint rotations indicated higher LLEs. Results indicated weakly chaotic response of the whole body. Increase in the task difficulty by adding sensory interference had difference effects on parameters. Linear and nonlinear metrics of the perturbed stance showed that a combination of them may properly represent the body behavior.

Instability analysis of cosmic viscoelastic gyro-gravitating clouds in the presence of dark matter

NASA Astrophysics Data System (ADS)

Karmakar, Pralay Kumar; Das, Papari

2017-08-01

A classical formalism for the weakly nonlinear instability analysis of a gravitating rotating viscoelastic gaseous cloud in the presence of gyratory dark matter is presented on the cosmic Jeans flat scales of space and time. The constituent neutral gaseous fluid (NGF) and dark matter fluid (DMF) are inter-coupled frictionally via mutual gravity alone. Application of standard nonlinear perturbation techniques over the complex gyro-gravitating clouds results in a unique conjugated pair of viscoelastic forced Burgers (VFB) equations. The VFB pair is conjointly twinned by correlational viscoelastic effects. There is no regular damping term here, unlike, in the conventional Burgers equation for the luminous (bright) matter solely. Instead, an interesting linear self-consistent derivative force-term naturalistically appears. A numerical illustrative platform is provided to reveal the micro-physical insights behind the weakly non-linear natural diffusive eigen-modes. It is fantastically seen that the perturbed NGF evolves as extended compressive solitons and compressive shock-like structures. In contrast, the perturbed DMF grows as rarefactive extended solitons and hybrid shocks. The latter is micro-physically composed of rarefactive solitons and compressive shocks. The consistency and reliability of the results are validated in the panoptic light of the existing reports based on the preeminent nonlinear advection-diffusion-based Burgers fabric. At the last, we highlight the main implications and non-trivial futuristic applications of the explored findings.

Simulation of Non-resonant Internal Kink Mode with Toroidal Rotation in NSTX

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

Fu, Guoyong

2013-07-16

Plasmas in spherical and conventional tokamaks, with weakly reversed shear q pro le and minimum q above but close to unity, are susceptible to an non-resonant (m, n ) = (1, 1) internal kink mode. This mode can saturate and persist and can induce a (2; 1) seed island for Neoclassical Tearing Mode (NTMs)1 . The mode can also lead to large energetic particle transport and signi cant broadening of beam-driven current. Motivated by these important e ects, we have carried out extensive nonlinear simulations of the mode with nite toroidal rotation using parameters and pro les of an NTSXmore » plasma with a weakly reversed shear pro le. The numerical results show that, at the experimental level, plasma rotation has little e ect on either equilibrium or linear stability. However, rotation can signi cantly inuence the nonlinear dynamics of the (1, 1) mode and the the induced (2, 1) magnetic island. The simulation results show that a rotating helical equilibrium is formed and maintained in the nonlinear phase at nite plasma rotation. In contrast, for non-rotating cases, the nonlinear evolution exhibits dynamic oscillations between a quasi-2D state and a helical state. Furthermore, the e ects of rotation are found to greatly suppress the (2, 1) magnetic island even at a low level.« less

Nonlinear Ion Harmonics in the Paul Trap with Added Octopole Field: Theoretical Characterization and New Insight into Nonlinear Resonance Effect.

PubMed

Xiong, Caiqiao; Zhou, Xiaoyu; Zhang, Ning; Zhan, Lingpeng; Chen, Yongtai; Nie, Zongxiu

2016-02-01

The nonlinear harmonics within the ion motion are the fingerprint of the nonlinear fields. They are exclusively introduced by these nonlinear fields and are responsible to some specific nonlinear effects such as nonlinear resonance effect. In this article, the ion motion in the quadrupole field with a weak superimposed octopole component, described by the nonlinear Mathieu equation (NME), was studied by using the analytical harmonic balance (HB) method. Good accuracy of the HB method, which was comparable with that of the numerical fourth-order Runge-Kutta (4th RK), was achieved in the entire first stability region, except for the points at the stability boundary (i.e., β = 1) and at the nonlinear resonance condition (i.e., β = 0.5). Using the HB method, the nonlinear 3β harmonic series introduced by the octopole component and the resultant nonlinear resonance effect were characterized. At nonlinear resonance, obvious resonant peaks were observed in the nonlinear 3β series of ion motion, but were not found in the natural harmonics. In addition, both resonant excitation and absorption peaks could be observed, simultaneously. These are two unique features of the nonlinear resonance, distinguishing it from the normal resonance. Finally, an approximation equation was given to describe the corresponding working parameter, q nr , at nonlinear resonance. This equation can help avoid the sensitivity degradation due to the operation of ion traps at the nonlinear resonance condition.

Weakly Nonlinear Rayleigh–Taylor Instability in Cylindrically Convergent Geometry

NASA Astrophysics Data System (ADS)

Guo, Hong-Yu; Wang, Li-Feng; Ye, Wen-Hua; Wu, Jun-Feng; Zhang, Wei-Yan

2018-05-01

Not Available Supported by the National Natural Science Foundation of China under Grant Nos 11275031, 11475034, 11575033 and 11274026, and the National Basic Research Program of China under Grant No 2013CB834100.

A statistical approach to EMI - Theory and experiment

NASA Astrophysics Data System (ADS)

Weiner, Donald; Capraro, Gerard

A probabilistic approach to electromagnetic interference (EMI) is presented. The approach is illustrated by analyzing an experimental circuit in which EMI occurs. Both random and weakly nonlinear effects are accounted for in the analysis.

Nonlinear mechanics of thermoreversibly associating dendrimer glasses

NASA Astrophysics Data System (ADS)

Srikanth, Arvind; Hoy, Robert S.; Rinderspacher, Berend C.; Andzelm, Jan W.

2013-10-01

We model the mechanics of associating trivalent dendrimer network glasses with a focus on their energy dissipation properties. Various combinations of sticky bond (SB) strength and kinetics are employed. The toughness (work to fracture) of these systems displays a surprising deformation-protocol dependence; different association parameters optimize different properties. In particular, “strong, slow” SBs optimize strength, while “weak, fast” SBs optimize ductility via self-healing during deformation. We relate these observations to breaking, reformation, and partner switching of SBs during deformation. These studies point the way to creating associating-polymer network glasses with tailorable mechanical properties.

Strain-enhanced stress relaxation impacts nonlinear elasticity in collagen gels

PubMed Central

Nam, Sungmin; Hu, Kenneth H.; Chaudhuri, Ovijit

2016-01-01

The extracellular matrix (ECM) is a complex assembly of structural proteins that provides physical support and biochemical signaling to cells in tissues. The mechanical properties of the ECM have been found to play a key role in regulating cell behaviors such as differentiation and malignancy. Gels formed from ECM protein biopolymers such as collagen or fibrin are commonly used for 3D cell culture models of tissue. One of the most striking features of these gels is that they exhibit nonlinear elasticity, undergoing strain stiffening. However, these gels are also viscoelastic and exhibit stress relaxation, with the resistance of the gel to a deformation relaxing over time. Recent studies have suggested that cells sense and respond to both nonlinear elasticity and viscoelasticity of ECM, yet little is known about the connection between nonlinear elasticity and viscoelasticity. Here, we report that, as strain is increased, not only do biopolymer gels stiffen but they also exhibit faster stress relaxation, reducing the timescale over which elastic energy is dissipated. This effect is not universal to all biological gels and is mediated through weak cross-links. Mechanistically, computational modeling and atomic force microscopy (AFM) indicate that strain-enhanced stress relaxation of collagen gels arises from force-dependent unbinding of weak bonds between collagen fibers. The broader effect of strain-enhanced stress relaxation is to rapidly diminish strain stiffening over time. These results reveal the interplay between nonlinear elasticity and viscoelasticity in collagen gels, and highlight the complexity of the ECM mechanics that are likely sensed through cellular mechanotransduction. PMID:27140623

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

Nonlinear convective analysis of a rotating Oldroyd-B nanofluid layer under thermal non-equilibrium utilizing Al2O3-EG colloidal suspension

NASA Astrophysics Data System (ADS)

Agarwal, Shilpi; Rana, Puneet

2016-04-01

In this paper, we examine a layer of Oldroyd-B nanofluid for linear and nonlinear regimes under local thermal non-equilibrium conditions for the classical Rayleigh-Bénard problem. The free-free boundary condition has been implemented with the flux for nanoparticle concentration being zero at edges. The Oberbeck-Boussinesq approximation holds good and for the rotational effect Coriolis term is included in the momentum equation. A two-temperature model explains the effect of local thermal non-equilibrium among the particle and fluid phases. The criteria for onset of stationary convection has been derived as a function of the non-dimensionalized parameters involved including the Taylor number. The assumed boundary conditions negate the possibility of overstability due to the absence of opposing forces responsible for it. The thermal Nusselt number has been obtained utilizing a weak nonlinear theory in terms of various pertinent parameters in the steady and transient mode, and has been depicted graphically. The main findings signify that the rotation has a stabilizing effect on the system. The stress relaxation parameter λ_1 inhibits whereas the strain retardation parameter λ_2 exhibits heat transfer utilizing Al2O3 nanofluids.

Convection and reaction in a diffusive boundary layer in a porous medium: nonlinear dynamics.

PubMed

Andres, Jeanne Therese H; Cardoso, Silvana S S

2012-09-01

We study numerically the nonlinear interactions between chemical reaction and convective fingering in a diffusive boundary layer in a porous medium. The reaction enhances stability by consuming a solute that is unstably distributed in a gravitational field. We show that chemical reaction profoundly changes the dynamics of the system, by introducing a steady state, shortening the evolution time, and altering the spatial patterns of velocity and concentration of solute. In the presence of weak reaction, finger growth and merger occur effectively, driving strong convective currents in a thick layer of solute. However, as the reaction becomes stronger, finger growth is inhibited, tip-splitting is enhanced and the layer of solute becomes much thinner. Convection enhances the mass flux of solute consumed by reaction in the boundary layer but has a diminishing effect as reaction strength increases. This nonlinear behavior has striking differences to the density fingering of traveling reaction fronts, for which stronger chemical kinetics result in more effective finger merger owing to an increase in the speed of the front. In a boundary layer, a strong stabilizing effect of reaction can maintain a long-term state of convection in isolated fingers of wavelength comparable to that at onset of instability.

Bubble and Drop Nonlinear Dynamics (BDND)

NASA Technical Reports Server (NTRS)

Trinh, E. H.; Leal, L. Gary; Thomas, D. A.; Crouch, R. K.

1998-01-01

Free drops and bubbles are weakly nonlinear mechanical systems that are relatively simple to characterize experimentally in 1-G as well as in microgravity. The understanding of the details of their motion contributes to the fundamental study of nonlinear phenomena and to the measurement of the thermophysical properties of freely levitated melts. The goal of this Glovebox-based experimental investigation is the low-gravity assessment of the capabilities of a modular apparatus based on ultrasonic resonators and on the pseudo- extinction optical method. The required experimental task is the accurate measurements of the large-amplitude dynamics of free drops and bubbles in the absence of large biasing influences such as gravity and levitation fields. A single-axis levitator used for the positioning of drops in air, and an ultrasonic water-filled resonator for the trapping of air bubbles have been evaluated in low-gravity and in 1-G. The basic feasibility of drop positioning and shape oscillations measurements has been verified by using a laptop-interfaced automated data acquisition and the optical extinction technique. The major purpose of the investigation was to identify the salient technical issues associated with the development of a full-scale Microgravity experiment on single drop and bubble dynamics.

Numerical model for the weakly nonlinear propagation of sound through turbulence

NASA Technical Reports Server (NTRS)

Lipkens, Bart; Blanc-Benon, Philippe

1994-01-01

When finite amplitude (or intense) sound, such as a sonic boom, propagates through a turbulent atmosphere, the propagation is strongly affected by the turbulence. The interaction between sound and turbulence has mostly been studied as a linear phenomenon, i.e., the nonlinear behavior of the intense sound has been neglected. It has been shown that turbulence has an effect on the perceived loudness of sonic booms, mainly by changing its peak pressure and rise time. Peak pressure and rise time are important factors that determine the loudness of the sonic boom when heard outdoors. However, the interaction between turbulence and nonlinear effects has mostly not been included in propagation studies of sonic booms. It is therefore important to investigate the influence of acoustical nonlinearity on the interaction of intense sound with turbulence.

Uncertainty Quantification of Nonlinear Electrokinetic Response in a Microchannel-Membrane Junction

NASA Astrophysics Data System (ADS)

Alizadeh, Shima; Iaccarino, Gianluca; Mani, Ali

2015-11-01

We have conducted uncertainty quantification (UQ) for electrokinetic transport of ionic species through a hybrid microfluidic system using different probabilistic techniques. The system of interest is an H-configuration consisting of two parallel microchannels that are connected via a nafion junction. This system is commonly used for ion preconcentration and stacking by utilizing a nonlinear response at the channel-nafion junction that leads to deionization shocks. In this work, the nafion medium is modeled as many parallel nano-pores where, the nano-pore diameter, nafion porosity, and surface charge density are independent random variables. We evaluated the resulting uncertainty on the ion concentration fields as well as the deionization shock location. The UQ methods predicted consistent statistics for the outputs and the results revealed that the shock location is weakly sensitive to the nano-pore surface charge and primarily driven by nano-pore diameters. The present study can inform the design of electrokinetic networks with increased robustness to natural manufacturing variability. Applications include water desalination and lab-on-a-chip systems. Shima is a graduate student in the department of Mechanical Engineering at Stanford University. She received her Master's degree from Stanford in 2011. Her research interests include Electrokinetics in porous structures and high performance computing.

Quasi-two-dimensional nonlinear evolution of helical magnetorotational instability in a magnetized Taylor-Couette flow

NASA Astrophysics Data System (ADS)

Mamatsashvili, G.; Stefani, F.; Guseva, A.; Avila, M.

2018-01-01

Magnetorotational instability (MRI) is one of the fundamental processes in astrophysics, driving angular momentum transport and mass accretion in a wide variety of cosmic objects. Despite much theoretical/numerical and experimental efforts over the last decades, its saturation mechanism and amplitude, which sets the angular momentum transport rate, remains not well understood, especially in the limit of high resistivity, or small magnetic Prandtl numbers typical to interiors (dead zones) of protoplanetary disks, liquid cores of planets and liquid metals in laboratory. Using direct numerical simulations, in this paper we investigate the nonlinear development and saturation properties of the helical magnetorotational instability (HMRI)—a relative of the standard MRI—in a magnetized Taylor-Couette flow at very low magnetic Prandtl number (correspondingly at low magnetic Reynolds number) relevant to liquid metals. For simplicity, the ratio of azimuthal field to axial field is kept fixed. From the linear theory of HMRI, it is known that the Elsasser number, or interaction parameter determines its growth rate and plays a special role in the dynamics. We show that this parameter is also important in the nonlinear problem. By increasing its value, a sudden transition from weakly nonlinear, where the system is slightly above the linear stability threshold, to strongly nonlinear, or turbulent regime occurs. We calculate the azimuthal and axial energy spectra corresponding to these two regimes and show that they differ qualitatively. Remarkably, the nonlinear state remains in all cases nearly axisymmetric suggesting that this HMRI-driven turbulence is quasi two-dimensional in nature. Although the contribution of non-axisymmetric modes increases moderately with the Elsasser number, their total energy remains much smaller than that of the axisymmetric ones.

Stability of dust ion acoustic solitary waves in a collisionless unmagnetized nonthermal plasma in presence of isothermal positrons

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

Sardar, Sankirtan; Bandyopadhyay, Anup, E-mail: abandyopadhyay1965@gmail.com; Das, K. P.

A three-dimensional KP (Kadomtsev Petviashvili) equation is derived here describing the propagation of weakly nonlinear and weakly dispersive dust ion acoustic wave in a collisionless unmagnetized plasma consisting of warm adiabatic ions, static negatively charged dust grains, nonthermal electrons, and isothermal positrons. When the coefficient of the nonlinear term of the KP-equation vanishes an appropriate modified KP (MKP) equation describing the propagation of dust ion acoustic wave is derived. Again when the coefficient of the nonlinear term of this MKP equation vanishes, a further modified KP equation is derived. Finally, the stability of the solitary wave solutions of the KPmore » and the different modified KP equations are investigated by the small-k perturbation expansion method of Rowlands and Infeld [J. Plasma Phys. 3, 567 (1969); 8, 105 (1972); 10, 293 (1973); 33, 171 (1985); 41, 139 (1989); Sov. Phys. - JETP 38, 494 (1974)] at the lowest order of k, where k is the wave number of a long-wavelength plane-wave perturbation. The solitary wave solutions of the different evolution equations are found to be stable at this order.« less

Kinetic theory for the ion humps at the foot of the Earth's bow shock

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

Jovanovic, D.; Krasnoselskikh, V. V.

2009-10-15

The nonlinear kinetic theory is presented for the ion acoustic perturbations at the foot of the Earth's quasiperpendicular bow shock, that is characterized by weakly magnetized electrons and unmagnetized ions. The streaming ions, due to the reflection of the solar wind ions from the shock, provide the free energy source for the linear instability of the acoustic wave. In the fully nonlinear regime, a coherent localized solution is found in the form of a stationary ion hump, which is traveling with the velocity close to the phase velocity of the linear mode. The structure is supported by the nonlinearities comingmore » from the increased population of the resonant beam ions, trapped in the self-consistent potential. As their size in the direction perpendicular to the local magnetic field is somewhat smaller that the electron Larmor radius and much larger that the Debye length, their spatial properties are determined by the effects of the magnetic field on weakly magnetized electrons. These coherent structures provide a theoretical explanation for the bipolar electric pulses, observed upstream of the shock by Polar and Cluster satellite missions.« less

A dynamical model of plasma turbulence in the solar wind

PubMed Central

Howes, G. G.

2015-01-01

A dynamical approach, rather than the usual statistical approach, is taken to explore the physical mechanisms underlying the nonlinear transfer of energy, the damping of the turbulent fluctuations, and the development of coherent structures in kinetic plasma turbulence. It is argued that the linear and nonlinear dynamics of Alfvén waves are responsible, at a very fundamental level, for some of the key qualitative features of plasma turbulence that distinguish it from hydrodynamic turbulence, including the anisotropic cascade of energy and the development of current sheets at small scales. The first dynamical model of kinetic turbulence in the weakly collisional solar wind plasma that combines self-consistently the physics of Alfvén waves with the development of small-scale current sheets is presented and its physical implications are discussed. This model leads to a simplified perspective on the nature of turbulence in a weakly collisional plasma: the nonlinear interactions responsible for the turbulent cascade of energy and the formation of current sheets are essentially fluid in nature, while the collisionless damping of the turbulent fluctuations and the energy injection by kinetic instabilities are essentially kinetic in nature. PMID:25848075

Design of an Internal Model Control strategy for single-phase grid-connected PWM inverters and its performance analysis with a non-linear local load and weak grid.

PubMed

Chaves, Eric N; Coelho, Ernane A A; Carvalho, Henrique T M; Freitas, Luiz C G; Júnior, João B V; Freitas, Luiz C

2016-09-01

This paper presents the design of a controller based on Internal Model Control (IMC) applied to a grid-connected single-phase PWM inverter. The mathematical modeling of the inverter and the LCL output filter, used to project the 1-DOF IMC controller, is presented and the decoupling of grid voltage by a Feedforward strategy is analyzed. A Proportional - Resonant Controller (P+Res) was used for the control of the same plant in the running of experimental results, thus moving towards the discussion of differences regarding IMC and P+Res performances, which arrived at the evaluation of the proposed control strategy. The results are presented for typical conditions, for weak-grid and for non-linear local load, in order to verify the behavior of the controller against such situations. Copyright © 2016 ISA. Published by Elsevier Ltd. All rights reserved.

A new energy transfer model for turbulent free shear flow

NASA Technical Reports Server (NTRS)

Liou, William W.-W.

1992-01-01

A new model for the energy transfer mechanism in the large-scale turbulent kinetic energy equation is proposed. An estimate of the characteristic length scale of the energy containing large structures is obtained from the wavelength associated with the structures predicted by a weakly nonlinear analysis for turbulent free shear flows. With the inclusion of the proposed energy transfer model, the weakly nonlinear wave models for the turbulent large-scale structures are self-contained and are likely to be independent flow geometries. The model is tested against a plane mixing layer. Reasonably good agreement is achieved. Finally, it is shown by using the Liapunov function method, the balance between the production and the drainage of the kinetic energy of the turbulent large-scale structures is asymptotically stable as their amplitude saturates. The saturation of the wave amplitude provides an alternative indicator for flow self-similarity.

Effects of Density Fluctuations on Weakly Nonlinear Alfven Waves: An IST Perspective

NASA Astrophysics Data System (ADS)

Hamilton, R.; Hadley, N.

2012-12-01

The effects of random density fluctuations on oblique, 1D, weakly nonlinear Alfven waves is examined through a numerical study of an analytical model developed by Ruderman [M.S. Ruderman, Phys. Plasmas, 9 (7), pp. 2940-2945, (2002).]. Consistent with Ruderman's application to the one-parameter dark soliton, the effects on both one-parameter bright and dark solitons, the two-parameter soliton as well as pairs of one-parameter solitons were similar to that of Ohmic dissipation found by Hamilton et al. [R. Hamilton, D. Peterson, and S. Libby, J. Geophys. Res 114, A03104,doi:10.1029/2008JA013582 (2009).] It was found in all cases where bright or two-parameter solitons are present initially, that the effects of density fluctuations results in the eventual damping of such compressive wave forms and the formation of a train of dark solitons, or magnetic depressions.

Distribution of hybrid entanglement and hyperentanglement with time-bin for secure quantum channel under noise via weak cross-Kerr nonlinearity.

PubMed

Heo, Jino; Kang, Min-Sung; Hong, Chang-Ho; Yang, Hyung-Jin; Choi, Seong-Gon; Hong, Jong-Phil

2017-08-31

We design schemes to generate and distribute hybrid entanglement and hyperentanglement correlated with degrees of freedom (polarization and time-bin) via weak cross-Kerr nonlinearities (XKNLs) and linear optical devices (including time-bin encoders). In our scheme, the multi-photon gates (which consist of XKNLs, quantum bus [qubus] beams, and photon-number-resolving [PNR] measurement) with time-bin encoders can generate hyperentanglement or hybrid entanglement. And we can also purify the entangled state (polarization) of two photons using only linear optical devices and time-bin encoders under a noisy (bit-flip) channel. Subsequently, through local operations (using a multi-photon gate via XKNLs) and classical communications, it is possible to generate a four-qubit hybrid entangled state (polarization and time-bin). Finally, we discuss how the multi-photon gate using XKNLs, qubus beams, and PNR measurement can be reliably performed under the decoherence effect.

The effect of an electric field on the morphological stability of the crystal-melt interface of a binary alloy. III - Weakly nonlinear theory

NASA Technical Reports Server (NTRS)

Wheeler, A. A.; Mcfadden, G. B.; Coriell, S. R.; Hurle, D. T. J.

1990-01-01

The effect of a constant electric current on the crystal-melt interface morphology during directional solidification at constant velocity of a binary alloy is considered. A linear temperature field is assumed, and thermoelectric effects and Joule heating are neglected; electromigration and differing electrical conductivities of crystal and melt are taken into account. A two-dimensional weakly nonlinear analysis is carried out to third order in the interface amplitude, resulting in a cubic amplitude equation that describes whether the bifurcation from the planar state is supercritical or subcritical. For wavelengths corresponding to the most dangerous mode of linear theory, the demarcation between supercritical and subcritical behavior is calculated as a function of processing conditions and material parameters. The bifurcation behavior is a sensitive function of the magnitude and direction of the electric current and of the electrical conductivity ratio.

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.

A numerical study on weak-dissipative two-mode perturbed Burgers' and Ostrovsky models: right-left moving waves

NASA Astrophysics Data System (ADS)

Jaradat, Imad; Alquran, Marwan; Ali, Mohammed

2018-04-01

The purpose of this study is threefold. First, it derives newly developed two-mode nonlinear equations, two-mode perturbed Burgers' and two-mode Ostrovsky models. Second, it investigates the values of the nonlinearity and dispersion parameters that support the existence of two right-left (R-L) moving wave solutions to these models. Finally, it provides a graphical analysis of the "two-mode" concept and the impact of its phase velocity on the field function.

A general nonlinear magnetomechanical model for ferromagnetic materials under a constant weak magnetic field

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

Shi, Pengpeng; Zheng, Xiaojing, E-mail: xjzheng@xidian.edu.cn; Jin, Ke

2016-04-14

Weak magnetic nondestructive testing (e.g., metal magnetic memory method) concerns the magnetization variation of ferromagnetic materials due to its applied load and a weak magnetic surrounding them. One key issue on these nondestructive technologies is the magnetomechanical effect for quantitative evaluation of magnetization state from stress–strain condition. A representative phenomenological model has been proposed to explain the magnetomechanical effect by Jiles in 1995. However, the Jiles' model has some deficiencies in quantification, for instance, there is a visible difference between theoretical prediction and experimental measurements on stress–magnetization curve, especially in the compression case. Based on the thermodynamic relations and themore » approach law of irreversible magnetization, a nonlinear coupled model is proposed to improve the quantitative evaluation of the magnetomechanical effect. Excellent agreement has been achieved between the predictions from the present model and previous experimental results. In comparison with Jiles' model, the prediction accuracy is improved greatly by the present model, particularly for the compression case. A detailed study has also been performed to reveal the effects of initial magnetization status, cyclic loading, and demagnetization factor on the magnetomechanical effect. Our theoretical model reveals that the stable weak magnetic signals of nondestructive testing after multiple cyclic loads are attributed to the first few cycles eliminating most of the irreversible magnetization. Remarkably, the existence of demagnetization field can weaken magnetomechanical effect, therefore, significantly reduces the testing capability. This theoretical model can be adopted to quantitatively analyze magnetic memory signals, and then can be applied in weak magnetic nondestructive testing.« less

Characteristics of plasma plume in ultrafast laser ablation with a weakly ionized air channel

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

Hou, Huaming; Yang, Bo; Mao, Xianglei

We report the influence of femtosecond (fs) laser weakly ionized air channel on characteristics of plasma induced from fs-laser ablation of solid Zr metal target. A novel method to create high temperature, low electron density plasma with intense elemental emission and weak bremsstrahlung emission was demonstrated. Weakly ionized air channel was generated as a result of a non-linear phenomenon. Two-dimensional time-resolved optical-emission images of plasma plumes were taken for plume dynamics analysis. Dynamic physical properties of filament channels were simulated. In particular, we investigated the influence of weakly ionized air channel on the evolution of solid plasma plume. Plasma plumemore » splitting was observed whilst longer weakly ionized air channel formed above the ablation spot. The domination mechanism for splitting is attributed to the long-lived underdense channel created by fs-laser induced weakly ionization of air. The evolutions of atomic/molecular emission intensity, peak broadening, and plasma temperature were analyzed, and the results show that the part of plasma entering weakly ionized air channel features higher initial temperature, lower electron density and faster decay.« less

Characteristics of plasma plume in ultrafast laser ablation with a weakly ionized air channel

DOE PAGES

Hou, Huaming; Yang, Bo; Mao, Xianglei; ...

2018-05-10

We report the influence of femtosecond (fs) laser weakly ionized air channel on characteristics of plasma induced from fs-laser ablation of solid Zr metal target. A novel method to create high temperature, low electron density plasma with intense elemental emission and weak bremsstrahlung emission was demonstrated. Weakly ionized air channel was generated as a result of a non-linear phenomenon. Two-dimensional time-resolved optical-emission images of plasma plumes were taken for plume dynamics analysis. Dynamic physical properties of filament channels were simulated. In particular, we investigated the influence of weakly ionized air channel on the evolution of solid plasma plume. Plasma plumemore » splitting was observed whilst longer weakly ionized air channel formed above the ablation spot. The domination mechanism for splitting is attributed to the long-lived underdense channel created by fs-laser induced weakly ionization of air. The evolutions of atomic/molecular emission intensity, peak broadening, and plasma temperature were analyzed, and the results show that the part of plasma entering weakly ionized air channel features higher initial temperature, lower electron density and faster decay.« less

Transcranial Random Noise Stimulation of Visual Cortex: Stochastic Resonance Enhances Central Mechanisms of Perception.

PubMed

van der Groen, Onno; Wenderoth, Nicole

2016-05-11

Random noise enhances the detectability of weak signals in nonlinear systems, a phenomenon known as stochastic resonance (SR). Though counterintuitive at first, SR has been demonstrated in a variety of naturally occurring processes, including human perception, where it has been shown that adding noise directly to weak visual, tactile, or auditory stimuli enhances detection performance. These results indicate that random noise can push subthreshold receptor potentials across the transfer threshold, causing action potentials in an otherwise silent afference. Despite the wealth of evidence demonstrating SR for noise added to a stimulus, relatively few studies have explored whether or not noise added directly to cortical networks enhances sensory detection. Here we administered transcranial random noise stimulation (tRNS; 100-640 Hz zero-mean Gaussian white noise) to the occipital region of human participants. For increasing tRNS intensities (ranging from 0 to 1.5 mA), the detection accuracy of a visual stimuli changed according to an inverted-U-shaped function, typical of the SR phenomenon. When the optimal level of noise was added to visual cortex, detection performance improved significantly relative to a zero noise condition (9.7 ± 4.6%) and to a similar extent as optimal noise added to the visual stimuli (11.2 ± 4.7%). Our results demonstrate that adding noise to cortical networks can improve human behavior and that tRNS is an appropriate tool to exploit this mechanism. Our findings suggest that neural processing at the network level exhibits nonlinear system properties that are sensitive to the stochastic resonance phenomenon and highlight the usefulness of tRNS as a tool to modulate human behavior. Since tRNS can be applied to all cortical areas, exploiting the SR phenomenon is not restricted to the perceptual domain, but can be used for other functions that depend on nonlinear neural dynamics (e.g., decision making, task switching, response inhibition, and many other processes). This will open new avenues for using tRNS to investigate brain function and enhance the behavior of healthy individuals or patients. Copyright © 2016 the authors 0270-6474/16/365289-10$15.00/0.

The development of magnetic field line wander in gyrokinetic plasma turbulence: dependence on amplitude of turbulence

NASA Astrophysics Data System (ADS)

Bourouaine, Sofiane; Howes, Gregory G.

2017-06-01

The dynamics of a turbulent plasma not only manifests the transport of energy from large to small scales, but also can lead to a tangling of the magnetic field that threads through the plasma. The resulting magnetic field line wander can have a large impact on a number of other important processes, such as the propagation of energetic particles through the turbulent plasma. Here we explore the saturation of the turbulent cascade, the development of stochasticity due to turbulent tangling of the magnetic field lines and the separation of field lines through the turbulent dynamics using nonlinear gyrokinetic simulations of weakly collisional plasma turbulence, relevant to many turbulent space and astrophysical plasma environments. We determine the characteristic time 2$ for the saturation of the turbulent perpendicular magnetic energy spectrum. We find that the turbulent magnetic field becomes completely stochastic at time 2$ for strong turbulence, and at 2$ for weak turbulence. However, when the nonlinearity parameter of the turbulence, a dimensionless measure of the amplitude of the turbulence, reaches a threshold value (within the regime of weak turbulence) the magnetic field stochasticity does not fully develop, at least within the evolution time interval 22$ . Finally, we quantify the mean square displacement of magnetic field lines in the turbulent magnetic field with a functional form 2\\rangle =A(z/L\\Vert )p$ ( \\Vert $ is the correlation length parallel to the magnetic background field \\mathbf{0}$ , is the distance along \\mathbf{0}$ direction), providing functional forms of the amplitude coefficient and power-law exponent as a function of the nonlinearity parameter.

DEMNUni: ISW, Rees-Sciama, and weak-lensing in the presence of massive neutrinos

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

Carbone, Carmelita; Petkova, Margarita; Dolag, Klaus, E-mail: carmelita.carbone@brera.inaf.it, E-mail: mpetkova@usm.lmu.de, E-mail: kdolag@mpa-garching.mpg.de

2016-07-01

We present, for the first time in the literature, a full reconstruction of the total (linear and non-linear) ISW/Rees-Sciama effect in the presence of massive neutrinos, together with its cross-correlations with CMB-lensing and weak-lensing signals. The present analyses make use of all-sky maps extracted via ray-tracing across the gravitational potential distribution provided by the ''Dark Energy and Massive Neutrino Universe'' (DEMNUni) project, a set of large-volume, high-resolution cosmological N-body simulations, where neutrinos are treated as separate collisionless particles. We correctly recover, at 1–2% accuracy, the linear predictions from CAMB. Concerning the CMB-lensing and weak-lensing signals, we also recover, with similarmore » accuracy, the signal predicted by Boltzmann codes, once non-linear neutrino corrections to HALOFIT are accounted for. Interestingly, in the ISW/Rees-Sciama signal, and its cross correlation with lensing, we find an excess of power with respect to the massless case, due to free streaming neutrinos, roughly at the transition scale between the linear and non-linear regimes. The excess is ∼ 5 – 10% at l ∼ 100 for the ISW/Rees-Sciama auto power spectrum, depending on the total neutrino mass M {sub ν}, and becomes a factor of ∼ 4 for M {sub ν} = 0.3 eV, at l ∼ 600, for the ISW/Rees-Sciama cross power with CMB-lensing. This effect should be taken into account for the correct estimation of the CMB temperature bispectrum in the presence of massive neutrinos.« less

Glassy phases and driven response of the phase-field-crystal model with random pinning.

PubMed

Granato, E; Ramos, J A P; Achim, C V; Lehikoinen, J; Ying, S C; Ala-Nissila, T; Elder, K R

2011-09-01

We study the structural correlations and the nonlinear response to a driving force of a two-dimensional phase-field-crystal model with random pinning. The model provides an effective continuous description of lattice systems in the presence of disordered external pinning centers, allowing for both elastic and plastic deformations. We find that the phase-field crystal with disorder assumes an amorphous glassy ground state, with only short-ranged positional and orientational correlations, even in the limit of weak disorder. Under increasing driving force, the pinned amorphous-glass phase evolves into a moving plastic-flow phase and then, finally, a moving smectic phase. The transverse response of the moving smectic phase shows a vanishing transverse critical force for increasing system sizes.

Raman parametric excitation effect upon the third harmonic generation by a metallic nanoparticle lattice

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

Sepehri Javan, N., E-mail: sepehri-javan@uma.ac.ir

2015-08-21

This work is a theoretical study on third harmonic generation in the nonlinear propagation of an intense laser pulse through a periodic three-dimensional lattice of nanoparticles. Using a perturbative method, the nonlinear equations that describe the laser–nanoparticle interaction in the weakly relativistic regime are derived. Additionally, the nonlinear dispersion relation and the amplitude of the third harmonic are obtained. Finally, the effects of the nanoparticle radius and separation length, the distribution of the nanoparticle electron density, and the laser frequency upon the third harmonic efficiency are investigated. In addition to the expected resonance that occurs when the third harmonic resonatesmore » with the plasmon wave, another resonance appears when the nonlinear interaction of the fundamental mode with the third harmonic excites a longitudinal collective plasmon wave via the parametric Raman mechanism.« less

Large optical nonlinearity of indium tin oxide in its epsilon-near-zero region.

PubMed

Alam, M Zahirul; De Leon, Israel; Boyd, Robert W

2016-05-13

Nonlinear optical phenomena are crucial for a broad range of applications, such as microscopy, all-optical data processing, and quantum information. However, materials usually exhibit a weak optical nonlinearity even under intense coherent illumination. We report that indium tin oxide can acquire an ultrafast and large intensity-dependent refractive index in the region of the spectrum where the real part of its permittivity vanishes. We observe a change in the real part of the refractive index of 0.72 ± 0.025, corresponding to 170% of the linear refractive index. This change in refractive index is reversible with a recovery time of about 360 femtoseconds. Our results offer the possibility of designing material structures with large ultrafast nonlinearity for applications in nanophotonics. Copyright © 2016, American Association for the Advancement of Science.

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

Entropy criteria applied to pattern selection in systems with free boundaries

NASA Astrophysics Data System (ADS)

Kirkaldy, J. S.

1985-10-01

The steady state differential or integral equations which describe patterned dissipative structures, typically to be identified with first order phase transformation morphologies like isothermal pearlites, are invariably degenerate in one or more order parameters (the lamellar spacing in the pearlite case). It is often observed that a different pattern is attained at the steady state for each initial condition (the hysteresis or metastable case). Alternatively, boundary perturbations and internal fluctuations during transition up to, or at the steady state, destroy the path coherence. In this case a statistical ensemble of imperfect patterns often emerges which represents a fluctuating but recognizably patterned and unique average steady state. It is cases like cellular, lamellar pearlite, involving an assembly of individual cell patterns which are regularly perturbed by local fluctuation and growth processes, which concern us here. Such weakly fluctuating nonlinear steady state ensembles can be arranged in a thought experiment so as to evolve as subsystems linking two very large mass-energy reservoirs in isolation. Operating on this discontinuous thermodynamic ideal, Onsager’s principle of maximum path probability for isolated systems, which we interpret as a minimal time correlation function connecting subsystem and baths, identifies the stable steady state at a parametric minimum or maximum (or both) in the dissipation rate. This nonlinear principle is independent of the Principle of Minimum Dissipation which is applicable in the linear regime of irreversible thermodynamics. The statistical argument is equivalent to the weak requirement that the isolated system entropy as a function of time be differentiable to the second order despite the macroscopic pattern fluctuations which occur in the subsystem. This differentiability condition is taken for granted in classical stability theory based on the 2nd Law. The optimal principle as applied to isothermal and forced velocity pearlites (in this case maximal) possesses a Le Chatelier (perturbation) Principle which can be formulated exactly via Langer’s conjecture that “each lamella must grow in a direction which is perpendicular to the solidification front”. This is the first example of such an equivalence to be experimentally and theoretically recognized in nonlinear irreversible thermodynamics. A further application to binary solidification cells is reviewed. In this case the optimum in the dissipation is a minimum and the closure between theory and experiment is excellent. Other applications in thermal-hydraulics, biology, and solid state physics are briefy described.

Multi-soliton solutions and Bäcklund transformation for a two-mode KdV equation in a fluid

NASA Astrophysics Data System (ADS)

Xiao, Zi-Jian; Tian, Bo; Zhen, Hui-Ling; Chai, Jun; Wu, Xiao-Yu

2017-01-01

In this paper, we investigate a two-mode Korteweg-de Vries equation, which describes the one-dimensional propagation of shallow water waves with two modes in a weakly nonlinear and dispersive fluid system. With the binary Bell polynomial and an auxiliary variable, bilinear forms, multi-soliton solutions in the two-wave modes and Bell polynomial-type Bäcklund transformation for such an equation are obtained through the symbolic computation. Soliton propagation and collisions between the two solitons are presented. Based on the graphic analysis, it is shown that the increase in s can lead to the increase in the soliton velocities under the condition of ?, but the soliton amplitudes remain unchanged when s changes, where s means the difference between the phase velocities of two-mode waves, ? and ? are the nonlinearity parameter and dispersion parameter respectively. Elastic collisions between the two solitons in both two modes are analyzed with the help of graphic analysis.

Does species diversity limit productivity in natural grassland communities?

USGS Publications Warehouse

Grace, J.B.; Anderson, T.M.; Smith, M.D.; Seabloom, E.; Andelman, S.J.; Meche, G.; Weiher, E.; Allain, L.K.; Jutila, H.; Sankaran, M.; Knops, J.; Ritchie, M.; Willig, M.R.

2007-01-01

Theoretical analyses and experimental studies of synthesized assemblages indicate that under particular circumstances species diversity can enhance community productivity through niche complementarity. It remains unclear whether this process has important effects in mature natural ecosystems where competitive feedbacks and complex environmental influences affect diversity-productivity relationships. In this study, we evaluated diversity-productivity relationships while statistically controlling for environmental influences in 12 natural grassland ecosystems. Because diversity-productivity relationships are conspicuously nonlinear, we developed a nonlinear structural equation modeling (SEM) methodology to separate the effects of diversity on productivity from the effects of productivity on diversity. Meta-analysis was used to summarize the SEM findings across studies. While competitive effects were readily detected, enhancement of production by diversity was not. These results suggest that the influence of small-scale diversity on productivity in mature natural systems is a weak force, both in absolute terms and relative to the effects of other controls on productivity. ?? 2007 Blackwell Publishing Ltd/CNRS.

Experimental study of three-wave interactions among capillary-gravity surface waves

NASA Astrophysics Data System (ADS)

Haudin, Florence; Cazaubiel, Annette; Deike, Luc; Jamin, Timothée; Falcon, Eric; Berhanu, Michael

2016-04-01

In propagating wave systems, three- or four-wave resonant interactions constitute a classical nonlinear mechanism exchanging energy between the different scales. Here we investigate three-wave interactions for gravity-capillary surface waves in a closed laboratory tank. We generate two crossing wave trains and we study their interaction. Using two optical methods, a local one (laser doppler vibrometry) and a spatiotemporal one (diffusive light photography), a third wave of smaller amplitude is detected, verifying the three-wave resonance conditions in frequency and in wave number. Furthermore, by focusing on the stationary regime and by taking into account viscous dissipation, we directly estimate the growth rate of the resonant mode. The latter is then compared to the predictions of the weakly nonlinear triadic resonance interaction theory. The obtained results confirm qualitatively and extend previous experimental results obtained only for collinear wave trains. Finally, we discuss the relevance of three-wave interaction mechanisms in recent experiments studying gravity-capillary turbulence.

Experimental study of three-wave interactions among capillary-gravity surface waves.

PubMed

Haudin, Florence; Cazaubiel, Annette; Deike, Luc; Jamin, Timothée; Falcon, Eric; Berhanu, Michael

2016-04-01

In propagating wave systems, three- or four-wave resonant interactions constitute a classical nonlinear mechanism exchanging energy between the different scales. Here we investigate three-wave interactions for gravity-capillary surface waves in a closed laboratory tank. We generate two crossing wave trains and we study their interaction. Using two optical methods, a local one (laser doppler vibrometry) and a spatiotemporal one (diffusive light photography), a third wave of smaller amplitude is detected, verifying the three-wave resonance conditions in frequency and in wave number. Furthermore, by focusing on the stationary regime and by taking into account viscous dissipation, we directly estimate the growth rate of the resonant mode. The latter is then compared to the predictions of the weakly nonlinear triadic resonance interaction theory. The obtained results confirm qualitatively and extend previous experimental results obtained only for collinear wave trains. Finally, we discuss the relevance of three-wave interaction mechanisms in recent experiments studying gravity-capillary turbulence.

The Role of the Pressure in the Partial Regularity Theory for Weak Solutions of the Navier-Stokes Equations

NASA Astrophysics Data System (ADS)

Chamorro, Diego; Lemarié-Rieusset, Pierre-Gilles; Mayoufi, Kawther

2018-04-01

We study the role of the pressure in the partial regularity theory for weak solutions of the Navier-Stokes equations. By introducing the notion of dissipative solutions, due to D uchon and R obert (Nonlinearity 13:249-255, 2000), we will provide a generalization of the Caffarelli, Kohn and Nirenberg theory. Our approach sheels new light on the role of the pressure in this theory in connection to Serrin's local regularity criterion.

General relativistic corrections to the weak lensing convergence power spectrum

NASA Astrophysics Data System (ADS)

Giblin, John T.; Mertens, James B.; Starkman, Glenn D.; Zentner, Andrew R.

2017-11-01

We compute the weak lensing convergence power spectrum, Cℓκκ, in a dust-filled universe using fully nonlinear general relativistic simulations. The spectrum is then compared to more standard, approximate calculations by computing the Bardeen (Newtonian) potentials in linearized gravity and partially utilizing the Born approximation. We find corrections to the angular power spectrum amplitude of order ten percent at very large angular scales, ℓ˜2 - 3 , and percent-level corrections at intermediate angular scales of ℓ˜20 - 30 .

Convection Regularization of High Wavenumbers in Turbulence ANS Shocks

DTIC Science & Technology

2011-07-31

dynamics of particles that adhere to one another upon collision and has been studied as a simple cosmological model for describing the nonlinear formation of...solution we mean a solution to the Cauchy problem in the following sense. Definition 5.1. A function u : R × [0, T ] 7→ RN is a weak solution of the...step 2 the limit function in the α → 0 limit is shown to satisfy the definition of a weak solution for the Cauchy problem. Without loss of generality

A Three-Dimensional Microdisplacement Sensing System Based on MEMS Bulk-Silicon Technology

PubMed Central

Wu, Junjie; Lei, Lihua; Chen, Xin; Cai, Xiaoyu; Li, Yuan; Han, Tao

2014-01-01

For the dimensional measurement and characterization of microsized and nanosized components, a three-dimensional microdisplacement sensing system was developed using the piezoresistive effect in silicon. The sensor was fabricated using microelectromechanical system bulk-silicon technology, and it was validated using the finite element method. A precise data acquisition circuit with an accuracy of 20 μV was designed to obtain weak voltage signals. By calibration, the sensing system was shown to have a sensitivity of 17.29 mV/μm and 4.59 mV/μm in the axial and lateral directions, respectively; the nonlinearity in these directions was 0.8% and 1.0% full scale, respectively. A full range of 4.6 μm was achieved in the axial direction. Results of a resolution test indicated that the sensing system had a resolution of 5 nm in the axial direction and 10 nm in the lateral direction. PMID:25360581

Microresonators for Nonlinear Quantum Optics

NASA Astrophysics Data System (ADS)

Vernon, Zachary

In this thesis I study in detail the quantum dynamics of several nonlinear optical processes in microresonator systems. A Heisenberg-picture input-output formalism is developed from first principles that includes the effects of scattering losses and independent quality factors and coupling ratios for different resonances. The task of calculating the device output is then reduced to solving a set of driven, damped, ordinary differential equations for the resonator mode operators alone. This theoretical framework is used to study photon pair generation via spontaneous four-wave mixing in the weakly pumped regime, on which the effects of scattering losses are appraised. A more strongly driven regime is studied for continuous wave pumps, demonstrating when self- and cross-phase modulation and multi-photon pair generation become important, and their effects on the spectral and power scaling properties of the system are examined; A detuning strategy is presented that compensates for some of these effects. The results of the weak-pump regime are applied to study microresonator-based heralded single photon sources. The impact of scattering losses is studied, revealing that typical systems suffer from low heralding efficiency due to these losses. A technique to improve heralding efficiency is presented through over-coupling the resonator-channel system, and a resultant trade-off between heralding rate and heralding efficiency is uncovered. Limitations to the spectral purity of the heralded single photon output for conventional microresonator systems are also analysed, and a more sophisticated coupling scheme presented to overcome the upper bound for spectral purity of 93% that exists in typical systems, permitting the generation of single photons with spectral purity arbitrarily close to 100% without spectral filtering or sophisticated phase-matching techniques. The theory of quantum frequency conversion in microresonators using four-wave mixing is then developed in detail, and the spectral conversion probability and conversion efficiency studied. Efficiencies exceeding 90% using less than 100 mW of pump power are predicted to be achievable with current technology. A dressed mode picture is developed to better understand the conversion dynamics. Rabi-like spectral splitting and temporal oscillations of the intraresonator mean photon number are predicted, exhibiting a novel regime of strongly coupled photonic modes.

Optical Sidebands Multiplier

NASA Technical Reports Server (NTRS)

Strekalov, Dmitry V.; Yu, Nan

2010-01-01

Optical sidebands have been generated with relative frequency tens to hundreds of GHz by using optical sidebands that are generated in a cascade process in high-quality optical resonators with Kerr nonlinearity, such as whispering gallery mode (WGM) resonators. For this purpose, the WGM resonator needs to be optically pumped at two frequencies matching its resonances. These two optical components can be one or several free spectral ranges (FSRs), equal to approximately 12 GHz, in this example, apart from each other, and can be easily derived from a monochromatic pump with an ordinary EOM (electro-optic modulation) operating at half the FSR frequency. With sufficient nonlinearity, an optical cascade process will convert the two pump frequencies into a comb-like structure extending many FSRs around the carrier frequency. This has a demonstratively efficient frequency conversion of this type with only a few milliwatt optical pump power. The concept of using Kerr nonlinearity in a resonator for non-degenerate wave mixing has been discussed before, but it was a common belief that this was a weak process requiring very high peak powers to be observable. It was not thought possible for this approach to compete with electro-optical modulators in CW applications, especially those at lower optical powers. By using the high-Q WGM resonators, the effective Kerr nonlinearity can be made so high that, using even weak seeding bands available from a conventional EOM, one can effectively multiply the optical sidebands, extending them into an otherwise inaccessible frequency range.

Weakly nonlinear incompressible Rayleigh-Taylor instability growth at cylindrically convergent interfaces

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

Wang, L. F.; He, X. T.; HEDPS, Center for Applied Physics and Technology, Peking University, Beijing 100871

2013-04-15

A weakly nonlinear (WN) model has been developed for the incompressible Rayleigh-Taylor instability (RTI) in cylindrical geometry. The transition from linear to nonlinear growth is analytically investigated via a third-order solutions for the cylindrical RTI initiated by a single-mode velocity perturbation. The third-order solutions can depict the early stage of the interface asymmetry due to the bubble-spike formation, as well as the saturation of the linear (exponential) growth of the fundamental mode. The WN results in planar RTI [Wang et al., Phys. Plasmas 19, 112706 (2012)] are recovered in the limit of high-mode number perturbations. The difference between the WNmore » growth of the RTI in cylindrical geometry and in planar geometry is discussed. It is found that the interface of the inward (outward) development spike/bubble is extruded (stretched) by the additional inertial force in cylindrical geometry compared with that in planar geometry. For interfaces with small density ratios, the inward growth bubble can grow fast than the outward growth spike in cylindrical RTI. Moreover, a reduced formula is proposed to describe the WN growth of the RTI in cylindrical geometry with an acceptable precision, especially for small-amplitude perturbations. Using the reduced formula, the nonlinear saturation amplitude of the fundamental mode and the phases of the Fourier harmonics are studied. Thus, it should be included in applications where converging geometry effects play an important role, such as the supernova explosions and inertial confinement fusion implosions.« less

Impact of nonlinear effective interactions on group field theory quantum gravity condensates

NASA Astrophysics Data System (ADS)

Pithis, Andreas G. A.; Sakellariadou, Mairi; Tomov, Petar

2016-09-01

We present the numerical analysis of effectively interacting group field theory models in the context of the group field theory quantum gravity condensate analog of the Gross-Pitaevskii equation for real Bose-Einstein condensates including combinatorially local interaction terms. Thus, we go beyond the usually considered construction for free models. More precisely, considering such interactions in a weak regime, we find solutions for which the expectation value of the number operator N is finite, as in the free case. When tuning the interaction to the strongly nonlinear regime, however, we obtain solutions for which N grows and eventually blows up, which is reminiscent of what one observes for real Bose-Einstein condensates, where a strong interaction regime can only be realized at high density. This behavior suggests the breakdown of the Bogoliubov ansatz for quantum gravity condensates and the need for non-Fock representations to describe the system when the condensate constituents are strongly correlated. Furthermore, we study the expectation values of certain geometric operators imported from loop quantum gravity in the free and interacting cases. In particular, computing solutions around the nontrivial minima of the interaction potentials, one finds, already in the weakly interacting case, a nonvanishing condensate population for which the spectra are dominated by the lowest nontrivial configuration of the quantum geometry. This result indicates that the condensate may indeed consist of many smallest building blocks giving rise to an effectively continuous geometry, thus suggesting the interpretation of the condensate phase to correspond to a geometric phase.

An Experimental Concept for Probing Nonlinear Physics in Radiation Belts

NASA Astrophysics Data System (ADS)

Crabtree, C. E.; Ganguli, G.; Tejero, E. M.; Amatucci, B.; Siefring, C. L.

2017-12-01

A sounding rocket experiment, Space Measurement of Rocket-Released Turbulence (SMART), can be used to probe the nonlinear response to a known stimulus injected into the radiation belt. Release of high-speed neutral barium atoms (8- 10 km/s) generated by a shaped charge explosion in the ionosphere can be used as the source of free energy to seed weak turbulence in the ionosphere. The Ba atoms are photo-ionized forming a ring velocity distribution of heavy Ba+ that is known to generate lower hybrid waves. Induced nonlinear scattering will convert the lower hybrid waves into EM whistler/magnetosonic waves. The escape of the whistlers from the ionospheric region into the radiation belts has been studied and their observable signatures quantified. The novelty of the SMART experiment is to make coordinated measurement of the cause and effect of the turbulence in space plasmas and from that to deduce the role of nonlinear scattering in the radiation belts. Sounding rocket will carry a Ba release module and an instrumented daughter section that includes vector wave magnetic and electric field sensors, Langmuir probes and energetic particle detectors. The goal of these measurements is to determine the whistler and lower hybrid wave amplitudes and spectrum in the ionospheric source region and look for precipitated particles. The Ba release may occur at 600-700 km near apogee. Ground based cameras and radio diagnostics can be used to characterize the Ba and Ba+ release. The Van Allen Probes can be used to detect the propagation of the scattering-generated whistler waves and their effects in the radiation belts. By detecting whistlers and measuring their energy density in the radiation belts the SMART mission will confirm the nonlinear generation of whistlers through scattering of lower hybrid along with other nonlinear responses of the radiation belts and their connection to weak turbulence.

Estimating nonlinear effects in forward dijet production in ultra-peripheral heavy ion collisions at the LHC

NASA Astrophysics Data System (ADS)

Kotko, P.; Kutak, K.; Sapeta, S.; Stasto, A. M.; Strikman, M.

2017-05-01

Using the framework that interpolates between the leading power limit of the color glass condensate and the high energy (or kT) factorization we calculate the direct component of the forward dijet production in ultra-peripheral Pb-Pb collisions at CM energy 5.1 TeV per nucleon pair. The formalism is applicable when the average transverse momentum of the dijet system PT is much bigger than the saturation scale Qs, PT≫ Qs, while the imbalance of the dijet system can be arbitrary. The cross section is uniquely sensitive to the Weizsäcker-Williams (WW) unintegrated gluon distribution, which is far less known from experimental data than the most common dipole gluon distribution appearing in inclusive small- x processes. We have calculated cross sections and nuclear modification ratios using WW gluon distribution obtained from the dipole gluon density through the Gaussian approximation. The dipole gluon distribution used to get WW was fitted to the inclusive HERA data with the nonlinear extension of unified BFKL + DGLAP evolution equation. The saturation effects are visible but rather weak for realistic pT cut on the dijet system, reaching about 20% with the cut as low as 6 GeV. We find that the LO collinear factorization with nuclear leading-twist shadowing predicts quite similar effects.

Parameter estimation in a structural acoustic system with fully nonlinear coupling conditions

NASA Technical Reports Server (NTRS)

Banks, H. T.; Smith, Ralph C.

1994-01-01

A methodology for estimating physical parameters in a class of structural acoustic systems is presented. The general model under consideration consists of an interior cavity which is separated from an exterior noise source by an enclosing elastic structure. Piezoceramic patches are bonded to or embedded in the structure; these can be used both as actuators and sensors in applications ranging from the control of interior noise levels to the determination of structural flaws through nondestructive evaluation techniques. The presence and excitation of patches, however, changes the geometry and material properties of the structure as well as involves unknown patch parameters, thus necessitating the development of parameter estimation techniques which are applicable in this coupled setting. In developing a framework for approximation, parameter estimation and implementation, strong consideration is given to the fact that the input operator is unbonded due to the discrete nature of the patches. Moreover, the model is weakly nonlinear. As a result of the coupling mechanism between the structural vibrations and the interior acoustic dynamics. Within this context, an illustrating model is given, well-posedness and approximations results are discussed and an applicable parameter estimation methodology is presented. The scheme is then illustrated through several numerical examples with simulations modeling a variety of commonly used structural acoustic techniques for systems excitations and data collection.

Investigation of Weibel-filament growth in the nonlinear regime using laser-irradiated foils of different materials

NASA Astrophysics Data System (ADS)

Manuel, Mario

2017-10-01

M.J.-E. MANUEL GENERAL ATOMICS, C.M. HUNTINGTON, D.P. HIGGINSON, B.B. POLLOCK, B.A. REMINGTON, H. RINDERKNECHT, J.S. ROSS, D. RYUTOV, G. SWADLING, S. WILKS, A.B. ZYLSTRA, H.-S. PARK LLNL, F. FIUZA, S. TOTORICASLAC, G. GREGORIOXFORD, J. PARK, A. SPITKOVSKYPRINCETON, Y. SAKAWA, H. TAKABEOSAKA, H. SIOMIT, A.B. ZYLSTRALANL. The Weibel instability is presently the leading mechanism proposed to amplify magnetic fields necessary to form `collisionless' shocks in weakly magnetized astrophysical systems, including young supernova remnants and gamma-ray bursts. These systems rely on the presence of strong self-generated magnetic fields to mediate shock formation since the typical collisional mean-free-path is much larger than the system size. The work presented here investigates the development of the Weibel instability in the nonlinear regime through experimental variation of plasma parameters using different ion species and separation distances. Our goal is to investigate the underlying physical mechanism that may allow the formation of collisionless shocks in astrophysical objects. Recent experimental and computational results will be presented and discussed. This work is funded by the NNSA-DS and SC-OFES Joint Program in High-Energy-Density Laboratory Plasmas, Grant Number DE-NA0002956 and in collaboration with LLNL under contract DE-AC52-07NA27344.

Transition Theory and Experimental Comparisons on (I) Amplification into Streets and (II) a Strongly Nonlinear Break-up Criterion

NASA Astrophysics Data System (ADS)

Smith, F. T.; Bowles, R. I.

1992-10-01

The two stages I, II are studied by using recent nonlinear theory and then compared with the experiments of Nishioka et al. (1979) on the transition of plane Poiseuille flow. The first stage I starts at low amplitude from warped input, which is deformed through weakly nonlinear interaction into a blow-up in amplitude and phase accompanied by spanwise focusing into streets. This leads into the strongly nonlinear stage II. It holds for a broad range of interactive boundary layers and related flows, to all of which the nonlinear break-up criterion applies. The experimental comparisons on I, II for channel flow overall show encouraging quantitative agreement, supporting recent comparisons (in the boundary-layer setting) of the description of stage I in Stewart & Smith (1992) with the experiments of Klebanoff & Tidstrom (1959) and of the break-up criterion of Smith (1988a) with the computations of Peridier et al. (1991 a, b).

Scattering theory of nonlinear thermoelectricity in quantum coherent conductors.

PubMed

Meair, Jonathan; Jacquod, Philippe

2013-02-27

We construct a scattering theory of weakly nonlinear thermoelectric transport through sub-micron scale conductors. The theory incorporates the leading nonlinear contributions in temperature and voltage biases to the charge and heat currents. Because of the finite capacitances of sub-micron scale conducting circuits, fundamental conservation laws such as gauge invariance and current conservation require special care to be preserved. We do this by extending the approach of Christen and Büttiker (1996 Europhys. Lett. 35 523) to coupled charge and heat transport. In this way we write relations connecting nonlinear transport coefficients in a manner similar to Mott's relation between the linear thermopower and the linear conductance. We derive sum rules that nonlinear transport coefficients must satisfy to preserve gauge invariance and current conservation. We illustrate our theory by calculating the efficiency of heat engines and the coefficient of performance of thermoelectric refrigerators based on quantum point contacts and resonant tunneling barriers. We identify, in particular, rectification effects that increase device performance.

Regional evaporation estimates in the eastern monsoon region of China: Assessment of a nonlinear formulation of the complementary principle

NASA Astrophysics Data System (ADS)

Liu, Xiaomang; Liu, Changming; Brutsaert, Wilfried

2016-12-01

The performance of a nonlinear formulation of the complementary principle for evaporation estimation was investigated in 241 catchments with different climate conditions in the eastern monsoon region of China. Evaporation (Ea) calculated by the water balance equation was used as the reference. Ea estimated by the calibrated nonlinear formulation was generally in good agreement with the water balance results, especially in relatively dry catchments. The single parameter in the nonlinear formulation, namely αe as a weak analog of the alpha parameter of Priestley and Taylor (), tended to exhibit larger values in warmer and humid near-coastal areas, but smaller values in colder, drier environments inland, with a significant dependency on the aridity index (AI). The nonlinear formulation combined with the equation relating the one parameter and AI provides a promising method to estimate regional Ea with standard and routinely measured meteorological data.

Numerical solution methods for viscoelastic orthotropic materials

NASA Technical Reports Server (NTRS)

Gramoll, K. C.; Dillard, D. A.; Brinson, H. F.

1988-01-01

Numerical solution methods for viscoelastic orthotropic materials, specifically fiber reinforced composite materials, are examined. The methods include classical lamination theory using time increments, direction solution of the Volterra Integral, Zienkiewicz's linear Prony series method, and a new method called Nonlinear Differential Equation Method (NDEM) which uses a nonlinear Prony series. The criteria used for comparison of the various methods include the stability of the solution technique, time step size stability, computer solution time length, and computer memory storage. The Volterra Integral allowed the implementation of higher order solution techniques but had difficulties solving singular and weakly singular compliance function. The Zienkiewicz solution technique, which requires the viscoelastic response to be modeled by a Prony series, works well for linear viscoelastic isotropic materials and small time steps. The new method, NDEM, uses a modified Prony series which allows nonlinear stress effects to be included and can be used with orthotropic nonlinear viscoelastic materials. The NDEM technique is shown to be accurate and stable for both linear and nonlinear conditions with minimal computer time.

Evaluation of a transfinite element numerical solution method for nonlinear heat transfer problems

NASA Technical Reports Server (NTRS)

Cerro, J. A.; Scotti, S. J.

1991-01-01

Laplace transform techniques have been widely used to solve linear, transient field problems. A transform-based algorithm enables calculation of the response at selected times of interest without the need for stepping in time as required by conventional time integration schemes. The elimination of time stepping can substantially reduce computer time when transform techniques are implemented in a numerical finite element program. The coupling of transform techniques with spatial discretization techniques such as the finite element method has resulted in what are known as transfinite element methods. Recently attempts have been made to extend the transfinite element method to solve nonlinear, transient field problems. This paper examines the theoretical basis and numerical implementation of one such algorithm, applied to nonlinear heat transfer problems. The problem is linearized and solved by requiring a numerical iteration at selected times of interest. While shown to be acceptable for weakly nonlinear problems, this algorithm is ineffective as a general nonlinear solution method.

Proceedings of the Conference on Moments and Signal

NASA Astrophysics Data System (ADS)

Purdue, P.; Solomon, H.

1992-09-01

The focus of this paper is (1) to describe systematic methodologies for selecting nonlinear transformations for blind equalization algorithms (and thus new types of cumulants), and (2) to give an overview of the existing blind equalization algorithms and point out their strengths as well as weaknesses. It is shown that all blind equalization algorithms belong in one of the following three categories, depending where the nonlinear transformation is being applied on the data: (1) the Bussgang algorithms, where the nonlinearity is in the output of the adaptive equalization filter; (2) the polyspectra (or Higher-Order Spectra) algorithms, where the nonlinearity is in the input of the adaptive equalization filter; and (3) the algorithms where the nonlinearity is inside the adaptive filter, i.e., the nonlinear filter or neural network. We describe methodologies for selecting nonlinear transformations based on various optimality criteria such as MSE or MAP. We illustrate that such existing algorithms as Sato, Benveniste-Goursat, Godard or CMA, Stop-and-Go, and Donoho are indeed special cases of the Bussgang family of techniques when the nonlinearity is memoryless. We present results that demonstrate the polyspectra-based algorithms exhibit faster convergence rate than Bussgang algorithms. However, this improved performance is at the expense of more computations per iteration. We also show that blind equalizers based on nonlinear filters or neural networks are more suited for channels that have nonlinear distortions.

Note: Fully integrated time-to-amplitude converter in Si-Ge technology.

PubMed

Crotti, M; Rech, I; Ghioni, M

2010-10-01

Over the past years an always growing interest has arisen about the measurement technique of time-correlated single photon counting TCSPC), since it allows the analysis of extremely fast and weak light waveforms with a picoseconds resolution. Consequently, many applications exploiting TCSPC have been developed in several fields such as medicine and chemistry. Moreover, the development of multianode PMT and of single photon avalanche diode arrays led to the realization of acquisition systems with several parallel channels to employ the TCSPC technique in even more applications. Since TCSPC basically consists of the measurement of the arrival time of a photon, the most important part of an acquisition chain is the time measurement block, which must have high resolution and low differential nonlinearity, and in order to realize multidimensional systems, it has to be integrated to reduce both cost and area. In this paper we present a fully integrated time-to-amplitude converter, built in 0.35 μm Si-Ge technology, characterized by a good time resolution (60 ps), low differential nonlinearity (better than 3% peak to peak), high counting rate (16 MHz), low and constant power dissipation (40 mW), and low area occupation (1.38×1.28 mm(2)).

Noise-Enhanced Human Balance Control

NASA Astrophysics Data System (ADS)

Priplata, Attila; Niemi, James; Salen, Martin; Harry, Jason; Lipsitz, Lewis A.; Collins, J. J.

2002-11-01

Noise can enhance the detection and transmission of weak signals in certain nonlinear systems, via a mechanism known as stochastic resonance. Here we show that input noise can be used to improve motor control in humans. Specifically, we show that the postural sway of both young and elderly individuals during quiet standing can be significantly reduced by applying subsensory mechanical noise to the feet. We further demonstrate with input noise a trend towards the reduction of postural sway in elderly subjects to the level of young subjects. These results suggest that noise-based devices, such as randomly vibrating shoe inserts, may enable people to overcome functional difficulties due to age-related sensory loss.

Amplitude and phase fluctuations of Van der Pol oscillator under external random forcing

NASA Astrophysics Data System (ADS)

Singh, Aman K.; Yadava, R. D. S.

2018-05-01

The paper presents an analytical study of noise in Van der Pol oscillator output subjected to an external force noise assumed to be characterized by delta function (white noise). The external fluctuations are assumed to be small in comparison to the average response of the noise free system. The autocorrelation function and power spectrum are calculated under the condition of weak nonlinearity. The latter ensures limit cycle oscillations. The total spectral power density is dominated by the contributions from the phase fluctuations. The amplitude fluctuations are at least two orders of magnitude smaller. The analysis is shown to be useful to interpretation microcantilever based biosensing data.

Spin noise spectroscopy beyond thermal equilibrium and linear response.

PubMed

Glasenapp, P; Sinitsyn, N A; Yang, Luyi; Rickel, D G; Roy, D; Greilich, A; Bayer, M; Crooker, S A

2014-10-10

Per the fluctuation-dissipation theorem, the information obtained from spin fluctuation studies in thermal equilibrium is necessarily constrained by the system's linear response functions. However, by including weak radio frequency magnetic fields, we demonstrate that intrinsic and random spin fluctuations even in strictly unpolarized ensembles can reveal underlying patterns of correlation and coupling beyond linear response, and can be used to study nonequilibrium and even multiphoton coherent spin phenomena. We demonstrate this capability in a classical vapor of (41)K alkali atoms, where spin fluctuations alone directly reveal Rabi splittings, the formation of Mollow triplets and Autler-Townes doublets, ac Zeeman shifts, and even nonlinear multiphoton coherences.

Coulomb disorder in three-dimensional Dirac materials

NASA Astrophysics Data System (ADS)

Skinner, Brian

2015-03-01

In three-dimensional materials with a Dirac spectrum, weak short-ranged disorder is essentially irrelevant near the Dirac point. This is manifestly not the case for Coulomb disorder, where the long-ranged nature of the potential produced by charged impurities implies large fluctuations of the disorder potential even when impurities are sparse, and these fluctuations are screened by the formation of electron/hole puddles. Here I outline a theory of such nonlinear screening of Coulomb disorder in three-dimensional Dirac systems, and present results for the typical magnitude of the disorder potential, the corresponding density of states, and the size and density of electron/hole puddles. The resulting conductivity is also discussed.

Noise assisted pattern fabrication

NASA Astrophysics Data System (ADS)

Roy, Tanushree; Agarwal, V.; Singh, B. P.; Parmananda, P.

2018-04-01

Pre-selected patterns on an n-type Si surface are fabricated by electrochemical etching in the presence of a weak optical signal. The constructive role of noise, namely, stochastic resonance (SR), is exploited for these purposes. SR is a nonlinear phenomenon wherein at an optimal amplitude of noise, the information transfer from weak input sub-threshold signals to the system output is maximal. In the present work, the amplitude of internal noise was systematically regulated by varying the molar concentration of hydrofluoric acid (HF) in the electrolyte. Pattern formation on the substrate for two different amplitudes (25 ± 2 and 11 ± 1 mW) of the optical template (sub-threshold signal) was considered. To quantify the fidelity/quality of pattern formation, the spatial cross-correlation coefficient (CCC) between the constructed pattern and the template of the applied signal was calculated. The maximum CCC is obtained for the pattern formed at an optimal HF concentration, indicating SR. Simulations, albeit using external noise, on a spatial array of coupled FitzHugh-Nagumo oscillators revealed similar results.

Nonlinear coherent structures of Alfvén wave in a collisional plasma

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

Jana, Sayanee; Chakrabarti, Nikhil; Ghosh, Samiran

2016-07-15

The Alfvén wave dynamics is investigated in the framework of two-fluid approach in a compressible collisional magnetized plasma. In the finite amplitude limit, the dynamics of the nonlinear Alfvén wave is found to be governed by a modified Korteweg-de Vries Burgers equation (mKdVB). In this mKdVB equation, the electron inertia is found to act as a source of dispersion, and the electron-ion collision serves as a dissipation. The collisional dissipation is eventually responsible for the Burgers term in mKdVB equation. In the long wavelength limit, this weakly nonlinear Alfvén wave is shown to be governed by a damped nonlinear Schrödingermore » equation. Furthermore, these nonlinear equations are analyzed by means of analytical calculation and numerical simulation to elucidate the various aspects of the phase-space dynamics of the nonlinear wave. Results reveal that nonlinear Alfvén wave exhibits the dissipation mediated shock, envelope, and breather like structures. Numerical simulations also predict the formation of dissipative Alfvénic rogue wave, giant breathers, and rogue wave holes. These results are discussed in the context of the space plasma.« less

Remarks on the regularity criteria of three-dimensional magnetohydrodynamics system in terms of two velocity field components

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

Yamazaki, Kazuo

2014-03-15

We study the three-dimensional magnetohydrodynamics system and obtain its regularity criteria in terms of only two velocity vector field components eliminating the condition on the third component completely. The proof consists of a new decomposition of the four nonlinear terms of the system and estimating a component of the magnetic vector field in terms of the same component of the velocity vector field. This result may be seen as a component reduction result of many previous works [C. He and Z. Xin, “On the regularity of weak solutions to the magnetohydrodynamic equations,” J. Differ. Equ. 213(2), 234–254 (2005); Y. Zhou,more » “Remarks on regularities for the 3D MHD equations,” Discrete Contin. Dyn. Syst. 12(5), 881–886 (2005)].« less

Le Chatelier Principle for Out-of-Equilibrium and Boundary-Driven Systems: Application to Dynamical Phase Transitions.

PubMed

Shpielberg, O; Akkermans, E

2016-06-17

A stability analysis is presented for boundary-driven and out-of-equilibrium systems in the framework of the hydrodynamic macroscopic fluctuation theory. A Hamiltonian description is proposed which allows us to thermodynamically interpret the additivity principle. A necessary and sufficient condition for the validity of the additivity principle is obtained as an extension of the Le Chatelier principle. These stability conditions result from a diagonal quadratic form obtained using the cumulant generating function. This approach allows us to provide a proof for the stability of the weakly asymmetric exclusion process and to reduce the search for stability to the solution of two coupled linear ordinary differential equations instead of nonlinear partial differential equations. Additional potential applications of these results are discussed in the realm of classical and quantum systems.

Le Chatelier Principle for Out-of-Equilibrium and Boundary-Driven Systems: Application to Dynamical Phase Transitions

NASA Astrophysics Data System (ADS)

Shpielberg, O.; Akkermans, E.

2016-06-01

A stability analysis is presented for boundary-driven and out-of-equilibrium systems in the framework of the hydrodynamic macroscopic fluctuation theory. A Hamiltonian description is proposed which allows us to thermodynamically interpret the additivity principle. A necessary and sufficient condition for the validity of the additivity principle is obtained as an extension of the Le Chatelier principle. These stability conditions result from a diagonal quadratic form obtained using the cumulant generating function. This approach allows us to provide a proof for the stability of the weakly asymmetric exclusion process and to reduce the search for stability to the solution of two coupled linear ordinary differential equations instead of nonlinear partial differential equations. Additional potential applications of these results are discussed in the realm of classical and quantum systems.

Rogue events in the group velocity horizon.

PubMed

Demircan, Ayhan; Amiranashvili, Shalva; Brée, Carsten; Mahnke, Christoph; Mitschke, Fedor; Steinmeyer, Günter

2012-01-01

The concept of rogue waves arises from a mysterious and potentially calamitous phenomenon of oceanic surfaces. There is mounting evidence that they are actually commonplace in a variety of different physical settings. A set of defining criteria has been advanced; this set is of great generality and therefore applicable to a wide class of systems. The question arises naturally whether there are generic mechanisms responsible for extreme events in different systems. Here we argue that under suitable circumstances nonlinear interaction between weak and strong waves results in intermittent giant waves with all the signatures of rogue waves. To obtain these circumstances only a few basic conditions must be met. Then reflection of waves at the so-called group-velocity horizon occurs. The connection between rogue waves and event horizons, seemingly unrelated physical phenomena, is identified as a feature common in many different physical systems.

Nonlinear spectral imaging of biological tissues

NASA Astrophysics Data System (ADS)

Palero, J. A.

2007-07-01

The work presented in this thesis demonstrates live high resolution 3D imaging of tissue in its native state and environment. The nonlinear interaction between focussed femtosecond light pulses and the biological tissue results in the emission of natural autofluorescence and second-harmonic signal. Because biological intrinsic emission is generally very weak and extends from the ultraviolet to the visible spectral range, a broad-spectral range and high sensitivity 3D spectral imaging system is developed. Imaging the spectral characteristics of the biological intrinsic emission reveals the structure and biochemistry of the cells and extra-cellular components. By using different methods in visualizing the spectral images, discrimination between different tissue structures is achieved without the use of any stain or fluorescent label. For instance, RGB real color spectral images of the intrinsic emission of mouse skin tissues show blue cells, green hair follicles, and purple collagen fibers. The color signature of each tissue component is directly related to its characteristic emission spectrum. The results of this study show that skin tissue nonlinear intrinsic emission is mainly due to the autofluorescence of reduced nicotinamide adenine dinucleotide (phosphate), flavins, keratin, melanin, phospholipids, elastin and collagen and nonlinear Raman scattering and second-harmonic generation in Type I collagen. In vivo time-lapse spectral imaging is implemented to study metabolic changes in epidermal cells in tissues. Optical scattering in tissues, a key factor in determining the maximum achievable imaging depth, is also investigated in this work.

The Effect of Detector Nonlinearity on WFIRST PSF Profiles for Weak Gravitational Lensing Measurements

NASA Astrophysics Data System (ADS)

Plazas, A. A.; Shapiro, C.; Kannawadi, A.; Mandelbaum, R.; Rhodes, J.; Smith, R.

2016-10-01

Weak gravitational lensing (WL) is one of the most powerful techniques to learn about the dark sector of the universe. To extract the WL signal from astronomical observations, galaxy shapes must be measured and corrected for the point-spread function (PSF) of the imaging system with extreme accuracy. Future WL missions—such as NASA’s Wide-Field Infrared Survey Telescope (WFIRST)—will use a family of hybrid near-infrared complementary metal-oxide-semiconductor detectors (HAWAII-4RG) that are untested for accurate WL measurements. Like all image sensors, these devices are subject to conversion gain nonlinearities (voltage response to collected photo-charge) that bias the shape and size of bright objects such as reference stars that are used in PSF determination. We study this type of detector nonlinearity (NL) and show how to derive requirements on it from WFIRST PSF size and ellipticity requirements. We simulate the PSF optical profiles expected for WFIRST and measure the fractional error in the PSF size (ΔR/R) and the absolute error in the PSF ellipticity (Δe) as a function of star magnitude and the NL model. For our nominal NL model (a quadratic correction), we find that, uncalibrated, NL can induce an error of ΔR/R = 1 × 10-2 and Δe 2 = 1.75 × 10-3 in the H158 bandpass for the brightest unsaturated stars in WFIRST. In addition, our simulations show that to limit the bias of ΔR/R and Δe in the H158 band to ˜10% of the estimated WFIRST error budget, the quadratic NL model parameter β must be calibrated to ˜1% and ˜2.4%, respectively. We present a fitting formula that can be used to estimate WFIRST detector NL requirements once a true PSF error budget is established.

Apparatus and method for characterizing ultrafast polarization varying optical pulses

DOEpatents

Smirl, Arthur; Trebino, Rick P.

1999-08-10

Practical techniques are described for characterizing ultrafast potentially ultraweak, ultrashort optical pulses. The techniques are particularly suited to the measurement of signals from nonlinear optical materials characterization experiments, whose signals are generally too weak for full characterization using conventional techniques.

Power Spectrum of a Noisy System Close to a Heteroclinic Orbit

NASA Astrophysics Data System (ADS)

Giner-Baldó, Jordi; Thomas, Peter J.; Lindner, Benjamin

2017-07-01

We consider a two-dimensional dynamical system that possesses a heteroclinic orbit connecting four saddle points. This system is not able to show self-sustained oscillations on its own. If endowed with white Gaussian noise it displays stochastic oscillations, the frequency and quality factor of which are controlled by the noise intensity. This stochastic oscillation of a nonlinear system with noise is conveniently characterized by the power spectrum of suitable observables. In this paper we explore different analytical and semianalytical ways to compute such power spectra. Besides a number of explicit expressions for the power spectrum, we find scaling relations for the frequency, spectral width, and quality factor of the stochastic heteroclinic oscillator in the limit of weak noise. In particular, the quality factor shows a slow logarithmic increase with decreasing noise of the form Q˜ [ln (1/D)]^2. Our results are compared to numerical simulations of the respective Langevin equations.

Multi-LED parallel transmission for long distance underwater VLC system with one SPAD receiver

NASA Astrophysics Data System (ADS)

Wang, Chao; Yu, Hong-Yi; Zhu, Yi-Jun; Wang, Tao; Ji, Ya-Wei

2018-03-01

In this paper, a multiple light emitting diode (LED) chips parallel transmission (Multi-LED-PT) scheme for underwater visible light communication system with one photon-counting single photon avalanche diode (SPAD) receiver is proposed. As the lamp always consists of multi-LED chips, the data rate could be improved when we drive these multi-LED chips parallel by using the interleaver-division-multiplexing technique. For each chip, the on-off-keying modulation is used to reduce the influence of clipping. Then a serial successive interference cancellation detection algorithm based on ideal Poisson photon-counting channel by the SPAD is proposed. Finally, compared to the SPAD-based direct current-biased optical orthogonal frequency division multiplexing system, the proposed Multi-LED-PT system could improve the error-rate performance and anti-nonlinearity performance significantly under the effects of absorption, scattering and weak turbulence-induced channel fading together.

New device to measure dynamic intrusion/extrusion cycles of lyophobic heterogeneous systems.

PubMed

Guillemot, Ludivine; Galarneau, Anne; Vigier, Gérard; Abensur, Thierry; Charlaix, Élisabeth

2012-10-01

Lyophobic heterogeneous systems (LHS) are made of mesoporous materials immersed in a non-wetting liquid. One application of LHS is the nonlinear damping of high frequency vibrations. The behaviour of LHS is characterized by P - ΔV cycles, where P is the pressure applied to the system, and ΔV its volume change due to the intrusion of the liquid into the pores of the material, or its extrusion out of the pores. Very few dynamic studies of LHS have been performed until now. We describe here a new apparatus that allows us to carry out dynamic intrusion/extrusion cycles with various liquid/porous material systems, controlling the temperature from ambient to 120 °C and the frequency from 0.01 to 20 Hz. We show that for two LHS: water/MTS and Galinstan/CPG, the energy dissipated during one cycle depends very weakly on the cycle frequency, in strong contrast to conventional dampers.

Amplitude-dependent topological edge states in nonlinear phononic lattices

NASA Astrophysics Data System (ADS)

Pal, Raj Kumar; Vila, Javier; Leamy, Michael; Ruzzene, Massimo

2018-03-01

This work investigates the effect of nonlinearities on topologically protected edge states in one- and two-dimensional phononic lattices. We first show that localized modes arise at the interface between two spring-mass chains that are inverted copies of each other. Explicit expressions derived for the frequencies of the localized modes guide the study of the effect of cubic nonlinearities on the resonant characteristics of the interface, which are shown to be described by a Duffing-like equation. Nonlinearities produce amplitude-dependent frequency shifts, which in the case of a softening nonlinearity cause the localized mode to migrate to the bulk spectrum. The case of a hexagonal lattice implementing a phononic analog of a crystal exhibiting the quantum spin Hall effect is also investigated in the presence of weakly nonlinear cubic springs. An asymptotic analysis provides estimates of the amplitude dependence of the localized modes, while numerical simulations illustrate how the lattice response transitions from bulk-to-edge mode-dominated by varying the excitation amplitude. In contrast with the interface mode of the first example studies, this occurs both for hardening and softening springs. The results of this study provide a theoretical framework for the investigation of nonlinear effects that induce and control topologically protected wave modes through nonlinear interactions and amplitude tuning.

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.

SEACAS Theory Manuals: Part 1. Problem Formulation in Nonlinear Solid Mechancis

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

Attaway, S.W.; Laursen, T.A.; Zadoks, R.I.

1998-08-01

This report gives an introduction to the basic concepts and principles involved in the formulation of nonlinear problems in solid mechanics. By way of motivation, the discussion begins with a survey of some of the important sources of nonlinearity in solid mechanics applications, using wherever possible simple one dimensional idealizations to demonstrate the physical concepts. This discussion is then generalized by presenting generic statements of initial/boundary value problems in solid mechanics, using linear elasticity as a template and encompassing such ideas as strong and weak forms of boundary value problems, boundary and initial conditions, and dynamic and quasistatic idealizations. Themore » notational framework used for the linearized problem is then extended to account for finite deformation of possibly inelastic solids, providing the context for the descriptions of nonlinear continuum mechanics, constitutive modeling, and finite element technology given in three companion reports.« less

Nonlinear Wavelength Selection in Surface Faceting under Electromigration

NASA Astrophysics Data System (ADS)

Barakat, Fatima; Martens, Kirsten; Pierre-Louis, Olivier

2012-08-01

We report on the control of the faceting of crystal surfaces by means of surface electromigration. When electromigration reinforces the faceting instability, we find perpetual coarsening with a wavelength increasing as t1/2. For strongly stabilizing electromigration, the surface is stable. For weakly stabilizing electromigration, a cellular pattern is obtained, with a nonlinearly selected wavelength. The selection mechanism is not caused by an instability of steady states, as suggested by previous works in the literature. Instead, the dynamics is found to exhibit coarsening before reaching a continuous family of stable nonequilibrium steady states.

Physical mechanisms of solar activity effects in the middle atmosphere

NASA Technical Reports Server (NTRS)

Ebel, A.

1989-01-01

A great variety of physical mechanisms of possibly solar induced variations in the middle atmosphere has been discussed in the literature during the last decades. The views which have been put forward are often controversial in their physical consequences. The reason may be the complexity and non-linearity of the atmospheric response to comparatively weak forcing resulting from solar activity. Therefore this review focuses on aspects which seem to indicate nonlinear processes in the development of solar induced variations. Results from observations and numerical simulations are discussed.

Complexity and Productivity Differentiation Models of Metallogenic Indicator Elements in Rocks and Supergene Media Around Daijiazhuang Pb-Zn Deposit in Dangchang County, Gansu Province

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

He, Jin-zhong, E-mail: viewsino@163.com; Yao, Shu-zhen; Zhang, Zhong-ping

2013-03-15

With the help of complexity indices, we quantitatively studied multifractals, frequency distributions, and linear and nonlinear characteristics of geochemical data for exploration of the Daijiazhuang Pb-Zn deposit. Furthermore, we derived productivity differentiation models of elements from thermodynamics and self-organized criticality of metallogenic systems. With respect to frequency distributions and multifractals, only Zn in rocks and most elements except Sb in secondary media, which had been derived mainly from weathering and alluviation, exhibit nonlinear distributions. The relations of productivity to concentrations of metallogenic elements and paragenic elements in rocks and those of elements strongly leached in secondary media can be seenmore » as linear addition of exponential functions with a characteristic weak chaos. The relations of associated elements such as Mo, Sb, and Hg in rocks and other elements in secondary media can be expressed as an exponential function, and the relations of one-phase self-organized geological or metallogenic processes can be represented by a power function, each representing secondary chaos or strong chaos. For secondary media, exploration data of most elements should be processed using nonlinear mathematical methods or should be transformed to linear distributions before processing using linear mathematical methods.« less

Magneto-electric transition in nickel-gallium arsenide-nickel multiferroic structure

NASA Astrophysics Data System (ADS)

Galichyan, T. A.; Filippov, D. A.; Laletin, V. M.; Firsova, T. O.; Poddubnaya, N. N.

2018-04-01

Experimental studies of the magnetoelectric effect are presented in structures manufactured by electrolytic deposition of nickel on a substrate of gallium arsenide. It is shown that the use of gold-germanium-nickel sublayer, when sprayed on a substrate, significantly improves the adhesion between electrolytically deposited nickel and substrate. Linear and nonlinear magnetoelectric effects on the alternating magnetic field are observed in these structures. Both effects have resonant character and the resonance frequency of the nonlinear effect is twice less than that of the linear effect. In weak fields, the value of the nonlinear magnetoelectric effect is in quadratic dependence on the alternating magnetic field and unlike the linear magnetoelectric effect, it does not depend on the bias field.

Derivation of nonlinear wave equations for ultrasound beam in nonuniform bubbly liquids

NASA Astrophysics Data System (ADS)

Kanagawa, Tetsuya; Yano, Takeru; Kawahara, Junya; Kobayashi, Kazumichi; Watanabe, Masao; Fujikawa, Shigeo

2012-09-01

Weakly nonlinear propagation of diffracted ultrasound beams in a nonuniform bubbly liquid is theoretically studied based on the method of multiple scales with the set of scaling relations of some physical parameters. It is assumed that the spatial distribution of the number density of bubbles in an initial state at rest is a slowly varying function of space coordinates and the amplitude of its variation is small compared with a mean number density. As a result, a Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation with dispersion and nonuniform effects for a low frequency case and a nonlinear Schrödinger (NLS) equation with dissipation, diffraction, and nonuniform effects for a high frequency case, are derived from the basic equations of bubbly flows.

Interfacial patterns in magnetorheological fluids: Azimuthal field-induced structures.

PubMed

Dias, Eduardo O; Lira, Sérgio A; Miranda, José A

2015-08-01

Despite their practical and academic relevance, studies of interfacial pattern formation in confined magnetorheological (MR) fluids have been largely overlooked in the literature. In this work, we present a contribution to this soft matter research topic and investigate the emergence of interfacial instabilities when an inviscid, initially circular bubble of a Newtonian fluid is surrounded by a MR fluid in a Hele-Shaw cell apparatus. An externally applied, in-plane azimuthal magnetic field produced by a current-carrying wire induces interfacial disturbances at the two-fluid interface, and pattern-forming structures arise. Linear stability analysis, weakly nonlinear theory, and a vortex sheet approach are used to access early linear and intermediate nonlinear time regimes, as well as to determine stationary interfacial shapes at fully nonlinear stages.

Random perturbations of a periodically driven nonlinear oscillator: escape from a resonance zone

NASA Astrophysics Data System (ADS)

Lingala, Nishanth; Sri Namachchivaya, N.; Pavlyukevich, Ilya

2017-04-01

For nonlinear oscillators, frequency of oscillations depends on the oscillation amplitude. When a nonlinear oscillator is periodically driven, the phase space consists of many resonance zones where the oscillator frequency and the driving frequency are commensurable. It is well known that, a small subset of initial conditions can lead to capture in one of the resonance zones. In this paper we study the effect of weak noise on the escape from a resonance zone. Using averaging techniques we obtain the mean exit time from a resonance zone and study the dependence of the exit rate on the parameters of the oscillator. Paper dedicated to Professor Peter W Sauer of University of Illinois on the occasion of his 70th birthday.

Amplification of a seed pumped by a chirped laser in the strong coupling Brillouin regime

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

Schluck, F.; Lehmann, G.; Spatschek, K. H.

Seed amplification via Brillouin backscattering of a long pump laser-pulse is considered. The interaction takes place in the so called strong coupling regime. Pump chirping is applied to mitigate spontaneous Raman backscattering of the pump before interacting with the seed. The strong coupling regime facilitates stronger exponential growth and narrower seeds compared to the so called weak coupling regime, although in the latter the scaling with pump amplitude is stronger. Strong coupling is achieved when the pump laser amplitude exceeds a certain threshold. It is shown how the chirp influences both the linear as well as the nonlinear amplification process.more » First, linear amplification as well as the seed profiles are determined in dependence of the chirping rate. In contrast to the weak coupling situation, the evolution is not symmetric with respect to the sign of the chirping rate. In the nonlinear stage of the amplification, we find an intrinsic chirp of the seed pulse even for an un-chirped pump. We show that chirping the pump may have a strong influence on the shape of the seed in the nonlinear amplification phase. Also, the influence of pump chirp on the efficiency of Brillouin seed amplification is discussed.« less

Thermal Non-Equilibrium Flows in Three Space Dimensions

NASA Astrophysics Data System (ADS)

Zeng, Yanni

2016-01-01

We study the equations describing the motion of a thermal non-equilibrium gas in three space dimensions. It is a hyperbolic system of six equations with a relaxation term. The dissipation mechanism induced by the relaxation is weak in the sense that the Shizuta-Kawashima criterion is violated. This implies that a perturbation of a constant equilibrium state consists of two parts: one decays in time while the other stays. In fact, the entropy wave grows weakly along the particle path as the process is irreversible. We study thermal properties related to the well-posedness of the nonlinear system. We also obtain a detailed pointwise estimate on the Green's function for the Cauchy problem when the system is linearized around an equilibrium constant state. The Green's function provides a complete picture of the wave pattern, with an exact and explicit leading term. Comparing with existing results for one dimensional flows, our results reveal a new feature of three dimensional flows: not only does the entropy wave not decay, but the velocity also contains a non-decaying part, strongly coupled with its decaying one. The new feature is supported by the second order approximation via the Chapman-Enskog expansions, which are the Navier-Stokes equations with vanished shear viscosity and heat conductivity.

Simulating faults and plate boundaries with a transversely isotropic plasticity model

NASA Astrophysics Data System (ADS)

Sharples, W.; Moresi, L. N.; Velic, M.; Jadamec, M. A.; May, D. A.

2016-03-01

In mantle convection simulations, dynamically evolving plate boundaries have, for the most part, been represented using an visco-plastic flow law. These systems develop fine-scale, localized, weak shear band structures which are reminiscent of faults but it is a significant challenge to resolve the large- and the emergent, small-scale-behavior. We address this issue of resolution by taking into account the observation that a rock element with embedded, planar, failure surfaces responds as a non-linear, transversely isotropic material with a weak orientation defined by the plane of the failure surface. This approach partly accounts for the large-scale behavior of fine-scale systems of shear bands which we are not in a position to resolve explicitly. We evaluate the capacity of this continuum approach to model plate boundaries, specifically in the context of subduction models where the plate boundary interface has often been represented as a planar discontinuity. We show that the inclusion of the transversely isotropic plasticity model for the plate boundary promotes asymmetric subduction from initiation. A realistic evolution of the plate boundary interface and associated stresses is crucial to understanding inter-plate coupling, convergent margin driven topography, and earthquakes.

Dispersive shock waves in Bose-Einstein condensates and nonlinear nano-oscillators in ferromagnetic thin films

NASA Astrophysics Data System (ADS)

Hoefer, Mark A.

This thesis examines nonlinear wave phenomena, in two physical systems: a Bose-Einstein condensate (BEC) and thin film ferromagnets where the magnetization dynamics are excited by the spin momentum transfer (SMT) effect. In the first system, shock waves generated by steep gradients in the BEC wavefunction are shown to be of the disperse type. Asymptotic and averaging methods are used to determine shock speeds and structure in one spatial dimension. These results are compared with multidimensional numerical simulations and experiment showing good, qualitative agreement. In the second system, a model of magnetization dynamics due to SMT is presented. Using this model, nonlinear oscillating modes---nano-oscillators---are found numerically and analytically using perturbative methods. These results compare well with experiment. A Bose-Einstein condensate (BEC) is a quantum fluid that gives rise to interesting shock wave nonlinear dynamics. Experiments depict a BEC that exhibits behavior similar to that of a shock wave in a compressible gas, e.g. traveling fronts with steep gradients. However, the governing Gross-Pitaevskii (GP) equation that describes the mean field of a BEC admits no dissipation hence classical dissipative shock solutions do not explain the phenomena. Instead, wave dynamics with small dispersion is considered and it is shown that this provides a mechanism for the generation of a dispersive shock wave (DSW). Computations with the GP equation are compared to experiment with excellent agreement. A comparison between a canonical 1D dissipative and dispersive shock problem shows significant differences in shock structure and shock front speed. Numerical results associated with laboratory experiments show that three and two-dimensional approximations are in excellent agreement and one dimensional approximations are in qualitative agreement. The interaction of two DSWs is investigated analytically and numerically. Using one dimensional DSW theory it is argued that the experimentally observed blast waves may be viewed as dispersive shock waves. A nonlinear mathematical model of spin-wave excitation using a point contact in a thin ferromagnetic film is introduced. This work incorporates a recently proposed spin-torque contribution to classical magnetodynamic theory with a variable coefficient terra in the magnetic torque equation. Large-amplitude magnetic solitary waves are computed, which help explain recent spin-torque experiments. Numerical simulations of the full nonlinear model predict excitation frequencies in excess of 0.2 THz for contact diameters smaller than 6 nm. Simulations also predict a saturation and red shift of the frequency at currents large enough to invert the magnetization tinder the point contact. In the weak nonlinear limit, the theory is approximated by a cubic complex Ginzburg-Landau type equation. The mode's nonlinear frequency shift is found by use of perturbation techniques, whose results agree with those of direct numerical simulations.

Instabilities and transport in Hall plasmas with ExB drift

NASA Astrophysics Data System (ADS)

Smolyakov, Andrei

2016-10-01

Low temperature plasma with moderate magnetic field, where the ions are not or just weakly magnetized, i.e. the ion Larmor radius being larger or comparable to the characteristic length scale of interest (e.g. the size ofthe system), have distinctly different properties from strongly magnetized plasmas such as that for fusion applications. Such parameters regimes are generally defined here as Hall plasmas. The natural scale separation between the ion and electron Larmor radii in Hall plasma, further exploited by the application of the external electric field, offers unique applications in various plasma devices for material processing and electric propulsion. Plasmas in such devices are in strongly non-equilibrium state making it prone to a number of instabilities. This talk presents physics description of the dominant unstable modes in ExB Hall plasmas resulting in highly turbulent state with nonlinear coherent structures and anomalous electron current. Since ions are un-magnetized, fundamental instabilities operating in low temperature Hall plasmas are very different from much studied gradients (density, temperature and magnetic field) driven drift-wave turbulence in strongly magnetized plasmas for fusion applications. As a result the nonlinear saturation mechanisms, role of the ExB shear flows are also markedly different in such plasmas. We review the basic instabilities in these plasmas which are related to the ion-sound, low-hybrid and anti-drift modes, discuss nonlinear saturation and anomalous transport mechanisms. The advanced nonlinear fluid model for such plasmas and results of nonlinear simulations of turbulence and anomalous transport performed within a modified BOUT++ framework will be presented. Research supported by NSERC Canada and US AFOSR FA9550-15-1-0226.

Millimeter-wave interconnects for microwave-frequency quantum machines

NASA Astrophysics Data System (ADS)

Pechal, Marek; Safavi-Naeini, Amir H.

2017-10-01

Superconducting microwave circuits form a versatile platform for storing and manipulating quantum information. A major challenge to further scalability is to find approaches for connecting these systems over long distances and at high rates. One approach is to convert the quantum state of a microwave circuit to optical photons that can be transmitted over kilometers at room temperature with little loss. Many proposals for electro-optic conversion between microwave and optics use optical driving of a weak three-wave mixing nonlinearity to convert the frequency of an excitation. Residual absorption of this optical pump leads to heating, which is problematic at cryogenic temperatures. Here we propose an alternative approach where a nonlinear superconducting circuit is driven to interconvert between microwave-frequency (7 ×109 Hz) and millimeter-wave-frequency photons (3 ×1011 Hz). To understand the potential for quantum state conversion between microwave and millimeter-wave photons, we consider the driven four-wave mixing quantum dynamics of nonlinear circuits. In contrast to the linear dynamics of the driven three-wave mixing converters, the proposed four-wave mixing converter has nonlinear decoherence channels that lead to a more complex parameter space of couplings and pump powers that we map out. We consider physical realizations of such converter circuits by deriving theoretically the upper bound on the maximum obtainable nonlinear coupling between any two modes in a lossless circuit, and synthesizing an optimal circuit based on realistic materials that saturates this bound. Our proposed circuit dissipates less than 10-9 times the energy of current electro-optic converters per qubit. Finally, we outline the quantum link budget for optical, microwave, and millimeter-wave connections, showing that our approach is viable for realizing interconnected quantum processors for intracity or quantum data center environments.

A 1.26 μW Cytomimetic IC Emulating Complex Nonlinear Mammalian Cell Cycle Dynamics: Synthesis, Simulation and Proof-of-Concept Measured Results.

PubMed

Houssein, Alexandros; Papadimitriou, Konstantinos I; Drakakis, Emmanuel M

2015-08-01

Cytomimetic circuits represent a novel, ultra low-power, continuous-time, continuous-value class of circuits, capable of mapping on silicon cellular and molecular dynamics modelled by means of nonlinear ordinary differential equations (ODEs). Such monolithic circuits are in principle able to emulate on chip, single or multiple cell operations in a highly parallel fashion. Cytomimetic topologies can be synthesized by adopting the Nonlinear Bernoulli Cell Formalism (NBCF), a mathematical framework that exploits the striking similarities between the equations describing weakly-inverted Metal-Oxide Semiconductor (MOS) devices and coupled nonlinear ODEs, typically appearing in models of naturally encountered biochemical systems. The NBCF maps biological state variables onto strictly positive subthreshold MOS circuit currents. This paper presents the synthesis, the simulation and proof-of-concept chip results corresponding to the emulation of a complex cellular network mechanism, the skeleton model for the network of Cyclin-dependent Kinases (CdKs) driving the mammalian cell cycle. This five variable nonlinear biological model, when appropriate model parameter values are assigned, can exhibit multiple oscillatory behaviors, varying from simple periodic oscillations, to complex oscillations such as quasi-periodicity and chaos. The validity of our approach is verified by simulated results with realistic process parameters from the commercially available AMS 0.35 μm technology and by chip measurements. The fabricated chip occupies an area of 2.27 mm2 and consumes a power of 1.26 μW from a power supply of 3 V. The presented cytomimetic topology follows closely the behavior of its biological counterpart, exhibiting similar time-dependent solutions of the Cdk complexes, the transcription factors and the proteins.

Gravitational Lensing Corrections in Flat ΛCDM Cosmology

NASA Astrophysics Data System (ADS)

Kantowski, Ronald; Chen, Bin; Dai, Xinyu

2010-08-01

We compute the deflection angle to order (m/r 0)2 and m/r 0 × Λr 2 0 for a light ray traveling in a flat ΛCDM cosmology that encounters a completely condensed mass region. We use a Swiss cheese model for the inhomogeneities and find that the most significant correction to the Einstein angle occurs not because of the nonlinear terms but instead occurs because the condensed mass is embedded in a background cosmology. The Swiss cheese model predicts a decrease in the deflection angle of ~2% for weakly lensed galaxies behind the rich cluster A1689 and that the reduction can be as large as ~5% for similar rich clusters at z ≈ 1. Weak-lensing deflection angles caused by galaxies can likewise be reduced by as much as ~4%. We show that the lowest order correction in which Λ appears is proportional to m/r_0× √{Λ r_0^2}}} and could cause as much as a ~0.02% increase in the deflection angle for light that passes through a rich cluster. The lowest order nonlinear correction in the mass is proportional to m/r_0× √{m/r_0} and can increase the deflection angle by ~0.005% for weak lensing by galaxies.

Stationary and moving solitons in spin-orbit-coupled spin-1 Bose-Einstein condensates

NASA Astrophysics Data System (ADS)

Li, Yu-E.; Xue, Ju-Kui

2018-04-01

We investigate the matter-wave solitons in a spin-orbit-coupled spin-1 Bose-Einstein condensate using a multiscale perturbation method. Beginning with the one-dimensional spin-orbit-coupled threecomponent Gross-Pitaevskii equations, we derive a single nonlinear Schrödinger equation, which allows determination of the analytical soliton solutions of the system. Stationary and moving solitons in the system are derived. In particular, a parameter space for different existing soliton types is provided. It is shown that there exist only dark or bright solitons when the spin-orbit coupling is weak, with the solitons depending on the atomic interactions. However, when the spin-orbit coupling is strong, both dark and bright solitons exist, being determined by the Raman coupling. Our analytical solutions are confirmed by direct numerical simulations.

Apparatus and method for characterizing ultrafast polarization varying optical pulses

DOEpatents

Smirl, A.; Trebino, R.P.

1999-08-10

Practical techniques are described for characterizing ultrafast potentially ultraweak, ultrashort optical pulses. The techniques are particularly suited to the measurement of signals from nonlinear optical materials characterization experiments, whose signals are generally too weak for full characterization using conventional techniques. 2 figs.

Perpendicular Diffusion Coefficient of Comic Rays: The Presence of Weak Adiabatic Focusing

NASA Astrophysics Data System (ADS)

Wang, J. F.; Qin, G.; Ma, Q. M.; Song, T.; Yuan, S. B.

2017-08-01

The influence of adiabatic focusing on particle diffusion is an important topic in astrophysics and plasma physics. In the past, several authors have explored the influence of along-field adiabatic focusing on the parallel diffusion of charged energetic particles. In this paper, using the unified nonlinear transport theory developed by Shalchi and the method of He and Schlickeiser, we derive a new nonlinear perpendicular diffusion coefficient for a non-uniform background magnetic field. This formula demonstrates that the particle perpendicular diffusion coefficient is modified by along-field adiabatic focusing. For isotropic pitch-angle scattering and the weak adiabatic focusing limit, the derived perpendicular diffusion coefficient is independent of the sign of adiabatic focusing characteristic length. For the two-component model, we simplify the perpendicular diffusion coefficient up to the second order of the power series of the adiabatic focusing characteristic quantity. We find that the first-order modifying factor is equal to zero and that the sign of the second order is determined by the energy of the particles.

Magnetic Field Amplification in Supernova Remnants

NASA Astrophysics Data System (ADS)

Xu, Siyao; Lazarian, Alex

2017-12-01

Based on the new findings on the turbulent dynamo in Xu & Lazarian, we examine the magnetic field amplification in the context of supernova remnants. Due to the strong ion-neutral collisional damping in the weakly ionized interstellar medium, the dynamo in the preshock turbulence remains in the damping kinematic regime, which leads to a linear-in-time growth of the magnetic field strength. The resultant magnetic field structure enables effective diffusion upstream and shock acceleration of cosmic rays to energies above the “knee.” Differently, the nonlinear dynamo in the postshock turbulence leads to a linear-in-time growth of the magnetic energy due to the turbulent magnetic diffusion. Given a weak initial field strength in the postshock region, the magnetic field saturates at a significant distance from the shock front as a result of the inefficiency of the nonlinear dynamo. This result is in a good agreement with existing numerical simulations and well explains the X-ray spots detected far behind the shock front.

Dynamical mean-field theory and weakly non-linear analysis for the phase separation of active Brownian particles

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

Speck, Thomas; Menzel, Andreas M.; Bialké, Julian

2015-06-14

Recently, we have derived an effective Cahn-Hilliard equation for the phase separation dynamics of active Brownian particles by performing a weakly non-linear analysis of the effective hydrodynamic equations for density and polarization [Speck et al., Phys. Rev. Lett. 112, 218304 (2014)]. Here, we develop and explore this strategy in more detail and show explicitly how to get to such a large-scale, mean-field description starting from the microscopic dynamics. The effective free energy emerging from this approach has the form of a conventional Ginzburg-Landau function. On the coarsest scale, our results thus agree with the mapping of active phase separation ontomore » that of passive fluids with attractive interactions through a global effective free energy (motility-induced phase transition). Particular attention is paid to the square-gradient term necessary for the phase separation kinetics. We finally discuss results from numerical simulations corroborating the analytical results.« less

Weakly Nonlinear Analysis of Vortex Formation in a Dissipative Variant of the Gross--Pitaevskii Equation

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

Tzou, J. C.; Kevrekidis, P. G.; Kolokolnikov, T.

2016-05-10

For a dissipative variant of the two-dimensional Gross--Pitaevskii equation with a parabolic trap under rotation, we study a symmetry breaking process that leads to the formation of vortices. The first symmetry breaking leads to the formation of many small vortices distributed uniformly near the Thomas$-$Fermi radius. The instability occurs as a result of a linear instability of a vortex-free steady state as the rotation is increased above a critical threshold. We focus on the second subsequent symmetry breaking, which occurs in the weakly nonlinear regime. At slightly above threshold, we derive a one-dimensional amplitude equation that describes the slow evolutionmore » of the envelope of the initial instability. Here, we show that the mechanism responsible for initiating vortex formation is a modulational instability of the amplitude equation. We also illustrate the role of dissipation in the symmetry breaking process. All analyses are confirmed by detailed numerical computations« less

Nonlinear soil response in the vicinity of the Van Norman Complex following the 1994 Northridge, California, earthquake

USGS Publications Warehouse

Cultrera, G.; Boore, D.M.; Joyner, W.B.; Dietel, C.M.

1999-01-01

Ground-motion recordings obtained at the Van Norman Complex from the 1994 Northridge, California, mainshock and its aftershocks constitute an excellent data set for the analysis of soil response as a function of ground-motion amplitude. We searched for nonlinear response by comparing the Fourier spectral ratios of two pairs of sites for ground motions of different levels, using data from permanent strong-motion recorders and from specially deployed portable instruments. We also compared the amplitude dependence of the observed ratios with the amplitude dependence of the theoretical ratios obtained from 1-D linear and 1-D equivalent-linear transfer functions, using recently published borehole velocity profiles at the sites to provide the low-strain material properties. One pair of sites was at the Jensen Filtration Plant (JFP); the other pair was the Rinaldi Receiving Station (RIN) and the Los Angeles Dam (LAD). Most of the analysis was concentrated on the motions at the Jensen sites. Portable seismometers were installed at the JFP to see if the motions inside the structures housing the strong-motion recorders differed from nearby free-field motions. We recorded seven small earthquakes and found that the high-frequency, low-amplitude motions in the administration building were about 0.3 of those outside the building. This means that the lack of high frequencies on the strong-motion recordings in the administration building relative to the generator building is not due solely to nonlinear soil effects. After taking into account the effects of the buildings, however, analysis of the suite of strong- and weak-motion recordings indicates that nonlinearity occurred at the JFP. As predicted by equivalent-linear analysis, the largest events (the mainshock and the 20 March 1994 aftershock) show a significant deamplification of the high-frequency motion relative to the weak motions from aftershocks occurring many months after the mainshock. The weak-motion aftershocks recorded within 12 hours of the mainshock, however, show a relative deamplification similar to that in the mainshock. The soil behavior may be a consequence of a pore pressure buildup during large-amplitude motion that was not dissipated until sometime later. The motions at (RIN) and (LAD) are from free-field sites. The comparison among spectral ratios of the mainshock, weak-motion coda waves of the mainshock, and an aftershock within ten minutes of the mainshock indicate that some nonlinearity occurred, presumably at (RIN) because it is the softer site. The spectral ratio for the mainshock is between that calculated for pure linear response and that calculated from the equivalent-linear method, using commonly used modulus reduction and damping ratio curves. In contrast to the Jensen sites, the ratio of motions soon after the high-amplitude portion of the mainshock differs from the ratio of the mainshock motions, indicating the mechanical properties of the soil returned to the low-strain values as the high-amplitude motion ended. This may indicate a type of nonlinear soil response different from that affecting motion at the Jensen administration building.

Flat nonlinear optics: metasurfaces for efficient frequency mixing

NASA Astrophysics Data System (ADS)

Nookala, Nishant; Lee, Jongwon; Liu, Yingnan; Bishop, Wells; Tymchenko, Mykhailo; Gomez-Diaz, J. Sebastian; Demmerle, Frederic; Boehm, Gerhard; Amann, Markus-Christian; Wolf, Omri; Brener, Igal; Alu, Andrea; Belkin, Mikhail A.

2017-02-01

Gradient metasurfaces, or ultrathin optical components with engineered transverse impedance gradients along the surface, are able to locally control the phase and amplitude of the scattered fields over subwavelength scales, enabling a broad range of linear components in a flat, integrable platform1-4. On the contrary, due to the weakness of their nonlinear optical responses, conventional nonlinear optical components are inherently bulky, with stringent requirements associated with phase matching and poor control over the phase and amplitude of the generated beam. Nonlinear metasurfaces have been recently proposed to enable frequency conversion in thin films without phase-matching constraints and subwavelength control of the local nonlinear phase5-8. However, the associated optical nonlinearities are far too small to produce significant nonlinear conversion efficiency and compete with conventional nonlinear components for pump intensities below the materials damage threshold. Here, we report multi-quantum-well based gradient nonlinear metasurfaces with second-order nonlinear susceptibility over 106 pm/V for second harmonic generation at a fundamental pump wavelength of 10 μm, 5-6 orders of magnitude larger than traditional crystals. Further, we demonstrate the efficacy of this approach to designing metasurfaces optimized for frequency conversion over a large range of wavelengths, by reporting multi-quantum-well and metasurface structures optimized for a pump wavelength of 6.7 μm. Finally, we demonstrate how the phase of this nonlinearly generated light can be locally controlled well below the diffraction limit using the Pancharatnam-Berry phase approach5,7,9, opening a new paradigm for ultrathin, flat nonlinear optical components.

Non-Markovian dynamics of open quantum systems

NASA Astrophysics Data System (ADS)

Fleming, Chris H.

An open quantum system is a quantum system that interacts with some environment whose degrees of freedom have been coarse grained away. This model describes non-equilibrium processes more general than scattering-matrix formulations. Furthermore, the microscopically-derived environment provides a model of noise, dissipation and decoherence far more general than Markovian (white noise) models. The latter are fully characterized by Lindblad equations and can be motivated phenomenologically. Non-Markovian processes consistently account for backreaction with the environment and can incorporate effects such as finite temperature and spatial correlations. We consider linear systems with bilinear coupling to the environment, or quantum Brownian motion, and nonlinear systems with weak coupling to the environment. For linear systems we provide exact solutions with analytical results for a variety of spectral densities. Furthermore, we point out an important mathematical subtlety which led to incorrect master-equation coefficients in earlier derivations, given nonlocal dissipation. For nonlinear systems we provide perturbative solutions by translating the formalism of canonical perturbation theory into the context of master equations. It is shown that unavoidable degeneracy causes an unfortunate reduction in accuracy between perturbative master equations and their solutions. We also extend the famous theorem of Lindblad, Gorini, Kossakowski and Sudarshan on completely positivity to non-Markovian master equations. Our application is primarily to model atoms interacting via a common electromagnetic field. The electromagnetic field contains correlations in both space and time, which are related to its relativistic (photon-mediated) nature. As such, atoms residing in the same field experience different environmental effects depending upon their relative position and orientation. Our more accurate solutions were necessary to assess sudden death of entanglement at zero temperature. In contrast to previous claims, we found that all initial states of two-level atoms undergo finite-time disentanglement. We were also able to access regimes which cannot be described by Lindblad equations and other simpler methods, such as near resonance. Finally we revisit the infamous Abraham-Lorentz force, wherein a single particle in motion experiences backreaction from the electromagnetic field. This leads to a number of well-known problems including pre-acceleration and runaway solutions. We found a more a more-suitable open-system treatment of the nonrelativistic particle to be perfectly causal and dissipative without any extraneous requirements for finite size of the particle, weak coupling to the field, etc..

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

NASA Astrophysics Data System (ADS)

Krommes, John A.

2010-12-01

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

Reflection and Transmission of a Focused Finite Amplitude Sound Beam Incident on a Curved Interface

NASA Astrophysics Data System (ADS)

Makin, Inder Raj Singh

Reflection and transmission of a finite amplitude focused sound beam at a weakly curved interface separating two fluid-like media are investigated. The KZK parabolic wave equation, which accounts for thermoviscous absorption, diffraction, and nonlinearity, is used to describe the high intensity focused beam. The first part of the work deals with the quasilinear analysis of a weakly nonlinear beam after its reflection and transmission from a curved interface. A Green's function approach is used to define the field integrals describing the primary and the nonlinearly generated second harmonic beam. Closed-form solutions are obtained for the primary and second harmonic beams when a Gaussian amplitude distribution at the source is assumed. The second part of the research uses a numerical frequency domain solution of the KZK equation for a fully nonlinear analysis of the reflected and transmitted fields. Both piston and Gaussian sources are considered. Harmonic components generated in the medium due to propagation of the focused beam are evaluated, and formation of shocks in the reflected and transmitted beams is investigated. A finite amplitude focused beam is observed to be modified due to reflection and transmission from a curved interface in a manner distinct from that in the case of a small signal beam. Propagation curves, beam patterns, phase plots and time waveforms for various parameters defining the source and media pairs are presented, highlighting the effect of the interface curvature on the reflected and transmitted beams. Relevance of the current work to biomedical applications of ultrasound is discussed.

Shock-induced heating and millisecond boiling in gels and tissue due to high intensity focused ultrasound

PubMed Central

Canney, Michael S.; Khokhlova, Vera A.; Bessonova, Olga V.; Bailey, Michael R.; Crum, Lawrence A.

2009-01-01

Nonlinear propagation causes high intensity ultrasound waves to distort and generate higher harmonics, which are more readily absorbed and converted to heat than the fundamental frequency. Although such nonlinear effects have previously been investigated and found not to significantly alter high intensity focused ultrasound (HIFU) treatments, two results reported here change this paradigm. One is that at clinically relevant intensity levels, HIFU waves not only become distorted but form shock waves in tissue. The other is that the generated shock waves heat the tissue to boiling in much less time than predicted for undistorted or weakly distorted waves. In this study, a 2-MHz HIFU source operating at peak intensities up to 25,000 W/cm2 was used to heat transparent tissue-mimicking phantoms and ex vivo bovine liver samples. Initiation of boiling was detected using high-speed photography, a 20-MHz passive cavitation detector, and fluctuation of the drive voltage at the HIFU source. The time to boil obtained experimentally was used to quantify heating rates and was compared to calculations using weak shock theory and the shock amplitudes obtained from nonlinear modeling and from measurements with a fiber optic hydrophone. As observed experimentally and predicted by calculations, shocked focal waveforms produced boiling in as little as 3 ms and the time to initiate boiling was sensitive to small changes in HIFU output. Nonlinear heating due to shock waves is therefore important to HIFU and clinicians should be aware of the potential for very rapid boiling since it alters treatments. PMID:20018433

Microwave phase conjugation using artificial nonlinear microwave surfaces

NASA Astrophysics Data System (ADS)

Chang, Yian

1997-09-01

A new technique is developed and demonstrated to simulate nonlinear materials in the microwave and millimeter wave regime. Such materials are required to extend nonlinear optical techniques into longer wavelength areas. Using an array of antenna coupled mixers as an artificial nonlinear surface, we have demonstrated two-dimensional free space microwave phase conjugation at 10 GHz. The basic concept is to replace the weak nonlinearity of electron distribution in a crystal with the strong nonlinear V-I response of a P-N junction. This demnstration uses a three-wave mixing method with the effective nonlinear susceptibility χ(2) provided by an artificial nonlinear surface. The pump signal at 2ω (20 GHz) can be injected to the mixing elements electrically or optically. Electrical injection was first used to prove the concept of artificial nonlinear surfaces. However, due to the loss and size of microwave components, electrical injection is not practical for an array of artificial nonlinear surfaces, as would be needed in a three-dimensional free space phase conjugation setup. Therefore optical injection was implemented to carry the 2ω microwave pump signal in phase to all mixing elements. In both cases, two-dimensional free space phase conjugation was observed by directly measuring the electric field amplitude and phase distribution. The electric field wavefronts exhibited retro-directivity and auto- correction characteristics of phase conjugation. This demonstration surface also shows a power gain of 10 dB, which is desired for potential communication applications.

Global, finite energy, weak solutions for the NLS with rough, time-dependent magnetic potentials

NASA Astrophysics Data System (ADS)

Antonelli, Paolo; Michelangeli, Alessandro; Scandone, Raffaele

2018-04-01

We prove the existence of weak solutions in the space of energy for a class of nonlinear Schrödinger equations in the presence of a external, rough, time-dependent magnetic potential. Under our assumptions, it is not possible to study the problem by means of usual arguments like resolvent techniques or Fourier integral operators, for example. We use a parabolic regularisation, and we solve the approximating Cauchy problem. This is achieved by obtaining suitable smoothing estimates for the dissipative evolution. The total mass and energy bounds allow to extend the solution globally in time. We then infer sufficient compactness properties in order to produce a global-in-time finite energy weak solution to our original problem.

Weak turbulence simulations with the Hermite-Fourier spectral method

NASA Astrophysics Data System (ADS)

Vencels, Juris; Delzanno, Gian Luca; Manzini, Gianmarco; Roytershteyn, Vadim; Markidis, Stefano

2015-11-01

Recently, a new (transform) method based on a Fourier-Hermite (FH) discretization of the Vlasov-Maxwell equations has been developed. The resulting set of moment equations is discretized implicitly in time with a Crank-Nicolson scheme and solved with a nonlinear Newton-Krylov technique. For periodic boundary conditions, this discretization delivers a scheme that conserves the total mass, momentum and energy of the system exactly. In this work, we apply the FH method to study a problem of Langmuir turbulence, where a low signal-to-noise ratio is important to follow the turbulent cascade and might require a lot of computational resources if studied with PIC. We simulate a weak (low density) electron beam moving in a Maxwellian plasma and subject to an instability that generates Langmuir waves and a weak turbulence field. We also discuss some optimization techniques to optimally select the Hermite basis in terms of its shift and scaling argument, and show that this technique improve the overall accuracy of the method. Finally, we discuss the applicability of the HF method for studying kinetic plasma turbulence. This work was funded by LDRD under the auspices of the NNSA of the U.S. by LANL under contract DE-AC52-06NA25396 and by EC through the EPiGRAM project (grant agreement no. 610598. epigram-project.eu).

Second-order accurate nonoscillatory schemes for scalar conservation laws

NASA Technical Reports Server (NTRS)

Huynh, Hung T.

1989-01-01

Explicit finite difference schemes for the computation of weak solutions of nonlinear scalar conservation laws is presented and analyzed. These schemes are uniformly second-order accurate and nonoscillatory in the sense that the number of extrema of the discrete solution is not increasing in time.

A Locally Modal B-Spline Based Full-Vector Finite-Element Method with PML for Nonlinear and Lossy Plasmonic Waveguide

NASA Astrophysics Data System (ADS)

Karimi, Hossein; Nikmehr, Saeid; Khodapanah, Ehsan

2016-09-01

In this paper, we develop a B-spline finite-element method (FEM) based on a locally modal wave propagation with anisotropic perfectly matched layers (PMLs), for the first time, to simulate nonlinear and lossy plasmonic waveguides. Conventional approaches like beam propagation method, inherently omit the wave spectrum and do not provide physical insight into nonlinear modes especially in the plasmonic applications, where nonlinear modes are constructed by linear modes with very close propagation constant quantities. Our locally modal B-spline finite element method (LMBS-FEM) does not suffer from the weakness of the conventional approaches. To validate our method, first, propagation of wave for various kinds of linear, nonlinear, lossless and lossy materials of metal-insulator plasmonic structures are simulated using LMBS-FEM in MATLAB and the comparisons are made with FEM-BPM module of COMSOL Multiphysics simulator and B-spline finite-element finite-difference wide angle beam propagation method (BSFEFD-WABPM). The comparisons show that not only our developed numerical approach is computationally more accurate and efficient than conventional approaches but also it provides physical insight into the nonlinear nature of the propagation modes.

On the nonlinear forced response of the North Atlantic atmosphere to meridional shifts of the Gulf Stream path

NASA Astrophysics Data System (ADS)

Seo, H.; Kwon, Y. O.; Joyce, T. M.; Ummenhofer, C.

2016-12-01

This study examines the North Atlantic atmospheric circulation response to the meridional shift of Gulf Stream path using a large-ensemble, high-resolution, and hemispheric-scale WRF simulations. The model is forced with wintertime SST anomalies derived from a wide range of Gulf Stream shift scenarios. The key result of the model experiments, supported in part by an independent analysis of a reanalysis data set, is that the large-scale, quasi-steady North Atlantic circulation response is unambiguously nonlinear about the sign and amplitude of chosen SST anomalies. This nonlinear response prevails over the weak linear response and resembles the negative North Atlantic Oscillation, the leading intrinsic mode of variability in the model and the observations. Further analysis of the associated dynamics reveals that the nonlinear responses are accompanied by the anomalous southward shift of the North Atlantic eddy-driven jet stream, which is reinforced nearly equally by the high-frequency transient eddy feedback and the low-frequency high-latitude wave breaking events. The result highlights the importance of the intrinsically nonlinear transient eddy dynamics and eddy-mean flow interactions in generating the nonlinear forced response to the meridional shift in the Gulf Stream.

Modelling of Resonantly Forced Density Waves in Dense Planetary Rings

NASA Astrophysics Data System (ADS)

Lehmann, M.; Schmidt, J.; Salo, H.

2014-04-01

Density wave theory, originally proposed to explain the spiral structure of galactic disks, has been applied to explain parts of the complex sub-structure in Saturn's rings, such as the wavetrains excited at the inner Lindblad resonances (ILR) of various satellites. The linear theory for the excitation and damping of density waves in Saturn's rings is fairly well developed (e.g. Goldreich & Tremaine [1979]; Shu [1984]). However, it fails to describe certain aspects of the observed waves. The non-applicability of the linear theory is already indicated by the "cusplike" shape of many of the observed wave profiles. This is a typical nonlinear feature which is also present in overstability wavetrains (Schmidt & Salo [2003]; Latter & Ogilvie [2010]). In particular, it turns out that the detailed damping mechanism, as well as the role of different nonlinear effects on the propagation of density waves remain intransparent. First attemps are being made to investigate the excitation and propagation of nonlinear density waves within a hydrodynamical formalism, which is also the natural formalism for describing linear density waves. A simple weakly nonlinear model, derived from a multiple-scale expansion of the hydrodynamic equations, is presented. This model describes the damping of "free" spiral density waves in a vertically integrated fluid disk with density dependent transport coefficients, where the effects of the hydrodynamic nonlinearities are included. The model predicts that density waves are linearly unstable in a ring region where the conditions for viscous overstability are met, which translates to a steep dependence of the shear viscosity with respect to the disk's surface density. The possibility that this dependence could lead to a growth of density waves with increasing distance from the resonance, was already mentioned in Goldreich & Tremaine [1978]. Sufficiently far away from the ILR, the surface density perturbation caused by the wave, is predicted to saturate to a constant value due to the effects of nonlinear viscous damping. A qualitatively similar behaviour has also been predicted for the damping of nonlinear density waves, as described within a streamline formalism (Borderies, Goldreich & Tremaine [1985]). The damping lengths which follow from the weakly nonlinear model depend more or less strongly on a set of different input parameters, such as the viscosity and the surface density of the unperturbed ring state. Further, they depend on the wave's amplitude at resonance. For a real wave, which has been excited by an external satellite, this amplitude can be deduced from the magnitude of the satellite's forcing potential. Appart from that, hydrodynamical simulations are being developed to study the nonlinear damping of resonantly forced density waves.

Nonlinear internal waves in the Gulf of Guinea: observations and modeling

NASA Astrophysics Data System (ADS)

Baquet, Emeric; Pichon, Annick; Raynaud, Stephane; Carton, Xavier

2017-04-01

Nonlinear internal waves are known hazards to offshore operations. They have been observed at different locations around the world and have been studied for a long time in Southeast Asia. However in West Africa, they are less documented. This research presents original data of currentmeters in northeastern part of the Gulf of Guinea, in the vicinity of offshore oil platforms. Nonlinear internal waves were observed. Their characteristics were determined under the assumptions of the weakly nonlinear and non-hydrostatic Korteweg-de Vries equation. Their directions of propagation were studied to determine generation zones. The monthly distribution was shown to assess seasonal variability. Their main generation mechanism was the barotropic tides over the shelf break, but other processes were at work too. The seasonal variability due to the monsoon, river discharges also played a part in the nonlinear internal wave dynamics. Since several processes, of different time and space scales, are at work, interactions between them must be investigated. Thus, a two-layered numerical model was used to reproduce nonlinear internal waves. Sensitivity experiments were made, in order to investigate the balance between nonlinearities, Coriolis and non-hydrostatic dispersions. The impact of non-uniform bathymetry and the presence of another flow in addition to the tides were also tested.

A theoretical and experimental investigation of the linear and nonlinear impulse responses from a magnetoplasma column

NASA Technical Reports Server (NTRS)

Grody, N. C.

1973-01-01

Linear and nonlinear responses of a magnetoplasma resulting from inhomogeneity in the background plasma density are studied. The plasma response to an impulse electric field was measured and the results are compared with the theory of an inhomogeneous cold plasma. Impulse responses were recorded for the different plasma densities, static magnetic fields, and neutral pressures and generally appeared as modulated, damped oscillations. The frequency spectra of the waveforms consisted of two separated resonance peaks. For weak excitation, the results correlate with the linear theory of a cold, inhomogeneous, cylindrical magnetoplasma. The damping mechanism is identified with that of phase mixing due to inhomogeneity in plasma density. With increasing excitation voltage, the nonlinear impulse responses display stronger damping and a small increase in the frequency of oscillation.

Nonlinear stability of Halley comethosheath with transverse plasma motion

NASA Technical Reports Server (NTRS)

Srivastava, Krishna M.; Tsurutani, Bruce T.

1994-01-01

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

Nonlinear modulation of the HI power spectrum on ultra-large scales. I

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

Umeh, Obinna; Maartens, Roy; Santos, Mario, E-mail: umeobinna@gmail.com, E-mail: roy.maartens@gmail.com, E-mail: mgrsantos@uwc.ac.za

2016-03-01

Intensity mapping of the neutral hydrogen brightness temperature promises to provide a three-dimensional view of the universe on very large scales. Nonlinear effects are typically thought to alter only the small-scale power, but we show how they may bias the extraction of cosmological information contained in the power spectrum on ultra-large scales. For linear perturbations to remain valid on large scales, we need to renormalize perturbations at higher order. In the case of intensity mapping, the second-order contribution to clustering from weak lensing dominates the nonlinear contribution at high redshift. Renormalization modifies the mean brightness temperature and therefore the evolutionmore » bias. It also introduces a term that mimics white noise. These effects may influence forecasting analysis on ultra-large scales.« less

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

Observation of three-photon bound states in a quantum nonlinear medium

NASA Astrophysics Data System (ADS)

Liang, Qi-Yu; Venkatramani, Aditya V.; Cantu, Sergio H.; Nicholson, Travis L.; Gullans, Michael J.; Gorshkov, Alexey V.; Thompson, Jeff D.; Chin, Cheng; Lukin, Mikhail D.; Vuletić, Vladan

2018-02-01

Bound states of massive particles, such as nuclei, atoms, or molecules, constitute the bulk of the visible world around us. By contrast, photons typically only interact weakly. We report the observation of traveling three-photon bound states in a quantum nonlinear medium where the interactions between photons are mediated by atomic Rydberg states. Photon correlation and conditional phase measurements reveal the distinct bunching and phase features associated with three-photon and two-photon bound states. Such photonic trimers and dimers possess shape-preserving wave functions that depend on the constituent photon number. The observed bunching and strongly nonlinear optical phase are described by an effective field theory of Rydberg-induced photon-photon interactions. These observations demonstrate the ability to realize and control strongly interacting quantum many-body states of light.

On structure-exploiting trust-region regularized nonlinear least squares algorithms for neural-network learning.

PubMed

Mizutani, Eiji; Demmel, James W

2003-01-01

This paper briefly introduces our numerical linear algebra approaches for solving structured nonlinear least squares problems arising from 'multiple-output' neural-network (NN) models. Our algorithms feature trust-region regularization, and exploit sparsity of either the 'block-angular' residual Jacobian matrix or the 'block-arrow' Gauss-Newton Hessian (or Fisher information matrix in statistical sense) depending on problem scale so as to render a large class of NN-learning algorithms 'efficient' in both memory and operation costs. Using a relatively large real-world nonlinear regression application, we shall explain algorithmic strengths and weaknesses, analyzing simulation results obtained by both direct and iterative trust-region algorithms with two distinct NN models: 'multilayer perceptrons' (MLP) and 'complementary mixtures of MLP-experts' (or neuro-fuzzy modular networks).

Rogue events in the group velocity horizon

PubMed Central

Demircan, Ayhan; Amiranashvili, Shalva; Brée, Carsten; Mahnke, Christoph; Mitschke, Fedor; Steinmeyer, Günter

2012-01-01

The concept of rogue waves arises from a mysterious and potentially calamitous phenomenon of oceanic surfaces. There is mounting evidence that they are actually commonplace in a variety of different physical settings. A set of defining criteria has been advanced; this set is of great generality and therefore applicable to a wide class of systems. The question arises naturally whether there are generic mechanisms responsible for extreme events in different systems. Here we argue that under suitable circumstances nonlinear interaction between weak and strong waves results in intermittent giant waves with all the signatures of rogue waves. To obtain these circumstances only a few basic conditions must be met. Then reflection of waves at the so-called group-velocity horizon occurs. The connection between rogue waves and event horizons, seemingly unrelated physical phenomena, is identified as a feature common in many different physical systems. PMID:23152941

Nonlinear instability and convection in a vertically vibrated granular bed

NASA Astrophysics Data System (ADS)

Shukla, Priyanka; Ansari, I. H.; van der Meer, D.; Lohse, Detlef; Alam, Meheboob

2015-11-01

The nonlinear instability of the density-inverted granular Leidenfrost state and the resulting convective motion in strongly shaken granular matter are analysed via a weakly nonlinear analysis. Under a quasi-steady ansatz, the base state temperature decreases with increasing height away from from the vibrating plate, but the density profile consists of three distinct regions: (i) a collisional dilute layer at the bottom, (ii) a levitated dense layer at some intermediate height and (iii) a ballistic dilute layer at the top of the granular bed. For the nonlinear stability analysis, the nonlinearities up-to cubic order in perturbation amplitude are retained, leading to the Landau equation. The genesis of granular convection is shown to be tied to a supercritical pitchfork bifurcation from the Leidenfrost state. Near the bifurcation point the equilibrium amplitude is found to follow a square-root scaling law, Ae √{ ▵} , with the distance ▵ from bifurcation point. The strength of convection is maximal at some intermediate value of the shaking strength, with weaker convection both at weaker and stronger shaking. Our theory predicts a novel floating-convection state at very strong shaking.

Nonlinear excitations in electron-positron-ion plasmas in accretion disks of active galactic nuclei

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

Moslem, W. M.; Kourakis, I.; Shukla, P. K.

2007-10-15

The propagation of acoustic nonlinear excitations in an electron-positron-ion (e-p-i) plasma composed of warm electrons and positrons, as well as hot ions, has been investigated by adopting a two-dimensional cylindrical geometry. The electrons and positrons are modeled by hydrodynamic fluid equations, while the ions are assumed to follow a temperature-parametrized Boltzmann distribution (the fixed ion model is recovered in the appropriate limit). This situation applies in the accretion disk near a black hole in active galactic nuclei, where the ion temperature may be as high as 3 to 300 times that of the electrons. Using a reductive perturbation technique, amore » cylindrical Kadomtsev-Petviashvili equation is derived and its exact soliton solutions are presented. Furthermore, real situations in which the strength of the nonlinearity may be weak are considered, so that higher-order nonlinearity plays an important role. Accordingly, an extended cylindrical Kadomtsev-Petviashvili equation is derived, which admits both soliton and double-layer solutions. The characteristics of the nonlinear excitations obtained are investigated in detail.« less

Traveling waves and conservation laws for highly nonlinear wave equations modeling Hertz chains

NASA Astrophysics Data System (ADS)

Przedborski, Michelle; Anco, Stephen C.

2017-09-01

A highly nonlinear, fourth-order wave equation that models the continuum theory of long wavelength pulses in weakly compressed, homogeneous, discrete chains with a general power-law contact interaction is studied. For this wave equation, all solitary wave solutions and all nonlinear periodic wave solutions, along with all conservation laws, are derived. The solutions are explicitly parameterized in terms of the asymptotic value of the wave amplitude in the case of solitary waves and the peak of the wave amplitude in the case of nonlinear periodic waves. All cases in which the solution expressions can be stated in an explicit analytic form using elementary functions are worked out. In these cases, explicit expressions for the total energy and total momentum for all solutions are obtained as well. The derivation of the solutions uses the conservation laws combined with an energy analysis argument to reduce the wave equation directly to a separable first-order differential equation that determines the wave amplitude in terms of the traveling wave variable. This method can be applied more generally to other highly nonlinear wave equations.

Envelope of coda waves for a double couple source due to non-linear elasticity

NASA Astrophysics Data System (ADS)

Calisto, Ignacia; Bataille, Klaus

2014-10-01

Non-linear elasticity has recently been considered as a source of scattering, therefore contributing to the coda of seismic waves, in particular for the case of explosive sources. This idea is analysed further here, theoretically solving the expression for the envelope of coda waves generated by a point moment tensor in order to compare with earthquake data. For weak non-linearities, one can consider each point of the non-linear medium as a source of scattering within a homogeneous and linear medium, for which Green's functions can be used to compute the total displacement of scattered waves. These sources of scattering have specific radiation patterns depending on the incident and scattered P or S waves, respectively. In this approach, the coda envelope depends on three scalar parameters related to the specific non-linearity of the medium; however these parameters only change the scale of the coda envelope. The shape of the coda envelope is sensitive to both the source time function and the intrinsic attenuation. We compare simulations using this model with data from earthquakes in Taiwan, with a good fit.

Nonlinear periodic wavetrains in thin liquid films falling on a uniformly heated horizontal plate

NASA Astrophysics Data System (ADS)

Issokolo, Remi J. Noumana; Dikandé, Alain M.

2018-05-01

A thin liquid film falling on a uniformly heated horizontal plate spreads into fingering ripples that can display a complex dynamics ranging from continuous waves, nonlinear spatially localized periodic wave patterns (i.e., rivulet structures) to modulated nonlinear wavetrain structures. Some of these structures have been observed experimentally; however, conditions under which they form are still not well understood. In this work, we examine profiles of nonlinear wave patterns formed by a thin liquid film falling on a uniformly heated horizontal plate. For this purpose, the Benney model is considered assuming a uniform temperature distribution along the film propagation on the horizontal surface. It is shown that for strong surface tension but a relatively small Biot number, spatially localized periodic-wave structures can be analytically obtained by solving the governing equation under appropriate conditions. In the regime of weak nonlinearity, a multiple-scale expansion combined with the reductive perturbation method leads to a complex Ginzburg-Landau equation: the solutions of which are modulated periodic pulse trains which amplitude and width and period are expressed in terms of characteristic parameters of the model.

Dielectric metamaterials with toroidal dipolar response

DOE PAGES

Basharin, Alexey A.; Kafesaki, Maria; Economou, Eleftherios N.; ...

2015-03-27

Toroidal multipoles are the terms missing in the standard multipole expansion; they are usually overlooked due to their relatively weak coupling to the electromagnetic fields. Here, we propose and theoretically study all-dielectric metamaterials of a special class that represent a simple electromagnetic system supporting toroidal dipolar excitations in the THz part of the spectrum. In addition, we show that resonant transmission and reflection of such metamaterials is dominated by toroidal dipole scattering, the neglect of which would result in a misunderstanding interpretation of the metamaterials’ macroscopic response. Due to the unique field configuration of the toroidal mode, the proposed metamaterialsmore » could serve as a platform for sensing or enhancement of light absorption and optical nonlinearities.« less

Dissipation in a rotating frame: Master equation, effective temperature, and Lamb shift

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

Verso, Alvise; Ankerhold, Joachim

Motivated by recent realizations of microwave-driven nonlinear resonators in superconducting circuits, the impact of environmental degrees of freedom is analyzed as seen from a rotating frame. A system plus reservoir model is applied to consistently derive in the weak coupling limit the master equation for the reduced density in the moving frame and near the first bifurcation threshold. The concept of an effective temperature is introduced to analyze to what extent a detailed balance relation exists. Explicit expressions are also found for the Lamb-shift. Results for ohmic baths are in agreement with experimental findings, while for structured environments population inversionmore » is predicted that may qualitatively explain recent observations.« less

Development of renormalization group analysis of turbulence

NASA Technical Reports Server (NTRS)

Smith, L. M.

1990-01-01

The renormalization group (RG) procedure for nonlinear, dissipative systems is now quite standard, and its applications to the problem of hydrodynamic turbulence are becoming well known. In summary, the RG method isolates self similar behavior and provides a systematic procedure to describe scale invariant dynamics in terms of large scale variables only. The parameterization of the small scales in a self consistent manner has important implications for sub-grid modeling. This paper develops the homogeneous, isotropic turbulence and addresses the meaning and consequence of epsilon-expansion. The theory is then extended to include a weak mean flow and application of the RG method to a sequence of models is shown to converge to the Navier-Stokes equations.

Tunable all-optical quasimonochromatic thomson x-ray source in the nonlinear regime.

PubMed

Khrennikov, K; Wenz, J; Buck, A; Xu, J; Heigoldt, M; Veisz, L; Karsch, S

2015-05-15

We present an all-laser-driven, energy-tunable, and quasimonochromatic x-ray source based on Thomson scattering from laser-wakefield-accelerated electrons. One part of the laser beam was used to drive a few-fs bunch of quasimonoenergetic electrons, while the remainder was backscattered off the bunch at weakly relativistic intensity. When the electron energy was tuned from 17-50 MeV, narrow x-ray spectra peaking at 5-42 keV were recorded with high resolution, revealing nonlinear features. We present a large set of measurements showing the stability and practicality of our source.